Fundamentals_of_Financial_Management,_12th_Edition by Eugene F. Brigha


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Fundamentals of Financial Management, 12th_Edition by Eugene F. Brigha


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FUNDAMENTALS OF FINANCIAL MANAGEMENT Twelfth Edition Eugene F. Brigham UNIVERSITY OF FLORIDA Joel F. Houston UNIVERSITY OF FLORIDA Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States

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Fundamentals of Financial Management 12 th edition Eugene F. Brigham Joel F. Houston Vice President of Editorial Business: Jack W. Calhoun Editor-in-Chief: Alex von Rosenberg Executive Editor: Michael R. Reynolds Development Editor: Michael Guendelsberger Executive Marketing Manager: Brian Joyner Marketing Manager: Nathan Anderson Senior Marketing Communications Manager: Jim Overly Marketing Coordinator: Suellen Ruttkay WebsiteProjectManager:BrianCourter Frontlist Buyer Manufacturing: Kevin Kluck Senior Art Director: Michelle Kunkler Content Project Manager: Jennifer A. Ziegler Director of Production: Sharon Smith Media Editor: Scott Fidler Senior Editorial Assistant: Adele T. Scholtz Production Service: Litten Editing and Publishing Compositor: Macmillan Publishing Solutions Cover and Internal Designer: Grannan Graphic Design Photography Manager: Sheri Blaney © 2009 2007 South-Western a part of Cengage Learning ALL RIGHTS RESERVED. No part of this work covered by the copyright hereon may be reproduced or used in any form or by any means—graphic electronic or mechanical including photocopying recording taping Web distribution information storage and retrieval systems or in any other manner—except as may be permitted by the license terms herein. For product information and technology assistance contact us at Cengage Learning Customer Sales Support 1-800-354-9706 For permission to use material from this text or product submit all requests online at Further permissions questions can be emailed to ExamView ® is a registered trademark of eInstruction Corp. © 2009 Cengage Learning. All Rights Reserved. Library of Congress Control Number: 2008941113 ISBN 13: 978-0-324-59771-4 ISBN 10: 0-324-59771-1 Student Edition ISBN 13: 978-0-324-59770-7 Student Edition ISBN 10: 0-324-59770-3 South-Western Cengage Learning 5191 Natorp Boulevard Mason OH 45040 USA Cengage Learning products are represented in Canada by Nelson Education Ltd. For your course and learning solutions visit Purchase any of our products at your local college store or at our preferred online store Printed in the United States of America 12345671211100908

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PREFACE When thefirst edition of Fundamentals was published 31 years ago we wanted to provide an introductory text that students would find interesting and easy to understand.Fundamentalsimmediatelybecametheleadingundergraduatefinance textandithasmaintainedthatpositioneversince.Ourgoalwiththis edition was to produce a book and ancillary package that would maintain its lead and set a new standard for finance textbooks. Important changes in the financial environment have occurred since the last edition. New technology and increased globalization continue to transform practices and markets. Continued improvements in communications and transportation have made it easier for businesses to operate on a worldwide basis—acompanycanbe headquartered in New York develop products in India manufacture them in China and sell them anywhere in the world. This has led to major changes in the labor marketsespeciallytoanincreaseinoutsourcingwhichhasresultedingenerallylower consumer prices but it has caused job losses for some U.S. workers and gains for others. There have also been dramatic rises and falls in the stock market and interest rates have remained low even as energy prices continue to rise. Corporate scandals have led to important changes in the laws governing corporate management and financial reporting as well as to equally important changes in managerial compen- sation. These issues are discussed in this edition of Fundamentals where we analyze them from financial and ethical perspectives. Our target audience is undergraduate students taking their first and often only financecourse.Somestudentswilldecidetomajorinfinanceandgoontotakecourses in investments money and capital markets and advanced corporate finance. Others will choose marketingmanagementor some other nonfinance major. Stillothers will majorinareasotherthanbusinessandtakefinance and a few other business courses to gain information that will help them in law real estate and other fields. Our challenge was to provide a book that serves all of these audiences well. Our conclusion was that we should focus on the core principles of finance i.e. on basic topics such as the time value of money risk analysis and valuation. Moreover we concluded that we should address these topics from two points of view: 1 as an investor who is seeking to make intelligent investment choices and 2 as a business manager trying to maximize the value of his or her firms stock. Note that both investors and managers need to know the same set of principles so the core topics are important to students regardless of what they choose to do after they finish the course. THE FINANCIAL CRISIS OF 2008 As everyone knows the financial markets experienced a meltdown in the fall of 2008. The average stocks price declined by about 50 which wiped out trillions of dollars of savings. The sick joke was that 401 k retirement plans were becoming 201 k plans. These market losses delayed many retirements and also caused many retirees to go back to work. Housing construction virtually ceased and home prices plunged by about 20 nationwide and by as much as 50 in some parts of the country wiping out trillions more of savings. Millions of homeowners found that their mortgages exceeded the value of their homes and defaults and foreclosures followed. This led to huge losses by banks and other lenders which in turn led to bankruptcies restructuring and massive layoffs. Threeyearsagothere weremanystrongold andindependent globalinvestment banks. Today all of those in the U.S. are gone—icons like Merrill Lynch and iii

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MorganStanleyhaveeithergonebankruptsoldoutatrockbottompricesorbeen forced to convert into regulated banks that are partially owned by the federal government. The credit markets literally froze up. Banks needed to conserve their cash to meetwithdrawalshencetheyrefusedtomakeloanseventostrongindustrialand retail companies or home and auto purchasers. This quickly led to a severe slowdown in non-financial businesses accompanied by still more bankruptcies and layoffs. This happened all over the world and the specter of a 1930s type depression was on the minds of central bankers and treasury officials worldwide. As aresultcoordinated government rescue plans were put into operation in most developed nations. We dont know at this point what will happen next. The best bet is that a depression will be avoided but a bad recession will occur. Going forward companies and individuals will recognize that an excessive use of debt was the root cause of the financial meltdown hence there will be a smaller and more responsible use of debt in the future—at least until memories of 2008 fade. How should the 2008 Crisis affect the contents of this textbook Here is our conclusion: l The fundamental concepts of finance are unchanged hence all the concepts covered in the book are still applicable. l The problems of 2008 resulted largely because businesses individuals and government officials did not pay sufficient attention to the basic principles of finance as covered in the book. l Therefore there is no reason to change most of the book. l We should however use the 2008 experience to illustrate the basic points made in the book. For example we talk about risk and 2008 can and should be used to drive home how risk can be measured and dealt with. The economic situation is fluid and dynamic. We may have a rapid recovery whichwouldbegreatbutwemighthavealongdeepandpainfulrecession.We plan to use the Internet in the years ahead while the book is in use to update the situation on a chapter-by-chapter basis. As events related to the different chapters occur we will provide updated vignettes and other information on the book web site.Weanticipatemanyimportantdevelopmentshencealotofupdates.Stillthe good news is that the basic fundamental contents of the book will remain the same. ORGANIZATION OF THE CHAPTERS: A VALUATION FOCUS As we discuss in Chapter 1 in an enterprise system such as that of the United States the primary goal of financial management is to help managers maximize their firms values subject to constraints such as not polluting the environment not engaging in unfair labor practices and not engaging in antitrust activities. Therefore valuation underlies everything in Fundamentals. In Chapter 1 we dis- cuss the concept of valuation explain how it depends on future cash flows and risk and show why value maximization is good for society in general. The val- uation theme runs throughout the text. Values are not established in a vacuum—stock and bond values are deter- mined in the financial markets so an understanding of those markets is essential to anyone involved with finance. Therefore Chapter 2 covers the major types of financialmarketsthe returns that investors have historicallyearnedand the risks inherent in different types of securities. This information is important for anyone working in finance. It is also important for anyone who has or hopes to own financial assets. iv Preface

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Asset values depend in a fundamental way on earnings and cash flows as reported in the accounting statements. Therefore we review those statements in Chapter 3.TheninChapter 4weshow howaccounting datacan beanalyzed and usedtomeasurehowwellacompanyhasoperatedinthepastandhowitislikely to perform in the future. Chapter 5 covers the time value of money TVM perhaps the most funda- mental concept in finance. The basic valuation model which ties together cash flows risk and interest rates is based on TVM concepts and these concepts are used throughout the remainder of the book. Therefore students should allocate plenty of time to Chapter 5. Chapter 6 deals with interest rates a key determinant of asset values. We discuss how interest rates are affected by risk inflation liquidity the supply of and demand for capital in the economy and the actions of the Federal Reserve. ThediscussionofinterestratesleadsdirectlytobondsinChapter7andstocks in Chapters 8 and 9. We show how stocks and bonds and all other financial assets are valued using the basic TVM model. Chapters 1 through 9 provide background information that is essential to investors and corporate managers. These are “finance” topics not “business” or “corporate finance” topics as those terms are commonly used. Thus Chapters 1 through 9discuss theconceptsandmodelsusedtoestablish valuesandwe goon in Chapters 10 through 21 to discuss specific actions managers can take to max- imize their firms values. As noted previously most business students dont plan to specialize in finance so they might not think the “businessfinance” chapters arerelevant tothem. This is not true and in the later chapters we show that all important business decisions involveallofafirmsdepartments—marketingaccountingproductionandsoforth. Thus while capital budgeting can be thought of as a financial decision marketing people provide input on likely unit sales and sales prices manufacturing people provide inputs on costs and so forth. Moreover capital budgeting decisions influ- ence the size of thefirm its products and its profits and those factors affect all the firms employees from the CEO to the mail room staff. STRUCTURAL CHANGES We made two important structural changes in this new edition: 1. We moved the material onfinancial markets and institutions from Chapter 5 to Chapter 2. Markets and institutions follow naturally from Chapter 1 and this materialprovidesusefulbackgroundinformationfortheremainderofthebook. 2. WemovedthetimevalueofmoneyTVMchapterfromChapter2toChapter5. Under the previous structure we covered TVM concepts then covered the accounting and financial markets chapters before applying TVM concepts to bond and stock valuation. We liked the idea of covering TVM early but we concluded that it was pedagogically better to cover TVM concepts and then immediately focus on applications as we do now. These changes improve the flow of the text significantly—there is a much smoother transition from chapter to chapter in the first part of the book. OTHER CHANGES We made many other changes but the following are the most significant: 1. Editing. We edit each new edition to improve clarity but we did more in this edition than ever before. We put the entire text on digital files which Preface v

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facilitated shifting things around to improve transitions and flow. Students will find it easier to read the book than in the past. 2. Beginning-of-Chapter Vignettes and Within-Chapter Boxes. Many events have transpired in the financial markets during the past three years—for example in 2008 credit markets tightened almost to the point of collapse the housing andautomarketsareinterribleshapethemajorinvestmentbanksallfailedor were forced to reorganize as regulated commercial banks and the heads of a number of major corporations were fired. We use these events as the subjects of many vignettes and boxes and they illustrate very well the points made in the chapters. 3. Learning Objectives. To help students see what we expect them to take away from the chapters we added a set of learning objectives at the beginning of each chapter. 4. Excel. Spreadsheets especially Excel are becoming increasingly important in business and students who are familiar with Excel have a significant advantage in the job market and later on the job. We used Excel in two ways. First we worked all the in-text examples end-of-chapter problems and test bank problems with both Excel and a calculator using the calculator to make sure the problem was workable with a calculator and using Excel to check for accuracy.SecondweusedExceltocreatemanyofthetablesandgraphsinthe text we displayed them as Excel pictures and we have made available the models we used. Students do not need to know how to use Excel to go through the book but if they are somewhat familiar with this software they will see how many common financial problems can be set up and solved efficiently with Excel. Students who are not familiar with Excel may also be motivated to learn something about it. 5. Tie-In between Self-Test Questions End-of-Chapter Questions and the Test Bank. Because testing is important we spent a great deal of time improving the test bank. Every question and problem was reviewed for clarity accuracy and consistency with the text. Alsowe set up self-testquestions atthe end ofeach major section within the text to enable students to take real-time tests on their ownbeforemovingon.Theend-of-chapterEOCquestionsandproblemsare similar to but often go beyond the self-test questions and the test bank questions and problems are similar to the EOC materials. If students read the text do the self-test questions as they go along and then work a sampling of the EOC questions and problems they should do well on exams drawn from the test bank. 6. Accounting Statements and Free Cash Flow. Most students in the basic finance course are familiar with balance sheets and income statements but many dont understand the statement of cash flows and its relationship to free cash flows. Reviewers told us that in the last edition we tried to do too many things—such as present alternative ways to calculate free cash flow—and that we should delete some of those items and better explain what remained. We agreed and this edition does a much better job in this regard. 7. Cash Flows and Risk in Capital Budgeting. In the last edition the first two chapters on capital budgeting Chapters 11 and 12 were not tied together very well. In that edition we used relatively simple and straightforward illustrative projects in Chapter 11 but switched to entirely different and more complex projects in Chapter 12. For this edition we rewrote Chapter 12 continuing with the Chapter 11 examples. We also reordered materials to presenttheminamorelogicalsequence.Onereviewerstatedthatthischapter was the single biggest improvement in the twelfth edition. 8. Financial Forecasting. As we were rewriting Chapter 17 GEs chairman announced that he expected to report higher earnings shortly but two weeks laterheannouncedasignificantearningsdeclinewhichledtoasharpdropin vi Preface

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GEsstockprice.Weusedthisexampletoillustratetheimportanceofaccurate forecasts and to liven up our discussion of strategic financial planning. In addition we used an improved Excel model to streamline our illustrative forecast and to make the forecasting process simpler and clearer to students. 9. Capital Budgeting. We moved the analysis of projects with unequal lives back from Chapter 13 to Chapter 12 because unequal life analysis is more closely related to the other topics in Chapter 12. An additional benefit is that Chapter 13 is now more streamlined and focuses on real options. 10. Derivatives. We rearranged some of the sections to improve the discussion in Chapter 18. More specifically we moved the “Using Derivatives to Reduce Risk” section so that it immediately follows the discussion of “Other Types of Derivatives”Wealsoreceivedfeedbacksuggestingthatwefocusedtoomuch on call options. With that in mind we added a new Appendix 18A entitled “Valuation of Put Options.” Finally we added some problems related to option pricing using the riskless hedge approach. 11. Mergers. We eliminated the discussion of purchase/pooling accounting treatment from Chapter 21 since all mergers are now accounted for as pur- chases. We also moved the discussion of merger regulation to a Web Appendix to help streamline the chapter. We could continue to list changes in this edition but these items provide instructors particularly those familiar with the last edition with a good idea of the kinds of revisions that were made to this text. It also lets students know how authors try to improve their texts. ACKNOWLEDGMENTS The book reflects the efforts of a great many people—those who worked on Fundamentals and our related books in the past and those who worked on this twelfth edition. First we would like to thank Dana Aberwald Clark who worked closely with us at every stage of the revision—her assistance was absolutely invaluable. Second Susan Whitman provided great typing and logistical support. Our colleagues Roy Crum Jim Keys Andy Naranjo M. Nimalendran Jay Ritter Mike Ryngaert Craig Tapley and Carolyn Takeda gave us many useful suggestions regarding the ancillaries and many parts of the book including the integrated cases. We also benefited from the work of Mike Ehrhardt and Phillip Daves of the University of Tennessee and Roy Crum of the University of Florida who worked with us on companion books. Also Christopher Buzzard did an outstanding job helping us develop the Excel models the web site and the PowerPoint ® presentations. Next we would like to thank the following professors who reviewed this edition in detail and provided many useful comments and suggestions: Rebecca Abraham—Nova Southeastern University Kavous Ardalan—Marist College Tom Arnold—University of Richmond Deborah Bauer—University of Oregon Gary Benesh—Florida State University Mark S. Bettner—Bucknell University Elizabeth Booth—Michigan State University Brian Boscaljon—Penn State University Erie Rajesh Chakrabarti—Georgia Institute of Technology Brent Dalrymple—University of Central Florida Jim DeMello—Western Michigan University Anne M. Drougas—Dominican University Preface vii

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Scott Ehrhorn—Liberty University David Feller—Brevard Community College Jennifer Foo—Stetson University Partha Gangopadhyay—St. Cloud State University Sharon H. Garrison—University of Arizona Robert P. Hoffman—College of St. Scholastica Benjamas Jirasakuldech—University of the Pacific Ashok Kapoor—Augsburg College Howard Keen—Temple University Christopher J. Lambert J.D.—Fairmont State University Alice Lee—San Francisco State University Denise Letterman—Robert Morris University Yulong Ma—California State University Long Beach Barry Marchman—Florida AM Brian Maris—Northern Arizona University Matthew Morey—Pace University Tom C. Nelson—Leeds School of Business University of Colorado at Boulder Darshana Palkar—Minnesota State University Mankato Narendar V. Rao—Northeastern Illinois University Charles R. Rayhorn—Northern Michigan University Oliver Schnusenberg—University of North Florida Dean S. Sommers—University of Delaware Michal Spivey—Clemson University Glenn L. Stevens—Franklin Marshall College Lowell E. Stockstill—Wittenberg University Samantha Thapa—Western Kentucky University David O. Vang—University of St. Thomas Sheng Yang—Black Hills State University David Zalewski—Providence College Sijing Zong—California State University—Stanislaus We would also like to thank the following professors whose reviews and comments on our earlier books contributed to this edition: Robert Adams Mike Adler Sharif Ahkam Syed Ahmad Ed Altman Bruce Anderson Ron Anderson Tom Anderson John Andrews Bob Angell Vince Apilado Harvey Arbalaez Henry Arnold Bob Aubey Gil Babcock Peter Bacon Kent Baker Robert Balik Tom Bankston Babu Baradwaj Les Barenbaum Charles Barngrover Sam Basu Greg Bauer Bill Beedles Brian Belt Moshe Ben-Horim Bill Beranek Tom Berry Will Bertin Scott Besley Dan Best Roger Bey Gilbert W. Bickum Dalton Bigbee John Bildersee Laurence E. Blose Russ Boisjoly Bob Boldin Keith Boles Michael Bond Geof Booth Waldo Born Steven Bouchard Kenneth Boudreaux Rick Boulware Helen Bowers Oswald Bowlin Don Boyd G. Michael Boyd Pat Boyer Joe Brandt Elizabeth Brannigan Mary Broske Christopher Brown David T. Brown Kate Brown Larry Brown Bill Brueggeman Paul Bursik Alva Butcher Bill Campsey Bob Carlson Severin Carlson David Cary Steve Celec Mary Chaffin Charles Chan Don Chance Antony Chang Susan Chaplinsky K. C. Chen Jay Choi S. K. Choudhary Lal Chugh Maclyn Clouse Bruce Collins Mitch Conover Margaret Considine Phil Cooley Joe Copeland viii Preface

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David Cordell Marsha Cornett M. P. Corrigan John Cotner Charles Cox David Crary John Crockett Jr. Bill Damon Morris Danielson Joel Dauten Steve Dawson Sankar De Fred Dellva Chad Denson James Desreumaux Bodie Dickerson Bernard Dill Gregg Dimkoff Les Dlabay Mark Dorfman Tom Downs Frank Draper Gene Drzycimski Dean Dudley David Durst Ed Dyl Fred J. Ebeid Daniel Ebels Richard Edelman Charles Edwards U. Elike John Ellis George Engler Suzanne Erickson Dave Ewert John Ezzell L. Franklin Fant Richard J. Fendler Michael Ferri Jim Filkins John Finnerty Robert Fiore Susan Fischer Peggy Fletcher Steven Flint Russ Fogler Jennifer Frazier Dan French Michael Garlington David Garraty Jim Garven Adam Gehr Jr. Jim Gentry Wafica Ghoul Erasmo Giambona Armand Gilinsky Jr. Philip Glasgo Rudyard Goode Raymond Gorman Walt Goulet Bernie Grablowsky Theoharry Grammatikos Owen Gregory Ed Grossnickle John Groth Alan Grunewald Manak Gupta Darryl Gurley Sam Hadaway Don Hakala Gerald Hamsmith William Hardin John Harris Paul Hastings Bob Haugen Steve Hawke Stevenson Hawkey Del Hawley Eric M. Haye Robert Hehre Kath Henebry David Heskel George Hettenhouse Hans Heymann Kendall Hill Roger Hill Tom Hindelang Linda Hittle Ralph Hocking J. Ronald Hoffmeister Robert Hollinger Jim Horrigan John Houston John Howe Keith Howe Steve Isberg Jim Jackson Keith Jakob Vahan Janjigian Narayanan Jayaraman Zhenhn Jin Kose John Craig Johnson Keith Johnson Ramon Johnson Steve Johnson Ray Jones Frank Jordan Manuel Jose Sally Joyner Alfred Kahl Gus Kalogeras Rajiv Kalra Ravi Kamath John Kaminarides Michael Keenan Bill Kennedy Peppi M. Kenny Carol Kiefer Joe Kiernan Richard Kish Robert Kleiman Erich Knehans Don Knight Ladd Kochman Dorothy Koehl Jaroslaw Komarynsky Duncan Kretovich Harold Krogh Charles Kroncke Don Kummer Robert A. Kunkel Reinhold Lamb Joan Lamm Larry Lang David Lange P. Lange Howard Lanser Edward Lawrence Martin Lawrence Wayne Lee Jim LePage David E. LeTourneau Jules Levine John Lewis Jason Lin Chuck Linke Bill Lloyd Susan Long Judy Maese Bob Magee Ileen Malitz Bob Malko Phil Malone Abbas Mamoozadeh Terry Maness Chris Manning Surendra Mansinghka Timothy Manuel Terry Martell David Martin D. J. Masson John Mathys Ralph May John McAlhany Andy McCollough Ambrose McCoy Thomas McCue Bill McDaniel John McDowell Charles McKinney Robyn McLaughlin James McNulty Jeanette Medewitz- Diamond Jamshid Mehran Larry Merville Rick Meyer Jim Millar Ed Miller John Miller John Mitchell Carol Moerdyk Bob Moore Scott Moore Barry Morris Gene Morris Dianne R. Morrison Chris Muscarella David Nachman Tim Nantell Don Nast Edward Nelling Bill Nelson Bob Nelson William Nelson Bob Niendorf Bruce Niendorf Ben Nonnally Jr. Preface ix

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Tom OBrien William OConnell Dennis OConnor John ODonnell Jim Olsen Robert Olsen Dean Olson Jim Pappas Stephen Parrish Helen Pawlowski Barron Peake Michael Pescow Glenn Petry Jim Pettijohn Rich Pettit Dick Pettway Aaron Phillips Hugo Phillips H. R. Pickett John Pinkerton Gerald Pogue Eugene Poindexter R. Potter Franklin Potts R. Powell Dianna Preece Chris Prestopino John Primus Jerry Prock Howard Puckett Herbert Quigley George Racette Bob Radcliffe David Rakowski Allen Rappaport Bill Rentz Ken Riener Charles Rini John Ritchie Bill Rives Pietra Rivoli Antonio Rodriguez James Rosenfeld Stuart Rosenstein E. N. Roussakis Dexter Rowell Arlyn R. Rubash Marjorie Rubash Bob Ryan Jim Sachlis Abdul Sadik Travis Sapp Thomas Scampini Kevin Scanlon Frederick Schadeler Patricia L. Schaeff David Schalow Mary Jane Scheuer David Schirm RobertSchwebach Carol Schweser John Settle Alan Severn James Sfiridis Sol Shalit Frederic Shipley Dilip Shome Ron Shrieves Neil Sicherman J. B. Silvers Clay Singleton Joe Sinkey Stacy Sirmans Jaye Smith Patricia Smith Patricia Matisz Smith Don Sorensen David Speairs Ken Stanley Kenneth Stanton Ed Stendardi Alan Stephens Don Stevens Jerry Stevens Glen Strasburg David Suk Katherine Sullivan Timothy Sullivan Philip Swensen Bruce Swenson Ernest Swift Paul Swink Eugene Swinnerton Gary Tallman Dular Talukdar Dennis Tanner Russ Taussig John Teall Richard Teweles Ted Teweles Madeline Thimmes Francis D. Thomas Andrew Thompson John Thompson Arlene Thurman Dogan Tirtirogu Janet Todd Holland J. Toles William Tozer Emery Trahan George Trivoli George Tsetsekos David Upton Howard Van Auken Pretorious Van den Dool Pieter Vandenberg Paul Vanderheiden JoAnn Vaughan Jim Verbrugge Patrick Vincent Steve Vinson Susan Visscher John Wachowicz Joe Walker Mike Walker Sam Weaver Marsha Weber Al Webster Shelton Weeks Kuo-Chiang Wei Bill Welch Fred Weston Richard Whiston Norm Williams Tony Wingler Ed Wolfe Criss Woodruff Don Woods Yangru Wu Robert Wyatt Steve Wyatt Michael Yonan John Zietlow Dennis Zocco Kent Zumwalt Special thanks are due to Chris Barry Texas Christian University and Shirley Love Idaho State University who wrote many of the boxes relating to small- business issues that are on the Web to Emery Trahan and Paul Bolster North- eastern University who developed and wrote the summaries and questions for NewsWire to Dilip Shome Virginia Polytechnic Institute who helped greatly with the capital structure chapter to Dave Brown and Mike Ryngaert University ofFloridawhohelpeduswiththebankruptcyandmergermaterialtoRoyCrum AndyNaranjoandSubuVenkataramanwhoworkedwithusontheinternational materials to Scott Below East Carolina University who developed the web site information and references to Laurie and Stan Eakins of East Carolina who developed the materials on Excel for the Technology Supplement and to Larry Wolken Texas AM University who offered his hard work and advice for the development of the Lecture Presentation Software. Finally the Cengage and LEAP x Preface

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Publishing staffs especially Mike Guendelsberger Erin Shelton Jennifer Ziegler Scott Fidler Mike Reynolds Mike Roche Adele Scholtz Suellen Ruttkay and AlexvonRosenberghelpedgreatlywithallphasesofthetextbooksdevelopment and production. ERRORS IN THE TEXTBOOK At this point most authors make a statement such as this: “We appreciate all the help we received from the people listed above but any remaining errors are of course our own responsibility.” And generally there are more than enough remaining errors Having experienced difficulties with errors ourselves both as students and instructors we resolved to avoid this problem in Fundamentals. As a result of our detection procedures we are convinced that few errors remain but primarily because we want to detect any errors that may have slipped by so that we can correct them in subsequent printings we decided to offer a reward of 10 pererrortothefirstpersonwhoreportsittous.Forpurposeofthisrewarderrors are defined as misspelled words nonrounding numerical errors incorrect state- ments and any other error that inhibits comprehension. Typesetting problems such as irregular spacing and differences of opinion regarding grammatical or punctuation conventions do not qualify for this reward. Given the ever-changing nature of the World Wide Web changes in web addresses also do not qualify as errors although we would like to learn about them. Finally any qualifying error that has follow-through effects is counted as two errors only. Please report any errors to Joel Houston through e-mail at or by regular mail at the address below. CONCLUSION Financeisinarealsensethecornerstoneoftheenterprisesystem—goodfinancial management is vitally important to the economic health of all firms and hence to thenationandtheworld.Becauseofitsimportancefinanceshouldbewidelyand thoroughlyunderstoodbutthisiseasiersaidthandone.Thefieldiscomplexand it undergoes constant change due to shifts in economic conditions. All of this makes finance stimulating and exciting but challenging and sometimes perplex- ing. We sincerely hope that this twelfth edition of Fundamentals will meet its own challenge by contributing to a better understanding of our financial system. EUGENE F. BRIGHAM JOEL F. HOUSTON 4723 N.W. 53rd Ave. Suite A Gainesville Florida 32653 September 2008 Preface xi

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BRIEF CONTENTS Preface iii PART 1 Introduction to Financial Management 1 CHAPTER 1 An Overview of Financial Management 2 PART 2 Fundamental Concepts in Financial Management 25 CHAPTER 2 Financial Markets and Institutions 26 CHAPTER 3 Financial Statements Cash Flow and Taxes 53 CHAPTER 4 Analysis of Financial Statements 84 CHAPTER 5 Time Value of Money 122 PART 3 Financial Assets 161 CHAPTER 6 Interest Rates 162 CHAPTER 7 Bonds and Their Valuation 194 CHAPTER 8 Risk and Rates of Return 229 CHAPTER 9 Stocks and Their Valuation 269 PART 4 Investing in Long-Term Assets: Capital Budgeting 305 CHAPTER 10 The Cost of Capital 306 CHAPTER 11 The Basics of Capital Budgeting 335 CHAPTER 12 Cash Flow Estimation and Risk Analysis 364 CHAPTER 13 Real Options and Other Topics in Capital Budgeting 398 PART 5 Capital Structure and Dividend Policy 415 CHAPTER 14 Capital Structure and Leverage 416 CHAPTER 15 Distributions to Shareholders: Dividends and Share Repurchases 456 PART 6 Working Capital Management and Financial Forecasting 487 CHAPTER 16 Working Capital Management 488 CHAPTER 17 Financial Planning and Forecasting 525 PART 7 Special Topics in Financial Management 551 CHAPTER 18 Derivatives and Risk Management 552 CHAPTER 19 Multinational Financial Management 592 CHAPTER 20 Hybrid Financing: Preferred Stock Leasing Warrants and Convertibles 623 CHAPTER 21 Mergers and Acquisitions 655 xii

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Appendixes APPENDIX A Solutions to Self-Test Questions and Problems A-1 APPENDIX B Answers to Selected End-of-Chapter Problems A-28 APPENDIX C Selected Equations and Tables A-32 Index I-1 Brief Contents xiii

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CONTENTS Preface iii PART 1 Introduction to Financial Management 1 CHAPTER 1 An Overview of Financial Management 2 Striking the Right Balance 2 PUTTING THINGS IN PERSPECTIVE 3 1-1 What is Finance 4 1-1a Finance versus Economics and Accounting 4 1-1b Finance within an Organization 4 1-1c Corporate Finance Capital Markets and Investments 5 1-2 Jobs in Finance 6 1-3 Forms of Business Organization 6 1-4 Stock Prices and Shareholder Value 8 1-5 Intrinsic Values Stock Prices and Executive Compensation 10 1-6 Important Business Trends 14 Global Perspectives: Is Shareholder Wealth Maximization a Worldwide Goal 14 1-7 Business Ethics 15 1-7a What Companies Are Doing 15 1-7b Consequences of Unethical Behavior 16 1-7c How Should Employees Deal with Unethical Behavior 17 Protection for Whistle-Blowers 17 1-8 Conflicts between Managers Stock- holders and Bondholders 18 1-8a Managers versus Stockholders 18 1-8b Stockholders versus Bondholders 20 TYING IT ALL TOGETHER 21 PART 2 Fundamental Concepts in Financial Management 25 CHAPTER 2 Financial Markets and Institutions 26 Efficient Financial Markets Are Necessary for a Growing Economy 26 PUTTING THINGS IN PERSPECTIVE 27 2-1 The Capital Allocation Process 28 2-2 Financial Markets 30 2-2a Types of Markets 30 2-2b Recent Trends 31 2-3 Financial Institutions 34 Citigroup Built to Compete in a Changing Environment 37 2-4 The Stock Market 38 Global Perspectives: The NYSE and NASDAQ Go Global 38 2-4a Physical Location Stock Exchanges 39 2-4b Over-the-Counter OTC and the Nasdaq Stock Markets 39 2-5 The Market for Common Stock 40 2-5a Types of Stock Market Transactions 41 2-6 Stock Markets and Returns 43 2-6a Stock Market Reporting 43 Measuring the Market 45 2-6b Stock Market Returns 46 2-7 Stock Market Efficiency 46 A Closer Look at Behavioral Finance Theory 49 2-7a Conclusions about Market Efficiency 50 TYING IT ALL TOGETHER 50 INTEGRATED CASE Smyth Barry Company 52 CHAPTER 3 FinancialStatementsCashFlowandTaxes 53 The “Quality” of Financial Statements 53 PUTTING THINGS IN PERSPECTIVE 54 3-1 Financial Statements and Reports 54 3-2 The Balance Sheet 56 3-2a Allieds Balance Sheet 57 3-3 The Income Statement 60 3-4 Statement of Cash Flows 62 Massaging the Cash Flow Statement 65 xiv

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3-5 Statement of Stockholders Equity 66 Financial Analysis on the Internet 67 3-6 Free Cash Flow 67 Free Cash Flow Is Important for Small Businesses 68 3-7 Income Taxes 69 3-7a Individual Taxes 69 3-7b Corporate Taxes 71 TYING IT ALL TOGETHER 75 INTEGRATED CASE DLeon Inc. Part I 80 THOMSON ONE: BUSINESS SCHOOL EDITION Exploring Starbucks Financial Statements 83 CHAPTER 4 Analysis of Financial Statements 84 Can You Make Money Analyzing Stocks 84 PUTTING THINGS IN PERSPECTIVE 85 4-1 Ratio Analysis 86 4-2 Liquidity Ratios 87 4-2a Current Ratio 87 4-2b Quick or Acid Test Ratio 88 4-3 Asset Management Ratios 88 4-3a Inventory Turnover Ratio 89 4-3b Days Sales Outstanding 89 4-3c Fixed Assets Turnover Ratio 90 4-3d Total Assets Turnover Ratio 91 4-4 Debt Management Ratios 91 4-4a Total Debt to Total Assets 93 4-4b Times-Interest-Earned Ratio 94 4-5 Profitability Ratios 95 4-5a Operating Margin 95 4-5b Profit Margin 95 Global Perspectives: Global Accounting Standards: Can One Size Fit All 96 4-5c Return on Total Assets 96 4-5d Basic Earning Power BEP Ratio 97 4-5e Return on Common Equity 97 4-6 Market Value Ratios 98 4-6a Price/Earnings Ratio 98 4-6b Market/Book Ratio 98 4-7 Trend Analysis 99 4-8 The DuPont Equation 100 4-9 Ratios in Different Industries 102 4-10 Summary of Allieds Ratios 103 4-11 Benchmarking 104 Looking for Warning Signs within the Financial Statements 105 4-12 Uses and Limitations of Ratios 105 Economic Value Added EVA versus Net Income 107 4-13 Potential Misuses of ROE 107 4-14 Looking Beyond the Numbers 108 TYING IT ALL TOGETHER 109 INTEGRATED CASE DLeon Inc. Part II 117 THOMSON ONE: BUSINESS SCHOOL EDITION Conducting a Financial Ratio Analysis on Ford Motor Company 121 CHAPTER 5 Time Value of Money 122 Will You Be Able to Retire 122 PUTTING THINGS IN PERSPECTIVE 123 5-1 Time Lines 123 5-2 Future Values 124 5-2a Step-by-Step Approach 125 Simple versus Compound Interest 125 5-2b Formula Approach 126 5-2c Financial Calculators 126 5-2d Spreadsheets 127 5-2e Graphic View of the Compounding Process 129 5-3 Present Values 130 5-3a Graphic View of the Discounting Process 131 5-4 Finding the Interest Rate I 132 5-5 Finding the Number of Years N 133 5-6 Annuities 133 5-7 Future Value of an Ordinary Annuity 134 5-8 Future Value of an Annuity Due 136 5-9 Present Value of an Ordinary Annuity 137 5-10 Finding Annuity Payments Periods and Interest Rates 138 5-10a Finding Annuity Payments PMT 138 5-10b Finding the Number of Periods N 138 5-10c Finding the Interest Rate I 139 5-11 Perpetuities 140 Contents xv

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5-12 Uneven Cash Flows 142 5-13 Future Value of an Uneven Cash Flow Stream 143 5-14 Solving for I with Uneven Cash Flows 144 5-15 Semiannual and Other Compounding Periods 145 5-16 Comparing Interest Rates 147 5-17 Fractional Time Periods 149 5-18 Amortized Loans 150 TYING IT ALL TOGETHER 151 INTEGRATED CASE First National Bank 158 WEB APPENDIX 5A Continuous Compounding and Discounting WEB APPENDIX 5B Growing Annuities PART 3 Financial Assets 161 CHAPTER 6 Interest Rates 162 Low Interest Rates Encourage Investment and Stimulate Consumer Spending 162 PUTTING THINGS IN PERSPECTIVE 163 6-1 The Cost of Money 163 6-2 Interest Rate Levels 165 6-3 The Determinants of Market Interest Rates 168 6-3a The Real Risk-Free Rate of Interest r 169 6-3b The Nominal or Quoted Risk-Free Rate of Interest r RF r + IP 170 6-3c Inflation Premium IP 170 An Almost Riskless Treasury Bond 171 6-3d Default Risk Premium DRP 172 6-3e Liquidity Premium LP 172 A 20 Liquidity Premium on a High-Grade Bond 173 6-3f Interest Rate Risk and the Maturity Risk Premium MRP 173 6-4 TheTermStructureofInterestRates 175 6-5 What Determines the Shape of the Yield Curve 176 The Links between Expected Inflation and Interest Rates: A Closer Look 178 6-6 Using the Yield Curve to Estimate Future Interest Rates 180 6-7 Macroeconomic Factors That Influence Interest Rate Levels 183 6-7a Federal Reserve Policy 183 6-7b Federal Budget Deficits or Surpluses 184 6-7c International Factors 184 6-7d Business Activity 185 6-8 Interest Rates and Business Decisions 185 TYING IT ALL TOGETHER 187 INTEGRATED CASE Morton Handley Company 192 CHAPTER 7 Bonds and Their Valuation 194 Sizing Up Risk in the Bond Market 194 PUTTING THINGS IN PERSPECTIVE 195 7-1 Who Issues Bonds 195 7-2 Key Characteristics of Bonds 196 7-2a Par Value 197 7-2b Coupon Interest Rate 197 7-2c Maturity Date 197 7-2d Call Provisions 198 7-2e Sinking Funds 199 7-2f Other Features 199 7-3 Bond Valuation 200 7-4 Bond Yields 203 7-4a Yield to Maturity 203 7-4b Yield to Call 204 7-5 Changes in Bond Values over Time 206 7-6 Bonds with Semiannual Coupons 209 7-7 Assessing a Bond’s Riskiness 210 7-7a Interest Rate Risk 210 7-7b Reinvestment Rate Risk 213 7-7c Comparing Interest Rate and Reinvestment Rate Risk 213 7-8 Default Risk 214 7-8a Various Types of Corporate Bonds 215 7-8b Bond Ratings 215 7-8c Bankruptcy and Reorganization 219 7-9 Bond Markets 220 TYING IT ALL TOGETHER 222 xvi Contents

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INTEGRATED CASE Western Money Management Inc. 228 WEB APPENDIX 7A Zero Coupon Bonds WEB APPENDIX 7B Bankruptcy and Reorganization CHAPTER 8 Risk and Rates of Return 229 A Tale of Three Markets—or Is It Four 229 PUTTING THINGS IN PERSPECTIVE 230 8-1 Stock Prices over the Last 20 Years 231 8-2 Stand-Alone Risk 232 8-2a Statistical Measures of Stand-Alone Risk 233 8-2b Measuring Stand-Alone Risk: The Standard Deviation 236 8-2c Using Historical Data to Measure Risk 237 8-2d Measuring Stand-Alone Risk: The Coefficient of Variation 238 8-2e Risk Aversion and Required Returns 238 The Trade-Off between Risk and Return 239 8-3 Risk in a Portfolio Context: The CAPM 240 8-3a Expected Portfolio Returns r P 241 8-3b Portfolio Risk 242 8-3c Risk in a Portfolio Context: The Beta Coefficient 245 Global Perspectives: The Benefits of Diversifying Overseas 250 8-4 The Relationship between Risk and Rates of Return 251 Estimating the Market Risk Premium 252 8-4a The Impact of Expected Inflation 253 8-4b Changes in Risk Aversion 255 8-4c Changes in a Stock’s Beta Coefficient 256 8-5 Some Concerns about Beta and the CAPM 257 8-6 Some Concluding Thoughts: Implications for Corporate Managers and Investors 258 TYING IT ALL TOGETHER 259 INTEGRATED CASE Merrill Finch Inc. 266 THOMSON ONE: BUSINESS SCHOOL EDITION Using Past Information to Estimate Required Returns 268 WEB APPENDIX 8A Calculating Beta Coefficients CHAPTER 9 Stocks and Their Valuation 269 Searching for the Right Stock 269 PUTTING THINGS IN PERSPECTIVE 270 9-1 Legal Rights and Privileges of Common Stockholders 270 9-1a Control of the Firm 271 9-1b The Preemptive Right 272 9-2 Types of Common Stock 272 9-3 Stock Price vs. Intrinsic Value 273 9-3a Why Do Investors and Companies Care About Intrinsic Value 274 9-4 The Discounted Dividend Model 275 9-4a Expected Dividends as the Basis for Stock Values 277 9-5 Constant Growth Stocks 278 9-5a Illustration of a Constant Growth Stock 279 9-5b Dividends Versus Growth 280 9-5c Which is Better: Current Dividends or Growth 282 9-5d Required Conditions for the Constant Growth Model 282 9-6 Valuing Nonconstant Growth Stocks 283 9-7 Valuing the Entire Corporation 286 Evaluating Stocks That Dont Pay Dividends 287 9-7a The Corporate Valuation Model 288 Other Approaches to Valuing Common Stocks 290 9-7b Comparingthe CorporateValuation and Discounted Dividend Models 290 9-8 Preferred Stock 291 TYING IT ALL TOGETHER 292 INTEGRATED CASE Mutual of Chicago Insurance Company 298 THOMSON ONE: BUSINESS SCHOOL EDITION Estimating ExxonMobil’s Intrinsic Stock Value 299 Contents xvii

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APPENDIX 9A Stock Market Equilibrium 301 PART 4 Investing in Long-Term Assets: Capital Budgeting 305 CHAPTER 10 The Cost of Capital 306 Creating Value at GE 306 PUTTING THINGS IN PERSPECTIVE 307 10-1 An Overview of the Weighted Average Cost of Capital WACC 307 10-2 Basic Definitions 309 10-3 Cost of Debt r d 1 − T 310 10-4 Cost of Preferred Stock r p 312 10-5 The Cost of Retained Earnings r s 312 10-5a The CAPM Approach 314 10-5b Bond-Yield-plus-Risk-Premium Approach 315 10-5c Dividend-Yield-plus-Growth- Rate or Discounted Cash Flow DCF Approach 315 10-5d Averaging the Alternative Estimates 317 10-6 Cost of New Common Stock r e 318 10-6a Add Flotation Costs to a Project’s Cost 318 10-6b Increase the Cost of Capital 318 How Much Does It Cost to Raise External Capital 319 10-6c When Must External Equity Be Used 320 10-7 Composite or Weighted Average Cost of Capital WACC 321 10-8 Factors that Affect the WACC 321 10-8a Factors the Firm Cannot Control 321 10-8b Factorsthe Firm Can Control 322 Global Perspectives: Global Variations in the Cost of Capital 322 10-9 Adjusting the Cost of Capital for Risk 323 10-10 Some Other Problems with Cost of Capital Estimates 325 TYING IT ALL TOGETHER 326 INTEGRATED CASE Coleman Technologies Inc. 333 THOMSON ONE: BUSINESS SCHOOL EDITION Calculating 3Ms Cost of Capital 334 WEB APPENDIX 10A The Cost of New Common Stock and WACC CHAPTER 11 The Basics of Capital Budgeting 335 Competition in the Aircraft Industry: Airbus vs. Boeing 335 PUTTING THINGS IN PERSPECTIVE 336 11-1 AnOverviewofCapitalBudgeting 336 11-2 Net Present Value NPV 338 11-3 Internal Rate of Return IRR 341 Why NPV Is Better Than IRR 343 11-4 Multiple Internal Rates of Return 344 11-5 Reinvestment Rate Assumptions 346 11-6 Modified Internal Rate of Return MIRR 347 11-7 NPV Profiles 349 11-8 Payback Period 353 11-9 Conclusions on Capital Budgeting Methods 355 11-10 Decision Criteria Used in Practice 356 TYING IT ALL TOGETHER 357 INTEGRATED CASE Allied Components Company 362 CHAPTER 12 Cash Flow Estimation and Risk Analysis 364 Home Depot Keeps Growing 364 PUTTING THINGS IN PERSPECTIVE 365 12-1 Conceptual Issues in Cash Flow Estimation 365 12-1a Cash Flow versus Accounting Income 365 12-1b Timing of Cash Flows 366 12-1c Incremental Cash Flows 366 12-1d Replacement Projects 366 12-1e Sunk Costs 366 xviii Contents

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12-1f Opportunity Costs Associated with Assets the Firm Owns 367 12-1g Externalities 367 12-2 Analysis of an Expansion Project 369 12-2a Effect of Different Depreciation Rates 371 12-2b Cannibalization 371 12-2c Opportunity Costs 371 12-2d Sunk Costs 371 12-2e Other Changes to the Inputs 372 12-3 Replacement Analysis 372 12-4 RiskAnalysisinCapitalBudgeting 374 12-5 Measuring Stand-Alone Risk 376 12-5a Sensitivity Analysis 376 12-5b Scenario Analysis 378 12-5c Monte Carlo Simulation 379 Global Perspectives: Capital Budgeting Practices in the Asian/Pacific Region 380 12-6 Within-Firm and Beta Risk 381 12-7 Unequal Project Lives 382 12-7a Replacement Chains 382 12-7b Equivalent Annual Annuities EAA 383 12-7c Conclusions about Unequal Lives 384 TYING IT ALL TOGETHER 384 INTEGRATED CASE Allied Food Products 393 APPENDIX 12A Tax Depreciation 396 WEB APPENDIX 12B Refunding Operations WEB APPENDIX 12C Using the CAPM to Estimate the Risk-Adjusted Cost of Capital WEB APPENDIX 12D Techniques for Measuring Beta Risk CHAPTER 13 Real Options and Other Topics in Capital Budgeting 398 Anheuser-Busch Used Real Options to Enhance Its Value 398 PUTTING THINGS IN PERSPECTIVE 399 13-1 Introduction to Real Options 399 13-2 Growth Expansion Options 400 13-3 Abandonment/Shutdown Options 402 13-4 Investment Timing Options 403 13-5 Flexibility Options 405 13-6 The Optimal Capital Budget 406 13-7 The Post-Audit 408 TYING IT ALL TOGETHER 409 INTEGRATED CASE 21st Century Educational Products 413 PART 5 Capital Structure and Dividend Policy 415 CHAPTER 14 Capital Structure and Leverage 416 Debt: Rocket Booster or Anchor 416 PUTTING THINGS IN PERSPECTIVE 417 14-1 The Target Capital Structure 417 14-2 Business and Financial Risk 419 14-2a Business Risk 419 14-2b Operating Leverage 421 14-2c Financial Risk 424 14-3 Determining the Optimal Capital Structure 429 14-3a WACC and Capital Structure Changes 430 14-3b The Hamada Equation 431 14-3c The Optimal Capital Structure 432 14-4 Capital Structure Theory 435 Yogi Berra on the MM Proposition 436 14-4a The Effect of Taxes 436 14-4b The Effect of Potential Bankruptcy 437 14-4c Trade-Off Theory 438 14-4d Signaling Theory 439 14-4e Using Debt Financing to Constrain Managers 440 14-5 Checklist for Capital Structure Decisions 441 14-6 Variations in Capital Structures 443 Global Perspectives: Taking a Look at Global Capital Structures 444 TYING IT ALL TOGETHER 445 INTEGRATED CASE Campus Deli Inc. 451 Contents xix

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THOMSON ONE: BUSINESS SCHOOL EDITION Exploring the Capital Structures for Four of the Worlds Leading Auto Companies 454 WEB APPENDIX 14A Degree of Leverage CHAPTER 15 Distributions to Shareholders: Dividends and Share Repurchases 456 Microsoft Shifts Gears and Begins to Unload Part of Its Vast Cash Hoard 456 PUTTING THINGS IN PERSPECTIVE 457 15-1 Dividends versus Capital Gains: What Do Investors Prefer 457 15-1a Dividend Irrelevance Theory 458 15-1b Reasons Some Investors Prefer Dividends 458 15-1c Reasons Some Investors Prefer Capital Gains 459 15-2 Other Dividend Policy Issues 460 15-2a InformationContentorSignaling Hypothesis 460 15-2b Clientele Effect 461 15-3 Establishing the Dividend Policy in Practice 461 15-3a Setting the Target Payout Ratio: TheResidualDividendModel 462 Global Perspectives: Dividend Yields around the World 466 15-3b Earnings Cash Flows and Dividends 467 15-3c Payment Procedures 469 15-4 Dividend Reinvestment Plans 470 15-5 Summary of Factors Influencing Dividend Policy 471 15-5a Constraints 472 15-5b Investment Opportunities 472 15-5c Alternative Sources of Capital 472 15-5d EffectsofDividendPolicyonr s 473 15-6 Stock Dividends and Stock Splits 473 15-6a Stock Splits 473 15-6b Stock Dividends 474 15-6c Effect on Stock Prices 474 15-7 Stock Repurchases 475 15-7a The Effects of Stock Repurchases 476 15-7b Advantages of Repurchases 477 15-7c Disadvantages of Repurchases 478 15-7d Conclusions on Stock Repurchases 478 TYING IT ALL TOGETHER 479 INTEGRATED CASE Southeastern Steel Company 484 THOMSON ONE: BUSINESS SCHOOL EDITION Microsofts Dividend Policy 486 WEB APPENDIX 15A An Example: The Residual Dividend Model PART 6 Working Capital Management and Financial Forecasting 487 CHAPTER 16 Working Capital Management 488 Best Buy Manages Its Working Capital Well 488 PUTTING THINGS IN PERSPECTIVE 489 16-1 Background on Working Capital 489 16-2 Current Asset Investment Policies 490 16-3 Current Asset Financing Policies 491 16-3a Maturity Matching or “Self- Liquidating” Approach 492 16-3b Aggressive Approach 492 16-3c Conservative Approach 494 16-3d Choosing between the Approaches 494 16-4 The Cash Conversion Cycle 495 16-4a Calculating the Targeted CCC 495 16-4b Calculating the CCC from Financial Statements 496 Some Firms Operate with Negative Working Capital 497 16-5 The Cash Budget 498 16-6 Cash and Marketable Securities 501 16-6a Currency 502 16-6b Demand Deposits 502 16-6c Marketable Securities 503 16-7 Inventories 504 Supply Chain Management 505 16-8 Accounts Receivable 506 16-8a Credit Policy 506 16-8b Setting and Implementing the Credit Policy 507 xx Contents

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16-8c Monitoring Accounts Receivable 508 16-9 Accounts Payable Trade Credit 509 16-10 Bank Loans 511 16-10a Promissory Note 511 16-10b Line of Credit 512 16-10c Revolving Credit Agreement 513 16-10d Costs of Bank Loans 513 16-11 Commercial Paper 515 16-12 Accruals Accrued Liabilities 516 16-13 Use of Security in Short-Term Financing 516 TYING IT ALL TOGETHER 517 INTEGRATED CASE Ski Equipment Inc. 522 WEB APPENDIX 16A Inventory Management WEB APPENDIX 16B Short-Term Loans and Bank Financing CHAPTER 17 Financial Planning and Forecasting 525 The Miss That Hit Like a Bombshell 525 PUTTING THINGS IN PERSPECTIVE 526 17-1 Strategic Planning 527 17-2 The Sales Forecast 528 17-3 The AFN Equation 530 17-3a Excess Capacity Adjustments 533 17-4 Forecasted Financial Statements 534 17-4a Part I. Inputs 534 17-4b Part II. Forecasted Income Statement 537 17-4c Part III. Forecasted Balance Sheet 537 17-4d Part IV. Ratios and EPS 537 17-4e Using the Forecast to Improve Operations 538 17-5 Using Regression to Improve Forecasts 539 17-6 Analyzing the Effects of Changing Ratios 540 17-6a Modifying Accounts Receivable 540 17-6b Modifying Inventories 540 17-6c Other “Special Studies” 541 TYING IT ALL TOGETHER 541 INTEGRATEDCASE NewWorldChemicalsInc. 547 THOMSON ONE: BUSINESS SCHOOL EDITION Forecasting the Future Performance of Abercrombie Fitch 549 WEB APPENDIX 17A Forecasting Financial Requirements When Financial Ratios Change PART 7 Special Topics in Financial Management 551 CHAPTER 18 Derivatives and Risk Management 552 Using Derivatives to Manage Risk 552 PUTTING THINGS IN PERSPECTIVE 553 18-1 Reasons to Manage Risk 553 18-2 Background on Derivatives 556 Global Perspectives: Barings and Sumitomo Suffer Large Losses in the Derivatives Market 558 18-3 Options 558 18-3a Option Types and Markets 558 18-3b Factors That Affect the Value of a Call Option 560 18-3c Exercise Value versus Option Price 561 18-4 Introduction to Option Pricing Models 563 Expensing Executive Stock Options 565 18-5 The Black-Scholes Option Pricing Model OPM 566 18-5a OPM Assumptions and Equations 567 18-5b OPM Illustration 568 18-6 Forward and Futures Contracts 571 18-7 Other Types of Derivatives 574 18-7a Swaps 574 18-7b Structured Notes 575 18-7c Inverse Floaters 576 Credit Instruments Create New Opportunities and Risks 577 18-8 Using Derivatives to Reduce Risks 577 18-8a Security Price Exposure 578 18-8b Futures 578 Contents xxi

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18-8c Swaps 579 18-8d Commodity Price Exposure 580 18-8e The Use and Misuse of Derivatives 581 18-9 Risk Management 581 18-9a An Approach to Risk Management 582 Microsoft’s Goal: Manage Every Risk 584 TYING IT ALL TOGETHER 585 INTEGRATED CASE Tropical Sweets Inc. 587 APPENDIX 18A Valuation of Put Options 590 CHAPTER 19 Multinational Financial Management 592 U.S. Firms Look Overseas to Enhance Shareholder Value 592 PUTTING THINGS IN PERSPECTIVE 593 19-1 Multinational or Global Corporations 593 19-2 Multinational versus Domestic Financial Management 596 19-3 The International Monetary System 598 19-3a International Monetary Terminology 598 19-3b Current Monetary Arrangements 599 19-4 Foreign Exchange Rate Quotations 600 19-4a Cross Rates 600 19-4b Interbank Foreign Currency Quotations 601 19-5 Trading in Foreign Exchange 602 19-5a Spot Rates and Forward Rates 603 19-6 Interest Rate Parity 604 19-7 Purchasing Power Parity 605 Hungry for a Big Mac Go to China 606 19-8 Inflation Interest Rates and Exchange Rates 608 19-9 International Money and Capital Markets 609 19-9a International Credit Markets 609 Stock Market Indices around the World 610 19-9b International Stock Markets 611 19-10 Investing Overseas 612 Global Perspectives: Measuring Country Risk 613 Global Perspectives: Investing in International Stocks 613 19-11 International Capital Budgeting 614 19-12 International Capital Structures 616 TYING IT ALL TOGETHER 618 INTEGRATED CASE Citrus Products Inc. 621 CHAPTER 20 Hybrid Financing: Preferred Stock Leasing Warrants and Convertibles 623 Now Enticing: Convertible Securities 623 PUTTING THINGS IN PERSPECTIVE 624 20-1 Preferred Stock 624 20-1a Basic Features 625 20-1b Adjustable Rate Preferred Stock 627 20-1c Advantages and Disadvantages of Preferred Stock 627 A Good Idea That Went Bad: Auction Rate Preferred Stock ARPS 628 20-2 Leasing 629 20-2a Types of Leases 629 20-2b Financial Statement Effects 630 20-2c Evaluation by the Lessee 632 20-2d Other Factors That Affect Leasing Decisions 635 20-3 Warrants 635 20-3a Initial Market Price of a Bond with Warrants 636 20-3b Use of Warrants in Financing 637 20-3c The Component Cost of Bonds with Warrants 638 20-3d Problems with Warrant Issues 639 20-4 Convertibles 639 20-4a Conversion Ratio and Conversion Price 640 20-4b The Component Cost of Convertibles 641 20-4c Use of Convertibles in Financing 644 20-4d Convertibles Can Reduce Agency Costs 645 xxii Contents

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20-5 A Final Comparison of Warrants and Convertibles 645 20-6 Reporting Earnings When Warrants or Convertibles Are Outstanding 646 TYING IT ALL TOGETHER 647 INTEGRATED CASE Fish Chips Inc. Part I 653 INTEGRATEDCASE FishChipsInc.PartII 653 CHAPTER 21 Mergers and Acquisitions 655 Mergers: Reshaping the Corporate Landscape 655 PUTTING THINGS IN PERSPECTIVE 656 21-1 Rationale for Mergers 656 21-1a Synergy 657 21-1b Tax Considerations 657 21-1c Purchase of Assets below Their Replacement Cost 657 21-1d Diversification 657 21-1e Managers’PersonalIncentives 658 21-1f Breakup Value 658 21-2 Types of Mergers 659 21-3 Level of Merger Activity 659 21-4 Hostile versus Friendly Takeovers 660 21-5 Merger Analysis 661 21-5a Valuing the Target Firm 662 21-5b Setting the Bid Price 665 More Than Just Financial Statements 667 21-5c Post-Merger Control 667 21-6 The Role of Investment Bankers 668 21-6a Arranging Mergers 669 21-6b Developing Defensive Tactics 669 21-6c Establishing a Fair Value 670 21-6d Financing Mergers 670 21-6e Arbitrage Operations 670 21-7 Do Mergers Create Value The Empirical Evidence 671 The Track Record of Recent Large Mergers 671 21-8 Corporate Alliances 672 21-9 Private Equity Investments 673 21-10 Divestitures 674 21-10a Types of Divestitures 674 21-10b Divestiture Illustrations 674 TYING IT ALL TOGETHER 676 INTEGRATED CASE Smittys Home Repair Company 679 WEB APPENDIX 21A Merger Regulation WEB APPENDIX 21B Holding Companies APPENDIXES APPENDIX A Solutions to Self-Test Questions and Problems A-1 APPENDIX B Answers to Selected End-of- Chapter Problems A-28 APPENDIX C Selected Equations and Tables A-32 INDEX I-1 Contents xxiii

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CHAPTER 1 An Overview of Financial Management Striking the Right Balance In 1776 Adam Smith described how an “invisible hand” guides companies as they strive for profits and that hand leads them to decisions that benefit society. Smith’s insights led him to con- clude that profit maximization is the right goal for a business and that the free enterprise system is best for society. But the world has changed since 1776. Firms today are much larger they operate globally they have thousands of employ- ees and they are owned by millions of stock- holders. This makes us wonder if the “invisible hand” still provides reliable guidance. Should companies still try to maximize profits or should they take a broader view and take more balanced actions designed to benefit customers employees suppliers and society as a whole Most academics today subscribe to the fol- lowing modified version of Adam Smith’s theory: l A firm’s principal goal should be to maximize the wealth of its stockholders which means maximizing the value of its stock. l Free enterprise is still the best economic system for the country as a whole. l However some constraints are needed—firms should not be allowed to pollute the air and water engage in unfair employment practices or create monopolies that exploit consumers. Profits depend on sales and sales require that firms develop desirable products and serv- ices produce them efficiently and sell them at competitive prices all of which benefit society. So the view today is that management should try to maximize stock prices but their actions should be subject to government-imposed constraints. Still some argue that the constrained max- imization theory is inadequate. For example GE Chief Executive Officer CEO Jeffrey Immelt believes that just obeying the law is not enough. GE is the world’s most valuable company and it has an excellent reputation. 1 Immelt argues that value and reputation go hand in hand and that © STR/AFP/Getty Images 1 Marc Gunther “Money and Morals at GE” Fortune November 15 2004 pp. 176–182. 2

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PUTTING THINGS IN PERSPECTIVE This chapter will give you an idea of what financial management is all about. We begin the chapter by describing how finance is related to the overall business and by discussing the different forms of business organization. For corporations management’s goal should be to maximize shareholder wealth which means maximizing the value of the stock. When we say “maximizing the value of the stock” we mean the “true long-run value” which may be different from the cur- rent stock price. Good managers understand the importance of ethics and they recognize that maximizing long-run value is consistent with being socially responsible. We conclude the chapter by discussing how firms must provide the right incentives if they are to get managers to focus on long-run value max- imization. When you finish this chapter you should be able to: l Explain the role of finance and the different types of jobs in finance. l Identify the advantages and disadvantages of different forms of business organization. l Explain the links betweenstock priceintrinsicvalue andexecutivecompensation. l Discuss the importance of business ethics and the consequences of unethical behavior. l Identify the potential conflicts that arise within the firm between stockholders and managers and between stockholders and bondholders and discuss the techniques that firms can use to mitigate these potential conflicts. having a good reputation with customers suppliers employees and regulators is essential if value is to be maximized. According to Immelt “The reason people come to work for GE is that they want to be part of something bigger than themselves. They want to work hard win promotions and be well compensated but they also want to work for a company that makes a difference a company that’s doing great things in the world. . . . It’suptoGEtobe a good citizen. Not only is that a nice thing to do it’s good for business and thus the price of our stock.” GE is by no means alone. An increasing number of companies see their mission as more than just making money for their shareholders. Google Inc.’s well-known corporate motto is “Don’t Be Evil.” Taking things a step further the company recently announced that it was set- ting aside another 30 million to be used for philanthropic ventures worldwide. The company’s in-house foundation now has assets in excess of 2 billion. Days later Microsoft Corporation’s chairperson Bill Gates gave a speech to the World Economic Forum in which he made the case for a “creative capitalism.” Gates stated that “Such a system would have a twin mission: making profits and also improving lives for those who don’t fully benefit from market forces.” Gates has certainly been true to his word. In 2000 he and his wife established the Bill Melinda Gates Founda- tion. Today the fund has assets totaling 37.6 billion. It received a notable boost in 2006 when famed investor Warren Buffett announced that he would donate a huge share of his fortune to the Foundation. To date Buffett has contributed more than 3 billion and over time he is scheduled to contribute additional shares of stock that are now worth in excess of 40 million. These efforts show that while there is more to life than money it often takes money to do good things. Sources:PatriciaSellers“MelindaGatesGoesPublic”CNNMoney.comJanuary72008KevinJ.Delaney“Google:From‘Don’tBeEvil’to How to Do Good” The Wall Street Journal January 18 2008 p. B1 and Robert A. Guth “Bill Gates Issues Call for Kinder Capitalism” The Wall Street Journal January 24 2008 p. A1. Chapter 1 An Overview of Financial Management 3

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1-1 WHAT IS FINANCE It’s hard to define finance—the term has many facets which makes it difficult to provide a clear and concise definition. The discussion in this section will give you an idea ofwhatfinance people do and what you might do ifyou enterthe finance field after you graduate. 1-1a Finance versus Economics and Accounting Finance as we know it today grew out of economics and accounting. Economists developed the notion that an asset’s value is based on the future cash flows the assetwillprovideandaccountantsprovidedinformationregardingthelikelysize of those cash flows. Finance then grew out of and lies between economics and accounting so people who work in finance need knowledge of those two fields. Also as discussed next in the modern corporation the accounting department falls under the control of the chief financial officer CFO. 1-1b Finance within an Organization Most businesses and not-for-profit organizations have an organization chart similar to the one shown in Figure 1-1. The board of directors is the top governing body and the chairperson of the board is generally the highest-ranking individual. The CEO comes next but note that the chairperson of the board often serves as the CEO as well. Below the CEO comes the chief operating officer COO who is often also designated as a firm’s president. The COO directs the firm’s operations which include marketing manufacturing sales and other operating departments. The CFO who is gener- allyaseniorvicepresidentandthethirdrankingofficerisinchargeofaccounting Finance within an Organization FIGURE 1-1 Chief Operating Ofcer COO Marketing Production Human Resources and Other Operating Departments Accounting Treasury Credit Legal Capital Budgeting and Investor Relations Board of Directors Chief Financial Ofcer CFO Chief Executive Ofcer CEO 4 Part 1 Introduction to Financial Management

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financing credit policy decisions regarding asset acquisitions and investor rela- tions which involves communications with stockholders and the press. If the firm is publicly owned the CEO and the CFO must both certify to the Securities and Exchange Commission SEC that reports released to stockholders and especially the annual report are accurate. If inaccuracies later emerge the CEOandtheCFOcouldbefinedorevenjailed.Thisrequirementwasinstitutedin 2002 as a part of the Sarbanes-Oxley Act. The Act was passed by Congress in the wake of a series of corporate scandals involving now-defunct companies such as Enron and WorldCom where investors workers and suppliers lost billions of dollars due to false information released by those companies. 1-1c Corporate Finance Capital Markets and Investments Finance as taught in universities is generally divided into three areas: 1 financial management 2 capital markets and 3 investments. Financial management also called corporate finance focuses on decisions relating to how much and what types of assets to acquire how to raise the capital needed to buy assets and how to run the firm so as to maximize its value. The same principles apply to both for-profit and not-for-profit organ- izations and as the title suggests much of this book is concerned with financial management. Capital marketsrelatetothemarketswhereinterestratesalongwithstock and bond prices are determined. Also studied here are the financial institutions that supply capital to businesses. Banks investment banks stockbrokers mutual fundsinsurancecompaniesandthelikebringtogether“savers”whohavemoney to invest and businesses individuals and other entities that need capital for various purposes. Governmental organizations such as the Federal Reserve Sys- temwhichregulatesbanksandcontrolsthesupplyofmoneyandtheSECwhich regulates the trading of stocks and bonds in public markets are also studied as part of capital markets. Investments relate to decisions concerning stocks and bonds and include a number of activities: 1 Security analysis deals with finding the proper values of individual securities i.e. stocks and bonds. 2 Portfolio theorydeals with the best way to structure portfolios or “baskets” of stocks and bonds. Rational investors want to hold diversified portfolios in order to limit risks so choosing a properly balanced portfolio is an important issue for any investor. 3 Market analysis deals with the issue of whether stock and bond markets at any given time are “too high”“toolow”or“aboutright.”Behavioralfinancewhereinvestorpsychologyis examined in an effort to determine if stock prices have been bid up to unrea- sonable heights in a speculative bubble or driven down to unreasonable lows in a fit of irrational pessimism is a part of market analysis. Although we separate these three areas they are closely interconnected. Banking is studied under capital markets but a bank lending officer evaluating a business’ loan request must understand corporate finance to make a sound deci- sion. Similarly a corporate treasurer negotiating with a banker must understand banking if the treasurer is to borrow on “reasonable” terms. Moreover a security analysttryingtodetermineastock’struevaluemustunderstandcorporatefinance andcapitalmarketstodohisorherjob.Inadditionfinancialdecisionsofalltypes depend on the level of interest rates so all people in corporate finance invest- ments and banking must know something about interest rates and the way they are determined. Because of these interdependencies we cover all three areas in this book. Sarbanes-Oxley Act A law passed by Congress that requires the CEO and CFO to certify that their firm’s financial statements are accurate. Chapter 1 An Overview of Financial Management 5

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SELFTEST What is the relationship between economics finance and accounting Who is the CFO where does this individual fit into the corporate hierarchy and what are some of his or her responsibilities Does it make sense for not-for-profit organizations such as hospitals and universities to have CFOs What three areas of finance does this book cover Are these areas inde- pendent of one another or are they interrelated in the sense that someone working in one area should know something about each of the other areas 1-2 JOBS IN FINANCE Next to health care jobs in finance have been growing faster than any other area. Finance prepares students for jobs in banking investments insurance corpo- rations and the government. Accounting students need to know finance mar- keting management and human resources they also need to understand finance for it affects decisions in all those areas. For example marketing people propose advertising programs but those programs are examined by finance people to judge the effects of the advertising on the firm’s profitability. So to be effective in marketing one needs to have a basic knowledge of finance. The same holds for management—indeed most important management decisions are evaluated in terms of their effects on the firm’s value. This is called value-based management and it is the “in” thing today. It is also worth noting that finance is important to individuals regardless of their jobs. Some years ago most businesses provided pensions to their employees so managing one’s personal investments was not critically important. That’sno longer true. Most firms today provide what’s called “defined contribution” pen- sion plans where each year the company puts a specified amount of money into an account that belongs to the employee. The employee must decide how those funds are to be invested—how much should be divided among stocks bonds or moneyfundsandhowriskythestocksandbondsshouldbe.Thesedecisionshave amajoreffectonpeople’slivesandtheconceptscoveredinthisbookcanimprove decision-making skills. 1-3 FORMS OF BUSINESS ORGANIZATION The basics offinancial management are the same for all businesses large or small regardless of how they are organized. Still a firm’s legal structure affects its operations and thus should be recognized. There are four main forms of business organizations: 1 sole proprietorships 2 partnerships 3 corporations and 4 limited liability companies LLCs and limited liability partnerships LLPs. In terms of numbers most businesses are sole proprietorships. However based on the dollar value of sales about 80 of all business is done by corporations. Because corporations conduct the most business and because most successful businesses eventually convert to corporations we concentrate on them in this book. Still it is important to understand the legal differences between firms. A proprietorship is an unincorporated business owned by one individual. Going into business as a sole proprietor is easy—a person begins business oper- ations. Proprietorships have three important advantages: 1 They are easily and inexpensively formed 2 they are subject to few government regulations and To find information about different finance careers go to com. This web site provides information about different finance areas and recommends different books about jobs in finance. Proprietorship An unincorporated busi- ness owned by one individual. 6 Part 1 Introduction to Financial Management

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3 they are subject to lower income taxes than are corporations. However pro- prietorships also have three important limitations: 1 Proprietors have unlimited personalliabilityforthebusiness’sdebtssotheycanlosemorethantheamountof moneytheyinvested in the company.You might invest 10000 tostartabusiness but be sued for 1 million if during company time one of your employees runs over someone with a car. 2 The life of the business is limited to the life of the individual who created it and to bring in new equity investors require a change in the structure of the business. 3 Because of the first two points proprietorships have difficulty obtaining large sums of capital hence proprietorships are used primarily for small businesses. However businesses are frequently started as proprietorships and then converted to corporations when their growth results in the disadvantages outweighing their advantages. Apartnershipisalegalarrangementbetweentwoormorepeoplewhodecide todobusinesstogether.Partnershipsaresimilartoproprietorshipsinthattheycan be established relatively easily and inexpensively. Moreover the firm’s income is allocated on a pro rata basis to the partners and is taxed on an individual basis. This allows the firm to avoid the corporate income tax. However all of the partnersaregenerallysubjecttounlimitedpersonalliabilitywhichmeansthatifa partnership goes bankrupt and any partner is unable to meet his or her pro rata shareofthefirm’sliabilitiestheremainingpartnerswillberesponsibleformaking good on the unsatisfied claims.Thus the actionsofaTexas partner can bring ruin toamillionaireNewYorkpartnerwhohadnothingtodowiththeactionsthatled to the downfall of the company. Unlimited liability makes it difficult for part- nerships to raise large amounts of capital. 2 Acorporationisalegalentitycreatedbyastateanditisseparateanddistinct fromitsownersandmanagers.Itisthisseparationthatlimitsstockholders’lossesto theamounttheyinvestedinthefirm—thecorporationcanloseallofitsmoneybutits owners canlose onlythe funds thatthey invested in the company. Corporations also have unlimited lives and it is easier to transfer shares of stock in a corporation than one’s interest in an unincorporated business. These factors make it much easier for corporations to raise the capital necessary to operate large businesses. Thus com- panies such as Hewlett-Packard and Microsoft generally begin as proprietorships or partnerships but at some point they find it advantageous to become a corporation. A major drawback to corporations is taxes. Most corporations’ earnings are subject to double taxation—the corporation’s earnings are taxed and then when its after-tax earnings are paid out as dividends those earnings are taxed again as personal income to the stockholders. However as an aid to small businesses Con- gresscreatedScorporationswhicharetaxedasiftheywerepartnershipsthusthey areexemptfromthecorporateincometax.ToqualifyforScorporationstatusafirm can have no more than 75 stockholders which limits their use to relatively small privately owned firms. Larger corporations are known as C corporations. The vast majorityofsmallcorporationselectSstatusandretainthatstatusuntiltheydecideto sell stock to the public at which time they become C corporations. A limited liability company LLC is a relatively new type of organization that is a hybrid between a partnership and a corporation. A limited liability partnershipLLPissimilartoanLLCbutLLPsareusedforprofessionalfirmsin 2 Originally there were just “plain vanilla” partnerships but over the years lawyers have created a number of variations. We leave the variations to courses on business law but we note that the variations are generally designed to limit the liabilities of some of the partners. For example a “limited partnership” has a general partner who has unlimited liability and one or more limited partners whose liability is limited to the amount of their investment. This sounds great from the standpoint of limited liability but the limited partners must cede sole control to the general partner which means that they have almost no say in the way the firm is managed. With a corporation the owners stockholders have limited liability but they also have the right to vote and thus change management if they think that a change is in order. Note too that LLCs and LLPs discussed later in this section are increasingly used in lieu of partnerships. Partnership An unincorporated busi- ness owned by two or more persons. Corporation A legal entity created by a state separate and dis- tinct from its owners and managers having unlim- ited life easy trans- ferability of ownership and limited liability. S Corporation A special designation that allows small businesses that meet qualifications to be taxed as if they were a proprietorship or a part- nership rather than a corporation. Limited Liability Company LLC A relatively new type of organization that is a hybrid between a part- nership and a corporation. Limited Liability Partnership LLP Similar to an LLC but used for professional firms in the fields of accounting law and architecture. It has limited liability like corporations but is taxed like partnerships. Chapter 1 An Overview of Financial Management 7

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the fields of accounting law and architecture while LLCs are used by other businesses. Both LLCs and LLPs have limited liability like corporations but are taxed like partnerships. Further unlike limited partnerships where the general partner has full control of the business the investors in an LLC or LLP have votes in proportion to their ownership interest. LLCs and LLPs have been gaining in popularity in recent years but large companies still find it advantageous to be C corporations because of the advantages in raising capital to support growth. LLCs/LLPs were dreamed up by lawyers and it is necessary to hire a good lawyer when establishing one. 3 When deciding on its form of organization a firm must trade off the advan- tages of incorporation against a possibly higher tax burden. However for the following reasons the value of any business other than a relatively small one will probably be maximized if it is organized as a corporation: 1. Limited liability reduces the risks borne by investors and other things held constant the lower the firm’s risk the higher its value. 2. Afirm’svalueisdependentonitsgrowthopportunitieswhicharedependent on its ability to attract capital. Because corporations can attract capital more easily than other types of businesses they are better able to take advantage of growth opportunities. 3. The value of an asset also depends on its liquidity which means the time and effortittakes tosell the assetfor cash atafairmarket value. Becausethestock ofacorporationiseasiertotransfertoapotentialbuyerthanisaninterestina proprietorshiporpartnershipandbecausemoreinvestorsarewillingtoinvest in stocks than in partnerships with their potential unlimited liability a cor- porate investment is relatively liquid. This too enhances the value of a corporation. SELFTEST What are the key differences between proprietorships partnerships and corporations How are LLCs and LLPs related to the other forms of organization What is an S corporation and what is its advantage over a C corporation Why don’t firms such as IBM GE and Microsoft choose S corporation status What are some reasons the value of a business other than a small one is generally maximized when it is organized as a corporation Suppose you are relatively wealthy and are looking for a potential invest- ment. You do not plan to be active in the business. Would you be more interestedininvesting ina partnershipor ina corporationWhy or whynot 1-4 STOCK PRICES AND SHAREHOLDER VALUE The primary goal of a corporation should be to maximize its owners’ value but a proprietor’s goal might be quite different. Consider Larry Jackson the proprietor of a local sporting goods store. Jackson is in business to make money but he likes to take time off to play golf on Fridays. He also has a few employees who are no longer very productive but he keeps them on the payroll out of friendship and loyalty. Jackson is running the business in a way that is consistent with his own 3 LLCs and LLPsare relativelycomplicatedstructures and whattheycan do and how theymustbe setup varies by state. Moreovertheyare stillevolving.If youareinterestedinlearningmoreaboutthemwerecommend thatyou go to Google or another search engine enter LLC or LLP and see the many references that are available. 8 Part 1 Introduction to Financial Management

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personalgoals.Heknowsthathecouldmakemoremoneyifhedidn’tplaygolfor if he replaced some of his employees. But he is comfortable with his choices and since it is his business he is free to make those choices. By contrast Linda Smith is CEO of a large corporation. Smith manages the companybutmostofthestockisownedbyshareholderswhopurchaseditbecause theywerelookingforaninvestmentthatwouldhelpthemretiresendtheirchildren to college pay for a long-anticipated trip and so forth. The shareholders elected a board of directors which then selected Smith to run the company. Smith and the firm’s other managers are working on behalf of the shareholders and they were hired to pursue policies that enhance shareholder value. At the same time the managers know that this does not mean maximize shareholder value “at all costs.” Managershaveanobligationtobehaveethicallyandtheymustfollowthelawsand other society-imposed constraints that we discussed in the opening vignette to this chapter. Throughout this book we focus primarily on publicly owned companies hence we operate on the assumption that management’s primary goal is share- holder wealth maximization. That translates into this rule: A manager should try to maximize the price of the firm’s stock subject to the constraints discussed in the opening vignette. If a manager is to maximizeshareholder wealth he or she must know how that wealth is determined. Essentially shareholder wealth is the number of shares out- standing times the market price per share. For example if you own 100 shares of GE’sstockand the price is40per shareyour wealth in GEis 4000.The wealth of allofGE’sstockholderscanbesummedandthatisthevalueofthefirm’sstockthe item that management should maximize. The number of shares outstanding is a given so what really determines shareholder wealth is the price of the stock. Throughout this book we will see that the value of any asset is the present valueofthestreamofcashflowstheassetprovidestoitsowners.Wediscussstock valuationindepthinChapter9wherewewillseethatastock’spriceatanygiven timedependsonthecashflowsa“marginal”investorexpectstoreceiveafterbuying thestock.ToillustratesupposeinvestorsareawarethatGEearned2.20persharein 2007 and paid out 52 of that amount or 1.15 per share in dividends. Suppose furtherthatmostinvestorsexpectearningsdividendsandthestockpricetoincrease by about 6 per year. It might turn out that these expectations are met exactly. Howevermanagementmightmakeaprudentdecisionthatcausesprofitstoriseata 12 rate causing the stock price to jump from 40 to 60 per share. Of course management might make a big mistake profits might suffer and the stock price mightdeclineto20.Thusinvestorsareexposedtoriskwhen theybuyGEstockor any other company’s stock. If instead the investor bought a U.S. Treasury bond he or shewouldreceiveaguaranteedinterest payment every 6monthsplusthebond’s par value when it matures so his or her risk would be minimal. We see then that if GE’s management makes good decisions its stock price will increase however if its managers make bad decisions the stock price will decrease. Management’s goal should be to make decisions designed to maximize the stock’s price. Note though that factors beyond management’s control also affect stock prices. Thus after the 9/11 terrorist attacks on the World Trade Center the priceofmoststocksfellnomatterhoweffectivetheirmanagementmayhavebeen. Firms have a number of different departments including marketing accounting production human resources and finance. The finance department’s principal taskistoevaluateproposeddecisionsandjudgehowtheywillaffectthe stock price and thus shareholder wealth. For example suppose the production manager wants to replace some old equipment with new automated machinery that will reduce labor costs. The finance staff will evaluate that proposal and determine whether the savings seem to be worth the cost. Similarly if marketing wants to sign a contract with Tiger Woods that will cost 10 million per year for Shareholder Wealth Maximization The primary goal for managers of publicly owned companies implies that decisions should be made to maximize the long-run value of the firm’s common stock. Chapter 1 An Overview of Financial Management 9

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5years the financial staff will evaluate the proposal look at the probable increase in salesandreachaconclusionastowhethersigningTigerwillleadtoahigherstock price.Mostsignificantdecisionsareevaluatedintermsoftheirfinancialconsequences. Note too that stock prices change over time as conditions change and as investors obtain new information about a company’s prospects. For example Apple Computer’s stock ranged from 77 to 193 per share during a recent 12-monthperiodrisingandfallingasgoodandbadnewswasreleased.Wal-Mart which is in a more stable industry had a narrower price range—from 42 to 52. Investors can predict future results for Wal-Mart more accurately than for Apple thus Wal-Mart is thought to be less risky. Also some projects are relatively straightforward and easy to evaluate and hence not very risky. For example if Wal-Mart were considering a proposed new store the revenues costs and profits for this project would be easier to estimate than for an Apple project related to a newvoice-activatedcomputer.Thesuccessorlackthereofofprojectssuchasthese determine the stock prices of Wal-Mart Apple and other companies. SELFTEST What is management’s primary goal What do investors expect to receive when they buy a share of stock Do investors know for sure how much they will receive Explain. Based just on the name which company would you expect to be riskier— General Foods or South Seas Oil Exploration Explain. When Boeing decides to invest 5 billion in a new jet airliner are its managers certain oftheproject’seffects on Boeing’sfuture profits and stock price Explain. Who would be better able to judge the effect of a new airliner on Boeing’s profits—its managers or its stockholders Explain. Would all Boeing stockholders expect the same outcome from a given new project and how would those expectations affect the stock’s price Explain. 1-5 INTRINSIC VALUES STOCK PRICES AND EXECUTIVE COMPENSATION Asnotedintheprecedingsectionstockpricesarebasedoncashflowsexpectedin future years not just in the current year. Thus stock price maximization requires us to take a long-run view of operations. Academics have generally assumed that managersadheretothislong-runfocusbutitisnowclearthatthefocusformany companies shifted to the short run in recent years. To give managers an incentive tofocusonstockpricesstockholdersactingthroughboardsofdirectorsawarded executives stock options that could be exercised on a specified future date. An executive could exercise the option on that date receive stock immediately sell it and earn a profit. The profit was based on the stock price on the option exercise date which led some managers to try to maximize the stock price on that specific datenotoverthelongrun.Thatinturnledtosomehorribleabuses.Projectsthat looked good from a long-run perspective were turned down because they would penalize profits in the short run and thus lower the stock price on the option exercise day. Even worse some managers deliberately overstated profits tem- porarily boosted the stock price exercised their options sold the inflated stock and left outside stockholders “holding the bag” when the true situation was revealed. Enron and WorldCom are examples of companies whose managers did this but there were many others. 10 Part 1 Introduction to Financial Management

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Othercompanieshavealsousedaggressivebutlegalaccountingpracticesthat boosted current profits but lowered profits in future years. For example knowing that an asset would be usable for only 5 years management might depreciate it over a 10-year life. This reduces reported costs—and raises reported income—for the next 5 years but raises costs and lowers income during the following 5 years. Manyotherlegalbutquestionableaccountingprocedureshavebeenusedallinan effort to boost reported profits and the stock price on the option exercise day. Obviouslyallthiscanmakeitdifficultforinvestorstodecidehowmuchastockis really worth and it helps explain why a firm’s reputation is an important deter- minant of its stock price. Fortunately most executives are honest. But even for honest companies it is hard for investors to determine the proper price of a stock. Figure 1-2 illustrates the situation. The top box indicates that managerial actions combined with the economy taxes and political conditions determine stock prices and thus invest- ors’ returns. Remember that no one knows for sure what those future returns will be—we can estimate them but expected and realized returns are often quite dif- ferent. Investors like high returns but they dislike risk so the larger the expected profits and the lower the perceived risk the higher the stock’s price. The second row of boxes differentiates what we call “true expected returns” and “true risk” from “perceived” returns and “perceived” risk. By “true” we mean the returns and risk that investors would expect if they had all of the information that existed about a company. “Perceived” means what investors expect given the limited information they actually have. To illustrate in early 2001 investors had information that caused them to think that Enron was highly profitable and would enjoy high and rising future profits. They also thought that actual results would be close to the expected levels and hence that Enron’s risk was low. However true estimates of Enron’s profits which were known by its executives but not the investing public were much lower and Enron’s true situ- ation was extremely risky. Determinants of Intrinsic Values and Stock Prices FIGURE 1-2 Managerial Actions the Economic Environment Taxes and the Political Climate “True” Investor Returns “True” Risk “Perceived” Investor Returns “Perceived” Risk Stock’s Intrinsic Value Stock’s Market Price Market Equilibrium: Intrinsic Value Stock Price Chapter 1 An Overview of Financial Management 11

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The third row of boxes shows that each stock has an intrinsic value which is an estimate of the stock’s “true” value as calculated by a competent analyst who hasthebestavailableriskandreturndataandamarketpricewhich istheactual market price based on perceived but possibly incorrect information as seen by the marginal investor. 4 Not all investors agree so it is the “marginal” investor who determines the actual price. For example investors at the margin might expect a firm to pay a 1.00 dividend with a 5 growth rate thereafter and on that basis they might set the firm’s stock price at 45 per share. However if they had all of the available facts they might conclude that the dividend would be 1.30 with a 7 growth rate which would lead to a price of 50 per share. In this case the actual market price would be 45 versus an intrinsic value of 50. Whenastock’sactualmarketpriceisequaltoitsintrinsicvaluethestockisin equilibrium which is shown in the bottom box in Figure 1-2 and when equi- librium exists there is no pressure for a change in the stock’s price. Market prices can and do differ from intrinsic values but eventually as the future unfolds the two values tend to converge. Actual stock prices are easy to determine—they can be found on the Internet and are published in newspapers every day. However intrinsic values are esti- mates and different analysts with different data and different views about the future form different estimates of a stock’s intrinsic value. Indeed estimating intrinsicvaluesiswhatsecurityanalysisisallaboutandiswhatdistinguishessuccessful from unsuccessful investors. Investing would be easy profitable and essentially riskless if we knew all stocks’ intrinsic values but of course we don’t. We can estimateintrinsicvaluesbutwecan’tbesurethatweareright.Afirm’smanagers have the best information about the firm’s future prospects so managers’ esti- mates of intrinsic values are generally better than those of outside investors. However even managers can be wrong. Figure1-3graphs ahypotheticalcompany’sactualprice andintrinsicvalue as estimatedbyitsmanagementovertime. 5 Theintrinsicvaluerisesbecausethefirm retainsandreinvestsearningseachyearwhichtendstoincreaseprofits.Thevalue jumped dramatically in 2003 when a research and development RD break- through raised management’s estimate of future profits before investors had this information. The actual stock price tended to move up and down with the esti- matedintrinsicvaluebutinvestoroptimismandpessimismalongwithimperfect knowledge about the true intrinsic value led to deviations between the actual prices and intrinsic values. Intrinsic value is a long-run concept. It reflects both improper actions like Enron’s overstating earnings and proper actions like GE’s efforts to improve the environment. Management’s goal should be to take actions designed to maximize the firm’s intrinsic value not its current market price. Note though that maximizing the intrinsic value will maximize the average price over the long run but not necessarily the current price at each point in time. For example management might make an investment that lowers profits for the current year but raises Intrinsic Value An estimate of a stock’s “true” value based on accurate risk and return data. The intrinsic value can be estimated but not measured precisely. Market Price The stock value based on perceived but possibly incorrect information as seen by the marginal investor. Marginal Investor An investor whose views determine the actual stock price. 4 Investors at the margin are the ones who actually set stock prices. Some stockholders think that a stock at its current price is a good deal and they would buy more if they had more money. Others think that the stock is priced too high so they would not buy it unless the price dropped sharply. Still others think that the current stock price is about where it should be so they would buy more if the price fell slightly sell it if the price rose slightly and maintain their current holdings unless something were to change. These are the marginal investors and it is their view that determines the current stock price. We discuss this point in more depth in Chapter 9 where we discuss the stock market in detail. 5 We emphasize that the intrinsic value is an estimate and that different analysts have different estimates for a company at any given time. Managers should also estimate their firm’s intrinsic value and then take actions to maximize that value. They should try to help outside security analysts improve their intrinsic value estimates by providing accurate information about the company’s financial position and operations but without releasing information that would help its competitors. Enron WorldCom and a number of other companies tried to deceive analysts and they succeeded all too well. Equilibrium The situation in which the actual market price equals the intrinsic value so investors are indifferent between buying or selling a stock. 12 Part 1 Introduction to Financial Management

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expected future profits. If investors are not aware of the true situation the stock price will be held down by the low current profit even though the intrinsic value wasactuallyraised.Management should provideinformationthat helps investors make better estimates of the firm’s intrinsic value which will keep the stock price closertoitsequilibriumlevel.Howevertherearetimeswhenmanagementcannot divulge the true situation because doing so would provide information that helps its competitors. 6 SELFTEST What’sthedifferencebetweenastock’scurrentmarketpriceanditsintrinsic value Do stocks have known and “provable” intrinsic values or might different people reach different conclusions about intrinsic values Explain. Should managers estimate intrinsic values or leave that to outside security analysts Explain. If a firm could maximize either its current market price or its intrinsic value what would stockholders as a group want managers to do Explain. Should a firm’s managers help investors improve their estimates of the firm’s intrinsic value Explain. Graph of Actual Prices versus Intrinsic Values FIGURE 1-3 RD Breakthrough Actual Stock Price Intrinsic Value Stock Undervalued Stock Overvalued 1983 1988 1993 1998 2003 2008 Stock Price and Intrinsic Value 6 As we discuss in Chapter 2 many academics believe that stock prices embody all publicly available information—hence that stock prices are typically reasonably close to their intrinsic values and thus at or close to an equilibrium. However almost no one doubts that managers have better information than the public at large that at times stock prices and equilibrium values diverge and thus that stocks can be temporarily undervalued or overvalued as we suggest in Figure 1-3. Chapter 1 An Overview of Financial Management 13

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1-6 IMPORTANT BUSINESS TRENDS Four important business trends should be noted. First the points discussed in the preceding section have led to profound changes in business practices. Executives at Enron WorldCom and other companies lied when they reported financial results leading to huge stockholder losses. These companies’ CEOs later claimed not to have been aware of what was happening and their knowledge or lack thereof was a central issue in their trials. As a result Congress passed the Sarbanes-Oxley bill which requires the CEO and CFO of a firm to certify that the firm’s financial statements are accurate. These executives can be sent to jail if it later turns out that the statements did not meet the required standards. Conse- quentlybusinessesbeefeduptheirinternalandexternalauditingproceduresand the accuracy of published statements has improved. A second trend is the increased globalization of business. Developments in com- munications technology have made it possible for Wal-Mart for example to obtain real-timedataonthesalesofhundredsofthousandsofitemsinstoresfromChina to ChicagoandtomanageallofitsstoresfromBentonvilleArkansas.IBMMicrosoftand other high-tech companies now have research labs and help desks in China India andRomaniaandcustomersofHomeDepotandotherretailershavetheirtelephone ande-mailquestionsansweredbycallcenteroperatorsincountriesaroundtheglobe. Coca-Cola Exxon Mobil GE and IBM among others generate more than half of theirsalesandincomeoverseas.Thetrendtowardglobalizationislikelytocontinue and companiesthatresist will havedifficulty competinginthe 21stcentury. 7 Athirdtrendthat’shavingaprofoundeffectonfinancialmanagementisever- improving information technology IT. Improvements in IT are spurring global- ization and they are changing financial management as it is practiced in the GLOBAL PERSPECTIVES IS SHAREHOLDER WEALTH MAXIMIZATION A WORLDWIDE GOAL Most academics agree that shareholder wealth max- imization should be a firm’s primary goal but it’snotclear that people elsewhere really know how to implement it. PricewaterhouseCoopers PWC a global consulting firm conducted a survey of 82 Singapore companies to test their understanding and implementation of shareholder value concepts. Ninety percent of the respondents said their firm’sprimary goal wasto enhance shareholder value but only 44 had taken steps to achieve this goal. Moreover almost half of the respondents who had shareholder value programs in place said they were dis- satisfied with the results achieved thus far. Even so respondents who focused on shareholder value were more likely to believe that their stock was fairly valued than those with other focuses and 50 of those without a specific program said they wanted to learn more and would probably adopt the goal of shareholder wealth maximization eventually. The study found that firms measure performance pri- marily with accounting-based measures such as the return on assets equity or invested capital. These measures are easy to understand and thus to implement even though they are not the best conceptually. When compensation was tied to shareholder value this was only for mid-level managers and above. It is unclear how closely these results correspond to U.S. firms but firms in the United States and Singapore would certainly agree on one thing: It is easier to set the goal of shareholder wealth maximization than it is to figure out how to achieve it. Source: Kalpana Rashiwala “Low Adoption of Shareholder Value Concepts Here” The Business Times Singapore February 14 2002. 7 To give you an idea of the prevalence of globalization the computer programming that causes the test bank problems for this book to vary randomly was outsourced to programmers in Moscow Russia. Our books have been translated into 11 languages and they are sold throughout the world. Globalization is alive and well 14 Part 1 Introduction to Financial Management

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United States and elsewhere. Firms are collecting massive amounts of data and using it to take much of the guesswork out of financial decisions. For example when Wal-Mart is considering a potential site for a new store it can draw on historical results from thousands of other stores to predict results at the proposed site. This lowers the risk of investing in new stores. A fourth trend relates to corporate governance or the way the top managers operateandinterfacewithstockholders.Someyearsagothechairpersonoftheboard of directors was almost always also the CEO and this individual decided who would be elected to the board. That made it almost impossible for stockholders to replaceapoormanagementteam.Todaythoughactiveinvestorswhocontrolhuge pools of capital hedge funds and private equity groups are constantly looking for underperforming firms and they will quickly pounceon laggards take control and replace managers. At the same time the SEC which has jurisdiction over the way stockholdersvoteandtheinformationtheymustbegivenhasbeenmakingiteasier for activist stockholders to change the way things are done within firms. For example the SEC is forcing companies to provide more transparent information on CEO compensation which is affecting managers’ actions. SELFTEST What four trends affect business management in general and financial management in particular 1-7 BUSINESS ETHICS AsaresultoftheEnronscandalandotherrecentscandalstherehasbeenastrong push toimprove business ethics.Thisis occurringon several fronts—actions begun by former New York attorney general and former governor Elliot Spitzer and others who sued companies for improper acts Congress’ passing of the Sarbanes Oxley bill to impose sanctions on executives who sign financial statements later found to be false and business schools trying to inform students about proper versus improper business actions. As noted earlier companies benefit from having good reputations and are penalized by having bad ones the same is true for individuals. Reputations reflect the extent to which firms and people are ethical. Ethics is defined in Webster’s Dic- tionaryas“standardsofconductormoralbehavior.”Businessethicscanbethought of as a company’s attitude and conduct toward its employees customers commu- nity and stockholders. A firm’s commitment to business ethics can be measured by the tendency of its employees from the top down to adhere to laws regulations and moral standards relating to product safety and quality fair employment prac- tices fair marketing and selling practices the use of confidential information for personal gain community involvement and illegal payments to obtain business. 1-7a What Companies Are Doing Most firms today have strong written codes of ethical behavior companies also conduct training programs to ensure that employees understand proper behavior in different situations. When conflicts arise involving profits and ethics ethical considerations sometimesaresoobviouslyimportantthat theydominate.Inother cases however the right choice is not clear. For example suppose that Norfolk Southern’smanagersknowthatitscoaltrainsarepollutingtheairbuttheamount of pollution is within legal limits and further reduction would be costly. Are the Business Ethics A company’s attitude and conduct toward its employees customers community and stockholders. Chapter 1 An Overview of Financial Management 15

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managers ethically bound to reduce pollution Similarly several years ago Merck’s research indicated that its Vioxx pain medicine might be causing heart attacks.Howevertheevidencewasnotoverlystrongandtheproductwasclearly helping some patients. Over time additional tests produced stronger evidence that Vioxx did pose a health risk. What should Merck have done and when should Merck have done it If the company released negative but perhaps incorrect information this announcement would have hurt sales and possibly prevented some patients who could have benefit from using the product. If the company delayed the release of this additional information more patients might have suffered irreversible harm. At what point should Merck have made the potentialproblemknowntothepublicTherearenoobviousanswerstoquestions such as these but companies must deal with them and a failure to handle them properly can lead to severe consequences. 1-7b Consequences of Unethical Behavior Over the past few years ethical lapses have led to a number of bankruptcies. The recent collapses of Enron and WorldCom as well as the accounting firm Arthur Andersendramaticallyillustratehowunethicalbehaviorcanleadtoafirm’srapid decline. In all three cases top executives came under fire because of misleading accounting practices that led to overstated profits. Enron and WorldCom execu- tives werebusilysellingtheir stock atthe sametimetheywererecommendingthe stocktoemployeesand outside investors.These executives reapedmillions before the stock declined while lower-level employees and outside investors were left “holdingthe bag.”Some of these executives arenowin jailand Enron’sCEO had a fatal heart attack while awaiting sentencing after being found guilty of con- spiracyandfraud.MoreoverMerrillLynchandCitigroupwhichwereaccusedof facilitating these frauds were fined hundreds of millions of dollars. Thesefraudsalsoseverelydamagedothercompaniesandevenwholeindustries. For example WorldCom understated its costs by billions of dollars. It then used those artificially low costs when it set prices for its customers. Not knowing that WorldCom’s results were built on lies ATT’s CEO put pressure on his own managers to match WorldCom’s costs and prices. ATT cut back on important projects put fartoo much stress on its employees acquired other companies at high pricesandendedupruiningasuccessful100-year-oldcompany. 8 Asimilarsituation occurred in the energy industry as a result of Enron’s cheating. These and other improper actions caused many investors to lose faith in American business and to turn away from the stock market which made it dif- ficult for firms to raise the capital they needed to grow create jobs and stimulate the economy. So unethical actions can have adverse consequences far beyond the companies that perpetrate them. All this raises a question: Are companies unethical or is it just a few of their employees That was a central issue that came up in the case of ArthurAndersen the accounting firm that audited Enron WorldCom and several other companies that committed accounting fraud. Evidence showed that relatively few of Andersen’s accountants helped perpetrate the frauds. Its top managers argued that while a few rogue employees did bad things most of the firm’s 85000 employees and the firm itself were innocent. The U.S. Justice Department dis- agreed concluding that the firm was guilty because it fostered a climate where unethical behavior was permitted and that Andersen used an incentive system 8 The original ATT was reorganized into a manufacturing company Lucent 8 regional telephone companies and a long-distance company that retained the ATT name. WorldCom was in the long-distance business and thus competed with the surviving ATT. Partly as the result of its efforts to match WorldCom’s phony costs and prices ATT lost billions. In the end ATT was acquired by the smallest of the 8 regional companies which then took the ATT name. 16 Part 1 Introduction to Financial Management

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that made such behavior profitable to both the perpetrators and the firm. As a result Andersen was put out of business its partners lost millions of dollars and its 85000 employees lost their jobs. In most other cases individuals rather than firms were tried and while the firms survived they suffered damage to their reputations which greatly lowered their future profit potential and value. 1-7c How Should Employees Deal with Unethical Behavior Far too often the desire for stock options bonuses and promotions drives man- agers to take unethical actions such as fudging the books to make profits in the manager’s division look good holding back information about bad products that would depress sales and failing to take costly but needed measures to protect the environment. Generally these acts don’t rise to the level of an Enron or a World- Com but they are still bad. If questionable things are going on who should take actionandwhatshouldthatactionbeObviouslyinsituationssuchasEnronand WorldCom where fraud was being perpetrated at or close to the top senior managersknewabouttheillegalactivities.Inothercasestheproblemiscausedby a mid-level manager trying to boost his or her unit’s profits and thus his or her bonus. In all cases though at least some lower-level employees are aware of what’s happening they may even be ordered to take fraudulent actions. Should the lower-levelemployees obey their boss’s ordersrefuse to obey those orders or report the situation to a higher authority such as the company’s board of direc- tors the company’s auditors or a federal prosecutor In the WorldCom and Enron cases it was clear to a number of employees that unethical and illegal acts were being committed but in cases such as Merck’sVioxx product the situation was less clear. Because early evidence that Vioxx led to heart attackswasweakandevidenceofitspainreductionwasstrongitwasprobablynot appropriatetosoundanalarmearlyon.Howeverasevidenceaccumulatedatsome point the public needed to be given a strong warning or the product should have been taken off the market. But judgment comes into play when deciding on what action to take and when to take it. If a lower-level employee thinks that a product should be pulled but the boss disagrees what should the employee do If an employee decides to report the problem trouble may ensue regardless of the merits ofthecase.Ifthealarmisfalsethecompanywillhavebeenharmedandnothingwill have been gained. In that case the employee will probably be fired. Even if the employee is right his or her career maystill be ruined because many companies or at least bosses don’t like “disloyal troublemaking” employees. PROTECTION FOR WHISTLE-BLOWERS As a result of the recent accounting and other frauds in 2002 Congress passed the Sarbanes-Oxley Act which codified certain rules pertaining to corporate behavior. One provision in the bill was designed to protect whistle-blowers or lower-level employees who sound an alarm over actions by their superiors. Employees who report improper actions are often fired or otherwise penalized which keeps many peoplefrom reportingactivities thatshould beinvestigated. The Sarbanes-Oxley provision was designed to alleviate this problem. If someone reports a corporate wrongdoing and is later penalized he or she can ask the Occupational Safety Health Administration OSHA to investigate the situation if the employee was improperly penalized the company can be required to reinstate the person along with back pay and a sizable penalty award. According to The Wall Street Journal some big awards have been handed out and a National Whistle-Blower Center has been established to help people sue companies. It’s still dangerous to blow the whistle but less so than before the Sarbanes-Oxley Act was passed. Source: Deborah Solomon and Kara Scannell “SEC Is Urged to Enforce ‘Whistle-Blower’ Provision” The Wall Street Journal November 15 2004 p. A6. Chapter 1 An Overview of Financial Management 17

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Such situations arise fairly often in contexts ranging from accounting fraud to product liability and environmental cases. Employees jeopardize their jobs if they come forward over their bosses’ objections. However if they don’t speak up they may suffer emotional problems and contribute to the downfall of their companies and the accompanying loss of jobs and savings. Moreover if employees obey orders regarding actions they know are illegal they may end up going to jail. Indeedinmostofthescandalsthathave gonetotrialthelower-levelpeoplewho physicallyentered the bad data received longer jail sentences than the bosses who presumablygavethe directives.Soemployeescanbe “stuckbetweenarock anda hard place” that is doing what they should do and possibly losing their jobs versus going along with the boss and possibly ending up in jail. This discussion shows why ethics is such an important consideration in business andinbusiness schools—and whywe areconcerned with itinthisbook. SELFTEST How would you define “business ethics” Can a firm’s executive compensation plan lead to unethical behavior Explain. Unethical acts are generally committed by unethical people. What are some things companies can do to help ensure that their employees act ethically 1-8 CONFLICTS BETWEEN MANAGERS STOCKHOLDERS AND BONDHOLDERS 9 1-8a Managers versus Stockholders It has long been recognized that managers’ personal goals may compete with shareholder wealth maximization. In particular managers might be more inter- ested in maximizing their own wealth than their stockholders’ wealth therefore managers might pay themselves excessive salaries. For example Disney paid its former president Michael Ovitz 140 million as a severance package after just 14 months on the job—140 million to go away—because he and Disney CEO Michael Eisner were having disagreements. Eisner was also handsomely com- pensated the year Ovitz was fired—a 750000 base salary plus a 9.9 million bonus plus 565 million in profits from stock options for a total of just over 575 million. As another example of corporate excesses Tyco CEO Dennis Kozlowski who is now in jail spent more than 1 million of the company’s money on a birthday party for his wife. Neither the Disney executives’ pay nor Kozlowski’s birthday party seem consistent with shareholder wealth maximization. Still good executive compen- sation plans can motivate managers to act in their stockholders’ best interests. Useful motivationaltools include 1reasonable compensation packages2firing of managers who don’t perform well and 3 the threat of hostile takeovers. Compensationpackagesshouldbesufficienttoattractandretainablemanagers but they should not go beyond what is needed. Also compensation should be structured so that managers are rewarded on the basis of the stock’s performance overthelongrunnotthestock’spriceonanoptionexercisedate.Thismeansthat options or direct stock awards should be phased in over a number of years so that managers have an incentive to keep the stock price high over time. When the 9 These conflicts are studied under the heading of agency theory in finance literature. The classic work on agency theory is Michael C. Jensen and William H. Meckling “Theory of the Firm Managerial Behavior Agency Costs and Ownership Structure” Journal of Financial Economics October 1976 pp. 305–360. 18 Part 1 Introduction to Financial Management

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intrinsic value can be measured in an objective and verifiable manner perfor- mance pay can be based on changes in intrinsic value. However because intrinsic valueisnotobservablecompensationmustbebasedonthestock’smarketprice— but the price used should be an average over time rather than on a specific date. Stockholders can intervene directly with managers. Years ago most stock was owned by individuals. Today however the majority of stock is owned by insti- tutional investors such as insurance companies pension funds hedge funds and mutual funds and private equity groups are ready and able to step in and take over underperforming firms. These institutional money managers have the clout to exercise considerable influence over firms’ operations. First they can talk with managers and make suggestions about how the business should be run. In effect institutional investors such as CalPERS California Public Employees’ Retirement System with 165 billion of assets and TIAA-CREF Teachers Insurance and AnnuityAssociation–CollegeRetirementEquityFundaretirementplanoriginally set up for professors at private colleges that now has more than 300 billion of assetsactaslobbyistsforthebodyofstockholders.Whensuchlargestockholders speak companies listen. Second any shareholder who has owned 2000 of a company’s stock for one year can sponsor a proposal that may be voted on at the annual stockholders’ meeting even if management opposes the proposal. 10 Although shareholder-sponsored proposals are nonbinding the results of such votes are heard by top management. There is an ongoing debate regarding how much influence shareholders should have through the proxy process. For exam- ple shareholder activists sharply criticized a recent SEC vote that continued to allow companies to exclude shareholder proposals related to director elections. 11 Until recently the probability of a large firm’s management being ousted by itsstockholderswassoremotethatitposedlittlethreat.Mostfirms’shareswereso widely distributed and the CEO had so much control over the voting mechanism that it was virtually impossible for dissident stockholders to get the votes needed tooverthrow amanagement team. However that situation has changed.Inrecent years the top executives of ATT Coca-Cola Fannie Mae General Motors IBM and Xerox to name a few have been forced out. All of these departures were due to the firm’s poor performance. If a firm’s stock is undervalued corporate raiders will see it as a bargain and will attempt to capture the firm in a hostile takeover. If the raid is successful the target’s executives will almost certainly be fired. This situation gives managers a strongincentivetotakeactionstomaximizetheirstock’sprice.Inthewordsofone executive “If you want to keep your job never let your stock become a bargain.” Again note that the price managers should be trying to maximize is not the priceonaspecificday.Ratheritistheaveragepriceoverthelongrunwhich will be maximized if management focuses on the stock’s intrinsic value. However managers must communicate effectively with stockholders without divulging information that would aid their competitors to keep the actual price close to the intrinsic value. It’s bad for stockholders and managers when the intrinsic value is high but the actual price is low. In that situation a raider may swoop in buy the company at a bargain price and fire the managers. To repeat our earlier message: Managers should try to maximize their stock’s intrinsic value and then com- municate effectively with stockholders. That will cause the intrinsic value to be high and the actual stock price to remain close to the intrinsic value over time. 10 Under current guidelines shareholder proposals are restricted to governance issues and shareholders are not allowed to vote directly on items that are considered to be “operating issues.” 11 Kara Scannell “Cox in Denying Proxy Access Puts His Legacy on the Line” The Wall Street Journal Online November 29 2007 p. C1. Corporate Raider An individual who targets a corporation for takeover because it is undervalued. Hostile Takeover The acquisition of a com- pany over the opposition of its management. Chapter 1 An Overview of Financial Management 19

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Because the intrinsic value cannot be observed it is impossible to know whether it is really being maximized. Still as we will discuss in Chapter 9 there are procedures for estimating a stock’s intrinsic value. Managers can use these valuation models to analyze alternative courses of action and thus see how these actions are likely to impact the firm’s value. This type of value-based man- agement is not as precise as we would like but it is the best way to run a business. 1-8b Stockholders versus Bondholders Conflicts can also arise between stockholders and bondholders. Bondholders generally receive fixed payment regardless of how well the company does while stockholders do better when the company does better. This situation leads to conflicts between these two groups. 12 To illustrate the problem suppose a com- panyhasthechancetomakeaninvestmentthatwillresultinaprofitof10billion if it is successful but the company will be worthless and go bankrupt if the investmentisunsuccessful.Thefirmhasbondsthatpayan8annualinterestrate and have a value of 1000 per bond and stock that sells for 10 per share. If the newproject—sayacureforthecommoncold—issuccessfulthepriceofthestock will jump to 2000 per share but the value of the bonds will remain just 1000 perbond.Theprobabilityofsuccessis50andtheprobabilityoffailureis50so the expected stock price is Expected stock price ¼ 0:52000 þ 0:5ð0Þ¼ 1000 versus a current price of 10. The expected percentage gain on the stock is Expected percentage gain on stock¼ð1000 − 10Þ10 100 ¼ 9900 The project looks wonderful from the stockholders’ standpoint but lousy for the bondholders. They just break even if the project is successful but they lose their entire investment if it is a failure. Another type of bondholder/stockholder conflict arises over the use of additional debt. As we will see later in this book the more debt a firm uses to finance a given amount of assets the riskier the firm is. For example if a firm has 100 million of assets and finances them with 5 million of bonds and 95 million of common stock things will have to go terribly bad before the bondholders will suffer a loss. On the other hand if the firm uses 95 million of bonds and 5millionofstockthebondholderswillsufferalossevenifthevalueoftheassets declines only slightly. Bondholders attempt to protect themselves by including covenants in the bond agreements that limit firms’ use of additional debt and constrain managers’ actions in other ways. We will address these issues later in this book but they are quite important and everyone should be aware of them. SELFTEST What are three techniques stockholders can use to motivate managers to maximize their stock’s long-run price Should managers focus directly on the stock’s actual market price or its intrinsic value or are both important Explain. Why might conflicts arise between stockholders and bondholders 12 Managers represent stockholders so saying “stockholders versus bondholders” is the same as saying “managers versus bondholders.” 20 Part 1 Introduction to Financial Management

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TYING IT ALL TOGETHER This chapter provides a broad overview of financial management. Management’s primary goal should be to maximize the long-run value of the stock which means the intrinsic value as measured by the stock’s price over time. To maximize value firms must develop products that consumers want produce the products effi- ciently sell them at competitive prices and observe laws relating to corporate behavior. If firms are successful at maximizing the stock’s value they will also be contributing to social welfare and citizens’ well-being. Businesses can be organized as proprietorships partnerships corporations limited liability companies LLCs or limited liability partnerships LLPs. The vast majority of all business is done by corporations and the most successful firms end up as corporations which explains the focus on corporations in this book. We also discussed four important business trends: 1 the focus on business ethics that resulted from a series of scandals in the late 1990s 2 the trend toward global- ization 3 the ever-improving information technology and 4 the changes in corporate governance. These four trends are changing the way business is done. The primary tasks of the CFO are 1 to make sure the accounting system provides “good” numbers for internal decision making and for investors 2 to ensure that the firm is financed in the proper manner3 to evaluate the operating units to make sure they are performing in an optimal manner and 4 to evaluate all proposed capital expenditures to make sure they will increase the firm’s value. In the remainder of this book we discuss exactly how financial managers carry out these tasks. SELF-TEST QUESTION AND PROBLEM Solutions Appear in Appendix A ST-1 KEY TERMS Define each of the following terms: a. Sarbanes-Oxley Act b. Proprietorship partnership corporation c. S corporations limited liability companies LLCs limited liability partnerships LLPs d. Stockholder wealth maximization e. Intrinsic value market price f. Equilibrium marginal investor g. Business ethics h. Corporate raider hostile takeover QUESTIONS 1-1 Ifyouboughtashareofstockwhat wouldyouexpecttoreceivewhenwouldyouexpect to receive it and would you be certain that your expectations would be met 1-2 If most investors expect the same cash flows from Companies A and B but are more confidentthatA’scashflowswillbeclosertotheirexpectedvaluewhichcompanyshould have the higher stock price Explain. Chapter 1 An Overview of Financial Management 21

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1-3 What is a firm’s intrinsic value its current stock price Is the stock’s “true long-run value” more closely related to its intrinsic value or to its current price 1-4 When is a stock said to be in equilibrium At any given time would you guess that most stocks are in equilibrium as you defined it Explain. 1-5 Suppose three honest individuals gave you their estimates of Stock X’s intrinsic value. One person is your current roommate the second person is a professional security analyst with an excellent reputation on Wall Street and the third person is Company X’s CFO. If the three estimates differed in which one would you have the most confidence Why 1-6 Isitbetterforafirm’sactualstockpriceinthemarkettobeunderoverorequaltoitsintrinsic valueWouldyouranswerbethesamefromthestandpointsofstockholdersingeneralanda CEO who is about to exercise a million dollars in options and then retire Explain. 1-7 If a company’s board of directors wants management to maximize shareholder wealth should the CEO’s compensation be set as a fixed dollar amount or should the compen- sation depend on how well the firm performs If it is to be based on performance how should performance be measured Would it be easier to measure performance by the growth rate in reported profits or the growth rate in the stock’s intrinsic value Which would be the better performance measure Why 1-8 What are the four forms of business organization What are the advantages and dis- advantages of each 1-9 Shouldstockholderwealthmaximizationbethoughtofasalong-termorashort-termgoal For example ifone action increases afirm’s stockprice froma current level of20to25in 6 months and then to 30 in 5 years but another action keeps the stock at 20 for several years but then increases it to 40 in 5 years which action would be better Think of some specific corporate actions that have these general tendencies. 1-10 What are some actions that stockholders can take to ensure that management’s and stockholders’ interests are aligned 1-11 The president of Southern Semiconductor Corporation SSC made this statement in the company’s annual report: “SSC’s primary goal is to increase the value of our common stockholders’ equity.” Later in the report the following announcements were made: a. The company contributed 1.5 million to the symphony orchestra in Birmingham Alabama its headquarters city. b. The company is spending 500 million to open a new plant and expand operations in China. No profits will be produced by the Chinese operation for 4 years so earnings will be depressed during this period versus what they would have been had the decision been made not to expand in China. c. The company holds about half of its assets in the form of U.S. Treasury bonds and it keeps these funds available for use in emergencies. In the future though SSC plans to shift its emergency funds from Treasury bonds to common stocks. Discuss how SSC’s stockholders might view each of these actions and how the actions might affect the stock price. 1-12 Investors generally can make one vote for each share of stock they hold. TIAA-CREF is the largest institutional shareholder in the United States therefore it holds many shares and has more votes than any other organization. Traditionally this fund has acted as a passive investor just going along with management. However in 1993 it mailed a notice to all 1500 companies whose stocks it held that henceforth it planned to actively intervene if in its opinion management was not performing well. Its goal was to improve corporate performance to boost the prices of the stocks it held. It also wanted to encourage corporate boards to appoint a majority of independent outside directors and it stated that it would voteagainstanydirectorsoffirmsthat“don’thaveaneffectiveindependentboardthatcan challenge the CEO.” In the past TIAA-CREF responded to poor performance by “voting with its feet” which means selling stocks that were not doing well. However by 1993 that position had become difficult to maintain for two reasons. First the fund invested a large part of its assets in “index funds” which hold stocks in accordance with their percentage value in the broad stock market. Furthermore TIAA-CREF owns such large blocks of stocks in many companies that if it tried to sell out doing so would severely depress the prices of those stocks.ThusTIAA-CREFislockedintoalargeextentwhichledtoitsdecisiontobecomea more active investor. a. Is TIAA-CREF an ordinary shareholder Explain. b. Due to its asset size TIAA-CREF owns many shares in a number of companies. The fund’s management plans to vote those shares. However TIAA-CREF is owned by 22 Part 1 Introduction to Financial Management

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many thousands of investors. Should the fund’s managers vote its shares or should it pass those votes on a pro rata basis back to its own shareholders Explain. 1-13 Edmund Enterprises recently made a large investment to upgrade its technology. While these improvements won’t have much effect on performance in the short run they are expected to reduce future costs significantly. What effect will this investment have on Edmund Enterprises’ earnings per share this year What effect might this investment have on the company’s intrinsic value and stock price 1-14 Suppose you were a member of Company X’s board of directors and chairperson of the company’s compensation committee. What factors should your committee consider when setting the CEO’s compensation Should the compensation consist of a dollar salary stock options that depend on the firm’s performance or a mix of the two If “performance” is to be considered how should it be measured Think of both theoretical and practical that is measurement considerations. If you were also a vice president of Company X might your actions be different than if you were the CEO of some other company 1-15 Supposeyouareadirectorofanenergycompanythathasthreedivisions—naturalgasoil and retail gas stations. These divisions operate independently from one another but all divisionmanagers report tothe firm’s CEO.Ifyouwere onthe compensation committeeas discussed in Question 1–14 and your committee was asked to set the compensation for the three division managers would you use the same criteria as that used for the firm’s CEO Explain your reasoning. Chapter 1 An Overview of Financial Management 23

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PART 2 FUNDAMENTAL CONCEPTS IN FINANCIAL MANAGEMENT 2 Financial Markets and Institutions 3 Financial Statements Cash Flow and Taxes 4 Analysis of Financial Statements 5 Time Value of Money CHAPTER

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CHAPTER 2 Financial Markets and Institutions Efficient Financial Markets Are Necessary for a Growing Economy Over the past few decades changing technology and improving communications have increased cross-border transactions and expanded the scope and efficiency of the global financial system. Companies routinely raise funds throughout the world and with the click of a mouse an investor can buy GE stock on the New York Stock Exchange deposit funds in a European bank or purchase a mutual fund that invests in Chinese securities. This globalization was dramatically illustrated in the fall of 2007. The U.S. housing market had been exceedingly strong which bolstered the entire economy. Rising home values enabled people to borrow on home equity loans to buy everything from autos to Caribbean vacations. However lenders had been making loans that required no down payment that had “teaser” rates programmed to rise sharply after a year or two and that were made to borrowers whose credit had not been carefully checked. These relaxed lending standards enabled people who could not have bought homes in the past to buy a home now but the loans were getting riskier and about 30 were classified as “subprime.” The risk buildup was obscured by fancy “financial engineering.” A few years ago people obtained mortgage loans primarily from local banks. The banks kept the mortgages collected the interest and likely knew how risky the loans were. In recent years the situation has changed. Now mortgage brokers originate for example 500 loans for 200000 each or 100 million in total and then sell them to an investment bank. The bank uses the loans as collateral for 100 million of bonds which are divided into classes such as A B and C. The A bonds have first claim on cash from the mortgages and are rated AAA the Bs are next which are also highly rated and even the Cs are rated “investment grade.” Initially times were good the interest and repayment of principal from the mortgages were sufficient to cover required payments to all of the bonds. However recently some of the mortgages began going into default and ª HIROKO MASUIKE/GETTY IMAGES 26

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PUTTING THINGS IN PERSPECTIVE In Chapter 1 we saw that a firm’s primary goal is to maximize the price of its stock. Stock prices are determined in the financialmarkets so iffinancial managers are to make good decisions they must understand how these markets operate. In addi- tion individuals make personal investment decisions so they too need to know something about financial markets and the institutions that operate in those markets. Thereforein thischapter we describe the markets where capital israised securities are traded and stock prices are established and the institutions that operate in these markets. When you finish this chapter you should be able to: l Identify the different types of financial markets and financial institutions and explain how these markets and institutions enhance capital allocation. l Explain how the stock market operates and list the distinctions between the different types of stock markets. l Explain how the stock market has performed in recent years. l Discuss the importance of market efficiency and explain why some markets are more efficient than others. inflows were no longer sufficient to cover required pay- ments to all of the bonds. When home prices are rising borrowers’ equity also rises. That enables borrowers who cannot keep up with their payments to refinance—or sell the house for enough to pay off the mortgage. But when home prices start falling refinancings and profitable sales are impossible. That trig- gers mortgage defaults which in turn triggers defaults on the riskiest bonds. People become worried about the B and even the A bonds so their values also fall. The banks and other institutions that own the bonds are forced to write them down on their balance sheets. Institutions that hold mortgage-backed bonds—many of which are subsidiaries of banks—raised the money to buy the bonds by borrowing on a 3-month basis from money market funds of similar lenders. As risks became more apparent the short-term lenders refused to roll over these loans thus the bondholders were forced to sell bonds to repay their short-term loans. Those sales depressed the bond market even further causing further bond sales lower bond prices and more write-downs. A downward spiral and a severe credit crunch began. Banks across the globe had invested in these bonds and huge losses were reported by Citigroup Deutsche Bank Germany’s largest and UBS Switzerland’s largest. These losses reduced banks’ willingness and ability to make new loans which threatened economies in many nations. The Federal Reserve and other central banks lowered interest rates and eased the terms under which they extended credit to banks and the banks themselves joined forces to head off a downward spiral. The headline in The Wall Street Journal on October 13 2007 read as follows: “Big Banks Push 100 Bil- lion Plan to Avert Credit Crunch.” The article described how governmentofficials are working withbankersto headoffan impending crisis. However working things out will be diffi- cult. Manythinkthat thebanks whose actionscontributedto the problems—especially Citigroup—should not be bailed out. Others think that the crisis must be averted because the U.S.economyandothereconomieswillbebadlydamagedif the downward spiral continues. All of this demonstrates the extent to which markets are interconnected the impact markets can have on countries and on individual companies and the complexity of capital markets. Source: Carrick Mollenkamp Ian McDonald and Deborah Solomon “Big Banks Push 100 Billion Plan to Avert Crunch: Fund Seeks to Prevent Mortgage-Debt Selloff Advice from Treasury” The Wall Street Journal October 13 2007 p. A1. Chapter 2 Financial Markets and Institutions 27

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2-1 THE CAPITAL ALLOCATION PROCESS Businessesindividualsandgovernmentsoftenneedtoraisecapital.Forexample CarolinaPowerLight CPL forecasts anincreaseinthe demandforelectricity in North and South Carolina so it will build a new power plant to meet those needs. Because CPL’s bank account does not contain the 1 billion necessary to pay for the plant the company must raise this capital in the financial markets. Similarly Mr. Fong the proprietor of a San Francisco hardware store wants to expand into appliances. Where will he get the money to buy the initial inventory of TV sets washers and freezers Or suppose the Johnson family wants to buy a home that costs 200000 but they have only 50000 in savings. Where will they get the additional 150000 The city of New York needs 200 million to build a newsewer plant.Where canitobtainthismoney Finally thefederal government needs more money than it receives from taxes. Where will the extra money come from Ontheotherhandsomeindividualsandfirmshaveincomesthatexceedtheir current expenditures in which case they have funds available to invest. For exampleCarolHawkhasanincomeof36000butherexpensesareonly30000. That leaves her with 6000 to invest. Similarly Microsoft has accumulated roughly 23.5 billion of cash. What can Microsoft do with this money until it is needed in the business People and organizations with surplus funds are saving today in order to accumulatefundsforsomefutureuse.Membersofahouseholdmightsavetopay for their children’s education and the parents’ retirement while a business might save to fund future investments. Those with surplus funds expect to earn a return ontheirinvestmentswhilepeopleandorganizationsthatneedcapitalunderstand that they must pay interest to those who provide that capital. In a well-functioning economy capital flows efficiently from those with sur- plus capital to those who need it. This transfer can take place in the three ways described in Figure 2-1. 1. Direct transfers of money and securities as shown in the top section occur when a business sells its stocks or bonds directly to savers without going Diagram of the Capital Formation Process FIGURE 2-1 Business Business Business 1. Direct Transfers 2. Indirect Transfers through Investment Bankers 3. Indirect Transfers through a Financial Intermediary Savers Savers Savers Financial Intermediary Investment Banks Securities Stocks or Bonds Dollars Securities Dollars Securities Dollars Intermediary’s Securities Dollars Business’ Securities Dollars 28 Part 2 Fundamental Concepts in Financial Management

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through any type of financial institution. The business delivers its securities to savers who in turn give the firm the money it needs. This procedure is used mainly by small firms and relatively little capital is raised by direct transfers. 2. As shown in the middle section transfers may also go through an investment bank iBank such as Citigroup which underwrites the issue. An underwriter serves as a middleman and facilitates the issuance of securities. The company sells its stocks or bonds to the investment bank which then sells these same securities to savers. The businesses’ securities and the savers’ money merely “pass through” the investment bank. However because the investment bank buys and holds the securities for a period of time it is taking a risk—it may notbeabletoresellthesecuritiestosaversforasmuchasitpaid.Becausenew securities are involved and the corporation receives the proceeds of the sale this transaction is called a primary market transaction. 3. Transfers can also be made through a financial intermediary such as a bank an insurance company or a mutual fund. Here the intermediary obtains funds fromsaversinexchangeforitssecurities.Theintermediaryusesthismoneyto buy and hold businesses’ securities while the savers hold the intermediary’s securities. For example a saver deposits dollars in a bank receiving a certif- icate of deposit then the bank lends the money to a business in the form of a mortgage loan. Thus intermediaries literally create new forms of capital—in this case certificates of deposit which are safer and more liquid than mort- gages and thus are better for most savers to hold. The existence of inter- mediaries greatly increases the efficiency of money and capital markets. Oftentheentityneedingcapitalisabusinessandspecificallyacorporationbutit is easy to visualize the demander of capital being a home purchaser a small business or a government unit. For example if your uncle lends you money to help you fund a new business a direct transfer of funds will occur. Alternatively if you borrow money to purchase a home you will probably raise the funds through a financial intermediary such as your local commercial bank or mortgage banker. That banker could sell your mortgage to an investment bank which then might use it as collateral for a bond that is bought by a pension fund. In a global context economic development is highly correlated with the level and efficiency of financial markets and institutions. 1 It is difficult if not impos- sible for an economy to reach its full potential if it doesn’t have access to a well- functioning financial system. In a well-developed economy like that of the United States an extensive set of markets and institutions has evolved over time to facilitate the efficient allocation of capital. To raise capital efficiently managers must understand how these markets and institutions work and individuals need to know how the markets and institutions work to get high rates of returns on their savings. SELFTEST Name three ways capital is transferred between savers and borrowers. Why are efficient capital markets necessary for economic growth 1 For a detailed review of the evidence linking financial development to economic growth see Ross Levine “Finance and Growth: Theory and Evidence” NBER Working Paper No. 10766 September 2004. Chapter 2 Financial Markets and Institutions 29

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2-2 FINANCIAL MARKETS People and organizations wanting to borrow money are brought together with those who have surplus funds in the financial markets. Note that markets is plural therearemanydifferent financial marketsinadevelopedeconomy suchasthatof the United States. We describe some of these markets and some trends in their development. 2-2a Types of Markets Different financial markets serve different types of customers or different parts of the country. Financial markets also vary depending on the maturity of the securitiesbeingtradedandthetypesofassetsusedtobackthesecurities.Forthese reasons it is useful to classify markets along the following dimensions: 1. Physical asset markets versus financial asset markets. Physical asset markets also called “tangible” or “real” asset markets are for products such as wheat autos real estate computers and machinery. Financial asset markets on the other hand deal with stocks bonds notes and mortgages. Financial markets alsodealwithderivativesecuritieswhosevaluesarederivedfromchangesinthe prices of other assets. A share of Ford stock is a “pure financial asset” while an option to buy Ford shares is a derivative security whose value depends on the price of Ford stock. The bonds backed by subprime mortgages discussed atthebeginningofthischapterareanothertypeofderivativeasthevaluesof these bonds are derived from the values of the underlying mortgages. 2. Spot markets versus futures markets. Spot markets are markets in which assets are bought or sold for “on-the-spot” delivery literally within a few days. Futures markets are markets in which participants agree today to buy or sell an asset at some future date. For example a farmer may enter into a futures contract in which he agrees today to sell 5000 bushels of soybeans 6 months fromnowatapriceof5abushel.Tocontinuethatexampleafoodprocessor that needs soybeans in the future may enter into a futures contract in which it agrees to buy soybeans 6 months from now. Such a transaction can reduce or hedge the risks faced by both the farmer and the food processor. 3. Moneymarketsversuscapitalmarkets.Moneymarketsarethemarketsforshort- termhighlyliquiddebtsecurities.TheNewYorkLondonandTokyomoney markets are among the world’s largest. Capital markets are the markets for intermediate- or long-term debt and corporate stocks. The New York Stock Exchange where the stocks of the largest U.S. corporations are traded is a prime example of a capital market. There is no hard-and-fast rule but in a description of debt markets short-term generally means less than 1 year intermediate-term means 1 to 10 years and long-term means more than 10 years. 4. Primary markets versus secondary markets. Primary markets are the markets in which corporations raise new capital. If GE were to sell a new issue of com- monstocktoraisecapitalaprimarymarkettransactionwouldtakeplace.The corporation selling the newly created stock GE receives the proceeds from the sale in a primary market transaction. Secondary markets are markets in which existing already outstanding securities are traded among investors. ThusifJaneDoedecidedtobuy1000sharesofGEstockthepurchasewould occur in the secondary market. The New York Stock Exchange is a secondary market because it deals in outstanding as opposed to newly issued stocks and bonds. Secondary markets also exist for mortgages other types of loans andotherfinancialassets.Thecorporationwhosesecuritiesarebeingtradedis not involved in a secondary market transaction and thus does not receive funds from such a sale. Spot Markets The markets in which assets are bought or sold for “on-the-spot” delivery. Futures Markets The markets in which participants agree today to buy or sell an asset at some future date. Money Markets The financial markets in which funds are borrowed or loaned for short periods less than one year. Capital Markets The financial markets for stocksandforintermediate- or long-term debt one year or longer. Primary Markets Markets in which corpo- rations raise capital by issuing new securities. Secondary Markets Markets in which securities and other financial assets are traded among invest- ors after they have been issued by corporations. 30 Part 2 Fundamental Concepts in Financial Management

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5. Private markets versus public markets. Private markets where transactions are negotiated directly between two parties are differentiated from public markets where standardized contracts are traded on organized exchanges. Bank loans and private debt placements with insurance companies are examples of private market transactions. Because these transactions are pri- vatetheymaybestructuredinanymannertowhichthetwopartiesagree.By contrast securities that are traded in public markets for example common stock and corporate bonds are held by a large number of individuals. These securities must have fairly standardized contractual features because public investors do not generally have the time and expertise to negotiate unique nonstandardized contracts. Broad ownership and standardization result in publicly traded securities being more liquid than tailor-made uniquely negotiated securities. Other classifications could be made but this breakdown shows that there are many types of financial markets. Also note that the distinctions among markets are often blurred and unimportant except as a general point of reference. For exampleitmakeslittledifferenceifafirmborrowsfor1112or13monthsthatis whether the transaction is a “money” or “capital” market transaction. You should beawareoftheimportantdifferencesamongtypesofmarketsbutdon’tbeoverly concerned about trying to distinguish them at the boundaries. Ahealthyeconomyisdependentonefficientfundstransfersfrompeoplewho are net savers to firms and individuals who need capital. Without efficient transfers theeconomycouldnotfunction:CarolinaPowerLightcouldnotraise capital so Raleigh’s citizens would have no electricity the Johnson family would not have adequate housing Carol Hawk would have no place to invest her sav- ings and so forth. Obviously the level of employment and productivity i.e. the standard of living would be much lower. Therefore it is essential that financial markets function efficiently—not only quickly but also inexpensively. 2 Table 2-1 is a listing of the most important instruments traded in the various financial markets. The instruments are arranged in ascending order of typical length of maturity. As we go through this book we will look in more detail at manyoftheinstrumentslistedinTable2-1.Forexamplewewillseethatthereare many varieties of corporate bonds ranging from “plain vanilla” bonds to bonds that can be converted to common stocks to bonds whose interest payments vary depending on the inflation rate. Still the table provides an overview of the characteristics and costs of the instruments traded in the major financial markets. 2-2b Recent Trends Financial markets have experienced many changes in recent years. Technological advances in computers and telecommunications along with the globalization of banking and commerce have led to deregulation which has increased competi- tion throughout the world. As a result there are more efficient internationally linked markets which are far more complex than what existed a few years ago. While these developments have been largely positive they have also created problems for policy makers. At one conference former Federal Reserve Board Chairperson Alan Greenspan stated that modern financial markets “expose national economies to shocks from new and unexpected sources and with little if anylag.”Hewentontosaythatcentralbanksmustdevelopnewwaystoevaluate and limit risks to the financial system. Large amounts of capital move quickly Private Markets Markets in which trans- actions are worked out directly between two parties. Public Markets Markets in which stand- ardized contracts are traded on organized exchanges. 2 As the countries of the former Soviet Union and other Eastern European nations move toward capitalism as much attention must be paid to the establishment of cost-efficient financial markets as to electrical power transportation communications and other infrastructure systems. Economic efficiency is impossible without a good system for allocating capital within the economy. Chapter 2 Financial Markets and Institutions 31

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Summary of Major Market Instruments Market Participants and Security Characteristics Table 2-1 SECURITY CHARACTERISTICS Instrument 1 Market 2 Major Participants 3 Riskiness 4 Original Maturity 5 Interest Rate on 2/5/08 a 6 U.S. Treasury bills Money Sold by U.S. Treasury to finance federal expenditures Default-free close to riskless 91 days to 1 year 2.23 Bankers’ acceptances Money A firm’s note but one guaranteed by a bank Low degree of risk if guaranteed by a strong bank Up to 180 days 3.11 Dealer commercial paper Money Issuedbyfinanciallysecurefirmstolarge investors Low default risk Up to 270 days 3.05 Negotiable certificates of deposit CDs Money Issued by major money-center commercial banks to large investors Default risk depends on the strength of the issuing bank Up to 1 year 3.10 Money market mutual funds Money Invest in Treasury bills CDs and commercial paper held by individuals and businesses Low degree of risk No specific maturity instant liquidity 2.84 Eurodollar market time deposits Money Issued by banks outside the United States Default risk depends on the strength of the issuing bank Up to 1 year 3.10 Consumer credit includ- ing credit card debt Money Issued by banks credit unions and finance companies to individuals Risk is variable Variable Variable but goes up to 20 or more U.S. Treasury notes and bonds Capital Issued by U.S. government No default risk but price will decline if interest rates rise hence there is some risk 2 to 30 years 1.919 on 2-year to 4.327 on 30-year bonds Mortgages Capital Loans to individuals and businesses secured by real estate bought by banks and other institutions Risk is variable risk is high in the case of subprime loans Up to 30 years 5.14 adjustable 5-year rate 5.62 30-year fixed rate State and local government bonds Capital Issued by state and local governments held by individuals and institutional investors Riskier than U.S. government securities but exempt from most taxes Up to 30 years 4.63 to 5.03 for A-rated 20- to 40-year bonds Corporate bonds Capital Issued by corporations held by individuals and institutional investors Riskier than U.S. government securities but less risky than preferred and common stocks varying degree of risk within bonds depends on strength of issuer Up to 40 years b 5.38 on AAA bonds 6.63 on BBB bonds Leases Capital Similar to debt in that firms can lease assets ratherthanborrowandthenbuytheassets Risk similar to corporate bonds Generally 3 to 20 years Similar to bond yields Preferred stocks Capital Issued by corporations to individuals and institutional investors Generally riskier than corporate bonds but less risky than common stock Unlimited 5.5 to 9 Common stocks c Capital Issued by corporations to individuals and institutional investors Riskier than bonds and preferred stock risk varies from company to company Unlimited NA a The yields reported are from the web site of The Wall Street Journal on February 5 2008 Money market rates assume a 3-month maturity. b A few corporations have issued 100-year bonds however the majority have issued bonds with maturities that are less than 40 years. c Whilecommonstocksdonotpayinteresttheyareexpectedtoprovidea “return”intheformofdividendsandcapitalgains.AsyouwillseeinChapter8historicallystockreturnshaveaveragedbetween 9 and 12 a year but they can be much higher or lower in a given year. Of course if you purchase a stock your actual return may be considerably higher or lower than these historical averages. 32 Part 2 Fundamental Concepts in Financial Management

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around the world inresponse to changes in interest and exchange ratesand these movements can disrupt local institutions and economies. The subprime mortgage crisis discussed in the opening chapter vignette illustrates how problems in one country quickly affect the economies of other nations. Globalization has exposed the need for greater cooperation among regulators at the international level but the task is not easy. Factors that complicate coor- dination include 1 the different structures in nations’ banking and securities industries 2 the trend toward financial services conglomerates which obscures developments in various market segments and 3 the reluctance of individual countries to give up control over their national monetary policies. Still regulators are unanimous about the need to close the gaps in the supervision of worldwide markets. Another important trend in recent years has been the increased use of derivatives. A derivative is any security whose value is derived from the price of some other “underlying” asset. An option to buy IBM stock is a derivative as is a contract to buy Japanese yen 6 months from now or a bond backed by subprime mortgages. The value of the IBM option depends on the price of IBM’s stock the valueoftheJapaneseyen “future”dependsontheexchangeratebetweenyenand dollars and the value of the bond depends on the value of the underlying mortgages. The market for derivatives has grown faster than any other market in recent years providing investors with new opportunities but also exposing them to new risks. Derivatives can be used to reduce risks or to speculate. Suppose a wheat processor’s costs rise and its net income falls when the price of wheat rises. The processor could reduce its risk by purchasing derivatives—wheat futures—whose value increases when the price of wheat rises. This is a hedging operation and its purpose is to reduce risk exposure. Speculation on the other hand is done in the hope of high returns but it raises risk exposure. For example several years ago Procter Gamble disclosed that it lost 150 million on derivative investments. More recently losses on mortgage-related derivatives helped contribute to the credit collapse in 2008. Thevaluesofmostderivativesaresubjecttomorevolatilitythanthevaluesof the underlying assets. For example someone might pay 500 for an option to buy 100 shares of IBM stock at 120 per share when the stock is selling for 120. If the stock rose by 5 per share a gain of 4.17 would result. However the options would be worth somewhere between 25 and 30 so the percentage gain would be between 400 and 500. 3 Of course if IBM stayed at 120 or fell the options wouldbeworthlessandtheoptionpurchaserwouldhavea100loss.Manyother derivatives have similar characteristics and are equally as risky or even more risky. If a bank or any other company reports that it invests in derivatives how can onetell if the derivatives areheld asahedge againstsomething like an increase in thepriceofwheatorasaspeculativebetthatwheatpriceswillriseTheansweris that it is very difficult to tell how derivatives are affecting the risk profile of the firm. In the case of financial institutions things are even more complicated—the derivatives are generally based on changes in interest rates foreign exchange rates or stock prices anda large international bank might have tens of thousands of separate derivative contracts. The size and complexity of these transactions concern regulators academics and members of Congress. Former Fed Chair- person Greenspan noted that in theory derivatives should allow companies to better manage risk but that it is not clear whether recent innovations have “increased or decreased the inherent stability of the financial system.” Derivative Any financial asset whose value is derived from the value of some other “underlying” asset. 3 For a discussion on options and option pricing refer to Chapter 18 in this text. Chapter 2 Financial Markets and Institutions 33

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SELFTEST Distinguish between physical asset markets and financial asset markets. What’s the difference between spot markets and futures markets Distinguish between money markets and capital markets. What’s the difference between primary markets and secondary markets Differentiate between private and public markets. Why are financial markets essential for a healthy economy and economic growth 2-3 FINANCIAL INSTITUTIONS Directfundstransfersarecommonamongindividualsandsmallbusinessesandin economies where financial markets and institutions are less developed. But large businesses in developed economies generally find it more efficient to enlist the services of a financial institution when it comes time to raise capital. In the United States and other developed nations a set of highly efficient financial intermediaries has evolved. Their original roles were generally quite specific and regulation prevented them from diversifying. However in recent years regulations against diversification have been largely removed and today the differences between institutions have become blurred. Still there remains a degree of institutional identity. Therefore it is useful to describe the major cate- gories of financial institutions here. Keep in mind though that one company can ownanumberofsubsidiariesthatengageinthedifferentfunctionsdescribednext. 1. Investment banks traditionally help companies raise capital. They a help corporations design securities with features that are currently attractive to investors b buy these securities from the corporation and c resell them to savers.Sincethe investmentbank generally guaranteesthat the firm will raise the needed capital the investment bankers are also called underwriters. The recent credit crisis has had a dramatic effect on the investment banking industry. Bear Stearns collapsed and was later acquired by J.P. Morgan Lehman Brothers went bankrupt and Merrill Lynch was forced to sell out to Bank of America. Moreover the two “surviving” major investment banks Morgan Stanley and Goldman Sachs received Federal Reserve approval to become commercial bank holding companies. Their future remains uncertain. 2. CommercialbankssuchasBankofAmericaCitibankWellsFargoWachovia andJPMorganChasearethetraditional“departmentstoresoffinance”because they serve a variety of savers and borrowers. Historically commercial banks were the major institutions that handled checking accounts and through which the Federal Reserve System expanded or contracted the money supply. Today however several other institutions also provide checking services and sig- nificantly influence the money supply. Note too that the larger banks are generally part of financial services corporations as described next. 4 3. Financial services corporations are large conglomerates that combine many different financial institutions within a single corporation. Most financial serv- ices corporations started in one area but have now diversified to cover most of the financial spectrum. For example Citigroup owns Citibank a commercial bank Smith Barney an investment bank and securities brokerage organiza- tion insurance companies and leasing companies. Investment Bank An organization that underwrites and distrib- utes new investment securities and helps busi- nesses obtain financing. Commercial Bank The traditional depart- ment store of finance serving a variety of savers and borrowers. 4 Two other institutions that were important a few years ago were savings and loan associations and mutual savings banks. Most of these organizations have now been merged into commercial banks. Financial Services Corporation A firm that offers a wide range of financial services including investment banking brokerage oper- ations insurance and commercial banking. 34 Part 2 Fundamental Concepts in Financial Management

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4. Credit unions are cooperative associations whose members are supposed to have a common bond such as being employees of the same firm. Members’ savingsareloanedonlytoothermembersgenerallyforautopurchaseshome improvement loans and home mortgages. Credit unions are often the cheapest source of funds available to individual borrowers. 5. Pension funds are retirement plans funded by corporations or government agencies for their workers and administered primarily by the trust depart- ments of commercial banks or by life insurance companies. Pension funds invest primarily in bonds stocks mortgages and real estate. 6. Life insurance companies take savings in the form of annual premiums invest these funds in stocks bonds real estate and mortgages and make payments to the beneficiaries of the insured parties. In recent years life insurance companies have also offered a variety of tax-deferred savings plans designed to provide benefits to participants when they retire. 7. Mutual funds are corporations that accept money from savers and then use these funds to buy stocks long-term bonds or short-term debt instruments issuedbybusinessesorgovernmentunits.Theseorganizationspoolfundsand thus reduce risks by diversification. They also achieve economies of scale in analyzing securities managing portfolios and buying and selling securities. Differentfundsaredesignedtomeettheobjectivesofdifferenttypesofsavers. Hencetherearebondfundsforthosewhoprefersafetystockfundsforsavers who are willing to accept significant risks in the hope of higher returns and still other funds that are used as interest-bearing checking accounts money market funds. There are literally thousands of different mutual funds with dozens of different goals and purposes. Mutual funds have grown more rapidly than most other institutions in recentyearsinlargepartbecauseofachangeinthewaycorporationsprovide for employees’ retirement. Before the 1980s most corporations said in effect “Come work for us and when you retire we will give you a retirement income based on the salary you were earning during the last five years before you retired.” The company was then responsible for setting aside funds each year to make sure it had the money available to pay the agreed-upon retire- ment benefits. That situation is changing rapidly. Today new employees are likely to be told “Come work for us and we will give you some money each payday that you can invest for your future retirement. You can’t get the money until you retire without paying a huge tax penalty but if you invest wisely you can retire in comfort.” Most workers recognize that they don’t know how to invest wisely so they turn their retirement funds over to a mutualfund.Hencemutualfundsaregrowingrapidly.Excellentinformation on the objectives and past performances of the various funds are provided in publications such as Value Line Investment Survey and Morningstar Mutual Funds which are available in most libraries and on the Internet. 8. Exchange Traded Funds ETFs are similar to regular mutual funds and are often operated by mutual fund companies. ETFs buy a portfolio of stocks of a certain type—for example the SP 500 or media companies or Chinese companies—and then sell their own shares to the public. ETF shares are generally traded in the public markets so an investor who wants to invest in theChinesemarketforexamplecanbuysharesinanETFthatholdsstocksin that particular market. 9. Hedge funds are also similar to mutual funds because they accept money from savers and use the funds to buy various securities but there are some important differences. While mutual funds and ETFs are registered and regulatedbythe SecuritiesandExchangeCommission SEC hedge fundsare largely unregulated. This difference in regulation stems from the fact that Mutual Funds Organizations that pool investor funds to purchase financial instruments and thus reduce risks through diversification. Money Market Funds Mutual funds that invest in short-term low-risk securities and allow investors to write checks against their accounts. Chapter 2 Financial Markets and Institutions 35

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mutual funds typically target small investors whereas hedge funds typically have large minimum investments often exceeding 1 million and are mar- keted primarily to institutions and individuals with high net worths. Hedge funds received their name because they traditionally were used when an individualwastryingtohedgerisks.Forexampleahedgefundmanagerwho believes that interest rate differentials between corporate and Treasury bonds aretoolargemightsimultaneouslybuyaportfolioofcorporatebondsandsell a portfolio of Treasury bonds. In this case the portfolio would be “hedged” against overall movements in interest rates but it would perform especially well if the spread between these securities were to narrow. However some hedge funds take on risks that are considerably higher thanthatofanaverageindividualstockormutualfund.Forexamplein1998 Long-Term Capital Management LTCM a high-profile hedge fund whose managers included several well-respected practitioners as well as two Nobel Prize–winning professorswho were experts in investment theory made some incorrect assumptions and “blew up.” 5 LTCM had many billions of dollars under management and it owed large amounts of money to a number of banks.To avertaworldwide crisis the Federal Reserve orchestrateda buyout of the firm by a group of New York banks. As hedge fundshave become morepopular many ofthem have begun to lower their minimum investment requirements. Perhaps not surprisingly theirrapidgrowthandshifttowardsmallerinvestorshavealsoledtoacallfor more regulation. 10. Private equity companies are organizations that operate much like hedge funds but rather than buying some of the stock of a firm private equity players buy and then manage entire firms. Most of the money used to buy the target companies is borrowed. Recent examples include Cerberus Capital’s buyout of Chrysler and private equity company JC Flowers’ proposed 25 billion purchase of Sallie Mae the largest student loan company. The Sallie Mae deal is in jeopardy—Flowers planned to borrow most of the money for the pur- chase but the subprime situation has made borrowing more difficult and expensive. Flowers tried to back out of the deal but Sallie Mae executives insisted that it complete the transaction or pay a 900 million “breakup fee.” With the exception of hedge funds and private equity companies financial insti- tutions are regulated to ensure the safety of these institutions and to protect investors. Historically many of these regulations—which have included a prohi- bition on nationwide branch banking restrictions on the types of assets the institutionscouldbuyceilingsontheinterestratestheycouldpayandlimitations on the types of services they could provide—tended to impede the free flow of capital and thus hurt the efficiency of the capital markets. Recognizing this fact policy makers took several steps during the 1980s and 1990s to deregulate financial services companies. For example the restriction barring nationwide branching by banks was eliminated in 1999. Panel A of Table 2-2 lists the 10 largest U.S. bank holding companies while PanelBshowstheleadingworldbankingcompanies.Amongtheworld’s10largest onlytwoCitigroupandBankofAmericaarebasedintheUnitedStates.WhileU.S. banks have grown dramatically as a result of recent mergers they are still small by global standards. Panel C of the table lists the 10 leading underwriters in terms of dollar volume of new debt and equity issues. Six of the top underwriters are also major commercialbanks or are part of bank holding companies whichconfirms the continued blurring of distinctions between different types of financial institutions. 5 See Franklin Edwards “Hedge Funds and the Collapse of Long-Term Capital Management” Journal of Economic Perspectives Vol. 13 no. 2 Spring 1999 pp. 189–210 for a thoughtful review of the implications of Long-Term Capital Management’s collapse. 36 Part 2 Fundamental Concepts in Financial Management

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Largest Banks and Underwriters Table 2-2 Panel A U.S. Bank Holding Companies a Panel B World Banking Companies b Panel C Leading Global Underwriters c Citigroup Inc. UBS AG Zurich Citigroup Inc. Bank of America Corp. Barclays PLC London JPMorgan JPMorgan Chase Co. BNP Paribas Paris Deutsche Bank AG Wachovia Corp. Citigroup Inc. New York Merrill Lynch Taunus Corp. HSBC Holdings PLC London Morgan Stanley Wells Fargo Co. Royal Bank of Scotland Group PLC Edinburgh Lehman Brothers HSBC North America Holdings Inc. Credit Agricole Paris Goldman Sachs U.S. Bancorp Mitsubishi UFJ Financial Group Tokyo Barclays Capital Bank of New York The Mellon Corp. Deutsche Bank AG Frankfurt UBS AG SunTrust Banks Inc. Bank of America Corp. Charlotte Credit Suisse Notes: a Ranked by total assets as of December 31 2007. Source: National Information Center b Ranked by total assets as of December 31 2007. Source: Thomson One Banker. c Rankedbydollaramountraisedthroughnewissuesstocksandbondsin2007.Forthisrankingtheleadunderwritermanagerisgivencreditfor the entire issue. Source: Adapted from The Wall Street Journal January 2 2008 p. R18. CITIGROUP BUILT TO COMPETE IN A CHANGING ENVIRONMENT The financial environment has been undergoing tremen- dous changes including breakthroughs in technology increased globalization and shifts in the regulatory envi- ronment. All of these factors have presented financial managers and investors with opportunities but those opportunities are accompanied by substantial risks. Consider the case of Citigroup Inc. which was created in 1998 when Citicorp and Travelers Group which included the investment firm Salomon Smith Barney merged. Citi- group today operates in more than 100 countries has roughly 200 million customers and 275000 employees and holds more than 2.2 trillion that’s over two thousand bil- lion worth of assets. Citigroup resulted from three important trends: 1. Regulatory changes made it possible for U.S. corpo- rations to engage in commercial banking investment banking insurance and other activities. 2. Increased globalization made it essential for financial institutions to follow their clients and thus operate in many countries. 3. Changing technology led to increased economies of scale and scope both of which increased the relative efficiency of huge diversified companies such as Citigroup. Citigroup has grown and it is now the largest financial institution in the world. But as the chapter opening vignette indicated Citigroup has been hit hard by the mortgage debacle and its chairperson Charles Prince recently lost his job. When you read this you might access the Internet to findtheextenttowhichCitigrouphasbeenabletorebound from its recent difficulties. Chapter 2 Financial Markets and Institutions 37

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SELFTEST What’s the difference between a commercialbank and an investment bank List the major types of financial institutions and briefly describe the primary function of each. What are some important differences between mutual funds Exchange Traded Funds and hedge funds How are they similar 2-4 THE STOCK MARKET As noted earlier outstanding previously issued securities are traded in the sec- ondary markets. By far the most active secondary market—and the most importantonetofinancialmanagers—isthestockmarketwherethepricesoffirms’ stocks are established. Because the primary goal of financial managers is to maximize their firms’ stock prices knowledge of the stock market is important to anyone involved in managing a business. There are a number of different stock markets. The two leaders are the New York Stock Exchange NYSE and the Nasdaq stock market. Stocks are traded usingavarietyofmarketproceduresbuttherearejusttwobasictypes:1physical location exchanges which include the NYSE the American Stock Exchange AMEX and several regional stock exchanges and 2 electronic dealer-based markets which include the Nasdaq the less formal over-the-counter market and the recently developed electronic communications networks ECNs. See the box entitled “The NYSE and Nasdaq Go Global.” Because the physical location exchanges are easier to describe and understand we discuss them first. GLOBAL PERSPECTIVES THE NYSE AND NASDAQ GO GLOBAL Advances in computers and telecommunications that spurred consolidation in the financial services industry have also promoted online trading systems that bypass the tra- ditional exchanges. These systems which are known as electronic communications networks ECNs use electronic technology to bring buyers and sellers together. The rise of ECNs accelerated the move toward 24-hour trading. U.S. investors who wanted to trade after the U.S. markets closed could utilize an ECN thus bypassing the NYSE and Nasdaq. RecognizingthenewthreattheNYSEandNasdaqtook action. First both exchanges went public which enabled them to use their stock as “currency” that could be used to buy ECNs and other exchanges across the globe. For example Nasdaq acquired the American Stock Exchange AMEX several ECNs and 25 of the London Stock Exchange and it is actively seeking to merge with other exchanges around the world. The NYSE has taken similar actions including a merger with the largest European exchange Euronext to form NYSE Euronext. These actions illustrate the growing importance of global trading especially electronic trading. Indeed many pundits have concluded that the floor traders who buy and sell stocks on the NYSE and other physical exchanges will soon become a thing of the past. That may or may not be true but it is clear that stock trading will continue to undergo dramatic changes in the upcoming years. To find a wealth of up-to-date information on the NYSE and Nasdaq go to Google or another search engine and do NYSE history and Nasdaq history searches. 38 Part 2 Fundamental Concepts in Financial Management

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2-4a Physical Location Stock Exchanges Physicallocationexchangesare tangible entities. Each ofthe larger ones occupies its own building allows a limited number of people to trade on its floor and has an elected governing body—its board of governors. Members of the NYSE for- merlyhad “seats”ontheexchangealthougheverybodystoodup.Todaytheseats have been exchanged for trading licenses which are auctioned to member organizations and cost about 50000 per year. Most of the larger investment banks operate brokerage departments. They purchase seats on the exchanges and designate one or more of their officers as members. The exchanges are open on all normal working days with the members meeting in a large room equipped with telephones and other electronic equipment that enable each member to commu- nicate with his or her firm’s offices throughout the country. Like other markets security exchanges facilitate communication between buyers and sellers. For example Merrill Lynch the fourth largest brokerage firm might receive an order in its Atlanta office from a customer who wants to buy shares of GE stock. Simultaneously the Denver office of Morgan Stanley the fifth largest brokerage firm might receive an order from a customer wanting to sell shares of GE. Each broker communicates electronically with the firm’s represen- tativeontheNYSE.Otherbrokersthroughoutthecountryarealsocommunicating with their own exchange members. The exchange members with sell orders offer the shares for sale and they are bid for by the members with buy orders. Thus the exchanges operate as auction markets. 6 2-4b Over-the-Counter OTC and the Nasdaq Stock Markets While the stocks of most large companies trade on the NYSE a larger number of stocks trade off the exchange in what was traditionally referred to as the over- the-counter OTC market. An explanation of the term over-the-counter will help clarify how this term arose. As noted earlier the exchanges operate as auction markets—buy and sell orders come in more or less simultaneously and exchange members match these orders. When a stock is traded infrequently perhaps because the firm is new or small few buy and sell orders come in and matching them within a reasonable amountof time is difficult. To avoid this problem some brokeragefirmsmaintainaninventoryofsuchstocksandstandpreparedtomake a market for them. These “dealers” buy when individual investors want to sell and they sell part of their inventory when investors want to buy. At one time the inventory of securities was kept in a safe and the stocks when bought and sold were literally passed over the counter. Physical Location Exchanges Formal organizations having tangible physical locations that conduct auction markets in designated “listed” securities. 6 The NYSE is actually a modified auction market wherein people through their brokers bid for stocks. Originally —in 1792—brokers would literally shout “I have 100 shares of Erie for sale how much am I offered” and then sell to the highest bidder. If a broker had a buy order he or she would shout “I want to buy 100 shares of Erie who’ll sell at the best price” The same general situation still exists although the exchanges now have members known as specialists who facilitate the trading process by keeping an inventory of shares of the stocks in which they specialize. If a buy order comes in at a time when no sell order arrives the specialist will sell off some inventory. Similarly if a sell order comes in the specialist will buy and add to inventory. The specialist sets a bid price the price the specialist will pay for the stock and an ask price the price at which shares will be sold out of inventory. The bid and ask prices are set at levels designed to keep the inventory in balance. If many buy orders start coming in because of favorable developments or many sell orders come in because of unfavorable events the specialist will raise or lower prices to keep supply and demand in balance. Bid prices are somewhat lower than ask prices with the difference or spread representing the specialist’s profit margin. Special facilities are available to help institutional investors such as mutual or pension funds sell large blocks of stock without depressing their prices. In essence brokerage houses that cater to institutional clients will purchase blocksdefined as10000ormoreshares andthenresellthe stocktootherinstitutionsor individuals. Alsowhena firm has a major announcement that is likely to cause its stock price to change sharply it will ask the exchange to halt trading in its stock until the announcement has been made and the resulting information has been digested by investors. Over-the-Counter OTC Market A large collection of brok- ers and dealers connected electronically by tele- phones and computers that provides for trading in unlisted securities. Chapter 2 Financial Markets and Institutions 39

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Today these markets are often referred to as dealer markets. A dealer market includes all facilities that are needed to conduct security transactions but the transactions are not made on the physical location exchanges. The dealer market system consists of 1 the relatively few dealers who hold inventories of these securities and who are said to “make a market” in these securities 2 the thou- sands of brokers who act as agents in bringing the dealers together with investors and 3 the computers terminals and electronic networks that provide a com- municationlinkbetweendealersandbrokers.Thedealerswhomakeamarketina particular stock quote the price at which they will pay for the stock the bid price and the price at which they will sell shares the ask price. Each dealer’s prices which are adjusted as supply and demand conditions change can be seen on computer screens across the world. The bid-ask spread which is the difference betweenbidandaskpricesrepresents thedealer’smarkuporprofit. Thedealer’s risk increases when the stock is more volatile or when the stock trades infre- quently. Generally we would expect volatile infrequently traded stocks to have wider spreads inordertocompensate the dealersforassumingthe risk ofholding them in inventory. BrokersanddealerswhoparticipateintheOTCmarketaremembersofaself- regulatory body known as the National Association of Securities Dealers NASD which licenses brokers and oversees trading practices. The computerized network used by the NASD is known as the NASD Automated Quotation System Nasdaq. Nasdaq started as just a quotation system but it has grown to become an organized securities market with its own listing requirements. Over the past decade the competition between the NYSE and Nasdaq has become increasingly fierce. As noted earlier the Nasdaq has invested in the London Stock Exchange and other market makers while the NYSE merged with Euronext. Since most of thelargercompaniestradeontheNYSEthemarketcapitalizationofNYSE-traded stocks is much higher than for stocks traded on Nasdaq. However reported volumenumberofsharestradedisoftenlargeronNasdaqandmorecompanies are listed on Nasdaq. 7 Interestingly many high-tech companies such as Microsoft Google and Intel have remained on Nasdaq even though they meet the listing requirements of the NYSE.Atthesametimehoweverotherhigh-techcompanieshaveleftNasdaqfor the NYSE. Despite these defections Nasdaq’s growth over the past decade has been impressive. In the years ahead competition between Nasdaq and NYSE Euronext will no doubt remain fierce. SELFTEST What are the differences between the physical location exchanges and the Nasdaq stock market What is the bid-ask spread 2-5 THE MARKET FOR COMMON STOCK Some companies are so small that their common stocks are not actively traded they are owned by relatively few people usually the companies’ managers. These firmsaresaidtobeprivatelyownedorcloselyheldcorporationsandtheirstockis called closely held stock. In contrast the stocks of most large companies are owned Dealer Market Includes all facilities that are needed to conduct security transactions not conducted on the physical location exchanges. 7 One transaction on Nasdaq generally shows up as two separate trades the buy and the sell. This “double counting” makes it difficult to compare the volume between stock markets. Closely Held Corporation A corporation that is owned by a few individu- als who are typically associated with the firm’s management. 40 Part 2 Fundamental Concepts in Financial Management

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by thousands of investors most of whom are not active in management. These companies are called publicly owned corporations and their stock is called publicly held stock. A recent study found that institutional investors owned about 46 of all publicly held common stocks. Included are pension plans 26 mutual funds 10 foreign investors 6 insurance companies 3 and brokerage firms 1. However because these institutions buy and sell relatively actively they account for about 75 of all transactions. Thus institutional investors have a significant influence on the prices of individual stocks. 2-5a Types of Stock Market Transactions We can classify stock market transactions into three distinct categories: 1. Outstanding shares of established publicly owned companies that are traded: the secondary market. Allied Food Products the company we will study in Chapters 3 and 4 has 50 million shares of stock outstanding. If the owner of 100 shares sells his or her stock the trade is said to have occurred in the secondarymarket.Thusthemarketforoutstandingsharesorusedsharesisthe secondary market. The company receives no new money when sales occur in this market. 2. Additionalsharessoldbyestablishedpubliclyownedcompanies:theprimarymarket. If Allied Food decides to sell or issue an additional 1 million shares to raise new equity capital this transaction is said to occur in the primary market. 8 3. Initial public offerings made by privately held firms: the IPO market. In the sum- merof2004Googlesoldsharestothepublicforthefirsttimeat85pershare. By February 2008 the stock was selling for 495 so it had increased by over 480. In 2006 McDonald’s owned Chipotle Mexican Grill. McDonald’s then solditssharestothepublicforabout47.50toraisecapital tosupport itscore business and by February 2008 Chipotle’s stock price was 117. Making these types of offerings is called going public. Whenever stock in a closely held corporation isoffered tothe public for the first timethe company is said tobegoingpublic.Themarketforstockthat isjustbeingofferedtothe public is called the initial public offering IPO market. 9 ThenumberofnewIPOsrisesandfallswiththestockmarket.Whenthemarketis strong many companies go public to bring in new capital and to give their founders an opportunity to cash out some of their shares. Table 2-3 lists the largest the best performing and the worst performing IPOs of 2007 and shows howthey performedfrom their offering dates through year-end 2007. Asthe table showsnotallIPOsareaswellreceivedasGoogleandChipotle.Moreoverevenif you are able to identify a “hot” issue it is often difficult to purchase shares in the initialoffering.These dealsareoften oversubscribedwhich means that the demand for shares at the offering price exceeds the number of shares issued. In such instances investment bankers favor large institutional investors who are their bestcustomersandsmallinvestorsfindithardifnotimpossibletogetinonthe ground floor. They can buy the stock in the aftermarket but evidence suggests Publicly Owned Corporation A corporation that is owned by a relatively large number of individu- als who are not actively involved in the firm’s management. 8 Allied has 60 million shares authorized but only 50 million outstanding thus it has 10 million authorized but unissuedshares. If it had noauthorizedbut unissued sharesmanagementcouldincreasetheauthorizedsharesby obtaining stockholders’ approval which would generally be granted without any arguments. 9 A number of years ago Coors the beer company offered some of its shares to the public. These shares were designated Class B and they were nonvoting. The Coors family retained the founders’ shares called Class A stock which carried full voting privileges. This illustrates how the managers of a company can use different classes of shares to maintain control. However the nonvoting shares always sell for less than the voting shares so using nonvoting shares does not maximize the value of the firm. Going Public The act of selling stock to the public at large by a closely held corporation or its principal stockholders. Initial Public Offering IPO Market The market for stocks of companies that are in the process of going public. Chapter 2 Financial Markets and Institutions 41

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Initial Public Offerings in 2007 Table 2-3 THE BIGGEST IPOs PERCENT CHANGE FROM OFFER Issuer Issue Date U.S. Proceeds Millions First-Day Trading Through 12/31/07 Blackstone 06/21/07 4753.3 +13.1 –28.6 MF Global 07/18/07 2921.4 –8.2 +4.9 MetroPCS Communications 04/18/07 1322.5 +19.1 –15.4 Cosan 08/16/07 1172.7 unch. +20.0 Och-Ziff Capital Management Group 11/13/07 1152.0 –4.2 –17.9 VMware 08/13/07 1100.6 +75.9 +193.1 Giant Interactive Group 10/31/07 1019.5 +17.6 –16.3 National CineMedia 02/07/07 882.0 +22.2 +20.0 AECOM Technology 05/09/07 808.5 +5.5 +42.9 Energy Solutions 11/14/07 765.9 +0.04 +17.3 THE BEST PERFORMERS PERCENT CHANGE FROM OFFER Issuer Issue Date Offer Price U.S. Proceeds Millions First-Day Trading Through 12/31/07 JA Solar Holdings 02/06/07 15.00 258.8 +18.7 +365.4 MercadoLibre 08/09/07 18.00 332.8 +58.3 +310.4 Yingli Green Energy Holding 06/07/07 11.00 324.5 –4.6 +251.8 VMware 08/13/07 29.00 1100.6 +75.9 +193.1 Lululemon Athletica 07/26/07 18.00 376.7 +55.6 +163.2 Masimo 08/07/07 17.00 233.0 +22.9 +132.1 MSCI 11/14/07 18.00 289.8 +38.7 +113.3 American Public Education 11/08/07 20.00 107.8 +79.6 +108.9 WuXi PharmaTech Cayman 08/08/07 14.00 212.3 +40.0 +108.9 Dolan Media 08/01/07 14.50 224.4 +22.2 +101.2 THE WORST PERFORMERS PERCENT CHANGE FROM OFFER Issuer Issue Date Offer Price U.S. Proceeds Millions First-Day Trading Through 12/31/07 Superior Offshore International 04/19/07 15.00 175.4 +16.9 –66.5 VeriChip 02/09/07 6.50 20.2 unch. –65.4 ImaRx Therapeutics 07/25/07 5.00 15.0 –4.2 –61.4 BigBand Networks 03/14/07 13.00 160.0 +30.8 –60.5 Meruelo Maddux Properties 01/24/07 10.00 455.5 +6.0 –60.0 HFF 01/30/07 18.00 296.0 +3.9 –57.0 Glu Mobile 03/21/07 11.50 86.2 +6.9 –54.6 Limelight Networks 06/07/07 15.00 276.0 +47.9 –54.1 Xinhua Finance Media 03/08/07 13.00 300.0 –12.7 –53.8 GSI Technology 03/29/07 5.50 35.4 –3.8 –53.6 Source: Lynn Cowan “IPOs Tally Record Amount of Cash” The Wall Street Journal January 2 2008 p. R10. 42 Part 2 Fundamental Concepts in Financial Management

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that when an investor does not get in on the ground floor IPOs often underper- form the overall market over the long run. 10 Google Inc.’s highly publicized IPO attracted attention because of its size Google raised 1.67 billion in stock and because of the way the sale was con- ducted. Rather than having the offer price set by its investment bankers Google conducted a Dutch auction where individual investors placed bids for shares directly. In a Dutch auction the actual transaction price is set at the highest price the clearing price that causes all of the offered shares to be sold. All investors who set their bids at or above the clearing price received all of the shares they subscribed to at the offer price which turned out to be 85. While Google’s IPO wasin manyways precedent-settingfewcompanies goingpublicsince thenhave been willing or able to use the Dutch auction method to allocate their IPO shares. It is important to recognize that firms can go public without raising any additional capital. For example the Ford Motor Company was once owned exclusivelybytheFordfamily.WhenHenryForddiedheleftasubstantialpartof his stock to the Ford Foundation. When the Foundation later sold some of the stock to the general public the Ford Motor Company went public even though the company itself raised no capital in the transaction. SELFTEST Differentiate between closely held and publicly owned corporations. Differentiate between primary and secondary markets. What is an IPO What is a Dutch auction and what company used this procedure for its IPO 2-6 STOCK MARKETS AND RETURNS Anyone who has invested in the stock market knows that there can be and generally are large differences between expected and realized prices and returns. Figure 2-2 shows how total realized portfolio returns have varied from year to year. As logic would suggest and as is demonstrated in Chapter 8 a stock’s expected return as estimated by investors at the margin is always positive oth- erwiseinvestorswouldnotbuythestock. HoweverasFigure2-2showsinsome years actual returns are negative. 2-6a Stock Market Reporting Up until a few years ago the best source of stock quotations was the business section of daily newspapers such as The Wall Street Journal. One problem with newspapers however is that they report yesterday’s prices. Now it is possible to obtain real-time quotes throughout the day from a wide variety of Internet sources. 11 One of the best is Yahoo and Figure 2-3 shows a detailed quote for GlaxoSmithKlinePLCGSK.AstheheadingshowsGlaxoSmithKlineistradedon the NYSE under the symbol GSK. The NYSE is just one of many world markets on which the stock trades. The first two rows of information show that GSK had lasttradedat45.89andthatthestockhadtradedthusfaronthisdayfromaslow as 45.42 to as high as 46.23. Note that the price is reported in decimals rather than fractions reflecting a recent change in trading conventions. The last trade 10 See Jay R. Ritter “The Long-Run Performance of Initial Public Offerings” Journal of Finance Vol. 46 no. 1 March 1991 pp. 3–27. 11 Most free sources provide quotes that are delayed 15 minutes. Real-time quotes can be obtained for a fee. Chapter 2 Financial Markets and Institutions 43

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shownwasat2:20p.m.ETonFebruary52008anditspricerangeduringthepast 52 weeks was between 45.89 and 59.98. The next three lines show that GSK opened trading on February 5 at 46.07 that it closed on February 4 at 46.87 and that its price fell by 0.98 or a 2.09 decrease from the previous close to the current price. So far during the day 1835434shareshadtradedhands.GSK’saveragedailytradingvolumebasedon thepastthreemonthswas1968960sharessotradingsofarthatdaywascloseto the average. The total value of all of GSK’s stock called its market cap was 125.39 billion. ThelastthreelinesreportothermarketinformationforGSK.Ifitweretrading on Nasdaq rather than a listed exchange the most recent bid and ask quotes from dealers would have been shown. However because it trades on the NYSE these dataarenotavailable.GSK’sP/Eratiopricepersharedividedbythemostrecent 12 months’ earnings was 12.30 and its earnings per share for the most recent 12 months was 3.73 ttm stands for “trailing 12 months”—in other words the SP 500 Index Total Returns: Dividend Yield + Capital Gain or Loss 1968–2007 FIGURE 2-2 Returns 1992 1995 1998 1989 1983 1986 1980 1974 1977 1971 1968 40 30 20 10 0 –10 –20 –30 50 Years 2001 2004 2007 Source: Data taken from various issues of The Wall Street Journal “Investment Scoreboard” section. 44 Part 2 Fundamental Concepts in Financial Management Text not available due to copyright restrictions

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MEASURING THE MARKET Stock market indexes are designed to show the perfor- mance of the stock market. However there are many stock indexes and it is difficult to determine which index best reflects market actions. Some are designed to represent the entire stock market some track the returns of certain industry sectors and others track the returns of small-cap mid-cap or large-cap stocks. In addition there are indexes for different countries. We discuss here the three leading U.S. indexes. These indexes are used as a benchmark for com- paring individual stocks with the overall market for measur- ing the trend in stock prices over time and for determining how various economic factors affect the market. Dow Jones Industrial Average Unveiled in 1896 by Charles H. Dow the Dow Jones Industrial Average DJIA began with just 10 stocks was expanded in 1916 to 20 stocks and then was increased to 30 stocks in 1928 when the editors of The Wall Street Journal began adjusting the index for stock splits and making periodic substitutions. Today the DJIA still includes 30 companies. They represent almost a fifth of the market value of all U.S. stocks and all are leading companies in their industries and widely held by individual and institu- tional investors. Visit to get more information about the DJIA. You can find out how it is cal- culated the companies that make up the DJIA and more history about the DJIA. In addition a DJIA time line shows various historical events. SP 500 Index Created in 1926 the SP 500 Index is widely regarded as the standard for measuring large-cap U.S. stock market perfor- mance.ThestocksintheSP500areselectedbytheStandard Poor’s Index Committee and they are the leading compa- nies in the leading industries. It is weighted by each stock’s market value so the largest companies have the greatest influence.The SP 500 is used for benchmarkingby 97of all U.S. money managers and pension plan sponsors and approximately 700 billion is held in index funds designed to mirror the same performance of the index. Nasdaq Composite Index The Nasdaq Composite Index measures the performance of all stocks listed on the Nasdaq. Currently it includes more than 5000 companies and because many companies in the technology sector are traded on the computer-based Nas- daq exchange this index is generally regarded as an eco- nomic indicator of the high-tech industry. Microsoft Intel Google and Cisco Systems are the four largest Nasdaq companies and they make up a high percentage of the index’s value-weighted market capitalization. For this rea- son substantial movements in the same direction by these four companies can move the entire index. Recent Performance The accompanying figure plots the value that an investor would now have if he or she had invested 1 in each of the three indexes on January 1 1995. The returns on the three indexes are compared with an investment strategy that invests only in 1-year T-bills. Each of these indexes performed quite well through 1999. However for a couple of years each index stumbled before beginning to rebound again in 2003. During the last 13 years the average annualized returns of these indexes ranged from 8.8 for the SP 500 to 9.6 for the Dow. Nasdaq experienced a huge bubble in 1999 reflecting overly optimistic valuations of technology compa- nies.Howeverin2000thebubbleburstandtechnologystock valuations spiraled downward causing the Nasdaq Index to revert back to a level comparable to the SP 500 and Dow Jones Industrial Average Index. Growth of a 1 Investment Made on January 1 1995 1995 1996 1997 1998 1999 2000 2001 2002 Nasdaq DJIA SP 500 T-bills 2003 2004 2005 7 Value of 1 Investment 2006 2007 2008 Years 6 5 4 3 2 1 0 Chapter 2 Financial Markets and Institutions 45

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most recent 12 months. The mean of the analysts’ one-year target price for GSK was 56.10. GSK’s dividend was 2.13 per share so the quarterly dividend was 0.5325 per share and the dividend yield which is the annual dividend divided by the previous closing price is 4.50. In Figure 2-3 the chart to the right plots the stock price during the day however the links below the chart allow you to pick different time intervals for plotting data. As you can see Yahoo provides a great deal of information in its detailed quote and even more detail is available on the screen page below the basic quote information. 2-6b Stock Market Returns In Chapters 8 and 9 we will discuss in detail how a stock’s rate of return is calculated what the connection is between risk and returns and what techniques analystsusetovaluestocks.Howeveritisusefulatthispointtogiveyouarough idea of how stocks have performed in recent years. Figure 2-2 shows how the returns on large U.S. stocks have varied over the past years and the box entitled “Measuring the Market” provides information on the major U.S. stock market indices and their performances since the mid-1990s. Themarkettrendhas been strongly up since 1968 butbyno meansdoes itgo up every year. Indeed as we can see from Figure 2-2 the overall market was down in 9of the 40years including the three consecutive years of 2000–2002. The stock prices of individual companies have likewise gone up and down. 12 Of courseeveninbadyearssomeindividualcompaniesdowellso“thenameofthe game” in security analysis is to pick the winners. Financial managers attempt to do this but they don’t always succeed. In subsequent chapters we will examine the decisions managers make to increase the odds that their firms will perform well in the marketplace. SELFTEST Would you expect a portfolio that consisted of the NYSE stocks to be more or less risky than a portfolio of Nasdaq stocks If we constructed a chart like Figure 2-2 for an average SP 500 stock do you think it would show more or less volatility Explain. 2-7 STOCK MARKET EFFICIENCY To begin this section consider the following definitions: Market price: The current price of a stock. For example the Internet showed that on one day GSK’s stock traded at 45.89. The market price had varied from 45.42 to 46.23 during that same day as buy and sell orders came in. Intrinsic value: The price at which the stock would sell if all investors had all knowableinformationaboutastock.ThisconceptwasdiscussedinChapter1 wherewesawthatastock’sintrinsicvalueisbasedonitsexpectedfuturecash flows and its risk. Moreover the market price tends to fluctuate around the 12 If we constructed a graph like Figure 2-2 for individual stocks rather than for the index far greater variability would be shown. Also if we constructed a graph like Figure 2-2 for bonds it would have similar ups and downs but the bars would be far smaller indicating that gains and losses on bonds are generally much smaller than those on stocks. Above-average bond returns occur in years when interest rates decline losses occur when interest rates rise sharply but interest payments tend to stabilize bonds’ total returns. We will discuss bonds in detail in Chapter 7. 46 Part 2 Fundamental Concepts in Financial Management

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intrinsic value and the intrinsic value changes over time as the company succeeds or fails with new projects competitors enter or exit the market and so forth. We can guess or estimate GSK’s intrinsic value but different ana- lysts will reach somewhat different conclusions. Equilibriumprice:Thepricethatbalancesbuyandsellordersatanygiventime. When a stock is in equilibrium the price remains relatively stable until new information becomes available and causes the price to change. For example GSK’s equilibrium price appears to be about 45.89 as it has been fluctuating narrowly around this amount. Efficient market: A market in which prices are close to intrinsic values and stocks seem to be in equilibrium. Whenmarketsareefficientinvestorscanbuyandsellstocksandbeconfidentthat theyaregettinggoodprices.Whenmarketsareinefficientinvestorsmaybeafraid to invest and may put their money “under the pillow” which will lead to a poor allocation of capital and economic stagnation. So from an economic standpoint market efficiency is good. Academics and financial professionals have studied the issue of market effi- ciency extensively. 13 As generally happens some people think that markets are highly efficient others think that markets are highly inefficient and others think that the issue is too complex for a simple answer. Those who believe that markets are efficient note that there are 100000 or so full-timehighlytrainedprofessionalanalystsandtradersoperatinginthemarket. Many have PhDs in physics chemistry and other technical fields in addition to advanceddegreesinfinance.Moreovertherearefewerthan3000majorstocksso if each analyst followed 30 stocks which is about right as analysts tend to focus on a specific industry on average 1000 analysts would be following each stock. Further these analysts work for organizations such as Goldman Sachs Merrill Lynch Citigroup and Deutsche Bank or for Warren Buffett and other billionaire investors who have billions of dollars available to take advantage of bargains. Also the SEC has disclosure rules which combined with electronic information networks means that new information about a stock is received by all analysts at about the same time causing almost instantaneous revaluations. All of these factors help markets be efficient and cause stock prices to move toward their intrinsic values. However other people point to data that suggests that markets are not very efficient. For example on October 15 1987 the SP 500 lost 25 of its value. Many of the largest U.S. companies did worse watching their prices get cut in half. In 2000 Internet stocks rose to phenomenally high prices then fell to zero or close to it the following year. No truly important news was announced that could havecausedeitherofthesechangesandifthemarketwasefficientit’shardtosee how such drastic changes could have occurred. Another situation that causes people to question market efficiency is the apparent ability of some analysts to consistently outperform the market over long periods. Warren Buffett comes to mind but there are others. If markets are truly efficient then each stock’s price 13 The general name for these studies is the efficient markets hypothesis or EMH. It was and still is a hypothesis that needs to be proved or disproved empirically. In the literature researchers identified three levels of efficiency: weak form which contends that information on past stock price movements cannot be used to predict future stock prices semi-strong form which contends that all publicly available information is immediately incorporated into stock prices i.e. that one cannot analyze published reports and then beat the market and strong form which contends that even company insiders with inside information cannot earn abnormally high returns. Few people believe the strong form today as a number of insiders have made large profits been caught it’s illegal to trade on inside information and gone to jail. Martha Stewart is one and she helped disprove the strong form of the EMH. Chapter 2 Financial Markets and Institutions 47

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should be close to its intrinsic value. That would make it hard for any analyst to consistently pick stocks that outperform the market. The following diagram sums up where most observers seem to be today. There is an “efficiency continuum” with the market for some companies’ stocks being highly efficient and the market for other stocks being highly inefficient. The key factor is the size of the company—the larger the firm the more analysts tend to follow it and thus the faster new information is likely to be reflected in the stock’s price. Also different companies communicate better with analysts and investorsandthebetterthecommunicationsthemoreefficientthemarketforthe stock. Highly Inefficient Highly Efficient Small companies Large companies not followed by many followed by many analysts. Not much analysts. Good contact with investors. communications with investors. Asaninvestorwouldyouprefertopurchaseastockwhosepricewasdetermined in an efficient or an inefficient market If you thought you knew something that others didn’t know you might prefer inefficient markets. But if you thought that those physics PhDs with unlimited buying power and access to company CEOs might know more than you you would probably prefer efficient markets where thepriceyoupaidwaslikelytobethe“right”price.Fromaneconomicstandpoint it is good to have efficient markets in which everyone is willing to participate. So theSECandotherregulatoryagenciesshoulddoeverythingtheycantoencourage market efficiency. Thusfarwehavebeendiscussingthemarketforindividualstocks.Thereisalso amarketforentirecompanieswhereothercompaniesprivateequitygroupsand largeinvestorslikeWarrenBuffettbuytheentirecompanyoracontrollingstakein it.SupposeforexamplethatCompanyXisinequilibriumsellingatapricethatis closetoitsintrinsicvaluebutwheretheintrinsicvalueisbasedonitbeingoperated byitscurrentmanagerswhoown51ofthestock.Howeversupposethatastute analysts study the company and conclude that it could produce much higher earningsandcashflowsunderadifferentmanagementteamorifitwerecombined withsomeothercompanyorifitwerebrokenupintoanumberofseparatepieces. Inthiscasethestockmightbethoughtofastradinginanefficientmarketwhilethe company as a whole was not efficiently priced. Some years ago quite a few companies were inefficiently priced. But then alongcomesWarrenBuffetttheprivateequityplayersandhedgefundmanagers who are willing to contest entrenched managers. For example Dow Jones the owner of The Wall Street Journal was controlled by its founding family the Ban- crofts.DowJones’sstocklaggedthemarketforyears.ThenRupertMurdochwho controls News Corporation arguably the largest media company in the world offered 60 per share for Dow Jones which was then selling for about 35 per share.Murdoch plannedto change The Wall Street Journaland combineits content with his Fox News and new financial channel. To Murdoch Dow Jones’ intrinsic value was 60. Without him or someone else who would operate the company differently the intrinsic value was about 35. One could of course argue that Dow Jones’ intrinsic value was 60 all along but it was hard to know that until Murdoch came along and made his offer. Alternatively one could argue that Murdochraisedtheintrinsicvaluefrom35to60.Finallyyoucanbetthatmany analysts on Wall Street are looking for the next Dow Jones. If they succeed they will surely beat the market 48 Part 2 Fundamental Concepts in Financial Management

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ACLOSER LOOK AT BEHAVIORAL FINANCE THEORY The efficient markets hypothesis EMH remains one of the cornerstones of modern finance theory. It implies that on average asset prices are about equal to their intrinsic val- ues. The logic behind the EMH is straightforward. If a stock’s price is “too low” rational traders will quickly take advan- tage of this opportunity and buy the stock pushing prices up to the proper level. Likewise if prices are “too high” rationaltraderswillsellthestockpushingthepricedownto its equilibrium level. Proponents of the EMH argue that these forces keep prices from being systematically wrong. While the logic behind the EMH is compelling many events in the real world seem inconsistent with the hypothesis which has spurred a growing field called behavioral finance. Rather than assuming that investors are rational behavioral finance theorists borrow insights from psychology to better understand how irrational behavior can be sustained over time. Pioneers in this field include psychologists Daniel Kahneman Amos Tversky and Richard Thaler. Their work has encouraged a growing number of scholars to work in this promising area of research. 14 Professor Thaler and his colleague Nicholas Barberis summarizedmuchofthisresearchinthearticlecitedbelow. They argue that behavioral finance’s criticism of the EMH rests on two key points. First it is often difficult or risky for traders to take advantage of mispriced assets. For example even if you know that a stock’s price is too low because investors have overreacted to recent bad news a trader with limited capital may be reluctant to buy the stock for fear that the same forces that pushed the price down may work to keep it artificially low for a long time. Similarly during the recent stock market bubble many traders who believed correctly that stock prices were too high lost a great deal of money selling stocks short in the early stages of the bubble because prices went even higher before they eventually collapsed. Thus mispricings may persist. The second point deals with why mispricings can occur in the first place. Here insights from psychology come into play. For example Kahneman and Tversky suggested that individuals view potential losses and gains differently. If you askaverageindividualswhethertheywouldratherhave500 with certainty or flip a fair coin and receive 1000 if a head comes up and nothing if a tail comes up most would prefer the certain 500 which suggests an aversion to risk. How- ever if you ask people whether they would rather pay 500 with certainty or flip a coin and pay 1000 if it’s a head and nothing if it’s a tail most would indicate that they prefer to flip the coin. Other studies suggest that people’s willingness to take a gamble depends on recent performance. Gamblers who are ahead tend to take on more risks whereas those who are behind tend to become more conservative. Theseexperimentssuggestthatinvestorsandmanagers behave differently in down markets than they do in up markets which might explain why those who made money early in the stock market bubble continued to invest their money in the market even as prices went ever higher. Other evidencesuggests thatindividuals tendtooverestimate their trueabilities.Forexamplealargemajorityupwardof90in some studies of people believe that they have above-aver- age driving ability and above-average ability to get along with others. Barberis and Thaler point out that: Overconfidence may in part stem from two other biases self-attribution bias and hindsight bias. Self- attribution bias refers to people’s tendency to ascribe any success they have in some activity to their own talents while blaming failure on bad luck rather than on their ineptitude. Doing this repeatedly will lead peopletothepleasingbuterroneousconclusionthat they are very talented. For example investors might become overconfident after several quarters of inves- ting success Gervais and Odean 2001. Hindsight biasisthetendencyofpeopletobelieveafteranevent has occurred that they predicted it before it hap- pened. If people think they predicted the past better thantheyactuallydidtheymayalsobelievethatthey can predict the future better than they actually can. Behavioral finance has been studied in both the cor- porate finance and investments areas. Ulrike Malmendier of Stanford and Geoffrey Tate of Wharton found that over- confidence leads managers to overestimate their ability and thus the profitability of their projects. This result may explain why so many corporate projects fail to live up to their stated expectations. Sources: Nicholas Barberis and Richard Thaler “A Survey of Behavioral Finance” Chapter 18 Handbook of the Economics of Finance edited by George Constantinides Milt Harris and René Stulz part of the Handbooks in Economics Series New York: Elsevier/North-Holland 2003 and Ulrike Malmendier and Geoffrey Tate “CEO Overconfidence and Corporate Investment” Stanford Graduate School of Business Research Paper 1799 June 2004. 14 Three noteworthy sources for students interested in behavioral finance are Richard H. Thaler Editor Advances in BehavioralFinanceNewYork:RussellSageFoundation1993HershShefrin“BehavioralCorporateFinance”Journalof Applied Corporate Finance Vol. 14.3 Fall 2001 pp. 113–125 and Nicholas Barberis and Richard Thaler “ASurveyof Behavioral Finance” Chapter 18 Handbook of the Economics of Finance edited by George Constantinides Milt Harris andRenéStulzpartoftheHandbooksinEconomicsSeriesNewYork:Elsevier/North-Holland2003.Studentsinterested in learning more about the efficient markets hypothesis should consult Burton G. Malkiel A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing 9th ed. New York: W.W. Norton Company 2007. Chapter 2 Financial Markets and Institutions 49

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2-7a Conclusions about Market Efficiency As noted previously if the stock market is efficient it is a waste of time for most people to seek bargains by analyzing published data on stocks. That follows because if stock prices already reflect all publicly available information they will be fairly priced and a person can beat the market only with luck or inside information. So rather than spending time and money trying to find undervalued stocks it would be better to buy an index fund designed to match the overall marketasreflectedinanindexsuchastheSP500.Howeverifweworkedforan institution with billions of dollars we would try to find undervalued stocks or companies because even a small undervaluation would amount to a great deal of money when investing millions rather than thousands. Also markets are more efficient for individual stocks than for entire companies so for investors with enoughcapitalitdoesmakesensetoseekoutbadlymanagedcompaniesthatcan be acquired and improved. Note though that a number of private equity players aredoing exactlythat sothe market forentirecompanies maysoonbe asefficient as that for individual stocks. However even if markets are efficient and all stocks and companies are fairly priced an investor should still be careful when selecting stocks for his or her portfolio. Most importantly the portfolio should be diversified with a mix of stocks from various industries along with some bonds and other fixed income securities.Wewilldiscussdiversification ingreaterdetailinChapter8butitisan important consideration for most individual investors. SELFTEST What does it mean for a market to be “efficient” Is the market for all stocks equally efficient Explain. Why is it good for the economy that markets be efficient Is it possible that the market for individual stocks could be highly efficient but the market for whole companies could be less efficient What is behavioral finance What are the implications of behavioral finance for market efficiency TYING IT ALL TOGETHER In this chapter we provided a brief overview of how capital is allocated and dis- cussed the financial markets instruments and institutions used in the allocation process. We discussed physical location exchanges and electronic markets for common stocks stock market reporting and stock indexes. We demonstrated that security prices are volatile—investors expect to make money which they generally do over time but losses can be large in any given year. Finally we discussed the efficiency of the stock market and developments in behavioral finance. After reading this chapter you should have a general understanding of the financial environment in which businesses and individuals operate realize that actual returns are often different from expected returnsand be ableto read stock market quotations from business newspapers or various Internet sites. You should also recognize that the theory of financial markets is a “work in progress” and much work remains to be done. 50 Part 2 Fundamental Concepts in Financial Management

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SELF-TEST QUESTION AND PROBLEM Solutions Appear in Appendix A ST-1 KEY TERMS Define each of the following terms: a. Spot markets futures markets b. Money markets capital markets c. Primary markets secondary markets d. Private markets public markets e. Derivatives f. Investment banks iBanks commercial banks financial services corporations g. Mutual funds money market funds h. Physical location exchanges over-the-counter OTC market dealer market i. Closely held corporation publicly owned corporation j. Going public initial public offering IPO market k. Efficient markets hypothesis EMH l. Behavioral finance QUESTIONS 2-1 How does a cost-efficient capital market help reduce the prices of goods and services 2-2 Describe the different ways in which capital can be transferred from suppliers of capital to those who are demanding capital. 2-3 Is an initial public offering an example of a primary or a secondary market transaction Explain. 2-4 Indicate whether the following instruments are examples of money market or capital market securities. a. U.S. Treasury bills b. Long-term corporate bonds c. Common stocks d. Preferred stocks e. Dealer commercial paper 2-5 What would happen to the U.S. standard of living if people lost faith in the safety of the financial institutions Explain. 2-6 What types of changes have financial markets experienced during the last two decades Have they been perceived as positive or negative changes Explain. 2-7 Differentiate between dealer markets and stock markets that have a physical location. 2-8 Identify and briefly compare the two leading stock exchanges in the United States today. 2-9 Describe the three different forms of market efficiency. 2-10 Investors expect a company to announce a 10 increase in earnings instead the company announces a1increase. Ifthemarketissemi-strongform efficient whichofthefollowing would you expect to happen Hint: Refer to Footnote 13 in this chapter. a. The stock’s price will increase slightly because the company had a slight increase in earnings. b. The stock’s price will fall because the earnings increase was less than expected. c. The stock’s price will stay the same because earnings announcements have no effect if the market is semi-strong form efficient. 2-11 Briefly explain what is meant by the term efficiency continuum. 2-12 Explain whether the following statements are true or false. a. Derivativetransactionsaredesignedtoincreaseriskandareusedalmostexclusivelyby speculators who are looking to capture high returns. Chapter 2 Financial Markets and Institutions 51

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b. Hedge funds typically have large minimum investments and are marketed to institu- tions and individuals with high net worths. c. Hedge funds have traditionally been highly regulated. d. The New York Stock Exchange is an example of a stock exchange that has a physical location. e. A larger bid-ask spread means that the dealer will realize a lower profit. f. The efficient markets hypothesis assumes that all investors are rational. INTEGRATED CASE SMYTH BARRY COMPANY 2-1 FINANCIAL MARKETS AND INSTITUTIONS Assume that you recently graduated with a degree in finance and have just reported to work as an investment adviser at the brokerage firm of Smyth Barry Co. Your first assignment is to explain the nature of the U.S. financial markets to Michelle Varga a professional tennis player whorecentlycametotheUnitedStatesfromMexico.Vargaisahighlyrankedtennisplayerwhoexpectstoinvest substantial amounts of money through Smyth Barry. She is very bright therefore she would like to understand ingeneraltermswhatwillhappentohermoney.Yourbosshasdevelopedthefollowingquestionsthatyoumust use to explain the U.S. financial system to Varga. a. What are the three primary ways in which capital is transferred between savers and borrowers Describe each one. b. What is a market Differentiate between the following types of markets: physical asset markets versus financial asset markets spot markets versus futures markets money markets versus capital markets pri- mary markets versus secondary markets and public markets versus private markets. c. Why are financial markets essential for a healthy economy and economic growth d. Whatarederivatives Howcanderivatives beused toreduceriskCanderivatives beusedtoincreaserisk Explain. e. Briefly describe each of the following financial institutions: commercial banks investment banks mutual funds hedge funds and private equity companies. f. What are the two leading stock markets Describe the two basic types of stock markets. g. If Apple Computer decided to issue additional common stock and Varga purchased 100 shares of this stock from Smyth Barrythe underwriter would this transaction be a primary ora secondary market transaction Would it make a difference if Varga purchased previously outstanding Apple stock in the dealer market Explain. h. What is an initial public offering IPO i. What does it mean for a market to be efficient Explain why some stock prices may be more efficient than others. j. After your consultation with Michelle she asks to discuss these two scenarios with you: 1 WhileinthewaitingroomofyourofficesheoverheardananalystonafinancialTVnetworksaythata particular medical research company just received FDA approval for one of its products. On the basis of this “hot” information Michelle wants to buy many shares of that company’s stock. Assuming the stock market is highly efficient what advice would you give her 2 She has read a number of newspaper articles about a huge IPO being carried out by a leading technology company. She wants to get as many shares in the IPO as possible and would even be willingtobuythesharesintheopenmarketimmediatelyaftertheissue.Whatadvicedoyouhavefor her 52 Part 2 Fundamental Concepts in Financial Management

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ª F1 ONLINE/PHOTOLIBRARY CHAPTER 3 Financial Statements Cash Flow and Taxes The “Quality” of Financial Statements The financial statements presented in a typical company’s annual report look quite official. They are signed by the firm’s top executives and are certified by a Big Four accounting firm so one would think that they must be accurate. That may not be true though for three reasons: legitimate misjudgments in valuing assets and measuring costs “flexible” accounting rules that result in differently reported results for similar companies and outright cheating. One blatant example of cheating involved WorldCom which reported asset values that exceeded their true value by about 11 billion. This led to an understatement of costs and a corresponding overstatement of profits. Enron is another example. That company overstated the value of certain assets reported those artificial value increases as profits and transferred the assets to subsidiary companies to hide the true facts. Enron’s and WorldCom’s investors eventu- ally learned what was happening the companies were forced into bankruptcy their top execu- tives went to jail the accounting firm that audited their books was forced out of business and millions of investors lost billions of dollars. After the Enron and WorldCom blowups Congress passed the Sarbanes-Oxley Act SOX which required companies to improve their internal auditing standards and required the CEO and CFO to certify that the financial statements were properly prepared. The SOX bill also cre- ated a new watchdog organization to help make sure that the outside accounting firms were doing their job. From all indications financial statements are generally more accurate and clearer than they were in the past. But the world is dynamic and a new accounting problem surfaced in 2007. Big banks most notably Citigroup owned many risky but high-yielding subprime mortgages. The banks invented a complex legal procedure that they called a structured investment vehicle SIV to conceal the fact that they held all of these risky mortgages. They correctly feared that people wouldn’t want to do business with a risky bank. But when the subprime market fell apart in 2007 53

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PUTTING THINGS IN PERSPECTIVE Amanager’sprimarygoalistomaximizethevalueofhisorherfirm’sstockandvalue isbasedonthefirm’sfuturecashflows.Buthowdomanagersdecidewhichactionsare mostlikelytoincreasethoseflowsandhowdoinvestorsestimatefuturecashflows The answers to both questions lie in a study of financial statements that publicly tradedfirmsmustprovidetoinvestors.Hereinvestorsincludebothinstitutionsbanks insurance companies pension funds and the like and individuals like you. Much of the materialin this chapter deals with conceptsyoucovered in abasic accounting course. However the information is important enough to warrant a review. Also in accounting you probably focused on how accounting statements are made the focus here is on how investors and managers interpret and use them. Accounting is the basic language of business so everyone engaged in business needs a good working knowledge of it. It is used to “keep score” and if investors and managers do not know the score they won’t know whether their actions are appropriate. If you took midterm exams but were not told your scores you would haveadifficulttimeknowingwhetheryouneededtoimprove.Thesameideaholds in business. If a firm’s managers—whether they are in marketing personnel pro- duction or finance—do not understand financial statements they will not be able to judge the effects of their actions which will make it hard for the firm to survive much less to have a maximum value. When you finish this chapter you should be able to: l List each of the key financial statements and identify the kinds of information they provide to corporate managers and investors. l Estimate a firm’s free cash flow and explain why free cash flow has such an important effect on firm value. l Discuss the major features of the federal income tax system. 3-1 FINANCIAL STATEMENTS AND REPORTS The annual report is the most important report that corporations issue to stock- holders and it contains two types of information. 2 First there is a verbal section oftenpresentedasaletterfromthechairpersonwhichdescribesthefirm’soperating the banks had to acknowledge their losses which ran into many billions of dollars. It turns out that the banks had tried to avoid writing down their mortgages but a newly formed organization set up by the Big Four accounting firms called the Center for Audit Quality took a hard line and forced the write- downs. That led Lynn Turner former chief accountant for the SEC and a frequent critic of the accounting profession to state “The accounting firms are doing a much better job than they did in the past.” 1 Annual Report A report issued annually by a corporation to its stockholders. It contains basic financial statements as well as management’s analysis of the firm’s past operations and future prospects. 2 Firms also provide quarterly reports but these are much less comprehensive than the annual report. In addition larger firms file even more detailed statements with the Securities and Exchange Commission SEC giving breakdowns for each major division or subsidiary. These reports called 10-K reports are made available to stockholders upon request to a company’s corporate secretary. In this chapter we focus on annual data—balance sheets at the ends of years and income statements for entire years rather than for shorter periods. 1 David Reilly “Behind Bank’s Credit Rescue Fund: “With New United Voice Auditors Stand Ground on How to Treat Crunch” The Wall Street Journal October 17 2007 p. C1. 54 Part 2 Fundamental Concepts in Financial Management

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resultsduringthepastyearanddiscussesnewdevelopmentsthatwillaffectfuture operations.Secondthereport providesthesefourbasicfinancialstatements: 1. The balance sheet which shows what assets the company owns and who has claims on those assets as of a given date—for example December 31 2008. 2. Theincomestatementwhichshowsthefirm’ssalesandcostsandthusprofits during some past period—for example 2008. 3. The statement of cash flows which shows how much cash the firm began the year with how much cash it ended up with and what it did to increase or decrease its cash. 4. The statement of stockholders’ equity which shows the amount of equity the stockholders had at the start of the year the items that increased or decreased equity and the equity at the end of the year. These statements are related to one another and taken together they provide an accounting picture of the firm’s operations and financial position. The quantitative and verbal materials are equally important. The firm’s financial statements report what has actually happened to its assets earnings and dividends over the past few years whereas management’s verbal statements attempt to explain why things turned out the way they did and what might happen in the future. For discussion purposes we use data for Allied Food Products a processor and distributor of a wide variety of food products to illustrate the basic financial statements.Alliedwasformedin1981whenseveralregionalfirmsmergedandit has grown steadily while earning a reputation as one of the best firms in its industry. Allied’s earnings dropped from 121.8 million in 2007 to 117.5 million in2008.Managementreportedthatthedropresultedfromlossesassociatedwitha drought as well as increased costs due to a three-month strike. However man- agement then went on to describe a more optimistic picture for the future stating that full operations had been resumed that several unprofitable businesses had beeneliminatedandthat2009profits were expectedtorise sharply.Ofcourse an increase in profit-ability may not occur and analysts should compare manage- ment’s past statements with subsequent results. In any event the information containedintheannualreportcanbeusedtohelpforecastfutureearningsanddividends. Therefore investors are very interested in this report. We should note that Allied’s financial statements are relatively simple and straightforward we also omitted some details often shown in the statements. Allied finances with only debt and common stock—it has no preferred stock convertibles or complex derivative securities. Also the firm has made no acqui- sitionsthatresultedingoodwillthatmustbecarriedonthebalancesheet.Finallyall of its assets are used in its basic business operations hence no nonoperating assets must be pulled out when we evaluate its operating performance. We deliberately chose such a company because this is an introductory text as such we want to explain the basics of financial analysis not wander into arcane accounting matters thatarebestlefttoaccountingandsecurityanalysiscourses.Wedopoint outsome of the pitfalls that can be encountered when trying to interpret accounting state- mentsbutweleaveittoadvancedcoursestocovertheintricaciesofaccounting. SELFTEST What is the annual report and what two types of information does it provide What four financial statements are typically included in the annual report Why is the annual report of great interest to investors Chapter 3 Financial Statements Cash Flow and Taxes 55

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3-2 THE BALANCE SHEET The balance sheet is a “snapshot” of a firm’s position at a specific point in time. Figure3-1showsthelayoutofatypicalbalancesheet.Theleftsideofthestatement shows the assets that the company owns while the right side shows the firm’s liabilities and stockholders’ equity which are claims against the firm’s assets. As Figure 3-1 indicates assets are divided into two major categories: current assets and fixed or long-term assets. Current assets consist of assets that should be converted to cashwithin one year and they include cash andcash equivalents accounts receivable and inventory. 3 Long-term assets are assets expected to be used for more than one year they include plant and equipment in addition to intellectual property such as patents and copyrights. Plant and equipment is generally reported net of accumulated depreciation. Allied’s long-term assets consist entirely of net plant and equipment and we often refer to them as “net fixed assets.” Balance Sheet A statement of a firm’s financial position at a specific point in time. 3 Allied and most other companies hold some currency in addition to a bank checking account. They may also hold short-term interest-bearing securities that can be sold and thus converted to cash immediately with a simple telephone call. These securities are called “cash equivalents” and they are generally included with checking account balances for financial reporting purposes. If a company owns stocks or other marketable securities that it regards as short-term investments these items will be shown separately on the balance sheet. Allied does not hold any marketable securities other than cash equivalents. A Typical Balance Sheet FIGURE 3-1 Total Assets Total Liabilities and Equity Current Assets Current Liabilities Long-Term Fixed Assets Long-Term Debt Cash and equivalents Accounts receivable Inventory Net plant and equipment Other long-term assets Stockholders’ Equity Common stock + Retained earnings must equal Total assets – Total liabilities Accrued wages and taxes Accounts payable Notes payable Note: This is the typical layout of a balance sheet for one year. When balance sheets for two or more years are shown assets are listed in the top section liabilities and equity in the bottom section. See Table 3-1. 56 Part 2 Fundamental Concepts in Financial Management

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The claims against assets are of two basic types—liabilities or money the companyowestoothersandstockholders’equity.Liabilitiesconsistofclaimsthat must be paid off within one year current liabilities including accounts payable accruals total of accrued wages and accrued taxes and notes payable to banks that are due within one year. Long-term debt includes bonds that mature in more than a year. Stockholders’equitycanbethoughtofintwoways.Firstitistheamountthat stockholders paid to the company when they bought shares the company sold to raise capital in addition to all of the earnings the company has retained over the years: Stockholders equity¼ Paid-in capitalþRetained earnings Theretainedearningsarenotjusttheearningsretainedinthelatestyear—theyare the cumulative total of all of the earnings the company has earned during its life. Stockholders’ equity can also be thought of as a residual: Stockholders equity¼ Total assets -- Total liabilities IfAllied had invested surplus fundsin bonds backed by subprimemortgages and the bonds’ value fell below their purchase price the true value of the firm’s assets would have declined. The amount of its liabilities would not have changed—the firm would still owe the amount it had promised to pay its creditors. Therefore the reported value of the common equity must decline. The accountants would makeaseriesofentriesandtheresultwouldbeareductioninretainedearnings— and thus in common equity. In the end assets would equal liabilities and equity and the balance sheet would balance. This example shows why common stock is moreriskythanbonds—anymistakethatmanagementmakeshasabigimpacton thestockholders.Ofcoursegainsfromgooddecisionsalsogotothestockholders so with risk comes possible rewards. Assets on the balance sheet are listed by the length of time before they will be converted to cash inventories and accounts receivable or used by the firm fixed assets. Similarly claims are listed in the order in which they must be paid: Accountspayablemustgenerallybepaidwithinafewdaysaccrualsmustalsobe paidpromptlynotespayabletobanksmustbepaidwithinoneyearandsoforth down to the stockholders’ equity accounts which represent ownership and need never be “paid off.” 3-2a Allied’s Balance Sheet Table 3-1 showsAllied’syear-endbalancesheetsfor2008and2007.Fromthe2008 statement we see that Allied had 2 billion of assets—half current and half long term.Theseassetswerefinancedwith310millionofcurrentliabilities750million of long-term debt and 940 million of common equity. Comparing the balance sheets for 2008 and 2007 we see that Allied’s assets grew by 320 million and its liabilitiesandequitynecessarilygrewbythatsameamount.Assetsmustofcourse equal liabilities and equity otherwise the balance sheet does not balance. Several additional points about the balance sheet should be noted: 1. Cash versus other assets. Although assets are reported in dollar terms only the cash and equivalents account represents actual spendable money. Accounts receivable represents credit sales that have not yet been collected. Inventories showthecostofrawmaterialsworkinprocessandfinishedgoods.Netfixed assets represent the cost of the buildings and equipment used in operations minusthedepreciationthathasbeentakenontheseassets.Attheendof2008 Alliedhas10millionofcashhenceitcouldwritecheckstotalingthatamount. The noncash assets should generate cash over time but they do not represent cashinhand.Andthecashtheywouldbringiniftheyweresoldtodaycouldbe higher or lower than the values reported on the balance sheet. Chapter 3 Financial Statements Cash Flow and Taxes 57

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2. Working capital. Current assets are often called working capital because these assets“turnover”thatistheyareusedandthenreplacedthroughouttheyear. 4 3. Net working capital. When Allied buys inventory items on credit its suppliers in effect lend it the money used to finance the inventory items. Allied could haveborrowedfromitsbankorsoldstocktoobtainthemoneybutitreceived the funds from its suppliers. These loans are shown as accounts payable and they typically are “free” in the sense that they do not bear interest. Similarly Allied pays its workers every two weeks and it pays taxes quarterly so Allied Food Products: December 31 Balance Sheets Millions of Dollars Table 3-1 2008 2007 Assets Current assets: Cash and equivalents 10 80 Accounts receivable 375 315 Inventories 615 415 Total current assets 1000 810 Net fixed assets: Net plant and equipment cost minus depreciation 1000 870 Other assets expected to last more than a year 0 0 Total assets 2000 1680 Liabilities and Equity Current liabilities: Accounts payable 60 30 Accruals 140 130 Notes payable 110 60 Total current liabilities 310 220 Long-term bonds 750 580 Total debt 1060 800 Common equity: Common stock 50000000 shares 130 130 Retained earnings 810 750 Total common equity 940 880 Total liabilities and equity 2000 1680 Notes: 1. Inventories can be valued by several different methods and the method chosen can affect both the balance sheet value and the cost of goods sold and thus net income as reported on the income statement. Similarly companies can use different depreciation methods. The methods used must be reported in the notes to the financial statements and security analysts can make adjustments when they compare companies if they think the differences are material. 2. Book value per share: Total common equity/Shares outstanding ¼ 940/50 ¼ 18.80. 3. Also note that a relatively few firms use preferred stock which we discuss in Chapter 9. Preferred stock can take several different forms but it is generally like debt because it pays a fixed amount each year. However it is like common stock because a failure to pay the preferred dividend does not expose the firm to bankruptcy. If a firm does use preferred stock it is shown on the balance sheet between Total debt and Common stock. There is no set rule on how preferred stock should be treated when financial ratios are calculated—it could be considered as debt or as equity. Bondholders often think of it as equity while stockholders think of it as debt because it is a fixed charge. In truth it is a hybrid somewhere between debt and common equity. Working Capital Current assets. 4 Any current assets not used in normal operations such as excess cash held to pay for a plant under construction are deducted and thus not included in working capital. Allied requires all of its current assets for operations. 58 Part 2 Fundamental Concepts in Financial Management

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Allied’s labor force and tax authorities provide it with loans equal to its accrued wages and taxes. If we subtract the sum of payables plus accruals from current assets the difference is called net working capital. That repre- sents the amount of money that Allied must obtain from non-free sources to carry its current assets 800 million in 2008: Net working capital¼ Current assetsð PayablesþAccrualsÞ ¼ 1000ð 60þ140Þ¼ 800 4. Other sources of funds. Most companies including Allied finance their assets with a combination of current liabilities long-term debt and common equity. Some companies also use “hybrid” securities such as preferred stock con- vertible bonds and long-term leases. Preferred stock is a hybrid between common stock and debt while convertible bonds are debt securities that give thebondholderanoptiontoexchangetheirbondsforsharesofcommonstock. In the event of bankruptcy debt is paid off first then preferred stock. Com- monstockislastreceivingapaymentonlywhensomethingremainsafterthe debt and preferred stock are paid off. 5 5. Depreciation. Most companies prepare two sets of financial statements—one is based on Internal Revenue Service IRS rules and is used to calculate taxes the other is based on generally accepted accounting principles GAAP and is used for reporting to investors. Firms often use accelerated depreciation for tax purposes but straight line depreciation for stockholder reporting. Allied uses accelerated depreciation for both. 6 6. Market values versus book values. Companies generally use GAAP to determine the values reported on their balance sheets. In most cases these accounting numbersor“bookvalues”aredifferentfromwhattheassetswouldsellforif theywereputupforsaleor “marketvalues”.ForexampleAlliedpurchased its headquarters in Chicago in 1988. Under GAAP the company must report the value of this asset at its historical cost what it originally paid for the building in 1988 less accumulated depreciation. Given that Chicago real estate prices have increased over the last 20 years the market value of the building is higher than its book value. Other assets’ market values also differ from their book values. WecanalsoseefromTable3-1thatthebookvalueofAllied’scommonequity attheendof2008was940million.Because50millionshareswereoutstanding thebookvaluepersharewas940/50¼18.80.Howeverthemarketvalueofthe common stock was 23.06. As is true for most companies in 2008 shareholders are willing to pay more than book value for Allied’s stock. This occurs in part because the values of assets haveincreased duetoinflation and in part because shareholders expect earnings to grow. Allied like most other companies has learnedhow tomake investmentsthat willincreasefuture profits. Apple provides an example of the effect of growth on the stock price. When Apple first introduced the iPod and iPhone its balance sheet didn’t budge Net Working Capital Current assets minus accounts payable and accruals. 5 Other forms of financing are discussed in Brigham and Daves Intermediate Financial Management 9th ed. Mason OH: Thomson/South-Western 2007 Chapter 20. In Fundamentals of Financial Management 12th ed. readers should refer to Chapter 20. 6 Depreciation over an asset’s life is equal to the asset’s cost but accelerated depreciation results in higher initial depreciation charges—and thus lower taxable income—than straight line. Due to the time value of money it is better to delay taxes so most companies use accelerated depreciation for tax purposes. Either accelerated or straight line can be used for stockholder reporting. Allied is a relatively conservative company hence it uses accelerated depreciation for stockholder reporting. Had Allied elected to use straight line for stockholder reporting its 2008 depreciation expense would have been 25 million lower the 1 billion shown for “net plant” on its balance sheet would have been 25 million higher and its reported income would also have been higher. Depreciation is also important in capital budgeting where we make decisions regarding new investments in fixed assets. We will have more to say about depreciation in Chapter 12 when we take up capital budgeting. Chapter 3 Financial Statements Cash Flow and Taxes 59

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but investors recognized that these were great products that would lead to higher future profits. So Apple’s stock quickly rose above its book value—it now Spring 2008 has a stock price of 185 versus a 20 book value. If a company has problems its stock price can fall below its book value. For example Countrywide Financial the largest originator of subprime mortgages saw its stock price fall to 13 versus a book value of 25 when the sub-prime market blew up in 2007. 7. The time dimension. The balance sheet is a snapshot of the firm’s financial position at a point in time—for example on December 31 2008. Thus we see thatonDecember312007Alliedhad80millionofcashbutthatbalancefell to 10 million by year-end 2008. The balance sheet changes every day as inventories rise and fall as bank loans are increased or decreased and so forth. A company such as Allied whose business is seasonal experiences especially large balance sheet changes during the year. Its inventories are low just before the harvest season but high just after the fall crops have been harvested and processed. Similarly most retailers have large inventories just before Christmas but low inventories and high accounts receivable just after Christmas. We will examine the effects of these changes in Chapter 4 when we compare companies’ financial statements and evaluate their performance. SELFTEST What is the balance sheet and what information does it provide Howistheorderinwhichitemsareshownonthebalancesheetdetermined What was Allied’s net working capital on December 31 2007 650 million What items on Allied’s December 31 balance sheet would probably be different from its June 30 values Would these differences be as large if Allied were a grocery chain rather than a food processor Explain. Inven- tories accounts receivable and accounts payable would experience seasonal fluctuations no—less seasonality 3-3 THE INCOME STATEMENT Table 3-2 showsAllied’s2007and2008incomestatements.Netsalesareshownat the top of the statement then operating costs interest and taxes are subtracted to obtain the net income available to common shareholders. We also show earnings anddividendspershareinadditiontosomeotherdataatthebottomofTable3-2. EarningspershareEPSisoftencalled“thebottomline”denotingthatofallitems on the income statement EPS is the one that is most important to stockholders. Allied earned 2.35 per share in 2008 down from 2.44 in 2007. In spite of the decline in earnings the firm still increased the dividend from 1.06 to 1.15. A typical stockholder focuses on the reported EPS but professional security analysts and managers differentiate between operating and non-operating income. Operating income is derived from the firm’s regular core business—in Allied’s case from producing and selling food products. Moreover it is calculated before deducting interest expenses and taxes which are considered to be non-operating costs. Operating income is also called EBIT or earnings before interest and taxes. Here is its equation: Operating income ðor EBITÞ¼ Sales revenues Operating costs ¼ 3000:0 2716:2 ¼ 283:8 3-1 This figure must of course match the one reported on the income statement. Income Statement A report summarizing a firm’s revenues expenses and profits during a reporting period generally a quarter or a year. Operating Income Earnings from operations before interest and taxes i.e. EBIT. 60 Part 2 Fundamental Concepts in Financial Management

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Different firms have different amounts of debt different tax carry-backs and carry-forwardsanddifferentamountsofnon-operating assets such asmarketable securities. These differences can cause two companies with identical operations to report significantly different net incomes. For example suppose two companies have identical sales operating costs and assets. However one company uses some debt and the other uses only common equity. Despite their identical oper- atingperformancesthecompanywithnodebtandthereforenointerest expense would report a higher net income because no interest was deducted from its operating income. Consequently if you want to compare two companies’ oper- ating performances it is best to focus on their operating income. 7 From Allied’s income statement we see that its operating income increased from263.0millionin2007to283.8millionin2008orby20.8million.However 7 Operating income is important for several reasons. First as we noted in Chapter 1 managers are generally compensated based on the performance of the units they manage. A division manager can control his or her division’s performance but not the firm’s capital structure policy or other corporate decisions. Second if one firm is considering acquiring another it will be interested in the value of the target firm’s operations and that value is determined by the target firm’s operating income. Third operating income is normally more stable than total income as total income can be heavily influenced by write-offs of bonds backed by subprime mortgages and the like. Therefore analysts focus on operating income when they estimate firms’ long-run stock values. Allied Food Products: Income Statements for Years Ending December 31 Millions of Dollars Except for Per-Share Data Table 3-2 2008 2007 Net sales 3000.0 2850.0 Operating costs except depreciation and amortization 2616.2 2497.0 Depreciation and amortization 100.0 90.0 Total operating costs 2716.2 2587.0 Operating income or earnings before interest and taxes EBIT 283.8 263.0 Less interest 88.0 60.0 Earnings before taxes EBT 195.8 203.0 Taxes 40 78.3 81.2 Net income 117.5 121.8 Here are some related items: Total dividends 57.5 53.0 Addition to retained earnings ¼ Net income – Total dividends 60.0 68.8 Per-share data: Common stock price 23.06 26.00 Earnings per share EPS a 2.35 2.44 Dividends per share DPS a 1.15 1.06 Book value per share BVPS 18.80 17.60 a Allied has 50 million shares of common stock outstanding. Note that EPS is based on net income available to common stockholders. Calculations of EPS and DPS for 2008 are as follows: Earnings per share ¼ EPS ¼ Net income Common shares outstanding ¼ 117500000 50000000 ¼ 2:35 Dividends per share ¼ DPS ¼ Dividends paid to common stockholders Common shares outstanding ¼ 57500000 50000000 ¼ 1:15 When a firm has options or convertibles outstanding or it recently issued new common stock a more comprehensive EPS “diluted EPS” must be calculated. Its calculation is a bit more complicated but you may refer to any financial accounting text for a discussion. Chapter 3 Financial Statements Cash Flow and Taxes 61

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its 2008 net income declined. This decline occurred because it increased its debt in 2008 and the 28 million interest increase lowered its net income. Taking a closer look at the income statement we see that depreciation and amortizationareimportantcomponentsofoperatingcosts.Recallfromaccounting that depreciation is an annual charge against income that reflects the estimated dollarcostofthe capital equipmentand othertangibleassetsthat were usedup in the production process. Amortization amounts to the same thing except that it represents the decline in value of intangible assets such as patents copyrights trademarks and goodwill. Because depreciation and amortization are so similar they are generally lumped together for purposes of financial analysis on the incomestatementandforotherpurposes.Theybothwriteofforallocatethecosts of assets over their useful lives. Even though depreciation and amortization arereported ascosts on the income statements they are not cash expenses—cash wasspent in the past when the assets being written off were acquired but no cash is paid out to cover depreciation. Therefore managers security analysts and bank loan officers who are concerned with the amount of cash a company is generating often calculate EBITDAan acronym for earnings before interest taxes depreciation and amortization. Allied has no amortization charges so Allied’s depreciation and amortization consist entirely of depreciation. In 2008 Allied’s EBITDA was 383.8 million. While the balance sheet represents a snapshot in time the income statement reports on operations over a period of time. For example during 2008 Allied had sales of 3 billion and its net income was 117.5 million. Income statements are prepared monthly quarterly and annually. The quarterly and annual statements are reported to investors while the monthly statements are used internally for planning and control purposes. Finallynotethattheincomestatementistiedtothebalancesheetthroughthe retained earnings account on the balance sheet. Net income as reported on the income statement less dividends paid is the retained earnings for the year e.g.2008.Thoseretainedearningsareaddedtothecumulativeretainedearnings from prior years to obtain the year-end 2008 balance for retained earnings. The retained earnings for the year are also reported in the statement of stockholders’ equity. All four of the statements provided in the annual report are tied together. SELFTEST Why is earnings per share called “the bottom line” What is EBIT or operating income What is EBITDA Which ismore likeasnapshotofthefirm’soperations—thebalance sheetor the income statement Explain your answer. 3-4 STATEMENT OF CASH FLOWS Net income as reported on the income statement is not cash and in finance “cash is king.” Management’s goal is to maximize the price of the firm’s stock and the valueofanyassetincludingashareofstockisbasedonthecashflowstheassetis expected to produce. Therefore managers strive to maximize the cash flows available to investors. The statement of cash flows as shown in Table 3-3 is the accountingreportthatshowshowmuchcashthefirmisgenerating.Thestatement is divided into four sections and we explain it on a line-by-line basis. 8 Depreciation The charge to reflect the cost of assets used up in the production process. Depreciation is not a cash outlay. Amortization A noncash charge similar to depreciation except that it is used to write off the costs of intangible assets. EBITDA Earnings before interest taxes depreciation and amortization. Statement of Cash Flows A report that shows how things that affect the bal- ance sheet and income statement affect the firm’s cash flows. 0 Our statement of cash flows is relatively simple because Allied is a relatively uncomplicated company. Many cash flow statements are more complicated but if you understand Table 3-3 you should be able to follow more complicated statements. 62 Part 2 Fundamental Concepts in Financial Management

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Here is a line-by-line explanation of the statement shown in Table 3-3: a. Operating Activities. This section deals with items that occur as part of normal ongoing operations. b. Net income. The first operating activity is net income which is the first source of cash. If all sales were for cash if all costs required immediate cash pay- ments and if the firm were in a static situation net income would equal cash from operations. However these conditions don’t hold so net income is not equal to cash from operations. Adjustments shown in the remainder of the statement must be made. c. Depreciation and amortization. The first adjustment relates to depreciation and amortization. Allied’s accountants subtracted depreciation it has no amorti- zation expense which is a noncash charge when they calculated net income. Thereforedepreciationmustbeaddedbacktonetincomewhennetcashflow is determined. d. Increaseininventories.Tomakeorbuyinventoryitemsthefirmmustusecash. Itmaygetsomeofthiscashasloansfromitssuppliersand workers payables and accruals but ultimately any increase in inventories requires cash. Allied increased its inventories by 200 million in 2008. That amount is shown in parentheses on Line d because it is negative i.e. a use of cash. If Allied had reduced its inventories it would have generated positive cash. e. Increase in accounts receivable. If Allied chooses to sell on credit when it makes a sale it will not immediately get the cash that it would have received had it not extended credit. To stay in business it must replace the inventory that it soldoncreditbutitwon’tyethavereceivedcashfromthecreditsale.Soifthe firm’s accounts receivable increase this will amount to a use of cash. Allied’s Allied Food Products: Statement of Cash Flows for 2008 Millions of Dollars Table 3-3 2008 a. I. Operating Activities b. Net income 117.5 c. Depreciation and amortization 100.0 d. Increase in inventories 200.0 e. Increase in accounts receivable 60.0 f. Increase in accounts payable 30.0 g. Increase in accrued wages and taxes 10.0 h. Net cash provided by used in operating activities 2.5 i. II. Long-Term Investing Activities j. Additions to property plant and equipment 230.0 k. Net cash used in investing activities 230.0 l. III. Financing Activities m. Increase in notes payable 50.0 n. Increase in bonds outstanding 170.0 o. Payment of dividends to stockholders 57.5 p. Net cash provided by financing activities 162.5 q. IV. Summary r. Net decrease in cash Net sum of I II and III 70.0 s. Cash and equivalents at the beginning of the year 80.0 t. Cash and equivalents at the end of the year 10.0 Note: Here and throughout the book parentheses are sometimes used to denote negative numbers. Chapter 3 Financial Statements Cash Flow and Taxes 63

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receivables rose by 60 million in 2008 and that use of cash is shown as a negative on Line e. If Allied had reduced its receivables this would have showed up as a positive cash flow. Once cash is received for the sale the accompanying accounts receivable will be eliminated. f. Increase in accounts payable. Accounts payable represent a loan from suppliers. Allied bought goods on credit and its payables increased by 30 million this year. That is treated as a 30 million increase in cash on Line f. If Allied had reduced its payables that would have required or used cash. Note that as Allied grows it will purchase more inventories. That will give rise to addi- tional payables which will reduce the amount of new outside funds required to finance inventory growth. g. Increase in accrued wages and taxes. The same logic applies to accruals as to accounts payable. Allied’s accruals increased by 10 million this year which means that in 2008 it borrowed an additional 10 million from its workers and tax authorities. So this represents a 10 million cash inflow. h. Net cash provided by operating activities. All of the previous items are part of normal operations—they arise as a result of doing business. When we sum them we obtain the net cash flow from operations. Allied had positive flows from net income depreciation and increases in payables and accruals but it used cash to increase inventories and to carry receivables. The net result was that operations led to a 2.5 million net outflow of cash. i. Long-Term Investing Activities. All activities involving long-term assets are covered in this section. Allied had only one long-term investment activity— the acquisition of some fixed assets as shown on Line j. If Allied had sold some fixed assets its accountants would have reported it in this section as a positive amount i.e. as a source of cash. j. Additions to property plant and equipment. Allied spent 230 million on fixed assets during the current year. This is an outflow therefore it is shown in parentheses.IfAlliedhadsoldsomeofitsfixedassetsthiswouldhavebeena cash inflow. 9 k. Net cash used in investing activities. Since Allied had only one investment activity the total on this line is the same as that on the previous line. l. Financing Activities. Allied’s financing activities are shown in this section. m. Increase in notes payable. Allied borrowed an additional 50 million from its bankthisyearwhichwasacashinflow.WhenAlliedrepaystheloanthiswill be an outflow. n. Increase in bonds long-term debt. Allied borrowed an additional 170 million from long-term investors this year giving them newly issued bonds in exchange for cash. This is shown as an inflow. When the bonds are repaid some years hence this will be an outflow. o. Payment of dividends to stockholders. Dividends are paid in cash and the 57.5 million that Allied paid out is shown as a negative amount. p. Net cash provided by financing activities. The sum of the three financing entries which is a positive 162.5 million is shown here. These funds were used to help pay for the 230 million of new plant and equipment and to help cover the deficit resulting from operations. q. Summary. This section summarizes the change in cash and cash equivalents over the year. 9 The number on Line j is “gross” investment or total expenditures. It is also equal to the change in net plant and equipment from the balance sheet plus depreciation as shown on Line c: Gross investment¼ Net investmentþ Depreciation ¼ 130 þ 100 ¼ 230. 64 Part 2 Fundamental Concepts in Financial Management

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r. Netdecreaseincash.Thenetsumoftheoperatingactivitiesinvestingactivities andfinancingactivitiesisshownhere.Theseactivitiesresultedina70million net decrease in cash during 2008 mainly due to expenditures on new fixed assets. s. Cash and equivalents at the beginning of the year. Allied began the year with the 80 million of cash which is shown here. t. Cash and equivalents at the end of the year. Allied ended the year with 10 million of cash the 80 million it started with minus the 70 million net decreaseasshownpreviously.ClearlyAllied’scashposition isweakerthan it was at the beginning of the year. Allied’s statement of cash flows should be of concern to its managers and investors.Thecompanywasabletocoverthesmalloperatingdeficitandthelarge investment in fixed assets by borrowing and reducing its beginning balances of cash and equivalents. However that can’t continue indefinitely. In the long run Section I needs to show positive operating cash flows. In addition we would expectSectionIItoshowexpendituresonfixedassetsthatareaboutequalto1its depreciation charges to replace worn out fixed assets along with 2 some additionalspendingtoprovideforgrowth.SectionIIIwouldnormallyshowsome net borrowing in addition to a “reasonable” amount of dividends. 10 Finally Section IV should show a reasonably stable cash balance from year to year. These conditions don’t hold for Allied so something should be done to correct the situation. We will consider corrective actions in Chapter 4 when we analyze the firm’s financial statements. MASSAGING THE CASH FLOW STATEMENT Profits as reported on the income statement can be “mas- saged” by changes in depreciation methods inventory val- uation procedures and so on but “cash is cash” so management can’t messwith the cashflowstatement right Nope—wrong. A recent article in The Wall Street Journal described how Ford General Motors and several other companies overstated their operating cash flows the most important section of the cash flow statement. Indeed GM reported more than twiceasmuchcashfrom operationsasit really generated 7.6 billion versus a true 3.5 billion. What happened is that when GM sold cars to a dealer on credit it createdanaccountreceivablewhichshouldbeshowninthe “Operating Activities” section as a use of cash. However GM classified these receivables as loans to dealers and reported them as a financing activity. That decision more than dou- bled the reported cash flow from operations. It didn’taffect the end-of-year cash balance but it made operations look stronger than they really were. If Allied Foods in Table 3-3 had done this the 60 million increase in receivables which is correctly shown as a use of cash would have been shifted to the “Financing Activities” section causing Allied’s cash provided by oper- ations torise from2.5 million to+57.5million. That would have made Allied look better to investors and credit ana- lysts but it would have been just smoke and mirrors. GM’s treatment was first reported by Charles Mulford a professor at Georgia Tech. The SEC then sent GM a letter that basically required it to change its procedures. The company issued a statement saying that it thought at the timethatitwasactinginaccordancewithGAAP butthat it wouldreclassify itsaccountsinthefuture. GM’s action was not in the league of WorldCom’sorEnron’s fraudulent accounting but it does show that companies sometimes do things to make their statements look better than they really are. Source: Diya Gullapalli “Little Campus Lab Shakes Big Firms” The Wall Street Journal March 1 2005 p. C3. 10 The average company pays out about one third of its earnings as dividends but there is a great deal of variation between companies depending on each company’s needs for retained earnings to support its growth. We cover dividends in detail later in the text in Distributions to Shareholders: Dividends and Share Repurchases. Chapter 3 Financial Statements Cash Flow and Taxes 65

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SELFTEST Whatisthestatementofcashflowsandwhataresomequestionsitanswers Identify and briefly explain the three types of activities shown in the state- ment of cash flows. If a company has high cash flows from operations does this mean that cash as shown on its balance sheet will also be high Explain. Not necessarily. The company may have invested heavily in working capital and/or fixed assets itmay have borrowedagreatdeal oritmaynothave had much initial cash. 3-5 STATEMENT OF STOCKHOLDERS’ EQUITY Changes in stockholders’ equity during the accounting period are reported in the statement of stockholders’ equity. Table 3-4 shows that Allied earned 117.5 mil- lion during 2008 paid out 57.5 million in common dividends and plowed 60millionbackintothebusiness.Thusthebalancesheetitem“Retainedearnings” increased from 750 million at year-end 2007 to 810 million at year-end 2008. 11 Note that “retained earnings” represents a claim against assets not assets per se. Stockholders allowed management to retain earnings and reinvest them in the business using the retained earnings to increase plant and equipment add to inventories and the like. Companies do not just pile up cash in a bank account. Thusretainedearningsasreportedonthebalancesheetdonotrepresentcashandarenot “available” for dividends or anything else. 12 SELFTEST What is the statement of stockholders’ equity designed to tell us Why do changes in retained earnings occur Explain why the following statement is true: The retained earnings account reported onthebalancesheetdoesnotrepresentcashandisnot “available” for dividend payments or anything else. Statement of Stockholders’ Equity December 31 2008 Millions of Dollars Table 3-4 COMMON STOCK Retained Earnings Total Stockholders’ Equity Shares 000 Amount Balances December 31 2007 50000 130.0 750.0 880.0 2008 Net Income 117.5 Cash Dividends 57.5 Addition to Retained Earnings 60.0 60.0 Balances December 31 2008 50000 130.0 810.0 940.0 Statement of Stockholders’ Equity A statement that shows by how much a firm’s equity changed during the year and why this change occurred. 11 If they had been applicable columns would have been used to show Additional Paid-in Capital and Treasury Stock. Also additional rows would have contained information on such things as new issues of stock treasury stock acquired or reissued stock options exercised and unrealized foreign exchange gains or losses. 12 Cash as of the balance sheet date is found in the cash account an asset account. A positive number in the retained earnings account indicates only that the firm has in the past earned income and has not paid it all out as dividends.Even thougha companyreportsrecordearningsand showsan increaseinretainedearningsit stillmay be short of cash if it is using its available cash to purchase current and fixed assets to support growth. The same situation holds for individuals. You might own a new BMW no loan many clothes and an expensive stereo hence have a high net worth but if you had only 0.23 in your pocket plus 5.00 in your checking account you would still be short of cash. 66 Part 2 Fundamental Concepts in Financial Management

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3-6 FREE CASH FLOW Thus far we have focused on financial statements as they are prepared by accountants. However accounting statements are designed primarily for use by creditors and tax collectors not for managers and stock analysts. Therefore cor- porate decision makers and security analysts often modify accounting data to meettheirneeds.Themostimportantmodificationistheconceptoffreecashflow FCFdefinedas“theamountofcashthatcouldbewithdrawnwithoutharminga firm’s ability to operate and to produce future cash flows.” Here is the equation used to calculate free cash flow: FCF¼ EBIT ð1 TÞþ Depreciation Capital expenditures þ Increase in net working capital ¼ 283:8ð1 0:4Þþ 100 230 þ Change in current assets Change in payables and accruals ¼ 170:3 þ 100ð 230þ½ð1000 810Þð 200 160ÞÞ ¼ 170:3 þ 100 230 150 ¼ 109:7 million FINANCIAL ANALYSIS ON THE INTERNET A wide range of valuable financial information is available on the Internet. With just a couple of clicks an investor can find the key financial statements for most publicly traded companies. SupposeyouarethinkingofbuyingsomeDisneystock and you want to analyze its recent performance. Here’sa partial but by no means complete list of sites you can access to get started: l One source is Yahoo’s finance web site http://finance. Here you will find updated market infor- mation along with links to a variety of interesting research sites. Enter a stock’s ticker symbol click “Go” and you will see the stock’s current price along with recentnewsaboutthecompany.Click “KeyStatistics”to find a report on the company’s key financial ratios. Links to the company’s financials income statement balance sheet and statement of cash flows can also be found. The Yahoo site also has a list of insider trans- actions that will tell you whether a company’s CEO and other key insiders are buying or selling the company’s stock. In addition the site has a message board where investors share opinions about the company and a link is provided to the company’s filings with the Securities and Exchange Commission SEC. Note also that in most cases a more complete listing of SEC filings can be found at l Two other web sites with similar information are Google Finance and MSN Money After entering a stock’s ticker symbol you will see the current stock price and a list of recent news stories. At either of these sites you will find links to a company’s financial statements and keyratios aswellasotherinformationincludinganalyst ratings historical charts earnings estimates and a summary of insider transactions. Google Finance MSN Money and Yahoo Finance allow you to export the financial statements and historical prices to an Excel spreadsheet. l Other sources for up-to-date market information are and On these sites you also can obtain stock quotes financial statements links to Wall Street research and SEC filings company profiles and charts of a firm’s stock price over time. l After accumulating all of this information you may want to look at a site that provides opinions regarding the direction of the overall market and a particular stock. Two popular sites are The Motley Fool’s web site and the site for www. l Apopular source istheonlineweb siteof TheWallStreet Journal It is a great resource but you have to subscribe to access the full range of materials. Keep in mind that this list is just a small subset of the information available online. Also sites come and go and change their content over time. New and interesting sites are constantly being added to the Internet. Free Cash Flow FCF The amount of cash that could be withdrawn from a firm without harming its ability to operate and to produce future cash flows. Chapter 3 Financial Statements Cash Flow and Taxes 67

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EBIT1 –Tistheafter-taxoperatingincomethatwouldexistifthefirmhadno debtandthereforenointerestpayments. 13 ForAlliedEBIT1–T¼ 283.81–0.4¼ 170.3. Depreciation is then added back because it is a noncash expense. Allied’s business plan called for 230 million of capital expenditures plus a 150 million increase in net working capital. Those investments are necessary to sustain ongoing operations. Allied’s FCF is negative which is not good. Note though that the negative FCF is largely attributable to the 230 million expenditure for a new processing plant. This plant is large enough to meet production for several years so another new plant will not be needed until 2012. Therefore Allied’s FCF for 2009 and the next few years should increase which means that things are not as bad as the negative FCF might suggest. Note also that most rapidly growing companies have negative FCFs—the fixedassetsandworkingcapitalneededtosupportrapidgrowthgenerallyexceed cash flows from existing operations. This is not bad provided the new invest- ments are eventually profitable and contribute to FCF. ManyanalystsregardFCFasbeingthesinglemostimportantnumberthatcan be developed from accounting statements even more important than net income. 13 After tax operating income¼ EBIT – Taxes¼ EBIT – EBITT¼ EBIT1 – T where T is the firm’s marginal tax rate. FREE CASH FLOW IS IMPORTANT FOR SMALL BUSINESSES Free cash flow is important to large companies like Allied Foods. Security analysts use FCF to help estimate the value of the stock and Allied’s managers use it to assess the value of proposed capital budgeting projects and potential merger candidates. Note though that the concept is also relevant for small businesses. Let’s assume that your aunt and uncle own a small pizza shop and that they have an accountant who prepares their financial statements. The income statement shows their accounting profit for each year. While they are cer- tainly interested in this number what they probably care more about is how much money they can take out of the business each year to maintain their standard of living. Let’s assume that the shop’s net income for 2008 was 75000. However your aunt and uncle had to spend 50000 to refurbish the kitchen and restrooms. So while the business is generating a great deal of “profit” your aunt and uncle can’t take much money out because they have to put money back into the pizza shop. Stated another way their free cash flow is much less than their net income. The required investments could be so large that they even exceed the money made from selling pizza. In this case your aunt and uncle’s free cash flow would be negative. If so this means they must find funds from other sources just to maintain the pizza business. As astute businesspeople your aunt and uncle recog- nize that investments in the restaurant such as updating the kitchen and restrooms are nonrecurring and if nothing else comesup unexpectedly your aunt anduncle should be able to take more out of the business in upcoming years when their free cash flow increases. But some businesses never seem to produce cash for their owners—they con- sistently generate positive net income but this net income is swamped by the amount of cash that has to be plowed back into the business. Thus when it comes to valuing the pizza shop or any business small or large what really matters is the amount of free cash flow that the business generates over time. Looking ahead your aunt and uncle face competition from national chains that are moving into the area. To meet the competition your aunt and uncle will have to mod- ernize the dining room. This will again drain cash from the business and reduce its free cash flow although the hope is that it will enable them to increase sales and free cash flow in the years ahead. As we will see when we discuss capital budgeting evaluating projects requires us to estimate whether the future increases in free cash flow are sufficient to more than offset the initial project cost. And this comes down to free cash flows. 68 Part 2 Fundamental Concepts in Financial Management

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After all FCF shows how much the firm can distribute to its investors. We will discussFCFagaininChapter9whichdealswithstockvaluationandinChapter11 and Chapter 12 which deal with capital budgeting. SELFTEST What is free cash flow FCF Why is FCF an important determinant of a firm’s value A company has EBIT of 30 million depreciation of 5 million and a 40 tax rate. It needs to spend 10 million on new fixed assets and 15 million to increaseitscurrentassetsanditexpectsitspayablestoincreaseby2million and its accruals to increase by 3 million. What is its free cash flow 3 million 3-7 INCOME TAXES Individualsandcorporationspayoutasignificantportionoftheirincomeastaxes so taxes are important in both personal and corporate decisions. We summarize the key aspects of the U.S. tax system for individuals in this section and for corporations in the next section using 2008 data. The details of our tax laws change fairly often—annually for things that are indexed for inflation—but the basic nature of the tax system is likely to remain intact. 3-7a Individual Taxes Individuals pay taxes on wages and salaries on investment income dividends interest and profits from the sale of securities and on the profits of proprietor- ships and partnerships. The tax rates are progressive—that is the higher one’s income the larger the percentage paid in taxes. Table 3-5 gives the tax rates that were in effect April 2008. Taxable income is defined as “gross income less a set of exemptions and deductions.” When filing a tax return in 2008 for the tax year 2007 taxpayers receivedanexemptionof3400foreachdependentincludingthetaxpayerwhich reduces taxableincome.Howeverthisexemptionisindexedtorise withinflation and the exemption is phased out taken away for high-income taxpayers. Also certain expenses including mortgage interest paid state and local income taxes paid and charitable contributions can be deducted and thus be used to reduce taxable income but again high-income taxpayers lose most of these deductions. The marginal tax rate is defined as “the tax rate on the last dollar of income.” Marginal rates begin at 10 and rise to 35. Note though that when consider- ation is given to the phase-out of exemptions and deductions to Social Security and Medicare taxes and to state taxes the marginal tax rate may actually exceed 50.AveragetaxratescanbecalculatedfromthedatainTable3-5.Forexampleif a single individual had taxable income of 35000 his or her tax bill would be 4386.25 þ 35000 – 318500.25 ¼ 4386.25 þ 787.50 ¼ 5173.75. Her average tax rate would be 5173.75/35000 ¼ 14.78 versus a marginal rate of 25. If she received a raise of 1000 bringing her income to 36000 she would have to pay 250 of it as taxes so her after-tax raise would be 750. Note too that interest income received by individuals from corporate securities is added to other income and thus is taxed at federal rates going up to 35 plus state taxes. 14 Capital gains and losses on the other hand are treated differently. Progressive Tax A tax system where the tax rate is higher on higher incomes. The per- sonal income tax in the United States which ranges from 0 on the lowest incomes to 35 on the highest incomes is progressive. Marginal Tax Rate The tax rate applicable to the last unit of a person’s income. Average Tax Rate Taxes paid divided by taxable income. 14 Under U.S. tax laws interest on most state and local government bonds called municipals or “munis” is not subjectto federalincome taxes.This has a significanteffect on thevalues of munis andon their rates of return. We discuss rates and returns in Chapter 8. Chapter 3 Financial Statements Cash Flow and Taxes 69

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Assetssuchasstocksbondsandrealestatearedefinedascapitalassets.Whenyou buyacapitalassetandlatersellitformorethanyoupaidyouearnaprofitthatis called a capital gain when you suffer a loss it is called a capital loss. If you held the asset for less than oneyearyou will have a short-term gain or loss while ifyou helditformorethanayearyouwillhavealong-termgainorloss.Thusifyoubuy 100sharesofDisneystockfor42pershareandsellitfor52pershareyoumake a capital gain of 100 × 10 or 1000. However if you sell the stock for 32 per share you will have a 1000 capital loss. Depending on how long you hold the stock you will have a short-term or long-term gain or loss. 15 If you sell the stock for exactly 42 per share you make neither a gain nor a loss so no tax is due. A short-term capital gain is added to such ordinary income as wages and interest then is taxed at the same rate as ordinary income. However long-term capital gains are taxed differently. The top rate on long-term gains in 2008 is 15. Thusifin2008youwereinthe35taxbracketanyshort-termgainsyouearned would be taxed just like ordinary income but your long-term gains would be taxedat15.Thuscapitalgainsonassetsheldformorethan12monthsarebetter than ordinary income for many people because the tax bite is smaller. However Individual Tax Rates in April 2008 Table 3-5 SINGLE INDIVIDUALS If Your Taxable Income Is You Pay This Amount on the Base of the Bracket Plus This Percentage on the ExcessovertheBase Marginal Rate Average Tax Rate at Top of Bracket Up to 7825 0 10.0 10.0 7825–31850 782.50 15.0 13.8 31850–77100 4386.25 25.0 20.4 77100–160850 15698.75 28.0 24.3 160850–349700 39148.75 33.0 29.0 Over 349700 101469.25 35.0 35.0 MARRIED COUPLES FILING JOINT RETURNS If Your Taxable Income Is You Pay This Amount on the Base of the Bracket Plus This Percentage on the ExcessovertheBase Marginal Rate Average Tax Rate at Top of Bracket Up to 15650 0 10.0 10.0 15650–63700 1565.00 15.0 13.8 63700–128500 8772.50 25.0 19.4 128500–195850 24972.50 28.0 22.4 195850–349700 43830.50 33.0 27.0 Over 349700 94601.00 35.0 35.0 Notes: a. These are the tax rates as of April 2008. The income ranges at which each tax rate takes effect are indexed with inflation so they change each year. b. The average tax rates are always below the marginal rates but the average at the top of the brackets approaches 35 as taxable income rises without limit. c. In 2007 a personal exemption of 3400 per person or dependent could be deducted from gross income to determine taxable income. Thus a husband and wife with two children would have a 2007 exemption of 4 × 3400 ¼ 13600. The exemption increases with inflation but if gross income exceeds certain limits the exemption is phased out which has the effect of raising the effective tax rate on incomes over the specified limit. In addition taxpayers can claim itemized deductions for charitable contributions and certain other items but these deductions are also phased out for high-income taxpayers. In addition there are Social Security and Medicare taxes. All of this pushes the effective tax rate to well above 35. Capital Gain or Loss The profit loss from the sale of a capital asset for more less than its pur- chase price. 15 If you have a net capital loss your capital losses exceed your capital gains for the year you can deduct up to 3000 of this loss against your other income for example salary interest and dividends. 70 Part 2 Fundamental Concepts in Financial Management

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the15maximumrateisscheduledtoincreaseto20after2010.That’sstillbetter than 35 though so from a tax standpoint capital gains income is good. Dividends received by individuals in 2008 are also taxed at the same 15 rate as long-term capital gains. However the rate is scheduled to rise after 2010. Note that since corporations pay dividends out of earnings that have already been taxed there is double taxation of corporate income—income is first taxed at the corporate rate and when what is left is paid out as dividends it is taxed again. This double taxation motivated Congress to reduce the tax rate on dividends. Taxrates ondividends andcapital gainshave varied overtimebuttheyhave generallybeenlowerthanratesonordinaryincome.Congresswantstheeconomy to grow. For growth we need investment in productive assets and low capital gains and dividend tax rates encourage investment. Individuals with money to invest understand the tax advantages associated with making equity investments in newly formed companies versus buying bonds so new ventures have an easier time attracting capital under the tax system. All in all lower capital gains and dividend tax rates stimulate capital formation and investment. One other tax feature should be addressed—the Alternative Minimum Tax AMT. The AMT was created in 1969 because Congress learned that 155 million- aires with high incomes paid no taxes because they had so many tax shelters from items such as depreciation on real estate and municipal bond interest. Under the AMT law people must calculate their tax under the “regular” system and then undertheAMTsystemwheremanydeductionsareaddedbacktoincomeandthen taxed at a special AMT rate. The law was not indexed for inflation and by 2007 literally millions of taxpayers’ found themselves subject to this very complex tax. 16 3-7b Corporate Taxes ThecorporatetaxstructureshowninTable3-6isrelativelysimple.Toillustrateif a firm had 65000 of taxable income its tax bill would be 11250. Taxes ¼ 7500 þ 0:25ð15000Þ ¼ 7500 þ 3750 ¼ 11250 Its average tax rate would be 11250/65000 ¼ 17.3. Note that corporate income above 18333333 has an average and marginal tax rate of 35. Corporate Tax Rates as of January 2008 Table 3-6 If a Corporation’s Taxable Income Is It Pays This Amount on the Base of the Bracket Plus This Percentage ontheExcessoverthe Base Marginal Rate Average Tax Rate at Top of Bracket Up to 50000 0 15 15.0 50000–75000 7500 25 18.3 75000–100000 13750 34 22.3 100000–335000 22250 39 34.0 335000–10000000 113900 34 34.0 10000000–15000000 3400000 35 34.3 15000000–18333333 5150000 38 35.0 Over 18333333 6416667 35 35.0 Alternative Minimum Tax AMT Created by Congress to make it more difficult for wealthy individuals to avoid paying taxes through the use of various deductions. 16 On December 26 2007 President Bush signed legislation that 1 increases the AMT exemption amounts for 2007 to 44350 for single taxpayers and 66250 for joint filers and 2 allows taxpayers to take several tax credits for AMT purposes through 2007. Chapter 3 Financial Statements Cash Flow and Taxes 71

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Interest and Dividends Received by a Corporation Corporations earn most of their income from operations but they may also own securities—bonds and stocks—and receive interest and dividend income. Interest incomereceivedbyacorporation is taxed asordinaryincomeat regular corporate tax rates. However dividends are taxed more favorably: 70 of dividends received is excluded from taxable income while the remaining 30 is taxed at the ordinary tax rate. 17 Thus a corporation earning more than 18333333 and paying a 40 marginal federal plus state tax rate would normally pay only 0.300.4 ¼ 0.12 ¼ 12 of its dividend income as taxes. If this firm had 10000 in pretax dividend income its after-tax dividend income would be 8800. A-T income¼ B-T incomeð1 TÞ¼ 10000ð1 0:12Þ¼ 8800 The reason for this exclusion is that when a corporation receives dividends and then pays out its own after-tax income as dividends to its stockholders the div- idends received are subjected to triple taxation: 1 The original corporation is taxed 2 the second corporation is taxed on the dividends it receives and 3 the individualswhoreceivethefinaldividendsaretaxedagain.Thisexplainsthe70 intercorporate dividend exclusion. Suppose a firm has excess cash that it does not need for operations and it plans to invest this cash in marketable securities. The tax factor favors stocks which pay dividends rather than bonds which pay interest. For example sup- poseAlliedhad100000toinvestanditcouldbuybondsthatpaid8interestor 8000 per year or stock that paid 7 in dividends or 7000. Allied is in the 40 federal-plus-state tax bracket. Therefore if Allied bought bonds and received interestitstaxonthe8000ofinterestwouldbe0.48000¼3200anditsafter- taxincomewouldbe4800.Ifitboughtstockitstaxwouldbe70000.12¼840 and its after-tax income would be 6160. Other factors might lead Allied to invest in bonds but the tax factor favors stock investments when the investor is a corporation. Interest and Dividends Paid by a Corporation AfirmlikeAlliedcanfinanceitsoperationswitheitherdebtorstock.Ifafirmuses debt it must pay interest whereas if it uses stock it is expected to pay dividends. Interest paid can be deducted from operating income to obtain taxable income but div- idendspaid cannot bededucted.ThereforeAlliedwouldneed1ofpretax incometo pay 1 of interest but since it is in the 40 federal-plus-state tax bracket it must earn 1.67 of pretax income to pay 1 of dividends: Pretax income needed to pay 1 of dividends ¼ 1 1 Tax rate ¼ 1 0:60 ¼ 1:67 WorkingbackwardifAlliedhas1.67inpretaxincomeitmustpay0.67intaxes 0.41.67 ¼ 0.67. This leaves it with after-tax income of 1.00. Table 3-7 shows the situation for a firm with 10 million of assets sales of 5millionand1.5millionofearningsbeforeinterestandtaxesEBIT.Asshown in Column 1 if the firm were financed entirely by bonds and if it made interest payments of 1.5 million its taxable income would be zero taxes would be zero anditsinvestorswouldreceivetheentire1.5million.Theterminvestorsincludes both stockholders and bondholders. However as shown in Column 2 if the firm had no debt and was therefore financed entirely by stock all of the 1.5 million of EBITwouldbetaxableincometothecorporationthetaxwouldbe15000000.40 ¼600000andinvestorswouldreceiveonly0.9millionversus1.5millionunder debt financing. Therefore the rate of return to investors on their 10 million investment is much higher when debt is used. 17 The exclusion depends on the percentage of the paying company’s stock the receiving company owns. If it owns 100 hencethe payer is a subsidiary all of the dividend will be excluded.If it owns lessthan 20 whichis the case if the stock held is just an investment 70 will be excluded. Also state tax rules vary but in our example we assume that Allied also has a state tax exclusion. 72 Part 2 Fundamental Concepts in Financial Management

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Ofcourseitisgenerallynot possible tofinance exclusively with debt and the risk of doing so would offset the benefits of the higher expected income. Still the fact that interest is a deductible expense has a profound effect on the way businesses are financed—thecorporatetaxsystemfavorsdebtfinancingoverequityfinancing.Thispoint isdiscussedinmoredetailinthechaptersoncostofcapitalandcapitalstructure. 18 Corporate Capital Gains Before 1987 corporate long-term capital gains were taxed at lower rates than corporate ordinary income so the situation was similar for corporations and individuals. Currently though corporations’ capital gains are taxed at the same rates as their operating income. Corporate Loss Carry-Back and Carry-Forward Ordinary corporate operating losses can be carried backcarry-back to each of the preceding 2 years and carried forward carry-forward for the next 20 years and used tooffset taxable incomeinthose years. For example anoperatingloss in2008 could be carried back and used to reduce taxable income in 2006 and 2007 it also could be carried forward if necessary and used in 2009 2010 up until 2028. The loss is applied to the earliest year first then to the next earliest year and so forth until losseshavebeenused uporthe 20-yearcarry-forward limithas been reached. To illustrate suppose Company X had 2 million of pretax profits taxable incomein2006and2007andthenin2008itlost12million.Itsfederal-plus-statetax rate is 40. As shown in Table 3-8 Company X would use the carry-back feature to recomputeitstaxesfor2006using2millionofthe2008operatinglossestoreducethe 2006 pretax profit to zero. This would permit it to recover the taxes paid in 2006. Therefore in 2008 it would receive a refund of its 2006 taxes because of the loss experienced in 2008. Because 10 million of the unrecovered losses would still be available X would repeat this procedure for 2007. Thus in 2008 the company would payzerotaxesfor2008andwouldreceivearefundfortaxespaidin2006and2007.It would still have 8 million of unrecovered losses to carry forward subject to the 20-year limit. This 8 million could be used until the entire 12 million loss had been usedtooffsettaxableincome.Thepurposeofpermittingthislosstreatmentistoavoid penalizing corporations whose incomes fluctuate substantially from year to year. Consolidated Corporate Tax Returns If a corporation owns 80 or more of another corporation’s stock it can aggregate incomeandfileoneconsolidatedtaxreturn.Thisallowsthelossesofonecompanyto Returns to Investors under Bond and Stock Financing Table 3-7 Use Bonds 1 Use Stock 2 Sales 5000000 5000000 Operating costs 3500000 3500000 Earnings before interest and taxes EBIT 1500000 1500000 Interest 1500000 0 Taxable income 0 1500000 Federal-plus-state taxes 40 0 600000 After-tax income 0 900000 Income to investors 1500000 900000 Rate of return on 10 million of assets 15.0 9.0 18 A company could in theory refrain from paying dividends to help prevent its stockholders from having to pay taxes on dividends received. The IRS has a rule against the improper accumulation of retained earnings that would permit this. However in our experience it is easy for firms to justify retaining earnings and we have never seen a firm have a problem with the improper accumulation rule. Tax Loss Carry-Back or Carry-Forward Ordinary corporate oper- ating losses can be carried backward for 2 years and carried forward for 20 years to offset taxable income in a given year. Chapter 3 Financial Statements Cash Flow and Taxes 73

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beusedtooffsettheprofitsofanother.Similarlyonedivision’slossescanbeusedto offset another division’s profits. No business wants to incur losses but tax offsets makeitmorefeasibleforlargemultidivisionalcorporationstoundertakeriskynew venturesor venturesthatwillsufferlosses during adevelopmentalperiod. Taxation of Small Businesses: S Corporations As we noted in Chapter 1 the Tax Code allows small businesses that meet certain conditions to be set up as corporations and thus receive the benefits of the cor- porate form of organization—especially limited liability—yet still be taxed as proprietorships or partnerships rather than as corporations. These corporations are called S corporations. Regular corporations are called C corporations. If a corporation elects S all of its income is reported as personal income by its stockholders on a pro rata basis and thus is taxed at the stockholders’ individual rates. Because the income is taxed only once this is an important benefit to the owners of small corporations in which all or most of the income earned each year will be distributed as dividends. The situation is similar for LLCs. Depreciation Depreciation plays an important role in income tax calculations—the larger the depreciation the lower the taxable income the lower the tax bill and thus the higher the operating cash flow. Congress specifies the life over which assets can be depreciated for tax purposes and the depreciation methods that can be used. We will discuss in detail how depreciation is calculated and how it affects income and cash flows when we study capital budgeting. SELFTEST Explain this statement: Our tax rates are progressive. What’s the difference between marginal and average tax rates What’s the AMT and why was it instituted What’s a muni bond and how are these bonds taxed What are long-term capitalgains Are they taxed like other income Explain. Howdoesourtaxsysteminfluencetheuseofdebtfinancingbycorporations What is the logic behind allowing tax loss carry-backs/carry-forwards Differentiate between S and C corporations. Calculation of Loss Carry-Back and Carry-Forward for 2006–2007 Using a 12 Million 2008 Loss Table 3-8 2006 2007 Original taxable income 2000000 2000000 Carry-back credit 2000000 2000000 Adjusted profit 0 0 Taxes previously paid 40 800000 800000 Difference ¼ Tax refund 800000 800000 Total refund check received in 2009: 800000 þ 800000 ¼ 1600000 Amount of loss carry-forward available for use in 2009–2028: 2008 loss 12000000 Carry-back losses used 4000000 Carry-forward losses still available 8000000 S Corporation A small corporation that under Subchapter S of the Internal Revenue Code elects to be taxed as a proprietorship or a part- nership yet retains limited liability and other benefits of the corporate form of organization. 74 Part 2 Fundamental Concepts in Financial Management

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TYING IT ALL TOGETHER The primary purposes of this chapter were to describe the basic financial state- ments to present background information on cash flows to differentiate between cash flow and accounting income and to provide an overview of the federal income tax system. In the next chapter we build on this information to analyze a firm’s financial statements and to determine its financial health. SELF-TEST QUESTIONS AND PROBLEMS Solutions Appear in Appendix A ST-1 KEY TERMS Define each of the following terms: a. Annual reportbalancesheetincomestatementstatementofcashflowsstatementof stockholders’ equity b. Stockholders’ equity retained earnings working capital net working capital c. Depreciation amortization operating income EBITDA free cash flow d. Progressive tax marginal tax rate average tax rate e. Tax loss carry-back carry-forward AMT f. Capital gain loss g. S corporation ST-2 NET INCOME AND CASH FLOW Last year Rattner Robotics had 5 million in operating incomeEBIT.Itsdepreciationexpensewas1millionitsinterestexpensewas1million and its corporate tax rate was 40. At year-end it had 14 million in current assets 3 million in accounts payable 1 million in accruals and 15 million in net plant and equipment. Assume that Rattner’s only noncash item was depreciation. a. What was the company’s net income b. What was its net working capital NWC c. Rattner had 12 million in net plant and equipment the prior year. Its net working capital has remained constant over time. What is the company’s free cash flow FCF for the year that just ended d. If the firm had 4.5 million in retained earnings at the beginning of the year and paid out total dividends of 1.2 million what was its retained earnings at the end of the year Assume that all dividends declared were actually paid. QUESTIONS 3-1 What four financial statements are contained in most annual reports 3-2 Who are some of the basic users of financial statements and how do they use them 3-3 If a “typical” firm reports 20 million of retained earnings on its balance sheet could its directors declare a20millioncashdividend withouthaving anyqualmsaboutwhat they were doing Explain your answer. 3-4 Explain the following statement: While the balance sheet can be thought of as a snapshot of a firm’s financial position at a point in time the income statement reports on operations over a period of time. Chapter 3 Financial Statements Cash Flow and Taxes 75

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3-5 FinancialstatementsarebasedongenerallyacceptedaccountingprinciplesGAAPandare audited by CPA firms. Therefore do investors need to worry about the validity of those statements Explain your answer. 3-6 What is free cash flow If you were an investor why might you be more interested in free cash flow than net income 3-7 Would it be possible for a company to report negative free cash flow and still be highly valuedbyinvestorsthatiscouldanegativefreecashfloweverbeagoodthingintheeyes of investors Explain your answer. 3-8 What is meant by the following statement: Our tax rates are progressive. 3-9 What does double taxation of corporate income mean Could income ever be subject to triple taxation Explain your answer. 3-10 How does the deductibility of interest and dividends by the paying corporation affect the choice of financing that is the use of debt versus equity PROBLEMS Easy Problems 1–3 3-1 INCOME STATEMENT Little Books Inc. recently reported 3 million of net income. Its EBIT was 6 million and its tax rate was 40. What was its interest expense Hint: Write out the headings for an income statement and fill in the known values. Then divide 3 million of net income by 1 – T ¼ 0.6 to find the pretax income. The difference between EBIT and taxable income must be the interest expense. Use this same procedure to complete similar problems. 3-2 INCOME STATEMENT Pearson Brothers recently reported an EBITDA of 7.5 million and net income of 1.8 million. It had 2.0 million of interest expense and its corporate tax rate was 40. What was its charge for depreciation and amortization 3-3 STATEMENT OF STOCKHOLDERS’ EQUITY In its most recent financial statements Newhouse Inc. reported 50 million of net income and 810 million of retained earnings. The previous retained earnings were 780 million. How much in dividends were paid to shareholders during the year Assume that all dividends declared were actually paid. Intermediate Problems 4–7 3-4 BALANCESHEET Whichofthefollowingactionsaremostlikelytodirectlyincreasecashas shown on a firm’s balance sheet Explain and state the assumptions that underlie your answer. a. It issues 2 million of new common stock. b. It buys new plant and equipment at a cost of 3 million. c. It reports a large loss for the year. d. It increases the dividends paid on its common stock. 3-5 STATEMENT OF STOCKHOLDERS’ EQUITY Computer World Inc. paid out 22.5 million in total common dividends and reported 278.9 million of retained earnings at year-end. The prior year’s retained earnings were 212.3 million. What was the net income Assume that all dividends declared were actually paid. 3-6 STATEMENT OF CASH FLOWS W.C. Cycling had 55000 in cash at year-end 2007 and 25000 in cash at year-end 2008. Cash flow from long-term investing activities totaled 250000 and cash flow from financing activities totaled þ170000. a. What was the cash flow from operating activities b. Ifaccrualsincreasedby25000receivablesandinventoriesincreasedby100000and depreciation and amortization totaled 10000 what was the firm’s net income 3-7 FREE CASH FLOW Bailey Corporation’s financial statements dollars and shares are in millions are provided here. 76 Part 2 Fundamental Concepts in Financial Management

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Balance Sheets as of December 31 2008 2007 Assets Cash and equivalents 14000 13000 Accounts receivable 30000 25000 Inventories 28125 21000 Total current assets 72125 59000 Net plant and equipment 50000 47000 Total assets 122125 106000 Liabilities and Equity Accounts payable 10800 9000 Notes payable 6700 5150 Accruals 7600 6000 Total current liabilities 25100 20150 Long-term bonds 15000 15000 Total debt 40100 35150 Common stock 5000 shares 50000 50000 Retained earnings 32025 20850 Common equity 82025 70850 Total liabilities and equity 122125 106000 Income Statement for Year Ending December 31 2008 Sales 214000 Operating costs excluding depreciation and amortization 170000 EBITDA 44000 Depreciation amortization 5000 EBIT 39000 Interest 1750 EBT 37250 Taxes 40 14900 Net income 22350 Dividends paid 11175 a. What was net working capital for 2007 and 2008 b. What was Bailey’s 2008 free cash flow c. Construct Bailey’s 2008 statement of stockholders’ equity. Challenging Problems 8–10 3-8 INCOME STATEMENT Hermann Industries is forecasting the following income statement: Sales 8000000 Operating costs excluding depr. amort. 4400000 EBITDA 3600000 Depreciation amortization 800000 EBIT 2800000 Interest 600000 EBT 2200000 Taxes 40 880000 Net income 1320000 The CEO would like to see higher sales and a forecasted net income of 2500000. Assume that operating costs excluding depreciation and amortization are 55 of sales and that depreciationandamortizationandinterestexpenseswillincreaseby10.Thetaxratewhich is 40 will remain the same. What level of sales would generate 2500000 in net income Chapter 3 Financial Statements Cash Flow and Taxes 77

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3-9 FINANCIAL STATEMENTS The Davidson Corporation’s balance sheet and income statement are provided here. Davidson Corporation: Balance Sheet as of December 31 2008 Millions of Dollars Assets Liabilities and Equity Cash and equivalents 15 Accounts payable 120 Accounts receivable 515 Notes payable 220 Inventories 880 Accruals 280 Total current assets 1410 Total current liabilities 620 Net plant and equipment 2590 Long-term bonds 1520 Total debt 2140 Common stock 100 million shares 260 Retained earnings 1600 Common equity 1860 Total assets 4000 Total liabilities and equity 4000 Davidson Corporation: Income Statement For Year Ending December 31 2008 Millions of Dollars Sales 6250 Operating costs excluding depreciation and amortization 5230 EBITDA 1020 Depreciation amortization 220 EBIT 800 Interest 180 EBT 620 Taxes 40 248 Net income 372 Common dividends paid 146 Earnings per share 3.72 a. Construct the statement of stockholders’ equity for December 31 2008. b. How much money has been reinvested in the firm over the years c. At the present time how large a check could be written without it bouncing d. How much money must be paid to current creditors within the next year 3-10 FREE CASH FLOW Financial information for Powell Panther Corporation is shown here. Powell Panther Corporation: Income Statements For Year Ending December 31 Millions of Dollars 2008 2007 Sales 1200.0 1000.0 Operating costs excluding depreciation and amortization 1020.0 850.0 EBITDA 180.0 150.0 Depreciation amortization 30.0 25.0 Earnings before interest and taxes 150.0 125.0 Interest 21.7 20.2 Earnings before taxes 128.3 104.8 Taxes 40 51.3 41.9 Net income 77.0 62.9 Common dividends 60.5 46.4 78 Part 2 Fundamental Concepts in Financial Management

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Powell Panther Corporation: Balance Sheets as of December 31 Millions of Dollars 2008 2007 Assets Cash and equivalents 12.0 10.0 Accounts receivable 180.0 150.0 Inventories 180.0 200.0 Total current assets 372.0 360.0 Net plant and equipment 300.0 250.0 Total assets 672.0 610.0 Liabilities and Equity Accounts payable 108.0 90.0 Notes payable 67.0 51.5 Accruals 72.0 60.0 Total current liabilities 247.0 201.5 Long-term bonds 150.0 150.0 Total debt 397.0 351.5 Common stock 50 million shares 50.0 50.0 Retained earnings 225.0 208.5 Common equity 275.0 258.5 Total liabilities and equity 672.0 610.0 a. What was net working capital for 2007 and 2008 b. What was the 2008 free cash flow c. How would you explain the large increase in 2008 dividends COMPREHENSIVE/SPREADSHEET PROBLEM 3-11 FINANCIAL STATEMENTS CASH FLOW AND TAXES Laiho Industries’ 2007 and 2008 balance sheets in thousands of dollars are shown. 2008 2007 Cash 102850 89725 Accounts receivable 103365 85527 Inventories 38444 34982 Total current assets 244659 210234 Net fixed assets 67165 42436 Total assets 311824 252670 Accounts payable 30761 23109 Accruals 30477 22656 Notes payable 16717 14217 Total current liabilities 77955 59982 Long-term debt 76264 63914 Total liabilities 154219 123896 Common stock 100000 90000 Retained earnings 57605 38774 Total common equity 157605 128774 Total liabilities and equity 311824 252670 a. Sales for 2008 were 455150000 and EBITDA was 15 of sales. Furthermore depreciationandamortizationwere11ofnetfixedassetsinterestwas8575000the corporate tax rate was 40 and Laiho pays 40 of its net income in dividends. Given this information construct the firm’s 2008 income statement. Chapter 3 Financial Statements Cash Flow and Taxes 79

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b. Constructthestatementofstockholders’equityfortheyearendingDecember312008 and the 2008 statement of cash flows. c. Calculate 2007 and 2008 net working capital and 2008 free cash flow. d. If Laiho increased its dividend payout ratio what effect would this have on corporate taxes paidWhateffect would this haveontaxes paidbythecompany’sshareholders INTEGRATED CASE D’LEON INC. PART I 3-1 FINANCIALSTATEMENTSANDTAXES DonnaJamisona2003graduateoftheUniversityofFloridawith4yearsof bankingexperiencewasrecentlybroughtinasassistanttothechairpersonoftheboardofD’LeonInc.asmallfood producerthatoperatesinnorthFloridaandwhosespecialtyishigh-qualitypecanandothernutproductssoldinthe snack foods market. D’Leon’s president Al Watkins decided in 2007 to undertake a major expansion and to “go national” in competition with Frito-Lay Eagle and other major snack foods companies. Watkins believed that D’Leon’s products were of higher quality than the competition’s that this quality differential would enable it to charge a premium price and that the end result would be greatly increased sales profits and stock price. The company doubled its plant capacity opened new sales offices outside its home territory and launched an expensiveadvertisingcampaign.D’Leon’sresultswerenotsatisfactorytoputitmildly.Itsboardofdirectorswhich consisted of its president vice president and major stockholders who were all local businesspeople was most upsetwhen directorslearnedhowthe expansion wasgoing.Unhappysupplierswerebeing paidlateandthebank was complaining about the deteriorating situation threatening to cut off credit. As a result Watkins was informed that changes would have to be made—and quickly otherwise he would be fired. Also at the board’s insistence Donna Jamison was brought in and given the job of assistant to Fred Campo a retired banker who was D’Leon’s chairpersonandlargeststockholder.Campoagreedtogiveupafewofhisgolfingdaysandhelpnursethecompany back to health with Jamison’shelp. Jamison began by gathering the financial statements and other data given in Tables IC 3-1 IC 3-2 IC 3-3 and IC 3-4. Assume that you are Jamison’s assistant. You must help her answer the following questions for Campo.Note:WewillcontinuewiththiscaseinChapter4andyouwillfeelmorecomfortablewiththeanalysis there. But answering these questions will help prepare you for Chapter 4. Provide clear explanations. a. Whateffectdidtheexpansionhaveonsalesafter-taxoperatingincomenetworkingcapitalNWCandnet income b. What effect did the company’s expansion have on its free cash flow c. D’Leon purchases materials on 30-day terms meaning that it is supposed to pay for purchases within 30 days of receipt. Judging from its 2008 balance sheet do you think that D’Leon pays suppliers on time Explain including what problems might occur if suppliers are not paid in a timely manner. d. D’Leon spends money for labor materials and fixed assets depreciation to make products—and spends stillmoremoneytosellthoseproducts.Thenthefirmmakessalesthatresultinreceivableswhicheventually resultincashinflows. DoesitappearthatD’Leon’ssalespriceexceedsitscostsperunitsoldHowdoesthis affect the cash balance e. Suppose D’Leon’s sales manager told the sales staff to start offering 60-day credit terms rather than the 30-day terms now being offered. D’Leon’s competitors react by offering similar terms so sales remain constant. What effect would this have on the cash account How would the cash account be affected if sales doubled as a result of the credit policy change f. Can you imagine a situation in which the sales price exceeds the cost of producing and selling a unit of output yet a dramatic increase in sales volume causes the cash balance to decline Explain. g. Did D’Leon finance its expansion program with internally generated funds additions to retained earnings plus depreciation or with external capital How does the choice of financing affect the company’s financial strength h. Refer to Tables IC 3-2 and IC 3-4. Suppose D’Leon broke even in 2008 in the sense that sales revenues equaled total operating costs plus interest charges. Would the asset expansion have caused the company to experience a cash shortage that required it to raise external capital Explain. i. IfD’Leon startsdepreciating fixed assetsover7 years ratherthan 10 yearswould thataffect 1 thephysical stock of assets 2 the balance sheet account for fixed assets 3 the company’s reported net income and 4 the company’s cash position Assume that the same depreciation method is used for stockholder reporting and for tax calculations and that the accounting change has no effect on assets’ physical lives. j. Explainhowearningspersharedividendspershareandbookvaluepersharearecalculatedandwhatthey mean. Why does the market price per share not equal the book value per share k. Explain briefly the tax treatment of 1 interest and dividends paid 2 interest earned and dividends received 3 capital gains and 4 tax loss carry-back and carry-forward. How might each of these items affect D’Leon’s taxes 3-2 80 Part 2 Fundamental Concepts in Financial Management

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Balance Sheets Table IC 3-1 2008 2007 Assets Cash 7282 57600 Accounts receivable 632160 351200 Inventories 1287360 715200 Total current assets 1926802 1124000 Gross fixed assets 1202950 491000 Less accumulated depreciation 263160 146200 Net fixed assets 939790 344800 Total assets 2866592 1468800 Liabilities and Equity Accounts payable 524160 145600 Notes payable 636808 200000 Accruals 489600 136000 Total current liabilities 1650568 481600 Long-term debt 723432 323432 Common stock 100000 shares 460000 460000 Retained earnings 32592 203768 Total equity 492592 663768 Total liabilities and equity 2866592 1468800 Income Statements Table IC 3-2 2008 2007 Sales 6034000 3432000 Cost of goods sold 5528000 2864000 Other expenses 519988 358672 Total operating costs excluding depreciation and amortization 6047988 3222672 Depreciation and amortization 116960 18900 EBIT 130948 190428 Interest expense 136012 43828 EBT 266960 146600 Taxes 40 106784 a 58640 Net income 160176 87960 EPS 1.602 0.880 DPS 0.110 0.220 Book value per share 4.926 6.638 Stock price 2.25 8.50 Shares outstanding 100000 100000 Tax rate 40.00 40.00 Lease payments 40000 40000 Sinking fund payments 0 0 Note: a The firm had sufficient taxable income in 2006 and 2007 to obtain its full tax refund in 2008. Chapter 3 Financial Statements Cash Flow and Taxes 81

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Statement of Cash Flows 2008 Table IC 3-4 Operating Activities Net income 160176 Depreciation and amortization 116960 Increase in accounts payable 378560 Increase in accruals 353600 Increase in accounts receivable 280960 Increase in inventories 572160 Net cash provided by operating activities 164176 Long-Term Investing Activities Additions to property plant and equipment 711950 Net cash used in investing activities 711950 Financing Activities Increase in notes payable 436808 Increase in long-term debt 400000 Payment of cash dividends 11000 Net cash provided by financing activities 825808 Summary Net decrease in cash 50318 Cash at beginning of year 57600 Cash at end of year 7282 Statement of Stockholders’ Equity 2008 Table IC 3-3 COMMON STOCK Retained Earnings Total Stockholders’ Equity Shares Amount Balances 12/31/07 100000 460000 203768 663768 2008 Net Income 160176 Cash Dividends 11000 Addition Subtraction to Retained Earnings 171176 171176 Balances 12/31/08 100000 460000 32592 492592 82 Part 2 Fundamental Concepts in Financial Management

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Access the Thomson ONE problems through the CengageNOW™ web site. Use the Thomson ONE—Business School Edition online database to answer this chapter’s questions. Exploring Starbucks’ Financial Statements Over the past decade Starbucks coffee shops have become an increasingly familiar part of the urban landscape. Currently 2008 the company operates more than 8000 coffee shops in all 50 states in the DistrictofColumbiaandininternationalmarketsandin2008ithadapproximately145000employees. ThomsonONEcanaccessawealthoffinancialinformationforcompaniessuchasStarbucks.Tofind somebackgroundinformationbeginbyenteringthecompany’stickersymbolSBUXandthenselecting “GO.” On the opening screen you will see a great deal of useful information including a summary of whatStarbucksdoesachartofitsrecentstockpriceEPSestimatesrecentnewsstoriesandalistofkey financial data and ratios. In researching a company’s operating performance a good place to start is the recent stock price performance. At the top of the Stock Price Chart click on the section labeled “Interactive Chart.” From thispointyoucanobtainachartofthecompany’sstockpriceperformancerelativetotheoverallmarket as measured by the SP 500 between 1998 and 2008. To obtain a 10-year chart go to “Time Frame” click on the down arrow and select “10 years.” Then click on “Draw” a 10-year price chart should appear. As you can see Starbucks has had its ups and downs. But the company’s overall performance has been quite strong and it has beaten the overall market handily. You can also find Starbucks’ recent financial statements. Click on Financials to find the company’s annualbalancesheetsforthepast5years.SelectingThomsonFinancialsprovidesbalancesheetsincome statements and statements of cash flows for various time periods. Clicking on the Microsoft Excel icon downloads these statements directly to a spreadsheet. Discussion Questions 1. LookingatthemostrecentyearavailablewhatistheamountoftotalassetsonStarbucks’balancesheetWhat percentageisfixedassetssuchasplantandequipmentWhatpercentageiscurrentassetsHowmuchhasthe company grown over the years that are shown 2. Does Starbucks have very much long-term debt What are the chief ways in which Starbucks has financed assets 3. Looking at the statement of cash flows what factors can explain the change in the company’s cash position over the last couple of years 4. Looking at the income statement what are the company’s most recent sales and net income Over the past several years what has been the sales growth rate What has been the growth rate in net income 5. Over the past few years has there been a strong correlation between stock price performance and reported earnings Explain. Chapter 3 Financial Statements Cash Flow and Taxes 83

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CHAPTER 4 Analysis of Financial Statements Can You Make Money Analyzing Stocks For the past 40 years a debate has raged over the question posed above. Some argue that the stock market is highly efficient and that all available information regarding a stock is already reflected in its price. The “efficient market advocates” point out that there are thousands of smart well-trained analysts working for institu- tions with billions of dollars. These analysts have access to the latest information and they spring into action—buying or selling—as soon as a firm releases any information that has a bearing on its future profits. The “efficient markets advocates” also point out that few mutual funds which hire good people and pay them well actually beat the averages. If these experts earn only average returns how can the rest of us expect to beat the market Othersdisagreearguingthatanalysiscanpay off. They point out that some fund managers perform better than average year after year. Also they note that some “activist” investors analyze firms carefully identify those with weaknesses that appear to be correctable and then persuade their managers to take actions to improve the firms’ performances. One such investor is Warren Buffett perhaps the best known U.S. investor. Another is Carl Icahn—not a household name butsomeonewhoseinvestmentshavemadehim the 18th wealthiest American. Buffett and Icahn now have billions of dollars to work with and those billions give them better access to corpo- rate managers than most of us have. However neither of them started as billionaires—they workedtheirwayupdoingcarefulanalysisofthe type described in this chapter. When investors learn that an activist investor such as Icahn has bought a stock the price of that stock generally rises. Thus in the fall of 2007 Icahn began buying shares in BEA Systems a billion dollar software company that had been sellingforabout10.50.Onceinvestorslearnedof Icahn’s interest the price jumped to 18.94. You can bet that Icahn and his staff went through the type of analysis discussed in this chapter identi- fied BEA’s strengths and weaknesses and con- cluded that managerial actions could boost the ª CHIP SOMODEVILLA/GETTY IMAGES 84

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PUTTING THINGS IN PERSPECTIVE Theprimarygoaloffinancialmanagementistomaximizeshareholders’wealthnot accounting measures such as net income or EPS. However accounting data influ- ence stock prices and this data can be used to see why a company is performing the way it is and where it is heading. Chapter 3 described the key financial state- ments and showed how they change as a firm’s operations change. Now in Chapter 4 we show how the statements are used by managers to improve the firm’s stock price by lenders to evaluate the likelihood that borrowers will be able to pay off loans and by security analysts to forecast earnings dividends and stock prices. If management is to maximize a firm’s value it must take advantage of the firm’s strengths and correct its weaknesses. Financial analysis involves 1 com- paring the firm’s performance to that of other firms in the same industry and 2 evaluating trends in the firm’s financial position over time. These studies help managers identify deficiencies and then take corrective actions. In this chapter we focus on how managers and investors evaluate a firm’s financial position. Then in later chapters we examine the types of actions managers can take to improve future performance and thus increase the firm’s stock price. The most important ratio is the ROE or return on equity which tells us how much stockholders are earning on the funds they provide to the firm. When ROE is high thestock price also tends to behigh so actions thatincrease ROE generallyin- crease the stock price. Other ratios provide information about how well assets such as inventory accounts receivable and fixed assets are managed and about the firm’s capital structure. Managers use ratios related to these factors to help develop plans to improve ROE. When you finish this chapter you should be able to: l Explain what ratio analysis is. l List the 5 groups of ratios and identify calculate and interpret the key ratios in each group. In addition discuss each ratio’s relationship to the balance sheet and income statement. l Discuss why ROE is the key ratio under management’s control how the other ratios affect ROE and explain how to use the DuPont equation to see how the ROE can be improved. l Compare a firm’s ratios with those of other firms benchmarking and analyze a given firm’s ratios over time trend analysis. l Discuss the tendency of ratios to fluctuate over time which may or may not be problematic. Explain how they can be influenced by accounting practices and other factors and why they must be used with care. firm’s cash flows and value. Icahn’s views were shared by Larry Ellison chairperson of Oracle Corporation a 17 billion software company. As we write this Oracle and Icahn have combined forces and are trying to force a change in BEA’s operations. Thousands of analysts are doing similar analyses ofthousandsofothercompaniestryingtofindthenextBEA and becoming the next Buffett or Icahn. It’s fun and unless the efficient markets folks are correct it can be profitable. Chapter 4 Analysis of Financial Statements 85

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4-1 RATIO ANALYSIS Ratios help us evaluate financial statements. For example at the end of 2008 Allied Food Products had 1060 million of debt and interest charges of 88 million while Midwest Products had 52 million of debt and interest charges of 4 million. Which company is stronger The burden of these debts and the companies’abilitytorepaythemcanbestbeevaluatedbycomparingeachfirm’s debt to its assets and comparing interest expense to the income and cash avail- abletopaythatinterest.Ratiosareusedtomakesuchcomparisons.Wecalculate Allied’sratiosfor2008usingdatafromthebalancesheetsandincomestatements given in Tables 3-1 and 3-2. We also evaluate the ratios relative to food industry averages using data in millions of dollars. 1 As you will see we can calculate many different ratios with different ones used to examine different aspects of the firm’s operations. You will get to know some ratios by name but it’sbetter to understand what they are designed to do than to memorize names and equations. We divide the ratios into five categories: 1. Liquidity ratioswhich give us an ideaof the firm’s abilityto pay off debts that are maturing within a year. 2. Asset management ratios which give us an idea of how efficiently the firm is using its assets. 3. Debt management ratioswhich giveusanideaofhowthe firmhasfinanced its assets as well as the firm’s ability to repay its long-term debt. 4. Profitability ratios which give us an idea of how profitably the firm is oper- ating and utilizing its assets. 5. Market value ratios which bring in the stock price and give us an idea of what investors think about the firm and its future prospects. Satisfactoryliquidityratiosarenecessaryifthefirmistocontinueoperating.Good asset management ratios are necessary for the firm to keep its costs low and thus itsnetincomehigh.Debtmanagementratiosgiveusanideaofhowriskythefirm isandhowmuchofitsoperatingincomemustbepaidtobondholdersrather than stockholders. Profitability ratios bring together the asset and debt management ratios and show their effects on ROE. Finally market value ratios tell us what investors think about the company and its prospects. Alloftheratiosareimportantbutdifferentonesaremoreimportantforsome companies than for others. For example if a firm borrowed too much in the past and its debt now threatens to drive it into bankruptcy the debt ratios are key. Similarly if a firm expanded too rapidly and now finds itself with excess inven- tory and manufacturing capacity the asset management ratios take center stage. The ROE is always important but a high ROE depends on maintaining liquidity on efficient asset management and on the proper use of debt. Managers are of 1 Financial statement data for most publicly traded firms can be obtained from the Internet. A couple of free sites that provide this information include Google Finance and Yahoo Finance. These sites provide the financial statements which can be copied to an Excel file and used to create your own ratios but the web sites also provide calculated ratios. In addition to the ratios discussed in this chapter financial analysts often employ a tool known as common size analysis. To form a common size balance sheet simply divide each asset liability and equity item by total assets and then express the results as percentages. To develop a common size income statement divide each income statement item by sales. The resultant percentage statements can be compared with statements of larger or smaller firms or with those of the same firm over time. One would normally obtain the basic statements from a source such as Google Finance and copy them to Excel so constructing common size statements is quite easy. Note too that industry average data are generally given as percentages which makes them easy to compare with a firm’s own common size statements. 86 Part 2 Fundamental Concepts in Financial Management

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course vitally concerned with the stock price but managers have little direct controloverthestockmarketwhiletheydohavecontrolovertheirfirm’sROE.So ROE tends to be the main focal point. 4-2 LIQUIDITY RATIOS The liquidity ratios help answer this question: Will the firm be able to pay off its debtsastheycomedueandthusremainaviableorganizationIftheanswerisno liquidity must be the first order of business. A liquid asset is one that trades in an active market and thus can be quickly converted to cash at the going market price. As shown in Table 3-1 in Chapter 3 Allied has 310 million of debt that must be paid off within the coming year. Will ithavetroublemeetingthatobligationAfullliquidityanalysisrequirestheuseof a cash budget which we discuss in the working capital management chapter however by relating cash and other current assets to current liabilities ratio analysis provides a quick and easy-to-use measure of liquidity. Two of the most commonly used liquidity ratios are discussed below. 4-2a Current Ratio The primary liquidity ratio is the current ratio which is calculated by dividing current assets by current liabilities: Current ratio¼ Current assets Current liabilities ¼ 1000 310 ¼ 3:2 Industry average¼ 4:2 Current assets include cash marketable securities accounts receivable and inventories. Allied’s current liabilities consist of accounts payable accrued wages and taxes and short-term notes payable to its bank all of which are due within one year. If a company is having financial difficulty it typically begins to pay its accounts payable more slowly and to borrow more from its bank both of which increase current liabilities. If current liabilities are rising faster than current assets the current ratio will fall and this is a sign of possible trouble. Allied’s current ratiois3.2whichiswellbelowtheindustryaverageof4.2.Thereforeitsliquidity position is somewhat weak but by no means desperate. 2 Althoughindustryaveragefiguresarediscussedlaterinsomedetailnotethat anindustryaverageisnotamagicnumberthatallfirmsshouldstrivetomaintain infactsomeverywell-managedfirmsmaybeabovetheaveragewhileothergood firms are below it. However if a firm’s ratios are far removed from the averages for its industry an analyst should be concerned about why this variance occurs. Thus a deviation from the industry average should signal the analyst or man- agement to check further. Note too that a high current ratio generally indicates a very strong safe liquidity position it might also indicate that the firm has too much old inventory that will have to be written off and too many old accounts receivable that may turn into bad debts. Or the high current ratio might indicate that the firm has too much cash receivables and inventory relative to its sales in Liquid Asset An asset that can be con- verted to cash quickly without having to reduce the asset’s price very much. Liquidity Ratios Ratios that show the rela- tionship of a firm’s cash and other current assets to its current liabilities. Current Ratio This ratio is calculated by dividing current assets by current liabilities. It indi- cates the extent to which current liabilities are cov- ered by those assets expected to be converted to cash in the near future. 2 Since current assets should be convertible to cash within a year it is likely that they could be liquidated at close to their stated value. With a current ratio of 3.2 Allied could liquidate current assets at only 31 of book value and still pay off current creditors in full: 1/3.2 ¼ 0.31 or 31. Note also that 0.311000 ¼ 310 the current liabilities balance. Chapter 4 Analysis of Financial Statements 87

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whichcasetheseassetsarenotbeingmanagedefficiently.Soitisalwaysnecessary to look deeply into the full set of ratios before forming a judgment as to how well the firm is performing. 4-2b Quick or Acid Test Ratio The second liquidity ratio is the quick or acid test ratio which is calculated by deducting inventories from current assets and then dividing the remainder by current liabilities: Quick or acid test ratio ¼ Current assets Inventories Current liabilities ¼ 385 310 ¼ 1:2 Industry average ¼ 2:2 Inventoriesaretypicallytheleastliquidofafirm’scurrentassetsandifsalesslow down they might not be converted to cash as quickly as expected. Also inven- tories are the assets on which losses are most likely to occur in the event of liquidation.Thereforethequick ratiowhich measuresthefirm’sabilitytopayoff short-term obligations without relying on the sale of inventories is important. The industry average quick ratio is 2.2 so Allied’s 1.2 ratio is relatively low. Still if the accounts receivable can be collected the company can pay off its current liabilities even if it has trouble disposing of its inventories. SELFTEST What are the characteristics of a liquid asset Give examples of some liquid assets. What question are the two liquidity ratios designed to answer Which is the least liquid of the firm’s current assets A company has current liabilities of 500 million and its current ratio is 2.0. What is the total of its current assets 1000 million If this firm’s quick ratio is 1.6 how much inventory does it have 200 million Hint: To answer this problem and some of the other problems in this chapter write out the equation for the ratio in the question insert the given data and solve for the missing value. Examples: Current ratio ¼ 2.0 ¼ CA/CL ¼ CA/500 so CA ¼ 2500 ¼ 1000 Quick ratio¼ 1.6 ¼ CA− Inventories/CL ¼ 1000− Inventories/500 so 1000 − Inventories ¼ 1.6500 and Inventories ¼ 1000 − 800 ¼ 200 4-3 ASSET MANAGEMENT RATIOS The second group of ratios the asset management ratios measure how effec- tivelythefirmismanagingitsassets.Theseratiosanswerthisquestion:Doesthe amount of each type of asset seem reasonable too high or too low in view of currentandprojectedsalesTheseratiosareimportantbecausewhenAlliedand other companies acquire assets they must obtain capital from banks or other sourcesandcapital isexpensive.Thereforeif Alliedhastoomanyassetsitscost ofcapitalwillbetoohighwhichwilldepressitsprofits.Ontheotherhandifits assets are too low profitable sales will be lost. So Allied must strike a balance Quick Acid Test Ratio This ratio is calculated by deducting inventories from current assets and then dividing the remain- der by current liabilities. Asset Management Ratios A set of ratios that mea- sure how effectively a firm is managing its assets. 88 Part 2 Fundamental Concepts in Financial Management

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betweentoomanyandtoofewassetsandtheassetmanagementratioswillhelp it strike this proper balance. 4-3a Inventory Turnover Ratio “Turnover ratios” divide sales by some asset: Sales/Various assets. As the name implies these ratios show how many times the particular asset is “turned over” during the year. Here is the inventory turnover ratio: Inventory turnover ratio¼ Sales Inventories ¼ 3000 615 ¼ 4:9 Industry average¼ 10:9 As a rough approximation each item of Allied’s inventory is sold and restocked or“turnedover”4.9timesperyear.Turnoverisatermthatoriginatedmanyyears ago with the old Yankee peddler who would load up his wagon with pots and pans then go off on his route to peddle his wares. The merchandise was called workingcapitalbecauseitwaswhatheactuallysoldor“turnedover”toproduce his profits whereas his “turnover” was the number of trips he took each year. Annual sales divided by inventory equaled turnover or trips per year. If he made 10 trips per year stocked 100 pots and pans and made a gross profit of 5 per itemhisannualgrossprofitwas100510¼5000.Ifhewentfasterandmade 20 trips per year his gross profit doubled other things held constant. So his turnover directly affected his profits. Allied’s inventory turnover of 4.9 is much lower than the industry average of 10.9. This suggests that it is holding too much inventory. Excess inventory is of course unproductive and represents an investment with a low or zero rate of return. Allied’s low inventory turnover ratio also makes us question the current ratio. With such a low turnover the firm may be holding obsolete goods that are not worth their stated value. 3 Note that sales occur over the entire year whereas the inventory figure is for one point in time. For this reason it might be better to use an average inventory measure. 4 Ifthebusinessishighlyseasonaloriftherehasbeenastrongupwardor downward sales trend during the year it is especially useful to make an adjust- ment. Allied’s sales are not growing especially rapidly though and to maintain comparability with industry averages we used year-end rather than average inventories. 4-3b Days Sales Outstanding AccountsreceivableareevaluatedbythedayssalesoutstandingDSOratioalso called the average collection period ACP. 5 It is calculated by dividing accounts receivable by the average daily sales to find how many days’ sales are tied up in Inventory Turnover Ratio This ratio is calculated by dividing sales by inventories. 3 Our measure of inventory turnover is frequently used by established compilers of financial ratio statistics such as ValueLine and Dun Bradstreet.However you shouldrecognizethat other sourcescalculateinventory using cost of goods sold in place of sales in the formula’s numerator. The rationale for this alternative measure is that sales are stated at market prices so if inventories are carried at cost as they generally are the calculated turnover overstates the true turnover ratio. Therefore it might be more appropriate to use cost of goods sold in place of sales in the formula’s numerator. When evaluating and comparing financial ratios from various sources it is important to understand how those sources are specifically calculating financial ratios. 4 Preferably the average inventory value should be calculated by summing the monthly figures during the year and dividing by 12. If monthly data are not available the beginning and ending figures can be added and then divided by 2. Both methods adjust for growth but not for seasonal effects. 5 We could use the receivables turnover to evaluate receivables. Allied’s receivables turnover is 3000/375¼ 8×. However the DSO ratio is easier to interpret and judge. Days Sales Outstanding DSO This ratio is calculated by dividing accounts receiv- able by average sales per day it indicates the aver- age length of time the firm must wait after mak- ing a sale before itreceives cash. Chapter 4 Analysis of Financial Statements 89

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receivables. Thus the DSO represents the average length of time the firm must wait after making a sale before receiving cash. Allied has 46 days sales out- standing well above the 36-day industry average: Days sales outstanding ðDSOÞ¼ Receivables Average sales per day ¼ Receivables Annual sales365 ¼ 375 3000365 ¼ 375 8:2192 ¼ 45:625 days 46 days Industry average¼ 36 days The DSO can be compared with the industry average but it is also evaluated by comparing it with Allied’s credit terms. Allied’s credit policy calls for payment within 30 days. So the fact that 46 days’ sales are outstanding not 30 days’ indicates that Allied’s customers on average are not paying their bills on time. This deprives the company of funds that could be used to reduce bank loans or someothertypeofcostlycapital.MoreoverthehighaverageDSOindicatesthatif some customers are paying on time quite a few must be paying very late. Late- paying customers often default so their receivables may end up as bad debts that canneverbecollected. 6 NotetoothatthetrendintheDSOoverthepastfewyears has been rising but the credit policy has not been changed. This reinforces our belief that Allied’s credit manager should take steps to collect receivables faster. 4-3c Fixed Assets Turnover Ratio The fixed assets turnover ratio which is the ratio of sales to net fixed assets measures how effectively the firm uses its plant and equipment: Fixed assets turnover ratio¼ Sales Net fixed assets ¼ 3000 1000 ¼ 3:0 Industry average¼ 2:8 Allied’sratioof3.0timesisslightlyabovethe2.8industryaverageindicatingthat it is using its fixed assets at least as intensively as other firms in the industry. Therefore Allied seems to have about the right amount of fixed assets relative to its sales. Potential problems may arise when interpreting the fixed assets turnover ratio.Recallthatfixedassetsareshownonthebalancesheetattheirhistoricalcosts less depreciation. Inflation has caused the value of many assets that were pur- chased in the past to be seriously understated. Therefore if we compare an old firm whose fixed assets have been depreciated with a new company with similar operations that acquired its fixed assets only recently the old firm will probably have the higher fixed assets turnover ratio. However this would be more reflec- tive of the age of the assets than of inefficiency on the part of the new firm. The accounting profession is trying to develop procedures for making financial statements reflect current values rather than historical values which would help us make better comparisons. However at the moment the problem still exists so financial analysts must recognize this problem and deal with it judgmentally. In Allied’s case the issue is not serious because all firms in the industry have been 6 For example if further analysis along the lines suggested in Part 6 of this text indicates that 85 of the customers pay in 30 days for the DSO to average 46 days the remaining 15 must be paying on average in 136.67 days. Paying that late suggests financial difficulties. A DSO of 46 days would alert a good analyst of the need to dig deeper. Fixed Assets Turnover Ratio The ratio of sales to net fixed assets. 90 Part 2 Fundamental Concepts in Financial Management

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expanding at about the same rate hence the balance sheets of the comparison firms are reasonably comparable. 7 4-3d Total Assets Turnover Ratio The final asset management ratio the total assets turnover ratio measures the turnover of all of the firm’s assets and it is calculated by dividing sales by total assets: Total assets turnover ratio¼ Sales Total assets ¼ 3000 2000 ¼ 1:5 Industry average¼ 1:8 Allied’s ratio is somewhat below the industry average indicating that it is not generatingenoughsalesgivenitstotalassets.WejustsawthatAllied’sfixedassets turnover is in line with the industry average so the problem is with its current assets inventories and accounts receivable whose ratios were below the industry standards. Inventories should be reduced and receivables collected faster which would improve operations. SELFTEST Write the equations for four ratios that are used to measure how effectively a firm manages its assets. If one firm is growing rapidly and another is not how might this distort a comparison of their inventory turnover ratios If you wanted to evaluate a firm’s DSO with what could you compare it Other companies and the same company over time How might different ages distort comparisons of different firms’ fixed assets turnover ratios A firm has annual sales of 100 million 20 million of inventory and 30 million of accounts receivable. What is its inventory turnover ratio 5× What is its DSO 109.5 days 4-4 DEBT MANAGEMENT RATIOS Theuseofdebtwillincreaseor“leverageup”afirm’sROEifthefirmearnsmore on its assets than the interest rate it pays on debt. However debt exposes the firm to more risk than if it financed only with equity. In this section we discuss debt management ratios. Table4-1illustratesthepotentialbenefitsandrisksassociatedwithdebt. 8 Here we analyze two companies that are identical except for how they are financed. Firm U for Unleveraged has no debt thus it uses 100 common equity. Firm L for Leveraged obtained 50 of its capital as debt at an interest rate of 10. Both firmshave100ofassetsandtheirsalesareexpectedtorangefromahighof150 down to 75 depending on business conditions. Some of their operating costs 7 See FASB 89 Financial Reporting and Changing Prices December 1986 for a discussion of the effects of inflation on financial statements. The report’s age indicates how difficult it has been to solve this problem. 8 We discuss ROE in moredepth later in this chapter and we examine the effectsof leveragein detail in the capital structure and leverage chapter. Total Assets Turnover Ratio This ratio is calculated by dividing sales by total assets. Debt Management Ratios A set of ratios that mea- sure how effectively a firm manages its debt. Chapter 4 Analysis of Financial Statements 91

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e.g. rent and the president’s salary are fixed and will be the same regardless of the level of sales while other costs e.g. manufacturing labor and materials costs vary with sales. 9 9 The financial statements do not show the breakdown between fixed and variable operating costs but com- panies can and do make this breakdown for internal purposes. Of course the distinction is not always clear because what’s a fixed cost in the very short run can become a variable cost over a longer time horizon. It’s interesting to note that companies are moving towardmaking more of their costs variable using such techniques as increasing bonuses rather than base salaries switching to profit-sharing plans rather than fixed pension plans and outsourcing various operations. Effects of Financial Leverage on Stockholder Returns Table 4-1 FIRM U UNLEVERAGED NO DEBT Current assets 50 Debt 0 Fixed assets 50 Common equity 100 Total assets 100 Total liabilities and equity 100 STATE OF THE ECONOMY Good Expected Bad Sales revenues 150.0 100.0 75.0 Operating costs Fixed 45.0 45.0 45.0 Variable 60.0 40.0 30.0 Total operating costs 105.0 85.0 75.0 Operating income EBIT 45.0 15.0 0.0 Interest Rate 10 0.0 0.0 0.0 Earnings before taxes EBT 45.0 15.0 0.0 Taxes Rate 40 18.0 6.0 0.0 Net income NI 27.0 9.0 0.0 ROE U 27.0 9.0 0.0 FIRM L LEVERAGED SOME DEBT Current assets 50 Debt 50 Fixed assets 50 Common equity 50 Total assets 100 Total liabilities and equity 100 STATE OF THE ECONOMY Good Expected Bad Sales revenues 150.0 100.0 75.0 Operating costs Fixed 45.0 45.0 45.0 Variable 60.0 40.0 30.0 Total operating costs 105.0 85.0 75.0 Operating income EBIT 45.0 15.0 0.0 Interest Rate 10 5.0 5.0 5.0 Earnings before taxes EBT 40.0 10.0 − 5.0 Taxes Rate 40 16.0 4.0 0.0 Net income NI 24.0 6.0 − 5.0 ROE L 48.0 12.0 −10.0 92 Part 2 Fundamental Concepts in Financial Management

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Notice that everything is the same in the table for the leveraged and unleveraged firms down through operating income—thus their EBITs are the same in each state of the economy. However things differ below operating income.FirmUhasnodebtitpaysnointerestitstaxableincomeisthesameasits operating income it pays a 40 state and federal tax rate and its net income ranges from 27 under good conditions down to 0 under bad conditions. When U’s net income is divided by its common equity its ROEs range from 27 to 0 depending on the state of the economy. FirmLhasthesameEBITasUundereachstateoftheeconomybutLuses50 of debt with a 10 interest rate so it has 5 of interest charges regardless of the economy.This5isdeductedfromEBITtoarriveattaxableincometaxesaretaken out and the result is net income which ranges from 24 to −5 depending on conditions. 10 AtfirstitlooksasthoughFirmUisbetteroffunderallconditionsbut thisisnotcorrect—weneedtoconsiderhowmuchthetwofirms’stockholdershave invested. Firm L’s stockholders have put up only 50 so when that investment is divided into net income we see that their ROE under good conditions is a whop- ping 48 versus 27 for U and is 12 versus 9 for U under expected con- ditions. However L’s ROE falls to −10 under bad conditions which means that Firm L would go bankrupt if those conditions persisted for several years. Therearetworeasonsfortheleveragingeffect:1Interestisdeductiblesothe use of debt lowers the tax bill and leaves more of the firm’s operating income available to its investors. 2 If the rate of return on assets exceeds the interest rate on debt as is generally expected a company can use debt to acquire assets pay the interest on the debt and have something left over as a “bonus” for its stock- holders.Undertheexpectedconditionsourhypotheticalfirmsexpecttoearn15 on assets versus a 10 cost of debt. This combined with the tax benefit of debt pushes L’s expected ROE far above that of U. Thus firms with relatively high debt ratios typically have higher expected returnswhentheeconomyisnormalbutlowerreturnsandpossiblybankruptcyif the economy goes into a recession. Therefore decisions about the use of debt require firms to balance higher expected returns against increased risk. Deter- mining the optimal amount of debt is a complicated process and we defer a discussion of that subject until the capital structure chapter. For now we simply lookattwoproceduresthatanalystsusetoexaminethefirm’sdebt:1Theycheck the balance sheet to determine the proportion of total funds represented by debt and 2 they review the income statement to see the extent to which interest is covered by operating profits. 4-4a Total Debt to Total Assets The ratio of total debt to total assets generally called the debt ratio measures the percentage of funds provided by creditors: Debt ratio¼ Total debt Total assets ¼ 310þ750 2000 ¼ 1060 2000 ¼ 53:0 Industry average¼ 40:0 Total debt includes all current liabilities and long-term debt. Creditors prefer low debt ratios because the lower the ratio the greater the cushion against creditors’ lossesintheeventofliquidation.Stockholdersontheotherhandmaywantmore leverage because it can magnify expected earnings as we saw in Table 4-1. 10 As we discussed in the last chapter firms can carry losses back or forward for several years. Therefore if Firm L had profits and thus paid taxes in recent 2007 it could carry back the 2008 loss under bad conditions and receive a credit a check from the government. In Table 4-1 we disregard the carry-back/carry-forward provision. Debt Ratio The ratio of total debt to total assets. Chapter 4 Analysis of Financial Statements 93

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Allied’sdebtratiois53.0whichmeansthatitscreditorshavesuppliedmore than half of its total funds. As we will discuss in the capital structure chapter a numberoffactorsaffectacompany’soptimaldebtratio.Neverthelessthefactthat Allied’s debt ratio exceeds the industry average by a fairly large amount raises a red flag and this will make it relatively costly for Allied to borrow additional fundswithoutfirstraisingmoreequity.Creditorswillbereluctanttolendthefirm moremoneyandmanagementwouldprobablybesubjectingthefirmtotoohigha riskofbankruptcyifitsoughttoborrowasubstantialamountofadditionalfunds. 11 4-4b Times-Interest-Earned Ratio The times-interest-earned TIE ratio is determined by dividing earnings before interest and taxes EBIT in Table 3-2 by the interest charges: Times-interest-earned ðTIEÞ ratio¼ EBIT Interest charges ¼ 283:8 88 ¼ 3:2 Industry average¼ 6:0 The TIE ratio measures the extent to which operating income can decline before thefirmisunabletomeetitsannualinterestcosts.Failuretopayinterestwillbring legal action by the firm’s creditors and probably result in bankruptcy. Note that earnings before interest and taxes rather than net income is used in the numer- ator. Because interest is paid with pretax dollars the firm’s ability to pay current interest is not affected by taxes. Allied’sinterestiscovered3.2times.Theindustryaverageis6timessoAllied is covering its interest charges by a relatively low margin of safety. Thus the TIE ratio reinforces our conclusion from the debt rationamely that Allied would face difficulties if it attempted to borrow much additional money. 12 SELFTEST How does the use of financial leverage affect stockholders’ control position How does the U.S. taxstructure influence a firm’s willingness to financewith debt How does the decision to use debt involve a risk-versus-return trade-off Explain the following statement: Analysts look at both balance sheet and income statement ratios when appraising a firm’s financial condition. Name two ratios that are used to measure financial leverage and write their equations. 11 The ratio of debt to equity is also used in financial analysis. The debt-to-assets D/A and debt-to-equity D/E ratios are simply transformations of each other: DE¼ DA 1 DA and DA¼ DE 1þDE With a D/A ratio of 53 or 0.53 Allied’s Debt/Equity ratio is 0.53/1 − 0.53 ¼ 1.13. 12 Another commonly used debt management ratio is the following: EBITDA coverage¼ EBITDAþLease payments InterestþPrincipal paymentsþLease payments This ratiois morecompletethanthe TIEratio inthatit recognizesthat depreciation and amortization expensesare not cash charges and thus are available to service debt and that lease payments and principal repayments on debt are fixed charges. For more on this ratio see E. F. Brigham and P. R. Daves Intermediate Financial Man- agement 9th ed. Mason OH: Thomson/South-Western 2007 p. 258. Times-Interest-Earned TIE Ratio The ratio of earnings before interest and taxes EBIT to interest charges a measure of the firm’s ability to meet its annual interest payments. 94 Part 2 Fundamental Concepts in Financial Management

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4-5 PROFITABILITY RATIOS Accounting statements reflect events that happened in the past but they also provide clues about what’s really important—what’s likely to happen in the future. The liquidity asset management and debt ratios covered thus far tell us something about the firm’s policies and operations. Now we turn to the profit- ability ratios which reflect the net result of all of the financing policies and operating decisions. 4-5a Operating Margin The operating margin calculated by dividing operating income EBIT by sales gives the operating profit per dollar of sales: Operating margin¼ Operating income ðEBITÞ Sales ¼ 283:8 3000 ¼ 9:5 Industry average¼ 10:0 Allied’s 9.5 operating margin is below the industry average of 10.0. This subpar result indicatesthat Allied’soperating costsaretoohigh.This isconsistent with the low inventory turnover and high days’ sales outstanding ratios that we calculated earlier. 4-5b Profit Margin The profit margin also sometimes called the net profit margin is calculated by dividing net income by sales: Profit margin¼ Net income Sales ¼ 117:5 3000 ¼ 3:9 Industry average¼ 5:0 Allied’s 3.9 profit margin is below the industry average of 5.0 and this subpar result occurred for two reasons. First Allied’s operating margin was below the industry average because of the firm’s high operating costs. Second the profit margin is negatively impacted by Allied’s heavy use of debt. To see this second point recognize that net income is after interest. Suppose two firms have identical operations in the sense that their sales operating costs and operating income are identical. However one firm uses more debt hence it has higher interest charges. Those interest charges pull down its net income and since sales are constant the result is a relatively low net profit margin for the firmwithmoredebt.WeseethenthatAllied’soperatinginefficiencyanditshigh debt ratio combine to lower its net profit margin below the food processing industry average. It also follows that when two companies have the same operating margin but different debt ratios we can expect the company with a higher debt ratio to have a lower profit margin. Note too that while a high return on sales is good other things held constant otherthingsmaynotbeheldconstant—wemustalsobeconcernedwithturnover. Ifafirmsetsaveryhighpriceonitsproductsitmaygetahighreturnoneachsale butfailtomakemanysales.Thatstrategymightresultinahighprofitmarginlow salesandhencealownetincome.Wewillseeshortlyhowthroughtheuseofthe DuPont equation profit margins the use of debt and turnover ratios interact to affect overall stockholder returns. Profitability Ratios A group of ratios that show the combined effects of liquidity asset man- agement and debt on operating results. Operating Margin This ratio measures oper- ating income or EBIT per dollar of sales it is calcu- lated by dividing operat- ing income by sales. Profit Margin This ratio measures net income per dollar of sales and is calculated by dividing net income by sales. Chapter 4 Analysis of Financial Statements 95

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4-5c Return on Total Assets Net income divided by total assets gives us the return on total assets ROA: Return on total assets ðROAÞ¼ Net income Total assets ¼ 117:5 2000 ¼ 5:9 Industry average¼ 9:0 Allied’s 5.9 return is well below the 9.0 industry average. This is not good—it is obviously better to have a higher than a lower return on assets. Note though that alowROA can resultfrom aconscious decisionto use agreat deal ofdebt in which case high interest expenses will cause net income to be relatively low. That is part of the reason for Allied’s low ROA. Never forget—you must look at a number of ratios see what each suggests and then look at the overall situation when you judge the performance of a company and consider what actions it should undertake to improve. GLOBAL PERSPECTIVES GLOBAL ACCOUNTING STANDARDS:CAN ONE SIZE FIT ALL These days you must be a good financial detective to analyze financial statements especially when the company operates overseas. Despite attempts to standardize accounting practices there are still many differences in financial reporting in different countries and those differ- ences create headaches for investors making cross-border company comparisons. However as businesses become more global and as more foreign companies list on U.S. stock exchanges accountants and regulators are realizing the need for a global convergence of accounting standards. As a result the “writing is on the wall” regarding accounting standards and differences are disappearing. The effort to internationalize accounting standards began in 1973 with the formation of the International Accounting Standards Committee. However in 1998 it became apparent that a full-time rule-making body with global representation was necessary so the International Accounting Standards Board IASB with members repre- senting 9 major countries was established. The IASB was charged with the responsibility for creating a set of Inter- national Financial Reporting Standards IFRS. A survey of senior executives from 85 financial insti- tutions worldwide found that 92 of those responding favored a single set of international standards. The U.S. SEC has proposed allowing non-U.S. companies that operate in the United States to base their reports on IFRS rather than GAAP and it is considering requiring U.S. companies to shift to IFRS. Obviously the globalization of accounting stan- dards is a huge endeavor—one that will involve com- promises between the IASB and FASB. The main problem is that U.S. GAAP takes a rules-based approach while the IASB insists on using a principles-based approach. With a rules- based system companies can tell whether they are in compliance but they can also devise ways to get around a rule and thus subvert its intent. With a principles-based system there is more uncertainty about whether certain borderline procedures will be allowed but such a system makes it easier to prosecute on the basis of intent. A global accounting structure would enable investors and practitioners around the world to read and understand financial reports produced anywhere in the world. Accord- ing to SEC Chairman Christopher Cox “Having a set of globally accepted accounting standards is critical to the rapidly accelerating global integration of the world’s capital markets.” Even the chairman of the U.S. Financial Account- ing Standards Board Robert Herz has recommended that a target date be set for U.S. companies to transition from GAAP to IFRS. So it seems that the issue is when not if all companies will be playing by the same set of accounting rules. Sources: “All Accountants Soon May Speak the Same Language” The Wall Street Journal August 29 1995 p. A15 “For and Against Standards Need Time to Work” Accountancy Age June 5 2003 p. 16 and James Turley CEO Ernst Young “Mind the GAAP” The Wall Street Journal November 9 2007 p. A18. Return on Total Assets ROA The ratio of the net income to total assets. 96 Part 2 Fundamental Concepts in Financial Management

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4-5d Basic Earning Power BEP Ratio The basic earning power BEP ratio is calculated by dividing operating income EBIT by total assets: Basic earning power ðBEPÞ¼ EBIT Total assets ¼ 283:8 2000 ¼ 14:2 Industry average¼ 18:0 Thisratioshows the rawearning powerofthefirm’s assets before the influence of taxes and debt and it is useful when comparing firms with different debt and tax situations. Because of its low turnover ratios and poor profit margin on sales Allied has a lower BEP ratio than the average food processing company. 13 4-5e Return on Common Equity The most important or bottom-line accounting ratio is the return on common equity ROE found as follows: Return on common equity ðROEÞ¼ Net income Common equity ¼ 117:5 940 ¼ 12:5 Industry average¼ 15:0 Stockholders expect to earn a return on their money and this ratio tells how well they are doing in an accounting sense. Allied’s 12.5 return is below the 15.0 industryaveragebutnotasfarbelowasthereturnontotalassets.Thissomewhat better ROE results from the company’s greater use of debt a point discussed earlier in the chapter. SELFTEST Identify five profitability ratios and write their equations. Why does the use of debt lower the profit margin and the ROA Using more debt lowers profits and thus the ROA. Why doesn’tdebthavethe samenegativeeffectontheROEDebtlowersnetincomebutitalsolowers thefirm’sequityandtheequityreductioncanoffsetthelowernetincome. Acompanyhas20billionofsalesand1billionofnetincome.Itstotalassets are 10 billion financed half by debt and half by common equity. What is its profitmargin5WhatisitsROA10WhatisitsROE20Wouldthis firm’sROAincreaseifitusedlessleverageyesWoulditsROEincreaseno Basic Earning Power BEP Ratio This ratio indicates the ability of the firm’s assets to generate operating income it is calculated by dividing EBIT by total assets. 13 A related ratio is the return on investors’ capital defined as follows: Return on investors 0 capital ðROICÞ¼ Net incomeþInterest DebtþEquity The numerator shows the dollar returns to all investorsthe denominator shows the money investors have put up and the resulting ratio shows the rate of return on total investor capital. This ratio is especially important in regulated industries such as electric utilities where regulators are concerned about companies using their monopoly power to earn excessive returns on investors’ capital. In fact regulators often try to set electricity prices at a level that will force the return on investors’ capital to equal a company’s cost of capital as defined in Chapter 10. Return on Common Equity ROE The ratio of net income to common equity measures the rate of return on common stockholders’ investment. Chapter 4 Analysis of Financial Statements 97

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4-6 MARKET VALUE RATIOS ROEreflectstheeffectsofalloftheotherratiosanditisthesinglebestaccounting measure of performance. Investors like a high ROE and high ROEs are correlated with high stock prices. However other things come into play. For example financialleveragegenerallyincreases theROE butalsoincreasesthe firm’srisk so if a high ROE is achieved by using a great deal of debt the stock price might end up lower than if the firm had been using less debt and had a lower ROE. We use the final set of ratios—the market value ratios which relate the stock price to earnings and book value price—to help address this situation. If the liquidity asset management debt management and profitability ratios all look good and if investors think these ratios will continue to look good in the future the market value ratios will be high the stock price will be as high as can be expected and management will be judged to have been doing a good job. Themarketvalueratiosareusedinthreeprimaryways:1byinvestorswhen they are deciding to buy or sell a stock 2 by investment bankers when they are setting the share price for a new stock issue an IPO and 3 by firms when they are deciding how much to offer for another firm in a potential merger. 4-6a Price/Earnings Ratio The price/earnings P/E ratio shows how much investors are willing to pay per dollarofreportedprofits.Allied’sstocksellsfor23.06sowithanEPSof2.35its P/E ratio is 9.8×: PriceEarnings ðPEÞ ratio¼ Price per share Earnings per share ¼ 23:06 2:35 ¼ 9:8 Industry average¼ 11:3 As we will see in Chapter 9 P/E ratios are relatively high for firms with strong growth prospects and little risk but low for slowly growing and risky firms. Allied’sP/Eratioisbelow itsindustry averageso this suggests that the company is regarded as being relatively risky as having poor growth prospects or both. There is no “correct” P/E ratio but the SP 500’s historical average is 15.9× and it has ranged from 48.1× to 7.1× over the last 30 years. In the winter of 2008 the SP’s ratio was 21.7× versus 37.8× for Google. Countrywide Financial which was badly hurt by the subprime mortgage debacle had negative earnings and thus a negative P/E. The Google and Countrywide data demonstrate that strong companies with good growth prospects have high P/Es while weaker companies with poor prospects have low ratios. 14 4-6b Market/Book Ratio The ratio of a stock’s market price to its book value gives another indication of how investors regard the company. Companies that are well regarded by Market Value Ratios Ratios that relate the firm’s stock price to its earnings and book value per share. Price/Earnings P/E Ratio The ratio of the price per share to earnings per share shows the dollar amount investors will pay for 1 of current earnings. 14 Security analysts also look at the Price-to-Free-Cash-Flow ratio. In addition analysts consider the PEG or P/E to growth ratio where the P/E is divided by the firm’s forecasted growth rate. Allied’s growth rate as forecasted by a number of security analysts for the next 5 years is 7.0 so its PEG¼ 9.8/7.0¼ 1.4×. The lower the ratio the better and most firms have ratios in the range of 1.0× to 2.0×. We note though that P/E ratios jump around from year to year because earnings and forecasted growth rates fluctuate. Like other ratios PEG ratios are interesting but must be interpreted with care and judgment. 98 Part 2 Fundamental Concepts in Financial Management

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investors—which means low risk and high growth—have high M/B ratios. For Allied we first find its book value per share: Book value per share¼ Common equity Shares outstanding ¼ 940 50 ¼ 18:80 We then divide the market price per share by the book value per share to get the market/book M/B ratio which for Allied is 1.2×: Marketbook ðMBÞ ratio¼ Market price per share Book value per share ¼ 23:06 18:80 ¼ 1:2 Industry average¼ 1:7 Investors are willing to pay less for a dollar of Allied’s book value than for one of an average food processing company. This is consistent with our other findings. M/Bratiostypicallyexceed1.0whichmeansthatinvestorsarewillingtopay more for stocks than the accounting book values of the stocks. This situation occurs primarily because asset values as reported by accountants on corporate balance sheets do not reflect either inflation or goodwill. Assets purchased years ago at pre-inflation prices are carried at their original costs even though inflation might have caused their actual values to rise substantially and successful com- panies’ values rise above their historical costs whereas unsuccessful ones have low M/B ratios. 15 This point is demonstrated by Google and Countrywide: In the winterof2008Google’sM/Bratiowas6.9×whileCountrywide’swasonly0.26×. Google’s stockholders now have 6.90 in market value per 1.00 of equity whereas Countrywide’s stockholders have only 0.26 for each dollar they invested. SELFTEST Describe two ratios that relate a firm’s stock price to its earnings and book value per share and write their equations. In what sense do these market value ratios reflect investors’ opinions about a stock’s risk and expected future growth What does theprice/earnings P/E ratioshowIfonefirm’sP/Eratio islower than that of another firm what factors might explain the difference How is book value per share calculated Explain how inflation and RD programs might cause book values to deviate from market values. 4-7 TREND ANALYSIS Itisimportanttoanalyzetrendsinratiosaswellastheirabsolutelevelsfortrends give clues as to whether a firm’s financial condition is likely to improve or to deteriorate. To do a trend analysis simply plot a ratio over time as shown in Figure4-1.ThisgraphshowsthatAllied’sROEhasbeendecliningsince2005even thoughtheindustryaveragehasbeenrelativelystable.Alloftheotherratioscould be analyzed similarly and such an analysis can be quite useful in gaining insights as to why the ROE behaved as it did. Market/Book M/B Ratio The ratio of a stock’s market price to its book value. 15 The second point is known as “survivor bias.” Successful companies survive and are reflected in the averages whereas unsuccessful companies vanish and their low numbers are not reflected in the averages. Trend Analysis An analysis of a firm’s financial ratios over time used to estimate the like- lihood of improvement or deterioration in its finan- cial condition. Chapter 4 Analysis of Financial Statements 99

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SELFTEST How is a trend analysis done What important information does a trend analysis provide 4-8 THE DUPONT EQUATION We have discussed many ratios so it would be useful to see how they work together to determine the ROE. For this we use the DuPont equation a formula developed by the chemical giant’s financial staff in the 1920s. It is shown here for Allied and the food processing industry. ROE ¼ Profit margin Total assets turnover Equity multiplier ¼ Net income Sales Sales Total assets Total assets Total common equity ¼ 117:5 3000 3000 2000 2000 940 ¼ 3:92 1:5 times 2:13 times ¼ 12:5 Industry ¼ 5:0 1:8 times 1:67 times ¼ 15:0 4-1 l Thefirst term the profit margin tellsus how much the firm earns on itssales. Thisratiodependsprimarilyoncostsandsalesprices—ifafirmcancommand apremiumpriceandholddownitscostsitsprofitmarginwillbehighwhich will help its ROE. l The second term is the total assets turnover. It is a “multiplier” that tells us how many times the profit margin is earned each year—Allied earned 3.92 on each dollar of sales and its assets were turned over 1.5 times each year so itsreturnonassetswas3.92×1.5¼5.9.Notethoughthatthisentire5.9 belongs to the common stockholders—the bondholders earned a return in the form of interest and that interest was deducted before we calculated net income to stockholders. Therefore the whole 5.9 return on assets belongs to DuPont Equation A formula that shows that the rate of return on equity can be found as the product of profit margin total assets turnover and the equity multiplier. It shows the relationships among asset manage- ment debt management and profitability ratios. Rate of Return on Common Equity 2004−2008 FIGURE 4-1 16 14 12 10 ROE 2004 2005 2006 2007 2008 Industry Allied 100 Part 2 Fundamental Concepts in Financial Management

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the stockholders. Therefore the return on assets must be adjusted upward to obtain the return on equity. l Thatbringsustothethirdtermtheequitymultiplierwhichistheadjustment factor. Allied’s assets are 2.13 times its equity so we must multiply the 5.9 return on assets by the 2.13× equity multiplier to arrive at its ROE of 12.5. Note that ROE as calculated using the DuPont equation is identical to Allied’s ROE 12.5 which we calculated earlier. What’s the point of going through all of the steps required to implement the DuPont equation to find ROE The answer is that the DuPont equation helps us see why Allied’s ROE is only 12.5 versus 15.0 for the industry. First its profit margin is below average which indicates that its costs are not being controlled as well as they should be and that it cannot charge premium prices. In addition because it uses more debt than most com- panies its high interest charges also reduce the net profit margin. Second its total assets turnover is below the industry average which indicates that it has more assets than it needs. Finally because its equity multiplier is relatively high its heavy use of debt offsets to some extent its low profit margin and turnover. However the high debt ratio exposes Allied to above-average bankruptcy risk so it might want to cut back on its financial leverage. But if it reduced its debt to the same level asthe average firm inits industry its ROE would declinesignificantly to 3.92 × 1.5 × 1.67 ¼ 9.8. 16 Allied’s management can use the DuPont equation to help identify ways to improve its performance. Focusing on the profit margin its marketing people can studytheeffectsofraisingsalespricesorofintroducingnewproductswithhigher margins. Its cost accountants can study various expense items and working with engineers purchasing agents and other operating personnel seek ways to cut costs. The credit manager can investigate ways to speed up collections which would reduce accounts receivable and therefore improve the quality of the total assets turnover ratio. And the financial staff can analyze the effects of alternative debt policies showing how changes in leverage would affect both the expected ROE and the risk of bankruptcy. As a result of this analysis Ellen Jackson Allied’s chief executive officer CEO undertook a series of moves that are expected to cut operating costs by more than 20. Jackson and Allied’s other executives have a strong incentive to improve the firm’s financial performance—their compensation depends on how well the company operates. If Allied meets or exceeds its growth and profit tar- gets Jackson and the other executives—and the stockholders—will do well. Otherwise someone like Warren Buffett or Carl Icahn whom we discussed at the beginning of the chapter may come calling. SELFTEST Write the equation for the basic DuPont equation. What is the equity multiplier and why is it used How can management use the DuPont equation to analyze ways of improving the firm’s performance 16 The ROE reduction would actually be somewhat less because if debt were lowered interest payments would also decline which would raise the profit margin. Allied’s analysts determined that the net effect of a reduction in debt would still be a significant reduction in ROE. Chapter 4 Analysis of Financial Statements 101

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4-9 RATIOS IN DIFFERENT INDUSTRIES Table 4-2 provides a list of the ratios for a number of different industries in early 2008. ROEs vary across industries ranging from 45.7 for education and training services to 0.9 for newspapers. The education and training services industry has been positively impacted by enrollment growth of online operations in schools. The newspaper industry has been in decline because the proportion of the pop- ulation that reads newspapers has been in a long-term decline which has a neg- ative impact on the demand for newspaper advertising. Industry rankings change from yeartoyear becausefirms and industries go through cycles ofgood and bad times. When times are good companies often overexpand which leads to hard times. Note too that there are huge differences between individual companiesin a given industry. That point isn’t illustrated in Table 4-2 but it shows up dramati- cally in Table 4-4 in Section 4-11. SELFTEST Why might railroads have such low total assets turnovers and food wholesalers and grocery stores such high turnovers Railroads require many long-term assets while grocery companies have more perishable products and thus high turnovers. If competition causes all companies to have similar ROEs in the long run would companies with high turnovers tend to have high or low profit margins Explain your answer. Low DuPont Financial Ratios for Selected Industries a Table 4-2 Industry Name ROE Profit Margin × Total Assets Turnover × Equity Multiplier b Aerospace/defense—major diversified 41.4 6.8 1.0 6.1 Apparel stores 37.2 6.7 1.8 3.1 Auto mfg.—major 12.9 3.9 0.8 4.1 Beverage soft drink 21.6 14.1 0.8 1.9 Education and training services 45.7 13.0 1.4 2.5 Electronics—equipment 6.8 4.7 0.9 1.6 Food wholesaling 17.8 1.5 3.3 3.6 Grocery stores 19.1 3.7 2.5 2.1 Lodging 30.6 12.6 0.9 2.7 Medical instruments and supplies 9.6 4.5 0.7 3.0 Metals and minerals—industrial 34.8 10.9 0.7 4.6 Newspapers 0.9 8.5 0.3 0.4 Paper and paper products 15.1 13.5 0.8 1.4 Railroad 15.3 15.0 0.4 2.6 Restaurant 15.3 8.1 0.7 2.7 Retail—department stores 18.4 4.8 1.7 2.3 Scientific and technical instruments 12.9 9.0 0.8 1.8 Sporting goods 15.2 4.1 1.7 2.2 Steel and iron 36.3 23.5 0.8 1.9 Telecommunications services— domestic 11.9 10.1 0.4 2.9 Tobacco cigarettes 14.4 15.4 0.3 3.1 a The ratios presented are averages for each industry. Ratios for the individual companies are also available. b Calculated as ROE/ROA. Source: Data obtained from the Key Ratios section February 7 2008. 102 Part 2 Fundamental Concepts in Financial Management

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4-10 SUMMARY OF ALLIED’S RATIOS Table4-3providesasummaryofthe ratioswe have discussedinthechapter. This table is useful as a quick reference for the formulas for calculations and for the ratios of Allied and the average food processing company. Allied Food Products: Summary of Financial Ratios Millions of Dollars Table 4-3 Ratio Formula Calculation Ratio Industry Average Comment Liquidity Current Current assets Current liabilities 1000 310 3.2× 4.2× Poor Quick Current assets Inventories Current liabilities 385 310 1.2× 2.2× Poor Asset Management Inventory turnover Sales Inventories 3000 615 4.9× 10.9× Poor Days sales outstanding DSO Receivables Annual sales365 375 8:2192 46 days 36 days Poor Fixed assets turnover Sales Net fixed assets 3000 1000 3.0× 2.8× OK Total assets turnover Sales Total assets 3000 2000 1.5× 1.8× Somewhat low Debt Management Total debt to total assets Total debt Total assets 1060 2000 53.0 40.0 High risky Times interest earned TIE Earnings before interest and taxes ðEBITÞ Interest charges 283:8 88 3.2× 6.0× Low risky Profitability Operating margin Operating income ðEBITÞ Sales 283:8 3000 9.5 10.0 Low Profit margin Net income Sales 117:5 3000 3.9 5.0 Poor Return on total assets ROA Net income Total assets 117:5 2000 5.9 9.0 Poor Basic earning power BEP Earnings before interest and taxes ðEBITÞ Total assets 283:8 2000 14.2 18.0 Poor Return on common equity ROE Net income Common equity 117:5 940 12.5 15.0 Poor Market Value Price/earnings P/E Price per share Earnings per share 23:06 2:35 9.8× 11.3× Low Market/book M/B Market price per share Book value per share 23:06 18:80 1.2× 1.7× Low Chapter 4 Analysis of Financial Statements 103

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4-11 BENCHMARKING RatioanalysisinvolvescomparisonswithindustryaveragefiguresbutAlliedand many other firms also compare themselves with the top firms in their industry. This is called benchmarking and the companies used for the comparison are called benchmark companies. Table 4-4 provides data for Allied and its seven benchmarks. The companies are ranked by ROE and the other ratios used in a DuPontanalysisareshowninthetableaswell.TheROEmakesiteasyforAllied’s managers to see where the firm stands relative to top food processors and the other data give management an idea of why Allied’s ROE ranking compares unfavorably with most of the other benchmark companies. Perhaps the most interesting feature of Table 4-4 is the wide range of ROEs. This range is caused primarily by variations in profit margins and equity multi- pliers. These companies also have the most widely recognized brands—their excellent marketing programs enabled them to charge relatively high prices which boosted their profit margins and thus their ROEs. Their high and stable profits enable them to use a great deal of debt which boosted their equity mul- tipliers and provided another boost to their ROEs. Note too that the averages for Allied and its benchmark companies differ significantly from the averages for its industry. The benchmarks are all very large companieswhiletherearemanysmallfoodprocessingcompanieswhosedataare included in the industry averages. Since Allied is a relatively large company its chief financial officer CFO believes it makes more sense to compare Allied to other large companies than to industry averages. SELFTEST Why are comparative ratio analyses useful Benchmarking The process of comparing a particular company with a set of benchmark companies. Benchmark Companies Ranked by ROE Table 4-4 ROE Profit Margin × Turnover × Equity Multiplier Campbell Soup 59.4 10.3 1.1 5.24 H.J. Heinz 39.3 8.8 0.9 4.96 Hershey Foods 33.6 4.3 1.2 6.51 Sara Lee 21.9 4.8 1.1 4.15 Dean Foods 17.4 1.6 1.6 6.80 Flowers Foods 15.5 4.8 2.2 1.47 Allied Foods 12.5 3.9 1.5 2.13 Del Monte Foods 8.0 3.2 0.7 3.57 Averages 25.9 5.2 1.3 4.35 Averages for entire food industry 26.8 10.5 1.1 2.32 Note: Rounding causes some variations in the numbers. Source: Data on the benchmark companies were obtained from February 11 2008. Similar data can be obtained from Yahoo Google and a number of other online and print sources. 104 Part 2 Fundamental Concepts in Financial Management

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4-12 USES AND LIMITATIONS OF RATIOS Asnotedearlierratioanalysisisusedbythreemaingroups:1managerswhouse ratios to help analyze control and thus improve their firms’ operations 2 credit analystsincludingbankloanofficersandbondratinganalystswhoanalyzeratios tohelp judgeacompany’sabilitytorepay itsdebtsand 3 stock analystswhoare interested in a company’s efficiency risk and growth prospects. In later chapters we will look more closely at the basic factors that underlie each ratio. Note though that while ratio analysis can provide useful information concerning a company’s operations and financial condition it does have limitations. Some potential problems are listed here: 1. Many firms have divisions that operate in different industries and for such companies it is difficult to develop a meaningful set of industry averages. Therefore ratio analysis is more useful for narrowly focused firms than for multidivisional ones. 2. Most firms want to be better than average so merely attaining average per- formance is not necessarily good. As a target for high-level performance it is besttofocusontheindustryleaders’ratios.Benchmarkinghelpsinthisregard. 3. Inflation has distorted many firms’ balance sheets—book values are often different from market values. Market values would be more appropriate for most purposes but we cannot generally get market value figures because LOOKING FOR WARNING SIGNS WITHIN THE FINANCIAL STATEMENTS Enron’s decline spurred a renewed interest in financial accounting and analysts now scour companies’ financial statementstoseeiftroubleislurking.Thisrenewedinteresthas ledtoalistofredflagstoconsiderwhenreviewingacompany’s financial statements. For example after conferring with New York University Accounting Professor Baruch Lev Fortune magazine’sShawnTullyidentifiedthefollowingwarningsigns: l Year after year a company reports restructuring charges and/or write-downs. This practice raises concerns because companies can use write-downs to mask oper- ating expenses which results in overstated earnings. l Acompany’s earnings have been propped up through a seriesofacquisitions.Acquisitionscanincreaseearningsifthe acquiringcompanyhasahigherP/Ethantheacquiredfirm butsuch“growth”cannotbesustainedoverthelongrun. l A company depreciates its assets more slowly than the industry average. Lower depreciation boosts current earnings but again this cannot be sustained because eventually depreciation must be recognized. l A company routinely has high earnings but low cash flow. As Tully points out this warning sign would have exposed Enron’s problems. In the second quarter of 2001 a few months before its problems began to unfold Enron reported earnings of 423 million versus a cash flow of minus 527 million. Along similar lines after consulting with various pro- fessionals Ellen Simon of the Newark Star Ledger came up with her list of red flags: l You wouldn’t buy the stock at today’s price. l You don’t really understand the company’s financial statements. l The company is in a business that lends itself to “cre- ative accounting.” l The company keeps taking nonrecurring charges. l Accounts receivable and inventory are increasing faster than sales revenues. l The company’s insiders are selling their stock. l The company is making aggressive acquisitions espe- cially in unrelated fields. Thereissomeoverlapbetweenthesetwolists. Alsononeof these items automatically means there is something wrong with the company—instead the items should be viewed as warning signs that cause you to take a closer look at the company’s performance before making an investment. To find information about a company quickly link to Here you can find company profiles and snapshots stock price quotes and share information key ratios and comparative ratios. Chapter 4 Analysis of Financial Statements 105

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assets such as used machinery are not traded in the marketplace. Further inflation affects asset values depreciation charges inventory costs and thus profits. Therefore a ratio analysis for one firm over time or a comparative analysisoffirmsofdifferentagesmustbeinterpretedwithcareandjudgment. 4. Seasonal factors can also distort a ratio analysis. For example the inventory turnover ratio for a food processor will be radically different if the balance sheet figure used for inventory is the one just before versus just after the close of the canning season. This problem can be mitigated by using monthly averages for inventory and receivables when calculating turnover ratios. 5. Firms can employ “window dressing” techniques to improve their financial statements. To illustrate people tend to think that larger hedge funds got large becausetheirhighreturnsattractedmanyinvestors.Howeverwelearnedin2007 thatsomefundssimplyborrowedandinvestedmoneytoincreasetheirapparent size. One fund Wharton Asset Management reported 2 billion “under man- agement”butithadactuallyattractedlessthan100millionofinvestors’capital. 6. Different accounting practices can distort comparisons. As noted earlierinven- toryvaluationanddepreciationmethodscanaffectfinancialstatementsandthus distortcomparisonsamongfirms.Alsoifonefirmleasesmuchofitsproductive equipmentitsfixedassetsturnovermaybeartificiallyhighbecauseleasedassets oftendonotappearonthebalancesheet.Atthesametimetheliabilityassociated with the lease may not appearas debt keeping the debt ratio low eventhough failure to make lease payments can bankrupt the firm. Therefore leasing can artificiallyimprovebothturnoverandthedebtratios.Theaccountingprofession hastakensteps toreducethisproblembutit stillcan cause distortions. 7. It is difficult to generalize about whether a particular ratio is “good” or “bad.” Forexampleahighcurrentratiomayindicateastrongliquiditypositionwhich isgoodbutitcanalsoindicateexcessivecashwhichisbadbecauseexcesscash inthebankisanonearningasset.Similarlyahighfixedassetsturnoverratiomay indicatethatthefirmusesitsassetsefficientlybutitcouldalsoindicatethatthe firmisshortofcashand cannotaffordtomakeneededfixed asset investments. 8. Firms often have some ratios that look “good” and others that look “bad” making it difficult to tell whether the company is on balance strong or weak. To deal with this problem banks and other lending organizations often use statistical procedures to analyze the net effects of a set of ratios and to classify firms according to their probability of getting into financial trouble. 17 We see then that ratio analysis is useful but analysts should be aware of the problems just listed and make adjustments as necessary. Ratio analysis conducted in a mechanical unthinking manner is dangerous but used intelligently and with good judgment it can provide useful insights into firms’ operations. Your judg- mentininterpretingratiosisboundtobeweakatthispointbutitwillimproveas you go through the remainder of the book. SELFTEST List three types of users of ratio analysis. Would the different users emphasize the same or different types of ratios Explain. List several potential difficulties with ratio analysis. “Window Dressing” Techniques Techniques employed by firms to make their finan- cial statements look better than they really are. 17 The technique used is discriminant analysis. The seminal work on this subject was undertaken by Edward I. Altman “Financial Ratios Discriminant Analysis and the Prediction of Corporate Bankruptcy” Journal of Finance September 1968 pp. 589−609. 106 Part 2 Fundamental Concepts in Financial Management

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4-13 POTENTIAL MISUSES OF ROE We know that managers should strive to maximize shareholder wealth. If a firm takesstepsthatimproveitsROEdoesthatmeanthatshareholderwealthwillalso beincreasedTheansweris“notnecessarily.”Indeedthreeproblemsarelikelyto arise if a firm relies too heavily on ROE to measure performance. ECONOMIC VALUE ADDED EVA VERSUS NET INCOME Economic Value Added EVA is a measure of how much management has added to shareholders’ wealth during the year. To better understand the idea behind EVA let’s look at Allied’s 2008 numbers in millions. All of the firm’s capital was supplied by investors except for 60 of accounts pay- able and 140 of accruals or 200 in total so its investor- supplied capital consists of 110 of notes payable 750 of long-term debt and 940 of common equity totaling 1800. Debt represents 47.78 of this total and equity is 52.22.Laterinthetextwewilldiscusshowtocalculatethe cost of Allied’s capital but for now to simplify things we will estimate its capital cost at 10. Thus the firm’s total dollar cost of capital which includes both debt and equity per year is 0.101800 ¼ 180. Now let’s look at Allied’s income statement. Its oper- ating income EBIT is 283.8 and its interest expense is 88.0. Therefore its taxable income is 283.8 − 88.0 ¼ 195.8. Taxes equal 40 of taxable income or 0.4195.8¼ 78.3 so the firm’s net income is 117.5. Its return on equity ROE is 117.5/940 ¼ 12.5. Given this data we can now calculate Allied’s EVA. The basic formula for EVA is as follows: EVA ¼ EBIT ð1 Corporate tax rateÞ ½ð Total investors 0 capitalÞð After tax cost of capitalÞ ¼ 283:8ð1 0:40Þð 1 800Þð0:10Þ ¼ 170:3 180 ¼ 9:7 This negative EVA indicates that Allied’s shareholders actually earned9.7millionlessthantheycould have earnedelsewherebyinvestinginotherstockswiththe same risk as Allied. To see where this −9.7 comes from let’s trace what happened to the money. l The firm generated 283.8 of operating income. l 78.3 went to the government to pay taxes leaving 205.5 available for investors—stockholders and bondholders. l 88.0 went to the bondholders in the form of interest payments thus leaving 117.5 for the stockholders. l HoweverAllied’sshareholdersmustalsoearnareturnon theequitycapitalthey haveinvestedinthefirm because they could have invested in other companies of compa- rable risk. We call this the cost of Allied’sequity. l Once Allied’s shareholders are “paid” their return the firm comes up 9.7 million short—that’s the economic valuemanagementaddedanditisnegative.Inasense Allied’s management created negative wealth because it provided shareholders with a lower return than they could have earned on alternative investments with the same risk as Allied’s stock. l In practice it is often necessary to make several adjustments to arrive at a “better” measure of EVA. The adjustments deal with nonoperating assets leased assets depreciation and other accounting details that we leave to advanced finance courses. The Connection between ROE and EVA EVA is different from traditional accounting profit because EVA reflects the cost of equity as well as the cost of debt. Indeed using the previous example we could also express EVA as net income minus the dollar cost of equity: EVA¼ Net Income Equity capital Cost of equity capital That expression could be rewritten as follows: EVA ¼ Equity capital Net income Equity capital Cost of equity capital which can be rewritten as EVA ¼ðEquity capitalÞðROE Cost of equity capitalÞ This last expression implies that EVA depends on three factors: rate of return as reflected in ROE risk which affects thecostofequityandsize whichismeasuredbytheequity employed. Recall that earlier in this chapter we said that shareholder value depends on risk return and capital invested. This final equation illustrates that point. Chapter 4 Analysis of Financial Statements 107

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First ROE does not consider risk. Shareholders care about ROE but they also careaboutrisk.Toillustrateconsidertwodivisionswithinthesamefirm.Division Shasstablecashflowsandapredictable15ROE.DivisionRhasa16expected ROE but its cash flows are quite risky so the expected ROE may not materialize. If managers were compensated solely on the basis of ROE and if the expected ROEs were actually achieved during the coming year Division R’s manager would receive a higher bonus than S’s even though S might actually be creating more value for shareholders as a result of its lower risk. Similarly financial leverage can increase expected ROE but more leverage means higher risk so raising ROE through the use of leverage may not be good. Second ROE does not consider the amount of invested capital. To illustrate consideracompanythatischoosingbetweentwomutuallyexclusiveprojects.Project A calls for investing 50000 at an expected ROE of 50 while Project B calls for investing1000000ata45ROE.Theprojectsareequallyriskyandthecompany’s costofcapitalis10.ProjectAhasthehigherROEbutitismuchsmaller.ProjectB should be chosenbecauseitwouldadd moretoshareholder wealth. Third a focus on ROE can cause managers to turn down profitable projects. For example suppose you manage a division of a large firm and the firm deter- minesbonusessolelyonthebasisofROE.Youprojectthatyourdivision’sROEfor the year will be an impressive 45. Now you have an opportunity to invest in a large low-risk project with an estimated ROE of 35 which is well above the firm’s 10 cost of capital. Even though this project is extremely profitable you might still be reluctant to undertake it because it would reduce your division’s average ROE and therefore your year-end bonus. These three examples suggest that a project’s ROE must be combined with its size and risk to determine its effect on the firm’s stock price: Contribution of a project to stock price ¼ fðROE Risk SizeÞ Wewilldiscussthisinmoredepthwhenweconsidercapitalbudgetingwherewe look in detail at how projects are selected so as to maximize stock prices. SELFTEST If a firm takes steps that increase its expected future ROE does this nec- essarily mean that the stock price will also increase Explain. 4-14 LOOKING BEYOND THE NUMBERS Working through this chapter should increase your ability to understand and interpret financial statements. This is critically important for anyone making business decisions or forecasting stock prices. However sound financial analysis involves more than just numbers—good analysis requires that certain qualitative factors also be considered. These factors as summarized by the American Asso- ciation of Individual Investors AAII include the following: 1. Are the company’s revenues tied to one key customer If so the company’s performancemaydeclinedramaticallyifthatcustomergoeselsewhere.Onthe other hand if the customer has no alternative to the company’s products this might actually stabilize sales. 2. To what extent are the company’s revenues tied to one key product Firms that focus on a single product are often efficient but a lack of diversification Students might want to refer to AAII’s educational web site at The site provides information on investing basics financial planning portfolio management and the like so that individuals can manage their own assets more effectively. 108 Part 2 Fundamental Concepts in Financial Management

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also increases risk because having revenues from several products stabilizes profits and cash flows in a volatile world. 3. To what extent does the company rely on a single supplier Depending on a single supplier may lead to an unanticipated shortage and a hit to sales and profits. 4. What percentage of the company’s business is generated overseas Compa- nies with a large percentage of overseas business are often able to realize higher growth and larger profit margins. However overseas operations may expose the firm to political risks and exchange rate problems. 5. How much competition does the firm face Increases in competition tend to lower prices and profit margins so when forecasting future performance it is important to assess the likely actions of current competitors and the entry of new ones. 6. Is it necessary for the company to continually invest in research and develop- ment If so its future prospects will depend critically on the success of new products in the pipeline. For example investors in a pharmaceutical company want to know whether the company has a strong pipeline of potential block- buster drugs and whether those products are doing well in the required tests. 7. Are changes in laws and regulations likely to have important implications for the firm For example when the future of electric utilities are forecasted it is crucial tofactorinthe effectsofproposed regulations affectingthe use ofcoal nuclear and gas-fired plants. SELFTEST What are some qualitative factors that analysts should consider when evaluating a company’s likely future financial performance TYING IT ALL TOGETHER In the last chapter we discussed the key financial statements and in this one we described how ratios are used to analyze the statements to identify weaknesses that need to be strengthened to maximize the stock price. Ratios are grouped into five categories: l Liquidity l Asset management l Debt management l Profitability l Market value The firm’s ratios are compared with averages for its industry and with the leading firms in the industry benchmarking and these comparisons are used to help formulate policies that will lead to improved future performance. Similarly the firm’sownratios canbeanalyzedovertimetoseeifitsfinancialsituationisgetting better or worse trend analysis. Chapter 4 Analysis of Financial Statements 109

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The single most important ratio over which management has control is the ROE—the other ratios are also important but mainly because they affect the ROE. OnetoolusedtoshowhowROEisdeterminedistheDuPontequation:ROE¼Profit margin × Total assets turnover × Equity multiplier. If the firm’s ROE is below the industryaverageandthatofthebenchmarkcompaniesaDuPontanalysiscanhelp identify problem areas that should be strengthened. In later chapters we consider specificactionsthatcanbetakentoimproveROEandthusafirm’sstockprice.One closing note: Although ratio analysis is useful it must be applied with care and good judgment. Actions taken to improve one ratio can have negative effects on some other ratio or ratios. For example it might be possible to improve the ROE by using more debt but the risk of the additional debt may lead to a decrease in the P/E ratio and thus in the firm’s stock price. Quantitative analysis such as ratio analysis can be useful but thinking through the results is even more important. SELF-TEST QUESTIONS AND PROBLEMS Solutions Appear in Appendix A ST-1 KEY TERMS Define each of the following terms: a. Liquidity ratios: current ratio acid test ratio b. Asset management ratios: inventory turnover ratio days sales outstanding DSO fixed assets turnover ratio total assets turnover ratio c. Debt management ratios: debt ratio times-interest-earned TIE ratio d. Profitability ratios: operating margin profit margin basic earning power BEP ratio return on total assets ROA return on common equity ROE e. Market value ratios: price/earnings P/E ratio market/book M/B ratio f. Trend analysis g. DuPont equation h. Benchmarking i. “Window dressing” techniques ST-2 DEBTRATIO LastyearK.BillingsworthCo.hadearningspershareof4anddividends per share of 2. Total retained earnings increased by 12 million during the year while book value per share at year-end was 40. Billingsworth has no preferred stock and no newcommonstockwasissuedduringtheyear.Ifitsyear-endtotaldebtwas120million what was the company’s year-end debt/assets ratio ST-3 RATIO ANALYSIS The following data apply to A.L. Kaiser Company millions of dollars: Cash and equivalents 100.00 Fixed assets 283.50 Sales 1000.00 Net income 50.00 Current liabilities 105.50 Current ratio 3.00× DSO a 40.55 days ROE 12.00 a This calculation is based on a 365-day year. 110 Part 2 Fundamental Concepts in Financial Management

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Kaiserhasnopreferred stock—onlycommonequitycurrentliabilitiesandlong-term debt. a. Find Kaiser’s 1 accounts receivable 2 current assets 3 total assets 4 ROA 5 common equity 6 quick ratio and 7 long-term debt. b. In Part a you should have found that Kaiser’s accounts receivable A/R ¼ 111.1 million. If Kaiser could reduce its DSO from 40.55 days to 30.4 days while holding other things constant how much cash would it generate If this cashwere used to buy back common stock at book value thus reducing common equity how would this affect 1 the ROE 2 the ROA and 3 the total debt/total assets ratio QUESTIONS 4-1 Financialratioanalysisisconductedbythreemaingroupsofanalysts:creditanalystsstock analysts and managers. What is the primary emphasis of each group and how would that emphasis affect the ratios they focus on 4-2 Why would the inventory turnover ratio be more important for someone analyzing a grocery store chain than an insurance company 4-3 OverthepastyearM.D.RyngaertCo.hadanincreaseinitscurrentratioandadeclinein its total assets turnover ratio. However the company’s sales cash and equivalents DSO and fixed assets turnover ratio remained constant. What balance sheet accounts must have changed to produce the indicated changes 4-4 Profit margins and turnover ratios vary from one industry to another. What differences would you expect to find between the turnover ratios profit margins and DuPont equa- tions for a grocery chain and a steel company 4-5 How does inflation distort ratio analysis comparisons for one company over time trend analysis and for different companies that are being compared Are only balance sheet items or both balance sheet and income statement items affected 4-6 If a firm’s ROE is low and management wants to improve it explain how using more debt might help. 4-7 Give some examples that illustrate how a seasonal factors and b different growth rates might distort a comparative ratio analysis. How might these problems be alleviated 4-8 Whyisitsometimesmisleadingtocompareacompany’sfinancialratioswiththoseofother firms that operate in the same industry 4-9 Suppose you were comparing a discount merchandiser with a high-end merchandiser. Suppose further that both companies had identical ROEs. If you applied the DuPont equation to both firms would you expect the three components to be the same for each company If not explain what balance sheet and income statement items might lead to the component differences. 4-10 Indicate the effects of the transactions listed in the following table on total current assets current ratioandnetincome.Use+toindicateanincrease−toindicate adecreaseand 0 toindicate either no effect oranindeterminate effect.Be prepared tostate anynecessary assumptionsandassumeaninitialcurrentratioofmorethan1.0.Note:Agoodaccounting background is necessary to answer some of these questions if yours is not strong answer just the questions you can. Total Current Assets Current Ratio Effect on Net Income a. Cash is acquired through issuance of additional common stock. b. Merchandise is sold for cash. c. Federal income tax due for the previous year is paid. d. A fixed asset is sold for less than book value. e. A fixed asset is sold for more than book value. f. Merchandise is sold on credit. g. Payment is made to trade creditors for previous purchases. h. A cash dividend is declared and paid. Chapter 4 Analysis of Financial Statements 111

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Total Current Assets Current Ratio Effect on Net Income i. Cash is obtained through short-term bank loans. j. Short-term notes receivable are sold at a discount. k. Marketable securities are sold below cost. l. Advances are made to employees. m. Current operating expenses are paid. n. Short-term promissory notes are issued to trade creditors in exchange for past due accounts payable. o. 10-year notes are issued to pay off accounts payable. p. A fully depreciated asset is retired. q. Accounts receivable are collected. r. Equipment is purchased with short-term notes. s. Merchandise is purchased on credit. t. The estimated taxes payable are increased. PROBLEMS Easy Problems 1–6 4-1 DAYSSALESOUTSTANDING BakerBrothershasaDSOof40daysanditsannualsalesare 7300000. What is its accounts receivable balance Assume that it uses a 365-day year. 4-2 DEBT RATIO Bartley Barstools has an equity multiplier of 2.4 and its assets are financed with some combination of long-term debt and common equity. What is its debt ratio 4-3 DuPONT ANALYSIS Doublewide Dealers has an ROA of 10 a 2 profit margin and an ROE of 15. What is its total assets turnover What is its equity multiplier 4-4 MARKET/BOOK RATIO Jaster Jets has 10 billion in total assets. Its balance sheet shows 1 billionin currentliabilities3billion inlong-termdebtand6billion incommonequity.It has 800 million shares of common stock outstanding and its stock price is 32 per share. What is Jaster’s market/book ratio 4-5 PRICE/EARNINGS RATIO A company has an EPS of 2.00 a cash flow per share of 3.00 and a price/cash flow ratio of 8.0×. What is its P/E ratio 4-6 DuPONT AND ROE A firm has a profit margin of 2 and an equity multiplier of 2.0. Its sales are 100 million and it has total assets of 50 million. What is its ROE Intermediate Problems 7–18 4-7 DuPONTANDNETINCOME EbersollMininghas6millioninsalesitsROEis12andits total assets turnover is 3.2×. The company is 50 equity financed. What is its net income 4-8 BASICEARNINGPOWER DuvalManufacturingrecentlyreportedthefollowinginformation: Net income 600000 ROA 8 Interest expense 225000 Duval’s tax rate is 35. What is its basic earning power BEP 4-9 M/B AND SHARE PRICE You are given the following information: Stockholders’ equity ¼ 3.75 billion price/earnings ratio ¼ 3.5 common shares outstanding ¼ 50 million and market/book ratio ¼ 1.9. Calculate the price of a share of the company’s common stock. 4-10 RATIO CALCULATIONS Assume the following relationships for the Brauer Corp.: Sales total assets 1.5× Return on assets ROA 3 Return on equity ROE 5 Calculate Brauer’s profit margin and debt ratio. 4-11 RATIOCALCULATIONS GraserTruckinghas12billioninassetsanditstaxrateis40.Its basic earning power BEP ratio is 15 and its return on assets ROA is 5. What is its times-interest-earned TIE ratio 112 Part 2 Fundamental Concepts in Financial Management

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4-12 TIE RATIO The H.R. PickettCorp. has500000 ofdebt outstanding and itpays an annual interest rate of 10. Its annual sales are 2 million its average tax rate is 30 and its net profit margin is 5. What is its TIE ratio 4-13 RETURN ON EQUITY Midwest Packaging’s ROE last year was only 3 but its manage- menthasdevelopedanewoperatingplanthatcallsforatotaldebtratioof60whichwill resultinannualinterestchargesof300000.ManagementprojectsanEBITof1000000on sales of 10000000 and it expects to have a total assets turnover ratio of 2.0. Under these conditions the tax rate will be 34. If the changes are made what will be the company’s return on equity 4-14 RETURN ON EQUITY AND QUICK RATIO Lloyd Inc. has sales of 200000 a net income of 15000 and the following balance sheet: Cash 10000 Accounts payable 30000 Receivables 50000 Other current liabilities 20000 Inventories 150000 Long-term debt 50000 Net fixed assets 90000 Common equity 200000 Total assets 300000 Total liabilities and equity 300000 Thenewownerthinksthatinventories areexcessiveandcanbeloweredtothepointwhere thecurrentratioisequaltotheindustryaverage2.5×withoutaffectingsalesornetincome. If inventories are sold off and not replaced thus reducing the current ratio to 2.5× if the funds generated are used to reduce common equity stock can be repurchased at book valueand ifnoother changesoccur byhowmuchwill theROEchangeWhatwill bethe firm’s new quick ratio 4-15 RETURN ON EQUITY Central City Construction CCC needs 1 million of assets to get started and it expects to have a basic earning power ratio of 20. CCC will own no securitiessoallofitsincomewillbeoperatingincome.IfitsochoosesCCCcanfinanceup to50ofitsassetswith debtwhichwillhavean8interest rate.Assuming a40taxrate onalltaxableincomewhatisthe differencebetweenCCC’sexpectedROEifitfinanceswith 50 debt versus its expected ROE if it finances entirely with common stock 4-16 CONCEPTUAL: RETURN ON EQUITY Which of the following statements is most correct Hint:WorkProblem4-15beforeanswering4-16andconsiderthesolutionsetupfor4-15as you think about 4-16. a. If a firm’s expected basic earning power BEP is constant for all of its assets and exceeds the interest rate on its debt adding assets and financing them with debt will raise the firm’s expected return on common equity ROE. b. The higher a firm’s tax rate the lower its BEP ratio other things held constant. c. The higher the interest rate on a firm’s debt the lower its BEP ratio other things held constant. d. The higher a firm’s debt ratio the lower its BEP ratio other things held constant. e. Statement a is false but statements b c and d are true. 4-17 TIE RATIO AEI Incorporated has 5 billion in assets and its tax rate is 40. Its basic earningpowerBEPratiois10anditsreturnonassetsROAis5.WhatisAEI’stimes- interest-earned TIE ratio 4-18 CURRENT RATIO The Petry Company has 1312500 in current assets and 525000 in current liabilities. Its initial inventory level is 375000 and it will raise funds as additional notespayableandusethemtoincreaseinventory.Howmuchcanitsshort-termdebtnotes payable increase without pushing its current ratio below 2.0 Challenging Problems 19−23 4-19 DSO AND ACCOUNTS RECEIVABLE Harrelson Inc. currently has 750000 in accounts receivableanditsdayssalesoutstandingDSOis55days.ItwantstoreduceitsDSOto35 daysbypressuringmoreofitscustomerstopaytheirbillsontime.Ifthispolicyisadopted the company’s average sales will fall by 15. What will be the level of accounts receivable following the change Assume a 365-day year. 4-20 P/E AND STOCK PRICE Fontaine Inc. recently reported net income of 2 million. It has 500000 shares of common stock which currently trades at 40 a share. Fontaine continues to expand and anticipates that 1 year from now its net income will be 3.25 million. Over the next year it also anticipates issuing an additional 150000 shares of stock so that 1 year fromnowitwillhave650000sharesofcommonstock.AssumingFontaine’sprice/earnings ratio remains at its current level what will be its stock price 1 year from now Chapter 4 Analysis of Financial Statements 113

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4-21 BALANCE SHEET ANALYSIS Complete the balance sheet and sales information using the following financial data: Debt ratio: 50 Current ratio: 1.8× Total assets turnover: 1.5× Days sales outstanding: 36.5 days a Gross profit margin on sales: Sales − Cost of goods sold/Sales ¼ 25 Inventory turnover ratio: 5× a Calculation is based on a 365-day year. Balance Sheet Cash Accounts payable Accounts receivable Long-term debt 60000 Inventories Common stock Fixed assets Retained earnings 97500 Total assets 300000 Total liabilities and equity Sales Cost of goods sold 4-22 RATIO ANALYSIS Data for Barry Computer Co. and its industry averages follow. a. Calculate the indicated ratios for Barry. b. Construct the DuPont equation for both Barry and the industry. c. Outline Barry’s strengths and weaknesses as revealed by your analysis. d. Suppose Barryhaddoubleditssalesaswellasitsinventoriesaccountsreceivableand common equity during 2008. How would that information affect the validity of your ratio analysis Hint: Think about averages and the effects of rapid growth on ratios if averages are not used. No calculations are needed. Barry Computer Company: Balance Sheet as of December 31 2008 In Thousands Cash 77500 Accounts payable 129000 Receivables 336000 Notes payable 84000 Inventories 241500 Other current liabilities 117000 Total current assets 655000 Total current liabilities 330000 Long-term debt 256500 Net fixed assets 292500 Common equity 361000 Total assets 947500 Total liabilities and equity 947500 Barry Computer Company: Income Statement for Year Ended December 31 2008 In Thousands Sales 1607500 Cost of goods sold Materials 717000 Labor 453000 Heat light and power 68000 Indirect labor 113000 Depreciation 41500 1392500 Gross profit 215000 Selling expenses 115000 General and administrative expenses 30000 Earnings before interest and taxes EBIT 70000 Interest expense 24500 Earnings before taxes EBT 45500 Federal and state income taxes 40 18200 Net income 27300 114 Part 2 Fundamental Concepts in Financial Management

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Ratio Barry Industry Average Current 2.0× Quick 1.3× Days sales outstanding a 35.0 days Inventory turnover 6.7× Total assets turnover 3.0× Profit margin 1.2 ROA 3.6 ROE 9.0 Total debt/total assets 60.0 a Calculation is based on a 365-day year. 4-23 DuPONT ANALYSIS A firm has been experiencing low profitability in recent years. Per- formananalysisofthefirm’sfinancialpositionusingtheDuPontequation.Thefirmhasno lease payments but has a 2 million sinking fund payment on its debt. The most recent industry average ratios and the firm’s financial statements are as follows: Industry Average Ratios Current ratio 2× Fixed assets turnover 6× Debt/total assets 30 Total assets turnover 3× Times interest earned 7× Profit margin 3 EBITDA coverage 9× Return on total assets 9 Inventory turnover 10× Return on common equity 12.86 Days sales outstanding a 24 days a Calculation is based on a 365-day year. Balance Sheet as of December 31 2008 Millions of Dollars Cash and equivalents 78 Accounts payable 45 Net receivables 66 Notes payable 45 Inventories 159 Other current liabilities 21 Total current assets 303 Total current liabilities 111 Long-term debt 24 Total liabilities 135 Gross fixed assets 225 Less depreciation 78 Common stock 114 Net fixed assets 147 Retained earnings 201 Total stockholders’ equity 315 Total assets 450 Total liabilities and equity 450 Income Statement for Year Ended December 31 2008 Millions of Dollars Net sales 795.0 Cost of goods sold 660.0 Gross profit 135.0 Selling expenses 73.5 EBITDA 61.5 Depreciation expense 12.0 Earnings before interest and taxes EBIT 49.5 Interest expense 4.5 Earnings before taxes EBT 45.0 Taxes 40 18.0 Net income 27.0 Chapter 4 Analysis of Financial Statements 115

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a. Calculate those ratios that you think would be useful in this analysis. b. Construct a DuPont equation and compare the company’s ratios to the industry average ratios. c. Do the balance sheet accounts or the income statement figures seem to be primarily responsible for the low profits d. Which specific accounts seem to be most out of line relative to other firms in the industry e. If the firm had a pronounced seasonal sales pattern or if it grew rapidly during the year how might that affect the validity of your ratio analysis How might you correct for such potential problems COMPREHENSIVE/SPREADSHEET PROBLEM 4-24 RATIO ANALYSIS The Corrigan Corporation’s 2007 and 2008 financial statements follow along with some industry average ratios. a. Assess Corrigan’s liquidity position and determine how it compares with peers and how the liquidity position has changed over time. b. Assess Corrigan’s asset management position and determine how it compares with peers and how its asset management efficiency has changed over time. c. Assess Corrigan’s debt management position and determine how it compares with peers and how its debt management has changed over time. d. Assess Corrigan’s profitability ratios and determine how they compare with peers and how its profitability position has changed over time. e. Assess Corrigan’s market value ratios and determine how its valuation compares with peers and how it has changed over time. f. Calculate Corrigan’s ROE as well as the industry average ROE using the DuPont equation. From this analysis how does Corrigan’s financial position compare with the industry average numbers g. What do you think would happen to its ratios if the company initiated cost-cutting measures that allowed it to hold lower levels of inventory and substantially decreased the cost of goods sold No calculations are necessary. Think about which ratios would be affected by changes in these two accounts. Corrigan Corporation: Balance Sheets as of December 31 2008 2007 Cash 72000 65000 Accounts receivable 439000 328000 Inventories 894000 813000 Total current assets 1405000 1206000 Land and building 238000 271000 Machinery 132000 133000 Other fixed assets 61000 57000 Total assets 1836000 1667000 Accounts and notes payable 432000 409500 Accrued liabilities 170000 162000 Total current liabilities 602000 571500 Long-term debt 404290 258898 Common stock 575000 575000 Retained earnings 254710 261602 Total liabilities and equity 1836000 1667000 116 Part 2 Fundamental Concepts in Financial Management

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Corrigan Corporation: Income Statements for Years Ending December 31 2008 2007 Sales 4240000 3635000 Cost of goods sold 3680000 2980000 Gross operating profit 560000 655000 General administrative and selling expenses 236320 213550 Depreciation 159000 154500 Miscellaneous 134000 127000 Earnings before taxes EBT 30680 159950 Taxes 40 12272 63980 Net income 18408 95970 Per-Share Data 2008 2007 EPS 0.80 4.17 Cash dividends 1.10 0.95 Market price average 12.34 23.57 P/E ratio 15.4× 5.65× Number of shares outstanding 23000 23000 Industry Financial Ratios a 2008 Current ratio 2.7× Inventory turnover b 7.0× Days sales outstanding c 32.0 days Fixed assets turnover b 13.0× Total assets turnover b 2.6× Return on assets 9.1 Return on equity 18.2 Debt ratio 50.0 Profit margin 3.5 P/E ratio 6.0× Price/cash flow ratio 3.5× a Industry average ratios have been constant for the past 4 years. b Based on year-end balance sheet figures. c Calculation is based on a 365-day year. INTEGRATED CASE D’LEON INC. PART II 4-25 FINANCIAL STATEMENT ANALYSIS PartIofthiscasepresented inChapter 3discussedthe situationofD’Leon Inc. a regional snack foods producer after an expansion program. D’Leon had increased plant capacity and undertaken a major marketing campaign in an attempt to “go national.” Thus far sales have not been up to the forecasted level costs have been higher than were projected and a large loss occurred in 2008 rather than the expected profit. As a result its managers directors and investors are concerned about the firm’s survival. Donna Jamison was brought in as assistant to Fred Campo D’Leon’s chairman who had the task of getting thecompanybackintoasoundfinancialposition.D’Leon’s2007and2008balancesheetsandincomestatements together with projections for 2009 are given in Tables IC 4-1 and IC 4-2. In addition Table IC 4-3 gives the Chapter 4 Analysis of Financial Statements 117

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company’s 2007 and 2008 financial ratios together with industry average data. The 2009 projected financial statementdatarepresentJamison’sandCampo’sbestguessfor2009resultsassumingthatsomenewfinancingis arranged to get the company “over the hump.” Jamison examined monthly data for 2008 not given in the case and she detected an improving pattern duringtheyear.Monthlysaleswererisingcostswerefallingandlargelossesintheearlymonthshadturnedtoa small profit by December. Thus the annual data look somewhat worse than final monthly data. Also it appears tobetakinglongerfortheadvertisingprogramtogetthemessageoutforthenewsalesofficestogeneratesales andforthenewmanufacturing facilitiestooperateefficiently. Inotherwords thelagsbetweenspendingmoney and deriving benefits were longer than D’Leon’s managers had anticipated. For these reasons Jamison and Campo see hope for the company—provided it can survive in the short run. Jamison must prepare an analysis of where the company is now what it must do to regain its financial healthandwhatactionsshouldbetaken.Yourassignmentistohelpheranswerthefollowingquestions.Provide clear explanations not yes or no answers. a. Why are ratios useful What are the five major categories of ratios b. CalculateD’Leon’s2009currentandquickratiosbasedontheprojectedbalancesheetandincomestatement data. What can you say about the company’s liquidity positions in 2007 in 2008 and as projected for 2009 We often think of ratios as being useful 1 to managers to help run the business 2 to bankers for credit analysis and 3 to stockholders for stock valuation. Would these different types of analysts have an equal interest in the company’s liquidity ratios c. Calculate the 2009 inventory turnover days sales outstanding DSO fixed assets turnover and total assets turnover. How does D’Leon’s utilization of assets stack up against other firms in the industry d. Calculate the 2009 debt and times-interest-earned ratios. How does D’Leon compare with the industry with respect to financial leverage What can you conclude from these ratios e. Calculate the 2009 operating margin profit margin basic earning power BEP return on assets ROA and return on equity ROE. What can you say about these ratios f. Calculate the 2009 price/earnings ratio and market/book ratio. Do these ratios indicate that investors are expected to have a high or low opinion of the company g. Use the DuPont equation to provide a summary and overview of D’Leon’s financial condition as projected for 2009. What are the firm’s major strengths and weaknesses h. Use thefollowing simplified 2009balance sheet toshow in general termshow an improvement in the DSO would tend to affect the stock price. For example if the company could improve its collection procedures andtherebyloweritsDSOfrom45.6daystothe32-dayindustryaveragewithoutaffectingsaleshowwould that change “ripple through” the financial statements shown in thousands below and influence the stock price Accounts receivable 878 Debt 1545 Other current assets 1802 Net fixed assets 817 Equity 1952 Total assets 3497 Liabilities plus equity 3497 i. Does it appear that inventories could be adjusted If so how should that adjustment affect D’Leon’s prof- itability and stock price j. In 2008 thecompany paid its suppliers muchlater than the duedates alsoit wasnot maintaining financial ratiosatlevelscalledforinitsbankloanagreements.Thereforesupplierscouldcutthecompanyoffandits bank could refuse to renew the loan when it comes due in 90 days. On the basis of data provided would youasacreditmanagercontinuetoselltoD’LeononcreditYoucoulddemandcashondelivery—thatis sell on terms of COD—but that might cause D’Leon to stop buying from your company. Similarly if you werethebankloanofficerwouldyourecommendrenewingtheloanordemanditsrepaymentWouldyour actions be influenced if in early 2009 D’Leon showed you its 2009 projections along with proof that it was going to raise more than 1.2 million of new equity k. In hindsight what should D’Leon have done in 2007 l. What are some potential problems and limitations of financial ratio analysis m. What are some qualitative factors that analysts should consider when evaluating a company’s likely future financial performance 118 Part 2 Fundamental Concepts in Financial Management

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Balance Sheets Table IC 4-1 2009E 2008 2007 Assets Cash 85632 7282 57600 Accounts receivable 878000 632160 351200 Inventories 1716480 1287360 715200 Total current assets 2680112 1926802 1124000 Gross fixed assets 1197160 1202950 491000 Less accumulated depreciation 380120 263160 146200 Net fixed assets 817040 939790 344800 Total assets 3497152 2866592 1468800 Liabilities and Equity Accounts payable 436800 524160 145600 Notes payable 300000 636808 200000 Accruals 408000 489600 136000 Total current liabilities 1144800 1650568 481600 Long-term debt 400000 723432 323432 Common stock 1721176 460000 460000 Retained earnings 231176 32592 203768 Total equity 1952352 492592 663768 Total liabilities and equity 3497152 2866592 1468800 Note: E indicates estimated. The 2009 data are forecasts. Income Statements Table IC 4-2 2009E 2008 2007 Sales 7035600 6034000 3432000 Cost of goods sold 5875992 5528000 2864000 Other expenses 550000 519988 358672 Total operating costs excluding depreciation amortization 6425992 6047988 3222672 EBITDA 609608 13988 209328 Depreciation amortization 116960 116960 18900 EBIT 492648 130948 190428 Interest expense 70008 136012 43828 EBT 422640 266960 146600 Taxes 40 169056 106784 a 58640 Net income 253584 160176 87960 EPS 1.014 1.602 0.880 DPS 0.220 0.110 0.220 Book value per share 7.809 4.926 6.638 Stock price 12.17 2.25 8.50 Shares outstanding 250000 100000 100000 Tax rate 40.00 40.00 40.00 Lease payments 40000 40000 40000 Sinking fund payments 0 0 0 Note: E indicates estimated. The 2009 data are forecasts. a The firm had sufficient taxable income in 2006 and 2007 to obtain its full tax refund in 2008. Chapter 4 Analysis of Financial Statements 119

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Ratio Analysis Table IC 4-3 2009E 2008 2007 Industry Average Current 1.2× 2.3× 2.7× Quick 0.4× 0.8× 1.0× Inventory turnover 4.7× 4.8× 6.1× Days sales outstanding DSO a 38.2 37.4 32.0 Fixed assets turnover 6.4× 10.0× 7.0× Total assets turnover 2.1× 2.3× 2.6× Debt ratio 82.8 54.8 50.0 TIE −1.0× 4.3× 6.2× Operating margin −2.2 5.6 7.3 Profit margin −2.7 2.6 3.5 Basic earning power −4.6 13.0 19.1 ROA −5.6 6.0 9.1 ROE −32.5 13.3 18.2 Price/earnings −1.4× 9.7× 14.2× Market/book 0.5× 1.3× 2.4× Book value per share 4.93 6.64 n.a. Note: E indicates estimated. The 2009 data are forecasts. a Calculation is based on a 365-day year. 120 Part 2 Fundamental Concepts in Financial Management

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Access the Thomson ONE problems through the CengageNOW™ web site. Use the Thomson ONE—Business School Edition online database to answer this chapter’s questions. Conducting a Financial Ratio Analysis on Ford Motor Company In Chapter 3 we looked at Starbucks’ financial statements. Now we use Thomson ONE to analyze Ford Motor Company. Enter Ford’s ticker symbol F and select “GO.” Select “Financial Statements” and “Thomson Financials”tofind Ford’s key financial statementsfor the past several years. Click on “FinancialRatios” and then “SEC Ratios.” From here you can select either annual or quarterly ratios. Under annual ratios there is an in-depth summary of Ford’s various ratios over the past 3 years. This information enables you to evaluate Ford’s performance over time for each of the ratio categories mentioned in the text liquidity asset management debt management profitability and market-based ratios. The text mentions that financial statement analysis has two major components: a trend analysis whereweevaluatechangesinthe keyratiosovertimeandapeer analysiswherewecomparefinancial ratios with firms that are in the same industry and/or line of business. We have already used Thomson ONE to conduct a trend analysis—next we use this tool to conduct a peer analysis. Click on “Com- parables”tofindsomesummaryfinancialinformationforFordandafewofitspeers.Byclickingonthe PeerSetsyoucanmodifythelistofpeerfirms.Thedefaultsetupis “PeerssetbySICCode.”Toobtaina comparison of many of the key ratios presented in the text click on “Financials” and select “Key Financial Ratios.” Discussion Questions 1. WhathashappenedtoFord’sliquiditypositionoverthepast3yearsHowdoesFord’sliquiditycomparewith thatofitspeersHint:Youmayuseboththepeerkeyfinancialratiosandliquiditycomparisontoanswerthis question. 2. Take a look at Ford’s inventory turnover ratio. How does this ratio compare with that of its peers Have there beenanyinterestingchangesovertimeinthismeasureDoyouconsiderFord’sinventorymanagementtobea strength or a weakness Explain. 3. Construct a DuPont analysis for Ford and its peers. What are Ford’s strengths and weaknesses compared to those of its competitors Chapter 4 Analysis of Financial Statements 121

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CHAPTER 5 Time Value of Money WillYouBeAbletoRetire Your reaction to that question is probably “First things first I’m worried about getting a job not about retiring” However understanding the retirement situation can help you land a job because 1 this is an important issue today 2 employers like to hire people who know what’s happening in the real world and 3 pro- fessors often test on the time value of money with problems related to saving for future pur- poses including retirement. A recent Fortune article began with some interesting facts: 1 The U.S. savings rate is the lowest of any industrial nation. 2 The ratio of U.S. workers to retirees which was 17 to 1 in 1950 is now down to 3 to 1 and it will decline to less than 2 to 1 after 2020. 3 With so few people paying into the Social Security system and so many drawing funds out Social Security is going to be in serious trouble. The article concluded that even people making 85000 per year will have trouble maintaining a reasonable standard of living after they retire and many of today’s college students will have to support their parents. This is an important issue for millions of Americans but many don’t know how to deal with it. When Fortune studied the retirement issue using the tools and techniques described in this chapter they concluded that most Americans have been ignoring what is most certainly going to be a huge personal and social problem. However if you study this chapter carefully you can avoid the trap that is likely to catch so many people. ª REIMAR/ALAMY 122

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PUTTING THINGS IN PERSPECTIVE Time value analysis has many applications including planning for retirement valuing stocks and bonds setting up loan payment schedules and making cor- porate decisions regarding investing in new plant and equipment. In fact of all financial concepts time value of money is the single most important concept. Indeed time value analysis is used throughout the book so it is vital that you understand this chapter before continuing. You need to understand basic time value concepts but conceptual knowledge will do you little good if you can’t do the required calculations. Therefore this chapter isheavyoncalculations. Most studentsstudyingfinance haveafinancialor scientific calculator some also own or have access to a computer. One of these tools is necessary to work many finance problems in a reasonable length of time. However when students start on this chapter many of them don’t know how to use the time value functions on their calculator or computer. If you are in that situation you will find yourself simultaneously studying concepts and trying to learntouseyourcalculatorandyouwillneedmoretimetocoverthischapterthan you might expect. 1 When you finish this chapter you should be able to: l Explain how the time value of money works and discuss why it is such an important concept in finance. l Calculate the present value and future value of lump sums. l Identify the different types of annuities and calculate the present value and futurevalueof bothanordinaryannuityandanannuitydue.You shouldalso be able to calculate relevant annuity payments. l Calculate the present value and future value of an unevencash flowstream. You willuse thisknowledgein later chapters thatshowhow tovaluecommon stocks and corporate projects. l Explain the difference between nominal periodic and effective interest rates. l Discuss the basics of loan amortization. 5-1 TIME LINES The first step in time value analysis is to set up a time line which will help you visualize what’s happening in a particular problem. As an illustration consider the following diagram where PV represents 100 that is on hand today and FV is the value that will be in the account on a future date: 02 1 3 5 Periods Cash PV 100 FV The intervals from 0 to 1 1 to 2 and 2 to 3 are time periods such as years or months. Time 0 is today and it is the beginning of Period 1 Time 1 is one period from today and it is both the end of Period 1 and the beginning of Period 2 and Excellent retirement calculators are available at and calculators. These calculators allow you to input hypothetical retirement savings information the program then shows if current retirement savings will be sufficient to meet retirement needs. 1 Calculator manuals tend to be long and complicated partly because they cover a number of topics that aren’t required in the basic finance course. Therefore on the textbook’s web site we provide tutorials for the most commonly used calculators. The tutorials are keyed to this chapter and they show exactly how to do the required calculations. If you don’t know how to use your calculator go to the textbook’s web site find the relevant tutorial and work through it as you study the chapter. Time Line An important tool used in time value analysis it is a graphical representation used to show the timing of cash flows. Chapter 5 Time Value of Money 123

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so forth. Although the periods are often years periods can also be quarters or months or even days. Note that each tick mark corresponds to both the endof one period and the beginning of the next one. Thus if the periods are years the tick mark at Time 2 represents the end of Year 2 and the beginning of Year 3. Cash flows are shown directly below the tick marks and the relevant interest rate is shown just above the time line. Unknown cash flows which you are trying to find are indicated by question marks. Here the interest rate is 5 a single cash outflow 100 is invested at Time 0 and the Time 3 value is an unknown inflow. In this example cash flows occur only at Times 0 and 3 with no flows at Times 1 or 2. Note that in our example the interest rate is constant for all 3 years. That condition is generally true but if it were not we would show different interest rates for the different periods. Time lines are essential when you are first learning time value concepts but even experts use them to analyze complex finance problems and we use them throughout the book. We begin each problem by setting up a time line to show what’shappeningafterwhichweprovideanequationthatmustbesolvedtofind theanswer.Thenweexplainhowtousearegularcalculatorafinancialcalculator and a spreadsheet to find the answer. SELFTEST Do time lines deal only with years or can other periods be used Set up a time line to illustrate the following situation: You currently have 2000 in a 3-year certificate of deposit CD that pays a guaranteed 4 annually. 5-2 FUTURE VALUES A dollar in hand today is worth more than a dollar to be received in the future becauseifyouhaditnowyoucouldinvestitearninterestandendupwithmore than a dollar in the future. The process of going to future values FVs from presentvaluesPVs is calledcompounding. For an illustration refer back to our 3-year time line and assume that you plan to deposit 100 in a bank that pays a guaranteed 5 interest each year. How much would you have at the end of Year 3Wefirstdefinesometermsafterwhichwesetupatimelineandshowhowthe future value is calculated. PV ¼ Present value or beginning amount. In our example PV ¼ 100. FV N ¼ Future value or ending amount of your account after N periods. Whereas PV is the value now or the present value FV N is the value N periods into the future after the interest earned has been added to the account. CF t ¼ Cash flow. Cash flows can be positive or negative. The cash flow for a particular period is often given as a subscript CF t where t is theperiod.ThusCF 0 ¼PV¼thecashflowatTime0whereasCF 3 is the cash flow at the end of Period 3. I ¼ Interest rate earned per year. Sometimes a lowercase i is used. Interest earned is based on the balance at the beginning of each year and we assume that it is paid at the end of the year. Here I¼ 5 or expressed as a decimal 0.05. Throughout this chapter we Future Value FV The amount to which a cash flow or series of cash flows will grow over a given period of time when compounded at a given interest rate. Present Value PV The value today of a future cash flow or series of cash flows. Compounding The arithmetic process of determining the final value of a cash flow or series of cash flows when compound interest is applied. 124 Part 2 Fundamental Concepts in Financial Management

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designate the interest rate as I because that symbol or I/YR for interest rate per year is used on most financial calculators. Note though that in later chapters we use the symbol r to denote rates because r for rate of return is used more often in the finance literature. Note too that in this chapter we generally assume that interest payments are guaranteed by the U.S. government hence they are certain. In later chapters we will consider risky investments where the interest rate earned might differ from its expected level. INT ¼ Dollarsofinterestearnedduringtheyear¼Beginningamount I. In our example INT ¼ 1000.05 ¼ 5. N ¼ Numberofperiodsinvolvedintheanalysis.InourexampleN¼3. Sometimesthenumberofperiodsisdesignatedwithalowercasen so both N and n indicate a number of periods. We can use four different procedures to solve time value problems. 2 These methods are described in the following sections. 5-2a Step-by-Step Approach The time line used to find the FV of 100 compounded for 3 years at 5 along with some calculations is shown. Multiply the initial amount and each succeeding amount by 1 þ I ¼ 1.05: Time Amount at beginning of period 100.00 02 1 5 3 105.00 110.25 115.76 SIMPLE VERSUS COMPOUND INTEREST As noted in the text interest earned on the interest earned in prior periods as was true in our example and is always true when we apply Equation 5-1 is called compound interest. If interest is not earned on interest we have simple interest. The formula for FV with simple interest is FV¼ PVþ PVIN so in our example FV would have been 100 þ 1000.053 ¼ 100 þ 15 ¼ 115 based on simple interest. Most financial contracts are based on compound interest but in legal proceedings the law often specifiesthatsimpleinterestmustbeused.Forexample Maris Distributing a company founded by home run king Roger Maris won a lawsuit against Anheuser-Busch A-B because A-B had breached a contract and taken away Maris’s franchise to sell Budweiser beer. The judge awarded Maris 50 million plus interest at 10 from 1997 when A-B breached the contract until the payment is actually made. The interest award was based on simple interest which as of 2008 had raised the total from 50 million to 50 million þ 0.1050 million11 years ¼ 105 million. If the law had allowed compound interest the award would have totaled 50 million1.10 11 ¼ 142.66 million or 37.66 million more. This legal proce- dure dates back to the days before calculators and com- puters. The law moves slowly 2 A fifth procedure using tables that show “interest factors” was used before financial calculators and computers became available. Now though calculators and spreadsheets such as Excel are programmed to calculate the specific factor needed for a given problem and then to use it to find the FV. This is more efficient than using the tables. Moreover calculators and spreadsheets can handle fractional periods and fractional interest rates such as the FV of 100 after 3.75 years when the interest rate is 5.375 whereas tables provide numbers only for whole periods and rates. For these reasons tables are not used in business today hence we do not discuss them in the text. Compound Interest Occurs when interest is earned on prior periods’ interest. Simple Interest Occurs when interest is not earned on interest. Chapter 5 Time Value of Money 125

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You start with 100 in the account—this is shown at t ¼ 0: l You earn1000.05¼5ofinterestduring the first yearsothe amountat the end of Year 1 or t ¼ 1 is 100 þ 5 ¼ 105. l You begin the second year with 105 earn 0.05105 ¼ 5.25 on the now larger beginning-of-period amount and end the year with 110.25. Interest during Year 2 is 5.25 and it is higher than the first year’s interest 5.00 because you earned 50.05¼ 0.25 interest on the first year’sinterest. This is called compounding and interest earned on interest is called compound interest. l This process continues and because the beginning balance is higher each successive year the interest earned each year increases. l The total interest earned 15.76 is reflected in the final balance 115.76. The step-by-step approach is useful because it shows exactly what is happening. Howeverthisapproachistime-consumingespeciallywhenanumberofyearsare involved so streamlined procedures have been developed. 5-2b Formula Approach In the step-by-step approach we multiply the amount at the beginning of each period by 1 þ I ¼ 1.05. If N ¼ 3 we multiply by 1 þ I three different times which is the same as multiplying the beginning amount by 1 þ I 3 . This concept can be extended and the result is this key equation: FV N ¼ PVð1þIÞ N 5-1 We can apply Equation 5-1 to find the FV in our example: FV 3 ¼ 100ð1:05Þ 3 ¼ 115:76 Equation 5-1 can be used with any calculator that has an exponential function making it easy to find FVs no matter how many years are involved. 5-2c Financial Calculators Financial calculators are extremely helpful in working time value problems. Their manuals explain calculators in detail and on the textbook’s web site we provide summaries of the features needed to work the problems in this book for several popular calculators. Also see the box entitled “Hints on Using Financial Calcu- lators”onpage128forsuggestionsthatwillhelpyouavoidcommonmistakes.If you are not yet familiar with your calculator we recommend that you work through the tutorial as you study this chapter. First note that financial calculators have five keys that correspond to the five variables in the basic time value equations. We show the inputs for our example abovethekeysandtheoutputtheFVbelowitskey.Becausetherearenoperiodic payments we enter 0 for PMT. We describe the keys in more detail below the diagram. FV PV I/YR N PMT 0 –100 35 115.76 126 Part 2 Fundamental Concepts in Financial Management

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N ¼ Number of periods. Some calculators use n rather than N. I/YR ¼ Interestrateperperiod.SomecalculatorsuseiorIratherthanI/YR. PV ¼ Presentvalue.Inourexamplewebeginbymakingadepositwhich is an outflow so the PV should be entered with a negative sign. On most calculators you must enter the 100 then press theþ/− key to switch from þ100 to −100. If you enter −100 directly 100 will be subtracted from the last number in the calculator giving you an incorrect answer. PMT ¼ Payment. This key is used when we have a series of equal or constant payments. Because there are no such payments in our illustrative problem we enter PMT ¼ 0. We will use the PMT key when we discuss annuities later in this chapter. FV ¼ Future value.Inthisexamplethe FVispositivebecauseweentered thePVasanegativenumber.Ifwehadenteredthe100asapositive number the FV would have been negative. AsnotedinourexampleyoufirstentertheknownvaluesNI/YRPMTand PV and then press the FV key to get the answer 115.76. Again note that if you enter the PV as 100 without a minus sign the FV will be given as a negative. The calculator assumes that either the PV or the FV is negative. This should not be confusing if you think about what you are doing. 5-2d Spreadsheets 3 Students generally use calculators for homework and exam problems but in business people generally use spreadsheets for problems that involve the time value of money TVM. Spreadsheets show in detail what is happening and they helpreducebothconceptualanddata-entryerrors.Thespreadsheetdiscussioncan be skipped without loss of continuity but if you understand the basics of Excel andhaveaccesstoacomputerwerecommendthatyoureadthroughthissection. Even if you aren’t familiar with spreadsheets the discussion will still give you an idea of how they operate. We used Excel to create Table 5-1 which summarizes the four methods of finding the FV and shows the spreadsheet formulas toward the bottom. Note that spreadsheets can be used to do calculations but they can also be used like a word processor to create exhibits like Table 5-1 which includes text drawings and calculations. The letters across the top designate columns the numbers to the left designate rowsandtherowsandcolumnsjointlydesignatecells.ThusC14isthe cell in which we specify the −100 investment C15 shows the interest rate and C16 shows the number of periods. We then created a time line on Rows 17 to 19 and on Row 21 we have Excel go through the step-by-step calculations multi- plyingthebeginning-of-yearvaluesby1þItofindthecompoundedvalueatthe end of each period. Cell G21 shows the final result. Then on Row 23 we illustrate the formula approachusing Excel tosolve Equation 5-1 and find the FV 115.76. Next on Rows 25 to 27 we show a picture of the calculator solution. Finally on Rows 29 and 30 we use Excel’s built-in FV function to find the answers given in Cells G29 and G30. The G29 answer is based on fixed inputs while the G30 answer is based on cell references which makes it easy to change inputs and see the effects on the output. Table 5-1 demonstrates that all four methods get the same result but they use different calculating procedures. It also shows that with Excel all inputs are 3 If you have never worked with spreadsheets you may choose to skip this section. However you might want to read through it and refer to this chapter’s Excel model to get an idea of how spreadsheets work. Chapter 5 Time Value of Money 127

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shown in one place which makes checking data entries relatively easy. Finally it shows that Excel can be used to create exhibits which are quite important in the real world. In business it’s often as important to explain what you are doing as it is to “get the right answer” because if decision makers don’t understand your analysis they may reject your recommendations. HINTS ON USING FINANCIAL CALCULATORS When using a financial calculator make sure your machine is set up as indicated here. Refer to your calculator manual or to our calculator tutorial on the text’s web site for information on setting up your calculator. l One payment per period. Many calculators “come out of the box” assuming that 12 pay- ments are made per year that is they assume monthly payments. However in this book we generally deal with problems in which only one payment is made each year. Therefore you should set your calculator at one payment per year and leave it there. See our tutorial or your calculator manual if you need assistance. l End mode. With most contracts payments are made at the end of each period. However some contracts call for payments at the beginning of each period. You can switch between “End Mode” and “Begin Mode” depending on the problem you are solving. Because most of the problems in this book call for end-of-period payments you should return your calculator to End Mode after you work a problem where payments are made at the beginning of periods. l Negative sign for outflows. Outflows must be entered as negative numbers. This generally means typing the outflow as a positive number and then pressing theþ− key to convert from þ to − before hitting the enter key. l Decimal places. With most calculators you can specify from 0 to 11 decimal places. When working with dollars we generally specify two decimal places. When dealing with interest rates we generally specifytwoplaceswhentherateisexpressedasapercentagee.g.5.25 but we specify four places when the rate is expressed as a decimal e.g. 0.0525. l Interest rates. For arithmetic operations with a nonfinancial calculator the 0.0525 must be used but with a financial calculator you must enter 5.25 not .0525 because financial calculators assume that rates are stated as percentages. Summary of Future Value Calculations Table 5-1 115.76 ABCDEFG 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Investment Interest rate No. of periods 100.00 5.00 3 CF 0 I N PV Periods: Cash Flow Time Line: 0 100 100 105.00 110.25 Step-by-Step Approach: FV 12 3 115.76 Formula Approach: FV N PV1 I N Calculator Approach: In the Excel formula the terms are entered in this sequence: interest periods 0 to indicate no intermediate cash fows and then the PV. The data can be entered as fxed numbers or as cell references. Excel Approach: Fixed inputs: Cell references: N I/YR PV PMT 3 5 100.00 0 FV 115.76 115.76 FV0.0530 100 FVC15C160C14 115.76 FV N 1001.05 3 FV N FV N 32 128 Part 2 Fundamental Concepts in Financial Management

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5-2e Graphic View of the Compounding Process Figure 5-1 shows how a 1 investment grows over time at different interest rates. WemadethecurvesbysolvingEquation5-1withdifferentvaluesforNandI.The interest rate is a growth rate: If a sum is deposited and earns 5 interest per year thefundsondepositwillgrowby5peryear.Note alsothat timevalueconcepts can be applied to anything that grows—sales population earnings per share or future salary. SELFTEST Explain why this statement is true: A dollar in hand today is worth more than a dollar to be received next year. What is compounding What’s the difference between simple interest and compound interest What would the future value of 100 be after 5 years at 10 compound interest at 10 simple interest 161.05 150.00 Suppose you currently have 2000 and plan to purchase a 3-year certificate of deposit CD that pays 4 interest compounded annually. How much will you have when the CD matures How would your answer change if the interest rate were 5 or 6 or 20 2249.73 2315.25 2382.03 3456.00 Hint: With a calculator enter N ¼ 3 I/YR ¼ 4 PV ¼ −2000 and PMT¼ 0 then press FV to get 2249.73. Enter I/YR¼ 5 to override the 4 and press FV again to get the second answer. In general you can change one input at a time to see how the output changes. A company’s sales in 2008 were 100 million. If sales grow at 8 what will they be 10 years later in 2018 215.89 million How much would 1 growing at 5 per year be worth after 100 years What would FV be if the growth rate was 10 131.50 13780.61 Growth of 1 at Various Interest Rates and Time Periods FIGURE 5-1 Future Value of 1 8 9 10 6 7 4 5 2 1 3 0 1.00 2.00 3.00 4.00 5.00 6.00 I 0 I 5 I 10 I 20 Periods Chapter 5 Time Value of Money 129

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5-3 PRESENT VALUES Finding apresentvalue isthereverseoffinding afuturevalue.Indeedwesimply solve Equation 5-1 the formula for the future value for the PV to produce the basic present value Equation 5-2: Future value ¼ FV N ¼ PVð1 þ IÞ N 5-1 Present value ¼ PV ¼ FV N ð1þIÞ N 5-2 WeillustratePVswiththefollowingexample.AbrokerofferstosellyouaTreasury bond that will pay 115.76 in 3 years from now. Banks are currently offering a guaranteed5intereston3-yearcertificatesofdepositCDsandifyoudon’tbuy the bond you will buy a CD. The 5 rate paid on the CDs is defined as your opportunitycostortherateofreturnyoucouldearnonanalternativeinvestmentof similarrisk.Giventheseconditionswhat’sthemostyoushouldpayforthebond Weanswerthisquestionusingthefourmethodsdiscussedinthelastsection—step- by-stepformulacalculatorandspreadsheet.Table5-2summarizestheresults. First recall from the future value example in the last section that if you invested 100 at 5 it would grow to 115.76 in 3 years. You would also have 115.76after3yearsifyouboughttheT-bond.Thereforethemostyoushouldpay forthe bondis100—thisis its “fairprice.”Ifyou could buythe bondfor less than 100 you should buy it rather than invest in the CD. Conversely if its price was more than 100 you should buy the CD. If the bond’s price was exactly 100 you should be indifferent between the T-bond and the CD. The100isdefinedasthepresentvalueorPVof115.76duein3yearswhen the appropriate interest rate is 5. In general the present value of a cash flow due N years in the future is the amount which if it were on hand today would grow to equal the given future amount. Because 100 would grow to 115.76 in 3 years at a 5 interest rate 100 is the present value of 115.76 due in 3 years at a 5 rate. Finding present values is called discounting and as noted above it is the reverse ofcompounding—ifyouknowthePVyoucancompoundtofindtheFVwhileif you know the FV you can discount to find the PV. Opportunity Cost The rate of return you could earn on an alterna- tive investment of similar risk. Discounting The process of finding the present value of a cash flow or a series of cash flows discounting is the reverse of compounding. Summary of Present Value Calculations Table 5-2 115.76 ABCDEFG 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 Future payment Interest rate No. of periods 115.76 5.00 3 CF N I N FV Periods: Cash Flow Time Line: 0 PV 100.00 105.00 110.25 Step-by-Step Approach: 115.76 12 3 100.00 Formula Approach: PV FV N /1 I N Calculator Approach: In the Excel formula 0 indicates that there are no intermediate cash fows. Excel Approach: Fixed inputs: Cell references: N I/YR PV PMT 3 5 100.00 0 FV 115.76 100.00 PV0.0530115.76 PVC65C660C64 100.00 PV 115.76/1.05 3 PV PV 130 Part 2 Fundamental Concepts in Financial Management

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ThetopsectionofTable5-2calculatesthePVusingthestep-by-stepapproach. When we found the future value in the previous section we worked from left to right multiplying the initial amount and each subsequent amount by 1 þ I. To find present values we work backward or from right to left dividing the future value and each subsequent amount by 1 þ I. This procedure shows exactly what’s happening which can be quite useful when you are working complex problems. However it’s inefficient especially when you are dealing with a number of years. With the formula approach we use Equation 5-2 simply dividing the future value by 1 þ I N . This is more efficient than the step-by-step approach and it givesthesameresult.Equation5-2isbuiltintofinancialcalculatorsandasshown inTable5-2wecanfindthePVbyenteringvaluesforNI/YRPMTandFVand then pressing the PV key. Finally spreadsheets have a function that’s essentially the same as the calculator which also solves Equation 5-2. The fundamental goal of financial management is to maximize the firm’s valueandthevalueofabusinessoranyassetincludingstocksandbondsisthe present value of its expected future cash flows. Because present value lies at the heart of the valuation process we will have much more to say about it in the remainder of this chapter and throughout the book. 5-3a Graphic View of the Discounting Process Figure 5-2 shows that the present value of a sum to be received in the future decreases and approaches zero as the payment date is extended further into the future and that the present value falls faster at higher interest rates. At relatively high rates funds due in the future are worth very little today and even at rela- tively low rates present values of sums due in the very distant future are quite small. For example at a 20 discount rate 1 million due in 100 years would be worth only 0.0121 today. This is because 0.0121 would grow to 1 million in 100 years when compounded at 20. Present Value of 1 at Various Interest Rates and Time Periods FIGURE 5-2 Present Value of 1 40 50 20 30 10 0.20 0 0.40 0.60 0.80 1.00 I 20 I 10 I 5 I 0 Periods Chapter 5 Time Value of Money 131

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SELFTEST What is discounting and how is it related to compounding How is the future value equation 5-1 related to the present value equation 5-2 How does the present value of a future payment change as the time to receipt is lengthened as the interest rate increases Suppose a U.S. government bond promises to pay 2249.73 three years from now. If the going interest rate on three-year government bonds is 4 how much is the bond worth today How would your answer change if the bond matured in 5 years rather than 3 What if the interest rate on the 5-year bond was 6 rather than 4 2000 1849.11 1681.13 How much would 1000000 due in100 years be worth today if the discount rate was 5 if the discount rate was 20 7604.49 0.0121 5-4 FINDING THE INTEREST RATE I Thus far we have used Equations 5-1 and 5-2 to find future and present values. Thoseequationshavefourvariablesandifweknowthreeofthevariableswecan solveforthefourth.ThusifweknowPVIandNwe cansolve5-1forFVwhile if we know FV I and N we can solve 5-2 to find PV. That’s what we did in the preceding two sections. Now suppose we know PV FV and N and we want to find I. For example suppose we know that agiven bond has acost of 100 and that it will return 150 after 10 years. Thus we know PV FV and N and we want to find the rate of return we will earn if we buy the bond. Here’s the situation: FV ¼ PVð1þIÞ N 150 ¼ 100ð1þIÞ 10 150100 ¼ð1þIÞ 10 1:5 ¼ð1þIÞ 10 Unfortunatelywecan’tfactorIouttoproduceassimpleaformulaaswecouldfor FV and PV—we can solve for I but it requires a bit more algebra. 4 However financial calculators and spreadsheets can find interest rates almost instantly. Here’s the calculator setup: FV PV I/YR N PMT 0 150 –100 10 4.14 Enter N ¼ 10 PV ¼ −100 PMT ¼ 0 because there are no payments until the securitymaturesandFV¼150.ThenwhenyoupresstheI/YRkeythecalculator gives the answer 4.14. You would get this same answer with a spreadsheet. 4 Raise the left side of the equation the 1.5 to the power 1/N¼ 1/10¼ 0.1 getting 1.0414. That number is 1 plus the interest rate so the interest rate is 0.0414 ¼ 4.14. 132 Part 2 Fundamental Concepts in Financial Management

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SELFTEST The U.S. Treasury offers to sell you a bond for 585.43. No payments will be made until the bond matures 10 years from now at which time it will be redeemed for 1000. What interest rate would you earn if you bought this bond for 585.43 What rate would you earn if you could buy the bond for 550 for 600 5.5 6.16 5.24 Microsoft earned 0.33 per share in 1997. Ten years later in 2007 it earned 1.42. What was the growth rate in Microsoft’s earnings per share EPS over the 10-year period If EPS in 2007 had been 0.90 rather than 1.42 what would the growth rate have been 15.71 10.55 5-5 FINDING THE NUMBER OF YEARS N We sometimes need to know how long it will take to accumulate a certain sum of money given our beginning funds and the rate we will earn on those funds. For examplesupposewebelievethatwecouldretirecomfortablyifwehad1million. We want to find how long it will take us to acquire 1 million assuming we now have 500000 invested at 4.5. We cannot use a simple formula—the situation is like that with interest rates. We can set up a formula that uses logarithms but calculators and spreadsheets find N very quickly. Here’s the calculator setup: FV PV I/YR N PMT 0 1000000 –500000 4.5 15.7473 EnterI/YR¼4.5PV¼−500000PMT¼0andFV¼1000000.Thenwhenyoupress the N key you get the answer 15.7473 years. If you plug N¼ 15.7473 into the FV formula you can prove that this is indeed the correct number of years: FV¼ PVð1 þ IÞ N ¼ 500000ð1:045Þ 15:7473 ¼ 1000000 You would also get N ¼ 15.7473 with a spreadsheet. SELFTEST How long would it take 1000 to double if it was invested in a bank that paid 6 per year How long would it take if the rate was 10 11.9 years 7.27 years Microsoft’s 2007 earnings per share were 1.42 and its growth rate during the prior 10 years was 15.71 per year. If that growth rate was maintained how long would it take for Microsoft’s EPS to double 4.75 years 5-6 ANNUITIES Thus far we have dealt with single payments or “lump sums.” However many assets provide a series of cash inflows over time and many obligations such as auto student and mortgage loans require a series of payments. When the pay- ments are equal and are made at fixed intervals the series is an annuity. For example 100 paid at the end of each of the next 3 years is a 3-year annuity. If the payments occur at the end of each year the annuity is an ordinary or deferred Annuity A series of equal payments at fixed intervals for a specified number of periods. Chapter 5 Time Value of Money 133

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annuity. If the payments are made at the beginning of each year the annuity is an annuitydue.Ordinaryannuitiesaremorecommoninfinancesowhenweusethe term annuity in this book assume that the payments occur at the ends of the periods unless otherwise noted. Here are the time lines for a 100 3-year 5 ordinary annuity and for the same annuity on an annuity due basis. With the annuity due each payment is shifted tothe left byone year.A 100 deposit will be made each yearso we show the payments with minus signs: Ordinary Annuity: Periods Payments 100 100 100 01 5 23 Annuity Due: Periods Payments 100 100 100 01 5 23 As we demonstrate in the following sections we can find an annuity’s future and presentvaluesthe interest ratebuilt intoannuitycontractsandthelengthoftime it takes to reach a financial goal using an annuity. Keep in mind that annuities musthave constant paymentsandafixed numberofperiods.Iftheseconditionsdon’t hold we don’t have an annuity. SELFTEST What’s the difference between an ordinary annuity and an annuity due Why would you prefer to receive an annuity due for 10000 per year for 10 years than an otherwise similar ordinary annuity 5-7 FUTURE VALUE OF AN ORDINARY ANNUITY The future value of an annuity can be found using the step-by-step approach or using a formula a financial calculator or a spreadsheet. As an illustration con- sidertheordinaryannuitydiagrammedearlierwhereyoudeposit100attheend ofeachyearfor3yearsandearn5peryear.Howmuchwillyouhaveattheend of the third year The answer 315.25 is defined as the future value of the annuity FVA N it is shown in Table 5-3. Asshowninthestep-by-stepsectionofthetablewecompoundeachpayment out to Time 3 then sum those compounded values to find the annuity’s FV FVA 3 ¼ 315.25. The first payment earns interest for two periods the second payment earns interest for one period and the third payment earns no interest at all because it is made at the end of the annuity’s life. This approach is straight- forward but if the annuity extends out for many years the approach is cumber- some and time-consuming. Asyoucanseefromthetimelinediagramwiththestep-by-stepapproachwe apply the following equation with N ¼ 3 and I ¼ 5: FVA N ¼ PMTð1þIÞ N 1 þ PMTð1þIÞ N 2 þ PMTð1þIÞ N 3 ¼ 100ð1:05Þ 2 þ100ð1:05Þ 1 þ100ð1:05Þ 0 ¼ 315:25 Annuity Due An annuity whose pay- ments occur at the begin- ning of each period. FVA N The future value of an annuity over N periods. Ordinary Deferred Annuity An annuity whose pay- ments occur at the end of each period. 134 Part 2 Fundamental Concepts in Financial Management

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We can generalize and streamline the equation as follows: FVA N ¼ PMTð1þIÞ N 1 þPMTð1þIÞ N 2 þPMTð1þIÞ N 3 þ ...þPMTð1þIÞ 0 ¼ PMT ð1þIÞ N 1 I " 5-3 The first line shows the equation in its long form. It can be transformed to the second form which can be used to solve annuity problems with a nonfinancial calculator. 5 This equation is also built into financial calculators and spreadsheets. WithanannuitywehaverecurringpaymentshencethePMTkeyisused.Here’s the calculator setup for our illustrative annuity: FV PV I/YR N PMT –100 End Mode 0 5 3 315.25 We enter PV ¼ 0 because we start off with nothing and we enter PMT ¼ −100 because we plan to deposit this amount in the account at the end of each year. When we press the FV key we get the answer FVA 3 ¼ 315.25. Because this is an ordinary annuity with payments coming at the end of each yearwemust setthe calculator appropriately. As noted earlier calculators “come outofthebox”settoassumethatpaymentsoccurattheendofeachperiodthatis to deal with ordinary annuities. However there is a key that enables us to switch between ordinary annuities and annuities due. For ordinary annuities the 5 The long form of the equation is a geometric progression that can be reduced to the second form. Summary: Future Value of an Ordinary Annuity Table 5-3 ABCDEFG 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 Payment amount Interest rate No. of periods 100.00 5.00 3 PMT I N Periods: Cash Flow Time Line: 0 100 100 100 100.00 105.00 110.25 315.25 Step-by-Step Approach. Multiply each payment by 1 I N t and sum these FVs to fnd FVA N : 12 3 315.25 Formula Approach: FVA N PMT Calculator Approach: Excel entries correspond with these calculator keys: Excel Function Approach: Fixed inputs: Cell references: N I/YR PV PMT 3 5 0 100.00 FV 315.25 315.25 FV0.053 1000 FVC132C133 C1310 315.25 I/YR N PMT PV FV FVA N FVA N 1 I N 1 I Chapter 5 Time Value of Money 135

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designation is “End Mode” or something similar while for annuities due the designation is “Begin” or “Begin Mode” or “Due” or something similar. If you make a mistake and set your calculator on Begin Mode when working with an ordinary annuity each payment will earn interest for one extra year. That will cause the compounded amounts and thus the FVA to be too large. The last approach in Table 5-3 shows the spreadsheet solution using Excel’s built-in function. We can put in fixed values for N I and PMT or set up an Input Section where we assign values to those variables and then input values into the functionascellreferences.Usingcellreferencesmakesiteasytochangetheinputs to see the effects of changes on the output. SELFTEST For an ordinary annuity with five annual payments of 100 and a 10 interest rate how many years will the first payment earn interest What will this payment’s value be at the end Answer this same question for the fifth payment. 4 years 146.41 0 years 100 Assume that you plan to buy a condo 5 years from now and you estimate that you can save 2500 per year. You plan to deposit the money in a bank that pays 4 interest and you will make the first deposit at the end of the year. How much will you have after 5 years How will your answer change if the interest rate is increased to 6 or lowered to 3 13540.81 14092.73 13272.84 5-8 FUTURE VALUE OF AN ANNUITY DUE Because each payment occurs one period earlier with an annuity due all of the payments earn interest for one additional period. Therefore the FV of an annuity duewillbegreaterthanthatofasimilarordinaryannuity.Ifyouwentthroughthe step-by-stepprocedureyouwouldseethat ourillustrativeannuityduehasanFV of 331.01 versus 315.25 for the ordinary annuity. Withtheformulaapproachwefirst use Equation5-3butsinceeach payment occurs one period earlier we multiply the Equation 5-3 result by 1 þ I: FVA due ¼ FVA ordinary ð1þIÞ 5-4 Thus for the annuity due FVA due ¼ 315.251.05 ¼ 331.01 which is the same result when the period-by-period approach is used. With a calculator we input the variables just as we did with the ordinary annuity but now we set the cal- culator to Begin Mode to get the answer 331.01. SELFTEST Why does an annuity due always have a higher future value than an ordi- nary annuity If you calculated the value of an ordinary annuity how could you find the value of the corresponding annuity due Assume that you plan to buy a condo 5 years from now and you need to save for a down payment. You plan to save 2500 per year with the first deposit made immediately and you will deposit the funds in a bank account that pays 4 interest. How much will you have after 5 years How much will you have if you make the deposits at the end of each year 14082.44 13540.81 136 Part 2 Fundamental Concepts in Financial Management

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5-9 PRESENT VALUE OF AN ORDINARY ANNUITY The present value of an annuity PVA N can be found using the step-by-step formulacalculatororspreadsheetmethod.LookbackatTable5-3.TofindtheFV of the annuity we compounded the deposits. To find the PV we discount them dividing each payment by 1 þ I. The step-by-step procedure is diagrammed as follows: 2 1 0 5 Periods Payments 3 100 100 100 95.24 90.70 86.38 272.32 Present value of the annuity PVA N Equation 5-5 expresses the step-by-step procedure in a formula. The bracketed formofthe equationcanbeusedwithascientificcalculatorand itishelpfulifthe annuity extends out for a number of years: PVA N ¼ PMTð1þIÞ 1 þPMTð1þIÞ 2 þ þ PMTð1þIÞ N ¼ PMT 1 1 ð1þIÞ N I 2 6 6 4 3 7 7 5 ¼ 100½ 1 1ð1:05Þ 3 0:05¼ 272:32 5-5 Calculators are programmed to solve Equation 5-5 so we merely input the variables and press the PV key making sure the calculator is set to End Mode. The calculator setup follows for both an ordinary annuity and an annuity due. Note that the PV of the annuity due is larger because each payment is discounted back one less year. Note too that you can find the PV of the ordinary annuity and then multiply by 1 þ I ¼ 1.05 getting 272.321.05 ¼ 285.94 the PV of the annuity due. FV PV I/YR N PMT –100 0 End Mode Ordinary Annuity 5 3 272.32 FV PV I/YR N PMT –100 0 Begin Mode Annuity Due 5 3 285.94 PVA N The present value of an annuity of N periods. Chapter 5 Time Value of Money 137

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SELFTEST Compared to an ordinary annuity why does an annuity due have a higher present value If you know the present value of an ordinary annuity how can you find the PV of the corresponding annuity due What is the PVA of an ordinary annuity with 10 payments of 100 if the appropriate interest rate is 10 What would the PVA be if the interest rate was 4 What if the interest rate was 0 How would the PVA values differ if we were dealing with annuities due 614.46 811.09 1000.00 675.90 843.53 1000.00 Assumethatyouareofferedanannuitythatpays100attheendofeachyear for10years.Youcouldearn8onyourmoneyinotherinvestmentswithequal risk. What is the most you should pay for the annuity If the payments began immediately how much would the annuity be worth 671.01 724.69 5-10 FINDING ANNUITY PAYMENTS PERIODS AND INTEREST RATES Wecanfindpaymentsperiodsandinterestratesforannuities.Herefivevariables comeintoplay:NIPMTFVand PV.Ifweknowanyfourwe canfindthefifth. 5-10a Finding Annuity Payments PMT Suppose we need to accumulate 10000 and have it available 5 years from now. Suppose further that we can earn a return of 6 on our savings which are cur- rently zero. Thus we know that FV ¼ 10000 PV ¼ 0 N ¼ 5 and I/YR ¼ 6. We can enter these values in a financial calculator and press the PMT key to find how large our deposits must be. The answer will of course depend on whether we make deposits at the end of each year ordinary annuity or at the beginning annuity due. Here are the results for each type of annuity: FV PV I/YR N PMT 10000 0 End Mode Ordinary Annuity 6 5 –1773.96 FV PV I/YR N PMT 10000 0 Begin Mode Annuity Due 6 5 –1673.55 Thus you must save 1773.96 per year if you make payments at the end of each year but only 1673.55 if the payments begin immediately. Note that the required payment for the annuity due is the ordinary annuity payment divided by 1 þ I: 1773.96/1.06¼1673.55.Spreadsheetscanalsobeusedtofindannuitypayments. 5-10b Finding the Number of Periods N Suppose you decide to make end-of-year deposits but you can save only 1200 per year. Again assuming that you would earn 6 how long would it take to reach your 10000 goal Here is the calculator setup: 138 Part 2 Fundamental Concepts in Financial Management

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FV PV I/YR N PMT 10000 –1200 0 End Mode 6 6.96 With these smaller deposits itwouldtake6.96 yearstoreach the 10000 target.If you began the deposits immediately you would have an annuity due and N would be a bit less 6.63 years. 5-10c Finding the Interest Rate I Now suppose you can save only 1200 annually but you still want to have the 10000 in 5 years. What rate of return would enable you to achieve your goal Here is the calculator setup: FV PV I/YR N PMT 10000 –1200 0 End Mode 5 25.78 You would need to earn a whopping 25.78. About the only way to earn such a high return would be to invest in speculative stocks or head to the casinos in Las Vegas. Of course investing in speculative stocks and gambling aren’t like making depositsinabankwithaguaranteedrateofreturnsothere’sagoodchanceyou’d endupwithnothing.Youmightconsiderchanging yourplans—savemorelower your10000targetorextendyourtimehorizon.Itmightbeappropriatetoseeka somewhat higher return but trying to earn 25.78 in a 6 market would require taking on more risk than would be prudent. It’s easy to find rates of return using a financial calculator or a spreadsheet. However without one of these tools you would have to go through a trial-and- errorprocesswhichwouldbeverytime-consumingifmanyyearswere involved. SELFTEST Suppose you inherited 100000 and invested it at 7 per year. How much could you withdraw at the end of each of the next 10 years How would your answer change if you made withdrawals at the beginning of each year 14237.75 13306.31 If you had 100000 that was invested at 7 and you wanted to withdraw 10000 at the end of each year how long would your funds last How long wouldtheylastifyouearned0Howlongwouldtheylastifyouearnedthe 7 but limited your withdrawal to 7000 per year 17.8 years 10 years forever Your rich uncle named you beneficiary of his life insurance policy. The insurancecompanygivesyouachoiceof100000todayora12-yearannuity of 12000 at the end of each year. What rate of return is the insurance company offering 6.11 Assume thatyou just inheritedan annuity thatwill pay you 10000 peryear for 10 years with the first payment being made today. A friend of your mother offers to give you 60000 for the annuity. If you sell it what rate of return would your mother’s friend earn on his investment If you think a “fair” return would be 6 how much should you ask for the annuity 13.70 78016.92 Chapter 5 Time Value of Money 139

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5-11 PERPETUITIES Inthe lastsectionwe dealtwithannuities whose payments continueforaspecific number of periods—for example 100 per year for 10 years. However some securities promise to make payments forever. For example in 1749 the British government issued bonds whose proceeds were used to pay off other British bonds and since this action consolidated the government’s debt the new bonds were called consols. Because consols promise to pay interest forever they are “perpetuities.” The interest rate on the consols was 2.5 so a bond with a face value of 1000 would pay 25 per year in perpetuity. 6 A perpetuity is simply an annuity with an extended life. Because the pay- ments go on forever you can’t apply the step-by-step approach. However it’s easy to find the PV of a perpetuity with a formula found by solving Equation 5-5 with N set at infinity: 7 PV of a perpetuity¼ PMT I 5-6 NowwecanuseEquation5-6tofindthevalueofaBritishconsolwithafacevalue of1000 thatpays 25 per year inperpetuity. Theanswerdepends on the interest rate.In1888the“goingrate”asestablishedinthefinancialmarketplacewas2.5 so at that time the consol’s value was 1000: Consol value 1888 ¼ 250:025¼ 1000 In 2008 120 years later the annual payment was still 25 but the going interest rate had risen to 4.3 causing the consol’s value to fall to 581.40: Consol value 2008 ¼ 250:043¼ 581:40 Note though that if interest rates decline in the future say to 2 the value of the consol will rise: Consol value if rates decline to 2¼ 250:02¼ 1250:00 These examples demonstrate an important point: When interest rates change the prices of outstanding bonds also change. Bond prices decline when rates rise and increase when rates fall. We will discuss this point in more detail in Chapter 7 where we cover bonds in depth. Figure 5-3 gives a graphic picture of how much each payment contributes to thevalueofanannuity.Hereweanalyzeanannuitythatpays100peryearwhen the market interest rate is 10. We found the PV of each payment for the first 100 years and graphed those PVs. We also found the value of the annuity with a 25-year 50-year 100-year and infinite life. Here are some points to note: 1. The value of an ordinary annuity is the sum of the present values of its payments. 2. Wecanconstructgraphsforannuitiesofanylength—for3yearsor25yearsor 50 years or any other period. The fewer the years the fewer the bars in the graph. 3. As the years increase the PV of each additional payment—which represents the amount the payment contributes to the annuity’s value—decreases. This occurs because each payment is divided by 1 þ I t and that term increases exponentiallywitht.Indeedinourgraphthepaymentsafter62yearsaretoo small to be noticed. Consol A perpetual bond issued by the British government to consolidate past debts in general any perpetual bond. 6 The consols actually pay interest in pounds but we discuss them in dollar terms for simplicity. 7 Equation 5-6 was found by letting N in Equation 5-5 approach infinity. The result is Equation 5-6. Perpetuity A stream of equal pay- ments at fixed intervals expected to continue forever. 140 Part 2 Fundamental Concepts in Financial Management

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4. The data to the right of the graph show the value of a 100 annuity when the interestrate is10 andthe annuitylasts for2550and 100 years and forever. The difference between these values shows how much the additional years contribute to the annuity’s value. The payments for distant years are worth very little today so the value of the annuity is determined largely by the payments to be received in the near term.Note though that the discount rate affects the values of distant cash flows and thus the graph. The higher thediscountratethesteeperthedeclineandthusthesmallerthevaluesofthe distant flows. Figure5-3highlightssomeimportantimplicationsforfinancialissues.Forexample if you win a 10 million lottery that pays 500000 per year for 20 years beginning immediatelythelotteryisreallyworthmuchlessthan10million.Eachcashflow must be discounted and the sum of the cash flows is much less than 10million.Ata10discountratethe“10million”isworthonly4682460and that’s before taxes. Not bad but not 10 million. SELFTEST What’s the present value of a perpetuity that pays 1000 per year begin- ning one year from now if the appropriate interest rate is 5 What would the value be if payments on the annuity began immediately 20000 21000. Hint: Just add the 1000 to be received immediately to the value of the annuity. Would distant payments contribute more to the value of an annuity if interest rates were high or low Hint: When answering conceptual questionsitoftenhelpstomakeupanexampleanduseittoformulate your answer. PV of 100 at 5 after 25 years ¼ 29.53 PV at 20 ¼ 1.05. So distant payments contribute more at low rates. Contribution of Payments to Value of 100 Annuity at 10 Interest Rate FIGURE 5-3 81 91 71 61 51 41 31 21 11 Years PV of Each 100 Payment Addition to Annuity’s Value 50 0 1 100 Bars indicate PV of each payment. Sum of PVs from 0 to N Value of the Annuity Value of 25-Year Annuity: 907.70 Value of 50-Year Annuity: 991.48 Value of 100-Year Annuity: 999.93 Value of Perpetuity: 1000.00 Chapter 5 Time Value of Money 141

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5-12 UNEVEN CASH FLOWS Thedefinitionofanannuityincludesthewordsconstantpayment—inotherwords annuities involve payments that are equal in every period. Although many financial decisions involve constant payments many others involve uneven or nonconstantcashflows. For example the dividends on common stocks typically increase over time and investments in capital equipment almost always generate unevencashflows.ThroughoutthebookwereservethetermpaymentPMTfor annuities with their equal payments in each period and use the term cash flow CF t todenoteunevencashflowswheretdesignatestheperiodinwhichthecash flow occurs. There are two important classes of uneven cash flows: 1 a stream that con- sists of a series of annuity payments plus an additional final lump sum and 2 all other uneven streams. Bonds represent the best example of the first type while stocks and capital investments illustrate the second type. Here are numerical examples of the two types of flows: 4 2 1 0 I 12 Periods Cash fows 3 5 0 100 100 100 100 100 1000 1100 1. Annuity plus additional fnal payment: 4 2 1 0 I 12 Periods Cash fows 3 5 0 100 300 300 300 500 2. Irregular cash fows: Wecan findthe PV ofeitherstreambyusing Equation5-7 and followingthe step- by-step procedure where we discount each cash flow and then sum them to find the PV of the stream: PV¼ CF 1 ð1þIÞ 1 þ CF 2 ð1þIÞ 2 þþ CF N ð1þIÞ N ¼ X N t¼1 CF t ð1þIÞ t 5-7 If we did this we would find the PV of Stream 1 to be 927.90 and the PV of Stream 2 to be 1016.35. The step-by-step procedure is straightforward but if we have a large number of cash flows it is time-consuming. However financial calculators speed up the process considerably. First consider Stream 1 notice that we have a 5-year 12 ordinary annuity plus a final payment of 1000. We could find the PV of the annuity then find the PV of the final payment and sum them to obtain the PV of the stream. Financial calculators do this in one simple step—use the five TVM keys enter the data as shown below and press the PV key to obtain the answer 927.90. FV PV I/YR N PMT 1000 100 512 –927.90 The solution procedure is different for the second uneven stream. Here we must use the step-by-step approach as shown in Figure 5-4. Even calculators and spreadsheets solve the problem using the step-by-step procedure but they do it Uneven Nonconstant Cash Flows A series of cash flows where the amount varies from one period to the next. Payment PMT This term designates equal cash flows coming at regular intervals. Cash Flow CF t This term designates a cash flow that’s not part of an annuity. 142 Part 2 Fundamental Concepts in Financial Management

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quickly and efficiently. First you enter all of the cash flows and the interest rate then the calculator or computer discounts each cash flow to find its present value and sums these PVs to produce the PV of the stream. You must enter the cash flows in the calculator’s “cash flow register” enter the interest rate and then press the NPV key to find the PV of the stream. NPV stands for “net present value.” We cover the calculator mechanics in the tutorial and we discuss the process inmoredetailinChapters 9and 11where weuse the NPVcalculation to analyzestocksandproposedcapitalbudgetingprojects.Ifyoudon’tknowhowto do the calculation with your calculator it would be worthwhile to go to the tutorial or your calculator manual learn the steps and make sure you can do this calculation. Since you will have to learn to do it eventually now is a good time to begin. SELFTEST How could you use Equation 5-2 to find the PV of an uneven stream of cash flows What’s the present value of a 5-year ordinary annuity of 100 plus an additional500 at the end of Year 5 if the interest rate is 6 What is the PV ifthe100paymentsoccurinYears1through10andthe500comesatthe end of Year 10 794.87 1015.21 What’s the present value of the following uneven cash flow stream: 0 at Time0100inYear1oratTime1200inYear20inYear3and400in Year 4 if the interest rate is 8 558.07 Would a typical common stock provide cash flows more like an annuity or more like an uneven cash flow stream Explain. 5-13 FUTURE VALUE OF AN UNEVEN CASH FLOW STREAM We find the future value of uneven cash flow streams by compounding rather than discounting. Consider Cash Flow Stream 2 in the preceding section. We discountedthosecashflowstofindthePVbutwewouldcompoundthemtofind the FV. Figure 5-5 illustrates the procedure for finding the FV of the stream using the step-by-step approach. PV of an Uneven Cash Flow Stream FIGURE 5-4 89.29 239.16 213.53 190.66 283.71 1016.35 PV of cash fow stream Value of the asset 4 2 1 0 I 12 Periods Cash fows PV of CFs 3 5 0 100 300 300 300 500 Chapter 5 Time Value of Money 143

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The values of all financial assets—stocks bonds and business capital investments—are found as the present values of their expected future cash flows. Therefore we need to calculate present values very often far more often than futurevalues.Asaresultallfinancialcalculatorsprovideautomatedfunctionsfor finding PVs but they generally do not provide automated FV functions. On the relatively few occasions when we need to find the FV of an uneven cash flow stream we generally use the step-by-step procedure shown in Figure 5-5. That approach works for all cash flow streams even those for which some cash flows are zero or negative. SELFTEST Why are we more likely to need to calculate the PV of cash flow streams than the FV of streams What is the future value of this cash flow stream: 100 at the end of 1 year 150 due after 2 years and 300 due after 3 years if the appropriate interest rate is 15 604.75 5-14 SOLVING FOR I WITH UNEVEN CASH FLOWS 8 Before financial calculators and spreadsheets existed it was extremely difficult to find I when the cash flows were uneven. With spreadsheets and financial calcu- lators though it’s relatively easy to find I. If you have an annuity plus a final lump sum you can input values for N PV PMT and FV into the calculator’s TVM registers and then press the I/YR key. Here is the setup for Stream 1 from Section5-12assumingwemustpay927.90tobuytheasset.Therateofreturnon the 927.90 investment is 12. FV PV I/YR N PMT 1000 100 –927.90 5 12.00 8 This section is relatively technical. It can be deferred at this point but the calculations will be required in Chapter 11. FV of an Uneven Cash Flow Stream FIGURE 5-5 500.00 336.00 376.32 421.48 157.35 0.00 1791.15 4 2 1 0 I 12 Periods Cash fows 3 5 0 100 300 300 300 500 144 Part 2 Fundamental Concepts in Financial Management

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FindingtheinterestrateforanunevencashflowstreamsuchasStream2isa bit more complicated. First note that there is no simple procedure—finding the rate requires a trial-and-error process which means that a financial calculator or a spreadsheet is needed. With a calculator we enter the CFs into the cash flow register and then press the IRR key to get the answer. IRR stands for “internal rate of return” and it is the rate of return the investment provides. The invest- ment is the cash flow at Time 0 and it must be entered as a negative. As an illustration consider the cash flows given here where CF 0 ¼−1000 is the cost of the asset. 4 2 1 0 Periods Cash fows 3 5 1000 IRR I 12.55 100 300 300 300 500 When we enter those cash flows into the calculator’s cash flow register and press the IRR key we get the rate of return on the 1000 investment 12.55. You get the same answer using Excel’s IRR function. The process is covered in the cal- culator tutorial it is also discussed in Chapter 11 where we study capital budgeting. SELFTEST An investment costs 465 and is expected to produce cash flows of 100 at the end of each of the next 4 years then an extra lump sum payment of 200 at the end of the fourth year. What is the expected rate of return on this investment 9.05 An investment costs 465 and is expected to produce cash flows of 100 at the end of Year 1 200 at the end of Year 2 and 300 at the end of Year 3. What is the expected rate of return on this investment 11.71 5-15 SEMIANNUAL AND OTHER COMPOUNDING PERIODS In all of our examples thus far we assumed that interest was compounded once a year or annually. This is called annual compounding. Suppose however that you deposit 100 in a bank that pays a 5 annual interest rate but credits interest each6months.Sointhesecond6-monthperiodyouearninterestonyouroriginal 100 plus interest on the interest earned during the first 6 months. This is called semiannualcompounding.Notethatbanksgenerallypayinterestmorethanonce ayearvirtuallyallbondspayinterestsemiannuallyandmostmortgagesstudent loans and auto loans require monthly payments. Therefore it is important to understand how to deal with nonannual compounding. For an illustration of semiannual compounding assume that we deposit 100 in an account that pays 5 and leave it there for 10 years. First consider again what the future value would be under annual compounding: FV N ¼ PVð1þ IÞ N ¼ 100ð1:05Þ 10 ¼ 162:89 We would of course get the same answer using a financial calculator or a spreadsheet. How would things change in this example if interest was paid semiannually rather than annually First whenever payments occur more than once a year you must make two conversions: 1 Convert the stated interest rate into a “periodicrate”and2convertthenumberofyearsinto “numberofperiods.”The Annual Compounding The arithmetic process of determining the final value of a cash flow or series of cash flows when interest is added once a year. Semiannual Compounding The arithmetic process of determining the final value of a cash flow or series of cash flows when interest is added twice a year. Chapter 5 Time Value of Money 145

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conversionsaredoneasfollowswhereIisthestatedannualrateMisthenumber of compounding periods per year and N is the number of years: Periodic rateðI PER Þ¼ Stated annual rate Number of payments per year ¼ IM 5-8 With a stated annual rate of 5 compounded semiannually the periodic rate is 2.5: Periodic rate¼ 52¼ 2:5 The number of compounding periods per year is found with Equation 5-9: Number of periods¼ðNumber of yearsÞðPeriods per yearÞ¼ NM 5-9 With 10 years and semiannual compounding there are 20 periods: Number of periods¼ 10ð2Þ¼ 20 periods Under semiannual compounding our 100 investment will earn 2.5 every 6 months for 20 semiannual periods not 5 per year for 10 years. The periodic rate and number of periods not the annual rate and number of years must be shown on time lines and entered into the calculator or spreadsheet whenever you are working with nonannual compounding. 9 With this background we can find the value of 100 after 10 years if it is held in an account that pays a stated annual rate of 5.0 but with semiannual com- pounding. Here’s the time line and the future value: 19 2 1 0 Periods Cash fows I 2.5 20 100 PV 1 + I N 1001.025 20 FV 20 163.86 With a financial calculator we get the same result using the periodic rate and number of periods: FV PV I/YR N PMT 0 –100 2.5 20 163.86 The future value under semiannual compounding 163.86 exceeds the FV under annual compounding 162.89 because interest starts accruing sooner thus you earn more interest on interest. How would things change in our example if interest was compounded quarterly or monthly or daily With quarterly compounding there would be NM¼104¼40periodsandtheperiodicratewouldbeI/M¼5/4¼1.25per quarter. Using those values we would find FV ¼ 164.36. If we used monthly compounding we would have 1012 ¼ 120 periods the monthly rate would be 5/12 ¼ 0.416667 and the FV would rise to 164.70. If we went to daily compounding we would have 10365 ¼ 3650 periods the daily rate would be 5/365¼ 0.0136986 per day and the FV would be 164.87 based on a 365-day year. 9 With some financial calculators you can enter the annual nominal rate and the number of compounding periods per year rather than make the conversions we recommend. We prefer the conversions because they must be used on time lines and because it is easy to forget to reset your calculator after you change its settings which may lead to an error on your next problem. 146 Part 2 Fundamental Concepts in Financial Management

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The same logic applies when we find present values under semiannual compounding.Again weuseEquation 5-8toconvert thestatedannual rate tothe periodic semiannual rate and Equation 5-9 to find the number of semiannual periods. We then use the periodic rate and number of periods in the calculations. ForexamplewecanfindthePVof100dueafter10yearswhenthestatedannual rate is 5 with semiannual compounding: Periodic rate ¼ 52 ¼ 2:5 per period Number of periods ¼ 10ð2Þ¼ 20 periods PV of 100 ¼ 100ð1:025Þ 20 ¼ 61:03 We would get this same result with a financial calculator: FV PV I/YR N PMT 0 –100 2.5 20 61.03 If we increased the number of compounding periods from 2 semiannual to 12 monthly the PV would decline to 60.72 and if we went to daily com- pounding the PV would fall to 60.66. SELFTEST Would you rather invest in an account that pays 7 with annual com- pounding or 7 with monthly compounding Would you rather borrow at 7 and make annual or monthly payments Why What’sthe future value of100after3yearsiftheappropriateinterest rateis 8 compounded annually compounded monthly 125.97 127.02 What’s the present value of 100 due in three years if the appropriate interest rate is 8 compounded annually compounded monthly 79.38 78.73 5-16 COMPARING INTEREST RATES Different compounding periods are used for different types of investments. For example bank accounts generally pay interest daily most bonds pay interest semiannually stocks pay dividends quarterly and mortgages auto loans and other instruments require monthly payments. 10 If we are to compare investments or loans with different compounding periods properly we need to put them on a common basis. Here are some terms you need to understand: l The nominal interest rate I NOM also called the annual percentage rate APR or quoted or stated rate is the rate that credit card companies stu- dent loan officers auto dealers and so forth tell you they are charging on loans. Note that if two banks offer loans with a stated rate of 8 but one requires monthly payments and the other quarterly payments they are not charging the same “true” rate—the one that requires monthly payments is charging more than the one with quarterly payments because it will get your 10 Some banks even pay interest compounded continuously. Continuous compounding is discussed in Web Appendix 5A. Nominal Quoted or Stated Interest Rate I NOM The contracted or quoted or stated interest rate. Annual Percentage Rate APR The periodic rate times the number of periods per year. Chapter 5 Time Value of Money 147

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money sooner. So to compare loans across lenders or interest rates earned on different securities you should calculate effective annual rates as described here. 11 l The effective annual rate abbreviated EFF is also called the equivalent annual rate EAR. This is the rate that would produce the same future value underannualcompoundingaswould morefrequent compounding at agiven nominal rate. l If a loan or an investment uses annual compounding its nominal rate is also its effective rate. However if compounding occurs more than once a year the EFF is higher than I NOM . l To illustrate a nominal rate of 10 with semiannual compounding is equiv- alent to a rate of 10.25 with annual compounding because both rates will cause 100 to grow to the same amount after 1 year. The top line in the following diagram shows that 100 will grow to 110.25 at a nominal rate of 10.25. The lower line shows the situation if the nominal rate is 10 but semiannual compounding is used. 0 Nom EFF 10.25 1 100.00 110.25 0 Nom 10.00 semi EFF 10.25 12 100.00 105 110.25 Giventhenominalrateandthe number ofcompoundingperiodsperyearwecan find the effective annual rate with this equation: Effective annual rate ðEFFÞ¼ 1þ I NOM M M 1:0 5-10 Here I NOM is the nominal rate expressed as a decimal and M is the number of compounding periods per year. In our example the nominal rate is 10 but with semiannual compounding I NOM ¼ 10 ¼ 0.10 and M ¼ 2. This results in EFF ¼ 10.25: 12 Effective annual rate ðEFFÞ¼ 1þ 0:10 2 2 1¼ 0:1025¼ 10:25 Thus if one investment promises to pay 10 with semiannual compounding and an equally risky investment promises 10.25 with annual compounding we would be indifferent between the two. 11 Note though that if you are comparing two bonds that both pay interest semiannually it’s OK to compare their nominal rates. Similarly you can compare the nominal rates on two money funds that pay interest daily. But don’t compare the nominal rate on a semiannual bond with the nominal rate on a money fund that compounds daily because that will make the money fund look worse than it really is. 12 Most financial calculators are programmed to find the EFF or given the EFF to find the nominal rate. This is called interest rate conversion. You enter the nominal rate and the number of compounding periods per year and then press the EFF key to find the effective annual rate. However we generally use Equation 5-10 because it’s as easy to use as the interest conversion feature and the equation reminds us of what we are really doing. If you use the interest rate conversion feature on your calculator don’t forget to reset your calculator settings. Interest rate conversion is discussed in the calculator tutorials. Interest rate conversion is also very easy using Excel. For details look at the spreadsheet model that accompanies this chapter. Effective Equivalent Annual Rate EFF or EAR The annual rate of interest actually being earned as opposed to the quoted rate. Also called the “equivalent annual rate.” 148 Part 2 Fundamental Concepts in Financial Management

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SELFTEST Define the terms annual percentage rate APR effective annual rate EFF and nominal interest rate I NOM . A bank pays 5 with daily compounding on its savings accounts. Should it advertisethenominaloreffectiverateifitisseekingtoattractnewdeposits By law credit card issuers must print their annual percentage rate on their monthlystatements.A commonAPRis18 with interestpaidmonthly.What istheEFFonsuchaloanEFF¼1þ0.18/12 12 −1¼0.1956¼19.56 Some years ago banks didn’t haveto revealthe rates they charged on credit cards. Then Congress passed the Truth in Lending Act that required banks to publish their APRs. Is the APR really the “most truthful” rate or would the EFF be “more truthful” Explain. 5-17 FRACTIONAL TIME PERIODS Thusfarwehaveassumedthatpaymentsoccuratthebeginningortheendofperiodsbut notwithinperiods.Howeverweoftenencountersituationsthatrequirecompounding ordiscountingoverfractionalperiods.Forexamplesupposeyoudeposited100ina bankthatpaysanominalrateof10butaddsinterestdailybasedona365-dayyear. Howmuchwouldyouhaveafter9monthsTheansweris107.79foundasfollows: 13 Periodic rate ¼ I PER ¼ 0:10365 ¼ 0:000273973 per day Number of days¼ð912Þð365Þ¼ 0:75ð365Þ¼ 273:75 rounded to 274 Ending amount ¼ 100ð1:000273973Þ 274 ¼ 107:79 Now suppose you borrow 100 from a bank whose nominal rate is 10 per year simple interest which means that interest is not earned on interest. If the loan is outstanding for 274 days how much interest would you have to pay Here we would calculate a daily interest rate I PER as just shown but multiply it by 274 rather than use the 274 as an exponent: Interest owed ¼ 100ð0:000273973Þð274Þ¼ 7:51 You would owe the bank a total of 107.51 after 274 days. This is the procedure that most banks use to calculate interest on loans except that they require bor- rowers to pay the interest on a monthly basis rather than after 274 days. SELFTEST Supposeacompanyborrowed1millionatarateof9simpleinterestwith interest paid at the end of each month. The bank uses a 360-day year. How muchinterestwouldthefirmhavetopayina30-daymonthWhatwouldthe interest be if the bank used a 365-day year 0.09/360301000000 ¼ 7500 interest for the month. For the 365-day year 0.09/36530 1000000¼7397.26ofinterest.Theuseofa360-dayyearraisesthe interestcostby 102.74 which is why banks like to use it onloans. Suppose you deposited 1000 in a credit union that pays 7 with daily compounding and a 365-day year. What is the EFF and how much could you withdraw after seven months assuming this is seven-twelfths of a year EFF ¼ 1 þ 0.07/365 365 − 1 ¼ 0.07250098 ¼ 7.250098. Thus your account would grow from 1000 to 10001.07250098 0.583333 ¼ 1041.67 and you could withdraw that amount. 13 Bank loan contracts specifically state whether they are based on a 360- or a 365-day year. If a 360-day year is used the daily rate is higher which means that the effective rate is also higher. Here we assumed a 365-day year. Also note that in real-world calculations banks’ computers have built-in calendars so they can calculate the exact number of days taking account of 30-day 31-day and 28- or 29-day months. Chapter 5 Time Value of Money 149

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5-18 AMORTIZED LOANS 14 An important application of compound interest involves loans that are paid off in installments over time. Included are automobile loans home mortgage loans student loans and many business loans. A loan that is to be repaid in equal amounts on a monthly quarterly or annual basis is called an amortized loan. 15 Table5-4illustratestheamortizationprocess.Ahomeownerborrows100000 on amortgage loan and the loan is to be repaid in five equal payments at the end ofeachofthenext5years. 16 Thelendercharges6onthebalanceatthebeginning of each year. Our first task is to determine the payment the homeowner must make each year. Here’s a picture of the situation: 0 I 6 34 PMT PMT PMT PMT PMT 100000 5 2 1 The payments must be such that the sum of their PVs equals 100000: 100000¼ PMT ð1:06Þ 1 þ PMT ð1:06Þ 2 þ PMT ð1:06Þ 3 þ PMT ð1:06Þ 4 þ PMT ð1:06Þ 5 ¼ X 5 t¼1 PMT ð1:06Þ t We could insert values into a calculator as follows to get the required payments 23739.64: 17 FV PV I/YR N PMT 100000 0 6 5 –23739.64 14 Amortized loans are important but this section can be omitted without loss of continuity. 15 The word amortized comes from the Latin mors meaning “death” so an amortized loan is one that is “killed off ” over time. 16 Most mortgage loans call for monthly payments over 10 to 30 years but we use a shorter period to reduce the calculations. 17 You could also factor out the PMT term find the value of the remaining summation term 4.212364 and divide it into the 100000 to find the payment 23739.64. Amortized Loan A loan that is repaid in equal payments over its life. Loan Amortization Schedule 100000 at 6 for 5 Years Table 5-4 Amount borrowed: 100000 Years: 5 Rate: 6 PMT: −23739.64 Year Beginning Amount 1 Payment 2 Interest a 3 Repayment of Principal b 4 Ending Balance 5 1 100000.00 23739.64 6000.00 17739.64 82260.36 2 82260.36 23739.64 4935.62 18804.02 63456.34 3 63456.34 23739.64 3807.38 19932.26 43524.08 4 43524.08 23739.64 2611.44 21128.20 22395.89 5 22395.89 23739.64 1343.75 22395.89 0.00 a Interest in each period is calculated by multiplying the loan balance at the beginning of the year by the interest rate. Therefore interest in Year 1 is 100000.000.06 6000 in Year 2 it is 4935.62 and so forth. b Repayment of principal is equal to the payment of 23739.64 minus the interest charge for the year. 150 Part 2 Fundamental Concepts in Financial Management

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Therefore the borrower must pay the lender 23739.64 per year for the next 5 years. Eachpaymentwillconsistoftwoparts—interestandrepaymentofprincipal. This breakdown is shown on an amortization schedule such as the one in Table 5-4. The interest component is relatively high in the first year but it declines as the loan balance decreases. For tax purposes the borrower would deduct the interest component while the lender would report the same amount as taxable income. SELFTEST Suppose you borrowed 30000 on a student loan at a rate of 8 and must repay it in three equal installments at the end of each of the next 3 years. How large would your payments be how much of the first payment would represent interest how much would be principal and what would your endingbalancebeafterthefirstyearPMT¼11641.01Interest¼2400 Principal¼ 9241.01 Balance atend ofYear 1¼ 20758.99 TYING IT ALL TOGETHER In this chapter we worked with single payments ordinary annuities annuities due perpetuitiesandunevencashflowstreams.OnefundamentalequationEquation5-1 is used to calculate the future value of a given amount. The equation can be trans- formed to Equation 5-2 and then used to find the present value of a given future amount. We used time lines to show when cash flows occur and we saw that time valueproblemscanbesolvedinastep-by-stepmannerwhenweworkwithindividual cashflowswithformulasthatstreamlinetheapproachwithfinancialcalculatorsand with spreadsheets. As wenotedatthe outsetTVMisthe single most importantconceptin finance and the procedures developed in Chapter 5 are used throughout this book. Time value analysis is used to find the values of stocks bonds and capital budgeting projects. It is also used to analyze personal finance problems such as the retire- ment issue set forth in the opening vignette. You will become more familiar with time value analysis as you go through the book but we strongly recommend that you get a good handle on Chapter 5 before you continue. Amortization Schedule A table showing precisely how a loan will be repaid. It gives the required pay- ment on each payment date and a breakdown of the payment showing how much is interest and how much is repayment of principal. SELF-TEST QUESTIONS AND PROBLEMS Solutions Appear in Appendix A ST-1 KEY TERMS Define each of the following terms: a. Time line b. FV N PV I INT N FVA N PMT PVA N c. Compounding discounting d. Simple interest compound interest e. Opportunity cost f. Annuity ordinary deferred annuity annuity due g. Consol perpetuity Chapter 5 Time Value of Money 151

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h. Uneven cash flow payment cash flow CFt i. Annual compounding semiannual compounding j. Nominal quoted interest rate annual percentage rate APR effective equivalent annual rate EAR or EFF k. Amortized loan amortization schedule ST-2 FUTURE VALUE It is now January 1 2009. Today you will deposit 1000 into a savings account that pays 8. a. If the bank compounds interest annually how much will you have in your account on January 1 2012 b. What will your January 1 2012 balance be if the bank uses quarterly compounding c. Suppose you deposit 1000 in three payments of 333.333 each on January 1 of 2010 2011and2012.HowmuchwillyouhaveinyouraccountonJanuary12012basedon 8 annual compounding d. How much will be in your account if the three payments begin on January 1 2009 e. Suppose you deposit three equal payments into your account on January 1 of 2010 2011 and 2012. Assuming an 8 interest rate how large must your payments be to have the same ending balance as in Part a ST-3 TIME VALUE OF MONEY ItisnowJanuary12009and youwill need 1000onJanuary 1 2013 in 4 years. Your bank compounds interest at an 8 annual rate. a. How much must you deposit today to have a balance of 1000 on January 1 2013 b. IfyouwanttomakefourequalpaymentsoneachJanuary1from2010through2013to accumulate the 1000 how large must each payment be Note that the payments begin a year from today. c. If your father offers to make the payments calculated in Part b 221.92 or to give you 750 on January 1 2010 a year from today which would you choose Explain. d. Ifyouhaveonly750onJanuary 12010what interestratecompounded annually for 3 years must you earn to have 1000 on January 1 2013 e. Suppose you can deposit only 200 each January 1 from 2010 through 2013 4 years. Whatinterestratewithannualcompoundingmustyouearntoendupwith1000on January 1 2013 f. Your father offers to give you 400 on January 1 2010. You will then make six additional equal payments each 6 months from July 2010 through January 2013. If your bank pays 8 compounded semiannually how large must each payment be for you to end up with 1000 on January 1 2013 g. What is the EAR or EFF earned on the bank account in Part f What is the APR earned on the account ST-4 EFFECTIVE ANNUAL RATES Bank A offers loans at an 8 nominal rate its APR but requires that interest be paid quarterly that is it uses quarterly compounding. Bank B wants to charge the same effective rate on its loans but it wants to collect interest on a monthly basis that is use monthly compounding. What nominal rate must Bank B set QUESTIONS 5-1 What is an opportunity cost How is this concept used in TVM analysis and where is it shown on a time line Is a single number used in all situations Explain. 5-2 Explain whether the following statement is true or false: 100 a year for 10 years is an annuity but 100 in Year 1 200 in Year 2 and 400 in Years 3 through 10 does not constitute an annuity. However the second series contains an annuity. 5-3 If a firm’s earnings per share grew from 1 to 2 over a 10-year period the total growth would be 100 but the annual growth rate would be less than 10. True or false Explain. Hint: If you aren’t sure plug in some numbers and check it out. 5-4 Would you ratherhave a savings account that pays 5 interest compounded semiannually or one that pays 5 interest compounded daily Explain. 152 Part 2 Fundamental Concepts in Financial Management

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5-5 To find the present value of an uneven series of cash flows you must find the PVs of the individual cash flows and then sum them. Annuity procedures can never be of use even when some of the cash flows constitute an annuity because the entire series is not an annuity. True or false Explain. 5-6 The present value of a perpetuity is equal to the payment on the annuity PMT divided by the interest rate I: PV− PMT/I. What is the future value of a perpetuity of PMT dollars per year Hint: The answer is infinity but explain why. 5-7 Banks and other lenders are required to disclose a rate called the APR. What is this rate Why did Congress require that it be disclosed Is it the same as the effective annual rate IfyouwerecomparingthecostsofloansfromdifferentlenderscouldyouusetheirAPRsto determine the loan with the lowest effective interest rate Explain. 5-8 What is a loan amortization schedule and what are some ways these schedules are used PROBLEMS Easy Problems 1–8 5-1 FUTURE VALUE If you deposit 10000 in a bank account that pays 10 interest annually how much will be in your account after 5 years 5-2 PRESENT VALUE What is the present value of a security that will pay 5000 in 20 years if securities of equal risk pay 7 annually 5-3 FINDING THE REQUIRED INTEREST RATE Your parents will retire in 18 years. They currently have 250000 and they think they will need 1000000 at retirement. What annual interest rate must they earn to reach their goal assuming they don’t save any additional funds 5-4 TIME FOR A LUMP SUM TO DOUBLE If you deposit money today in an account that pays 6.5 annual interest how long will it take to double your money 5-5 TIMETOREACHAFINANCIALGOAL Youhave42180.53inabrokerageaccountandyou plantodepositanadditional5000attheendofeveryfutureyearuntilyouraccounttotals 250000. You expect to earn 12 annually on the account. How many years will it take to reach your goal 5-6 FUTURE VALUE: ANNUITY VERSUS ANNUITY DUE What’s the future value of a 7 5-year ordinary annuity that pays 300 each year If this was an annuity due what would its future value be 5-7 PRESENT AND FUTURE VALUES OF A CASH FLOW STREAM An investment will pay 100 attheendofeachofthenext3years200attheendofYear4300attheendofYear5and 500 at the end of Year 6. If other investments of equal risk earn 8 annually what is its present value its future value 5-8 LOAN AMORTIZATION AND EAR You want to buy a car and a local bank will lend you 20000.Theloanwillbefullyamortizedover5years60monthsandthenominalinterest ratewillbe12withinterestpaidmonthly.WhatwillbethemonthlyloanpaymentWhat will be the loan’s EAR Intermediate Problems 9–26 5-9 PRESENT AND FUTURE VALUES FOR DIFFERENT PERIODS Findthefollowing values using the equations and then a financial calculator. Compounding/discounting occurs annually. a. An initial 500 compounded for 1 year at 6 b. An initial 500 compounded for 2 years at 6 c. The present value of 500 due in 1 year at a discount rate of 6 d. The present value of 500 due in 2 years at a discount rate of 6 5-10 PRESENT AND FUTURE VALUES FOR DIFFERENT INTEREST RATES Find the following values. Compounding/discounting occurs annually. a. An initial 500 compounded for 10 years at 6 b. An initial 500 compounded for 10 years at 12 c. The present value of 500 due in 10 years at 6 d. The present value of 1552.90 due in 10 years at 12 and at 6 e. Define present value and illustrate it using a time line with data from Part d. How are present values affected by interest rates Chapter 5 Time Value of Money 153

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5-11 GROWTH RATES Shalit Corporation’s 2008 sales were 12 million. Its 2003 sales were 6 million. a. At what rate have sales been growing b. Suppose someone made this statement: “Sales doubled in 5 years. This represents a growth of 100 in 5 years so dividing 100 by 5 we find the growth rate to be 20 per year.” Is that statement correct 5-12 EFFECTIVE RATE OF INTEREST Find the interest rates earned on each of the following: a. You borrow 700 and promise to pay back 749 at the end of 1 year. b. You lend 700 and the borrower promises to pay you 749 at the end of 1 year. c. You borrow 85000 and promise to pay back 201229 at the end of 10 years. d. You borrow 9000 and promise to make payments of 2684.80 at the end of each year for 5 years. 5-13 TIME FOR A LUMP SUM TO DOUBLE How long will it take 200 to double if it earns the following rates Compounding occurs once a year. a. 7 b. 10 c. 18 d. 100 5-14 FUTURE VALUE OF AN ANNUITY Find the future values of these ordinary annuities. Compounding occurs once a year. a. 400 per year for 10 years at 10 b. 200 per year for 5 years at 5 c. 400 per year for 5 years at 0 d. Rework Parts a b and c assuming they are annuities due. 5-15 PRESENT VALUE OF AN ANNUITY Find the present values of these ordinary annuities. Discounting occurs once a year. a. 400 per year for 10 years at 10 b. 200 per year for 5 years at 5 c. 400 per year for 5 years at 0 d. Rework Parts a b and c assuming they are annuities due. 5-16 PRESENT VALUE OF A PERPETUITY What is the present value of a 100 perpetuity if the interest rate is 7 If interest rates doubled to 14 what would its present value be 5-17 EFFECTIVE INTEREST RATE You borrow 85000 the annual loan payments are 8273.59 for 30 years. What interest rate are you being charged 5-18 UNEVEN CASH FLOW STREAM a. Findthepresentvaluesofthefollowingcashflowstreamsat8compoundedannually. 023 300 100 400 400 400 400 400 400 100 300 0 0 Stream A Stream B 45 1 b. What are the PVs of the streams at 0 compounded annually 5-19 FUTUREVALUEOFANANNUITY Yourclientis40yearsoldandshewantstobeginsaving for retirement with the first payment to come one year from now. She can save 5000 per year and you advise her to invest it in the stock market which you expect to provide an average return of 9 in the future. a. If she follows your advice how much money will she have at 65 b. How much will she have at 70 c. She expects to live for 20 years if she retires at 65 and for 15 years if she retires at 70. If her investments continue to earn the same rate how much will she be able to withdraw at the end of each year after retirement at each retirement age 154 Part 2 Fundamental Concepts in Financial Management

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5-20 PV OF A CASH FLOW STREAM A rookie quarterback is negotiating his first NFL contract. His opportunity cost is 10. He has been offered three possible 4-year contracts. Payments are guaranteed and they would be made at the end of each year. Terms of each contract are as follows: 12 3 3000000 5000000 1000000 3000000 4000000 1000000 3000000 3000000 1000000 3000000 2000000 7000000 Contract 1 Contract 2 Contract 3 4 As his adviser which contract would you recommend that he accept 5-21 EVALUATING LUMP SUMS AND ANNUITIES Crissie just won the lottery and she must choose between three award options. She can elect to receive a lump sum today of 61 million to receive 10 end-of-year payments of 9.5 million or to receive 30 end-of-year payments of 5.5 million. a. If she thinks she can earn 7 annually which should she choose b. If she expects to earn 8 annually which is the best choice c. If she expects to earn 9 annually which option would you recommend d. Explain how interest rates influence the optimal choice. 5-22 LOANAMORTIZATION JansoldherhouseonDecember31andtooka10000mortgageas part of the payment. The 10-year mortgage has a 10 nominal interest rate but it calls for semiannual payments beginning next June 30. Next year Jan must report on Schedule B of her IRS Form 1040 the amount of interest that was included in the two payments she received during the year. a. What is the dollar amount of each payment Jan receives b. How much interest was included in the first payment How much repayment of principal was included How do these values change for the second payment c. How much interest must Jan report on Schedule B for the first year Will her interest income be the same next year d. Ifthepaymentsareconstantwhydoestheamountofinterestincomechangeovertime 5-23 FUTURE VALUE FOR VARIOUS COMPOUNDING PERIODS Find the amount to which 500 will grow under each of these conditions: a. 12 compounded annually for 5 years b. 12 compounded semiannually for 5 years c. 12 compounded quarterly for 5 years d. 12 compounded monthly for 5 years e. 12 compounded daily for 5 years f. Why does the observed pattern of FVs occur 5-24 PRESENT VALUE FOR VARIOUS DISCOUNTING PERIODS Find the present value of 500 due in the future under each of these conditions: a. 12 nominal rate semiannual compounding discounted back 5 years b. 12 nominal rate quarterly compounding discounted back 5 years c. 12 nominal rate monthly compounding discounted back 1 year d. Why do the differences in the PVs occur 5-25 FUTURE VALUE OF AN ANNUITY Find the future values of the following ordinary annuities: a. FV of 400 paid each 6 months for 5 years at a nominal rate of 12 compounded semiannually b. FVof200paideach3monthsfor5yearsatanominalrateof12compoundedquarterly c. These annuities receive the same amount of cash during the 5-year period and earn interest at the same nominal rate yet the annuity in Part b ends up larger than the one in Part a. Why does this occur Chapter 5 Time Value of Money 155

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5-26 PV AND LOAN ELIGIBILITY Youhave saved4000fora downpayment on a newcar.The largest monthly payment you can afford is 350. The loan will have a 12 APR based on end-of-month payments.Whatisthemostexpensive caryoucanaffordifyoufinanceitfor 48 months for 60 months Challenging Problems 27−40 5-27 EFFECTIVE VERSUS NOMINAL INTEREST RATES Bank A pays 4 interest compounded annually on deposits while Bank B pays 3.5 compounded daily. a. Based on the EAR or EFF which bank should you use b. Couldyourchoiceofbanksbeinfluencedbythefactthatyoumightwanttowithdrawyour fundsduringtheyearasopposedtoattheendoftheyearAssumethatyourfundsmustbe leftondepositduringanentirecompoundingperiodinordertoreceiveanyinterest. 5-28 NOMINALINTERESTRATEANDEXTENDINGCREDIT Asajewelrystoremanageryouwant to offer credit with interest on outstanding balances paid monthly. To carry receivables youmust borrow funds from yourbank at a nominal 6monthlycompounding. Tooffset youroverheadyouwanttochargeyourcustomersanEARorEFFthatis2morethan the bank is charging you. What APR rate should you charge your customers 5-29 BUILDING CREDIT COST INTO PRICES Yourfirmsellsforcashonlybutitisthinkingof offeringcreditallowingcustomers90daystopay.Customersunderstandthetimevalueof moneysotheywouldallwaitandpayonthe90thday.Tocarrythesereceivablesyouwould havetoborrowfundsfromyourbankatanominal12dailycompoundingbasedona360-day year.Youwanttoincreaseyourbasepricesbyexactlyenoughtooffsetyourbankinterestcost. Totheclosestwholepercentagepointbyhowmuchshouldyouraiseyourproductprices 5-30 REACHING A FINANCIAL GOAL ErikaandKittywhoaretwinsjustreceived30000eachfor their25th birthday. They both have aspirationsto becomemillionaires. Each plansto makea 5000annualcontributiontoher“earlyretirementfund”onherbirthdaybeginningayearfrom today.ErikaopenedanaccountwiththeSafetyFirstBondFundamutualfundthatinvestsin high-quality bonds whose investorshave earned 6 peryear in the past. Kitty invested in the NewIssueBio-TechFund whichinvests in smallnewly issued bio-tech stocksand whose investorshave earned an average of 20 peryear in the fund’s relatively short history. a. If the two women’s funds earn the same returns in the future as in the past how old will each be when she becomes a millionaire b. How large would Erika’s annual contributions have to be for her to become a mil- lionaire at the same age as Kitty assuming their expected returns are realized c. Is it rational or irrational for Erika to invest in the bond fund rather than in stocks 5-31 REQUIRED LUMP SUM PAYMENT Starting next year you will need 10000 annually for 4 years to complete your education. One year from today you will withdraw the first 10000. Your uncle deposits an amount today in a bank paying 5 annual interest which will provide the needed 10000 payments. a. How large must the deposit be b. How much will be in the account immediately after you make the first withdrawal 5-32 REACHINGAFINANCIALGOAL Sixyearsfromtodayyouneed10000.Youplantodeposit 1500annuallywiththefirstpaymenttobemadeayearfromtodayinanaccountthatpays an8effectiveannualrate.YourlastdepositwhichwilloccurattheendofYear6willbefor less than 1500 if less is needed to reach 10000. How large will your last payment be 5-33 FVOFUNEVENCASHFLOW Youwanttobuyahousewithin3yearsandyouarecurrently saving for the down payment. You plan to save 5000 at the end of the first year and you anticipate that your annual savings will increase by 10 annually thereafter. Your expected annual return is 7. How much will you have for a down payment at the end of Year 3 5-34 AMORTIZATION SCHEDULE a. Set upanamortizationschedule fora25000loantoberepaidinequalinstallments at the end of each of the next 3 years. The interest rate is 10 compounded annually. b. What percentage of the payment represents interest and what percentage represents principal for each of the 3 years Why do these percentages change over time 5-35 AMORTIZATION SCHEDULE WITH A BALLOON PAYMENT You want to buy a house that costs100000.Youhave10000foradownpaymentbutyourcreditissuchthatmortgage companieswillnotlendyoutherequired90000.Howevertherealtorpersuadestheseller totakea90000mortgagecalledasellertake-backmortgageatarateof7providedthe loanispaidoffin fullin 3years.You expecttoinherit 100000in 3yearsbut right nowall youhave is10000and youcanafford to makepayments ofno more than 7500per year 156 Part 2 Fundamental Concepts in Financial Management

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given your salary. The loan would call for monthly payments but assume end-of-year annual payments to simplify things. a. If the loan was amortized over 3 years how large would each annual payment be Could you afford those payments b. If the loan was amortized over 30 years what would each payment be Could you afford those payments c. To satisfy the seller the 30-year mortgage loan would be written as a balloon note which means that at the end of the third year you would have to make the regular payment plus the remaining balance on the loan. What would the loan balance be at the end of Year 3 and what would the balloon payment be 5-36 NONANNUAL COMPOUNDING a. Youplantomakefivedepositsof1000eachoneevery6monthswiththefirstpayment beingmadein6months.Youwillthenmakenomoredeposits.Ifthebankpays4nominal interest compounded semiannually howmuch will be in youraccountafter3 years b. One year from today you must make a payment of 10000. To prepare for this payment you plan to make two equal quarterly deposits at the end of Quarters 1 and 2 in a bank that pays 4 nominal interest compounded quarterly. How large must each of the two payments be 5-37 PAYING OFF CREDIT CARDS Simon recently received a credit card with an 18 nominal interest rate. With thecard he purchased anew stereo for 350.The minimum payment on the card is only 10 per month. a. If Simon makes the minimum monthly payment and makes no other charges how many months will it be before he pays off the card Round to the nearest month. b. If Simon makes monthly payments of 30 how many months will it be before he pays off the debt Round to the nearest month. c. How much more in total payments will Simon make under the 10-a-month plan than under the 30-a-month plan Make sure you use three decimal places for N. 5-38 PVANDALAWSUITSETTLEMENT ItisnowDecember312008t¼0andajuryjustfound in favor of a woman who sued the city for injuries sustained in a January 2007 accident. She requested recovery of lost wages plus 100000 for pain and suffering plus 20000 for legal expenses. Her doctor testified that she has been unable to work since the accident and that she will not be able to work in the future. She is now 62 and the jury decided that she would have worked for another 3 years. She was scheduled to have earned 34000 in 2007. To simplify this problem assume that the entire annual salary amount would have been received on December 31 2007. Her employer testified that she probably would have received raises of 3 per year. The actual payment will be made on December 31 2009. The judge stipulated that all dollar amounts are to be adjusted to a present value basis on December312009usinga7annualinterestrateandusingcompoundnotsimpleinterest. Furthermorehestipulatedthatthepainandsufferingandlegalexpensesshouldbebasedon a December 31 2008 date. How large a check must the city write on December 31 2009 5-39 REQUIRED ANNUITY PAYMENTS Your father is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires until he is 85. He wants a fixed retirement incomethathasthesamepurchasingpoweratthetimeheretiresas40000hastoday.The real value of his retirement income will decline annually after he retires. His retirement income will begin the day he retires 10 years from today at which time he will receive 24 additional annual payments. Annual inflation is expected to be 5. He currently has 100000savedandheexpectstoearn8annuallyonhissavings.Howmuchmusthesave during each of the next 10 years end-of-year deposits to meet his retirement goal 5-40 REQUIRED ANNUITY PAYMENTS A father is now planning a savings program to put his daughter through college. She is 13 she plans to enroll at the university in 5 years and she should graduate in 4 years. Currently the annual cost for everything—food clothing tuition books transportation and so forth is 15000 but these costs are expected to increase by 5 annually. The college requires that this amount be paid at the start of the year.Shenowhas7500inacollegesavingsaccountthatpays6annually.Herfatherwill makesixequalannualdepositsintoheraccountthefirstdeposittodayandthesixthonthe dayshestartscollege.HowlargemusteachofthesixpaymentsbeHint:Calculatethecost inflated at 5 for each year of college and find the total present value of those costs discounted at 6 as of the day she enters college. Then find the compounded value of her initial 7500 on that same day. The difference between the PV costs and the amount that would be in the savings account must be made up by the father’s deposits so find the six equal payments starting immediately that will compound to the required amount. Chapter 5 Time Value of Money 157

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COMPREHENSIVE/SPREADSHEET PROBLEM 5-41 TIME VALUE OF MONEY Answer the following questions: a. Assuming a rate of 10 annually find the FV of 1000 after 5 years. b. What is the investment’s FV at rates of 0 5 and 20 after 0 1 2 3 4 and 5 years c. Find the PV of 1000 due in 5 years if the discount rate is 10. d. Whatistherateofreturnonasecuritythatcosts1000andreturns2000after5years e. Suppose California’s population is 30 million people and its population is expected to grow by 2 annually. How long will it take for the population to double f. Find the PV of an ordinary annuity that pays 1000 each of the next 5 years if the interest rate is 15. What is the annuity’s FV g. How will the PV and FV of the annuity in f change if it is an annuity due h. What will the FV and the PV be for 1000 due in 5 years if the interest rate is 10 semiannual compounding i. What will the annual payments be for an ordinary annuity for 10 years with a PV of 1000 if the interest rate is 8 What will the payments be if this is an annuity due j. Find the PV and the FV of an investment that pays 8 annually and makes the following end-of-year payments: 1 023 400 200 100 k. Five banks offer nominal rates of 6 on deposits but A pays interest annually B pays semiannually C pays quarterly D pays monthly and E pays daily. 1 What effective annual rate does each bank pay If you deposit 5000 in each bank today how much will you have at the end of 1 year 2 years 2 IfallofthebanksareinsuredbythegovernmenttheFDICandthusareequally risky will they be equally able to attract funds If not and the TVM is the only considerationwhatnominalratewillcauseallofthebankstoprovidethesame effective annual rate as Bank A 3 Suppose you don’t have the 5000 but need it at the end of 1 year. You plan to make a series of deposits—annually for A semiannually for B quarterly for C monthly for D and daily for E—with payments beginning today. How large must the payments be to each bank 4 Even if the five banks provided the same effective annual rate would a rational investor be indifferent between the banks Explain. l. Suppose youborrow15000.Theloan’sannualinterestrateis8anditrequires four equal end-of-year payments. Set up an amortization schedule that shows the annual payments interest payments principal repayments and beginning and ending loan balances. INTEGRATED CASE FIRST NATIONAL BANK 5-42 TIME VALUE OF MONEY ANALYSIS You have applied for a job with a local bank. As part of its evaluation process you must take an examination on time value of money analysis covering the following questions: a. Drawtimelinesfor1a100lumpsumcashflowattheendofYear22anordinaryannuityof100peryear for 3 years and 3 an uneven cash flow stream of−50 100 75 and 50 at the end of Years 0 through 3. b. 1 What’s the future value of 100 after 3 years if it earns 10 annual compounding 2 What’sthepresentvalueof100tobereceivedin3yearsiftheinterestrateis10annualcompounding 158 Part 2 Fundamental Concepts in Financial Management

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c. What annual interest rate would cause 100 to grow to 125.97 in 3 years d. If a company’s sales are growing at a rate of 20 annually how long will it take sales to double e. What’s the difference between an ordinary annuity and an annuity due What type of annuity is shown here How would you change it to the other type of annuity 01 2 3 0 100 100 100 f. 1 What is the future value of a 3-year 100 ordinary annuity if the annual interest rate is 10 2 What is its present value 3 What would the future and present values be if it was an annuity due g. A 5-year 100 ordinary annuity has an annual interest rate of 10. 1 What is its present value 2 What would the present value be if it was a 10-year annuity 3 What would the present value be if it was a 25-year annuity 4 What would the present value be if this was a perpetuity h. A20-year-old studentwantstosave3adayforherretirement.Everydaysheplaces3inadrawer.Atthe end of each year she invests the accumulated savings 1095 in a brokerage account with an expected annual return of 12. 1 If she keeps saving in this manner how much will she have accumulated at age 65 2 If a 40-year-old investor began saving in this manner how much would he have at age 65 3 How much would the 40-year-old investor have to save each year to accumulate the same amount at 65 as the 20-year-old investor i. What is the present value of the following uneven cash flow stream The annual interest rate is 10. 01 2 3 0 50 300 300 100 4 Years j. 1 Will the future value be larger or smaller if we compound an initial amount more often than annually e.g. semiannually holding the stated nominal rate constant Why 2 Define a the stated or quoted or nominal rate b the periodic rate and c the effective annual rate EAR or EFF. 3 What is the EAR corresponding to a nominal rate of 10 compounded semiannually compounded quarterly compounded daily 4 What is the future value of 100 after 3 years under 10 semiannual compounding quarterly compounding k. When will the EAR equal the nominal quoted rate l. 1 WhatisthevalueattheendofYear3ofthefollowingcashflowstreamifinterestis10compounded semiannually Hint: You can use the EAR and treat the cash flows as an ordinary annuity or use the periodic rate and compound the cash flows individually. 02 4 6 Periods 100 100 100 0 2 What is the PV 3 WhatwouldbewrongwithyouranswertoPartsl1andl2ifyouusedthenominalrate10rather than the EAR or the periodic rate I NOM /2 ¼ 10/2 ¼ 5 to solve the problems m. 1 Construct anamortizationschedulefora 100010 annualinterest loanwiththree equalinstallments. 2 What is the annual interest expense for the borrower and the annual interest income for the lender during Year 2 Chapter 5 Time Value of Money 159

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PART 3 FINANCIAL ASSETS 6 Interest Rates 7 Bonds and Their Valuation 8 Risk and Rates of Return 9 Stocks and Their Valuation CHAPTER

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CHAPTER 6 Interest Rates Low Interest Rates Encourage Investment and Stimulate Consumer Spending The U.S. economy performed well from the early 1990s through 2007. Economic growth was positive unemployment was fairly low and inflation remained under control. One reason for the economy’s good performance was the low level of interest rates over most of that period with the rate on 10-year Treasury bonds gener- ally at or below 5 a level last seen in the 1960s and rates on most other bonds correspondingly low. These low interest rates reduced the cost of capital for businesses which encouraged cor- porate investment. They also stimulated con- sumer spending and helped produce a massive growth in the housing market. The drop in interest rates was due to a num- ber of factors—low inflation foreign investors’ purchases of U.S. securities which drove their rates down and effective management of the economy by the Federal Reserve and other gov- ernment policy makers. However some shocks hit the system in 2007 including 100 per barrel oil and massive write-offs by banks and other insti- tutions that resulted from the subprime mortgage debacle. Higher oil prices and a weakening dollar could lead to higher inflation which in turn would push interest rates up. Likewise the grow- ing federal budget deficit combined with the weakening dollar could cause foreigners to sell U.S. bonds which would put more upward pres- sure on rates. At the same time though the economy seems to be weakening which has led the Federal Reserve to lower its key short-term rate in hopes of staving off a general recession. So some forces are trying to drive rates higher but other forces are operating to keep rates low. Because corporations and individuals are greatly affected by interest rates this chapter takes a closer look at the major factors that determine those rates. As we will see there is no single interest rate—various factors determine the rate that each borrower pays—and in some cases rates on different types of debt move in different directions. For example in the after- math of the recent subprime mortgage crisis investors rushed to put their money in liquid securities with little or no default risk. This “flight ª NICHOLAS KAMM/AFP/GETTY IMAGES 162

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PUTTING THINGS IN PERSPECTIVE Companies raise capital in two main forms: debt and equity. In a free economy capital like other items is allocated through a market system where funds are transferred and prices are established. The interest rate is the price that lenders receive and borrowers pay for debt capital. Similarly equity investors expect to receive dividends and capital gains the sum of which represents the cost of equity. We will take up the cost of equity in a later chapter but our focus in this chapter is on the cost of debt. We begin by examining the factors that affect the supply of and demand for capital which in turn affects the cost of money. We will see that there is no single interest rate—interest rates on different types of debt vary depending on the borrower’s risk the use of the funds borrowed the type of collateralusedtobacktheloanandthelengthoftimethemoneyisneeded.Inthis chapterweconcentratemainlyonhowthesevariousfactorsaffectthecostofdebt for individuals but in later chapters we delve into cost of debt for a business and its role in investment decisions. As you will see in Chapters 7 and 9 the cost of debt is a key determinant of bond and stock prices it is also an important com- ponent of the cost of corporate capital which we take up in Chapter 10. When you finish this chapter you should be able to: l List the various factors that influence the cost of money. l Discuss how market interest rates are affected by borrowers’ need for capital expected inflation different securities’ risks and securities’ liquidity. l Explain what the yield curve is what determines its shape and how you can use the yield curve to help forecast future interest rates. 6-1 THE COST OF MONEY The four most fundamental factors affecting the cost of money are 1 production opportunities 2 time preferences for consumption 3 risk and 4 inflation. To see how these factors operate visualize an isolated island community where people live on fish. They have a stock of fishing gear that permits them to survive reasonably well but they would like to have more fish. Now suppose one of the island’s inhabitants Mr. Crusoe had a bright idea for a new type of fishnet that wouldenablehimtodouble hisdailycatch. However itwouldtakehimayearto perfect the design build the net and learn to use it efficiently. Mr. Crusoe would probably starve before he could put his new net into operation. Therefore he might suggest to Ms. Robinson Mr. Friday and several others that if they would givehimonefisheachdayforayearhewouldreturntwofishadaythenextyear. If someone accepted the offer the fish that Ms. Robinson and the others gave to Mr. Crusoe would constitute savings these savings would be invested in the to quality” led to a decline in the rate the government had to pay when it borrowed. At the same time investors demanded much higher rates from corporate borrowers— particularly those thought to be especially risky. The subprime mortgage crisis demonstrates how major shocks to the economy can have profound effects on interest rates in a wide number of markets all of which are interconnected. Looking ahead it will be interesting to see if interest rates can continue to remain low and if not whether the economy can continue to perform as well as it has in the past. Production Opportunities The investment oppor- tunities in productive cash-generating assets. Time Preferences for Consumption The preferences of consumers for current consumption as opposed to saving for future consumption. Risk In a financial market context the chance that an investment will provide a low or negative return. Inflation The amount by which prices increase over time. Chapter 6 Interest Rates 163

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fishnet and the extra fish the net produced would constitute a return on the investment. Obviously the more productive Mr. Crusoe thought the new fishnet would be the more he could afford to offer potential investors for their savings. In this example we assume that Mr. Crusoe thought he would be able to pay and thus heoffereda100rateofreturn—heofferedtogivebacktwofishforeveryonehe received. He might have tried to attract savings for less—for example he might have offered only 1.5 fish per day next year for every one he received this year which would represent a 50 rate of return to Ms. Robinson and the other potential savers. HowattractiveMr.Crusoe’sofferappearedtoapotentialsaverwoulddepend in large part on the saver’s time preference for consumption. For example Ms. Robinson might be thinking of retirement and she might be willing to trade fish today for fish in the future on a one-for-one basis. On the other hand Mr. Friday might have a wife and several young children and need his current fish so he might be unwilling to “lend” a fish today for anything less than three fish next year. Mr. Friday would be said to have a high time preference for current con- sumption Ms. Robinson a low time preference. Note also that if the entire pop- ulation was living right at the subsistence level time preferences for current consumption wouldnecessarily be high aggregate savings wouldbe low interest rates would be high and capital formation would be difficult. The risk inherent in the fishnet project and thus in Mr. Crusoe’s ability to repay the loan also affects the return that investors require: The higher the per- ceivedriskthehighertherequiredrateofreturn.Alsoinamorecomplexsociety there are many businesses like Mr. Crusoe’s many goods other than fish and many savers like Ms. Robinson and Mr. Friday. Therefore people use money as a mediumofexchangeratherthanbarterwithfish.Whenmoneyisuseditsvaluein the future which is affected by inflation comes into play: The higher the expected rate of inflation the larger the required dollar return. We discuss this point in detail later in the chapter. Thusweseethattheinterestratepaidtosaversdepends1ontherateofreturnthat producers expect to earn on invested capital 2 on savers’ time preferences for current versusfutureconsumption3ontheriskinessoftheloanand4ontheexpectedfuture rate of inflation. Producers’ expected returns on their business investments set an upper limit to how much they can pay for savings while consumers’ time pref- erences for consumption establish how much consumption they are willing to defer and hence how much they will save at different interest rates. 1 Higher risk and higher inflation also lead to higher interest rates. SELFTEST What is the price paid to borrow debt capital called What are the two items whose sum is the cost of equity What four fundamental factors affect the cost of money 1 The term producers is too narrow. A better word might be borrowers which would include corporations home purchasers people borrowing to go to college and even people borrowing to buy autos or to pay for vacations. Also the wealth of a society and its demographics influence its people’s ability to save and thus their time preferences for current versus future consumption. 164 Part 3 Financial Assets

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6-2 INTEREST RATE LEVELS Borrowers bid for the available supply of debt capital using interest rates: The firms with the most profitable investment opportunities are willing and able to pay the most for capital so they tend to attract it away from inefficient firms and firms whose products are not in demand. Of course the economy is not com- pletely free in the sense of being influenced only by market forces. For example the federal government has agencies that help designated individuals or groups obtain credit on favorable terms. Among those eligible for this kind of assistance are small businesses certain minorities and firms willing to build plants in areas with high unemployment. Still most capital in the United States is allocated through the price system where the interest rate is the price. Figure 6-1 shows how supply and demand interact to determine interest rates in two capital markets. Markets L and H represent two of the many capital markets in existence. The supply curve in each market is upward-sloping which indicates that investors are willing to supply more capital the higher the interest rate they receive on their capital. Likewise the downward-sloping demand curve indicates that borrowers will borrow more if interest rates are lower. The interest rate in each market is the point where the supply and demand curves intersect. Thegoing interest rate designated asr is initially 5 for the low-risksecurities in Market L. Borrowers whose credit is strong enough to participate in this market can obtain funds at a cost of 5 and investors who want to put their money to work without much risk can obtain a 5 return. Riskier borrowers must obtain higher-costfundsinMarketHwhereinvestorswhoaremorewillingtotakerisks expect to earn a 7 return but also realize that they might receive much less. In this scenario investors are willing to accept the higher risk in Market H in exchange for a risk premium of 7 – 5 ¼ 2. Now let’s assume that because of changing market forces investors perceive that Market H has become relatively more risky. This changing perception will induce many investors to shift toward safer investments—along the lines of the recent “flight to quality” discussed in the opening vignette to this chapter. As investors move their money from Market H to Market L this supply of funds is increased in Market L from S 1 to S 2 and the increased availability of capital will push down interest rates in this market from 5 to 4. At the same time as investors move their money out of Market H there will be a decreased supply in that market and tighter credit in that market will force interest rates up from 7 to 8. In this new environment money is transferred from Market H to Market L and the risk premium rises from 2 to 8 – 4 ¼ 4. Interest Rates as a Function of Supply and Demand for Funds FIGURE 6-1 Interest Rate r r L 5 4 Dollars 00 Market L: Low-Risk Securities Market H: High-Risk Securities D S 1 S 2 Interest Rate r r H 7 8 Dollars D S 2 S 1 Chapter 6 Interest Rates 165

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TherearemanycapitalmarketsintheUnitedStatesandFigure6-1highlights the fact that they are interconnected. U.S. firms also invest and raise capital throughout the world and foreigners both borrow and lend in the United States. There are markets for home loans farm loans business loans federal state and local government loans and consumer loans. Within each category there are regional markets as well as different types of submarkets. For example in real estate there are separate markets for first and second mortgages and for loans on single-family homes apartments office buildings shopping centers and vacant land.Andofcoursethereareseparatemarketsforprimeandsubprimemortgage loans. Within the business sector there are dozens of types of debt securities and there are several different markets for common stocks. There is a price for each type of capital and these prices change over time as supply and demand conditions change. Figure 6-2 shows how long- and short- term interest rates to business borrowers have varied since the early 1970s. Notice that short-term interest rates are especially volatile rising rapidly during booms and falling equally rapidly during recessions. The shaded areas of the chart indicate recessions. When the economy is expanding firms need capital and this demand pushes rates up. Also inflationary pressures are strongest during busi- ness booms also exerting upward pressure on rates. Conditions are reversed during recessions: Slack business reduces the demand for credit inflation falls and the Federal Reserve increases the supply of funds to help stimulate the economy. The result is a decline in interest rates. Long- and Short-Term Interest Rates 1971–2007 FIGURE 6-2 Interest Rate 1971 1975 1979 1983 1987 1991 1995 1999 2003 2007 Years 18 16 14 12 10 8 6 4 2 0 Long-Term Rates Short-Term Rates Notes: a. The shaded areas designate business recessions. b. Short-term rates are measured by 3- to 6-month loans to very large strong corporations and long-term rates are measured by AAA corporate bonds. Source: St. Louis Federal Reserve web site FRED database 166 Part 3 Financial Assets

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These tendencies do not hold exactly as demonstrated by the period after 1984. Oilpricesfell dramatically in 1985 and 1986 reducinginflationarypressures on other prices and easing fears of serious long-term inflation. Earlier these fears had pushed interest rates to record levels. The economy from 1984 to 1987 was strong but the declining fears of inflation more than offset the normal tendency for interest rates to rise during good economic times the net result was lower interest rates. 2 The relationship between inflation and long-term interest rates is highlighted in Figure 6-3 which plots inflation over time along with long-term interest rates. In the early 1960s inflation averaged 1 per year and interest rates on high- quality long-term bonds averaged 4. Then the Vietnam War heated up leading to an increase in inflation and interest rates began an upward climb. When the war ended in the early 1970s inflation dipped a bit but then the 1973 Arab oil embargo led to rising oil prices much higher inflation rates and sharply higher interest rates. Inflation peaked at about 13 in 1980. But interest rates continued to increase into1981and1982andtheyremainedquitehighuntil1985becausepeoplefeared another increase in inflation. Thus the “inflationary psychology” created during the 1970s persisted until the mid-1980s. People gradually realized that the Federal Reserve was serious about keeping inflation down that global competition was keeping U.S. auto producers and other corporations from raising prices as they Relationship between Annual Inflation Rates and Long-Term Interest Rates 1972–2007 FIGURE 6-3 Long-Term Interest Rates 16 14 12 10 8 6 4 2 0 1972 1977 1982 1987 1992 1997 2007 Years 2002 Infation Interest Rate Notes: a. Interest rates are rates on AAA long-term corporate bonds. b. Inflation is measured as the annual rate of change in the consumer price index CPI. Source: St. Louis Federal Reserve web site FRED database 2 Short-term rates are responsive to current economic conditions whereas long-term rates primarily reflect long- run expectations for inflation. As a result short-term rates are sometimes above and sometimes below long-term rates. The relationship between long-term and short-term rates is called the term structure of interest rates and it is discussed later in this chapter. Chapter 6 Interest Rates 167

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hadinthepastandthatconstraintsoncorporatepriceincreaseswerediminishing labor unions’ ability to push through cost-increasing wage hikes. As these real- izations set in interest rates declined. Thecurrentinterestrateminusthecurrentinflationratewhichisalsothegap between the inflation bars and the interest rate curve in Figure 6-3 is defined as the “current real rate of interest.” It is called a “real rate” because it shows how much investors really earned after the effects of inflation were removed. The real rate was extremely high during the mid-1980s but it has generally been in the range of 3 to 4 since 1987. In recent years inflation has been about 2 a year. However long-term interest rates have been volatile because investors are not sure if inflation is truly under controlorisabouttojumpbacktothehigherlevelsofthe1980s.Intheyearsahead we can be sure of two things: 1Interest rates will vary and 2 they will increase if inflation appears to be headed higher or decrease if inflation is expected to decline. We don’t know where interest rates will go but we do know they will vary. SELFTEST What role do interest rates play in allocating capital to different potential borrowers What happens to market-clearing or equilibrium interest rates in a capital market when the supply of funds declines What happens when expected inflation increases or decreases How does the price of capital tend to change during a boom during a recession How does risk affect interest rates If inflation during the last 12 months was 2 and the interest rate during that period was 5 what was the real rate of interest If inflation is expected to average 4 during the next year and the real rate is 3 what should the current rate of interest be 3 7 6-3 THE DETERMINANTS OF MARKET INTEREST RATES In general the quoted or nominal interest rate on a debt security r is composed ofarealrisk-freeraterplusseveralpremiumsthatreflectinflationthesecurity’s riskitsliquidityormarketabilityand theyearstoitsmaturity.Thisrelationship can be expressed as follows: Quoted interest rate¼ r¼ r þIPþDRPþLPþMRP 6-1 Here r ¼ the quoted or nominal rate of interest on a given security. 3 r ¼ the real risk-free rate of interest. r is pronounced “r-star” and it is the rate that would exist on a riskless security in a world where no inflation was expected. 3 The term nominal as it is used here means the stated rate as opposed to the real rate where the real rate is adjusted to remove inflation’s effects. If you had bought a 10-year Treasury bond in January 2008 the quoted or nominal rate would have been about 3.7 but if inflation averages 2.5 over the next 10 years the real rate would turn out to be about 3.7−2.5¼1.2. Also note that in later chapters when we discuss both debt and equity we use the subscripts d and s to designate returns on debt and stock that is r d and r s . 168 Part 3 Financial Assets

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r RF ¼ r þ IP. It is the quoted rate on a risk-free security such as a U.S. Treasury bill which is very liquid and is free of most types of risk. NotethatthepremiumforexpectedinflationIPisincludedinr RF . IP ¼ inflation premium. IP is equal to the average expected rate of inflation over the life of the security. The expected future inflation rateisnotnecessarilyequaltothecurrentinflationratesoIPisnot necessarily equal to current inflation as shown in Figure 6-3. DRP ¼ defaultriskpremium.Thispremiumreflectsthepossibilitythatthe issuer will not pay the promised interest or principal at the stated time. DRP is zero for U.S. Treasury securities but it rises as the riskiness of the issuer increases. LP ¼ liquidity or marketability premium. This is a premium charged by lenders to reflect the fact that some securities cannot be convertedtocashonshortnoticeata“reasonable”price.LPisvery lowforTreasurysecuritiesandforsecuritiesissuedbylargestrong firms but it is relatively high on securities issued by small privately held firms. MRP ¼ maturity risk premium. As we will explain later longer-term bonds even Treasury bonds are exposed to a significant risk of price declines due to increases in inflation and interest rates and a maturity risk premium is charged by lenders to reflect this risk. Because r RF ¼ r + IP we can rewrite Equation 6-1 as follows: Nominal or quoted rate¼ r¼ r RF þDRPþLPþMRP We discuss the components whose sum makes up the quoted or nominal rate on a given security in the following sections. 6-3a The Real Risk-Free Rate of Interest r The real risk-free rate of interest r is the interest rate that would exist on a riskless security if no inflation were expected. It may be thought of as the rate of interest on short-term U.S. Treasury securities in an inflation-free world. The real risk-free rate is not static—it changes over time depending on economic con- ditions especially on 1 the rate of return that corporations and other borrowers expect to earn on productive assets and 2 people’s time preferences for current versus future consumption. Borrowers’ expected returns on real assets set an upper limit on how much borrowers can afford to pay for funds while savers’ time preferences for consumption establish how much consumption savers will defer—hence the amount of money they will lend at different interest rates. It is difficult to measure the real risk-free rate precisely but most experts think that r has fluctuated in the range of 1 to 5 in recent years. 4 The best estimate of r is the rate of return on indexed Treasury bonds which are discussed later in the chapter. Real Risk-Free Rate of Interest r The rate of interest that would exist on default-free U.S. Treasury securities if no inflation were expected. 4 The real rate of interest as discussed here is different from the current real rate as discussed in connection with Figure6-3.Thecurrent realrate is thecurrent interestrate minusthe currentor latestpastinflationrate whilethe real rate without the word current is the current interest rate minus the expected future inflation rate over the life of the security. For example suppose the current quoted rate for a one-year Treasury bill is 2.7 inflation during the latest year was 1.2 and inflation expected for the coming year is 2.2. The current real rate would be 2.7 – 1.2 1.5 but the expected real rate wouldbe 2.7 – 2.2 0.5. The rate on a 10-year bond would be related to the average expected inflation rate over the next 10 years and so on. In the press the term real rate generally means the current real rate but in economics and finance hence in this book unless otherwise noted the real rate means the one based on expected inflation rates. Chapter 6 Interest Rates 169

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6-3b The Nominal or Quoted Risk-Free Rate of Interest r RF ¼ r þ IP The nominal or quoted risk-free rate r RF is the real risk-free rate plus a pre- mium for expected inflation: r RF ¼ r þ IP. To be strictly correct the risk-free rate should be the interest rate on a totally risk-free security—one that has no default risknomaturityrisknoliquidityrisknoriskoflossifinflationincreasesandno riskofanyothertype.Thereisnosuchsecurityhencethereisnoobservabletruly risk-free rate. However one security is free of most risks—a Treasury Inflation Protected Security TIPS whose value increases with inflation. TIPS are free of defaultmaturityandliquidityrisksandofriskduetochangesinthegenerallevel of interest rates. However they are not free of changes in the real rate. 5 If the term risk-free rate is used without the modifiers real or nominal people generallymeanthequotedornominalrateandwefollowthatconventioninthis book. Therefore when we use the term risk-free rate r RF we mean the nominal risk-free rate which includes an inflation premium equal to the average expected inflation rate over the remaining life of the security. In general we use the T-bill rate to approximate the short-term risk-free rate and the T-bond rate to approxi- mate the long-term risk-free rate. So whenever you see the term risk-free rate assume thatwearereferringtothequoted U.S.T-billrate ortothequotedT-bond rate. 6-3c Inflation Premium IP Inflation has a major impact on interest rates because it erodes the real value of whatyoureceivefromtheinvestment.Toillustratesupposeyousaved1000and invested it in a Treasury bill that pays a 3 interest rate and matures in one year. At the end of the year you will receive 1030—your original 1000 plus 30 of interest.Nowsupposetheinflationrateduringtheyearturnedouttobe3.5and it affected all goods equally. If heating oil had cost 1 per gallon at the beginning of the year it would cost 1.035 at the end of the year. Therefore your 1000 would have bought 1000/1 1000 gallons at the beginning of the year but only1030/1.035995gallonsattheend.Inrealtermsyouwouldbeworseoff —you would receive 30 of interest but it would not be sufficient to offset inflation.Youwouldthusbebetteroffbuying1000gallonsofheatingoilorsome other storable asset such as land timber apartment buildings wheat or gold than buying the Treasury bill. Investors are well aware of all this so when they lend money they build an inflationpremiumIPequaltotheaverageexpectedinflationrateoverthelifeof the security into the rate they charge. As discussed previously the actual interest rate on a short-term default-free U.S. Treasury bill r T-bill would be the real risk- free rate r plus the inflation premium IP: r T bill ¼ r RF ¼ r þIP Thereforeiftherealrisk-freeratewasr1.7andifinflationwasexpectedtobe 1.5 and hence IP ¼ 1.5 during the next year the quoted rate of interest on one-year T-bills would be 1.7 þ 1.5 ¼ 3.2. It is important to note that the inflation rate built into interest rates is the inflation rate expected in the future not the rate experienced in the past. Thus the Nominal Quoted Risk- Free Rate r RF The rate of interest on a security that is free of all risk r RF is proxied by the T-bill rate or the T-bond rate. r RF includes an inflation premium. 5 Indexed Treasury securities are the closest thing we have to a riskless security but even they are not totally riskless because r can change and cause a decline in the prices of these securities. For example between its issue date in February 1998 and December 2004 the TIPS that matures on February 15 2028 first declined from 100 to 89 or by almost 10 but it then rose and in February 2008 the bond sold for 130. The cause of the initial price decline was an increase in the real rate on long-term securities from 3.625 to 4.4 and the cause of the subsequent price increase was a decline in real rates to 2.039. Inflation Premium IP A premium equal to expected inflation that investors add to the real risk-free rate of return. 170 Part 3 Financial Assets

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latest reported figures might show an annual inflation rate of 3 over the past 12 months but thatis forthe pastyear. If people on averageexpecta 4 inflation rate in the future 4 would be built into the current interest rate. Note also that the inflation rate reflected in the quoted interest rate on any security is the average inflation rate expected over the security’s life. Thus the inflation rate built into a 1-year AN ALMOST RISKLESS TREASURY BOND Investors who purchase bonds must constantly worry about inflation. If inflation turns out to be greater than expected bonds will provide a lower-than-expected real return. To protect themselves against expected increases in inflation investors build an inflation risk premium into their required rate of return. This raises borrowers’ costs. To provide investors with an inflation-protected bond and to reduce the cost of debt to the government the U.S. Treasury issues Treasury Inflation Protected Securities TIPS which are bonds that are indexed to inflation. For example in 2004 the Treasury issued 10-year TIPS with a 2 coupon. These bonds pay an interest rate of 2 plus an additional amountthatisjustsufficienttooffsetinflation.Attheendof each 6-month period the principal originally set at par or 1000 is adjusted by the inflation rate. To understand how TIPS work consider that during the first 6-month interest period inflation as measured by the CPI was 2.02. The inflation-adjusted principal was then calculated as 10001 + Inflation 1000 × 1.0202 1020.20. So on July 15 2004 each bond paid interest of 0.02/2 × 1020.20 10.202. Note that the interest rate is divided by 2 because interest on Treasury and most other bonds is paid twice a year. This same adjustment process will continue each year until the bonds mature on January 15 2014 at which time they will pay the adjusted maturity value. Thus the cash income provided by the bonds rises by exactly enough to cover inflation producing a real inflation-adjusted rate of 2 for those who hold the bond from the beginning to the end. Further since the principal also rises by the inflation rate it too is protected from inflation. Both the annual interest received and the increase in principal are taxed each year as interest income even though cashfrom theappreciation willnotbereceiveduntil the bond matures. Therefore these bonds are not good for accounts subject to current income taxes but they are excellent for individual retirement accounts IRAs and 401 k plans which are not taxed until funds are withdrawn. The Treasury regularly conducts auctions to issue indexed bonds. The 2 rate was based on the relative supply and demand for the issue and it will remain fixed over the life of the bond. However after the bonds are issued they continue to trade in the open market and their price will vary as investors’ perceptions of the real rate of interest changes. Indeed as we can see in the following graph the real rate of interest on this bond has varied quite a bit since it was issued and as the real rate changes so does the price of the bond. Real rates fell in 2005 causing the bond’s price to rise rates then rose to a peak in 2007 at which point the bond sold below its par value. They fell again in late 2007 and 2008 as investors sought safety in Treasury securities. Thus despite their protection against inflation indexed bonds are not completely riskless. The real rate can change and if r rises the prices of indexed bonds will decline. This confirms again that there is no such thing as a free lunch or a riskless security. r 10-Yr. 2 Treasury Infation-Indexed Note Due 1/15/2014 3.00 0.00 1-12-04 1-12-05 1-12-06 1-12-07 1-12-08 0.50 1.00 1.50 2.00 2.50 Source: St. Louis Federal Reserve web site FRED database Chapter 6 Interest Rates 171

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bondistheexpectedinflationrateforthenext yearbuttheinflationratebuiltintoa 30-year bond is the average inflation rate expected over the next 30 years. 6 Expectations for future inflation are closely but not perfectly correlated with ratesexperiencedintherecentpast.Thereforeiftheinflationratereportedforlast monthincreasedpeoplewouldtendtoraisetheirexpectationsforfutureinflation and this change in expectations would cause an increase in current rates. Also consumer prices change with a lag following changes at the producer level. Thus if the price of oil increases this month gasoline prices are likely to increase in the coming months. This lagged situation between final product and producer goods prices exists throughout the economy. Note that Germany Japan and Switzerland have over the past several years had lower inflation rates than the United States hence their interest rates have generally been lower than those of the United States. Italy and most South American countries have experienced higher inflation so their rates have been higher than those of the United States. 6-3d Default Risk Premium DRP The risk that a borrower will default which means the borrower will not make scheduled interest or principal payments also affects the market interest rate on a bond: The greater the bond’s risk of default the higher the market rate. Treasury securities have no default risk hence they carry the lowest interest rates on tax- able securities in the United States. For corporate bonds the higher the bond’s rating the lower its default risk and consequently the lower its interest rate. 7 Here are some representative interest rates on long-term bonds in January 2008: Rate DRP U.S. Treasury 4.28 — AAA corporate 4.83 0.55 AA corporate 4.93 0.65 A corporate 5.18 0.90 BBB corporate 6.03 1.75 The difference between the quoted interest rate on a T-bond and that on a cor- porate bond with similar maturity liquidity and other features is thedefaultrisk premiumDRP.Thereforeifthebondspreviouslylistedhavethesamematurity liquidity and so forth the default risk premium will be DRP 4.83 – 4.28 0.55 for AAAs 4.93 – 4.28 0.65 for AAs 5.18 – 4.28 0.90 for A corporatebondsandsoforth.Ifwehadgonedowninto“junkbond”territorywe would have seen DRPs of as much as 8. Default risk premiums vary somewhat over timebut the January 2008 figuresare representative of levels inrecent years. 6-3e Liquidity Premium LP A “liquid” asset can be converted to cash quickly at a “fair market value.” Real assets are generally less liquid than financial assets but different financial assets 6 To be theoretically precise we should use a geometric average. Also since millions of investors are active in the market it is impossible to determine exactly the consensus-expected inflation rate. Survey data are available however that give us a reasonably good idea of what investors expect over the next few years. For example in 1980 the University of Michigan’s Survey Research Center reported that people expectedinflation during the next year to be 11.9 and that the average rate of inflation expected over the next 5 to 10 years was 10.5. Those expectations led to record-high interest rates. However the economy cooled thereafter and as Figure 6-3 showed actual inflation dropped sharply. This led to a gradual reduction in the expected future inflation rate and as inflationary expectations dropped so did quoted market interest rates. 7 Bond ratings and bonds’ riskinessin generalare discussedindetail inChapter7. Fornow merelynote thatbonds rated AAA are judged to have less default risk than bonds rated AA while AA bonds are less risky than A bonds and so forth. Ratings are designated AAA or Aaa AA or Aa and so forth depending on the rating agency. In this book the designations are used interchangeably. Students should go to www. rates to find current interest rates in the United States as well as in Australia Brazil Germany Japan and Great Britain. Default Risk Premium DRP The difference between the interest rate on a U.S. Treasury bond and a cor- porate bond of equal maturity and marketability. 172 Part 3 Financial Assets

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varyintheirliquidity.Becauseliquidityisimportantinvestorsincludealiquidity premium LP in the rates charged on different debt securities. Although it is difficult to measure liquidity premiums accurately a differential of at least two andprobablyfourorfivepercentagepointsexistsbetweentheleastliquidandthe most liquid financial assets of similar default risk and maturity. 6-3f Interest Rate Risk and the Maturity Risk Premium MRP U.S. Treasury securities are free of default risk in the sense that one can be vir- tually certain that the federal government will pay interest on its bonds and pay them off when they mature. Therefore the default risk premium on Treasury securities is essentially zero. Further active markets exist for Treasury securities so their liquidity premiums are close to zero. Thus as a first approximation the rateofinterestonaTreasury security should betherisk-freerater RF which isthe real risk-free rate plus an inflation premium r RF ¼ r + IP. However the prices of long-term bonds decline whenever interest rates rise and because interest rates can and do occasionally rise all long-term bonds even Treasury bonds have an element of risk called interest rate risk. As a general rule the bonds of any organization from the U.S. government to Delta Airlines have more interest rate riskthelongerthematurityofthebond. 8 ThereforeamaturityriskpremiumMRP A 20 LIQUIDITY PREMIUM ON A HIGH-GRADE BOND Since the yield curve is normally upward-sloping short-term debt is normally less expensive than long-term debt. How- ever it’s dangerous to finance long-term assets with short- term debt. To get around this problem investment bankers created a new instrument auction rate securities ARS which are long-term bonds with this wrinkle: Weekly or monthly for some auctions are held. The borrower buys back at par the bonds of holders who want to get out and simultaneously sells those reclaimed bonds to new lenders. Potential new lenders indicate the lowest interest rate they will accept and the actual rate paid on the entire issue is the lowest rate that causes the auction to clear. Most of the bonds were insured by AAA insurance companies which gave them a AAA rating. To illustrate the total issue might be for 100 million and the initial rate might be 3. One week later holders of 5 million of bonds might turn in their bonds which would thenbe offered inan auction topotential buyers. To get the bonds resold an annual rate of 3.1 might be required. Then for the next week all 100 million of the bonds would earn 3.1. There was a cap on the interest rate tied to an index of rates on regular long-term bonds. Investors liked the ARS because they paid a somewhat higherratethanmoneymarketfundsandtheywereequally safe and almost as liquid. They were underwritten by major financial institutions such as Goldman Sachs Merrill Lynch and Citigroup which would buy the excess if more bonds were turned inthanwere bid foratrates below thecap. The institutions wouldhold repurchased bonds in inventory and then sell them to their customers. Everything worked fine until the credit market melt- down of 2008. The banks who back-stopped the auction had lost billions in the subprime mortgage debacle and they didn’t have the capital to step in. After a couple of failed auctions many ARS holders became concerned about liquidity and tried to turn in their bonds. That rush to the exits caused the whole market to freeze up. Highly liquid securities suddenly became totally illiquid. Penalty rates for frozen securities kicked in some as high as 20. That’s much higher than “normal” liquidity premiums but it does demonstrate that liquidity is valuable and that high liquidity premiums are built into illiquid securities’ rates. Source: Stan Rosenberg and Romy Varghese “Auction-Rate Bonds May Come to Rescue” The Wall Street Journal February 15 2008 p. C2. Liquidity Premium LP A premium added to the equilibrium interest rate on a security if that secu- rity cannot be converted to cash on short notice and at close to its “fair market value.” Interest Rate Risk The risk of capital losses to which investors are exposed because of changing interest rates. Maturity Risk Premium MRP A premium that reflects interest rate risk. 8 For example if someone had bought a 20-year Treasury bond for 1000 in October 1998 when the long-term interest rate was 5.3 and sold it in May 2002 when long-term T-bond rates were about 5.8 the value of the bond would have declined to about 942. That would represent a loss of 5.8 and it demonstrates that long- term bonds even U.S. Treasury bonds are not riskless. However had the investor purchased short-term T-bills in 1998 and subsequently reinvested the principal each time the bills matured he or she would still have had the original 1000. This point is discussed in detail in Chapter 7. Chapter 6 Interest Rates 173

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which is higher the greater the years to maturity is included in the required interest rate. The effect of maturity risk premiums is to raise interest rates on long-term bonds relative to those on short-term bonds. This premium like the others is difficult to measure but 1 it varies somewhat over time rising when interest rates are more volatile and uncertain then falling when interest rates are more stable and 2 in recent years the maturity risk premium on 20-year T-bonds has generally been in the range of one to two percentage points. 9 We should also note that although long-term bonds are heavily exposed to interest rate risk short-term bills are heavily exposed to reinvestment rate risk. When short-term bills mature and the principal must be reinvested or “rolled over” a decline in interest rates would necessitate reinvestment at a lower rate which would result in a decline in interest income. To illustrate suppose you had 100000 invested in T-bills and you lived on the income. In 1981 short-term Treasury rates were about 15 so your income would have been about 15000. However your income would have declined to about 9000 by 1983 and to just 2700byJanuary2008.Hadyouinvestedyourmoneyinlong-termT-bondsyour income but not the value of the principal would have been stable. 10 Thus although “investingshort”preservesone’sprincipaltheinterestincomeprovided by short-term T-bills is less stable than that on long-term bonds. SELFTEST Write an equation for the nominal interest rate on any security. Distinguish between the real risk-free rate of interest r and the nominalor quoted risk-free rate of interest r RF . How do investors deal with inflation when they determine interest rates in the financial markets Does the interest rate on a T-bond include a default risk premium Explain. Distinguish between liquid and illiquid assets and list some assets that are liquid and some that are illiquid. Briefly explain the following statement: Although long-term bonds are heavily exposed to interest rate risk short-term T-bills are heavily exposed to reinvestment rate risk. The maturity risk premium reflects the net effects of those two opposing forces. Assume that the real risk-free rate is r 2 and the average expected inflation rate is 3 for each future year. The DRP and LP for Bond X are each 1 and the applicable MRP is 2. What is Bond X’s interest rate Is Bond X 1 a Treasury bond or a corporate bond and 2 more likely to have a 3- month or a 20-year maturity 9 corporate 20-year 9 The MRP for long-term bonds has averaged 1.4 over the last 82 years. See Stocks Bonds Bills and Inflation: Valuation Edition 2008 Yearbook Chicago: Morningstar Inc. 2008. 10 Most long-term bonds also have some reinvestment rate risk. If a person is saving and investing for some future purpose say to buy a house or to retire to actually earn the quoted rate on a long-term bond each interest payment must be reinvested at the quoted rate. However if interest rates fall the interest payments would be reinvested at a lower rate so the realized return would be less than the quoted rate. Note though that reinvestment rate risk is lower on long-term bonds than on short-term bonds because only the interest payments rather than interest plus principal on a long-term bond are exposed to reinvestment rate risk. Non-callable zero coupon bonds which are discussed in Chapter 7 are completely free of reinvestment rate risk during their lifetime. Reinvestment Rate Risk The risk that a decline in interest rates will lead to lower income when bonds mature and funds are reinvested. 174 Part 3 Financial Assets

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6-4 THE TERM STRUCTURE OF INTEREST RATES The term structure of interest rates describes the relationship between long- and short-term rates. The term structure is important to corporate treasurers deciding whether to borrow by issuing long- or short-term debt and to investors who are decidingwhethertobuylong-orshort-termbonds.Thereforebothborrowersand lenders should understand 1 how long- and short-term rates relate to each other and 2 what causes shifts in their relative levels. Interest rates for bonds with different maturities can be found in a variety of publications including The Wall Street Journal and the Federal Reserve Bulletin and on a number of web sites including Bloomberg Yahoo CNN Financial and the Federal Reserve Board. Using interest rate data from these sources we can determine the term structure at any given point in time. For example the tabular section below Figure 6-4 presents interest rates for different maturities on three different dates. The set of data for a given date when plotted on a graph such as Figure 6-4 is called the yield curve for that date. U.S. Treasury Bond Interest Rates on Different Dates FIGURE 6-4 0 0 Short Term Intermediate Term Long Term 10 20 30 Yield Curve for January 2008 Yield Curve for February 2000 Yield Curve for March 1980 Years to Maturity 2 4 6 8 10 12 14 16 Interest Rate INTEREST RATE Term to Maturity March 1980 February 2000 January 2008 1 year 14.0 6.2 2.7 5 years 13.5 6.7 3.0 10 years 12.8 6.7 3.7 30 years 12.3 6.3 4.3 Term Structure of Interest Rates The relationship between bond yields and maturities. Yield Curve A graph showing the relationship between bond yields and maturities. Chapter 6 Interest Rates 175

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As the figure shows the yield curve changes in position and in slope over time.InMarch1980allrateswerequitehighbecausehighinflationwasexpected. However the rate of inflation was expected to decline so short-term rates were higher than long-term rates and the yield curve was thus downward-sloping.By February 2000 inflation had indeed declined thus all rates were lower and the yield curve had become humped—medium-term rates were higher than either short- or long-term rates. By January 2008 all rates had fallen below the 2000 levels and because short-term rates had dropped below long-term rates the yield curve was upward-sloping. Figure 6-4 shows yield curves for U.S. Treasury securities but we could have constructed curves for bonds issued by GE IBM Delta Air Lines or any other company that borrows money over a range of maturities. Had we constructed suchcorporateyieldcurvesandplottedthemonFigure6-4theywouldhavebeen above those for Treasury securities because corporate yields include default risk premiums and somewhat higher liquidity premiums. Even so the corporate yield curves would have had the same general shape as the Treasury curves. Also the riskier the corporation the higher its yield curve so Delta which has been flirting with bankruptcy would have a higher yield curve than GE or IBM. Historically long-term rates are generally above short-term rates because of the maturity risk premium so all yield curves usually slope upward. For this reason people often call an upward-sloping yield curve a “normal” yield curve and a yield curve that slopes downward an inverted or “abnormal” curve. Thus in Figure 6-4 the yield curve for March 1980 was inverted while the one for January2008wasnormal.HowevertheFebruary2000curvewashumpedwhich means that interest rates on medium-term maturities were higher than rates on both short- and long-term maturities. We will explain in detail why an upward slope is the normal situation. Briefly however the reason is that short-term securities have less interest rate risk than longer-term securities hence they have smaller MRPs. So short-term rates are normally lower than long-term rates. SELFTEST Whatisayieldcurveandwhatinformationwouldyouneedtodrawthiscurve Distinguish among the shapes of a “normal” yield curve an “abnormal” curve and a “humped” curve. Iftheinterest rateson1-5-10-and30-yearbondsare456and7 respectively how would you describe the yield curve If the rates were reversed how would you describe it 6-5 WHAT DETERMINES THE SHAPE OF THE YIELD CURVE Because maturity risk premiums are positive if other things were held constant long-term bonds would always have higher interest rates than short-term bonds. Howevermarketinterestratesalsodependonexpectedinflationdefaultriskand liquidity each of which can vary with maturity. Expected inflation has an especially important effect on the yield curve’s shapeespeciallythecurveforU.S.Treasurysecurities.Treasurieshaveessentially nodefaultorliquidityrisksotheyieldonaTreasurybondthatmaturesintyears can be expressed as follows: T-bond yield¼ r t þIP t þMRP t While the real risk-free rate r varies somewhat over time because of changes in the economy and demographics these changes are random rather than “Normal” Yield Curve An upward-sloping yield curve. Inverted “Abnormal” Yield Curve A downward-sloping yield curve. Humped Yield Curve A yield curve where inter- est rates on medium-term maturities are higher than rates on both short-and long-term maturities. 176 Part 3 Financial Assets

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predictable. Therefore the best forecast for the future value of r is its current value. However the inflation premium IP varies significantly over time and in a somewhat predictable manner. Recall that the inflation premium is the average level of expected inflation over the life of the bond. Thus if the market expects inflation toincrease inthe futuresayfrom3to4to5overthenext3years the inflation premium will be higher on a 3-year bond than on a 1-year bond. On the other hand if the market expects inflation to decline in the future long-term bonds will have a smaller inflation premium than will short-term bonds. Finally since investors consider long-term bonds to be riskier than short-term bonds because of interest rate risk the maturity risk premium always increases with maturity. Panel a of Figure 6-5 shows the yield curve when inflation is expected to increase. Here long-term bonds have higher yields for two reasons: 1 Inflation is expected to be higher in the future and 2 there is a positive maturity risk pre- mium. Panel bshows the yieldcurve when inflation is expectedto decline. Such a downward-slopingyieldcurveoftenforeshadowsaneconomicdownturnbecause Illustrative Treasury Yield Curves FIGURE 6-5 Interest Rate a. When Infation Is Expected to Increase Interest Rate b. When Infation Is Expected to Decrease 8 7 6 5 4 3 2 1 Years to Maturity Maturity Risk Premium Infation Premium Real Risk- Free Rate 8 7 6 5 4 3 2 1 Years to Maturity Maturity Risk Premium Infation Premium Real Risk- Free Rate 0 20 10 30 0 20 10 30 WITH INFLATION EXPECTED TO INCREASE WITH INFLATION EXPECTED TO DECREASE Maturity r IP MRP Yield Maturity r IP MRP Yield 1 year 2.50 3.00 0.00 5.50 1 year 2.50 5.00 0.00 7.50 5 years 2.50 3.40 0.18 6.08 5 years 2.50 4.60 0.18 7.28 10 years 2.50 4.00 0.28 6.78 10 years 2.50 4.00 0.28 6.78 20 years 2.50 4.50 0.42 7.42 20 years 2.50 3.50 0.42 6.42 30 years 2.50 4.67 0.53 7.70 30 years 2.50 3.33 0.53 6.36 Chapter 6 Interest Rates 177

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weaker economic conditions generally lead to declining inflation which in turn results in lower long-term rates. 11 Now let’s consider the yield curve for corporate bonds. Recall that corporate bonds include a default risk premium DRP and a liquidity premium LP. Therefore the yield on a corporate bond that matures in t years can be expressed as follows: Corporate bond yield ¼ r t þIP t þMRP t þDRP t þLP t Corporate bonds’ default and liquidity risks are affected by their maturities. For example the default risk on Coca-Cola’s short-term debt is very small since THELINKS BETWEENEXPECTEDINFLATION ANDINTERESTRATES:ACLOSERLOOK Throughout the text we use the following equation to describe the link between expected inflation and the nominal risk-free rate of interest r RF : r RF ¼ r þIP Recall that r is the real risk-free interest rate and IP is the corresponding inflation premium. This equation suggests that there is a simple link between expected inflation and nominal interest rates. It turns out however that this link is a bit more com- plex. To fully understand this relationship first recognize that individuals get utility through the consumption of real goodsandservicessuch asbreadwater haircuts pizzaand textbooks. When we save money we are giving up the opportunity to consume these goods today in return for beingable toconsume more of them inthe future. Our gain from waiting is measured by the real rate of interest r. To illustrate this point consider the following example. Assume that a loaf of bread costs 1 today. Also assume that the real rate of interest is 3 and that inflation is expected to be 5 over the next year. The 3 real rate indicates that the average consumer is willing to trade 100 loaves of bread today for 103 loaves next year. If a “bread bank” were available consumers who wanted to defer consumption untilnextyearcoulddeposit100 loaves today and withdraw 103 loaves next year. In practice most of us do not directly trade real goods such as bread—instead we purchase these goods with money because in a well-functioning economy it is more efficient to exchange money than goods. However when we lend money over time we worry that bor- rowers might pay us back with dollars that aren’t worth as much due to inflation. To compensate for this risk lenders build in a premium for expected inflation. With these concerns in mind let’s compare the dollar cost of 100 loaves of bread today to the cost of 103 loaves nextyear.Giventhecurrent price100loavesofbreadtoday would cost 100. Since expected inflation is 5 this means that a loaf of bread is expected to cost 1.05 next year. Consequently 103 loaves of bread are expected to cost 108.15 next year 103 × 1.05. So if consumers were to deposit 100 in a bank today they would need to earn 8.15 to realize a real return of 3. Putting this all together we see that the 1-year nomi- nal interest rate can be calculated as follows: r RF ¼ð1þr Þð1þIÞ 1 ¼ð1:03Þð1:05Þ 1¼ 0:0815¼ 8:15 Note that this expression can be rewritten as follows: r RF ¼ r þIþðr IÞ That equation is identical to our original expression for the nominal risk-free rate except that it includes a “cross-term” r × I. When real interest rates and expected inflation are relatively low the cross-term turns out to be quite small and thus is often ignored. Because it is normally insignifi- cant we disregard the cross-term in the text unless stated otherwise. One last point—you should recognize thatwhile it may be reasonable to ignore the cross-term when interest rates are low as they are in the United States today it is a mistake to do so when investing in a market where interest rates and inflation are quite high as is often the case in many emerging markets. In these markets the cross-term can be significant and thus should not be disregarded. 11 Note that yield curves tend to rise or fall relatively sharply over the first 5 to 10 years and then flatten out. One reason this occurs is that when forecasting future interest rates people often predict relatively high or low inflation for the next few years after which they assume an average long-run inflation rate. Consequently the short end of the yield curve tends to have more curvature and the long end of the yield curve tends to be more stable. 178 Part 3 Financial Assets

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thereisalmostnochancethatCoca-Colawillgobankruptoverthenextfewyears. However Coke has some bonds that have a maturity of almost 100 years and while the oddsof Coke defaultingon those bonds might not be veryhighthere is still a higher probability of default risk on Coke’s long-term bonds than its short- term bonds. Longer-term corporate bonds also tend to be less liquid than shorter-term bonds. Since short-term debt has less default risk someone can buy a short-term bond without doing as much credit checking as would be necessary for a long- term bond. Thus people can move in and out of short-term corporate debt rela- tively rapidly. As a result a corporation’s short-term bonds are typically more liquid and thus have lower liquidity premiums than its long-term bonds. Figure6-6showsyieldcurvesfortwohypotheticalcorporatebonds—anAA-rated bond with minimal default risk and a BBB-rated bond with more default risk— alongwiththeyieldcurveforTreasurysecuritiestakenfromPanelaofFigure6-5. Here we assume that inflation is expected to increase so the Treasury yield curve isupward-sloping.Becauseoftheiradditionaldefaultandliquidityriskcorporate bonds yield more than Treasury bonds with the same maturity and BBB-rated bondsyieldmorethanAA-ratedbonds.Finallynotethatthe yieldspreadbetween corporateandTreasurybondsislargerthelongerthematurity.Thisoccursbecause Illustrative Corporate and Treasury Yield Curves FIGURE 6-6 Interest Rate 12 10 8 6 4 2 0 20 10 30 Years to Maturity BBB-Rated Bond AA-Rated Bond Treasury Bond INTEREST RATE Term to Maturity Treasury Bond AA-Rated Bond BBB-Rated Bond 1 year 5.5 6.7 7.4 5 years 6.1 7.4 8.1 10 years 6.8 8.2 9.1 20 years 7.4 9.2 10.2 30 years 7.7 9.8 11.1 Chapter 6 Interest Rates 179

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longer-termcorporatebondshavemoredefaultandliquidityriskthanshorter-term bonds and both of these premiums are absent in Treasury bonds. SELFTEST How do maturity risk premiums affect the yield curve If the inflation rate is expected to increase would this increase or decrease the slope of the yield curve If the inflation rate is expected to remain constant at the current level in the future would the yield curve slope up slope down or be horizontal Consider all factors that affect the yield curve not just inflation. Explain why corporate bonds’ default and liquidity premiums are likely to increase with their maturity. Explain why corporate bonds always yield more than Treasury bonds and why BBB-rated bonds always yield more than AA-rated bonds. 6-6 USING THE YIELD CURVE TO ESTIMATE FUTURE INTEREST RATES 12 In the last section we saw that the slope of the yield curve depends primarily on two factors: 1 expectations about future inflation and 2 effects of maturity on bonds’ risk. We also saw how to calculate the yield curve given inflation and maturity-relatedrisks.Notethoughthatpeoplecanreversetheprocess:Theycan look at the yield curve and use information embedded in it to estimate the mar- ket’sexpectationsregardingfutureinflationriskandshort-terminterestrates.For example suppose a company is in the midst of a 5-year expansion program and the treasurer knows that she will need to borrow short-term funds a year from now. She knows the current cost of 1-year money read from the yield curve but she wants to know the cost of 1-year money next year. That information can be “backed out” by analyzing the current yield curve as will be discussed. The estimation process is straightforward provided we 1 focus on Treasury bonds and 2 assume that Treasury bonds contain no maturity risk premiums. 13 Thispositionhasbeencalledthepureexpectationstheoryofthetermstructureof interest rates often simply referred to as the “expectations theory.” The expec- tations theory assumes that bond traders establish bond prices and interest rates strictly on the basis of expectations for future interest rates and that they are indifferent to maturity because they do not view long-term bonds as being riskier than short-term bonds. If this were true the maturity risk premium MRP would be zero and long-term interest rates would simply be a weighted average of current and expected future short-term interest rates. Toillustratethepureexpectationstheoryassumethata1-yearTreasurybond currently yields 5.00 while a 2-year bond yields 5.50. Investors who want to invest for a 2-year horizon have two primary options: Option 1: Buy a two-year security and hold it for 2 years. 12 This section is relatively technical but instructors can omit it without loss of continuity. 13 Although most evidence suggests that there is a positive maturity risk premium some academics and prac- titioners contend that this second assumption is reasonable at least as an approximation. They argue that the market is dominated by large bond traders who buy and sell securities of different maturities each day that these traders focus only on short-term returns and that they are not concerned with maturity risk. According to this view a bond trader is just as willing to buy a 20-year bond to pick up a short-term profit as he or she is to buy a 3- month security. Proponents of this view argue that the shape of the Treasury yield curve is therefore determined only by market expectations about future interest rates. Later we show what happens when we include the effects of maturity risk premiums. Pure Expectations Theory A theory that states that the shape of the yield curve depends on invest- ors’ expectations about future interest rates. 180 Part 3 Financial Assets

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Option 2: Buy a 1-year security hold it for 1 year and then at the end of the year reinvest the proceeds in another 1-year security. If they select Option 1 for every dollar they invest today they will have accu- mulated 1.113025 by the end of Year 2: Funds at end of Year 2¼ 1ð 1:055Þ 2 ¼ 1:113025 If they select Option 2 they should end up with the same amount but this equation is used to find the ending amount: Funds at end of Year 2¼ 1ð 1:05Þð 1þXÞ HereXistheexpectedinterestrateona1-yearTreasurysecurity1yearfromnow. If the expectations theory is correct each option must provide the same amount of cash at the end of 2 years which implies the following: ð1:05Þð1þXÞ¼ð1:055Þ 2 We can rearrange this equation and then solve for X: 1þX ¼ð1:055Þ 2 1:05 X ¼ð1:055Þ 2 1:05 1¼ 0:0600238¼ 6:00238 Therefore X the 1-year rate 1 year from today must be 6.00238 otherwise one option will be better than the other and the market will not be in equilibrium. Howeverifthemarketisnotinequilibriumbuyingandsellingwillquicklybring aboutequilibrium.Forexamplesupposeinvestorsexpectthe1-yearTreasuryrate tobe6.00238ayearfromnowbuta2-yearbondnowyields5.25notthe5.50 rate required for equilibrium. Bond traders could earn a profit by adopting the following strategy: 1. Borrow money for 2 years at the 2-year rate 5.25 per year. 2. Invest the money in a series of 1-year securities expecting to earn 5.00 this yearand6.00238nextyearforanoverallexpectedreturnoverthe2yearsof 1.05 × 1.0600238 1/2 – 1 ¼ 5.50. Borrowing at 5.25 and investing to earn 5.50 is a good deal so bond traders would rush to borrow money demand funds in the 2-year market and invest or supply funds in the 1-year market. Recall from Figure 6-1 that a decline in the supply of funds raises interest rates while an increase in the supply lowers rates. Likewise an increase in the demand for funds raises rates while a decline in demand lowers rates. Therefore bond traders would push up the 2-year yield and simultaneously lower the yield on 1-year bonds. This buying and selling would cease when the 2-year rate becomes a weighted average of expected future 1-year rates. 14 The preceding analysis was based on the assumption that the maturity risk premium is zero. However most evidence suggests that a positive maturity risk premium exists. For example assume once again that 1- and 2-year maturities yield 5.00 and 5.50 respectively so we have a rising yield curve. However 14 In our calculations we used the geometric average of the current and expected 1-year rates: 1.05 × 1.0600238 1/2 – 1 ¼ 0.055 or 5.50. The arithmetic average of the two rates is 5 þ 6.00238/2 ¼ 5.50119. The geometric average is theoretically correct but the difference is only 0.00119. With interest rates at the levels they have been in the United States and most other nations in recent years the geometric and arithmetic averages are so close that many people use the arithmetic average especially given the other assumptions that underlie the estimation of future 1-year rates. Chapter 6 Interest Rates 181

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now assume that the maturity risk premium on the 2-year bond is 0.20 versus zero for the 1-year bond. This premium means that in equilibrium the expected annual return on a 2-year bond 5.50 must be 0.20 higher than the expected return on a series of two 1-year bonds 5.00 and X. Therefore the expected return on the series must be 5.50 – 0.20 5.30: Expected return on 2-year series ¼ Rate on 2-year bond MRP ¼ 0:055 0:002¼ 0:053¼ 5:30 Now recall that the annual expected return from the series of two 1-year bonds can be expressed as follows where X is the 1-year rate next year: ð1:05Þð1þXÞ¼ð1þExpected return on 2-year seriesÞ 2 ¼ð1:053Þ 2 1:05X ¼ð1:053Þ 2 1:05 X ¼ 0:0588090 1:05 ¼ 0:0560086¼ 5:60086 Undertheseconditionsequilibriumrequiresthatmarketparticipantsexpectthe 1-year rate next year to be 5.60086. Note that the rate read from the yield curve rises by 0.50 when the years to maturity increase from one to two: 5.50 – 5.00 0.50. Of this 0.50 increase 0.20 is attributable to the MRP and the remaining 0.30 is due to the increase in expected 1-year rates next year. Puttingallof thistogether we see that onecan use the yield curve to estimate what the market expects the short-term rate to be next year. However this requires an estimate of the maturity risk premium and if our estimated MRP is incorrect then so will our yield-curve-based interest rate forecast. Thus while the yield curve can be used to obtain insights into what the market thinks future interest rates will be we calculate out these expectations with precision unless the pure expectations theory holds or we know with certainty the exact maturity risk premium. Since neither of these conditions holds it is difficult to know for sure what the market is forecasting. Note too that even if we could determine the market’s consensus forecast for future rates the market is not always right. So a forecast of next year’s rate based on the yield curve could be wrong. Therefore obtaining an accurate forecast of rates for next year—or even for next month—is extremely difficult. SELFTEST What key assumption underlies the pure expectations theory Assuming that the pure expectations theory is correct how are expected short-term rates used to calculate expected long-term rates According to the pure expectations theory what would happen iflong-term rates were not an average of expected short-term rates Most evidence suggests that a positive maturity risk premium exists. How would this affect your calculations when determining interest rates Assume that the interest rate on a 1-year T-bond is currently 7 and the rate on a 2-year bond is 9. If the maturity risk premium is zero what is a reasonable forecast of the rate on a 1-year bond next year What would the forecast beifthe maturity risk premiumon the 2-year bond was 0.5 versus zero for the 1-year bond 11.04 10.02 182 Part 3 Financial Assets

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6-7 MACROECONOMIC FACTORS THAT INFLUENCE INTEREST RATE LEVELS We described how key components such as expected inflation default risk maturity risk and liquidity concerns influence the level of interest rates over time and across different markets. On a day-to-day basis a variety of macroeconomic factors may influence one or more of these components hence macroeconomic factors have an important effect on both the general level of interest rates and the shapeoftheyieldcurve.Theprimaryfactorsare1FederalReservepolicy2the federal budget deficit or surplus 3 international factors including the foreign trade balance and interest rates in other countries and 4 the level of business activity. 6-7a Federal Reserve Policy As you probably learned in your economics courses 1 the money supply has a significant effectonthelevelofeconomicactivityinflationandinterestratesand 2 in the United States the Federal Reserve Board controls the money supply. If the Fed wants to stimulate the economy it increases the money supply. The Fed buys and sells short-term securities so the initial effect of a monetary easing would be to cause short-term rates to decline. However a larger money supply might lead to an increase in expected future inflation which would cause long- termratestoriseevenasshort-termratesfell.ThereverseholdsiftheFedtightens the money supply. As you can see from Figure 6-2 interest rates in recent years have been rel- ativelylowwithshort-termratesespeciallylowin2003and2004.Thoselowrates enabled mortgage banks to write adjustable rate mortgage loans with very favorable rates and that helped stimulate a huge housing boom along with growth of the economy. The Fed became concerned that the economy would overheatsofrom2004to2006itraiseditstargetrate17timesgoingfrom2.0to 5.25 in 2006. Long-term rates remained relatively stable during those years. The Fed left its target rate unchanged from June 2006 to September 2007 but the subprime credit crunch that began in 2007 caused increasing concerns about a possible recession. Those fears led the Fed to cut rates five times from September 2007 to February 2008 taking the target rate down from 5.25 to 3.00. The Fed also signaled that more cuts were likely in the coming few months. Actions that lower short-term rates won’t necessarily lower long-term rates. This point was made in the following quote from the online edition of Investors’ Business Daily on February 15 2008: U.S. government debt prices ended mostly lower Thursday led by long-dated issues as traders turned their focus to potential inflation risks resulting from additional interest rate cuts signaled by the Federal Reserve. ItwasaroughdayfortheTreasuriesmarketastradersconcludedthatmore Fed rate cuts and the government’s fiscal stimulus program would come at the expense of higher long-term inflation. “Fiscal and monetary stimuli are focused on the current strain in the financial markets and its effect on the economy but there are fears about what these actions may do to inflation down the road” said Tom Sapio a managing director at Cantor Fitzgerald in New York. Lower rates could also cause foreigners to sell their holdings of U.S. bonds. These investors would be paid with dollars which they would then sell to buy their own currencies. The sale of dollars and the purchase of other currencies would lower the value of the dollar relative to other currencies which would The home page for the Board of Governors of the Federal Reserve System can be found at You can access general information about the Federal Reserve including press releases speeches and monetary policy. Chapter 6 Interest Rates 183

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make U.S.goods less expensive which would help manufacturers and thus lower the trade deficit. Note also that during periods when the Fed is actively inter- vening in the markets the yield curve may be temporarily distorted. Short-term ratesmaybedrivenbelowthelong-runequilibriumleveliftheFediseasingcredit and above the equilibrium rate if the Fed is tightening credit. Long-term rates are not affected as much by Fed intervention. 6-7b Federal Budget Deficits or Surpluses If the federal government spends more than it takes in as taxes it runs a deficit and that deficit must be covered by additional borrowing selling more Treasury bonds or by printing money. If the government borrows this increases the demand for funds and thus pushes up interest rates. If the government prints money investors recognize that with “more money chasing a given amount of goods” the result will be increased inflation which will also increase interest rates. So the larger the federal deficit other things held constant the higher the level of interest rates. Over thepastseveraldecades the federal governmenthas generallyrunlarge budgetdeficits.Thereweresomesurplusesinthelate1990sbuttheSeptember11 2001 terrorist attacks the subsequent recession and the Iraq war all boosted government spending and caused the deficits to return. It is difficult to tell where fiscal policy will go and consequently what effect it will have on interest rates. 6-7c International Factors Businesses and individuals in the United States buy from and sell to people and firmsallaroundtheglobe.Iftheybuymorethantheysellthatisiftherearemore imports than exports they are said to be running a foreign trade deficit. When trade deficits occur they must be financed and this generally means borrowing from nations with export surpluses. Thus if the United States imported 200 billionofgoodsbutexportedonly100billionitwouldrunatradedeficitof100 billion while other countries would have a 100 billion trade surplus. The United States would probably borrow the 100 billion from the surplus nations. 15 At any rate the larger the trade deficit the higher the tendency to borrow. Note that foreigners will hold U.S. debt if and only if the rates on U.S. securities are com- petitive with rates in other countries. This causes U.S. interest rates to be highly dependent on rates in other parts of the world. All this interdependency limits the ability of the Federal Reserve to use monetary policy to control economic activity in the United States. For example if the Fed attempts to lower U.S. interest rates and this causes rates to fall below rates abroad foreigners will begin selling U.S. bonds. Those sales will depress bond prices which will push up rates in the United States. Thus the large U.S. trade deficit and foreigners’ holdings of U.S. debt that resulted from many years of deficits hinders the Fed’s ability to combat a recession by lowering interest rates. For about 25 years following World War II the United States ran large trade surplusesandthe restoftheworldoweditmanybillionsofdollars. Howeverthe situation changed and the United States has been running trade deficits since the mid-1970s. The cumulative effect of these deficits has been to change the United States from being the largest creditor nation to being the largest debtor nation of Foreign Trade Deficit The situation that exists when a country imports more than it exports. 15 The deficit could also be financed by selling assets including gold corporate stocks entire companies and real estate.The United States has financedits massivetrade deficits by all of these meansin recent years.Althoughthe primary method has been by borrowing from foreigners in recent years there has been a sharp increase in foreign purchases of U.S. assets especially oil exporters’ purchases of U.S. businesses. 184 Part 3 Financial Assets

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all time. As a result interest rates are very much influenced by interest rates in other countries—higher or lower rates abroad lead to higher or lower U.S. rates. Because of all of this U.S. corporate treasurers and everyone else who is affected by interest rates should keep up with developments in the world economy. 6-7d Business Activity You can examine Figure 6-2 to see how business conditions influence interest rates. Here are the key points revealed by the graph: 1. Because inflation increased from 1972 to 1981 the general tendency during that period was toward higher interest rates. However since the 1981 peak the trend has generally been downward. 2. The shaded areas in the graph represent recessions during which a the demand for money and the rate of inflation tended to fall and b the Federal Reserve tended to increase the money supply in an effort to stimulate the economy. As a result there is a tendency for interest rates to decline during recessions. For example the economy began to slow down in 2000 and the country entered a mild recession in 2001. In response the Federal Reserve cut interest rates. In 2004 the economy began to rebound so the Fed began to raise rates. However the subprime debacle hit in 2007 so the Fed began loweringratesinSeptember2007.ByFebruarytheFed’stargetratehadfallen from 5.25 to 3.00 with indications that more reductions were likely. 3. Duringrecessionsshort-termratesdeclinemoresharplythanlong-termrates. This occurs for two reasons: a The Fed operates mainly in the short-term sector so its intervention has the strongest effect there. b Long-term rates reflecttheaverageexpectedinflationrateoverthenext20to30yearsandthis expectation generally does not change much even when the current inflation rate is low because of a recession or high because of a boom. So short-term ratesaremorevolatilethanlong-termrates.TakinganotherlookatFigure6-2 weseethatshort-termratesdiddeclinerecentlybymuchmorethanlong-term rates. SELFTEST Identify some macroeconomic factors that influence interest rates and explain the effects of each. How does the Fed stimulate the economy How does the Fed affect interest rates Does the Fed have complete control over U.S. interest rates That is can it set rates at any level it chooses Why or why not 6-8 INTEREST RATES AND BUSINESS DECISIONS The yield curve for January 2008 shown earlier in Figure 6-4 indicates how much the U.S. government had to pay in January 2008 to borrow money for 1 year 5 years 10 years and so forth. A business borrower would have paid somewhat more but assume for the moment that it is January 2008 and the yield curve shownforthatyearapplies toyourcompany.Nowsupposeyou decidetobuilda new plant with a 30-year life that will cost 1 million and you will raise the 1 million by borrowing rather than by issuing new stock. If you borrowed in Jan- uary 2008 on a short-term basis—say for 1 year—your annual interest cost would beonly2.7or27000.Ontheotherhandifyouusedlong-termfinancingyour annual cost would be 4.3 or 43000. Therefore at first glance it would seem that you should use short-term debt. Chapter 6 Interest Rates 185

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Howeverthiscouldprovetobeahorriblemistake.Ifyouuseshort-termdebt you will have to renew your loan every 6 months and the rate charged on each newloanwillreflectthethen-currentshort-termrate.Interestratescouldreturnto their previous highs in which case you would be paying 14 or 140000 per year. Those high interest payments would cut into and perhaps eliminate your profits. Your reduced profitability could increase your firm’s risk to the point where your bond rating was lowered causing lenders to increase the risk premium built into your interest rate. That would further increase your interest payments which would further reduce your profitability worry lenders still more and make them reluctant to renew your loan. If your lenders refusedtorenewtheloananddemandeditsrepaymentastheywouldhaveevery right to do you might have to sell assets at a loss which could result in bankruptcy. On the other hand if you used long-term financing in 2008 your interest costs would remain constant at 43000 per year so an increase in interest rates in the economy would not hurt you. You might even be able to acquire some of your bankrupt competitors at bargain prices—bankruptcies increase dramatically when interest rates rise primarily because many firms use so much short-term debt. Does all of this suggest that firms should avoid short-term debt Not at all. If inflation falls over the next few years so will interest rates. If you had borrowed on a long-term basis for 4.3 in January 2008 your company would be at a disadvantage if it was locked into 4.3 debt while its competitors who used short-term debt in 2008 had a borrowing cost of only 2.7. Financing decisions would be easy if we could make accurate forecasts of future interest rates. Unfortunately predicting interest rates with consistent accuracy is nearly impossible. However although it is difficult to predict future interestratelevelsitiseasytopredictthatinterestrateswillfluctuate—theyalways have and they always will. That being the case sound financial policy calls for using a mix of long- and short-term debt as well as equity to position the firm so that it can survive in any interest rate environment. Further the optimal financial policy depends in an important way on the nature of the firm’s assets—the easier itistoselloffassetstogeneratecashthemorefeasibleitistousemoreshort-term debt. This makes it logical for a firm to finance current assets such as inventories and receivables with short-term debt and to finance fixed assets such as buildings and equipment with long-term debt. We will return to this issue later in the book when we discuss capital structure and financing policy. Changes in interest rates also have implications for savers. For example if you had a 401k plan—and someday most of you will—you would probably want to invest some of your money in a bond mutual fund. You could choose a fund that had an average maturity of 25 years 20 years on down to only a few months a money market fund. How would your choice affect your investment resultsandhenceyourretirementincomeFirstyourdecisionwouldaffectyour annual interest income. For example if the yield curve was upward- sloping as it normally is you would earn more interest if you chose a fund that held long- term bonds. Note though that if you chose a long-term fund and interest rates then rose the market value of your fund would decline. For example as we will see in Chapter 7 if you had 100000 in a fund whose average bond had a maturity of 25 years and a coupon rate of 6 and if interest rates then rose from 6 to 10 the market value of your fund would decline from 100000 to about 63500. On the other hand if rates declined your fund would increase in value. If you invested in a short-term fund its value would be stable but it would probably provide less interest per year. In any event your choice of maturity would have a major effect on your investment performance and hence on your future income. 186 Part 3 Financial Assets

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SELFTEST If short-term interest rates are lower than long-term rates why might a borrower still choose to finance with long-term debt Explain the following statement: The optimal financial policy depends in an important way on the nature of the firm’s assets. TYING IT ALL TOGETHER In this chapter we discussed the way interest rates are determined the term structure of interest rates and some of the ways interest rates affect business decisions. We saw that the interest rate on a given bond r is based on this equation: r¼ r þIPþDRPþLPþMRP Here r is the real risk-free rate IP is the premium for expected inflation DRP is the premium for potential default risk LP is the premium for lack of liquidity and MRP is the premium to compensate for the risk inherent in bonds with long maturities. Both r and the various premiums can and do change over time depending on economic conditions Federal Reserve actions and the like. Since changes in these factors are difficult to predict it is hard to forecast the future direction of interest rates. The yield curve which relates bonds’ interest rates to their maturities usually has an upward slope but it can slope up or down and both its slope and level change over time. The main determinants of the slope of the curve are expec- tationsfor future inflation and the MRP. Wecan analyze yield curve data toestimate what market participants think future interest rates are likely to be. We will use the insights gained from this chapter in later chapters when we analyze the values of bonds and stocks and when we examine various corporate investment and financing decisions. SELF-TEST QUESTIONS AND PROBLEMS Solutions Appear in Appendix A ST-1 KEY TERMS Define each of the following terms: a. Production opportunities time preferences for consumption risk inflation b. Real risk-free rate of interest r nominal quoted risk-free rate of interest r RF c. Inflation premium IP d. Default risk premium DRP e. Liquidity premium LP maturity risk premium MRP f. Interest rate risk reinvestment rate risk g. Term structure of interest rates yield curve h. “Normal” yield curve inverted “abnormal” yield curve humped yield curve i. Pure expectations theory Chapter 6 Interest Rates 187

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ST-2 INFLATION AND INTEREST RATES The real risk-free rate of interest r is 3 and it is expected to remain constant over time. Inflation is expected to be 2 per year for the next 3 years and 4 per year for the next 5 years. The maturity risk premium is equal to 0.1 t – 1 where t the bond’s maturity. The default risk premium for a BBB-rated bond is 1.3. a. What is the average expected inflation rate over the next 4 years b. What is the yield on a 4-year Treasury bond c. What is the yield on a 4-year BBB-rated corporate bond with a liquidity premium of 0.5 d. What is the yield on an 8-year Treasury bond e. What is the yield on an 8-year BBB-rated corporate bond with a liquidity premium of 0.5 f. If the yield on a 9-year Treasury bond is 7.3 what does that imply about expected inflation in 9 years ST-3 PURE EXPECTATIONS THEORY The yield on 1-year Treasury securities is 6 2-year securities yield 6.2 and 3-year securities yield 6.3. There is no maturity risk premium. Using expectations theory forecast the yields on the following securities: a. A 1-year security 1 year from now b. A 1-year security 2 years from now c. A 2-year security 1 year from now QUESTIONS 6-1 Supposeinterestratesonresidentialmortgagesofequalriskare5.5inCaliforniaand7.0 in New York. Could this differential persist What forces might tend to equalize rates WoulddifferentialsinborrowingcostsforbusinessesofequalrisklocatedinCaliforniaand New York be more or less likely to exist than differentials in residential mortgage rates Would differentials in the cost of money for New York and California firms be more likely toexistifthefirmsbeingcomparedwereverylargeoriftheywereverysmallWhatarethe implications of all of this with respect to nationwide branching 6-2 Which fluctuate more—long-term or short-term interest rates Why 6-3 Suppose you believe that the economy is just entering a recession. Your firm must raise capital immediately and debt will be used. Should you borrow on a long-term or a short- term basis Why 6-4 Suppose the population of Area Y is relatively young and the population of Area O is relatively old but everything else about the two areas is the same. a. Would interest rates likely be the same or different in the two areas Explain. b. Would a trend toward nationwide branching by banks and the development of nationwide diversified financial corporations affect your answer to part a Explain. 6-5 Suppose a new process was developed that could be used to make oil out of seawater. The equipmentrequiredisquiteexpensivebutitwouldintimeleadtolowpricesforgasoline electricity and other types of energy. What effect would this have on interest rates 6-6 Suppose a new and more liberal Congress and administration are elected. Their first order ofbusinessistotakeawaytheindependenceoftheFederalReserveSystemandtoforcethe Fed to greatly expand the money supply. What effect will this have: a. On the level and slope of the yield curve immediately after the announcement b. On the level and slope of the yield curve that would exist two or three years in the future 6-7 It is a fact that the federal government 1 encouraged the development of the savings and loan industry 2 virtually forced the industry to make long-term fixed-interest-rate mortgages and 3 forced the savings and loans to obtain most of their capital as deposits that were withdrawable on demand. a. Would the savings and loans have higher profits in a world with a “normal” or an inverted yield curve 188 Part 3 Financial Assets

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b. Would the savings and loan industry be better off if the individual institutions sold their mortgages to federal agencies and then collected servicing fees or if the institu- tions held the mortgages that they originated 6-8 Suppose interest rates on Treasury bonds rose from 5 to 9 as a result of higher interest ratesinEurope.Whateffectwouldthishaveonthepriceofanaveragecompany’scommon stock 6-9 What does it mean when it is said that the United States is running a trade deficit What impact will a trade deficit have on interest rates PROBLEMS Easy Problems 1–7 6-1 YIELD CURVES The following yields on U.S. Treasury securities were taken from a recent financial publication: Term Rate 6 months 5.1 1 year 5.5 2 years 5.6 3 years 5.7 4 years 5.8 5 years 6.0 10 years 6.1 20 years 6.5 30 years 6.3 a. Plot a yield curve based on these data. b. What type of yield curve is shown c. What information does this graph tell you d. Basedonthisyieldcurveifyouneededtoborrowmoneyforlongerthan1yearwould it make sense for you to borrow short-term and renew the loan or borrow long-term Explain. 6-2 REAL RISK-FREE RATE You read in The Wall Street Journal that 30-day T-bills are currently yielding5.5.Yourbrother-in-lawabrokeratSafeandSoundSecuritieshasgivenyouthe following estimates of current interest rate premiums: l Inflation premium ¼ 3.25 l Liquidity premium ¼ 0.6 l Maturity risk premium ¼ 1.8 l Default risk premium ¼ 2.15 On the basis of these data what is the real risk-free rate of return 6-3 EXPECTED INTEREST RATE The real risk-free rate is 3. Inflation is expected to be 2 this year and 4 during the next 2 years. Assume that the maturity risk premium is zero. What is the yield on 2-year Treasury securities What is the yield on 3-year Treasury securities 6-4 DEFAULT RISK PREMIUM A Treasury bond that matures in 10 years has a yield of 6. A 10-year corporate bond has a yield of 8. Assume that the liquidity premium on the corporate bond is 0.5. What is the default risk premium on the corporate bond 6-5 MATURITY RISK PREMIUM The real risk-free rate is 3 and inflation is expected to be 3 for the next 2 years. A 2-year Treasury security yields 6.2. What is the maturity risk premium for the 2-year security Chapter 6 Interest Rates 189

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6-6 INFLATION CROSS-PRODUCT An analyst is evaluating securities in a developing nation where the inflation rate is very high. As a result the analyst has been warned not to ignore the cross-product between the real rate and inflation. If the real risk-free rate is 5 and inflationisexpectedtobe16eachofthenext4yearswhatistheyieldona4-yearsecurity with no maturity default or liquidity risk Hint: Refer to “The Links between Expected Inflation and Interest Rates: A Closer Look” on Page 178. 6-7 EXPECTATIONS THEORY One-year Treasury securities yield 5. The market anticipates that 1 year from now 1-year Treasury securities will yield 6. If the pure expectations theory is correct what is the yield today for 2-year Treasury securities Intermediate Problems 8–16 6-8 EXPECTATIONS THEORY Interest rates on 4-year Treasury securities are currently 7 while 6-year Treasury securities yield 7.5. If the pure expectations theory is correct what does the market believe that 2-year securities will be yielding 4 years from now 6-9 EXPECTED INTEREST RATE The real risk-free rate is 3. Inflation is expected to be 3 this year 4 next year and 3.5 thereafter. The maturity risk premium is estimated to be 0.05 × t – 1 where t ¼ number of years to maturity. What is the yield on a 7-year Treasury note 6-10 INFLATION Due to a recession expected inflation this year is only 3. However the inflation rate in Year 2 and thereafter is expected to be constant at some level above 3. Assume that the expectations theory holds and the real risk-free rate is r 2. If the yield on 3-year Treasury bonds equals the 1-year yield plus 2 what inflation rate is expected after Year 1 6-11 DEFAULTRISKPREMIUM Acompany’s5-yearbondsareyielding7.75peryear.Treasury bonds with the same maturity are yielding 5.2 per year and the real risk-free rate r is 2.3.Theaverageinflationpremiumis2.5andthematurityriskpremiumisestimatedto be 0.1 × t – 1 where t ¼ number of years to maturity. If the liquidity premium is 1 what is the default risk premium on the corporate bonds 6-12 MATURITY RISK PREMIUM An investor in Treasury securities expects inflation to be 2.5 inYear13.2inYear2and3.6eachyearthereafter.Assumethattherealrisk-freerateis 2.75 and that this rate will remain constant. Three-year Treasury securities yield 6.25 while 5-year Treasury securities yield 6.80. What is the difference in the maturity risk premiums MRPs on the two securities that is what is MRP 5 – MRP 3 6-13 DEFAULTRISKPREMIUM Therealrisk-freerateris2.5.Inflationisexpectedtoaverage 2.8 a year for the next 4 years after which time inflation is expected to average 3.75 a year. Assume thatthere isno maturity riskpremium. An8-year corporate bond hasa yield of 8.3 which includes a liquidity premium of 0.75. What is its default risk premium 6-14 EXPECTATIONS THEORY AND INFLATION Suppose 2-year Treasury bonds yield 4.5 while 1-year bonds yield 3. r is 1 and the maturity risk premium is zero. a. Using the expectations theory what is the yield on a 1-year bond 1 year from now b. What is the expected inflation rate in Year 1 Year 2 6-15 EXPECTATIONS THEORY Assume that the real risk-free rate is 2 and that the maturity riskpremiumiszero.Ifthe1-yearbondyieldis5anda2-yearbondofsimilarriskyields 7 what is the 1-year interest rate that is expected for Year 2 What inflation rate is expected during Year 2 Comment on why the average interest rate during the 2-year period differs from the 1-year interest rate expected for Year 2. 6-16 INFLATION CROSS-PRODUCT An analyst is evaluating securities in a developing nation where the inflation rate is very high. As a result the analyst has been warned not to ignore the cross-product between the real rate and inflation. A 6-year security with no maturity default or liquidity risk has a yield of 20.84. If the real risk-free rate is 6 what average rate ofinflation isexpected in this country overthe next 6years Hint:Refer to “The Links between Expected Inflation and Interest Rates: A Closer Look” on Page 178. Challenging Problems 17−19 6-17 INTEREST RATE PREMIUMS A 5-year Treasury bond has a 5.2 yield. A 10-year Treasury bond yields 6.4 and a 10-year corporate bond yields 8.4. The market expects that inflation will average 2.5 over the next 10 years IP 10 ¼ 2.5. Assume that there is no maturity risk premium MRP ¼ 0 and that the annual real risk-free rate r will remain constant over the next 10 years. Hint: Remember that the default risk premium and the liquiditypremiumarezeroforTreasurysecurities:DRP¼LP¼0.A5-yearcorporatebond 190 Part 3 Financial Assets

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has the same default risk premium and liquidity premium as the 10-year corporate bond described. What is the yield on this 5-year corporate bond 6-18 YIELDCURVES Supposetheinflationrateisexpectedtobe7nextyear5thefollowing year and 3 thereafter. Assume that the real risk-free rate r will remain at 2 and that maturity risk premiums on Treasury securities rise from zero on very short-term bonds those that mature in a few days to 0.2 for 1-year securities. Furthermore maturity risk premiumsincrease0.2foreachyeartomaturityuptoalimitof1.0on5-yearorlonger- term T-bonds. a. Calculate the interest rate on 1- 2- 3- 4- 5- 10- and 20-year Treasury securities and plot the yield curve. b. SupposeaAAA-ratedcompanywhichisthehighestbondratingafirmcanhavehad bonds with the same maturities as the Treasury bonds. Estimate and plot what you believe a AAA-rated company’s yield curve would look like on the same graph with theTreasurybondyieldcurve.Hint:Thinkaboutthedefaultriskpremiumonitslong- term versus its short-term bonds. c. On the same graph plot the approximate yield curve of a much riskier lower-rated company with a much higher risk of defaulting on its bonds. 6-19 INFLATION AND INTEREST RATES In late 1980 the U.S. Commerce Department released new data showing inflation was 15. At the time the prime rate of interest was 21 a recordhigh.Howevermanyinvestorsexpected thenewReaganadministrationtobemore effective in controlling inflation than the Carter administration had been. Moreover many observers believed that the extremely high interest rates and generally tight credit which resultedfromtheFederalReserveSystem’sattemptstocurbtheinflationratewouldleadto a recession which in turn would lead to a decline in inflation and interest rates. Assume thatat thebeginning of 1981theexpected inflation ratefor1981was13for 19829for 1983 7 and for 1984 and thereafter 6. a. What was the average expected inflation rate over the 5-year period 1981–1985 Use the arithmetic average. b. Over the 5-year period what average nominal interest rate would be expected to produce a 2 real risk-free return on 5-year Treasury securities Assume MRP ¼ 0. c. Assumingarealrisk-freerateof2andamaturityriskpremiumthatequals0.1×t wheretisthenumberofyearstomaturityestimatetheinterestrateinJanuary1981on bonds that mature in 1 2 5 10 and 20 years. Draw a yield curve based on these data. d. Describe the general economic conditions that could lead to an upward-sloping yield curve. e. Ifinvestorsinearly1981expectedtheinflationrateforeveryfutureyeartobe10that is I t ¼ I tþ1 ¼ 10 for t ¼1to ∞ what would the yield curve have looked like Consider all the factors that are likely to affect the curve. Does your answer here make you question the yield curve you drew in part c COMPREHENSIVE/SPREADSHEET PROBLEM 6-20 INTEREST RATE DETERMINATION AND YIELD CURVES a. What effect would each of the following events likely have on the level of nominal interest rates 1 Households dramatically increase their savings rate. 2 Corporations increase their demand for funds following an increase in investment opportunities. 3 The government runs a larger-than-expected budget deficit. 4 There is an increase in expected inflation. b. Suppose you are considering two possible investment opportunities: a 12-year Trea- sury bond and a 7-year A-rated corporate bond. The current real risk-free rate is 4 and inflation is expected to be 2 for the next 2 years 3 for the following 4 years and4thereafter. Thematurityriskpremiumisestimated bythisformula:MRP¼0.1 t –1.Theliquiditypremiumforthecorporatebondisestimatedtobe0.7.Finally Chapter 6 Interest Rates 191

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you may determine the default risk premium given the company’s bond rating from the default risk premium table in the text. What yield would you predict for each of these two investments c. Given the following Treasury bond yield information from a recent financial publica- tion construct a graph of the yield curve. Maturity Yield 1 year 5.37 2 years 5.47 3 years 5.65 4 years 5.71 5 years 5.64 10 years 5.75 20 years 6.33 30 years 5.94 d. Based onthe information aboutthe corporatebond providedin partb calculate yields and then construct a new yield curve graph that shows both the Treasury and the corporate bonds. e. Which part of the yield curve the left side or right side is likely to be most volatile over time f. Using the Treasury yield information in part c calculate the following rates: 1 The 1-year rate 1 year from now 2 The 5-year rate 5 years from now 3 The 10-year rate 10 years from now 4 The 10-year rate 20 years from now INTEGRATED CASE MORTON HANDLEY COMPANY 6-21 INTEREST RATE DETERMINATION Maria Juarez is a professional tennis player and your firm manages her money.Shehasaskedyoutogiveherinformationaboutwhatdeterminesthelevelofvariousinterestrates.Your boss has prepared some questions for you to consider. a. What are the four most fundamental factors that affect the cost of money or the general level of interest rates in the economy b. What is the real risk-free rate of interest r and the nominal risk-free rate r RF How are these two rates measured c. Define the terms inflation premium IP default risk premium DRP liquidity premium LP and maturity risk premium MRP.Which ofthese premiums isincludedin determining theinterest rate on 1 short-term U.S. Treasury securities 2 long-term U.S. Treasury securities 3 short-term corporate securities and 4 long- term corporate securities Explain how the premiums would vary over time and among the different securities listed. d. What is the term structure of interest rates What is a yield curve e. Supposemostinvestorsexpecttheinflationratetobe5nextyear6thefollowingyearand8thereafter. The real risk-free rate is 3. The maturity risk premium is zero for bonds that mature in 1 year or less and 0.1 for 2-year bonds then the MRP increases by 0.1 per year thereafter for 20 years after which it is stable. What is the interest rate on 1- 10- and 20-year Treasury bonds Draw a yield curve with these data. What factors can explain why this constructed yield curve is upward-sloping f. At any given time how would the yield curve facing a AAA-rated company compare with the yield curve for U.S. Treasury securities At any given time how would the yield curve facing a BB-rated company compare with the yield curve for U.S. Treasury securities Draw a graph to illustrate your answer. 192 Part 3 Financial Assets

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g. What is the pure expectations theory What does the pure expectations theory imply about the term structure of interest rates h. Suppose you observe the following term structure for Treasury securities: Maturity Yield 1 year 6.0 2 years 6.2 3 years 6.4 4 years 6.5 5 years 6.5 i. Assume that the pure expectations theory of the term structure is correct. This implies that you can use the yield curve provided to “back out” the market’s expectations about future interest rates. What does the market expect will be the interest rate on 1-year securities 1 year from now What does the market expect will be the interest rate on 3-year securities 2 years from now Chapter 6 Interest Rates 193

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CHAPTER 7 Bonds and Their Valuation Sizing Up Risk in the Bond Market Many people view Treasury securities as a lack- luster but ultra-safe investment. From a default standpoint Treasuries are indeed our safest investments but their prices can still decline in any given year if interest rates increase. This is especially true for long-term bonds which lost nearly 9 in 1999. However bonds can perform well—in fact they outgained stocks in 5 of the 8 years between 2000 and 2007. All bonds aren’t alike and they don’t neces- sarily all move in the same direction. For exam- ple corporate bonds are callable and they can default whereas Treasury bonds are not exposed to these risks. This results in higher nominal yields on corporates but the spread between corporate and Treasury yields differs widely depending on the risk of the particular corporate bond. Moreover yield spreads vary substantially over time especially for lower-rated securities. For example as information about WorldCom’s deteriorating condition began coming out in 2002 the spread on its 5-year bonds jumped from 1.67 to over 20 in mid-2002. These bonds subsequently defaulted so greedy people who bought them expecting a high return ended up with a large loss. Whentheeconomyisstrongcorporatebonds generallyproducehigherreturnsthanTreasuries— their promised returns are higher and most make their promised payments because few go into default. However when the economy weakens concerns about defaults rise which leads to declines in corporate bond prices. For example from the beginning of 2000 to the end of 2002 a sluggish economy and a string of accounting scandals led to some major corporate defaults which worried investors. All corporate bond prices then declined relative to Treasuries and the result was an increase in yield spreads. As the economy rebounded in 2003 yield spreads declined to their former levels which resulted in good gains in corporate bond prices. The situ- ation is once again worrisome in 2008. The subprime mortgage crisis has led to fears of recession and this has caused spreads to rise dramatically especially for lower-rated bonds. ª JOHN CLARK 2008/USED UNDER LICENSE FROM SHUTTERSTOCK.COM 194

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PUTTING THINGS IN PERSPECTIVE In previous chapters we noted that companies raise capital in two main forms: debt and equity. In this chapter we examine the characteristics of bonds and discussthe various factors thatinfluencebond prices. InChapter9wewillturnour attention to stocks and their valuation. If you skim through The Wall Street Journal you will see references to a wide variety of bonds. This variety may seem confusing but in actuality only a few char- acteristics distinguish the various types of bonds. When you finish this chapter you should be able to: l Identify the different features of corporate and government bonds. l Discuss how bond prices are determined in the market what the relationship is between interest rates and bond prices and how a bond’s price changes over time as it approaches maturity. l Calculate a bond’s yield to maturity and its yield to call if it is callable and determine the “true” yield. l Explain the different types of risk that bond investors and issuers face and the way a bond’s terms and collateral can be changed to affect its interest rate. 7-1 WHO ISSUES BONDS Abond isalong-term contractunder which aborrower agrees tomakepayments of interest and principal on specific dates to the holders of the bond. Bonds are issued by corporations and government agencies that are looking for long-term debt capital. For example on January 3 2009 Allied Food Products borrowed 50 million by issuing 50 million of bonds. For convenience we assume that Allied sold 50000 individual bonds for 1000 each. Actually it could have sold one 50 million bond 10 bonds each with a 5 million face value or any other combinationthattotaled50million.InanyeventAlliedreceivedthe50million and in exchange it promised to make annual interest payments and to repay the 50 million on a specified maturity date. For example the spread on junk bonds over Treasuries rose from 2.4 to 7.5 in the 6 months from mid-2007 to January 2008. Bond investors are rightly worried today. If a recession does occur this will lead to increased defaults on corporate bonds.ArecessionmightbenefitinvestorsinTreasurybonds. However because there have alreadybeen several rounds of Federal Reserve rate cuts Treasury rates may not have much room to fall. Also there is concern that recent Fed easing is sowing the seeds for higher inflation down the road which would lead to higher rates and lower bond prices. In the face of similar risks in 2001 a BusinessWeek Online article gave investors the following advice which is still applicable today: Take the same diversified approach to bonds as you do with stocks. Blend in U.S. government corporate— both high-quality and high-yield—and perhaps even some foreign government debt. If you’re investing taxable dollars consider tax-exempt municipal bonds. And it doesn’t hurt to layer in some inflation-indexed bonds. Sources:ScottPatterson“AheadoftheTape:JunkYieldsFlashingBackto’01Slump”TheWallStreetJournalJanuary302008p.C1Stocks BondsBills and Inflation: Valuation Edition 2008 YearbookChicago:Morningstar Inc. 2008andSusan Scherreik “Getting theMost Bang Out of Your Bonds” BusinessWeek Online November 12 2001. Bond A long-term debt instrument. Chapter 7 Bonds and Their Valuation 195

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Until the 1970s most bonds were beautifully engraved pieces of paper and their keytermsincludingtheir facevalueswere spelledoutonthe bonds.Today though virtually all bonds are represented by electronic data stored in secure computers much like the “money” in a bank checking account. Bonds are grouped in several ways. One grouping is based on the issuer: the U.S. Treasury corporations state and local governments and foreigners. Each bond differs with respect to risk and consequently its expected return. Treasury bonds generally called Treasuries and sometimes referred to as government bonds are issued by the federal government. 1 It is reasonable to assume that the U.S. government will make good on its promised payments so Treasuries have no default risk. However these bonds’ prices do decline when interest rates rise so they are not completely riskless. Corporate bonds are issued by business firms. Unlike Treasuries corporates are exposed to default risk—if the issuing company gets into trouble it may be unable to make the promised interest and principal payments and bondholders may suffer losses. Different corporate bonds have different levels of default risk depending on the issuing company’s characteristics and the terms of the specific bond.Defaultriskisoftenreferredtoas “creditrisk”andaswesawinChapter6 the larger this risk the higher the interest rate investors demand. Municipal bonds or munis is the term given to bonds issued by state and local governments. Like corporates munis are exposed to some default risk but theyhaveonemajoradvantageoverallotherbonds:AswediscussedinChapter3 theinterestearnedonmostmunisisexemptfromfederaltaxesandfromstatetaxes iftheholderisaresidentoftheissuingstate.Consequentlythemarketinterestrate on a muni is considerably lower than on a corporate of equivalent risk. Foreign bonds are issued by a foreign government or a foreign corporation. All foreign corporate bonds are exposed to default risk as are some foreign governmentbonds.Anadditionalriskexistswhenthebondsaredenominatedina currencyother thanthat ofthe investor’shomecurrency.Consider forexamplea U.S. investor who purchases a corporate bond denominated in Japanese yen. At some point the investor will want toclose out hisinvestment andconvert the yen back to U.S. dollars. If the Japanese yen unexpectedly falls relative to the dollar the investor will have fewer dollars than he originally expected to receive. Conse- quently the investor could still lose money even if the bond does not default. SELFTEST What is a bond What are the four main issuers of bonds Why are U.S. Treasury bonds not completely riskless In addition to default risk what key risk do investors in foreign bonds face 7-2 KEY CHARACTERISTICS OF BONDS Although all bonds have some common characteristics different bonds can have differentcontractual features. For examplemostcorporatebonds have provisions that allow the issuer to pay them off early “call” features but the specific call Treasury Bonds Bonds issued by the federal government sometimes referred to as government bonds. 1 The U.S. Treasury actually calls its debt “bills”“notes” or “bonds.” T-bills generally have maturities of 1 year or less at the time of issue notes generally have original maturities of 2 to 7 years and bonds originally mature in 8 to 30 years. There are technical differences between bills notes and bonds but they are not important for our purposes. So we generally call all Treasury securities “bonds.” Note too that a 30-year T-bond at the time of issue becomes a 29-year bond the next year and it is a 1-year bond after 29 years. Corporate Bonds Bonds issued by corporations. Municipal Bonds Bonds issued by state and local governments. Foreign Bonds Bonds issued by foreign governments or by foreign corporations. 196 Part 3 Financial Assets

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provisions vary widely among different bonds. Similarly some bonds are backed by specific assets that must be turned over to the bondholders if the issuer defaults while other bonds have no such collateral backup. Differences in con- tractual provisions and in the fundamental underlying financial strength of the companies backing the bonds lead to differences in bonds’ risks prices and expected returns. To understand bonds it is essential that you understand the following terms. 7-2a Par Value The par value is the stated face value of the bond for illustrative purposes we generally assume a par value of 1000 although any multiple of 1000 e.g. 5000 or 5 million can be used. The par value generally represents the amount of money the firm borrows and promises to repay on the maturity date. 7-2b Coupon Interest Rate AlliedFoodProducts’bondsrequirethecompanytopayafixednumberofdollars of interest each year. This payment generally referred to as the coupon payment is set at the time the bond is issued and remains in force during the bond’s life. 2 Typicallyatthetimeabondisissueditscouponpaymentissetatalevelthatwill induceinvestorstobuythebondatornearitsparvalue.Mostoftheexamplesand problems throughout this text will focus on bonds with fixed coupon rates. When this annual coupon payment is divided by the par value the result is thecouponinterestrate.ForexampleAllied’sbondshavea1000parvalueand they pay 100 in interest each year. The bond’s coupon payment is 100 so its coupon interest rate is 100/1000 ¼ 10. In this regard the 100 is the annual income that an investor receives when he or she invests in the bond. Allied’s bonds are fixed-rate bonds because the coupon rate is fixed for the life of the bond. In some cases however a bond’s coupon payment is allowed to vary over time. Thesefloating-rate bonds work as follows: The coupon rate is set for an initial period often 6 months after which it is adjusted every 6 months based onsome open market rate.Forexample thebond’sratemaybeadjustedso as to equal the 10-year Treasury bond rate plus a “spread” of 1.5 percentage points. Other provisions can be included in corporate bonds. For example some canbeconvertedattheholders’optionintofixed-ratedebtandsomefloatershave upper limits caps and lower limits floors on how high or low the rate can go. Some bonds pay no coupons at all but are offered at a discount below their par values and hence provide capital appreciation rather than interest income. These securities are called zero coupon bonds zeros. Other bonds pay some couponinterestbutnotenoughtoinduceinvestorstobuythematpar.Ingeneral any bond originally offered at a price significantly below its par value is called an originalissuediscountOIDbond.Someofthedetailsassociatedwithissuingor investing in zero coupon bonds are discussed more fully in Web Appendix 7A. 7-2c Maturity Date Bonds generally have a specified maturity date on which the par value must be repaid. Allied’s bonds which were issued on January 3 2009 will mature on Par Value The face value of a bond. Coupon Payment The specified number of dollars of interest paid each year. 2 Back when bonds were ornate they were engraved pieces of paper rather than electronic information stored on a computer. Each bond had a number of small 1/2- by 2-inch dated coupons attached to them and on each interest payment date the owner would “clip the coupon” for that date send it to the company’s paying agent and receive a check for the interest. A 30-year semiannual bond would start with 60 coupons whereas a 5-year annual payment bond would start with only 5 coupons. Today no physical coupons are involved and interest checks are mailed or deposited automatically to the bonds’ registered owners on the payment date. Even so people continue to use the terms coupon and coupon interest rate when discussing bonds. You can think of the coupon interest rate as the promised rate. Coupon Interest Rate The stated annual interest rate on a bond. Fixed-Rate Bond A bond whose interest rate is fixed for its entire life. Floating-Rate Bond A bond whose interest rate fluctuates with shifts in the general level of interest rates. Zero Coupon Bond A bond that pays no annual interest but is sold at a discount below par thus compensating investors in the form of capital appreciation. Original Issue Discount OID Bond Any bond originally offered at a price below its par value. Maturity Date A specified date on which the par value of a bond must be repaid. Chapter 7 Bonds and Their Valuation 197

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January 2 2024 thus they had a 15-year maturity at the time they were issued. Most bonds have original maturities the maturity at the time the bond is issued ranging from 10 to 40 years but any maturity is legally permissible. 3 Of course the effective maturity of a bond declines each year after it has been issued. Thus Allied’s bonds had a 15-year original maturity. But in 2010 a year later they will have a 14-year maturity a year after that they will have a 13-year maturity and so forth. 7-2d Call Provisions Most corporate and municipal bonds but not Treasuries contain a call provision that gives the issuer the right to call the bonds forredemption. 4 The call provision generally states that the issuer must pay the bondholders an amount greater than the par value if they are called. The additional sum which is termed a call pre- mium is often equal to one year’s interest. For example the call premium on a 10-year bond with a 10 annual coupon and a par value of 1000 might be 100 which means that the issuer would have to pay investors 1100 the par value plus the call premium if it wanted to call the bonds. In most cases the provisions in the bond contract are set so that the call premium declines over time as the bonds approach maturity. Also while some bonds are immediately callable in most cases bonds are often not callable until several years after issue generally 5 to 10 years. This is known as a deferred call and such bonds are said to have call protection. Companies are not likely to call bonds unless interest rates have declined significantly since the bonds were issued. Suppose a company sold bonds when interest rates were relatively high. Provided the issue is callable the company could sell a new issue of low-yielding securities if and when interest rates drop use the proceeds of the new issue to retire the high-rate issue and thus reduce its interestexpense.Thisprocessiscalledarefundingoperation.Thusthecallprivilege is valuable to the firm but detrimental to long-term investors who will need to reinvest the funds they receive at the new and lower rates. Accordingly the interest rate on a new issue of callable bonds will exceed that on the company’s new noncallable bonds. For example on February 29 2008 Pacific Timber Com- pany sold a bond issue yielding 8 that was callable immediately. On the same dayNorthwestMillingCompanysoldanissuewithsimilarriskandmaturitythat yielded only 7.5 but its bonds were noncallable for 10 years. Investors were willing to accept a 0.5 lower coupon interest rate on Northwest’s bonds for the assurance that the 7.5 interest rate would be earned for at least 10 years. Pacific ontheotherhandhadtoincura0.5higherannual interest ratefortheoptionof calling the bonds in the event of a decline in rates. Notethattherefundingoperationissimilartoahomeownerrefinancinghisor her home mortgage after a decline in rates. Consider for example a homeowner with an outstanding mortgage at 8. If mortgage rates have fallen to 5 the homeowner will probably find it beneficial to refinance the mortgage. There may Original Maturity The number of years to maturity at the time a bond is issued. 3 In July 1993 The Walt Disney Company attempting to lock in a low interest rate stretchedthe meaningof “long- term bond” by issuing the first 100-year bonds sold by any borrower in modern times. Soon after Coca-Cola became the second company to sell 100-year bonds. A number of other companies have followed. 4 The number of new corporate issues with call provisions has declined somewhat in recent years. In the 1980s nearly 80 of new issues contained call provisions but in recent years this number has fallen to about 35. The use of call provisions also varies with credit quality. Roughly 25 of investment-grade bonds in recent years have call provisions versus about 75 of non-investment-grade bonds. Interest rates were historically high in the 1980s so issuers wanted to be able to refund their debt if and when rates fell. Similarly companies with low ratings hoped their ratings would rise lowering their market rates and giving them an opportunity to refund. For more information on the use of callable bonds see Levent Güntay N. R. Prabhala and Haluk Unal “Callable Bonds Interest-Rate Risk and the Supply Side of Hedging” May 2005 a Wharton Financial Institutions Center working paper. Call Provision A provision in a bond contract that gives the issuer the right to redeem the bonds under specified terms prior to the normal maturity date. 198 Part 3 Financial Assets

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be some fees involved in the refinancing but the lower rate may be more than enough to offset those fees. The analysis required is essentially the same for homeowners and corporations. 7-2e Sinking Funds Some bonds include a sinking fund provision that facilitates the orderly retire- ment of the bond issue. Years ago firms were required to deposit money with a trusteewhichinvestedthefundsandthenusedtheaccumulatedsumtoretirethe bonds when they matured. Today though sinking fund provisions require the issuer to buy back a specified percentage of the issue each year. A failure to meet thesinkingfundrequirementconstitutesadefaultwhichmaythrowthecompany into bankruptcy. Therefore a sinking fund is a mandatory payment. Suppose a company issued 100 million of 20-year bonds and it is required to call5oftheissueor5million ofbondseachyear.Inmostcasestheissuercan handle the sinking fund requirement in either of two ways: 1. It can call in for redemption at par value the required 5 million of bonds. The bonds are numbered serially and those called for redemption would be determined by a lottery administered by the trustee. 2. The company can buy the required number of bonds on the open market. The firm will choose the least-cost method. If interest rates have fallen since the bond was issued the bond will sell for more than its par value. In this case the firm will use the call option. However if interest rates have risen the bonds will sellatapricebelowparsothefirmcanandwillbuy5millionparvalueofbonds in the open market for less than 5 million. Note that a call for sinking fund purposes is generally different from a refunding call because most sinking fund calls require no call premium. However only a small percentage of the issue is normally callable in a given year. Althoughsinking fundsaredesigned toprotect investors by ensuring that the bondsareretiredinanorderlyfashionthesefundsworktothedetrimentofbond- holders if the bond’s coupon rate is higher than the current market rate. For example suppose the bond has a 10 coupon but similar bonds now yield only 7.5. A sinking fund call at par would require a long-term investor to give up a bond that pays 100 of interest and then to reinvest in a bond that pays only 75 per year. This is an obvious disadvantage to those bondholders whose bonds are called. On balance however bonds that have a sinking fund are regarded as being safer than those without such a provision so at the time they are issued sinking fund bonds have lower coupon rates than otherwise similar bonds with- out sinking funds. 7-2f Other Features Several other types ofbondsare usedsufficiently often towarrantmention. 5 First convertible bonds are bonds that are exchangeable into shares of common stock at a fixed price at the option of the bondholder. Convertibles offer investors the chance for capital gains if the stock increases but that feature enables the issuing companytosetalowercouponratethanonnonconvertibledebtwithsimilarcredit risk. Bonds issued with warrants are similar to convertibles but instead of giving theinvestoranoptiontoexchangethebondsforstockwarrantsgivetheholderan optiontobuystockforastatedpricetherebyprovidingacapitalgainifthestock’s price rises. Because of this factor bonds issued with warrants like convertibles carry lower coupon rates than otherwise similar nonconvertible bonds. Sinking Fund Provision A provision in a bond contract that requires the issuer to retire a portion of the bond issue each year. 5 A recent article by John D. Finnerty and Douglas R. Emery reviews new types of debt and other securities that have been created in recent years. See “Corporate Securities Innovations: An Update” Journal of Applied Finance: Theory Practice Education Vol. 12 no. 1 Spring/Summer 2002 pp. 21–47. Convertible Bond A bond that is exchange- able at the option of the holder for the issuing firm’s common stock. Warrant A long-term option to buy a stated number of shares of common stock at a specified price. Chapter 7 Bonds and Their Valuation 199

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Whereas callable bonds give the issuer the right to retire the debt prior to maturityputablebondsallowinvestorstorequirethecompanytopayinadvance. Ifinterestratesriseinvestorswillputthebondsbacktothecompanyandreinvest inhighercouponbonds.Yetanothertypeofbondistheincomebondwhichpays interest only if the issuer has earned enough money to pay the interest. Thus incomebondscannotbankruptacompanybutfromaninvestor’sstandpointthey are riskier than “regular” bonds. Yet another bond is the indexed or purchasing powerbond.Theinterestrateisbasedonaninflationindexsuchastheconsumer price index so the interest paid rises automatically when the inflation rate rises thus protecting bondholders against inflation. As we mentioned in Chapter 6 the U.S. Treasury is the main issuer of indexed bonds. Recall that these Treasury InflationProtectedSecuritiesTIPSgenerallypayarealreturnvaryingfrom1to 3 plus the rate of inflation during the past year. SELFTEST Define floating-rate bonds zero coupon bonds callable bonds putable bonds income bonds convertible bonds and inflation-indexed bonds TIPS. Which is riskier to an investor other things held constant—a callable bond or a putable bond In general how is the rate on a floating-rate bond determined What are the two ways sinking funds can be handled Which alternative will be used if interest rates have risen if interest rates have fallen 7-3 BOND VALUATION The value of any financial asset—a stock a bond a lease or even a physical asset suchasanapartmentbuildingorapieceofmachinery—isthepresentvalueofthe cash flows the asset is expected to produce. The cash flows for a standard coupon-bearing bond like those of Allied Foodsconsistofinterestpaymentsduringthebond’s15-yearlifeplustheamount borrowed generally the par value when the bond matures. In the case of a floating-rate bond the interest payments vary over time. For zero coupon bonds there are no interest payments so the only cash flow is the face amount when the bond matures. For a “regular” bond with a fixed coupon like Allied’s here is the situation: 3 2 1 0 Bond’s value r d N INT INT INT M INT Here r d ¼ the market rate of interest on the bond 10. This is the discount rate used to calculate the present value of the cash flows which is also the bond’s price. In Chapter 6 we discussed in detail the various factors that determine market interest rates. Note that r d is not the coupon interest rate. However r d is equal to the coupon rate at times especially the day the bond is issued and when the two rates are equal as in this case the bond sells at par. Putable Bond A bond with a provision that allows its investors to sell it back to the com- pany prior to maturity at a prearranged price. Income Bond A bond that pays interest only if it is earned. Indexed Purchasing Power Bond A bond that has interest payments based on an inflation index so as to protect the holder from inflation. 200 Part 3 Financial Assets

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N ¼ thenumberofyearsbeforethebondmatures¼15.Ndeclinesover time after the bond has been issued so a bond that had a maturity of 15 years when it was issued original maturity ¼ 15 will have N¼14after1yearN¼13after2yearsandsoforth.Atthispoint we assume that the bond pays interest once a year or annually so N is measured in years. Later on we will analyze semiannual payment bonds which pay interest every 6 months. INT ¼ dollarsofinterestpaideachyear¼Couponrate Parvalue¼0.10 1000¼100.IncalculatorterminologyINT¼PMT¼100.Ifthe bond had been a semiannual payment bond the payment would havebeen50every6months.Thepaymentwouldhavebeenzero if Allied had issued zero coupon bonds and it would have varied over time if the bond had been a “floater.” M ¼ theparormaturityvalueofthebond¼1000.Thisamountmust bepaidatmaturity.Backinthe1970sandbeforewhenpaperbonds with paper coupons were used most bonds had a 1000 value. Now with computer-entry bonds the par amount purchased can vary but we use 1000 for simplicity. We can now redraw the time line to show the numerical values for all variables except the bond’s value and price assuming an equilibrium exists V B : 3 2 1 0 Bond’s value 10 15 100 100 100 100 1000 1100 The following general equation can be solved to find the value of any bond: Bond 0 s value ¼ V B ¼ INT ð1þr d Þ 1 þ INT ð1þr d Þ 2 þþ INT ð1þr d Þ N þ M ð1þr d Þ N ¼ X N t¼1 INT ð1þr d Þ t þ M ð1þr d Þ N 7-1 Inserting values for the Allied bond we have V B ¼ X 15 t¼1 100 ð1:10Þ t þ 1000 ð1:10Þ 15 The cash flows consist of an annuity of N years plus a lump sum payment at the end of Year N and this fact is reflected in Equation 7-1. We could simply discount each cash flow back to the present and sum those PVs to find the bond’s value see Figure 7-1 for an example. However this proce- dure is not very efficient especially when the bond has many years to maturity. Therefore we use a financial calculator to solve the problem. Here is the setup: FV PV I/YR N PMT 1000 100 10 15 –1000 Output: Inputs: SimplyinputN¼15r d ¼I/YR¼10INT¼PMT¼100andM¼FV¼1000then pressthePVkeytofindthebond’svalue1000. 6 SincethePVisanoutflowtothe 6 Spreadsheets can also be used to solve for the bond’s value as we show in the Excel model for this chapter. Chapter 7 Bonds and Their Valuation 201

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investor it is shown with a negative sign. The calculator is programmed to solve Equation7-1:ItfindsthePVofanannuityof100peryearfor15yearsdiscounted at10thenitfindsthePVofthe1000maturitypaymentthenitaddsthosetwo PVs to find the bond’s value. In this example the bond is selling at a price equal to its par value. Whenever the bond’s market or going rate r d is equal to its coupon rate a fixed-rate bond will sell at its par value. Normally the coupon rate is set at the going rate in the market the day a bond is issued causing it to sell at par initially. The coupon rate remains fixed after the bond is issued but interest rates in the market move up and down. Looking at Equation 7-1 we see that an increase in the market interest rate r d causes the price of an outstanding bond to fall whereas a decreaseintheratecausesthebond’s price to rise. For example if the market interest rate on Allied’s bond increased to 15 immediately after it was issuedwewouldrecalculatethepricewiththenewmarketinterestrateas follows: FV PV I/YR N PMT 1000 100 15 15 –707.63 Output: Inputs: Thebond’spricewouldfallto707.63wellbelowparasaresultoftheincreasein interest rates. Whenever the going rate of interest rises above the coupon rate a fixed-rate bond’s price will fall below its par value this type of bond is called a discount bond. Time Line for Allied Food Products’ Bonds 10 Interest Rate FIGURE 7-1 100 Payments Present Value 100 1000 1000.00 when r d 10 100 100 100 100 100 100 100 100 100 100 100 100 100 1/3/10 1/2/2024 1/11 1/12 1/13 1/14 1/15 1/16 1/17 1/18 1/19 1/20 1/21 1/22 1/23 90.91 82.64 75.13 68.30 62.09 56.45 51.32 46.65 42.41 38.55 35.05 31.86 28.97 26.33 23.94 239.39 Discount Bond A bond that sells below its par value occurs whenever the going rate of interest is above the coupon rate. 202 Part 3 Financial Assets

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On the other hand bond prices rise when market interest rates fall. For exampleifthe marketinterestrate onAllied’sbonddecreasedto5 immediately after it was issued we would once again recalculate its price as follows: FV PV I/YR N PMT 1000 100 5 15 –1518.98 Output: Inputs: Inthiscasethepricerisesto1518.98.Ingeneralwheneverthegoinginterestrate falls below the coupon rate a fixed-rate bond’s price will rise above its par value this type of bond is called a premium bond. To summarize here is the situation: r d ¼ coupon rate fixed-rate bond sells at par hence it is a par bond r d coupon rate fixed-rate bond sells below par hence it is a dis- count bond r d coupon rate fixed-rate bond sells above par hence it is a pre- mium bond SELFTEST A bond that matures in 8 years has a par value of 1000 and an annual coupon payment of 70 its market interest rate is 9. What is its price 889.30 Abondthatmaturesin12yearshasaparvalueof1000andanannualcoupon of 10 the market interest rate is 8. What is its price1150.72 Which of those two bonds is a discount bond and which is a premium bond 7-4 BOND YIELDS IfyouexaminethebondmarkettableofTheWallStreetJournalorapricesheetput out by a bond dealer you will typically see information regarding each bond’s maturity date price and coupon interest rate. You will also see a reported yield. Unlikethecouponinterestratewhichisfixedthebond’syieldvariesfromdayto day depending on current market conditions. To be most useful the bond’s yield should give us an estimate of the rate of return we would earn if we bought the bond today and held it over its remaining life. If the bond is not callable its remaining life is its years to maturity. If it is callable its remaining life is the years to maturity if it is not called or the years to the call if it is called. In the following sections we explain how to calculate those two possible yields and which one is likely to occur. 7-4a Yield to Maturity Suppose you were offered a 14-year 10 annual coupon 1000 par value bond at a price of 1494.93. What rate of interest would you earn on your investment if you bought the bond held it to maturity and received the promised interest and maturity payments This rate is called the bond’s yield to maturity YTM and it is the interest rate generally discussed by investors when they talk about rates of return and the rate reported by The Wall Street Journal and other Premium Bond A bond that sells above its par value occurs whenever the going rate of interest is below the coupon rate. Yield to Maturity YTM The rate of return earned on a bond if it is held to maturity. Chapter 7 Bonds and Their Valuation 203

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publications. To find the YTM all you need to do is solve Equation 7-1 for r d as follows: V B ¼ INT ð1 þ r d Þ 1 þ INT ð1 þ r d Þ 2 þ þ INT ð1 þ r d Þ N þ M ð1 þ r d Þ N 1494:93 ¼ 100 ð1 þ r d Þ 1 þ þ 100 ð1 þ r d Þ 14 þ 1000 ð1 þ r d Þ 14 You can substitute values for r d until you find a value that “works” and force the sum of the PVs in the equation to equal 1494.93. However finding r d ¼ YTM by trial and error would be a tedious time-consuming process. However as you might guess the calculation is easy with a financial calculator. 7 Here is the setup: FV PV I/YR N PMT 1000 100 –1494.93 14 5 Output: Inputs: Simply enter N ¼ 14 PV ¼ –1494.93 PMT ¼ 100 and FV ¼ 1000 then press the I/YR key. The answer 5 will appear. The yield to maturity can also be viewed as the bond’s promised rate of return which is the return that investors will receive if all of the promised payments are made. However the yield to maturity equals the expected rate of return only when 1 the probability of default is zero and 2 the bond cannot be called. If there is some default risk or the bond may be called there is some chance that the promised payments to maturity will not be received in which case the calculated yield to maturity will exceed the expected return. Notealsothatabond’scalculatedyieldtomaturitychangeswheneverinterest rates in the economy change which is almost daily. An investor who purchases a bond and holds it until it matures will receive the YTM that existed on the pur- chase date but the bond’s calculated YTM will change frequently between the purchase date and the maturity date. 7-4b Yield to Call If you purchase a bond that is callable and the company calls it you do not have the option of holding it to maturity. Therefore the yield to maturity would not be earned. For example if Allied’s 10 coupon bonds were callable and if interest rates fell from 10 to 5 the company could call in the 10 bonds replace them with 5 bonds and save 100 – 50¼ 50 interest per bond per year. This would be beneficial to the company but not to its bondholders. If current interest rates are well below an outstanding bond’s coupon rate a callable bond is likely to be called and investors will estimate its most likely rate of return as the yield to call YTC rather than the yield to maturity. To calculate theYTCwemodifyEquation7-1usingyearstocallasNandthecallpricerather than the maturity value as the ending payment. Here’s the modified equation: Price of bond ¼ X N t¼1 INT ð1 þ r d Þ t þ Call price ð1 þ r d Þ N 7-2 HereNisthenumberofyearsuntilthecompanycancallthebondcallpriceisthe price the company must pay in order to call the bond it is often set equal to the par value plus one year’s interest and r d is the YTC. 7 You can also find the YTM with a spreadsheet. In Excel you use the Rate function inputting N per ¼ 14 Pmt¼ 100 Pv ¼ –1494.93 Fv ¼ 1000 and 0 for Type and leaving Guess blank. Yield to Call YTC The rate of return earned onabondwhenitiscalled before its maturity date. 204 Part 3 Financial Assets

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To illustrate suppose Allied’s bonds had a provision that permitted the com- pany if it desired to call them 10 years after their issue date at a price of 1100. Suppose further that interest rates had fallen and that 1 year after issuance the goinginterestratehaddeclinedcausingtheirpricetoriseto1494.93.Hereisthe time line and the setup for finding the bonds’ YTC with a financial calculator: 8 2 1 0 1494.93 YTC 9 100 100 100 100 1100 FV PV I/YR N PMT 1100 100 –1494.93 9 4.21 YTC Output: Inputs: TheYTCis4.21—thisisthereturnyouwouldearnifyouboughtanAlliedbond at a price of 1494.93 and it was called 9 years from today. It could not be called until 10 years after issuance. One year has gone by so there are 9 years left until the first call date. Do you think Allied will call its 10 bonds when they become callable Allied’s action will depend on what the going interest rate is when they become callable.Ifthegoingrateremainsatr d ¼5Alliedcouldsave10 –5¼5or 50 per bond per year so it would call the 10 bonds and replace them with a new 5 issue. There would be some cost to the company to refund the bonds but because the interest savings would most likely be worth the cost Allied would probably refund them. Therefore you should expect to earn the YTC ¼ 4.21 rather than the YTM ¼ 5 if you bought the bond under the indicated conditions. In the balance of this chapter we assume that bonds are not callable unless otherwisenoted.Howeversomeoftheend-of-chapterproblemsdealwithyieldto call. 8 SELFTEST Explain the difference between yield to maturity and yield to call. Halley Enterprises’ bonds currently sell for 975. They have a 7-year matu- rity an annual coupon of 90 and a par value of 1000. What is their yield to maturity 9.51 The Henderson Company’s bonds currently sell for 1275. They pay a 120 annual coupon and have a 20-year maturity but they can be called in 5 years at 1120. What are their YTM and their YTC and which is “more relevant” in the sense that investors should expect to earn it 8.99 7.31 YTC 8 Brokerage houses occasionally report a bond’s current yield defined as the annual interest payment divided by the current price. For example if Allied’s 10 coupon bonds were selling for 985 the current yield would be 100/985 ¼ 10.15. Unlike the YTM or YTC the current yield does not represent the actual return that investors should expect because it does not account for the capital gain or loss that will be realized if the bond is held until it matures or is called. The current yield was popular before calculators and computers came along because it was easy to calculate. However it can be misleading and now it’s easy enough to calculate the YTM and YTC. Chapter 7 Bonds and Their Valuation 205

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7-5 CHANGES IN BOND VALUES OVER TIME When a coupon bond is issued the coupon is generally set at a level that causes the bond’s market price to equal its par value. If a lower coupon were set investors would not be willing to pay 1000 for the bond but if a higher coupon weresetinvestorswouldclamorforitandbiditspriceupover1000.Investment bankers can judge quite precisely the coupon rate that will cause a bond to sell at its 1000 par value. A bond that has just been issued is known as a new issue. Once it has been issued it is an outstanding bond also called a seasoned issue. Newly issued bonds generally sell at prices very close to par but the prices of outstanding bonds can vary widely from par. Except for floating-rate bonds coupon payments are con- stant so when economic conditions change a bond with a 100 coupon that sold at its 1000 par value when it was issued will sell for more or less than 1000 thereafter. Among its outstanding bonds Allied currently has three equally risky issues that will mature in 15 years: l Allied’s just-issued 15-year bonds have a 10 annual coupon. They were issued at par which means that the market interest rate on their issue date was also 10. Because the coupon rate equals the market interest rate these bonds are trading at par or 1000. l Five years ago Allied issued 20-year bonds with a 7 annual coupon. These bonds currently have 15 years remaining until maturity. They were originally issued at par which means that 5 years ago the market interest rate was 7. Currentlythisbond’scouponrateislessthanthe10marketratesotheysell at a discount. Using a financial calculator or spreadsheet we can quickly find thattheyhaveapriceof771.82.SetN¼15I/YR10PMT¼70andFV¼ 1000 and solve for the PV to get the price. l Ten years ago Allied issued 25-year bonds with a 13 coupon rate. These bonds currently have 15 years remaining until maturity. They were originally issued at par which means that 10 years ago the market interest rate must have been 13. Because their coupon rate is greater than the current market rate they sell at a premium. Using a financial calculator or spreadsheet we can find that their price is 1228.18. Set N¼ 15 I/YR¼ 10 PMT¼ 130 and FV ¼ 1000 and solve for the PV to get the price. Each of these three bonds has a 15-year maturity each has the same credit risk and thus each has the same market interest rate 10. However the bonds have different prices because of their different coupon rates. Nowlet’sconsiderwhatwouldhappentothepricesofthesethreebondsover the 15 years until they mature assuming that market interest rates remain con- stant at 10 and Allied does not default on its payments. Table 7-1 demonstrates howthepricesofeachofthesebondswillchangeovertimeifmarketinterestrates remain at 10. One year from now each bond will have a maturity of 14 years— thatisN¼14.WithafinancialcalculatoroverrideN¼15withN¼14andpress the PV key that gives you the value of each bond 1 year from now. Continuing set N ¼ 13 N ¼ 12 and so forth to see how the prices change over time. Table7-1alsoshowsthecurrentyieldwhichisthecouponinterestdividedby the bond’s price the capital gains yield and the total return over time. For any givenyearthe capital gains yieldiscalculatedasthe bond’sannualchange inprice divided by the beginning-of-year price. For example if a bond was selling for 1000 at the beginning of the year and 1035 at the end of the year its capital gains yield for the year would be 35/1000¼ 3.5. If the bond was selling at a premiumitsprice woulddeclineovertime.Thenthe capitalgainsyieldwould be negative but it would be offset by a high current yield. A bond’s total return is 206 Part 3 Financial Assets

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Calculation of Current Yields Capital Gains Yields and Total Returns for 7 10 and 13 Coupon Bonds When the Market Rate Remains Constant at 10 Table 7-1 7 COUPON BOND 10 COUPON BOND 13 COUPON BOND Number of Years Until Maturity Price a Expected Current Yield b Expected Capital Gains Yield c Expected Total Return d Price a Expected Current Yield b Expected Capital Gains Yield c Expected Total Return d Price a Expected Current Yield b Expected Capital Gains Yield c Expected Total Return d 15 771.82 9.1 0.9 10.0 1000.00 10.0 0.0 10.0 1228.18 10.6 0.6 10.0 14 779.00 9.0 1.0 10.0 1000.00 10.0 0.0 10.0 1221.00 10.6 0.6 10.0 13 786.90 8.9 1.1 10.0 1000.00 10.0 0.0 10.0 1213.10 10.7 0.7 10.0 12 795.59 8.8 1.2 10.0 1000.00 10.0 0.0 10.0 1204.41 10.8 0.8 10.0 11 805.15 8.7 1.3 10.0 1000.00 10.0 0.0 10.0 1194.85 10.9 0.9 10.0 10 815.66 8.6 1.4 10.0 1000.00 10.0 0.0 10.0 1184.34 11.0 1.0 10.0 9 827.23 8.5 1.5 10.0 1000.00 10.0 0.0 10.0 1172.77 11.1 1.1 10.0 8 839.95 8.3 1.7 10.0 1000.00 10.0 0.0 10.0 1160.05 11.2 1.2 10.0 7 853.95 8.2 1.8 10.0 1000.00 10.0 0.0 10.0 1146.05 11.3 1.3 10.0 6 869.34 8.1 1.9 10.0 1000.00 10.0 0.0 10.0 1130.66 11.5 1.5 10.0 5 886.28 7.9 2.1 10.0 1000.00 10.0 0.0 10.0 1113.72 11.7 1.7 10.0 4 904.90 7.7 2.3 10.0 1000.00 10.0 0.0 10.0 1095.10 11.9 1.9 10.0 3 925.39 7.6 2.4 10.0 1000.00 10.0 0.0 10.0 1074.61 12.1 2.1 10.0 2 947.93 7.4 2.6 10.0 1000.00 10.0 0.0 10.0 1052.07 12.4 2.4 10.0 1 972.73 7.2 2.8 10.0 1000.00 10.0 0.0 10.0 1027.27 12.7 2.7 10.0 0 1000.00 1000.00 1000.00 Notes: a Using a financial calculator the price of each bond is calculated by entering the data for N I/YR PMT and FV then solving for PV ¼ the bond’s value. b The expected current yield is calculated as the annual interest divided by the price of the bond. c The expected capital gains yield is calculated as the differece between the end-of-year bond price and the beginning-of-year bond price divided by the beginning-of-year price. d The expected total return is the sum of the expected current yield and the expected capital gains yield. Chapter 7 Bonds and Their Valuation 207

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equaltothecurrentyieldplusthecapitalgainsyield.Intheabsenceofdefaultrisk and assuming market equilibrium the total return is also equal to YTM and the market interest rate which in our example is 10. Figure 7-2 plots the three bonds’ predicted prices as calculated in Table 7-1. Notice that the bonds have very different price paths over time but that at maturityallthreewillsellattheirparvalueof1000.Herearesomepointsabout the prices of the bonds over time: l The price of the 10 coupon bond trading at par will remain at 1000 if the market interest rate remains at 10. Therefore its current yield will remain at 10 and its capital gains yield will be zero each year. l The 7 bond trades at a discount but at maturity it must sell at par because that is the amount the company will give to its holders. Therefore its price must rise over time. l The 13 coupon bond trades at a premium. However its price must be equal to its par value at maturity so the price must decline over time. While the prices of the 7 and 13 coupon bonds move in opposite directions over time each bond provides investors with the same total return 10 which is also the total return on the 10 coupon bond that sells at par. The discount bond hasalowcouponrateand therefore alow current yieldbutitprovidesacapital gain each year. In contrast the premium bond has a high current yield but it has an expected capital loss each year. 9 Time Paths of 7 10 and 13 Coupon Bonds When the Market Rate Remains Constant at 10 FIGURE 7-2 15 12 9 6 3 0 0 1000 1250 1500 500 750 Coupon 10 Coupon 7 Coupon 13 Bond Value Years Remaining until Maturity 9 In this example and throughout the text we ignore the tax effects associated with purchasing different types of bonds. For coupon bonds under the current Tax Code coupon payments are taxed as ordinary income whereas capital gains are taxed at the capital gains tax rate. As we mentioned in Chapter 3 for most investors the capital gains tax rate is lower than the personal tax rate. Moreover while coupon payments are taxed each year capital gains taxes are deferred until the bond is sold or matures. Consequently all else equal investors end up paying lower taxes on discount bonds because a greater percentage of their total return comes in the form of capital gains. For details on the tax treatment of zero coupon bonds see Web Appendix 7A. 208 Part 3 Financial Assets

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SELFTEST What is meant by the terms new issue and seasoned issue Lastyearafirmissued20-year8annualcouponbondsataparvalueof1000. 1 Supposethatoneyearlaterthegoingratedropsto6.Whatisthenewprice ofthebondsassumingtheynowhave19yearstomaturity1223.16 2 Suppose that one year after issue the going interest rate is 10 rather than 6. What would the price have been 832.70 Why do the prices of fixed-rate bonds fall if expectations for inflation rise 7-6 BONDS WITH SEMIANNUAL COUPONS Although some bonds pay interest annually the vast majority actually make payments semiannually. To evaluate semiannual bonds we must modify the valuation model Equation 7-1 as follows: 1. Divide the annual coupon interest payment by 2 to determine the dollars of interest paid each six months. 2. Multiply the years to maturity N by 2 to determine the number of semi- annual periods. 3. Divide the nominal quoted interest rate r d by 2 to determine the periodic semiannual interest rate. Onatimelinetherewouldbetwiceasmanypaymentsbuteachwouldbehalfas large as with an annual payment bond. Making the indicated changes results in the following equation for finding a semiannual bond’s value: V B ¼ X 2N t¼1 INT2 ð1 þ r d 2Þ t þ M ð1 þ r d 2Þ 2N 7-1a To illustrate assume that Allied Food’s 15-year bonds as discussed in Section 7-3 pay 50 of interest each 6 months rather than 100 at the end of each year. Thus eachinterestpaymentisonlyhalfaslargebuttherearetwiceasmanyofthem.We would describe the coupon rate as “10 with semiannual payments.” 10 When the going nominal rate isr d ¼ 5 with semiannual compounding the value of a 15-year 10 semiannual coupon bond that pays 50 interest every 6 months is found as follows: FV PV I/YR N PMT 1000 50 2.5 –1523.26 30 Output: Inputs: EnterN¼30r d ¼I/YR¼2.5PMT¼50andFV¼1000thenpressthePVkeyto obtainthebond’svalue1523.26.Thevaluewithsemiannualinterestpaymentsis slightly larger than 1518.98 the value when interest is paid annually as we 10 In this situation the coupon rate of “10 paid semiannually” is the rate that bond dealers corporate treasurers and investors generally discuss. Of course if this bond were issued at par its effective annual rate would be higher than 10. EAR ¼ EFF ¼ 1 þ r NOM M M 1 ¼ 1 þ 0:10 2 2 1¼ð1:05Þ 2 1 ¼ 10:25 Since 10 with annual payments is quite different from 10 with semiannual payments we have assumed a change in effective rates in this section from the situation in Section 7-3 where we assumed 10 with annual payments. Chapter 7 Bonds and Their Valuation 209

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calculatedinSection7-3.Thishighervalueoccursbecauseeachinterestpaymentis received somewhat faster under semiannual compounding. Alternatively when we know the price of a semiannual bond we can easily back out the bond’s nominal yield to maturity. In the previous example if you were told that a 15-year bond with a 10 semiannual coupon was selling for 1523.26 you could solve for the bond’s periodic interest rate as follows: FV PV I/YR N PMT 1000 50 2.5 –1523.26 30 Output: Inputs: In this case enter N¼ 30 PV¼ 1523.26 PMT¼ 50 and FV¼ 1000 then press the I/YR key to obtain the interest rate per semiannual period 2.5. Multiplying by 2 we calculate the bond’s nominal yield to maturity to be 5. 11 SELFTEST Describe how the annual payment bond valuation formula is changed to evaluate semiannual coupon bonds and write the revised formula. Hartwell Corporation’s bonds have a 20-year maturity an 8 semiannual coupon and a face value of 1000. The going interest rate r d is 7 based on semiannual compounding. What is the bond’s price 1106.78 7-7 ASSESSING A BOND’S RISKINESS In this section we identify and explain the two key factors that impact a bond’s riskiness. Once those factors are identified we differentiate between them and discuss how you can minimize these risks. 7-7a Interest Rate Risk AswesawinChapter6interestratesfluctuateovertimeandwhentheyrisethe value of outstanding bonds decline. This risk of a decline in bond values due to anincreaseininterestratesiscalledinterestrateriskorinterestratepricerisk. To illustrate refer back to Allied’s bonds assume once more that they have a 10 annual coupon and assume that you bought one of these bonds at its par value1000. Shortly afteryourpurchase the going interestrate rises from 10to 15. 12 As we saw in Section 7-3 this interest rate increase would cause the bond’spricetofallfrom1000to707.63soyouwouldhavealossof292.37on the bond. 13 Since interest rates can and do rise rising rates cause losses to bondholders people or firms who invest in bonds are exposed to risk from increasing interest rates. 11 We can use a similar process to calculate the nominal yield to call for a semiannual bond. The only difference would be that N should represent the number of semiannual periods until the bond is callable and FV should be the bond’s call price rather than its par value. 12 An immediate increase in rates from 10 to 15 would be quite unusual and it would occur only if something quite bad were revealed about the company or happened in the economy. Smaller but still significant rate increases that adversely affect bondholders do occur fairly often. 13 You would have an accounting and tax loss only if you sold the bond if you held it to maturity you would not have such a loss. However even if you did not sell you would still have suffered a real economic loss in an opportunity cost sense because you would have lost the opportunity to invest at 15 and would be stuck with a 10 bond in a 15 market. In an economic sense “paper losses” are just as bad as realized accounting losses. Interest Rate Price Risk The risk of a decline in a bond’s price due to an increase in interest rates. 210 Part 3 Financial Assets

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Interest rate risk is higher on bonds that have long maturities than on bonds thatwillmature inthenearfuture. 14 Thisfollowsbecausethe longerthe maturity the longer before the bond will be paid off and the bondholder can replace it with another bond with a higher coupon. This point can be demonstrated by showing howthevalueofa1-yearbondwitha10annualcouponfluctuateswithchanges in r d and then comparing those changes with changes on a 15-year bond. The 1-year bond’s values at different interest rates are shown here: Value of a 1-year bond at FV PV I/YR N PMT 1000 100 5 –1047.62 1 Output Bond Value: Inputs: r d 5: FV PV I/YR N PMT 1000 100 10 –1000.00 1 Output Bond Value: Inputs: r d 10: FV PV I/YR N PMT 1000 100 15 –956.52 1 Output Bond Value: Inputs: r d 15: You would obtain the first value with a financial calculator by entering N ¼ 1 I/YR¼ 5PMT¼ 100andFV¼ 1000and thenpressingPV toget1047.62. With everything still in your calculator enter I/YR ¼ 10 to override the old I/YR ¼ 5 and press PV to find the bond’s value at a 10 rate it drops to 1000. Then enter I/YR ¼ 15 and press the PV key to find the last bond value 956.52. The effects of increasing rates on the 15-year bond as found earlier can be compared with the just-calculated effects for the 1-year bond. This comparison is shown in Figure 7-3 where we show bond prices at several rates and then plot those prices on the graph. Compared to the 1-year bond the 15-year bond is far more sensitive to changes in rates. At a 10 interest rate both the 15-year and 1-yearbondsarevaluedat1000.Whenratesriseto15the15-yearbondfallsto 707.63 but the 1-year bond falls only to 956.52. The price decline for the 1-year bond is only 4.35 while that for the 15-year bond is 29.24. Forbondswithsimilarcouponsthisdifferentialinterestratesensitivityalwaysholds true—the longer its maturity the more its price changes in response to a givenchange in interestrates.Thuseveniftheriskofdefaultontwobondsisexactlythesamethe 14 Actually a bond’s maturity and coupon rate both affect interest rate risk. Low coupons mean that most of the bond’s return will come from repayment of principal whereas on a high-coupon bond with the same maturity more of the cash flows will come in during the early years due to the relatively large coupon payments. A measurement called duration which finds the average number of years the bond’s PV of cash flows remain outstanding has been developed to combine maturity and coupons. A zero coupon bond which has no interest payments and whose payments all come at maturity has a duration equal to its maturity. All coupon bonds have durations that are shorter than their maturity and the higher the coupon rate the shorter the duration. Bonds with longer duration are exposed to more interest rate risk. A discussion of duration would go beyond the scope of this book but see any investments text for a discussion of the concept. Chapter 7 Bonds and Their Valuation 211

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one with the longer maturity is typically exposed to more risk from a rise in interest rates. 15 The logical explanation for this difference in interest rate risk is simple. Sup- pose you bought a 15-year bond that yielded 10 or 100 a year. Now suppose interestratesoncomparable-riskbondsroseto15.Youwouldbestuckwithonly 100 of interest for the next 15 years. On the other hand had you bought a 1-year bondyouwouldhavehadalowreturnforonly1year.Attheendoftheyearyou would have received your 1000 back then you could have reinvested it and earned 15 or 150 per year for the next 14 years. Values of Long- and Short-Term 10 Annual Coupon Bonds at Different Market Interest Rates FIGURE 7-3 500 1000 1500 2000 2500 510 15 20 25 0 Bond Value 15-Year Bond 1-Year Bond Interest Rate Current Market Interest Rate r d VALUE OF 1-Year Bond 15-Year Bond 5 1047.62 1518.98 10 1000.00 1000.00 15 956.52 707.63 20 916.67 532.45 25 880.00 421.11 Note: Bond values were calculated using a financial calculator assuming annual or once-a-year compounding. 15 If a 10-year bond were plotted on the graph in Figure 7-3 its curve would lie between those of the 15-year and the 1-year bonds. The curve of a 1-month bond would be almost horizontal indicating that its price would change very little in response to an interest rate change but a 100-year bond would have a very steep slope and the slope of a perpetuity would be even steeper. Also a zero coupon bond’s price is quite sensitive to interest rate changes and the longer its maturity the greater its price sensitivity. Therefore a 30-year zero coupon bond would have a huge amount of interest rate risk. 212 Part 3 Financial Assets

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7-7b Reinvestment Rate Risk As we saw in the preceding section an increasein interest rateshurtsbondholders because it leads to a decline in the current value of a bond portfolio. But can a decreaseininterestratesalsohurtbondholdersActuallytheanswerisyesbecause if interest rates fall long-term investors will suffer a reduction in income. For example consider a retiree who has a bond portfolio and lives off the income it produces. The bonds in the portfolio on average have coupon rates of 10. Now suppose interest rates decline to 5. Many of the bonds will mature or be called as this occurs the bondholder will have to replace 10 bonds with 5 bonds. Thus the retiree will suffer a reduction of income. The risk of an income decline due to a drop in interest rates is called reinvestment rate risk and its importance has been demonstrated to all bond- holders in recent years as a result of the sharp drop in rates since the mid-1980s. Reinvestmentrateriskisobviouslyhighoncallablebonds.Itisalsohighonshort- termbondsbecausetheshorterthebond’smaturitythefewertheyearsbeforethe relatively high old-coupon bonds will be replaced with the new low-coupon issues. Thus retirees whose primary holdings are short-term bonds or other debt securities will be hurt badly by a decline in rates but holders of noncallable long- term bonds will continue to enjoy the old high rates. 7-7c Comparing Interest Rate and Reinvestment Rate Risk Note that interest rate risk relates to the current market value of the bond portfolio while reinvestment rate risk relates to the income the portfolio produces. If you hold long-term bonds you will face significant interest rate price risk because the valueofyourportfoliowilldeclineifinterestratesrisebutyouwillnotfacemuch reinvestment rate risk because your income will be stable. On the other hand if you hold short-term bonds you will not be exposed to much interest rate price risk but you will be exposed to significant reinvestment rate risk. Whichtypeofriskis “morerelevant”toagiveninvestordependscriticallyon how long the investor plans to hold the bonds—this is often referred to as his or her investment horizon. To illustrate consider an investor who has a relatively short 1-year investment horizon—say the investor plans to go to graduate school a year from now and needs money for tuition and expenses. Reinvestment rate risk is of minimal concern to this investor because there is little time for rein- vestment. The investor could eliminate interest rate risk by buying a 1-year Treasury security since he would be assured of receiving the face value of the bond 1 year from now the investment horizon. However if this investor were to buy a long-term Treasury security he would bear a considerable amount of interest rate risk because as we have seen long-term bond prices decline when interest rates rise. Consequently investors with shorter investment horizons should view long-term bonds as being more risky than short-term bonds. By contrast the reinvestment risk inherent in short-term bonds is especially relevant to investors with longer investment horizons. Consider a retiree who is living on income from her portfolio. If this investor buys 1-year bonds she will have to “roll them over” every year and if rates fall her income in sub- sequent years will likewise decline. A younger couple saving for their retire- ment or their children’s college costs for example would be affected similarly because if they buy short-term bonds they too will have to roll over their portfolio at possibly much lower rates. Since there is uncertainty today about the rates that will be earned on these reinvested cash flows long-term investors should be especially concerned about the reinvestment rate risk inherent in short-term bonds. Reinvestment Rate Risk The risk that a decline in interest rates will lead to a decline in income from a bond portfolio. Investment Horizon The period of time an investor plans to hold a particular investment. Chapter 7 Bonds and Their Valuation 213

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One way to manage both interest rate and reinvestment rate risk is to buy a zero coupon Treasury bond with a maturity that matches the investor’s invest- ment horizon. For example assume your investment horizon is 10 years. If you buya10-yearzeroyouwillreceiveaguaranteedpaymentin10yearsequaltothe bond’s face value. 16 Moreover as there are no coupons to reinvest there is no reinvestmentraterisk.Thisexplainswhyinvestors withspecificgoalsofteninvest in zero coupon bonds. 17 Recall from Chapter 6 that maturity risk premiums are generally positive. Moreover a positive maturity risk premium implies that investors on average regard longer-term bonds as being riskier than shorter-term bonds. That in turn suggests that the average investor is most concerned with interest rate price risk. Still it is appropriate for each investor to consider his or her own situation to recognize the risks inherent in bonds with different maturities and to construct a portfolio that deals best with the investor’s most relevant risk. SELFTEST Differentiate between interest rate risk and reinvestment rate risk. To which type of risk are holders of long-term bonds more exposed short- term bondholders What type of security can be used to minimize both interest rate and reinvestment rate risk for an investor with a fixed investment horizon 7-8 DEFAULT RISK Potential default is another important risk that bondholders face. If the issuer defaults investors will receive less than the promised return. Recall from Chapter 6 that the quoted interest rate includes a default risk premium—the higher the probability of default the higher the premium and thus the yield to maturity. Default risk on Treasuries is zero but this risk is substantial for lower-grade corporate and municipal bonds. To illustrate suppose two bonds have the same promised cash flows—their coupon rates maturities liquidity and inflation exposures are identical but one has more defaultrisk than the other. Investors will naturally pay moreforthe one withlesschanceofdefault.Asaresultbondswithhigherdefaultriskhavehigher marketrates:r d ¼rþIPþDRPþLPþMRP.Ifabond’sdefaultriskchangesr d and thus the price will be affected. Thus if the default risk on Allied’s bonds increases their price will fall and the yield to maturity YTM ¼ r d will increase. 16 Note that in this example the 10-year zero technically has a considerable amount of interest rate risk since its current price is highly sensitive to changes in interest rates. However the year-to year movements in price should not be of great concern to an investor with a 10-year horizon. The reason is that the investor knows that regardless of what happens to interest rates the bond’s price will still be 1000 when it matures. 17 Two words of caution about zeros are in order. First as we show in Web Appendix 7A investors in zeros must pay taxes each year on their accrued gain in value even though the bonds don’t pay any cash until they mature. Second buying a zero coupon with a maturity equal to your investment horizon enables you to lock in a nominal cash payoff but the real value of that payment still depends on what happens to inflation during your investment horizon. What we need is an inflation-indexed zero coupon Treasury bond but to date no such bond exists. Also the fact that maturity risk premiums are positive suggests that most investors have relatively short investment horizons or at least worry about short-term changes in their net worth. See Stocks Bonds Bills and Inflation: Valuation Edition 2008 Yearbook Chicago: Morningstar Inc. 2008 which finds that the maturity risk premium for long-term bonds has averaged 1.4 over the past 82 years. 214 Part 3 Financial Assets

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7-8a Various Types of Corporate Bonds Defaultriskisinfluencedbythefinancialstrengthoftheissuerandthetermsofthe bond contract including whether collateral has been pledged to secure the bond. The characteristics of some key types of bonds are described in this section. Mortgage Bonds Underamortgagebondthecorporation pledgesspecificassetsassecurityforthe bond. To illustrate in 2008 Billingham Corporation needed 10 million to build a regional distribution center. Bonds in the amount of 4 million secured by a first mortgage on the property were issued. The remaining 6 million was financed with equity capital. If Billingham defaults on the bonds the bondholders can foreclose on the property and sell it to satisfy their claims. If Billingham had chosen to it could have issued second mortgage bonds securedbythesame10millionofassets.Intheeventofliquidationtheholdersof the second mortgage bonds would have a claim against the property but only after the first mortgage bondholders had been paid off in full. Thus second mortgagesaresometimescalledjuniormortgagesbecausetheyarejuniorinpriority to the claims of senior mortgages or first mortgage bonds. All mortgage bonds are subject to an indenture which is a legal document that spells out in detail the rights of the bondholders and the corporation. The indenturesofmanymajorcorporations werewritten203040ormoreyearsago. These indentures are generally “open-ended” meaning that new bonds can be issued from time to time under the same indenture. However the amount of new bonds that can be issued is usually limited to a specified percentage of the firm’s total “bondable property” which generally includes all land plant and equip- ment. And of course the coupon interest rate on the newly issued bonds changes over time along with the market rate on the older bonds. Debentures A debenture is an unsecured bond and as such it provides no specific collateral as security for the obligation. Therefore debenture holders are general creditors whoseclaimsareprotectedbypropertynototherwisepledged.Inpracticetheuse of debentures depends on the nature of the firm’s assets and on its general credit strength. Extremely strong companies such as General Electric and ExxonMobil can use debentures because they do not need to put up property as security for their debt. Debentures are also issued by weak companies that have already pledged most of their assets as collateral for mortgage loans. In this case the debentures are quite risky and that risk will be reflected in their interest rates. Subordinated Debentures The term subordinate means “below” or “inferior to” and in the event of bank- ruptcy subordinated debt has a claim on assets only after senior debt has been paid in full. Subordinated debentures may be subordinated to designated notes payable usually bank loans or to all other debt. In the event of liquidation or reorganizationholdersofsubordinateddebenturesreceivenothinguntilallsenior debt as named in the debentures’ indenture has been paid. Precisely how sub- ordination works and how it strengthens the position of senior debtholders are explained in detail in Web Appendix 7B. 7-8b Bond Ratings Since the early 1900s bonds have been assigned quality ratings that reflect their probability of going into default. The three major rating agencies are Moody’s Investors Service Moody’s Standard Poor’s Corporation SP and Fitch Mortgage Bond A bond backed by fixed assets. First mortgage bonds are senior in priority to claims of second mortgage bonds. Indenture A formal agreement between the issuer and the bondholders. Debenture A long-term bond that is not secured by a mort- gage on specific property. Subordinated Debenture A bond having a claim on assets only after the senior debt has been paid off in the event of liquidation. Chapter 7 Bonds and Their Valuation 215

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Investor’sService.Moody’sandSP’sratingdesignationsareshowninTable7-2. 18 The triple- and double-A bondsare extremely safe. Single-A and triple-B bondsare also strong enough to be called investment-grade bonds and they are the lowest- ratedbondsthatmanybanksandotherinstitutionalinvestorsarepermittedbylawto hold. Double-B and lower bonds are speculative or junk bonds and they have a significant probabilityofgoing intodefault. Bond Rating Criteria BondratingsarebasedonfinancialratiossuchasthosediscussedinChapter4and onvarious qualitative factors. Theratiosespecially the debt and interest coverage ratios are generally the most important ratings determinants but at times other factorsthatareexpectedtoaffecttheratiosinthefuturetakecenterstage.In2008 firms’ exposures to subprime mortgages are leading to downgrades of firms whose ratios still look “reasonable.” Published ratios are of course historical— they show the firm’s condition in the past whereas bond investors are more interested in the firm’s condition in the future. The qualitative factors can be divided intotwo groups: factors that arerelated tothe bondcontract andall other factors. Following is an outline of the determinants of bond ratings: 1. Financial Ratios. All of the ratios are potentially important but the debt and interest coverage ratios are key. The rating agencies’ analysts go through a financial analysis along the lines discussed in Chapter 4 and forecast future ratios along the lines described in the financial planning and forecasting chapter.Fortheforecasts thequalitativefactors discussednextareimportant. 2. Qualitative Factors: Bond Contract Terms. Every bond is covered by a contract oftencalledanindenturebetweentheissuerandthebondholders.Theindenture spells out all the terms related to the bond. Included in the indenture are the maturitythecouponinterestrateastatementofwhetherthebondissecuredby a mortgage on specific assets any sinking fund provisions and a statement of whetherthebondisguaranteedbysomeotherpartywithahighcreditranking. Otherprovisionsmightincluderestrictivecovenantssuchasrequirementsthatthe firmnotletitsdebtratioexceedastatedlevelandthatitkeepitstimes-interest- earned ratio at or above a given level. Some bond indentures are hundreds of pageslong while othersare quiteshort andcover just the terms ofthe loan. 3. MiscellaneousQualitativeFactors.Includedhereareissueslikethesensitivityof the firm’s earnings to the strength of the economy the way it is affected by inflation a statement of whether it is having or likely to have labor problems the extent of its international operations including the stability of the coun- tries in which it operates potential environmental problems and potential antitrust problems. Today the most important factor is exposure to subprime loans including the difficulty to determine the extent of this exposure as a result of the complexity of the assets backed by such loans. 18 Inthe discussiontofollow referencetothe SP ratingisintendedtoimply the Moody’s and Fitch’s ratings aswell. Thus triple-B bonds mean both BBB and Baa bonds double-B bonds mean both BB and Ba bonds and so forth. Investment-Grade Bond Bonds rated triple-B or higher many banks and other institutional invest- ors are permitted by law to hold only investment- grade bonds. Junk Bond A high-risk high-yield bond. Moody’s and SP Bond Ratings Table 7-2 INVESTMENT GRADE JUNK BONDS Moody’s Aaa Aa A Baa Ba B Caa C SP AAA AA A BBB BB B CCC C Note: Both Moody’s and SP use “modifiers” for bonds rated below triple A. SP uses a plus and minus system. Thus Aþ designates the strongest A-rated bonds A- the weakest. Moody’s uses a 1 2 or 3 designation with 1 denoting the strongest and 3 denoting the weakest thus within the double-A category Aa1 is the best Aa2 is average and Aa3 is the weakest. 216 Part 3 Financial Assets

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We see that bond ratings are determined by a great many factors some quanti- tativeandsomequalitativeorsubjective.Alsotheratingprocessisdynamic—at timesonefactorisofprimaryimportanceatothertimessomeotherfactoriskey. Nevertheless as we can see from Table 7-3 there is a strong correlation between bond ratings and many of the ratios that we described in Chapter 4. Not sur- prisingly companies with lower debt ratios higher free cash flow to debt higher returns on invested capital higher EBITDA coverage ratios and higher TIE ratios typically have higher bond ratings. Importance of Bond Ratings Bond ratings are important to both firms and investors. First because a bond’s rating is an indicator of its default risk the rating has a direct measurable influ- enceonthebond’sinterestrateandthefirm’scostofdebt.Secondmostbondsare purchasedbyinstitutionalinvestorsratherthanindividualsandmanyinstitutions are restricted to investment-grade securities. Thus if a firm’s bonds fall below BBB it will have a difficult time selling new bonds because many potential pur- chasers will not be allowed to buy them. As aresultoftheir higherrisk and morerestricted market lower-grade bonds have higher required rates of return r d than high-grade bonds. Figure 7-4 illus- trates this point. In each of the years shown on the graph U.S. government bonds have had the lowest yields AAA bonds have been next and BBB bonds have had thehighestyields.Thefigurealsoshowsthat thegapsbetweenyieldsonthethree types of bonds vary over time indicating that the cost differentials or yield spreadsfluctuate from yearto year.This point is highlighted inFigure 7-5 which gives the yields on the three types of bonds and the yield spreads for AAA and BBB bonds over Treasuries in January 1994 and January 2008. 19 Note first from Bond Rating Criteria: Three-Year 2002–2004 Median Financial Ratios for Different Bond Rating Classifications of Industrial Companies a Table 7-3 AAA AA A BBB BB B CCC Times interest earned EBIT/Interest 23.8 19.5 8.0 4.7 2.5 1.2 0.4 EBITDA interest coverage EBITDA/Interest 25.5 24.6 10.2 6.5 3.5 1.9 0.9 Net cash flow/Total debt 203.3 79.9 48.0 35.9 22.4 11.5 5.0 Free cash flow/Total debt 127.6 44.5 25.0 17.3 8.3 2.8 2.1 Return on capital 27.6 27.0 17.5 13.4 11.3 8.7 3.2 Total debt/EBITDA 0.4 0.9 1.6 2.2 3.5 5.3 7.9 Total debt/Total capital 12.4 28.3 37.5 42.5 53.7 75.9 113.5 a Somewhat different criteria are applied to firms in different industries such as utilities and financial corporations. This table pertains to industrial companies which include manufacturers retailers and service firms. Source: Adapted from “CreditStats Adjusted Key Industrial Financial Ratios” Standard Poor’s 2006 Corporate Ratings Criteria September 10 2007 p. 43. 19 A yield spread is related to but not identical to risk premiums on corporate bonds. The true risk premium reflects only the difference in expected and required returns between two securities that results from differences in their risk. However yield spreads reflect 1 a true risk premium 2 a liquidity premium which reflects the fact that U.S. Treasury bonds are more readily marketable than most corporate bonds 3 a call premium because most Treasury bonds are not callable whereas corporate bonds are and 4 an expected loss differential which reflects the probability of loss on the corporate bonds. As an example of the last point suppose the yield to maturity on a BBB bond was 6.0 versus 4.8 on government bonds but there was a 5 probability of total default loss on the corporate bond. Inthis case the expected return on the BBBbond would be 0.956.0þ 0.050¼ 5.7 and the yield spread would be 0.9 not the full 1.2 percentage points difference in “promised” yields to maturity. Chapter 7 Bonds and Their Valuation 217

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Figure 7-5 that the risk-free rate or vertical axis intercept was lower in January 2008than it was in January 1994 primarilyreflecting the decline in both rates and expected inflation over the past few years. Second the slope of the line has increased indicating an increase in investors’ risk aversion largely due to the sub- prime mortgage problem and growing fears of a possible recession. Thus the penalty for having a low credit rating varies over time. Occasionally as in 2008 thepenaltyisquitelargebutattimesasin1994showninFigures7-4and 7-5it is small. These spread differences reflect investors’ risk aversion and their opti- mismorpessimismregardingtheeconomyandcorporateprofits.In2008asmore and more homeowners default on their loans and poor economic news continues investors were both pessimistic and risk-averse so spreads were quite high. Changes in Ratings Changes in a firm’s bond rating affect its ability to borrow funds capital and its cost of that capital. Rating agencies review outstanding bonds on a periodic basis occasionally upgrading or downgrading a bond as a result of its issuer’s changed circumstances. For example on March 4 2008 SP upgraded Reliant Energy’s secured debt facilities fromB to BB–however the firm’s “B” corporate credit rating remained unchanged. The secured debt’s upgrade was due to the firm’s refinancing the secured debt with unsecured debt reducing the size of its secured revolving loan and paying down the senior secured notes. On the other hand on March 6 2008 SP downgraded Airborne Health Inc.’scorporate creditratingfromB–toCCC+.ThedowngradewaslargelyduetoSP’sconcern about the company’s future sales following negative publicity from its recent settlementofaclassactionlawsuit.Thelawsuitcameaboutfromthecompany’s claims that its product helped prevent the common cold a fact that was proved to be untrue. Yields on Selected Long-Term Bonds 1994–2008 FIGURE 7-4 1994 1995 1996 1997 1998 1999 2000 U.S. Government Wide Spread Corporate AAA Narrow Spread Corporate BBB Yield Years 2001 2002 2003 2004 2005 2006 2007 2008 0 2 4 6 8 10 Source: Federal Reserve Statistical Release Selected Interest Rates Historical Data 218 Part 3 Financial Assets

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Over the long run rating agencies have done a reasonably good job of mea- suringtheaveragecreditriskofbondsandofchangingratingswheneverthereisa significant change in credit quality. However it is important to understand that ratings do not adjust immediately to changes in credit quality and in some cases there canbe aconsiderablelag betweenachange increditqualityand achange in rating. For example Enron’s bonds still carried an investment-grade rating on a Friday in December 2001 but the company declared bankruptcy 2 days later on Sunday. Many other abrupt downgrades occurred in 2007 and 2008 leading to callsbyCongressandtheSECforchangesinratingagenciesandthewaytheyrate bonds. Improvements can clearly be made but there will always be surprises when we learn that supposedly strong bonds were in fact quite weak. 7-8c Bankruptcy and Reorganization When a business becomes insolvent it doesn’t have enough cash to meet its interest and principal payments. A decision must then be made whether to dis- solve the firm through liquidation or to permit it to reorganize and thus continue to operate. These issues are addressed in Chapter 7 and Chapter 11 of the federal bankruptcy statutes and the final decision is made by a federal bankruptcy court judge. The decision to force a firm to liquidate versus permitting it to reorganize depends on whether the value of the reorganized business is likely to be greater thanthe valueofits assets ifthey weresold off piecemeal.In areorganizationthe firm’s creditors negotiate with management on the terms of a potential reorga- nization.Thereorganizationplanmaycallforrestructuringthedebtinwhichcase the interest rate may be reduced the term to maturity lengthened or some of the debt exchangedfor equity. Thepoint ofthe restructuring is toreduce the financial Relationship between Bond Ratings and Bond Yields 1994 and 2008 FIGURE 7-5 AAA BBB Treasury Yield 3 5 4 6 7 Yield Spread BBB 2.2 Yield Spread AAA 1.0 Yield Spread BBB 1.3 Yield Spread AAA 0.5 January 1994 January 2008 0 1 2 9 8 Long-Term Government Bonds Default-Free 1 AAA Corporate Bonds 2 BBB Corporate Bonds 3 YIELD SPREADS AAA 4 ¼ 2 1 BBB 5 ¼ 3 1 January 1994 6.4 6.9 7.7 0.5 1.3 January 2008 4.3 5.3 6.5 1.0 2.2 Source: Federal Reserve Statistical Release Selected Interest Rates Historical Data Chapter 7 Bonds and Their Valuation 219

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chargestoalevelthat issupportablebythefirm’sprojectedcashflows.Ofcourse the common stockholders also have to “take a haircut”—they generally see their position diluted as a result of additional shares being given to debtholders in exchange for accepting a reduced amount of debt principal and interest. A trustee may be appointed by the court to oversee the reorganization but the existing management generally is allowed to retain control. Liquidation occurs if the company is deemed to be worth more “dead” than “alive.” If the bankruptcy court orders a liquidation assets are auctioned off and the cash obtained is distributed as specified in Chapter 7 of the Bankruptcy Act. Web Appendix 7B provides an illustration of how a firm’s assets are distributed after liquidation. For now you should know that 1 the federal bankruptcy statutes govern reorganization and liquidation 2 bankruptcies occur frequently 3 a priority of the specified claims must be followed when the assets of a liq- uidated firm are distributed 4 bondholders’ treatment depends on the terms of the bond and 5 stockholders generally receive little in reorganizations and nothing in liquidations because the assets are usually worth less than the amount of debt outstanding. SELFTEST Differentiate between mortgage bonds and debentures. Namethemajorratingagenciesandlistsomefactorsthataffectbondratings. Why are bond ratings important to firms and investors Do bond ratings adjust immediately to changes in credit quality Explain. DifferentiatebetweenChapter7liquidationsandChapter11reorganizations. In general when should each be used 7-9 BOND MARKETS Corporate bonds aretradedprimarilyinthe over-the-counter market. Most bonds are owned by and traded among large financial institutions for example life insurancecompaniesmutual funds hedge fundsandpensionfunds all ofwhich dealinverylargeblocksofsecuritiesanditisrelativelyeasyforover-the-counter bond dealers to arrange the transfer of large blocks of bonds among the relatively few holders of the bonds. It would be more difficult to conduct similar operations inthestockmarketamongtheliterallymillionsoflargeandsmallstockholdersso a higher percentage of stock trades occur on the exchanges. The Wall Street Journal routinely reports key developments in the Treasury corporate and municipal bond markets. The online edition of The Wall Street Journal also lists for each trading day the most actively traded investment-grade bonds high-yield bonds and convertible bonds. Table 7-4 reprints portions of the online edition’s “Corporate Bonds Data” section which shows the most active issues that traded on March 6 2008 in descending order of sales volume. LookingatTable7-4youwillseethecouponratematuritydatebondrating high and low prices for the day closing last price change in price and yield to maturity. The table assumes that each bond has a par value of 100. Not sur- prisingly the high-yield bonds have much higher yields to maturity because of their higher default risk and the convertible bonds have much lower yields because investors are willing to accept lower yields in return for the option to convert their bonds to common stock. If you examine the table closely you will also see that the bonds with a yield to maturity above their coupon rate trade at a discount whereas bonds with a 220 Part 3 Financial Assets

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Most Active Investment-Grade High-Yield and Convertible Corporate Bonds March 6 2008 Table 7-4 CORPORATE BONDS Market Breadth Last updated: 3/6/2008 at 6:35 PM ET Total Issues Traded Advances Declines Unchanged 52 Week High 52 Week Low Dollar Volume 3774 1457 1873 126 170 344 15640 MERRlLL LYNCH BANK OF AMERICA CORP JPMORGAN CHASE CO SPRINT CAPITAL GOLDMAN SACHS GP GENERAL ELECTRIC CAPITAL SPRINT CAPITAL TELECOM ITALIA CAPITAL UNITED PARCEL SERVICE SPRINT CAPITAL MER.GDW BAC.HBM JPM.JPF S.GJ GS.YL GE.HEE S.HK Tl.GK UPS.QE S.GM 2587 1083 1187 53 161 191 7350 942 299 532 68 8 117 4989 245 75 154 5 1 36 3301 About This Information: End of Day data. Activity as reported to FINRA TRACE Trade Reporting and Compliance Engine. The Market breadth information represents activity in all TRACE eligible publicly traded securities. The most active information represents the most active fxed- coupon bonds ranked by par value traded. Inclusion in Investment Grade or High Yield tables based on TRACE dissemination criteria. ”C” indicates yield is unavailable because of issues call criteria. Most Active Investment Grade Bonds All Issues Issuer Name Symbol 4.125 5.750 6.000 6.875 5.950 5.250 8.750 5.250 4.500 6.900 Jan 2009 Dec 2017 Jan 2018 Nov 2028 Jan 2018 Dec 2017 Mar 2032 Nov 2013 Jan 2013 May 2019 100.886 103.143 104.566 74.000 100.516 101.750 81.120 100.834 103.964 76.313 99.500 99.280 100.632 69.000 95.956 97.678 76.063 95.908 103.617 73.950 100.886 99.280 101.587 72.563 98.520 98.770 80.000 95.908 103.734 76.313 3.051 5.847 5.784 10.048 6.151 5.413 11.159 6.112 3.651 10.565 0.910 –1.339 –0.413 0.063 0.576 –0.335 0.000 –1.949 1.053 0.563 A1/A+/A+ Aa1/AA/AA Aa2/AA–/AA– Baa3/BBB–/BB+ Aa3/AA–/AA– Aaa/AAA/-- Baa3/BBB–/BB+ Baa2/BBB+/BBB+ Aa2/AA–/-- Baa3/BBB–/BB+ Coupon Maturity Rating Moody’s/SP/ Fitch High Low Last Change Yield Issuer Name Symbol Coupon Maturity Rating Moody’s/SP/ Fitch High Low Last Change Yield Issuer Name Symbol Coupon Maturity Rating Moody’s/SP/ Fitch High Low Last Change Yield THORNBURG MORTGAGE GENERAL MOTORS E TRADE FINANClAL CCH I BLOCKBUSTER COMMUNITY HEALTH SYSTEMS HERTZ CORP GENERAL MOTORS ACCEPTANCE NEIMAN MARCUS GP INTELSATBERMUDA TMA.GB GM.HB ET.GF CHTR.HM BBI.GB CYH.GI F.GRY GMA.HE NMGA.GD INTEL.GR Most Active High Yield Bonds 8.000 8.375 8.000 11.000 9.000 8.875 8.875 6.875 9.000 9.250 May 2013 Jul 2033 Jun 2011 Oct 2015 Sep 2012 Jul 2015 Jan 2014 Sep 2011 Oct 2015 Jun 2016 49.000 79.750 86.000 70.125 87.500 99.500 99.000 81.710 98.250 101.250 35.500 74.000 85.000 69.688 83.000 98.750 94.750 79.000 97.000 100.875 40.000 75.938 86.000 70.070 83.500 98.750 97.086 80.516 97.250 100.875 32.807 11.262 13.429 18.517 14.096 9.108 9.535 14.099 9.511 9.093 –23.750 –1.063 0.500 –0.430 1.625 –0.750 0.586 –0.484 –0.688 0.000 Caa2/CCC+/CCC– Caa1/B–/B– Ba3/B/-- Caa2/CCC/CCC Caa2/CCC/CC B3/B–/CCC+ B1/B/BB– B1/B+/BB B2/B/B– B3/B–/BB– AMGEN SANDISK CORP NABORS INDUSTRlES PROTEIN DESIGN LABS AMGEN AMGN.GM SNDK.GC NBR.GP PDLI.GF AMGN.GN Most Active Convertible Bonds Source: FINRA TRACE data. Reference information from Reuters DataScope Data. Credit ratings from Moody’s Standard Poor’s and Fitch Ratings. 0.125 1.000 0.940 2.000 0.375 Feb 2011 May 2013 May 2011 Feb 2012 Feb 2013 92.438 74.000 100.500 80.608 88.467 91.813 72.690 96.000 78.882 87.000 91.883 74.000 100.000 79.443 87.587 3.083 7.086 0.940 8.231 3.133 –0.745 –0.116 –0.750 0.203 –0.663 A2/--/-- --/BB–/-- --/BBB+/A– --/--/-- A2/--/-- Investment Grade High Yield Convertibles Par value in millions. Source: “Corporate Bonds” The Wall Street Journal Online March 7 2008. Chapter 7 Bonds and Their Valuation 221

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yield belowtheircouponrate trade atapremiumabovepar.Weseethat the large majority of high-yield bonds trade at a discount to par which suggests that because of increased default risk most of these bonds now trade at higher yields relativetowhentheywereissued.Recallthatmostbondsareissuedatparsothe coupon rate tells us what the bond’s yield was at the time it was issued. You should also note that when bonds with similar ratings are compared bonds with longermaturitiestendtohavehigheryieldswhich isconsistentwiththeupward- sloping yield curve during this time period. SELFTEST Why do most bond trades occur in the over-the-counter market If a bond issue is to be sold at par at what rate must its coupon rate be set Explain. TYING IT ALL TOGETHER This chapter described the different types of bonds governments and corpo- rations issue explained how bond prices are established and discussed how investorsestimate ratesof returnon bonds.Italsodiscussed various types ofrisks that investors face when they purchase bonds. When an investor purchases a company’s bonds the investor is providing the company with capital. Moreover when a firm issues bonds the return that investors require on the bonds represents the cost of debt capital to the firm. This point is extended in Chapter 10 where the ideas developed in this chapter are used to help determine a company’s overall cost of capital which is a basic component of the capital budgeting process. Inrecentyearsmanycompanieshaveusedzerocouponbondstoraisebillionsof dollarswhilebankruptcyisanimportantconsiderationforcompaniesthatissuedebt and for investors. Thereforethese two related issues are discussed in detail in Web Appendixes7Aand7B.Gotothetextbook’swebsitetoaccesstheseappendixes. SELF-TEST QUESTIONS AND PROBLEMS Solutions Appear in Appendix A ST-1 KEY TERMS Define each of the following terms: a. Bond treasury bond corporate bond municipal bond foreign bond b. Par value maturity date original maturity c. Coupon payment coupon interest rate d. Fixed-rate bond floating-rate bond zero coupon bond original issue discount OID bond e. Call provision sinking fund provision f. Convertible bond warrant putable bond income bond indexed or purchasing power bond 222 Part 3 Financial Assets

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g. Discount bond premium bond h. Yield to maturity YTM yield to call YTC total return yield spread i. Interest rate risk reinvestment rate risk investment horizon default risk j. Mortgage bond indenture debenture subordinated debenture k. Investment-grade bond junk bond ST-2 BONDVALUATION ThePenningtonCorporationissuedanewseriesofbondsonJanuary1 1985. The bonds weresoldatpar 1000 hada 12couponandmaturein30yearson December312014.CouponpaymentsaremadesemiannuallyonJune30andDecember31. a. What was the YTM on January 1 1985 b. What was the price of the bonds on January 1 1990 5 years later assuming that interest rates had fallen to 10 c. FindthecurrentyieldcapitalgainsyieldandtotalreturnonJanuary11990giventhe price as determined in Part b. d. On July 1 2008 6½ years before maturity Pennington’s bonds sold for 916.42. What were the YTM the current yield the capital gains yield and the total return at that time e. Now assume that you plan to purchase an outstanding Pennington bond on March 1 2008 when the going rate of interest given its risk was 15.5. How large a check must you write to complete the transaction This is a difficult question. ST-3 SINKING FUND The Vancouver Development Company VDC is planning to sell a 100 million 10-year 12 semiannual payment bond issue. Provisions for a sinking fund toretire theissueoverits lifewillbeincludedintheindenture. Sinkingfund paymentswill be made at the end of each year and each payment must be sufficient to retire 10 of the original amount of the issue. The last sinking fund payment will retire the last of the bonds. The bonds to be retired each period can be purchased on the open market or obtained by calling up to 5 of the original issue at par at VDC’s option. a. How large must each sinking fund payment be if the company 1 uses the option to call bonds at par or 2 decides to buy bonds on the open market For Part 2 you can only answer in words. b. Whatwillhappentodebtservicerequirementsperyearassociatedwiththisissueover its 10-year life c. Now consider an alternative plan where VDC sets up its sinking fund so that equal annual amounts are paid into a sinking fund trust held by a bank with the proceeds being used to buy government bonds that are expected to pay 7 annual interest. The payments plus accumulated interest must total 100 million at the end of 10 years when the proceeds will be used to retire the issue. How large must the annual sinking fundpaymentsbeIsthisamountknownwithcertaintyormightitbehigherorlower d. What are the annual cash requirements for covering bond service costs under the trusteeship arrangement described in Part c Note: Interest must be paid on Vancouver’s outstanding bonds but not on bonds that have been retired. Assume level interest rates for purposes of answering this question. e. What would have to happen to interest rates to cause the company to buy bonds on the open market rather than call them under the plan where some bonds are retired each year QUESTIONS 7-1 A sinking fund can be set up in one of two ways: a. The corporation makes annual payments to the trustee who invests the proceeds in securities frequently government bonds and uses the accumulated total to retire the bond issue at maturity. b. Thetrusteeusestheannualpaymentstoretireaportionoftheissueeachyearcallinga given percentage of the issue by a lottery and paying a specified price per bond or buying bonds on the open market whichever is cheaper. What are the advantages and disadvantages of each procedure from the viewpoint of a the firm and b the bondholders Chapter 7 Bonds and Their Valuation 223

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7-2 IsittruethatthefollowingequationcanbeusedtofindthevalueofabondwithNyearsto maturitythatpaysinterestonceayearAssumethatthebondwasissuedseveralyearsago. V B ¼ X N t¼1 Annual interest ð1 þ r d Þ t þ Par value ð1 þ r d Þ N 7-3 The values of outstanding bonds change whenever the going rate of interest changes. In general short-term interest rates are more volatile than long-term interest rates. Therefore short-term bond prices are more sensitive to interest rate changes than are long-term bond prices. Is that statement true or false Explain. Hint: Make up a “reasonable” example based on a 1-year and a 20-year bond to help answer the question. 7-4 Ifinterestratesriseafterabondissuewhatwillhappentothebond’spriceandYTMDoes the time to maturity affect the extent to which interest rate changes affect the bond’s price Again an example might help you answer this question. 7-5 If you buy a callable bond and interest rates decline will the value of your bond rise by as much as it would have risen if the bond had not been callable Explain. 7-6 Assume that you have a short investment horizon less than 1 year. You are considering two investments: a 1-year Treasury security and a 20-year Treasury security. Which of the two investments would you view as being riskier Explain. 7-7 Indicate whether each of the following actions will increase or decrease a bond’s yield to maturity: a. The bond’s price increases. b. The bond is downgraded by the rating agencies. c. A change in the bankruptcy code makes it more difficult for bondholders to receive payments in the event the firm declares bankruptcy. d. Theeconomyseemstobeshiftingfromaboomtoarecession.Discusstheeffectsofthe firm’s credit strength in your answer. e. Investors learn that the bonds are subordinated to another debt issue. 7-8 Why is a call provision advantageous to a bond issuer When would the issuer be likely to initiate a refunding call 7-9 Are securities that provide for a sinking fund more or less risky from the bondholder’s perspective than those without this type of provision Explain. 7-10 What’s the difference between a call for sinking fund purposes and a refunding call 7-11 Why are convertibles and bonds with warrants typically offered with lower coupons than similarly rated straight bonds 7-12 Explain whether the following statement is true or false: Only weak companies issue debentures. 7-13 Would the yield spread on a corporate bond over a Treasury bond with the same maturity tend to become wider or narrower if the economy appeared to be heading toward a recession Would the change in the spread for a given company be affected by the firm’s credit strength Explain. 7-14 A bond’s expected return is sometimes estimated by its YTM and sometimes by its YTC. UnderwhatconditionswouldtheYTMprovideabetterestimateandwhenwouldtheYTC be better PROBLEMS Easy Problems 1–4 7-1 BOND VALUATION Callaghan Motors’ bonds have 10 years remaining to maturity. Interest is paid annually they have a 1000 par value the coupon interest rate is 8 and the yield to maturity is 9. What is the bond’s current market price 7-2 YIELD TO MATURITY AND FUTURE PRICE A bond has a 1000 par value 10 years to maturity and a 7 annual coupon and sells for 985. a. What is its yield to maturity YTM b. Assume that the yield to maturity remains constant for the next 3 years. What will the price be 3 years from today 224 Part 3 Financial Assets

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7-3 BOND VALUATION Nungesser Corporation’s outstanding bonds have a 1000 par value a 9 semiannual coupon 8 years to maturity and an 8.5 YTM. What is the bond’s price 7-4 YIELD TO MATURITY A firm’s bonds have a maturity of 10 years with a 1000 face value have an 8 semiannual coupon are callable in 5 years at 1050 and currently sell at a price of 1100. What are their nominal yield to maturity and their nominal yield to call What return should investors expect to earn on these bonds Intermediate Problems 5–14 7-5 BOND VALUATION An investor has two bonds in his portfolio that have a face value of 1000andpaya10annualcoupon.BondLmaturesin15yearswhileBondSmaturesin 1 year. a. What will the value of each bond be if the going interest rate is 5 8 and 12 Assume that only one more interest payment is to be made on Bond S at its maturity and that 15 more payments are to be made on Bond L. b. Why does the longer-term bond’s price vary more than the price of the shorter-term bond when interest rates change 7-6 BOND VALUATION An investor has two bonds in her portfolio Bond C and Bond Z. Each bond matures in 4 years has a face value of 1000 and has a yield to maturity of 9.6. Bond C pays a 10 annual coupon while Bond Z is a zero coupon bond. a. Assumingthattheyieldtomaturityofeachbondremainsat9.6overthenext4years calculate the price of the bonds at each of the following years to maturity: Years to Maturity Price of Bond C Price of Bond Z 4 3 2 1 0 b. Plot the time path of prices for each bond. 7-7 INTEREST RATE SENSITIVITY An investor purchased the following 5 bonds. Each bond had a par value of 1000 and an 8 yield to maturity on the purchase day. Immediately after the investor purchased them interest rates fell and each then had a new YTM of 7. What is the percentage change in price for each bond after the decline in interest rates Fill in the following table: Price 8 Price 7 Percentage Change 10-year 10 annual coupon 10-year zero 5-year zero 30-year zero 100 perpetuity 7-8 YIELD TO CALL Six years ago the Singleton Company issued 20-year bonds with a 14 annual coupon rate at their 1000 par value. The bonds had a 9 call premium with 5 years of call protection. Today Singleton called the bonds. Compute the realized rate of returnforaninvestorwhopurchasedthebondswhentheywereissuedandheldthemuntil they were called. Explain why the investor should or should not be happy that Singleton called them. 7-9 YIELD TO MATURITY Heymann Company bonds have 4 years left to maturity. Interest is paid annually and the bonds have a 1000 par value and a coupon rate of 9. a. What is the yield to maturity at a current market price of 1 829 and 2 1104 b. Would you pay 829for each bond if you thought that a “fair” market interest rate for such bonds was 12—that is if r d ¼ 12 Explain your answer. 7-10 CURRENT YIELD CAPITAL GAINS YIELD AND YIELD TO MATURITY Hooper Printing Inc. has bonds outstanding with 9 years left to maturity. The bonds have an 8 annual coupon rate and were issued 1 year ago at their par value of 1000. However due to changes in Chapter 7 Bonds and Their Valuation 225

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interest ratesthe bond’smarket pricehasfallen to901.40.The capital gains yield lastyear was –9.86. a. What is the yield to maturity b. For the coming year what are the expected current and capital gains yields Hint: Refer to Footnote 8 for the definition of the current yield and to Table 7-1. c. WilltheactualrealizedyieldsbeequaltotheexpectedyieldsifinterestrateschangeIf not how will they differ 7-11 BOND YIELDS Last year Clark Company issued a 10-year 12 semiannual coupon bond atitsparvalueof1000.Currentlythebondcanbecalledin4yearsatapriceof1060and it sells for 1100. a. Whatare thebond’snominal yieldtomaturity andits nominal yieldtocall Wouldan investor be more likely to earn the YTM or the YTC b. WhatisthecurrentyieldIsthisyieldaffectedbywhetherthebondislikelytobecalled Hint: Refer to Footnote 8 for the definition of the current yield and to Table 7-1. c. What is the expected capital gains or loss yield for the coming year Is this yield dependent on whether the bond is expected to be called 7-12 YIELD TO CALL It is now January 1 2009 and you are considering the purchase of an outstandingbond thatwasissuedonJanuary 12007. Ithasa 9.5annualcoupon andhad a 30-year original maturity. It matures on December 31 2036. There is 5 years of call protection until December 31 2011 after which time it can be called at 109—that is at 109 ofparor 1090.Interest rates have declined since itwas issued and itisnow selling at 116.575 of par or 1165.75. a. What is the yield to maturity What is the yield to call b. IfyouboughtthisbondwhichreturnwouldyouactuallyearnExplainyourreasoning. c. Supposethebondhadbeensellingatadiscountratherthanapremium.Wouldtheyieldto maturityhavebeenthemostlikelyreturnorwouldtheyieldtocallhavebeenmostlikely 7-13 PRICE AND YIELD An 8 semiannual coupon bond matures in 5 years. The bond has a face value of 1000 and a current yield of 8.21. What are the bond’s price and YTM Hint: Refer to Footnote 8 for the definition of the current yield and to Table 7-1. 7-14 EXPECTED INTEREST RATE Lloyd Corporation’s 14 coupon rate semiannual payment 1000parvaluebondswhichmaturein30yearsarecallable5yearsfromtodayat1050. They sell at a price of 1353.54 and the yield curve is flat. Assume that interest rates are expected to remain at their current level. a. What is the best estimate of these bonds’ remaining life b. IfLloydplanstoraiseadditionalcapitalandwantstousedebtfinancingwhatcoupon rate would it have to set in order to issue new bonds at par Challenging Problems 15–19 7-15 BOND VALUATION Bond X is noncallable and has 20 years to maturity a 9 annual coupon and a 1000 par value. Your required return on Bond X is 10 and if you buy it you plan to hold it for 5 years. You and the market have expectations that in 5 years the yield to maturity on a 15-year bond with similar risk will be 8.5. How much should you be willingto pay forBond X todayHint: You will need toknow how much the bond will be worth at the end of 5 years. 7-16 BOND VALUATION You are considering a 10-year 1000 par value bond. Its coupon rate is 9 and interest is paid semiannually. If you require an “effective” annual interest rate not a nominal rate of 8.16 how much should you be willing to pay for the bond 7-17 BONDRETURNS LastyearJoanpurchaseda1000facevaluecorporatebondwithan11 annual coupon rate and a 10-year maturity. At the time of the purchase it had an expected yield to maturity of 9.79. If Joan sold the bond today for 1060.49 what rate of return would she have earned for the past year 7-18 BONDREPORTING LookbackatTable7-4andexamineUnitedParcelServiceandTelecom Italia Capital bonds that mature in 2013. a. Ifthesecompaniesweretosellnew1000 parvalue long-termbondsapproximately whatcouponinterestratewouldtheyhavetosetiftheywantedtobringthemoutatpar b. If you had 10000 and wanted to invest in United Parcel Service bonds what return wouldyouexpecttoearnWhataboutTelecomItaliaCapitalbondsBasedjustonthe datainthetablewouldyouhavemoreconfidenceaboutearningyourexpectedrateof return if you bought United Parcel Service or Telecom Italia Capital bonds Explain. 226 Part 3 Financial Assets

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7-19 YIELD TO MATURITY AND YIELD TO CALL Kaufman Enterprises has bonds outstanding with a 1000 face value and 10 years left until maturity. They have an 11 annual coupon payment and their current price is 1175. The bonds may be called in 5 years at 109 of face value Call price ¼ 1090. a. What is the yield to maturity b. What is the yield to call if they are called in 5 years c. Which yield might investors expect to earn on these bonds Why d. The bond’s indenture indicates that the call provision gives the firm the right to call the bonds at the end of each year beginning in Year 5. In Year 5 the bonds may be called at 109 of face value but in each of the next 4 years the call percentage will declineby1.ThusinYear6theymaybecalledat108offacevalueinYear7they may be called at 107 of face value and so forth. If the yield curve is horizontal and interest rates remain at their current level when is the latest that investors might expect the firm to call the bonds COMPREHENSIVE/SPREADSHEET PROBLEM 7-20 BOND VALUATION Clifford Clarkisa recentretiree whoisinterested in investingsome of his savings in corporate bonds. His financial planner has suggested the following bonds: l Bond A has a 7 annual coupon matures in 12 years and has a 1000 face value. l Bond B has a 9 annual coupon matures in 12 years and has a 1000 face value. l Bond C has an 11 annual coupon matures in 12 years and has a 1000 face value. Each bond has a yield to maturity of 9. a. Before calculating the prices of the bonds indicate whether each bond is trading at a premium at a discount or at par. b. Calculate the price of each of the three bonds. c. Calculatethecurrentyieldforeachofthethreebonds.Hint:RefertoFootnote8forthe definition of the current yield and to Table 7-1. d. If the yield to maturity for each bond remains at 9 what will be the price of each bond1yearfromnowWhatistheexpectedcapitalgainsyieldforeachbondWhatis the expected total return for each bond e. Mr.ClarkisconsideringanotherbondBondD.Ithasan8semiannualcouponanda 1000 face value i.e. it pays a 40 coupon every 6 months. Bond D is scheduled to mature in9years andhasapriceof1150.Itisalsocallablein5yearsatacallpriceof 1040. 1 What is the bond’s nominal yield to maturity 2 What is the bond’s nominal yield to call 3 If Mr. Clark were to purchase this bond would he be more likely to receive the yield to maturity or yield to call Explain your answer. f. Explainbrieflythedifferencebetweeninterestrateorpriceriskandreinvestmentrate risk. Which of the following bonds has the most interest rate risk l A 5-year bond with a 9 annual coupon l A 5-year bond with a zero coupon l A 10-year bond with a 9 annual coupon l A 10-year bond with a zero coupon g. Onlydothispartifyouareusingaspreadsheet.CalculatethepriceofeachbondAB and C at the end of each year until maturity assuming interest rates remain constant. Create a graph showing the time path of each bond’s value similar to Figure 7-2. 1 What is the expected interest yield for each bond in each year 2 What is the expected capital gains yield for each bond in each year 3 What is the total return for each bond in each year Chapter 7 Bonds and Their Valuation 227

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INTEGRATED CASE WESTERN MONEY MANAGEMENT INC. 7-21 BOND VALUATION Robert Black and Carol Alvarez are vice presidents of Western Money Management and codirectors of the company’s pension fund management division. A major new client the California League of Cities has requested that Western present an investment seminar to the mayors of the represented cities. Black and Alvarez who will make the presentation have asked you to help them by answering the following questions. a. What are a bond’s key features b. What are call provisions and sinking fund provisions Do these provisions make bonds more or less risky c. How is the value of any asset whose value is based on expected future cash flows determined d. Howisabond’svaluedeterminedWhatisthevalueofa10-year1000parvaluebondwitha10annual coupon if its required return is 10 e. 1 What is the value of a 13 coupon bond that is otherwise identical to the bond described in Part d Would we now have a discount or a premium bond 2 What is the value of a 7 coupon bond with these characteristics Would we now have a discount or premium bond 3 What would happen to the values of the 7 10 and 13 coupon bonds over time if the required return remained at 10 Hint: With a financial calculator enter PMT I/YR FV and N then change override N to see what happens to the PV as it approaches maturity. f. 1 What is the yield to maturity on a 10-year 9 annual coupon 1000 par value bond that sells for 887.00 that sells for 1134.20 What does the fact that it sells at a discount or at a premium tell you about the relationship between r d and the coupon rate 2 Whatarethetotal returnthecurrent yieldandthecapital gainsyieldforthediscount bondAssume that it is held to maturity and the company does not default on it. Hint: Refer to Footnote 8 for the definition of the current yield and to Table 7-1. g. What is interest rate or price risk Which has more interest rate risk an annual payment 1-year bond or a 10-year bond Why h. What is reinvestment rate risk Which has more reinvestment rate risk a 1-year bond or a 10-year bond i. How does the equation for valuing a bond change if semiannual payments are made Find the value of a 10-year semiannual payment 10 coupon bond if nominal r d ¼ 13. j. Suppose for 1000 you could buy a 10 10-year annual payment bond or a 10 10-year semiannual payment bond. They are equally risky. Which would you prefer If 1000 is the proper price for the semiannual bond what is the equilibrium price for the annual payment bond k. Suppose a 10-year 10 semiannual coupon bond with a par value of 1000 is currently selling for 1135.90 producing a nominal yield to maturity of 8. However it can be called after 4 years for 1050. 1 What is the bond’s nominal yield to call YTC 2 If you bought this bond would you be more likely to earn the YTM or the YTC Why l. Does the yield to maturity represent the promised or expected return on the bond Explain. m. These bonds were rated AA- by SP. Would you consider them investment-grade or junk bonds n. What factors determine a company’s bond rating o. If this firm were to default on the bonds would the company be immediately liquidated Would the bond- holders be assured of receiving all of their promised payments Explain. 228 Part 3 Financial Assets

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ª FRANK SITEMAN/PHOTOLIBRARY CHAPTER 8 Risk and Rates of Return A Tale of Three Markets—or Is It Four The purpose of this vignette is to give you some additional perspective on the stock market. Refer to Figure 8-1 on page 232 as you read the fol- lowing paragraphs. Market 1: 1975–2000. These were great years especially the last five. Only 3 years saw losses and toward the end of the run most investors and money managers had never experienced a really bad market and acted as though bad markets had been banished and would never reappear again. However Alan Greenspan Chairman of the Federal Reserve Board at that time knew the wild ride couldn’t continue. In 1995 he stated that investors were exhibiting “irrational exuberance” but the market ignored him and kept roaring ahead. Market 2: 2000–2003. Greenspan was right. In 2000 the bubble started to leak and the market fell by 10. Then in 2001 the 9/11 terrorist attacks on the World Trade Center knocked stocks down another 14. Finally in 2002 fears of another attack in addition to a recession led to a gut-wrenching 24 decline. Those 3 years cost the average investor almost 50 of his or her beginning-of-2000 market value. People plan- ning to retire rich and young had to rethink those plans. Market 3: 2003–2007. Investors had over- reacted so in 2003 the market rebounded rising by just over 25. The market remained strong through 2007—the economy was robust profits were rising rapidly and the Federal Reserve encouraged a bull market by cutting interest rates 11 times. In 2007 the Dow Jones and other stock averages hit all-time highs. But the debt markets were suffering from the subprime mortgage debacle and institutions such as Merrill Lynch and Citigroup were writing off tens of billions of dollars of bad loans. Oil prices hit 100 per barrel gasoline prices hit new highs and unemployment rates were creeping up. With this backdrop some observers wondered if we were again suffering from irrational exuberance. 229

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PUTTING THINGS IN PERSPECTIVE We start this chapter from the basic premise that investors like returns and dislike risk hence they will invest in risky assets only if those assets offer higher expected returns. We define what risk means as it relates to investments examine proce- dures that are used to measure risk and discuss the relationship between risk and return. Investors should understand these concepts as should corporate managers as they develop the plans that will shape their firms’ futures. Risk can be measured in different ways and different conclusions about an asset’s riskiness can be reached depending on the measure used. Risk analysis can be confusing but it will help if you keep the following points in mind: 1. All business assets are expected to produce cash flows and the riskiness of an asset is based on the riskiness of its cash flows. The riskier the cash flows the riskier the asset. 2. Assets can be categorized as financial assets especially stocks and bonds and as real assetssuchastrucksmachinesandwholebusinesses.Intheoryriskanalysis for all types of assets is similar and the same fundamental concepts apply to all assets. However in practice differences in the types of available data lead to differentproceduresforstocksbondsandrealassets.Ourfocusinthischapteris on financial assets especially stocks. We considered bonds in Chapter 7 and we take up real assets in the capital budgeting chapters especially Chapter 12. 3. Astock’sriskcanbeconsideredintwoways:aon a stand-alone or single-stock basis or b in a portfolio context where a number of stocks are combined and their consolidated cash flows are analyzed. 1 There is an important difference between stand-alone and portfolio risk and a stock that has a great deal of risk held by itself may be much less risky when held as part of a larger portfolio. 4. In a portfolio context a stock’s risk can be divided into two components: a diversifiable risk which can be diversified away and is thus of little concern to diversifiedinvestorsandb market riskwhichreflectstheriskofageneralstock marketdeclineandcannotbeeliminatedbydiversificationhencedoesconcern investors. Only market risk is relevant to rational investors because diversifiable risk can and will be eliminated. 5. Astock withhighmarketriskmust offer arelatively highexpectedrate ofreturn to attract investors. Investors in general are averse to risk so they will not buy risky assets unless they are compensated with high expected returns. 6. If investors on average think a stock’s expected return is too low to compensate foritsrisktheywillstartsellingitdrivingdownitspriceandboostingitsexpected Market 4: 2008 and Thereafter: Bull or Bear In early 2008 the big question is this: Will the bull market continue or are we entering another bear market It turned out that the bears were right—by October 2008 the market had fallen nearly 30 from its high earlier in the year in the aftermath ofa credit crisisonWallStreet thecollapse ofseveral leading financial firms and fears of a sharp economic decline. In response Congress passed an unprecedented 700 billion plan to rescue the financial system. Whats next Will the marketstabilizeorwillitcontinuetoseefurtherdeclinesWe wish we knew By the time you read this you will know but it will be too late to profit from that knowledge. 1 A portfolio is a collection of investment securities. If you owned stock in General Motors ExxonMobil and IBM you would be holding a three-stock portfolio. Because diversification lowers risk without sacrificing much if any expected return most stocks are held in portfolios. 230 Part 3 Financial Assets

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return. Conversely if the expected return on a stock is more than enough to compensate for the risk people will start buying it raising its price and thus lowering its expected return. The stock will be in equilibrium with neither buying nor selling pressure when its expected return is exactly sufficient to compensate for its risk. 7. Stand-alone risk the topic of Section 8-2 is important in stock analysis primarily as a lead-in to portfolio risk analysis. However stand-alone risk is extremely important when analyzing real assets such as capital budgeting projects. When you finish this chapter you should be able to: l Explain the difference between stand-alone risk and risk in a portfolio context. l Explain how risk aversion affects a stock’s required rate of return. l Discuss the difference between diversifiable risk and market risk and explain how each type of risk affects well-diversified investors. l Explain what the CAPM is and how it can be used to estimate a stock’s required rate of return. l Discuss how changes in the general stock and the bond markets could lead to changes in the required rate of return on a firm’s stock. l Discuss how changes in a firm’s operations might lead to changes in the required rate of return on the firm’s stock. 8-1 STOCK PRICES OVER THE LAST 20 YEARS Figure 8-1 gives you an idea about how stocks have performed over the period from1988through2007. 2 ThetopgraphcomparesGeneralElectricGEthebroad stock market as measured by the SP 500 and General Motors GM. GE illus- trates companies that have done well GM illustrates those that have not done well and the SP 500 shows how an average company has performed. Most stocksclimbedsharplyuntil2000Market1inthevignettethendroppedequally sharply during Market 2 then rose nicely through most of Market 3. Since there arethousandsofstockswecouldhaveshown manydifferent pictureswithsome rising much faster than GE and others falling much faster than GM—with somegoingtozeroandvanishing.Mostoftheindexesriseandfalltogetherbutif wehadshowntheNasdaqindexitwouldhavelookedagreatdeallikeGErising much faster than the SP but then falling faster later on. Also note that the beginning and ending dates can lead to totally different “pictures” of stocks’ performances. If we had started in 1990 and ended in 2000 it would have looked as though stocks were wonderful investments. On the other hand if we had started in 2000 and ended in 2003 it would have looked as though stocks were a terrible place to put our money. It would be great if we knew when to get in and out of the market. ThelowergraphshowsGE’sP/Eratio.TheP/Eratiodependsonanumberof factors including fundamental factors such as interest rates and earnings growth ratesbutitalsoreflectsinvestors’optimismorpessimism—orinAlanGreenspan’s wordstheir “irrationalexuberance”orpessimism.Securityanalystsandinvestors forecastthefuturebuttheyseemtobeoverlyoptimisticatcertaintimesandoverly pessimisticatothertimes.Lookingbackwecanseethattheywereoverlyoptimistic in 2000. But what about in 1997 There had been a sharp run-up to that time and some “experts” thought the market was at a top and recommended getting out. Those experts turned out to be wrong and they “left a lot of money on the table.” 2 The graph reflects stock prices dividends are not included. If dividends were included the percentage gains would be somewhat higher. Chapter 8 Risk and Rates of Return 231

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Note also that if you had bought and held GE stock you would have done quitewellbutifyouhadboughtGMstockyouwouldn’thave donewellatall.If you had formed a portfolio with some GM and some GE stocks you would have had “average”performance.Theportfoliowouldhave limitedyourpotentialgain but also would have limited your low-end returns. We will have more to say about portfolios later but keep this in mind as you go through the chapter. 8-2 STAND-ALONE RISK Risk is defined by Webster as “a hazard a peril exposure to loss or injury.” Thus risk refers to the chance that some unfavorable event will occur. If you engage in skydivingyouaretakingachancewithyourlife—skydivingisrisky.Ifyoubeton the horses you are risking your money. As we saw in previous chapters individuals and firms invest funds today with the expectation of receiving additional funds in the future. Bonds offer rel- atively low returns but with relatively little risk—at least if you stick to Treasury and high-grade corporate bonds. Stocks offer the chance of higher returns but stocks are generally riskier than bonds. If you invest in speculative stocks or really any stock you are taking a significant risk in the hope of making an appreciable return. Stock Performance 1988–2007 FIGURE 8-1 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 © 10 20 30 40 50 60 0 88 89 90 91 92 93 94 P/E Ratio GE Daily 6/18/07 SP500 GM 95 96 97 98 99 00 01 02 03 04 05 06 07 +1600 +1400 +1200 +1000 +800 +600 +400 +200 +0 –200 Source: The Wall Street Journal Online January 12 2008. Risk The chance that some unfavorable event will occur. 232 Part 3 Financial Assets

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Anasset’srisk can beanalyzedin twoways:1 on astand-alonebasiswhere theassetisconsideredbyitselfand2onaportfoliobasiswheretheassetisheld as one of a number of assets in a portfolio. Thus an asset’sstand-alonerisk is the risk an investor would face if he or she held only this one asset. Most financial assets and stocks in particular are held in portfolios but it is necessary to understand stand-alone risk to understand risk in a portfolio context. To illustrate stand-alone risk suppose an investor buys 100000 of short-term Treasury bills with an expected return of 5. In this case the investment’s return 5 can be estimated quite precisely and the investment is defined as being essen- tially risk-free. This same investor could also invest the 100000 in the stock of a companyjust being organizedto prospect for oil in themid-Atlantic.Returnson the stock would be much harder to predict. In the worst case the company would go bankrupt and the investor would lose all of his or her money in which case the returnwouldbe 100.Inthebest-casescenariothecompanywoulddiscoverhuge amountsofoilandtheinvestorwouldreceivea1000return.Whenevaluatingthis investment the investor might analyze the situation and conclude that the expected rate of return in a statistical sense is 20 but the actual rate of return could range from sayþ1000to 100.Becausethereisasignificantdangerofearningmuch less than the expected return such a stock would be relatively risky. Noinvestment should beundertaken unless the expected rate ofreturn is highenough tocompensatefortheperceivedrisk.Inourexampleitisclearthatfewifanyinvestors wouldbewillingtobuytheoilexplorationstockifitsexpectedreturndidn’texceed that of the T-bill. This is an extreme example. Generally things are much less obvious and we need to measure risk in order to decide whether a potential investmentshouldbeundertaken.Thereforeweneedtodefineriskmoreprecisely. As you will see the risk of an asset is different when the asset is held by itself versuswhenitisheldasapartofagrouporportfolioofassets.Welookatstand- alone risk in this section then at portfolio risk in later sections. It’s necessary to know something about stand-alone risk in order to understand portfolio risk. Also stand-alone risk is important to the owners of small businesses and in our examination of physical assets in the capital budgeting chapters. For stocks and most financial assets though it is portfolio risk that is most important. Still you need to understand the key elements of both types of risk. 8-2a Statistical Measures of Stand-Alone Risk This is not a statistics book and we won’t spend a great deal of time on statistics. However you do need an intuitive understanding of the relatively simple sta- tistics presented in this section. All of the calculations can be done easily with a calculator or with Excel and while we show pictures of the Excel setup Excel is not needed for the calculations. Here are the five key items that are covered: l Probability distributions l Expected rates of return r “r hat” l Historical or past realized rates of return r “r bar” l Standard deviation sigma l Coefficient of variation CV Table 8-1 gives the probability distributions for Martin Products which makes enginesfor long-haultrucks18-wheelersandfor U.S.Waterwhich suppliesanes- sentialproductandthushasverystablesalesandprofits.Threepossiblestatesofthe economyareshowninColumn1andtheprobabilitiesoftheseoutcomesexpressed as decimals rather than percentages are given in Column 2 and then repeated in Column 5. There is a 30 chance of a strong economy and thus strong demand a 40 probability of normal demand and a 30 probability of weak demand. Stand-Alone Risk The risk an investor would face if he or she held only one asset. Probability Distribution A listing of possible outcomes or events with a probability chance of occurrence assigned to each outcome. Chapter 8 Risk and Rates of Return 233

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Columns 3 and 6 show the returns for the two companies under each state of the economy. Returns are relatively high when demand is strong and low when demand is weak. Notice though that Martin’s rate of return could vary far more widely than U.S. Water’s. Indeed there is a fairly high probability that Martin’s stock will suffer a 60 loss while at worst U.S. Water should have a 5 return. 3 Columns 4 and 7 show the products of the probabilities times the returns under the different demand levels. When we sum these products we obtain the expected rates of return r “r-hat” for the stocks. Both stocks have an expected return of 10. 4 We can graph the data in Table 8-1 as we do in Figure 8-2. The height of each barindicatestheprobabilitythatagivenoutcomewilloccur.Therangeofpossible returns for Martin is from 60 to þ80 and the expected return is 10. The expected return for U.S. Water is also 10 but its possible range and thus maximum loss is much narrower. InFigure8-2weassumedthatonlythreeeconomicstatescouldoccur:strong normal and weak. Actually the economy can range from a deep depression to a fantastic boom and there are an unlimited number of possibilities in between. Suppose we had the time and patience to assign a probability to each possible level of demand with the sum of the probabilities still equaling 1.0 and to assign a rate of return to each stock for each level of demand. We would have a table similartoTable8-1exceptthatitwouldhavemanymoredemandlevels.Thistable could be used to calculate expected rates of return as shown previously and the probabilitiesandoutcomescouldberepresentedbycontinuouscurvessuchasthose shown in Figure 8-3. Here we changed the assumptions so that there is essentially no chance that Martin’sreturnwillbelessthan 60 or more than 80 or that Expected Rate of Return r The rate of return expected to be realized from an investment the weighted average of the probability distribution of possible results. 3 It is completely unrealistic to think that any stock has no chance of a loss. Only in hypothetical examples could this occur. To illustrate the price of Countrywide Financial’s stock dropped from 45.26 to 4.43 in the 12 months ending January 2008. 4 The expected return can also be calculated with an equation that does the same thing as the table: Expected rate of return¼ r ¼ P 1 r 1 þP 2 r 2 þþ P N r N r ¼ X N i¼1 P i r i 8-1 The second form of the equation is a shorthand expression in which sigma ∑ means “sum up” or add the values of n factors. If i¼ 1 then P i r i ¼ P 1 r 1 ifi¼ 2 then P i r i ¼ P 2 r 2 and so forth until i¼ N the last possible outcome. The symbol X N i¼1 simply says “Go through the following process: First let i¼ 1 and find the first product then let i ¼ 2 and find the second product then continue until each individual product up to N has been found. Add these individual products to find the expected rate of return.” Probability Distributions and Expected Returns Table 8-1 ABCDEFG 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Economy Which Afects Demand 1 Strong Normal Weak Probability of This Demand Occurring 2 Rate of Return If This Demand Occurs 3 Probability of This Demand Occurring 5 Rate of Return If This Demand Occurs 6 Product 2 3 4 Product 5 6 7 Martin Products U.S. Water 0.30 0.40 0.30 1.00 10 80 10 -60 24 4 -18 Expected return 10.0 Expected return 0.30 0.40 0.30 1.00 15 10 5 4.5 4.0 1.5 234 Part 3 Financial Assets

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Probability Distributions of Martin Products’ and U.S. Water’s Rates of Return FIGURE 8-2 Probability of Occurrence a. Martin Products Rate of Return 80 10 0 –60 0.4 0.3 0.2 0.1 Expected Rate of Return Probability of Occurrence b. U.S. Water Rate of Return 15 10 05 0.4 0.3 0.2 0.1 Expected Rate of Return Continuous Probability Distributions of Martin Products’ and U.S. Water’s Rates of Return FIGURE 8-3 Probability Density U.S. Water Martin Products 80 10 0 –60 Expected Rate of Return Rate of Return Note: The assumptions regarding the probabilities of various outcomes have been changed from those in Figure 8-2. There the probability of obtaining exactly 10 was 40 here it is much smaller because there are many possible outcomes instead of just three. With continuous distributionsitismoreappropriatetoaskwhattheprobabilityisofobtainingatleastsomespecifiedrateofreturnthantoaskwhattheprobability is of obtaining exactly that rate. This topic is covered in detail in statistics courses. Chapter 8 Risk and Rates of Return 235

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U.S. Water’s return will be less than 5 or more than 15. However virtually any return within these limits is possible. ThetighterormorepeakedtheprobabilitydistributionsshowninFigure8-3 the more likely the actual outcome will be close to the expected value and con- sequently the less likely the actual return will end up far below the expected return. Thus the tighter the probability distribution the lower the risk. Since U.S. Waterhasarelativelytightdistribution itsactualreturnislikelytobecloser toits 10 expected return than is true for Martin so U.S. Water is less risky. 5 8-2b Measuring Stand-Alone Risk: The Standard Deviation 6 It is useful to measure risk for comparative purposes but risk can be defined and measured in several ways. A common definition that is simple and is satisfactory for our purpose is based on probability distributions such as those shown in Figure8-3:Thetightertheprobabilitydistributionofexpectedfuturereturnsthesmaller the risk of a given investment. According to this definition U.S. Water is less riskythanMartinProductsbecausethereisasmallerchancethattheactualreturn of U.S. Water will end up far below its expected return. We can use the standard deviation pronounced “sigma” to quantify the tightness of the probability distribution. 7 The smaller the standard deviation the tighter the probability distribution and accordingly the lower the risk. We cal- culate Martin’s in Table 8-2. We picked up Columns 1 2 and 3 from Table 8-1. Then in Column 4 we find the deviation of the return in each demand state from theexpectedreturn:Actualreturn–Expected10return.Thedeviationsaresquared and shown in Column 5. Each squared deviation is then multiplied by the relevant probability and shown in Column 6. The sum of the products in Column 6 is the variance of the distribution. Finally we find the square root of the variance—this is Calculating Martin Products’ Standard Deviation Table 8-2 AB C D E F 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Economy Which Afects Demand 1 Strong Normal Weak Rate of Return If This Demand Occurs 3 Deviation Squared 5 Squared Deviation x Prob. 6 Deviation: Actual - 10 Expected Return 4 0.30 0.40 0.30 1.00 Probability of This Demand Occurring 2 80 10 -60 70 0 -70 Variance: Standard deviation square root of variance: Standard deviation expressed as a percentage: 0.2940 0.5422 0.4900 0.0000 0.4900 0.1470 0.0000 0.1470 54.22 5 In this example we implicitly assume that the state of the economy is the only factor that affects returns. In reality many factors including labor materials and development costs influence returns. This is discussed at greater length in the chapters on capital budgeting. 6 This section is relatively technical but it can be omitted without loss of continuity. 7 There are actually two types of standard deviations one for complete distributions and one for situations that involve only a sample. Different formulas and notations are used. Also the standard deviation should be modified if the distribution is not normal or bell-shaped. Since our purpose is simply to get the general idea across we leave the refinements to advanced finance and statistics courses. 236 Part 3 Financial Assets

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the standard deviation and it is shown at the bottom of Column 6 as a fraction and apercentage. 8 The standard deviation is a measure of how far the actual return is likely to deviatefromtheexpectedreturn.Martin’sstandarddeviationis54.2soitsactual return is likely to be quite different from the expected 10. 9 U.S. Water’s standard deviation is 3.9 so its actual return should be much closer to the expected return of 10. The average publicly traded firm’s has been in the range of 20 to 30 in recentyearssoMartinismoreriskythanmoststockswhileU.S.Waterislessrisky. 8-2c Using Historical Data to Measure Risk 10 Inthelastsectionwefoundthemeanandstandarddeviationbasedonasubjective probability distribution. If we had actual historical data instead the standard deviationofreturnscouldbefoundasshowninTable8-3. 11 Becausepastresultsare often repeated in the future the historical is often used as an estimate of future risk. 12 Akeyquestionthatariseswhenhistoricaldataisusedtoforecastthefutureis howfarbackintimeweshouldgo.Unfortunatelythereisnosimpleanswer.Using a longer historical time series has the benefit of giving more information but some of that information may be misleading if you believe that the level of risk in the future is likely to be very different than the level of risk in the past. 8 This formula summarizes what we did in Table 8-2: Standard deviation¼ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X N i¼1 ðr i r Þ 2 P i v u u t 8-2 9 With a normal bell-shaped distribution the actual return should be within one about 68 of the time. 10 Again this section is relatively technical but it can be omitted without loss of continuity. 11 The 4 years of historical data are considered to be a “sample” of the full but unknown set of data and the procedure used to find the standard deviation is different from the one used for probabilistic data. Here is the equation for sample data and it is the basis for Table 8-3: Estimated ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P N t¼1 ðr t r Avg Þ 2 N 1 v u u t 8-2a Here r t “r bar t” denotes the past realized rate of return in Period t and r Avg is the average annual return earned over the last N years. 12 The average return for the past period 10.3 in our example may also be used as an estimate of future returns but this is problematic because the average historical return varies widely depending on the period examined. In our example if we went from 2005 to 2007 we would get a different average from the 10.3. The average historical return stabilizes with more years of data but that brings into question whether data from many years ago is still relevant today. Standard Deviation σ sigma A statistical measure of the variability of a set of observations. Finding Based On Historical Data Table 8-3 AB C D E F 35 36 37 38 39 40 41 42 43 44 45 46 47 48 Year 1 2005 2006 2007 2008 30.0 -10.0 -19.0 40.0 10.3 Average Return 2 Deviation from Average 3 Squared Deviation 4 19.8 -20.3 -29.3 29.8 Variance : 25.4 Variance/N–1 Variance/3: Standard deviation Square root of variance: 8.5 3.9 4.1 8.6 8.9 29.1 Chapter 8 Risk and Rates of Return 237

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All financial calculators and Excel have easy-to-use functions for finding based on historical data. 13 Simply enter the rates of return and press the key marked S or S x to obtain the standard deviation. However neither calculators nor Excel have a built-in formula for finding where probabilistic data are involved. In those cases you must go through the process outlined in Table 8-2. 8-2d Measuring Stand-Alone Risk: The Coefficient of Variation If a choice has to be made between two investments that have the same expected returnsbut different standard deviations most people would choose the one with the lower standard deviation and therefore the lower risk. Similarly given a choice between two investments with the same risk standard deviation but different expected returns investors would generally prefer the investment with the higher expected return. To most people this is common sense—return is “good” and risk is “bad” consequently investors want as much return and as little risk as possible. But how do we choose between two investments if one has thehigherexpectedreturnbuttheotherhasthelowerstandarddeviationTohelp answer that question we use another measure of risk thecoefficient ofvariation CV which is the standard deviation divided by the expected return: Coefficient of variation¼ CV¼ r 8-3 The coefficient of variation shows the risk per unit of return and it provides a more meaningful risk measure when the expected returns on two alternatives are not the same. Since U.S. Water and Martin Products have the same expected return the coeffi- cient of variation is not necessary in this case. Here the firm with the larger standard deviation Martin must have the larger coefficient of variation. In fact the coefficient of variation for Martin is 54.22/10 ¼ 5.42 and the coefficient of variation for U.S. Water is 3.87/10 ¼ 0.39. Thus Martin is about 14 times riskier than U.S. Water on the basis of this criterion. 8-2e Risk Aversion and Required Returns Suppose you inherited 1 million which you plan to invest and then retire on the income. You can buy a 5 U.S. Treasury bill and you will be sure of earning 50000 of interest. Alternatively you can buy stock in RD Enterprises. If RD’s research programs are successful your stock will increase to 2.1 million. How- everiftheresearchisafailurethevalueofyourstockwillbezeroandyouwillbe penniless.YouregardRD’schancesofsuccessorfailureas50-50sotheexpected value of the stock a year from now is 0.50 + 0.52100000 ¼ 1050000. Subtracting the 1 million cost leaves an expected 50000 profit and a 5 rate of return the same as for the T-bill: Expected rate of return ¼ Expected ending value Cost Cost ¼ 1050000 1000000 1000000 ¼ 50000 1000000 ¼ 5 Given the choice of the sure 50000 profit and 5 rate of return and the risky expected 50000profit and 5 return which one would youchoose If you choose the 13 See our tutorials on the text’s web site or your calculator manual for instructions on calculating historical standard deviations. Coefficient of Variation CV The standardized measure of the risk per unit of return calculated as the standard deviation divided by the expected return. 238 Part 3 Financial Assets

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lessriskyinvestmentyouarerisk-averse.Mostinvestorsarerisk-averseandcertainlytheav- erageinvestoriswithregardtohisorher“seriousmoney.”Becausethisisawell-documented fact we assume risk aversion in our discussions throughout the remainder of the book. What are the implications of risk aversion for security prices and rates of return The answer is that other things held constant the higher a security’s risk the higher its required return and if this situation does not hold prices will change to bring about the required condition. To illustrate this point look back at Figure 8-3 and consider again the U.S. Water and Martin Products stocks. Suppose each stock sells for 100 per share and each has an expected rate of return of 10. Investors are averse to risk so under those conditions there would be a general preference for U.S. Water. People with money to invest would bid for U.S. Water and Martin’s stockholders would want to sell and use the money to buy U.S. Water. Buying pressure would quickly drive U.S. Water’s stock up and selling pressure would simultaneously cause Martin’s price to fall. These price changes in turn would change the expected returns of the two securities. Suppose for example that U.S. Water’s stock was bid up from 100 to 125 and Martin’s stock declined from 100 to 77. These price changes would cause U.S. Water’s expected return to fall to 8 and Martin’s return to rise to 13. 14 The difference in returns 13 – 8¼ 5 would be a risk premium RP which represents the additional compensation investors require for bearing Martin’s higher risk. This example demonstrates a very important principle: In a market dominated by risk-averse investors riskier securities compared to less risky securities must have higher expected returns as estimated by the marginal investor. If this situation does not exist buying and selling will occur until it does exist. Later in the chapter we will consider the question of how much higher the returns on risky securities must be after we see how diversification affects the way risk should be measured. Risk Aversion Risk-averse investors dis- like risk and require higher rates of return as an inducement to buy riskier securities. 14 We assume that each stock is expected to pay shareholders 10 a year in perpetuity. The price of this perpetuity canbe foundbydividing theannual cashflow by thestock’s return. Thus ifthe stock’sexpectedreturnis 10 the price must be 10/0.10 ¼ 100. Likewise an 8 expected return would be consistent with a 125 stock price 10/0.08 ¼ 125 and a 13 return with a 77 stock price 10/0.13 ¼ 77. Risk Premium RP The difference between the expected rate of return on a given risky asset and that on a less risky asset. Chapter 8 Risk and Rates of Return 239 Text not available due to copyright restrictions

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SELFTEST What does investment risk mean Set up an illustrative probability distribution table for an investment with probabilities for different conditions returns under those conditions and the expected return. Which of the two stocks graphed in Figure 8-3 is less risky Why Explain why you agree or disagree with this statement: Most investors are risk-averse. How does risk aversion affect rates of return An investment has a 50 chance of producing a 20 return a 25 chance of producing an 8 return and a 25 chance of producing a 12 return. What is its expected return 9 8-3 RISK IN A PORTFOLIO CONTEXT: THE CAPM Inthissectionwediscusstheriskofstockswhentheyareheldinportfoliosrather than as stand-alone assets. Our discussion is based on an extremely important theory the Capital Asset Pricing Model or CAPM that was developed in the 1960s. 15 WedonotattempttocovertheCAPMindetail—ratherwesimplyuseits intuition to explain how risk should be considered in a world where stocks and otherassetsareheldinportfolios.Ifyougoontotakeacourseininvestmentsyou will cover the CAPM in detail. Thus far in the chapter we have considered the riskiness of assets when they are held in isolation. This is generally appropriate for small businesses many real estate investments and capital budgeting projects. However the risk of a stock held in a portfolio is typically lower than the stock’s risk when it is held alone. Since investors dislike risk and since risk can be reduced by holding portfolios most stocks are held in portfolios. Banks pension funds insurance companies mutual funds and other financial institutions are required by law to hold diver- sifiedportfolios.Mostindividualinvestors—atleastthosewhosesecurityholdings constitute a significant part of their total wealth—also hold portfolios. Therefore thefactthatoneparticularstock’spricegoesupordownisnotimportant—whatis important is the return on the portfolio and the portfolio’s risk. Logically then the risk and return of an individual stock should be analyzed in terms of how the security affects the risk and return of the portfolio in which it is held. ToillustratePayUpInc.isacollectionagencythatoperatesnationwidethrough 37 offices. The company is not well known its stock is not very liquid and its earnings have experienced sharp fluctuations in the past. This suggests that Pay Up isriskyandthatitsrequiredrateofreturnrshouldberelativelyhigh.HoweverPay Up’s required return in 2008 and all other years was quite low in comparison to most other companies. This indicates that investors think Pay Up is a low-risk company in spite of its uncertain profits. This counterintuitive finding has to do with diversification and its effect on risk. Pay Up’s earnings rise during recessions whereas most other companies’ earnings decline when the economy slumps. Thus Pay Up’s stockislikeinsurance—itpaysoffwhenotherthingsgobad—soaddingPayUptoa portfolio of “regular” stocks stabilizes theportfolio’s returns and makes it less risky. Capital Asset Pricing Model CAPM A model based on the proposition that any stock’s required rate of return is equal to the risk- free rate of return plus a risk premium that reflects only the risk remaining after diversification. 15 The CAPM was originated by Professor William F. Sharpe in his article “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk” Journal of Finance 1964. Literally thousands of articles exploring various aspects of the CAPM have been published subsequently and it is very widely used in investment analysis. 240 Part 3 Financial Assets

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8-3a Expected Portfolio Returns r p The expected return on a portfolio r p is the weighted average of the expected returns of the individual assets in the portfolio with the weights being the per- centage of the total portfolio invested in each asset : r p ¼ w 1 r 1 þw 2 r 2 þþ w N r N ¼ X N i¼1 w i r i 8-4 Here r i is the expected return on the ith stock the w i ’s are the stocks’ weights or the percentage of the total value of the portfolio invested in each stock and N is the number of stocks in the portfolio. Table8-4canbeusedtoimplementtheequation.Hereweassumethatananalyst estimated returns on the four stocks shown in Column 1 for the coming year as showninColumn2.Supposefurtherthatyouhad100000andyouplannedtoinvest 25000or25ofthetotalineachstock.Youcouldmultiplyeachstock’spercentage weightasshowninColumn4byitsexpectedreturngettheproducttermsinColumn 5 and then sum Column 5 to get the expected portfolio return 10.75. If you added a fifth stock with a higher expected return the portfolio’s expected return would increase and vice versa if you added a stock with a lower expectedreturn.Thekeypointtorememberisthattheexpectedreturnonaportfolioisa weighted average of expected returns on the stocks in the portfolio. Several additional points should be made: 1. The expected returns in Column 2 would be based on a study of some type buttheywouldstillbeessentiallysubjectiveandjudgmentalbecausedifferent analysts could look at the same data and reach different conclusions. There- forethistypeofanalysismustbeviewedwithacriticaleye.Neverthelessitis useful indeed necessary if one is to make intelligent investment decisions. 2. If we added companies such as Delta Airlines and Ford which are generally considered to be relatively risky their expected returns as estimated by the mar- ginalinvestorwouldberelativelyhighotherwiseinvestorswouldsellthemdrive downtheirpricesandforcetheexpectedreturnsabovethereturnsonsaferstocks. 3. After the fact and a year later the actual realized rates of return r i on the individual stocks—the r i or “r-bar” values—would almost certainly be dif- ferentfromtheinitialexpectedvalues.Thatwouldcause theportfolio’sactual return r p to differ from the expected return r p ¼ 10.75. For example Microsoft’s price might double and thus provide a return of þ100 whereas IBMmighthave aterrible yearfallsharplyandhave areturnof 75.Note thoughthatthosetwoeventswouldbeoffsettingsotheportfolio’sreturnstill mightbeclosetoitsexpectedreturneventhoughthereturnsontheindividual stocks were far from their expected values. Expected Return on a Portfolio r p Table 8-4 AB C D E F 52 53 54 55 56 57 58 59 60 61 62 Product: 2 4 5 Stock 1 100.0 100000 10.75 Microsoft IBM GE Exxon Expected Return 2 12.00 11.50 10.00 9.50 Dollars Invested 3 25000 25000 25000 25000 Percent of Total w i 4 25.0 25.0 25.0 25.0 3.000 2.875 2.500 2.375 Expected r p 10.750 Expected Return on a Portfolio r p The weighted average of the expected returns on the assets held in the portfolio. Realized Rate of Return r The return that was actually earned during some past period. The actual return r usually turns out to be different from the expected return r except for riskless assets. Chapter 8 Risk and Rates of Return 241

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8-3b Portfolio Risk Althoughthe expectedreturn on aportfolio is simply the weighted averageof the expected returns on its individual stocks the portfolio’s risk p is not the weighted average of the individual stocks’ standard deviations. The portfolio’s risk is generally smaller than the average of the stocks’ s because diversification lowers the portfolio’s risk. ToillustratethispointconsiderthesituationinFigure8-4.Thebottomsection gives data on Stocks W and M individually and data on a portfolio with 50 in each stock. The left graph plots the data in a time series format and it shows that the returns on the individual stocks vary widely from year to year. Therefore the individual stocks are risky. However the portfolio’s returns are constant at 15 indicatingthatit isnotrisky atall. Theprobability distribution graphs tothe right show the same thing—the two stocks would be quite risky if they were held in isolation but when they are combined to form Portfolio WM they have no risk whatsoever. If you invested all of your money in Stock W you would have an expected returnof15butyouwouldfaceagreatdealofrisk.Thesamethingwouldhold if you invested entirely in Stock M. However if you invested 50 in each stock you would have the same expected return of 15 but with no risk whatsoever. Being rational and averse to risk you and all other rational investors would choose to hold the portfolio not the stocks individually. Returns With Perfect Negative Correlation r¼ 1.0 FIGURE 8-4 ABCDEFG 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 Portfolio WM Stock M Stock W Year Rate of Return -20 15 40 Rate of Return -20 15 40 2004 2005 2006 2007 2008 Avg return Estimated 40.00 -10.00 40.00 -10.00 15.00 -10.00 40.00 -10.00 40.00 15.00 15.00 15.00 15.00 15.00 15.00 15.00 25.00 15.00 25.00 15.00 0.00 Correlation coefcient -1.00 Portfolio WM Stocks W and M held separately 2004 2005 2006 2007 2008 W M Rate of Return -15 0 15 30 45 WM 242 Part 3 Financial Assets

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Stocks W and M can be combined to form a riskless portfolio because their returns move countercyclically to each other—when W’s fall M’s rise and vice versa. The tendency of two variables to move together is called correlation and the correlation coefficient r pronounced “rho” measures this tendency. 16 In statisticaltermswesaythatthereturnsonStocksWandMare perfectlynegatively correlated with r¼ 1.0. The opposite of perfect negative correlation is perfect positive correlation with r¼þ1.0. If returns are not related to one another at all they are said to be independent and r ¼ 0. The returns on two perfectly positively correlated stocks with the same expected return would move up and down together and a portfolio consisting of thesestockswouldbeexactlyasriskyastheindividualstocks.Ifwedrewagraph likeFigure8-4wewouldseejustonelinebecausethetwostocksandtheportfolio would have thesamereturn ateach point intime. Thus diversification iscompletely useless for reducing risk if the stocks in the portfolio are perfectly positively correlated. Weseethenthatwhenstocksareperfectlynegativelycorrelatedr¼ 1.0all risk can be diversified away but when stocks are perfectly positively correlated r¼þ1.0 diversification does no good. In reality most stocks are positively correlated but not perfectly so. Past studies have estimated that on average the correlation coefficient between the returns of two randomly selected stocks is about0.30. 17 Underthisconditioncombiningstocksintoportfoliosreducesriskbutdoes notcompletelyeliminateit. 18 Figure8-5illustratesthispointusingtwostockswhose correlationcoefficientisr¼þ0.35.The portfolio’saverage return is 15 which is the same as the average return for the two stocks but its standard deviation is 18.62whichisbelowthestocks’standarddeviationsandtheiraverage .Again a rational risk-averse investor would be better off holding the portfolio rather than just one of the individual stocks. In our examples we considered portfolios with only two stocks. What would happen if we increased the number of stocks in the portfolio As a rule portfolio risk declines as the number of stocks in a portfolio increases. Ifweaddedenoughpartiallycorrelatedstockscouldwecompletelyeliminate risk In general the answer is no. For an illustration see Figure 8-5 on page 244 which shows that a portfolio’s risk declines as stocks are added. Here are some points to keep in mind about the figure: 1. The portfolio’s risk declines as stocks are added but at a decreasing rate and once40to50stocksareintheportfolioadditionalstocksdolittletoreducerisk. 2. The portfolio’s total risk can be divided into two partsdiversifiable risk and marketrisk. 19 Diversifiableriskistheriskthatiseliminatedbyaddingstocks. Market risk is the risk that remains even if the portfolio holds every stock in Correlation The tendency of two variables to move together. Correlation Coefficient r A measure of the degree of relationship between two variables. 16 The correlation coefficient r can range from +1.0 denoting that the two variables move up and down in perfect synchronization to 1.0 denoting that the variables move in exactly opposite directions. A correlation coefficient of zero indicates that the two variables are not related to each other—that is changes in one variable are independent of changes in the other. It is easy to calculate correlation coefficients with a financial calculator. Simply enter the returns on the two stocks and press a key labeled “r.” For W and Mr¼ 1.0. See our tutorial on the text’s web site or your calculator manual for the exact steps. Also note that the correlation coefficient is often denoted by the term r. We use r here to avoid confusion with r used to denote the rate of return. 17 A study by Chan Karceski and Lakonishok 1999 estimated that the average correlation coefficient between two randomly selected stocks was 0.28 while the average correlation coefficient between two large-company stocks was 0.33. The time period of their sample was 1968 to 1998. See Louis K. C. Chan Jason Karceski and Josef Lakonishok “On Portfolio Optimization: Forecasting Covariance and Choosing the Risk Model” The Review of Financial Studies Vol. 12 no. 5 Winter 1999 pp. 937–974. 18 If we combined a large number of stocks withr¼ 0 we could form a riskless portfolio. However there are not many stocks with r ¼ 0—stocks’ returns tend to move together not to be independent of one another. 19 Diversifiable risk is also known as company-specificor unsystematic risk. Market risk is also known as nondiversifi- able or systematic or beta risk it is the risk that remains in the portfolio after diversification has eliminated all company-specific risk. Diversifiable Risk That part of a security’s risk associated with ran- dom events it can be eliminated by proper diversification. This risk is also known as company- specific or unsystematic risk. Market Risk The risk that remains in a portfolio after diversifica- tion has eliminated all company-specific risk. This risk is also known as nondiversifiable or sys- tematic or beta risk. Chapter 8 Risk and Rates of Return 243

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the market. Market risk is the risk that we discussed in the opening vignette and in our discussion of Figure 8-1. 3. Diversifiable risk is caused by such random unsystematic events as lawsuits strikes successful and unsuccessful marketing and RD programs the win- ning or losing of a major contract and other events that are unique to the particular firm. Because these events are random their effects on a portfolio can be eliminated by diversification—badevents for one firm willbe offset by good events for another. Market risk on the other hand stems from factors that systematically affect most firms: war inflation recessions high interest rates and other macro factors. Because most stocks are affected by macro factors market risk cannot be eliminated by diversification. 4. If we carefully selected the stocks included in the portfolio rather than adding them randomly the graph would change. In particular if we chose stocks with low correlations with one another and with low stand-alone risk the portfolio’s risk would decline faster than if random stocks were added. The reverse would hold if we added stocks with high correlations and high s. 5. Most investors are rational in the sense that they dislike risk other things held constant. That being the case why would an investor ever hold one or a few stocksWhynotholdamarketportfolioconsistingofallstocksThereareseveral reasons.Firsthigh administrativecostsandcommissionswouldmorethanoffset Returns with Partial Correlation r¼þ 0.35 FIGURE 8-5 ABCDEFG 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 Rate of Return -20 15 40 Rate of Return -20 15 40 Portfolio WY Stocks W and Y held separately Portfolio WY Stock Y Stock W Year 2004 2005 2006 2007 2008 Avg return Estimated 40.00 -10.00 35.00 -5.00 15.00 40.00 15.00 -5.00 -10.00 35.00 40.00 2.50 15.00 -7.50 25.00 15.00 22.64 15.00 22.64 15.00 18.62 Correlation coefcient 0.35 2004 2005 2006 2007 2008 W Y Rate of Return -15 0 15 30 45 WY Market Portfolio A portfolio consisting of all stocks. 244 Part 3 Financial Assets

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the benefits for individual investors. Second index funds can diversify for investors and many individuals can and do get broad diversification through thesefunds.Thirdsomepeoplethinkthattheycanpickstocksthatwill“beatthe market”sotheybuythemratherthanthebroadmarket.Andfourthsomepeople canthroughsuperioranalysisbeatthemarketsotheyfindandbuyundervalued stocks and sell overvalued ones and in the process cause most stocks to be properly valued with their expected returns consistent with their risks. 6. One key question remains: How should the risk of an individual stock be measured The standard deviation of expected returns is not appropriate because it includes risk that can be eliminated by holding the stock in a portfolio. How then should we measure a stock’s risk in a world where most people hold portfolios That’s the subject of the next section. 8-3c Risk in a Portfolio Context: The Beta Coefficient When a stock is held by itself its risk can be measured by the standard deviation of its expected returns. However is not appropriate when the stock is held in a portfolioasstocksgenerallyare.Sohowdowe measure astock’srelevantrisk in a portfolio context Firstnotethatallriskexceptthatrelatedtobroadmarketmovementscanand will be diversified away by most investors—rational investors will hold enough stocks to move down the risk curve in Figure 8-6 to the point where only market risk remains in their portfolios. The risk that remains once a stock is in a diversified portfolio is its contribution to the portfolio’s market risk and that risk can be measured by the extent to which the stock moves up or down with the market. The tendency of a stock to move with the market is measured by its beta coefficient b. Ideally when estimating a stock’s beta we would like to have a crystalballthattellsushowthestockisgoingtomoverelativetotheoverallstock marketinthefuture.Butsincewecan’tlookintothefutureweoftenusehistorical data and assume that the stock’s historical beta will give us a reasonable estimate of how the stock will move relative to the market in the future. To illustrate the use of historical data consider Figure 8-7 which shows the historical returns on three stocks and a market index. In Year 1 “the market” as definedbyaportfoliocontainingallstockshadatotalreturndividendyieldplus capitalgainsyieldof10asdidthethreeindividualstocks.InYear2themarket wentupsharplyanditsreturnwas20.StocksHforhighsoaredby30Afor average returned 20 the same as the market and L for low returned 15. In Year3themarketdroppedsharplyitsreturnwas 10.Thethreestocks’returns also fell—H’s return was 30 A’s was 10 and L broke even with a 0 return. In Years 4 and 5 the market returned 0 and 5 respectively and the three stocks’ returns were as shown in the figure. A plot of the data shows that the three stocks moved up or down with the market but thatH was twice asvolatileasthe market A was exactlyasvolatileas the market and L had only half the market’s volatility. It is apparent that the steeperastock’slinethegreateritsvolatilityandthusthelargeritslossinadown market.Theslopesofthelinesarethestocks’betacoefficients.Weseeinthefigurethat the slope coefficient for H is 2.0 for A it is 1.0 and for L it is 0.5. 20 Thus beta measures a given stock’s volatility relative to the market and an average stock’s beta b A ¼ 1.0. Relevant Risk The risk that remains once a stock is in a diversified portfolio is its contribution to the portfolio’s market risk. It is measured by the extent to which the stock moves up or down with the market. Beta Coefficient b A metric that shows the extent to which a given stock’s returns move up and down with the stock market. Beta thus mea- sures market risk. 20 For more on calculating betas see Brigham and Daves Intermediate Financial Management 9th ed. Mason OH: Thomson/South-Western 2007 pp. 55–58 and pp. 89–94. Average Stock’s Beta b A By definition b A ¼ 1 because an average-risk stock is one that tends to move up and down in step with the general market. Chapter 8 Risk and Rates of Return 245

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Stock A is defined as an average-risk stock because it has a beta of b ¼ 1.0 and thus moves up and down in step with the general market. Thus an average stock will in general move up by 10 when the market moves up by 10 and fall by 10 when the market falls by 10. A large portfolio of such b¼ 1.0 stocks would 1haveallofitsdiversifiableriskremovedbut2wouldstillmoveupanddown with the broad market averages and thus have a degree of risk. Stock H which has b ¼ 2.0 is twice as volatile as an average stock which means that it istwice as risky. The value of a portfolio consisting of b¼ 2.0 stocks could double—or halve—in a short time and if you held such a portfolio you could quickly go from being a millionaire to being a pauper. Stock L on the other hand with b ¼ 0.5 is only half as volatile as the average stock and a portfolio of such stocks would rise and fall only half as rapidly as the market. Thus its risk would be half that of an average-risk portfolio with b ¼ 1.0. Betas for literally thousands of companies are calculated and published by MerrillLynchValueLineYahooGoogleandnumerousotherorganizationsand the beta coefficients of some well-known companies are shown in Table 8-5. Most stocks have betas in the range of 0.50 to 1.50 and the average beta for all stocks is 1.0 which indicates that the average stock moves in sync with the market. 21 Effects of Portfolio Size on Risk for a Portfolio of Randomly Selected Stocks FIGURE 8-6 35 30 25 15 10 5 0 20.4 10 1 20 30 40 2000+ Number of Stocks in the Portfolio σ M Portfolio’s Total Risk: Declines as Stocks Are Added Portfolio’s Market Risk: Remains Constant Portfolio’s Diversifable Risk: Could Be Reduced by Adding More Stocks Portfolio’s Risk p Portfolio Risk σ p Minimum Attainable Risk in a Portfolio of Average Stocks Note: This graph assumes that stocks in the portfolio are randomly selected from the universe of large publicly-traded stocks listed on the NYSE. 21 While fairly uncommon it is possible for a stock to have a negative beta. In that case the stock’s returns would tend to rise whenever the returns on other stocks fell. 246 Part 3 Financial Assets

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If a stock whose beta is greater than 1.0 say 1.5 is added to a b p ¼ 1.0 portfoliotheportfolio’sbetaandconsequentlyitsriskwillincrease.Converselyif a stock whose beta is less than 1.0 is added to a b p ¼ 1.0 portfolio the portfolio’s beta and risk will decline. Thus because a stock’s beta reflects its contribution to the riskiness of a portfolio beta is the theoretically correct measure of the stock’s riskiness. Betas: Relative Volatility of Stocks H A and L FIGURE 8-7 AB C D E F 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 Calculating beta: 1. Rise-Over-Run. Divide the vertical axis change that results from a given change on the horizontal axis i.e. the change in the stock’s return divided by the changes in the market return. For Stock H when the market rises from –10 to +20 or by 30 the stock’s return goes from –30 to +30 or by 60. Thus beta H by the rise-over-run method is 60/30 2.0. In the same way we fnd beta A to be 1.0 and beta L to be 0.5. This procedure is easy in our example because all of the points lie on a straight line but if the points were scattered around the trend line we could not calculate an exact beta. 2. Financial Calculator. Financial calculators have a built-in function that can be used to calculate beta. The procedure difers somewhat from calculator to calculator. See our tutorial on the text’s web site for instructions on several calculators. 3. Excel. Excel’s Slope function can be used to calculate betas. Here are the functions for our three stocks: Beta H 2.0 SLOPEC163:C164B163:B164 Beta A 1.0 SLOPED163:D164B163:B164 Beta L 0.5 SLOPEE163:E164B163:B164 1 2 3 4 5 10.0 20.0 -10.0 0.0 5.0 -30.0 -20.0 -10.0 10.0 20.0 30.0 -10.0 10.0 20.0 30.0 0 Return on Market High: b 2.0 Average: b 1.0 Low: b 0.5 Return on Stocks -20.0 Year r M r H r A r L 10.0 30.0 -30.0 -10.0 0.0 10.0 20.0 -10.0 0.0 5.0 10.0 15.0 0.0 5.0 7.5 Chapter 8 Risk and Rates of Return 247

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We can summarize our discussion up to this point as follows: 1. A stock’s risk has two components diversifiable risk and market risk. 2. Diversifiable risk can be eliminated and most investors do eliminate it either byholdingverylargeportfoliosorbybuyingshares inamutualfund.Weare left then with market risk which is caused by general movements in the stock market and reflects the fact that most stocks are systematically affected by events such as wars recessions and inflation. Market risk is the only risk that should matter to a rational diversified investor. 3. Investors must be compensated for bearing risk—the greater the risk of a stock the higher its required return. However compensation is required only for risk that cannot be eliminated by diversification. If risk premiums existed on a stock due to its diversifiable risk that stock would be a bargain to well- diversified investors. They would start buying it and bid up its price and the stock’s final equilibrium price would be consistent with an expected return that reflected only its market risk. To illustrate this point suppose half of Stock B’s risk is market risk it occurs because the stock moves up and down with the market while the otherhalfisdiversifiable.YouarethinkingofbuyingStockBandholdingitin a one-stock portfolio so you would be exposed to all of its risk. As com- pensation for bearing so much risk you want a risk premium of 8 over the 6 T-bond rate so your required return is r A ¼ 6 þ 8 ¼ 14. But other investorsincludingyourprofessorarewelldiversified.Theyarealsolooking at Stock B but they would hold it in diversified portfolios eliminate its diversifiable risk and thus be exposed to only half as much risk as you. Therefore their required risk premium would be half as large as yours and their required rate of return would be r B ¼ 6 þ 4 ¼ 10. If the stock was priced to yield the 14 you require those diversified investors including your professor would buy it push its price up and its yield down and prevent you from getting the stock at a price low enough to provide the 14 return. In the end you would have to accept a 10 return or keep your money in the bank. 4. Themarketriskofastockismeasuredbyitsbetacoefficientwhichisanindex of the stock’s relative volatility. Here are some benchmark betas: b ¼ 0.5: Stock is only half as volatile or risky as an average stock. b ¼ 1.0: Stock is of average risk. b ¼ 2.0: Stock is twice as risky as an average stock. Illustrative List of Beta Coefficients Table 8-5 Stock Beta Merrill Lynch 1.35 Best Buy 1.25 eBay 1.20 General Electric 0.95 Microsoft 0.95 ExxonMobil 0.90 Heinz 0.80 Coca-Cola 0.75 FPL Group 0.75 Procter Gamble 0.65 Source: Adapted from Value Line February 2008. 248 Part 3 Financial Assets

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5. Aportfolio consisting oflow-betastocks willalso have alowbeta because the beta of a portfolio is a weighted average of its individual securities’ betas found using this equation: b p ¼ w 1 b 1 þw 2 b 2 þþ w N b N ¼ X N i¼1 w i b i : 8-5 Here b p is the beta of the portfolio and it shows how volatile the portfolio is relative to the market w i is the fraction of the portfolio invested in the ith stock and b i is the beta coefficient of the ith stock. To illustrate if an investor holds a 100000 portfolio consisting of 33333.33 invested in each of three stocks and if each of the stocks has a beta of 0.70 the portfolio’s beta will be b p ¼ 0.70: b p ¼ 0:333ð0:70Þþ0:333ð0:70Þþ0:333ð0:70Þ¼ 0:70: Such a portfolio would be less risky than the market so it should experience relatively narrow price swings and have relatively small rate-of-return fluc- tuations. In terms of Figure 8-7 the slope of its regression line would be 0.70 which is less than that for a portfolio of average stocks. Now suppose one of the existing stocks is sold and replaced by a stock with b i ¼ 2.00. This action will increase the portfolio’s beta from b p1 ¼ 0.70 to b p2 ¼ 1.13: b p2 ¼ 0:333ð0:70Þþ0:333ð0:70Þþ0:333ð2:00Þ¼ 1:13: Had a stock with b i ¼ 0.20 been added the portfolio’s beta would have declined from 0.70 to 0.53. Adding a low-beta stock would therefore reduce the portfolio’s riskiness. Consequently changing the stocks in a portfolio can change the riskiness of that portfolio. 6. Because a stock’s beta coefficient determines how the stock affects the riski- nessofadiversifiedportfoliobetaisintheorythemostrelevantmeasureofa stock’s risk. SELFTEST Explain the following statement: An asset held as part of a portfolio is generally less risky than the same asset held in isolation. What is meant by perfect positive correlation perfect negative correlation and zero correlation In general can the riskiness of a portfolio be reduced to zero by increasing the number of stocks in the portfolio Explain. What is an average-risk stock What is the beta of such a stock Why is it argued that beta is the best measure of a stock’s risk If you plotted a particular stock’s returns versus those on the SP 500 Index over the past five years what would the slope of the regression line indicate about the stock’s risk An investor has a two-stock portfolio with 25000 invested in Stock X and 50000 invested in Stock Y. X’s beta is 1.50 and Y’s beta is 0.60. What is the beta of the investor’s portfolio 0.90 Chapter 8 Risk and Rates of Return 249

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GLOBAL PERSPECTIVES THE BENEFITS OF DIVERSIFYING OVERSEAS The increasing availability of international securities is making it possible to achieve a better risk-return trade-off than could be obtained by investing only in U.S. securities. So investing overseas might result in a portfolio with less risk but a higher expected return. This result occurs because of low correlations between the returns on U.S. and inter- national securities along with potentially high returns on overseas stocks. Figure 8-6 presented earlier demonstrated that an investor can reduce the risk of his or her portfolio by holdinganumberofstocks. Thefigurethatfollowssuggests that investors may be able to reduce risk even further by holding a portfolio of stocks from all around the world given the fact that the returns on domestic and interna- tional stocks are not perfectly correlated. Even though foreign stocks represent roughly 60 of the worldwide equity market and despite the apparent benefits from investing overseas the typical U.S. investor stillputslessthan10ofhisorher moneyinforeign stocks. One possible explanation for this reluctance to invest overseas is that investors prefer domestic stocks because of lower transactions costs. However this explanation is questionable because recent studies reveal that investors buy and sell overseas stocks more frequently than they trade their domestic stocks. Other explanations for the domestic bias include the additional risks from investing overseas for example exchange rate risk and the fact that the typical U.S. investor is uninformed about international investments and/or thinks that international investments are extremely risky. It has been argued that world capital markets have become more integrated causing the corre- lation of returns between different countries to increase which reduces the benefits from international diversifica- tion. In addition U.S. corporations are investing more internationally providing U.S. investors with international diversification even if they purchase only U.S. stocks. Whatever the reason for their relatively small holdings of international assets our guess is that in the future U.S. investors will shift more of their assets to overseas investments. U.S. Stocks U.S. and International Stocks Number of Stocks in the Portfolio Portfolio Risk σ p Source:For furtherreadingseealsoKennethKasa “MeasuringtheGainsfromInternationalPortfolioDiversification” Federal Reserve Bank of San Francisco Weekly Letter Number 94–14 April 8 1994. 250 Part 3 Financial Assets

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8-4 THE RELATIONSHIP BETWEEN RISK AND RATES OF RETURN TheprecedingsectiondemonstratedthatundertheCAPMtheorybetaisthemost appropriate measure of a stock’s relevant risk. The next issue is this: For a given level of risk as measured by beta what rate of return is required to compensate investors for bearing that risk To begin let us define the following terms: r i ¼ expected rate of return on the i th stock. r i ¼ requiredrate ofreturnonthe i th stock.Notethat ifr i islessthan r i the typical investor will not purchase this stock or will sell it if he orsheownsit.Ifr i isgreaterthanr i theinvestorwillpurchasethe stock because it looks like a bargain. Investors will be indifferent if r i ¼ r i . Buying and selling by investors tends to force the expected return to equal the required return although the two can differ from time to time before the adjustment is completed. r ¼ realizedafter-the-factreturn.Apersonobviouslydoesnotknowr at the time he or she is considering the purchase of a stock. r RF ¼ risk-freerateofreturn.Inthiscontextr RF isgenerallymeasuredby the return onU.S.Treasury securities.Some analysts recommend that short-term T-bills be usedothers recommend long-term T-bonds.WegenerallyuseT-bondsbecausetheirmaturityiscloser to the average investor’s holding period of stocks. b i ¼ betacoefficientoftheithstock.Thebetaofanaveragestockisb A ¼1.0. r M ¼ required rate of return on a portfolio consisting of all stocks which is called the market portfolio.r M is also the required rate of return on an average b A ¼ 1.0 stock. RP M ¼ r M –r RF ¼ riskpremiumon “themarket”andthepremiumonan average stock. This is the additional return over the risk-free rate requiredtocompensateanaverageinvestorforassuminganaverage amount ofrisk. Average risk means a stock where b i ¼ b A ¼ 1.0. RP i ¼ r M – r RF b i ¼ RP M b i ¼ risk premium on the ith stock. A stock’s risk premium will be less than equal to or greater than the premium on an average stock RP M depending on whether its betaislessthanequaltoorgreaterthan1.0.Ifb i ¼b A ¼1.0then RP i ¼ RP M . The market risk premium RP M shows the premium that investors require forbearingtheriskofanaveragestock.Thesizeofthispremiumdependsonhow risky investors think the stock market is and on their degree of risk aversion. Let us assume that at the current time Treasurybonds yield r RF ¼ 6and an average shareofstockhasarequiredrateofreturnofr M ¼11.Thereforethemarketrisk premium is 5 calculated as follows: RP M ¼ r M r RF ¼ 11 6¼ 5 It should be noted that the risk premium of an average stock r M – r RF is actually hard to measure because it is impossible to obtain a precise estimate of the expectedfuturereturnofthemarketr M . 22 Giventhedifficultyofestimatingfuture Market Risk Premium RP M The additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk. 22 Thisconceptaswell asotheraspectsofthe CAPMis discussedinmoredetailinChapter3of EugeneF. Brigham and Philip R. Daves Intermediate Financial Management 9th ed. Mason OH: Thomson/South-Western 2007. That chapter also discusses the assumptions embodied in the CAPM framework. Some of those assumptions are unrealistic and because of this the theory does not hold exactly. Chapter 8 Risk and Rates of Return 251

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market returns analysts often look to historical data to estimate the market risk premium. Historical data suggest that the market risk premium varies somewhat from year to year due to changes in investors’ risk aversion but that it has gen- erally ranged from 4 to 8. While historical estimates might be a good starting point for estimating the market risk premium those estimates would be misleading if investors’ attitudes toward risk changed considerably over time. See “Estimating the Market Risk Premium” box above. Indeed many analysts have argued that the market risk premium has fallen in recent years. If this claim is correct the market risk pre- mium is considerably lower than one based on historical data. Theriskpremiumonindividualstocksvariesinasystematicmannerfromthe market risk premium. For example if one stock is twice as risky as another stock as measured by their beta coefficients its risk premium should be twice as high. Therefore if we know the market risk premium RP M and the stock’s beta b i we can find its risk premium as the product RP M b i . For example if beta for Stock L ¼ 0.5 and RP M ¼ 5 RP L will be 2.5: ESTIMATING THE MARKET RISK PREMIUM The Capital Asset Pricing Model CAPM is more than a theory describing the trade-off between risk and return—it is also widely used in practice. As we will see later investors use the CAPM to determine the discount rate for valuing stocksandcorporatemanagersuseittoestimatethecostof equity capital. The market risk premium is a key component of the CAPManditshouldbethedifferencebetweenthe expected future return on the overall stock market and the expected future return on a riskless investment. However we cannot obtain investors’ expectations instead academicians and practitioners often use a historical risk premium as a proxy for the expected risk premium. The historical premium is foundbytakingthedifferencebetweentheactualreturnon the overall stock market and the risk-free rate during a number of different years and then averaging the annual results.MorningstarthroughitsrecentpurchaseofIbbotson Associates may provide the most comprehensive estimates of historical risk premiums. It reports that the annual pre- miums have averaged 7.1 over the past 82 years. However there are three potential problems with his- torical risk premiums. First what is the proper number of years over which to compute the average Morningstar goes back to 1926 when good data first became available but that is an arbitrary choice and the starting and ending points make a major difference in the calculated premium. Secondhistoricalpremiumsarelikelytobemisleadingat timeswhenthemarketriskpremiumischanging.Toillustrate the stock market was very strong from 1995 through 1999 in part because investors were becoming less risk-averse which means that they applied a lower risk premium when they valued stocks. The strong market resulted in stock returns of about 30peryearandwhenbondyieldsweresubtractedfrom the high stock returns the calculated risk premiums averaged 22.3 a year. When those high numbers were added to data from prior years they caused the long-run historical risk pre- mium as reported by Morningstar to increase. Thus a declining “true” risk premium led to very high stock returns which in turn led to an increase in the calculated historical risk premium. That’s a worrisome result to say the least. The third concern is that historical estimates may be biased upward because they include only the returns of firms that have survived—they do not reflect the losses incurred on investments in failed firms. Stephen Brown William Goetzmann and Stephen Ross discussed the implications of this “survivorship bias” in a 1995 Journal of Finance article. Putting these ideas into practice Tim Koller Marc Goedhart and David Wessels recently suggested that survivorship bias increases historical returns by 1 to 2 a year. Therefore they suggest that practitioners subtract 1 to 2 from the historical estimates to obtain the risk pre- mium used in the CAPM. Sources: Stocks Bonds Bills and Inflation: Valuation Edition 2008 Yearbook Chicago: Morningstar Inc. 2008 Stephen J. Brown William N. Goetzmann and Stephen A. Ross “Survival” Journal of Finance Vol. 50 no. 3 July 1995 pp. 853–873 and Tim Koller Marc Goedhart and David Wessels Valuation: Measuring and Managing the Value of Companies 4th edition New York: McKinsey Company 2005. Risk premium for Stock L ¼ RP i ¼ðRP M Þb i ¼ð5Þð0:5Þ ¼ 2:5 8-6 252 Part 3 Financial Assets

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As the discussion in Chapter 6 implied the required return for any stock can be found as follows: Required return on a stock ¼ Risk-free returnþPremium for the stock 0 s risk Here the risk-free return includes a premium for expected inflation and if we assume that the stocks under consideration have similar maturities and liquidity the required return on Stock L can be found using the Security Market Line SML equation: Required return on Stock L ¼ Risk-free return + Market risk premium Stock L 0 s beta r L ¼ r RF þðr M r RF Þb L ¼ r RF þðRP M Þb L ¼ 6þð11 6Þð0:5Þ ¼ 6þ2:5 ¼ 8:5 8-7 Stock H had b H ¼ 2.0 so its required rate of return is 16: r H ¼ 6þð5Þ2:0¼ 16 An average stock with b¼ 1.0 would have a required return of 11 the same as the market return: r A ¼ 6þð5Þ1:0¼ 11¼ r M The SML equation is plotted in Figure 8-8 using the data shown below the graph on Stocks L A and H and assuming that r RF ¼ 6 and r M ¼ 11. Note the following points: 1. Requiredratesofreturnareshownontheverticalaxiswhileriskasmeasured by beta is shown on the horizontal axis. This graph is quite different from the one shown in Figure 8-7 where we calculated betas. In the earlier graph the returns on individual stocks were plotted on the vertical axis and returns on the market index were shown on the horizontal axis. The betas found in Figure 8-7 were then plotted as points on the horizontal axis of Figure 8-8. 2. Risklesssecuritieshaveb i ¼0sothereturnontherisklessassetr RF ¼6.0is shown as the vertical axis intercept in Figure 8-8. 3. The slope of the SML in Figure 8-8 can be found using the rise-over-run procedure. When beta goes from 0 to 1.0 the required return goes from 6 to 11or5sotheslopeis5/1.0¼5.Thusa1-unitincreaseinbetacauses a 5 increase in the required rate of return. 4. The slope of the SML reflects the degree of risk aversion in the economy—the greatertheaverageinvestor’sriskaversionathesteepertheslopeoftheline and b the greater the risk premium for all stocks—hence the higher the required rate of return on all stocks. Both the SML and a company’s position on it change over time due to changes in interest rates investors’ risk aversion and individual companies’ betas. Such changes are discussed in the following sections. 8-4a The Impact of Expected Inflation As we discussed in Chapter 6 interest amounts to “rent” on borrowed money or the price ofmoney. Thus r RF isthe price ofmoney toa riskless borrower. We also Security Market Line SML Equation An equation that shows the relationship between risk as measured by beta and the required rates of return on individual securities. Chapter 8 Risk and Rates of Return 253

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saw that the risk-free rate as measured by the rate on U.S. Treasury securities is called the nominal or quoted rate and it consists of two elements: 1 a real inflation-free rate of return r and 2 an inflation premium IP equal to the antici- pated rate of inflation. 23 Thus r RF ¼ r + IP. The real rate on long-term Treasury bondshashistoricallyrangedfrom2to4withameanofabout3.Therefore if no inflation were expected long-term Treasury bonds would yield about 3. However as the expected rate of inflation increases a premium must be added to the real risk-free rate of return to compensate investors for the loss of purchasing powerthatresults from inflation.Thereforethe 6r RF showninFigure 8-8 might be thought of as consisting of a 3 real risk-free rate of return plus a 3 inflation premium: r RF ¼ r + IP ¼ 3 + 3 ¼ 6. The Security Market Line SML FIGURE 8-8 AB C D E F I H G 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 Beta Key Inputs 0.0 0.5 1.0 1.5 2.5 2.0 Required Rate of Return 6.0 11.0 5.0 r RF r M RP M r M – r RF Riskless asset: Stock L: Stock A: Stock H: 0.0 0.5 1.0 2.0 6.00 8.50 11.00 16.00 r RF 6.0 r L 8.5 r A r M 11.0 r H 16.0 H’s Risk Premium L’s Risk Premium Risk-Free Return r RF Market Risk Premium RP M . Also Stock A’s Risk Premium Beta Coefcient r i r RF + RP M b i SML r RF + RP M x b i r i 23 Long-term Treasury bonds also contain a maturity risk premium MRP. We include the MRP in r to simplify the discussion. 254 Part 3 Financial Assets

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If the expected inflation rate rose by 2 to 3 + 2 ¼ 5 r RF would rise to 8. Such a change is shown in Figure 8-9. Notice that the increase in r RF leads to anequalincreaseintheratesofreturnonallriskyassetsbecausethesameinflation premium is built into required rates of return on both riskless and risky assets. 24 Therefore the rate of return on our illustrative average stock r A increases from 11 to 13. Other risky securities’ returns also rise by two percentage points. 8-4b Changes in Risk Aversion The slope of the SML reflects the extent to which investors are averse to risk—the steeper the slope of the line the more the average investor requires as compen- sation for bearing risk. Suppose investors were indifferent to risk that is they were not at all risk-averse. If r RF was 6 risky assets would also have a required return of 6 because if there were no risk aversion there would be no risk pre- mium. In that case the SML would plot as a horizontal line. However because investorsarerisk-aversethereisariskpremiumandthegreatertheriskaversion the steeper the slope of the SML. 24 Recall that the inflation premium for any asset is the average expected rate of inflation over the asset’s life. Thus in this analysis we must assume that all securities plotted on the SML graph have the same life or that the expected rate of future inflation is constant. It should also be noted that r RF in a CAPM analysis can be proxied by either a long-term rate the T-bond rateora short-termratetheT-billrate. Traditionally theT-billrate wasusedbut inrecentyearstherehas beena movement toward use of the T-bond rate because there is a closer relationship between T-bond yields and stocks’ returns than between T-bill yields and stocks’ returns. See Stocks Bonds Bills and Inflation: Valuation Edition 2008 Yearbook Chicago: Morningstar Inc. 2008 for a discussion. Shift in the SML Caused by an Increase in Expected Inflation FIGURE 8-9 0 0.5 1.0 1.5 2.0 Risk b i r A2 r M2 13 r A1 r M1 11 r RF2 8 Required Rate of Return r RF1 6 r 3 Original IP 3 Increase in Anticipated Infation IP 2 Real Risk-Free Rate of Return r SML 2 8 + 5b i SML 1 6 + 5b i Chapter 8 Risk and Rates of Return 255

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Figure 8-10 illustrates an increase in risk aversion. The market risk premium rises from 5 to 7.5 causing r M to rise from r M1 ¼ 11 to r M2 ¼ 13.5. The returns on other risky assets also rise and the effect of this shift in risk aversion is morepronouncedonriskiersecurities.ForexampletherequiredreturnonStockL with b A ¼ 0.5 increases by only 1.25 percentage points from 8.5 to 9.75 whereas the required return on a stock with a beta of 1.5 increases by 3.75 per- centage points from 13.5 to 17.25. 8-4c Changes in a Stock’s Beta Coefficient As we will see later in the book a firm can influence its market risk hence its beta throughchangesinthecompositionofitsassetsandthroughchangesintheamount of debt it uses. A company’s beta can also change asaresult of external factorssuch as increased competition in its industry and expiration of basic patents. When such changes occur the firm’s required rate of return also changes and as we will see in Chapter 9 this change will affect its stock price. For example consider Allied Food Products with a beta of 1.48. Now suppose some action occurred that caused Allied’sbetatoincreasefrom1.48to2.0.IftheconditionsdepictedinFigure8-8held Allied’s required rate of return would increase from 13.4 to 16: r 1 ¼ r RF þðr M r RF Þb i ¼ 6þð11 6Þ1:48 ¼ 13:4 to r 2 ¼ 6þð11 6Þ2:0 ¼ 16:0 Shift in the SML Caused by Increased Risk Aversion FIGURE 8-10 0 0.5 1.0 1.5 2.0 Risk b i r A2 r M2 13.5 r RF 6 Required Rate of Return New Market Risk Premium r M2 – r RF RP M2 RP A2 7.5 Original Market Risk Premium r M1 – r RF 5 r L1 8.5 r L2 9.75 r A1 r M1 11 17.25 SML 2 6 + 7.5b i SML 1 6 + 5b i 256 Part 3 Financial Assets

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As we will see in Chapter 9 this change would have a negative effect on Allied’s stock price. 25 SELFTEST Differentiate between a stock’s expected rate of return r required rate of return r and realized after-the-fact historical return r . Which would have to be larger to induce you to buy the stock r or r At a given point in time would r r and r typically be the same or different Explain. What are the differences between the relative volatility graph Figure 8-7 where “betas are made” and the SML graph Figure 8-8 where “betas are used” Explain how both graphs are constructed and what information they convey. What would happen to the SML graph in Figure 8-8 if expected inflation increased or decreased What happens to the SML graph when risk aversion increases or decreases What would the SML look like if investors were indifferent to risk that is if they had zero risk aversion How can a firm influence the size of its beta Astockhas a betaof 1.2. Assume that the risk-freerate is 4.5 andthe market risk premium is 5. What is the stock’srequiredrateofreturn 10.5 8-5 SOME CONCERNS ABOUT BETA AND THE CAPM The Capital Asset Pricing Model CAPM is more than just an abstract theory described in textbooks—it has great intuitive appeal and is widely used by ana- lysts investors and corporations. However a number of recent studies have raised concerns about its validity. For example a study by Eugene Fama of the University of Chicago and Kenneth French of Dartmouth found no historical relationship between stocks’ returns and their market betas confirming aposition long held by some professors and stock market analysts. 26 As an alternative to the traditional CAPM researchers and practitioners are developing models with more explanatory variables than just beta. These multi- variable models represent an attractive generalization of the traditional CAPM model’s insight that market risk—risk that cannot be diversified away—underlies thepricingofassets.Inthemultivariablemodelsriskisassumedtobecausedbya number of different factors whereas the CAPM gauges risk only relative to returns on the market portfolio. These multivariable models represent a poten- tially important step forward in finance theory they also have some deficiencies 25 The concepts covered in this chapter are obviously important to investors but they are also important for managers in two key ways. First as we will see in the next chapter the risk of a stock affects the required rate of return on equity capital and that feeds directly into the important subject of capital budgeting. Second and also related to capital budgeting the “true” risk of individual projects is impacted by their correlation with the firm’s other projects and with other assets that the firm’s stockholders might hold. We will discuss these topics in later chapters. 26 See Eugene F. Fama and Kenneth R. French “The Cross-Section of Expected Stock Returns” Journal of Finance Vol. 47 1992 pp. 427–465 and Eugene F. Fama and Kenneth R. French “Common Risk Factors in the Returns on Stocks and Bonds” Journal of Financial Economics Vol. 33 1993 pp. 3–56. They found that stock returns are related to firm size and market/book ratios. Small firms and firms with low market/book ratios had higher returns however they found no relationship between returns and beta. Kenneth French’s web site http://mba.tuck.dartmouth. edu/pages/faculty/ken. french/index.html is an excellent resource for information regarding factors related to stock returns. Chapter 8 Risk and Rates of Return 257

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whenappliedinpractice.AsaresultthebasicCAPMisstillthemostwidelyused method for estimating required rates of return on stocks. SELFTEST Have there been any studies that question the validity of the CAPM Explain. 8-6 SOME CONCLUDING THOUGHTS: IMPLICATIONS FOR CORPORATE MANAGERS AND INVESTORS The connection between risk and return is an important concept and it has numerous implications for both corporate managers and investors.As we will see in later chapters corporate managers spend a great deal of time assessing the risk and returns on individual projects. Indeed given their concerns about the risk of individual projects it might be fair to ask why we spend so much time discussing the riskiness of stocks. Why not begin by looking at the riskiness of such business assetsasplantandequipment Thereasonisthatformanagementwhoseprimarygoal is stock price maximization the overriding consideration is the riskiness of the firm’s stockandtherelevantriskofanyphysicalassetmustbemeasuredintermsofitseffecton the stock’s risk as seen by investors. For example suppose Goodyear the tire com- pany is considering a major investment in a new product recapped tires. Sales of recaps hence earnings on the new operation are highly uncertain so on a stand- alone basis the new venture appears to be quite risky. However suppose returns intherecapbusinessarenegativelycorrelatedwithGoodyear’sotheroperations— when times are good and people have plenty of money they buy new cars with newtiresbutwhentimesarebadtheytendtokeeptheiroldcars andbuyrecaps for them. Therefore returns would be high on regular operations and low on the recap division during good times but the opposite would be true during reces- sions. The result mightbe apattern like that shown earlier inFigure 8-4 for Stocks W and M. Thus what appears to be a risky investment when viewed on a stand- alone basis might not be very risky when viewed within the context of the com- pany as a whole. This analysis can be extended to the corporation’s stockholders. Because Goodyear’s stock is owned by diversified stockholders the real issue each time managementmakesaninvestmentdecisionisthis:Howwillthisinvestmentaffect the risk of our stockholders Again the stand-alone risk of an individual project may look quite high however viewed in the context of the project’s effect on stockholder risk it may not be very large. We will address this issue again in Chapter12whereweexaminetheeffectsofcapitalbudgetingoncompanies’beta coefficients and thus on stockholders’ risks. While these concepts are obviously important for individual investors they arealso importantfor corporatemanagers.We summarize some key ideas that all investors should consider: 1. Thereisatrade-off between risk and return. The averageinvestorlikeshigher returns but dislikes risk. It follows that higher-risk investments need to offer investorshigherexpectedreturns.Putanotherway—ifyouareseekinghigher returns you must be willing to assume higher risks. 258 Part 3 Financial Assets

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2. Diversification is crucial. By diversifying wisely investors can dramatically reduce risk without reducing their expected returns. Don’t put all of your money in one or two stocks or in one or two industries. A huge mistake that many people make is to invest a high percentage of their funds in their employer’s stock. If the company goes bankrupt they not only lose their job but also their invested capital. While no stock is completely riskless you can smooth out the bumps by holding a well-diversified portfolio. 3. Real returns are what matters. All investors should understand the difference betweennominalandrealreturns.Whenassessingperformancetherealreturn what you have left over after inflation is what matters. It follows that as expected inflation increases investors need to receive higher nominal returns. 4. The risk of an investment often depends on how long you plan to hold the investment. Common stocks for example can be extremely risky for short- term investors. However over the long haul the bumps tend to even out thus stocks are less risky when held as part of a long-term portfolio. Indeed inhisbest-sellingbook Stocks for the Long RunJeremySiegeloftheUniversity of Pennsylvania concludes that “the safest long-term investment for the preservation of purchasing power has clearly been stocks not bonds.” 5. While the past gives us insights into the risk and returns on various invest- ments there is no guarantee that the future will repeat the past. Stocks that have performed well in recent years might tumble while stocks that have struggledmayrebound.Thesamethingmayholdtrueforthestockmarketas a whole. Even Jeremy Siegel who has preached that stocks have historically been good long-term investments also has argued that there is no assurance that returns inthe future will be as strong as they have been in the past. More importantly when purchasing a stock you always need to ask “Is this stock fairly valued or is it currently priced too high” We discuss this issue more completely in the next chapter. SELFTEST Explain the following statement: The stand-alone risk of an individual cor- porate project may be quite high but viewed in the context of its effect on stockholders’ risk the project’s true risk may not be very large. How does the correlation between returns on a project and returns on the firm’s other assets affect the project’s risk What are some important concepts for individual investors to consider when evaluating the risk and returns of various investments TYING IT ALL TOGETHER In this chapter we described the relationship between risk and return. We dis- cussed how to calculate risk and return for individual assets and for portfolios. In particular we differentiated between stand-alone risk and risk in a portfolio con- text and we explained the benefits of diversification. We also discussed the CAPM which describes how risk should be measured and how risk affects rates of return. In the chapters that follow we will give you the tools needed to estimate the required rates of return on a firm’s common stock and explain how that return and the yield on its bonds are used to develop the firm’s cost of capital. As you will see the cost of capital is a key element in the capital budgeting process. Chapter 8 Risk and Rates of Return 259

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SELF-TEST QUESTIONS AND PROBLEMS Solutions Appear in Appendix A ST-1 KEY TERMS Define the following terms using graphs or equations to illustrate your answers whenever feasible: a. Risk stand-alone risk probability distribution b. Expected rate of return r c. Standard deviation coefficient of variation CV d. Risk aversion risk premium RP realized rate of return r e. Risk premium for Stock i RP i market risk premium RP M f. Expected return on a portfolio r p market portfolio g. Correlation correlation coefficient r h. Market risk diversifiable risk relevant risk i. Capital Asset Pricing Model CAPM j. Beta coefficient b average stock’s beta b A k. Security Market Line SML equation ST-2 REALIZED RATES OF RETURN Stocks A and B have the following historical returns: Year Stock A’s Returns r A Stock B’s Returns r B 2004 24.25 5.50 2005 18.50 26.73 2006 38.67 48.25 2007 14.33 4.50 2008 39.13 43.86 a. Calculate the average rate of return for each stock during the period 2004 through 2008. Assume that someone held a portfolio consisting of 50 of Stock A and 50 of StockB.Whatwouldtherealizedrateofreturnontheportfoliohavebeenineachyear from 2004 through 2008 What would the average return on the portfolio have been during that period b. Calculate the standard deviation of returns for each stock and for the portfolio. Use Equation 8-2a. c. Lookingattheannualreturnsonthetwostockswouldyouguessthatthecorrelation coefficient between the two stocks is closer to +0.8 or to –0.8 d. If more randomly selected stocks had been included in the portfolio which of the following is the most accurate statement of what would have happened to p 1 p would have remained constant. 2 p would have been in the vicinity of 20. 3 p would have declined to zero if enough stocks had been included. ST-3 BETA AND THE REQUIRED RATE OF RETURN ECRI Corporation is a holding company with four main subsidiaries. The percentage of its capital invested in each of the sub- sidiaries and their respective betas are as follows: Subsidiary Percentage of Capital Beta Electric utility 60 0.70 Cable company 25 0.90 Real estate development 10 1.30 International/special projects 5 1.50 260 Part 3 Financial Assets

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a. What is the holding company’s beta b. If the risk-free rate is 6 and the market risk premium is 5 what is the holding company’s required rate of return c. ECRI is considering a change in its strategic focus it will reduce its reliance on the electric utility subsidiary so the percentage of its capital in this subsidiary will be reduced to 50. At the same time it will increase its reliance on the international/special projects division so the percentage of its capital in that subsidiary will rise to 15. What will the company’s required rate of return be after these changes QUESTIONS 8-1 Supposeyouownedaportfolioconsistingof250000oflong-termU.S.governmentbonds. a. Would your portfolio be riskless Explain. b. Now suppose the portfolio consists of 250000 of 30-day Treasury bills. Every 30 days your bills mature and you will reinvest the principal 250000 in a new batch of bills. You plan to live on the investment income from your portfolio and you want to maintain a constant standard of living. Is the T-bill portfolio truly riskless Explain. c. What is the least risky security you can think of Explain. 8-2 The probability distribution of a less risky expected return is more peaked than that of a riskier return. What shape would the probability distribution be for a completely certain returns and b completely uncertain returns 8-3 A life insurance policy is a financial asset with the premiums paid representing the investment’s cost. a. How would you calculate the expected return on a 1-year life insurance policy b. Supposetheownerofalifeinsurancepolicyhasnootherfinancialassets—theperson’s only other asset is “human capital” or earnings capacity. What is the correlation coefficient between the return on the insurance policy and the return on the human capital c. Life insurance companies must pay administrative costs and sales representatives’ commissions hence the expected rate of return on insurance premiums is generally low or even negative. Use portfolio concepts to explain why people buy life insurance in spite of low expected returns. 8-4 Is it possible to construct a portfolio of real-world stocks that has an expected return equal to the risk-free rate 8-5 Stock A has an expected return of 7 a standard deviation of expected returns of 35 a correlation coefficient with the market of –0.3 and a beta coefficient of –0.5. Stock B has an expected return of 12 a standard deviation of returns of 10 a 0.7 correlation with the market and a beta coefficient of 1.0. Which security is riskier Why 8-6 Astockhada12returnlastyearayearwhentheoverallstockmarketdeclined.Doesthis mean that the stock has a negative beta and thus very little risk if held in a portfolio Explain. 8-7 If investors’ aversion to risk increased would the risk premium on a high-beta stock increase by more or less than that on a low-beta stock Explain. 8-8 If a company’s beta were to double would its required return also double 8-9 In Chapter 7 we saw that if the market interest rate r d for a given bond increased the price of the bond would decline. Applying this same logic to stocks explain a how a decrease in risk aversion would affect stocks’ prices and earned rates of return b how this would affect risk premiums as measured by the historical difference between returns on stocks and returns on bonds and c what the implications of this would be for the use of historical risk premiums when applying the SML equation. Chapter 8 Risk and Rates of Return 261

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PROBLEMS Easy Problems 1–5 8-1 EXPECTED RETURN A stock’s returns have the following distribution: Demand for the Company’s Products Probability of This Demand Occurring Rate of Return If This Demand Occurs Weak 0.1 50 Below average 0.2 5 Average 0.4 16 Above average 0.2 25 Strong 0.1 60 1.0 Calculatethestock’sexpectedreturnstandarddeviationandcoefficientofvariation. 8-2 PORTFOLIO BETA An individual has 35000 invested in a stock with a beta of 0.8 and another 40000 invested in a stock with a beta of 1.4. If these are the only two investments in her portfolio what is her portfolio’s beta 8-3 REQUIRED RATE OF RETURN Assume that the risk-free rate is 6 and the expected return on the market is 13. What is the required rate of return on a stock with a beta of 0.7 8-4 EXPECTEDANDREQUIREDRATESOFRETURN Assumethattherisk-freerateis5andthe marketriskpremiumis 6.What istheexpected return fortheoverallstockmarketWhat is the required rate of return on a stock with a beta of 1.2 8-5 BETAANDREQUIREDRATEOFRETURN Astockhasarequiredreturnof11therisk-free rate is 7 and the market risk premium is 4. a. What is the stock’s beta b. Ifthemarketriskpremiumincreasedto6whatwouldhappentothestock’srequired rate of return Assume that the risk-free rate and the beta remain unchanged. Intermediate Problems 6–12 8-6 EXPECTED RETURNS Stocks X and Y have the following probability distributions of expected future returns: Probability X Y 0.1 10 35 0.2 2 0 0.4 12 20 0.2 20 25 0.1 38 45 a. Calculate the expected rate of return r Y for Stock Y r X ¼ 12. b. Calculate the standard deviation of expected returns X for Stock X Y ¼ 20.35. Now calculate the coefficient of variation for Stock Y. Is it possible that most investors will regard Stock Y as being less risky than Stock X Explain. 8-7 PORTFOLIO REQUIRED RETURN Suppose you are the money manager of a 4 million investmentfund.Thefundconsistsoffourstockswiththefollowinginvestmentsandbetas: Stock Investment Beta A 400000 1.50 B 600000 0.50 C 1000000 1.25 D 2000000 0.75 If the market’s required rate of return is 14 and the risk-free rate is 6 what is the fund’s required rate of return 8-8 BETA COEFFICIENT Given the following information determine the beta coefficient for Stock J that is consistent with equilibrium: r J ¼ 12.5 r RF ¼ 4.5 r M ¼ 10.5. 262 Part 3 Financial Assets

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8-9 REQUIRED RATE OF RETURN Stock R has a beta of 1.5 Stock S has a beta of 0.75 the expected rate ofreturn on anaveragestockis13and therisk-free rate ofreturn is7.By how much does the required return on the riskier stock exceed the required return on the less risky stock 8-10 CAPM AND REQUIRED RETURN Bradford Manufacturing Company has a beta of 1.45 while Farley Industries has a beta of 0.85. The required return on an index fund that holds the entire stock market is 12.0. The risk-free rate of interest is 5. By how much does Bradford’s required return exceed Farley’s required return 8-11 CAPM AND REQUIRED RETURN Calculate the required rate of return for Manning Enter- prisesassumingthatinvestorsexpecta3.5rateofinflationinthefuture.Therealrisk-free rate is 2.5 and the market risk premium is 6.5. Manning has a beta of 1.7 and its realized rate of return has averaged 13.5 over the past 5 years. 8-12 REQUIRED RATE OF RETURN Suppose r RF ¼ 9 r M ¼ 14 and b i ¼ 1.3. a. What is r i the required rate of return on Stock i b. Nowsupposethatr RF 1increasesto10or2decreasesto8.TheslopeoftheSML remains constant. How would this affect r M and r i c. Now assume that r RF remains at 9 but r M 1 increases to 16 or 2 falls to 13. The slope of the SML does not remain constant. How would these changes affect r i Challenging Problems 13–21 8-13 CAPM PORTFOLIO RISK AND RETURN Consider the following information for three stocksStocksXYandZ.Thereturnsonthethreestocksarepositivelycorrelatedbutthey are notperfectly correlated. That iseach ofthecorrelation coefficients isbetween0 and 1. Stock Expected Return Standard Deviation Beta X 9.00 15 0.8 Y 10.75 15 1.2 Z 12.50 15 1.6 Fund Q has one-third of its funds invested in each of the three stocks. The risk-free rate is 5.5 and the market is in equilibrium. That is required returns equal expected returns. a. What is the market risk premium r M – r RF b. What is the beta of Fund Q c. What is the expected return of Fund Q d. WouldyouexpectthestandarddeviationofFundQtobelessthan 15equalto15 or greater than 15 Explain. 8-14 PORTFOLIOBETA Supposeyouheldadiversifiedportfolioconsistingofa7500investment ineachof20differentcommonstocks.Theportfolio’sbetais1.12.Nowsupposeyoudecided toselloneofthe stocksinyourportfoliowithabetaof1.0for7500andusetheproceedsto buy another stock with a beta of 1.75. What would your portfolio’s new beta be 8-15 CAPMANDREQUIREDRETURN HRIndustriesHRIhasabetaof1.8whileLRIndustries’ LRIbetais0.6.Therisk-freerateis6andtherequiredrateofreturnonanaveragestock is 13. The expected rate of inflation built into r RF falls by 1.5 percentage points the real risk-free rate remains constant the required return on the market falls to 10.5 and all betasremainconstant.Afterallofthesechangeswhatwillbethedifferenceintherequired returns for HRI and LRI 8-16 CAPMANDPORTFOLIORETURN Youhavebeenmanaginga5millionportfoliothathasa betaof1.25andarequiredrateofreturnof12.Thecurrentrisk-freerateis5.25.Assume that you receive another 500000. If you invest the money in a stock with a beta of 0.75 what will be the required return on your 5.5 million portfolio 8-17 PORTFOLIO BETA A mutual fund manager has a 20 million portfolio with a beta of 1.5. The risk-free rate is 4.5 and the market risk premium is 5.5. The manager expects to receive an additional 5 million which she plans to invest in a number of stocks. After investingtheadditionalfundsshewantsthefund’srequiredreturntobe13.Whatshould be the average beta of the new stocks added to the portfolio 8-18 EXPECTED RETURNS Supposeyouwonthelottery andhad twooptions: 1receiving 0.5 million or 2 taking a gamble in which at the flip of a coin you receive 1 million if a head comes up but receive zero if a tail comes up. a. What is the expected value of the gamble b. Would you take the sure 0.5 million or the gamble Chapter 8 Risk and Rates of Return 263

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c. If you chose the sure 0.5 million would that indicate that you are a risk averter or a risk seeker d. Suppose the payoff was actually 0.5 million—that was the only choice. You now face the choiceofinvesting itin aU.S. Treasurybond thatwillreturn 537500 atthe endof a year or a common stock that has a 50-50 chance of being worthless or worth 1150000 at the end of the year. 1 The expected profit on the T-bond investment is 37500. What is the expected dollar profit on the stock investment 2 TheexpectedrateofreturnontheT-bondinvestmentis7.5.Whatistheexpected rate of return on the stock investment 3 Would you invest in the bond or the stock Why 4 Exactlyhowlargewouldtheexpectedprofitortheexpectedrateofreturnhavetobeon thestockinvestmenttomakeyouinvestinthestockgiventhe7.5returnonthebond 5 Howmightyourdecisionbeaffectedifratherthanbuyingonestockfor0.5million youcouldconstructaportfolioconsistingof100stockswith5000investedineach Each of these stocks has the same return characteristics as the one stock—that is a 50-50 chance of being worth zero or 11500 at year-end. Would the correlation between returns on thesestocks matter Explain. 8-19 EVALUATING RISK AND RETURN Stock X has a 10 expected return a beta coefficient of 0.9anda35standarddeviationofexpectedreturns.StockYhasa12.5expectedreturn a beta coefficient of 1.2 and a 25 standard deviation. The risk-free rate is 6 and the market risk premium is 5. a. Calculate each stock’s coefficient of variation. b. Which stock is riskier for a diversified investor c. Calculate each stock’s required rate of return. d. On the basis of the two stocks’ expected and required returns which stock would be more attractive to a diversified investor e. Calculate the required return of a portfolio that has 7500 invested in Stock X and 2500 invested in Stock Y. f. If the market risk premium increased to 6 which of the two stocks would have the larger increase in its required return 8-20 REALIZED RATES OF RETURN Stocks A and B have the following historical returns: Year Stock A’s Returns r A Stock B’s Returns r B 2004 18.00 14.50 2005 33.00 21.80 2006 15.00 30.50 2007 0.50 7.60 2008 27.00 26.30 a. Calculatetheaveragerateofreturnforeachstockduringtheperiod2004through2008. b. Assumethatsomeoneheldaportfolioconsistingof50ofStockAand50ofStockB. What would the realized rate of return on the portfolio have been each year What would the average return on the portfolio have been during this period c. Calculate the standard deviation of returns for each stock and for the portfolio. d. Calculate the coefficient of variation for each stock and for the portfolio. e. Assumingyouarearisk-averseinvestorwouldyouprefertoholdStockAStockBor the portfolio Why 8-21 SECURITY MARKET LINE You plan to invest in the Kish Hedge Fund which has total capital of 500 million invested in five stocks: Stock Investment Stock’s Beta Coefficient A 160 million 0.5 B 120 million 1.2 C 80 million 1.8 D 80 million 1.0 E 60 million 1.6 264 Part 3 Financial Assets

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Kish’s beta coefficient can be found as a weighted average of its stocks’ betas. The risk-free rate is 6 and you believe the following probability distribution for future market returns is realistic: Probability Market Return 0.1 28 0.2 0 0.4 12 0.2 30 0.1 50 a. What is the equation for the Security Market Line SML Hint: First determine the expected market return. b. Calculate Kish’s required rate of return. c. Suppose Rick Kish the president receives a proposal from a company seeking new capital. The amount needed to take a position in the stock is 50 million it has an expected return of 15 and its estimated beta is 1.5. Should Kish invest in the new companyAtwhatexpectedrateofreturnshouldKishbeindifferenttopurchasingthe stock COMPREHENSIVE/SPREADSHEET PROBLEM 8-22 EVALUATINGRISKANDRETURN BartmanIndustries’andReynoldsInc.’sstockpricesand dividends along with the Winslow 5000 Index are shown here for the period 2003–2008. The Winslow 5000 data are adjusted to include dividends. BARTMAN INDUSTRIES REYNOLDS INC. WINSLOW 5000 Year Stock Price Dividend Stock Price Dividend Includes Dividends 2008 17.250 1.15 48.750 3.00 11663.98 2007 14.750 1.06 52.300 2.90 8785.70 2006 16.500 1.00 48.750 2.75 8679.98 2005 10.750 0.95 57.250 2.50 6434.03 2004 11.375 0.90 60.000 2.25 5602.28 2003 7.625 0.85 55.750 2.00 4705.97 a. Use the data to calculate annual rates of return for Bartman Reynolds and the Winslow 5000 Index. Then calculate each entity’s average return over the 5-year period. Hint: Remember returns are calculated by subtracting the beginning price from the ending price to get the capital gain or loss adding the dividend to the capital gainorlossanddividing theresult bythebeginningprice.Assumethatdividendsare already included in the index. Also you cannot calculate the rate of return for 2003 because you do not have 2002 data. b. Calculate the standard deviations of the returns for Bartman Reynolds and the Winslow5000.Hint:UsethesamplestandarddeviationformulaEquation8-2ainthis chapter which corresponds to the STDEV function in Excel. c. Calculate the coefficients of variation for Bartman Reynolds and the Winslow 5000. d. ConstructascatterdiagramthatshowsBartman’sandReynolds’returnsonthevertical axis and the Winslow 5000 Index’s returns on the horizontal axis. e. EstimateBartman’sandReynolds’betasbyrunningregressionsoftheirreturnsagainst the index’s returns. Hint: Refer to Web Appendix 8A. Are these betas consistent with your graph f. Assume that the risk-free rate on long-term Treasury bonds is6.04. Assume also that the average annual return on the Winslow 5000 is not a good estimate of the market’s required return—it is too high. So use 11 as the expected return on the market. Use the SML equation to calculate the two companies’ required returns. g. If you formed a portfolio that consisted of 50 Bartman and 50 Reynolds what would the portfolio’s beta and required return be Chapter 8 Risk and Rates of Return 265

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h. Suppose an investor wants toinclude BartmanIndustries’stock inhis portfolio. Stocks A B and C are currently in the portfolio and their betas are 0.769 0.985 and 1.423 respectively. Calculate the new portfolio’s required return if it consists of 25 of Bartman 15 of Stock A 40 of Stock B and 20 of Stock C. INTEGRATED CASE MERRILL FINCH INC. 8-23 RISK AND RETURN Assume that you recently graduated with a major in finance. You just landed a job as a financial planner with Merrill Finch Inc. a large financial services corporation. Your first assignment is to invest 100000foraclient.Becausethefundsaretobeinvestedinabusinessattheendof1yearyouhavebeeninstructed to plan for a 1-year holding period. Further your boss has restricted you to the investment alternatives in the following table shown with their probabilities and associated outcomes. For now disregard the items at the bottom of the data you will fill in the blanks later. RETURNS ON ALTERNATIVE INVESTMENTS ESTIMATED RATE OF RETURN State of the Economy Probability T-Bills High Tech Collections U.S. Rubber Market Portfolio 2-Stock Portfolio Recession 0.1 5.5 27.0 27.0 6.0 a 17.0 0.0 Below average 0.2 5.5 7.0 13.0 14.0 3.0 Average 0.4 5.5 15.0 0.0 3.0 10.0 7.5 Above average 0.2 5.5 30.0 11.0 41.0 25.0 Boom 0.1 5.5 45.0 21.0 26.0 38.0 12.0 r 1.0 9.8 10.5 0.0 13.2 18.8 15.2 3.4 CV 13.2 1.9 1.4 0.5 b 0.87 0.88 Merrill Finch’s economic forecasting staff has developed probability estimates for the state of the economy and its security analysts have developed a sophisticated computer program which was used to estimate the rate of return on each alternative under each state of theeconomy. High Tech Inc. isan electronics firm Collections Inc. collects past-due debts and U.S. Rubber manufactures tires and various other rubber and plastics products. Merrill Finch also maintains a “market portfolio” that owns a market-weighted fraction of all publicly traded stocks you can invest in that portfolio and thus obtain average stock market results. Given the situation described answer the following questions: a. 1 Why is the T-bill’s return independent of the state of the economy Do T-bills promise a completely risk-free return Explain. 2 WhyareHighTech’sreturnsexpectedtomovewiththeeconomywhereasCollections’areexpectedto move counter to the economy b. Calculatetheexpectedrateofreturnoneachalternativeandfillintheblanksontherowforr intheprevious table. c. You should recognize that basing a decision solely on expected returns is appropriate only for risk-neutral individuals. Because your client like most people is risk-averse the riskiness of each alternative is an important aspect of the decision. One possible measure of risk is the standard deviation of returns. 1 Calculate this value for each alternative and fill in the blank on the row for in the table. 2 What type of risk is measured by the standard deviation a NotethattheestimatedreturnsofU.S.Rubberdonotalwaysmoveinthesamedirectionastheoveralleconomy.Forexamplewhen the economy is below average consumers purchase fewer tires than they would if the economy were stronger. However if the economy is in a flat-out recession a large number of consumers who were planning to purchase a new car may choose to wait and instead purchase new tires for the car they currently own. Under these circumstances we would expect U.S. Rubber’s stock price to be higher if there was a recession than if the economy was just below average. 266 Part 3 Financial Assets

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3 Draw a graph that shows roughly the shape of the probability distributions for High Tech U.S. Rubber and T-bills. d. Suppose you suddenly remembered that the coefficient of variation CV is generally regarded as being a better measure of stand-alone risk than the standard deviation when the alternatives being considered have widely differing expected returns. Calculate the missing CVsand fillin the blanks on therow forCV in the table.Does the CVproduce the same risk rankings as the standard deviation Explain. e. Suppose you created a two-stock portfolio by investing 50000 in High Tech and 50000 in Collections. 1 Calculate the expected return r p the standard deviation p and the coefficient of variation CV p for this portfolio and fill in the appropriate blanks in the table. 2 Howdoestheriskinessofthistwo-stockportfoliocomparewiththeriskinessoftheindividualstocksiftheywere held in isolation f. Suppose an investor starts with a portfolio consisting of one randomly selected stock. What would happen: 1 To the riskiness and to the expected return of the portfolio as more randomly selected stocks were added to the portfolio 2 What is the implication for investors Draw a graph of the two portfolios to illustrate your answer. g. 1 Should the effects of a portfolio impact the way investors think about the riskiness of individual stocks 2 If you decided to hold a 1-stock portfolio and consequently were exposed to more risk than diversified investors couldyou expect to be compensated for all of yourrisk thatis could you earn a riskpremium on the part of your risk that you could have eliminated by diversifying h. The expected rates of return and the beta coefficients of the alternatives supplied by Merrill Finch’scomputer program are as follows: Security Return r Risk Beta High Tech 12.4 1.32 Market 10.5 1.00 U.S. Rubber 9.8 0.88 T-bills 5.5 0.00 Collections 1.0 0.87 1 What is a beta coefficient and how are betas used in risk analysis 2 Do the expected returns appear to be related to each alternative’s market risk 3 Is it possible to choose among the alternatives on the basis of the information developed thus far Use the data given at the start of the problem to construct a graph that shows how the T-bill’s High Tech’s and the market’s beta coefficients are calculated. Then discuss what betas measure and how they are used in risk analysis. i. The yield curve is currently flat that is long-term Treasury bonds also have a 5.5 yield. Consequently Merrill Finch assumes that the risk-free rate is 5.5. 1 Write out the Security Market Line SML equation use it to calculate the required rate of return on each alternative and graph the relationship between the expected and required rates of return. 2 How do the expected rates of return compare with the required rates of return 3 Does the fact that Collections has an expected return that is less than the T-bill rate make any sense Explain. 4 Whatwould bethemarket risk andthe required return ofa 50-50 portfolio ofHigh Techand CollectionsofHigh Tech and U.S. Rubber j. 1 Suppose investors raised their inflation expectations by 3 percentage points over current estimates as reflected in the 5.5 risk-free rate. What effect would higher inflation have on the SML and on the returns required on high- and low-risk securities 2 Supposeinsteadthatinvestors’riskaversionincreasedenoughtocausethemarketriskpremiumtoincreaseby3 percentage points. Inflation remains constant. What effect would this have on the SML and on returns of high- and low-risk securities Chapter 8 Risk and Rates of Return 267

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Access the Thomson ONE problems through the CengageNOW™ web site. Use the Thomson ONE—Business School Edition online database to work this chapter’s questions. Using Past Information to Estimate Required Returns Chapter 8 discussed the basic trade-off between risk and return. In the Capital Asset Pricing Model CAPMdiscussionbetawasidentifiedasthecorrectmeasureofriskfordiversifiedshareholders.Recall that beta measures the extent to which the returns of a given stock move with the stock market. When using the CAPM to estimate required returns we would like to know how the stock will move with the market in the future but since we don’t have a crystal ball we generally use historical data to estimate this relationship with beta. As mentioned in the Web Appendix for this chapter beta can be estimated by regressing the individualstock’sreturnsagainstthereturnsoftheoverallmarket.Asanalternativetorunningourown regressions we can rely on reported betas from a variety of sources. These published sources make it easyforustoreadilyobtainbetaestimatesformostlargepubliclytradedcorporations.Howeveraword ofcautionisinorder.Betaestimatescanoftenbequite sensitivetothetimeperiodinwhich thedataare estimated the market index used and the frequency of the data used. Therefore it is not uncommon to findawiderangeofbetaestimatesamongthevariouspublishedsources.IndeedThomsonOnereports multiple beta estimates. These multiple estimates reflect the fact that Thomson One puts together data from a variety of different sources. Discussion Questions 1. Beginbylookingatthehistoricalperformanceoftheoverallstockmarket.Ifyouwanttoseeforexamplethe performance of the SP 500 select “INDICES” and enter SPCOMP. Click on “PERFORMANCE.” You will seeaquicksummaryofthemarket’sperformanceinrecentmonthsandyears.Howhasthemarketperformed over the past year the past 3 years the past 5 years the past 10 years 2. Nowlet’s takea closer lookat the stocksoffour companies: ColgatePalmolive Ticker¼CL CampbellSoup CPB Motorola MOT and Tiffany Co TIF. Before looking at the data which of these companies would youexpecttohavearelativelyhighbetagreaterthan1.0andwhichofthesecompanieswouldyouexpectto have a relatively low beta less than 1.0 3. Select one of the four stocks listed in Question 2 by selecting “COMPANY ANALYSIS” entering the com- pany’s ticker symbol in the blank companies box and clicking “GO.” On the company overview page you shouldseeachartthatsummarizeshowthestockhasdonerelativetotheSP500overthepast6months.Has the stock outperformed or underperformed the overall market during this time period 4. Ifyouscrolldownthecompanyoverviewpageyoushouldseeanestimateofthecompany’sbeta.Whatisthe company’s beta What was the source of the estimated beta 5. Click on “PRICES” on the left-hand side of the screen. What is the company’s current dividend yield What has been its total return to investors over the past 6 months over the past year over the past 3 years Remember that total return includes the dividend yield plus any capital gains or losses. 6. Assume that the risk-free rate is 5 and the market risk premium is 6. What is the required return on the company’s stock 7. Repeat the same exercise for each of the 3 remaining companies. Do the reported betas confirm your earlier intuition In general do you find that the higher-beta stocks tend to do better in up markets and worse in down markets Explain. 268 Part 3 Financial Assets

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ª SEBASTIAN KAULITZKI/SHUTTERSTOCK.COM CHAPTER 9 Stocks and Their Valuation Searching for the Right Stock A recent study by the securities industry found that roughly half of all U.S. households have in- vested in common stocks. As noted in Chapter 8 over the long run returns in the U.S. stock market have been quite strong averaging 12 per year. However the market’s performance recently has been less than stellar. Trying to put things in per- spective Fortune magazine’s senior editor Allan Sloan offered the following comments about the market’s performance: When the greatest bull market in U.S. history started in the summer of 1982 only a relative handful of people owned stocks which were cheap because they were considered highly risky. But by the time the Standard Poor’s 500 peaked in March 2000 amid a fully inflated stock bubble the masses were in the market. Stocks were magical a supposedly can’t- miss way to pay for your kids’ college save for retirement enrich employees by giving them options and regrow hair. Just kid- ding about the hair. Alas. Stocks might go down in any given year the mantra went butin the long term they’d produce double-digit returns. How- ever one of the lessons of the past eight years is that the long run can be . . . really long. As I write this in late February 2008 the U.S. market—which I’m defining as the Standard Poor’s 500—is well below the high that it set on March 24 2000. Even after you include dividends which have run a bit below 2 a year you’ve barely broken even according to calculations for Fortune by Aronson Johnson Ortiz a Philadel- phia money manager. One month later in March 2008 the stock market fell further in the aftermath of the star- tling collapse of Wall Street giant Bear Stearns. While most experts believe the stock market will ultimately rebound most doubt that investors will average double-digit returns from common stock returns in the years ahead. As we discussed in Chapter 8 the returns of individual stocks are more volatile than the 269

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PUTTING THINGS IN PERSPECTIVE In Chapter 7 we examined bonds. We now turn to stocks both common and preferred.Sincethecashflowsprovidedbybondsaresetbycontractitisgenerally easy to predict their cash flows. Preferred stock returns are also set by contract which makes them similar to bonds and they are valued in much the same way. However common stock returns are not contractual—they depend on the firm’s earnings which in turn depend on many random factors making their valuation more difficult. Two fairly straightforward models are used to estimate stocks’ intrinsic or “true” values: 1 the discounted dividend model and 2 the corporate valuation model. A stock should of course be bought if its price is less than its estimated intrinsic value and sold if its price exceeds its intrinsic value. By the time you finish this chapter you should be able to: l Discuss the legal rights of stockholders. l Explain the distinction between a stock’s price and its intrinsic value. l Identifythetwomodelsthatcanbeusedtoestimateastock’sintrinsicvalue:the discounted dividend model and the corporate model. l List the key characteristics of preferred stock and explain how to estimate the value of preferred stock. Stock valuation is interesting in its own right but you also need to understand valuation when you estimate the cost of capital for use in capital budgeting which is probably a firm’s most important task. 9-1 LEGAL RIGHTS AND PRIVILEGES OF COMMON STOCKHOLDERS A corporation’s common stockholders are the owners of the corporation and as such they have certain rights and privileges as discussed in this section. returns of the overall market. For example in 2007 the overall market as measured by the SP 500 Index was up slightly +5.49. That same year some individual stocks realized huge gains while others declined sharply. On the plus side Research in Motion was up 166 rose 135 and Apple Computer climbed 133. On the down side ETrade Financial plummeted 84 Circuit City 78 and Starbucks 42. This wide range in individual stocks’ returns shows first that diversification is important and second that when it comes to picking stocks it is not enough to simply pick a good company—the stock must also be “fairly” priced. To determine whether a stock is fairly priced you first need to estimate the stock’struevalueor “intrinsic value” a concept first discussed in Chapter 1. With this objective in mind in this chapter we describe some models that analysts have used to estimate intrinsic values. As you will see while it is difficult to predict stock prices we are not completely in the dark. Indeed after studying this chapter you should have a reasonably good understanding of the factors that influence stock prices and with that knowledge—plus a little luck—youshouldbeableto successfully navigate the market’s often-treacherous ups and downs. Sources:AllanSloan “TheIncredibleShrinkingBull” FortuneMarch172008p. 24andAlexandraTwin “BestandWorstStocksof2007” December 31 2007. Key trends in the securities industry are listed and explained at research/statistics/ key_industry_trends.html. 270 Part 3 Financial Assets

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9-1a Control of the Firm A firm’s common stockholders have the right to elect its directors who in turn elect the officers who manage the business. In a small firm usually the major stockholder is also the president and chair of the board of directors. In large publicly owned firms the managers typically have some stock but their personal holdings are generally insufficient to give them voting control. Thus the man- agementsofmostpubliclyownedfirms can beremovedbythe stockholdersifthe management team is not effective. State and federal laws stipulate how stockholder control is to be exercised. First corporations must hold elections of directors periodically usually once a year with the vote taken at the annual meeting. Each share of stock has one vote thustheownerof1000shareshas1000votesforeachdirector. 1 Stockholderscan appear at the annual meeting and vote in person but typically they transfer their right to vote to another person by means of a proxy. Management always solicits stockholders’ proxies and usually receives them. However if earnings are poor and stockholders are dissatisfied an outside group may solicit the proxies in an efforttooverthrowmanagementandtakecontrolofthebusiness.Thisisknownas a proxy fight. The question of control has become a central issue in finance in recent years. The frequency of proxy fights has increased as have attempts by one corporation to take over another by purchasing a majority of the outstanding stock. These actions are called takeovers. Some well-known examples of takeover battles in past years include KKR’s acquisition of RJR Nabisco Chevron’s acquisition of Gulf Oil and the QVC/Viacom fight to take over Paramount. More recently in February 2008 Microsoft made an unsolicited offer for Yahoo but thus far Yahoo’s management has resisted. Managers without more than 50 of their firms’ stock are very much con- cerned about proxy fights and takeovers and many of them have attempted to obtain stockholder approval for changes in their corporate charters that would make takeovers more difficult. For example a number of companies have gotten their stockholders to agree 1 to elect only one-third of the directors each year rather than electing alldirectorseach year 2 to require 75 ofthe stockholders rather than50toapprove amergerand3tovoteina “poisonpill”provision that would allow the stockholders of a firm that is taken over by another firm to buy shares in the second firm at a reduced price. The poison pill makes the acquisition unattractive and thus helps ward off hostile takeover attempts. Man- agersseekingsuchchangesgenerallyciteafearthatthefirmwillbepickedupata bargain price but it often appears that the managers’ concern about their own positions is the primary consideration. Managers’ moves to make takeovers more difficult have been countered by stockholders especially large institutional stockholders who do not like barriers erected to protect incompetent managers. To illustrate the California Public Employees Retirement System CalPERS which is one of the largest institutional investors has led proxy fights with several corporations whose financial per- formances were poor in CalPERS’ judgment. CalPERS wants companies to increaseoutsidenon-managementdirectors’abilitytoforcemanagerstobemore responsive to stockholder complaints. 1 In the situation described a 1000-share stockholder could cast 1000 votes for each of three directors if there were three contested seats on the board. An alternative procedure that may be prescribed in the corporate charter calls for cumulative voting. There the 1000-share stockholder would get 3000 votes if there were three vacancies and he or she could cast all of them for one director. Cumulative voting helps small groups obtain representation on the board. Proxy A document giving one person the authority to act for another typically the power to vote shares of common stock. Proxy Fight An attempt by a person or group to gain control of a firm by getting its stockholders to grant that person or group the authority to vote its shares to replace the current management. Takeover An action whereby a person or group succeeds in ousting a firm’s management and taking control of the company. Chapter 9 Stocks and Their Valuation 271

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Managers’ pay is another contentious issue. It has been asserted with con- siderable support that CEOs tend to pick other CEOs to serve on their boards with “you-scratch-my-back-and-I’ll-scratch-yours” behavior resulting in excessive compensation packagestotopmanagers.Boardshave triedtoconcealthe factsby making it extremely difficult for stockholders to know what the top managers are being paid. Investors are galled to see CEOs such as Stan O’Neil of Merrill Lynch who was fired because of his firm’s multibillion-dollar loss walkaway with stock and cash worth hundreds of millions. CalPERS and other institutional investors have weighed in on this issue and most firms today have been forced to make their compensation packages more transparent. For many years SEC rules prohibited large investors such as CalPERS from gettingtogethertoforcecorporatemanagerstoinstitutepolicychanges.However the SEC began changing its rules in 1993 and now large investors can work together to force management changes. These rulings have helped keep managers focused on stockholder concerns which means the maximization of stock prices. 9-1b ThePreemptiveRight Common stockholders often have the right called the preemptive righttopur- chaseonaproratabasisanyadditionalsharessoldbythefirm.Insomestatesthe preemptive right is automatically included in every corporate charter in other states it must be specifically inserted into the charter. The purpose of the preemptive right is twofold. First it prevents the man- agement of a corporation from issuing a large number of additional shares and purchasingthosesharesitself.Managementcouldusethistactictoseizecontrolof the corporationandfrustrate the will of the current stockholders. The secondand farmoreimportantreasonforthepreemptiverightistoprotectstockholdersfrom adilutionofvalue.Forexamplesuppose1000sharesofcommonstockeachwith a price of 100 were outstanding making the total market value of the firm 100000.If an additional 1000 shareswere sold at 50 ashareorfor 50000this would raise the firm’s total market value to 150000. When the new total market valueisdividedbythe2000totalsharesnowoutstandingavalueof75ashareis obtained. The old stockholders would thus lose 25 per share and the new stockholders would have an instant profit of 25 per share. Thus selling common stock at a price below the market value would dilute a firm’s price and transfer wealth from its present stockholders to those who were allowed to purchase the new shares. The preemptive right prevents this. SELFTEST Identify some actions that companies have taken to make takeovers more difficult. What is the preemptive right and what are the two primary reasons for its existence 9-2 TYPES OF COMMON STOCK Although most firms have only one type of common stock in some instances classified stock is used to meet special needs. Generally when special classi- fications are used one type is designated Class A another Class B and so forth. Smallnewcompaniesseekingfundsfromoutsidesourcesfrequentlyusedifferent types of common stock. For example when Google went public it sold Class A stock to the public while its Class B stock was retained bythe company’s insiders. Preemptive Right A provision in the corporate charter or bylaws that gives common stockholders the right to purchase on a pro rata basis new issues of common stock or convertible securities. Classified Stock Common stock that is given a special designation such as Class A or Class B to meet special needs of the company. 272 Part 3 Financial Assets

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ThekeydifferenceisthattheClassBstockhas10votespersharewhiletheClassA stock has 1 vote per share. Google’s Class B shares are predominantly held by the company’s two founders and its current CEO. The use of classified stock thus enables the company’s founders to maintain control over the company without having to own a majority of the common stock. For this reason Class B stock of this type is sometimes called founders’ shares. Since dual-class share structures of this type give special voting privileges to key insiders these structures are sometimes criticized because they may enable insiders to make decisions that are counter to the interests of the majority of stockholders. Note that “Class A”“Class B” and so forth have no standard meanings. Most firms have no classified shares but a firm that does could designate its Class B shares as founders’ shares and its Class A shares as those sold to the public while another could reverse those designations. Still other firms could use stock classifications for entirely different purposes. For example when General Motors acquired Hughes Aircraft for 5 billion it paid in part with anew Class H common GMH which had limited voting rights and whose dividends were tied to Hughes’s performance as a GM subsidiary. The reasons for the new stock were that 1 GM wanted to limit voting privileges on the new classified stock because of management’s concern about a possible takeover and 2 Hughes’s employees wanted to be rewarded more directly on Hughes’s own performance than would have been possible through regular GM stock. These Class H shares disappeared in 2003 when GM decided to sell off the Hughes unit. SELFTEST What are some reasons a company might use classified stock 9-3 STOCK PRICE VS. INTRINSIC VALUE We saw in Chapter 1 that a manager should seek to maximize the value of his or her firm’s stock. In that chapter we also emphasized the difference between stock price and intrinsic value. The stock price is simply the current market priceand it is easily observed for publicly traded companies. By contrast intrinsic value which represents the “true” value of the company’s stock cannot be directly observed and must instead be estimated. Figure 9-1 illustrates once again the connection between stock price and intrinsic value. As the figure suggests market equilibrium occurs when the stock’s price equals its intrinsic value. If the stock market is reasonably efficient gaps between the stock price and intrinsic value should not be very large and they should not persist for very long. However in some cases an individual stock price may be much higher or lower than its intrinsic value. During several years leading up to thecreditcrunchof2007–2008 mostofthe largeinvestment bankswere reporting record profits and selling at record prices. However much of those earnings were illusory in that they did not reflect the huge risks that existed in the mortgage- backed securities they were buying. So with hindsight we now know that the market prices of most financial firms’ stocks exceeded their intrinsic values just prior to 2007. Then when the market realized what was happening those stock pricescrashed.CitigroupMerrillLynchandotherslostover60oftheirvaluein a few short months and Bear Stearns the fifth largest investment bank saw its Founders’ Shares Stock owned by the firm’s founders that has sole voting rights but restricted dividends for a specified number of years. Chapter 9 Stocks and Their Valuation 273

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stock price drop from 171 in 2007 to 2 in mid-March 2008. It clearly pays to question market prices at times 9-3a Why Do Investors and Companies Care About Intrinsic Value The remainder of this chapter focuses primarily on different approaches for esti- mating a stock’s intrinsic value. Before these approaches are described it is worth asking why it is important for investors and companies to understand how to calculate intrinsic value. When investing in common stocks one’s goal is to purchase stocks that are undervalued i.e. the price is below the stock’s intrinsic value and avoid stocks that are overvalued. Consequently Wall Street analysts institutional investors who control mutual funds and pension funds and many individual investors are interested in finding reliable models that help predict intrinsic value. Investors obviously care about intrinsic value but managers also need to understand how intrinsic value is estimated. First managers need to know how alternativeactionsarelikelytoaffectstockpricesandthemodelsofintrinsicvalue that we cover help demonstrate the connection between managerial decisions and firm value. Second managers should consider whether their stock is significantly undervalued or overvalued before making certain decisions. For example firms should consider carefully the decision to issue new shares if they believe their stock is undervalued and an estimate of their stock’s intrinsic value is the key to such decisions. Two basic models are used to estimate intrinsic values: the discounted dividend modelandthe corporate valuation model.Thedividendmodelfocuses on dividends whilethecorporatemodelgoes beyonddividendsandfocusesonsalescosts and free cash flows. In the following sections we describe these approaches in more detail. Determinants of Intrinsic Values and Stock Prices FIGURE 9-1 Managerial Actions the Economic Environment Taxes and the Political Climate “True” Investor Returns “True” Risk “Perceived” Investor Returns “Perceived” Risk Stock’s Intrinsic Value Stock’s Market Price Market Equilibrium: Intrinsic Value Stock Price 274 Part 3 Financial Assets

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SELFTEST What is the difference between a stock’s price and its intrinsic value Why do investors and managers need to understand how to estimate a firm’s intrinsic value What are two commonly used approaches for estimating a stock’s intrinsic value 9-4 THE DISCOUNTED DIVIDEND MODEL The value of a share of common stock depends on the cash flows it is expected to provide and those flows consist of two elements: 1 the dividends the investor receives each year while he or she holds the stock and 2 the price received when the stock is sold. The final price includes the original price paid plus an expected capital gain. Keep in mind that there are many different investors in the market and thus many different sets of expectations. Therefore different investors will have different opinions about a stock’s true intrinsic value and thus proper price. The analysis as performed by the marginal investor whose actions actually determine the equilibrium stock price is critical but every investor marginal or not implicitly goes through the same type of analysis. The following terms are used in our analysis: 2 Marginal investor ¼ theinvestororgroupofinvestorswithsimilarviewswho is at the margin and would be willing to buy if the stock price was slightly lower or to sell if the price was slightly higher. It is this investor’s expectations about dividends growth and risk that are key in the valuation process. Other investors ¼ all except the marginal investor. Some will be more optimistic than the marginal investor others more pessimistic. These investors will place new buy or sell orders if events occur to cause them to change their current expectations. D t ¼ the dividenda stockholder expectstoreceive at the end of each Year t. D 0 is the last dividend the company paid. Sinceithasalreadybeenpaidabuyerofthestockwillnot receive D 0. The first dividend a new buyer will receive is D 1 which is paid at the end of Year 1. D 2 is the dividend expectedattheendofYear2D 3 attheendofYear3and so forth. D 0 is known with certainty but D 1 D 2 andall other future dividends are expected values and different investors can have different expectations. 3 Our primary concern is with D t as forecasted by the marginal investor. P 0 ¼ actualmarketpriceofthestocktoday.P 0 isknownwith certainty but predicted future prices are subject to uncertainty. Marginal Investor A representative investor whose actions reflect the beliefs of those people who are currently trading a stock. It is the marginal investor who determines a stock’s price. 2 Many terms are described here and students sometimes get concerned about having to memorize all of them. We tell our students that we will provide formula sheets for use on exams so they don’t have to try to memorize everything. With their minds thus eased they end up learning what the terms are rather than memorizing them. 3 Stocks generally pay dividends quarterly so theoretically we should evaluate them on a quarterly basis. However mostanalysts actually workwithannual databecauseforecastedstockdata arenotprecise enoughtowarrant the use of a quarterly model. For additional information on the quarterly model see Charles M. Linke and J. Kenton Zumwalt “Estimation Biases in Discounted Cash Flow Analysis of Equity Capital Costs in Rate Regulation” Financial Management Autumn 1984 pp. 15–21. Market Price P 0 The price at which a stock sells in the market. Chapter 9 Stocks and Their Valuation 275

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P t ¼ boththeexpectedpriceandtheexpectedintrinsicvalueof thestockattheendofeachYeartpronounced“Phatt” asseenbytheinvestordoingtheanalysis. P t isbasedon the investor’s estimates of the dividend stream and the riskiness of that stream. There are many investors in the marketsotherecanbemanyestimatesfor P t .However forthemarginalinvestorP 0 mustequal P 0 .Otherwisea disequilibriumwouldexistandbuyingandsellinginthe marketwouldsoonresultinP 0 equaling P 0 asseenbythe marginalinvestor. g ¼ expected growth rate in dividends as predicted by an investor. If dividends are expected to grow at a constant rate g should also equal the expected growth rate in earnings and the stock’s price. Different investors use differentg’stoevaluateafirm’sstockbutthemarketprice P 0 is based on g as estimated by the marginal investor. r s ¼ required or minimum acceptable rate of return on the stock considering its riskiness and the returns available on other investments. Different investors typically have different opinions but the key is again the marginal investor. The determinants of r s include factors discussed in Chapter 8 including the real rate of return expected inflation and risk. r s ¼ expected rate of return pronounced “r hat s” that an investor believes the stock will provide in the future. Theexpectedreturncanbeaboveorbelowtherequired return but a rational investor will buy the stock if r s exceeds r s sell the stock if r s is less than r s and simply hold the stock if these returns are equal. Again the key is the marginal investor whose views determine the actual stock price. r s ¼ actual or realized after-the-fact rate of return pronounced “rbars.” You can expect to obtain a return of r s ¼ 10 if you buy a stock today but if the market goesdownyoumayendupwithanactualrealizedreturn that is much lower perhaps even negative. D 1 /P 0 ¼ dividend yield expected during the coming year. If Company X’s stock is expected to pay a dividend of D 1 ¼ 1 during the next 12 months and if X’scurrentpriceis P 0 ¼20theexpecteddividendyieldwillbe1/20¼0.05 ¼5.Differentinvestorscouldhavedifferentexpectations for D 1 but again the marginal investor is the key. ð P 1 P 0 ÞP 0 ¼ expected capital gains yield on the stock during the coming year. If the stock sells for 20.00 today and if it is expected to rise to 21.00 by the end of the year the expected capital gain will be P 1 P 0 ¼ 21.00 – 20.00 ¼ 1.00 and the expected capital gains yield will be 1.00/20.00 ¼ 0.05 5. Different investors can have differentexpectationsfor P 1 butthemarginalinvestoriskey. Expectedtotalreturn¼ r s ¼ expected dividend yield D 1 /P 0 plus expected capital gains yield P 1 – P 0 /P 0 . In our example the expected total return ¼ r s ¼ 5 þ 5 ¼ 10. Growth Rate g The expected rate of growth in dividends per share. Required Rate of Return r s The minimum rate of return on a common stock that a stockholder considers acceptable. Expected Rate of Return r s The rate of return on a common stock that a stockholder expects to receive in the future. Actual Realized Rate of Return r s The rate of return on a common stock actually received by stockholders in some past period. r s may be greater or less than r s and/or r s . Dividend Yield The expected dividend divided by the current price of a share of stock. Capital Gains Yield The capital gain during a given year divided by the beginning price. Expected Total Return The sum of the expected dividend yield and the expected capital gains yield. 276 Part 3 Financial Assets

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Allactiveinvestorshopetobebetterthanaverage—theyhopetoidentifystocks whose intrinsic values exceed their current prices and whose expected returns expected by this investor exceed the required rate of return. Note though that abouthalfofallinvestorsarelikelytobedisappointed.Agoodunderstandingofthe points made in this chaptercan help you avoid being disappointed. 9-4a Expected Dividends as the Basis for Stock Values In our discussion of bonds we used Equation 7-1 to find the value of a bond the equation is the present value of interest payments over the bond’s life plus the present value of its maturity or par value: V B ¼ INT ð1þr d Þ 1 þ INT ð1þr d Þ 2 þþ INT ð1þr d Þ N þ M ð1þr d Þ N Stockpricesarelikewisedeterminedasthepresentvalueofastreamofcashflows andthebasicstockvaluationequationissimilartotheoneforbonds.Whatarethe cash flows that a corporation will provide to its stockholders To answer that question think of yourself as an investor who buys the stock of a company that is expected to go on indefinitely for example GE. You intend to hold it in your family forever. In this case all you and your heirs will receive is a stream of dividends and the value of the stock today can be calculated as the present value of an infinite stream of dividends: Value of stock ¼ P 0 ¼ PV of expected future dividends ¼ D 1 ð1þr s Þ 1 þ D 2 ð1þr s Þ 2 þþ D 1 ð1þr s Þ 1 ¼ X 1 t¼1 D t ð1þr s Þ t 9-1 What about the more typical case where you expect to hold the stock for a finite period and then sell it—what will be the value of P 0 in this case Unless the companyislikelytobeliquidatedorsoldandthusdisappearsthevalueofthestock is again determined by Equation 9-1. To see this recognize that for any individual investor the expected cash flows consist of expected dividends plus the expected sale price of the stock. However the sale price to the current investor depends on thedividendssomefutureinvestorexpectsandthatinvestor’sexpectedsaleprice isalsodependentonsomefuturedividendsandsoforth.Thereforeforallpresent and future investors in total expected cash flows must be based on expected future dividends. Put another way unless a firm is liquidated or sold to another concern the cash flows itprovidestoits stockholders will consist only ofastream of dividends. Therefore the value of a share of stock must be established as the present value of the stock’s expected dividend stream. 4 4 The general validity of Equation 9-1 can also be confirmed by asking yourself the following question: Suppose I buy a stock and expect to hold it for 1 year. I will receive dividends during the year plus the value P 1 when I sell it at the end of the year. But what will determine the value of P 1 The answer is that it will be determined as the present value of the dividends expected during Year 2 plus the stock price at the end of that year which in turn will be determined as the present value of another set of future dividends and an even more distant stock price. This process can be continued ad infinitum and the ultimate result is Equation 9-1. We should note that investors periodically lose sight of the long-run nature of stocks as investments and forget that in order to sell a stock at a profit one must find a buyer who will pay the higher price. If you analyze a stock’s value in accordance with Equation 9-1 conclude that the stock’s market price exceeds a reasonable value and buy the stock anyway you wouldbe followingthe “bigger fool” theory of investment—you think you may be a fool to buy the stock at its excessive price but you also believe that when you get ready to sell it you can find someone who is an even bigger fool. The bigger fool theory was widely followed in the summer of 2000 just before the stock market crashed. Chapter 9 Stocks and Their Valuation 277

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SELFTEST Explain the following statement: Whereas a bond contains a promise to pay interest a share of common stock typically provides an expectation of but no promise of dividends plus capital gains. What are the two parts of most stocks’ expected total return If D 1 ¼ 2.00 g ¼ 6 and P 0 ¼ 40.00 what are the stock’s expected dividend yield capital gains yield and total expected return for the coming year 5 6 11 Is it necessary for all investors to have the same expectations regarding a stock for the stock to be in equilibrium No but explain. What would happen to a stock’s price if the “marginal investor” examined a stock and concluded that its intrinsic value was greater than its current market price P 0 would rise. 9-5 CONSTANT GROWTH STOCKS Equation 9-1 is a generalized stock valuation model in the sense that the time patternofD t canbeanything:D t canberisingfallingorfluctuatingrandomlyorit canbezeroforseveralyears.Equation9-1canbeappliedinanyofthesesituations and with a computer spreadsheet we can easily use the equation to find a stock’s intrinsicvalue—providedwehaveanestimateofthefuturedividends.Howeverit is not easy to obtain accurate estimates of future dividends. Still for many companies it is reasonable to predict that dividends will grow at a constant rate. In this case Equation 9-1 may be rewritten as follows: P 0 ¼ D 0 ð1þgÞ 1 ð1þr s Þ 1 þ D 0 ð1þgÞ 2 ð1þr s Þ 2 þþ D 0 ð1þgÞ 1 ð1þr s Þ 1 ¼ D 0 ð1þgÞ r s g ¼ D 1 r s g 9-2 The last term of Equation 9-2 is the constant growth model or Gordon model named after Myron J. Gordon who did much to develop and popularize it. 5 Theterm r s inEquation 9-2 is the required rate of returnwhich is ariskless rate plus a risk premium. However we know that if the stock is in equilibrium the required rate of return must equal the expected rate of return which is the expected dividend yield plus an expected capital gains yield. So we can solve Equation 9-2 for r s but now using the hat to indicate that we are dealing with an expected rate of return: 6 Expected rate of return ¼ Expected dividend yield þ Expected growth rateor capital gains yield r s ¼ D 1 P 0 þ g 9-3 We illustrate Equations 9-2 and 9-3 in the following section. Constant Growth Gordon Model Used to find the value of a constant growth stock. 5 The last term in Equation9-2 is derivedin the Web/CDExtension of Chapter5 of EugeneF. Brighamand PhillipR. Daves Intermediate Financial Management 9th ed. Mason OH: Thomson/South-Western 2007. In essence Equation 9-2 is the sum of a geometric progression and the final result is the solution value of the progression. 6 Ther s valueinEquation9-2isarequiredrateofreturnbutwhenwetransformEquation9-2toobtainEquation9-3 wearefindinganexpectedrateofreturn.Obviouslythetransformationrequiresthatr s ¼r s .Thisequalitymustholdif the stock is in equilibrium as most normally are. 278 Part 3 Financial Assets

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9-5a Illustration of a Constant Growth Stock Table 9-1 presents an analysis of Allied Food Products’ stock as performed by a security analyst after a meeting for analysts and other investors presided over by Allied’s CFO. The table looks complicated but it is really quite straightforward. 7 PartIintheupperleftcornerprovidessomebasicdata.Thelastdividendwhich was just paid was 1.15 the stock’s last closing price was 23.06 and it is in equilibrium. Based on an analysis of Allied’s history and likely future the analyst forecaststhatearningsanddividendswillgrowataconstantrateof8.3peryear and that the stock’s price will grow at this same rate. Moreover the analyst believes that the most appropriate required rate of return is 13.7. Different analysts might use different inputs but we assume for now that since this analyst is widely followed her results represent those of the marginal investor. Now look at Part IV where we show the predicted stream of dividends and stock prices along with annual values for the dividend yield the capital gains yieldandtheexpectedtotalreturn.NoticethatthetotalreturnshowninColumn6 isequal to the required rate ofreturn shown in Part I. This indicatesthat the stock Analysis of a Constant Growth Stock Table 9-1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 I. Basic Information III. Examples: II. Formulas Used in the Analysis: D 0 P 0 g r s 1.15 23.06 8.30 13.70 Col. 2 Col. 3 Col. 4 Col. 5 Col. 6 Col. 7 At end of year: 1 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 1.15 1.25 1.35 1.46 1.58 1.71 1.86 2.01 2.18 2.36 2.55 23.06 24.98 27.05 29.30 31.73 34.36 37.21 40.30 43.65 47.27 51.19 5.40 5.40 5.40 5.40 5.40 5.40 5.40 5.40 5.40 5.40 8.30 8.30 8.30 8.30 8.30 8.30 8.30 8.30 8.30 8.30 13.70 13.70 13.70 13.70 13.70 13.70 13.70 13.70 13.70 13.70 1.10 1.04 0.99 0.95 0.90 0.86 0.82 0.78 0.74 0.71 Dividend 2 Price 3 Dividend yield 4 Capital gain yield 5 Total returns 6 Sum of PVs from 1 to P 0 23.06 PV of dividend at 13.7 7 1.25 23.06 5.40 8.30 13.70 1.10 D 1 1.15001.083 P 0 1.25/0.137 – 0.083 Dividend yield Year 1: 1.25/23.06 Cap gains yield Year 1: 24.98 – 23.06/23.06 Total return Year 1: 5.4 + 8.3 PV of D 1 discounted at 13.7 Dividend in Year t D t in Col. 2 Intrinsic value and price in Year t P t in Col. 3 Dividend yield constant in Col. 4 Capital gains yield constant in Col. 5 Total return constant in Col. 6 PV of dividends discounted at 13.7 Col. 7 D t–1 1 + g D t+1 /r s – g D t /P t–1 P t – P t–1 /P t–1 Div. yield + CG yield D t /1 + r s t AB C D E F G H I IV. Table: Forecasted Results over Time 7 You may notice some minor “errors” in the table. These are not errors—they are simply differences caused by rounding. Chapter 9 Stocks and Their Valuation 279

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analyst thinks that the stock is fairly priced hence it is in equilibrium. She fore- casted out 10 years but she could have forecasted out to infinity. Part II shows the formulas used to calculate the data in Part IV and Part III givesexamplesofthecalculations. ForexampleD 1 thefirstdividend apurchaser would receive is forecasted to be D 1 ¼ 1.151.083 ¼ 1.25 and the other fore- casted dividends in Column 2 were calculated similarly. The estimated intrinsic values shown in Column 3 are based on Equation 9-2 the constant growth model: P 0 ¼ D 1 /r s – g ¼ 1.25/0.137 – 0.083 ¼ 23.06 corrected for rounding P 1 ¼ 24.98 and so forth. Column4showsthedividendyieldwhichfor2009isD 1 /P 0 ¼5.40andthis number is constant thereafter. The capital gain expected during 2009 is P 1 – P 0 ¼ 24.98–23.06¼1.92whichwhendividedbyP 0 givestheexpectedcapitalgains yield1.92/23.06¼8.3againcorrectedforrounding.Thetotalreturnisfound as the dividend yield plus the capital gains yield 13.7 and it is both constant and equal to the required rate of return given in Part I. Finally look at Column 7 in the table. Here we find the present value of each ofthedividendsshowninColumn2discountedattherequiredrateofreturn.For example the PV of D 1 ¼ 1.25/1.137 1 ¼ 1.10 the PV of D 2 ¼ 1.35/1.137 2 ¼ 1.04 and so forth. If you extended the table out to about 170 years with Excel thisiseasythensummedthePVsofthedividendsyouwouldgetthesamevalue as that found using Equation 9-2 23.06. 8 Figure 9-2 shows graphically what’s happening. We extended the table out 20 years and then plotted dividends from Column 2 in the upper step function curve and the PV of those dividends in the lower curve. The sum of the PVs is an estimate of the stock’s forecasted intrinsic value. Note that in Table 9-1 the forecasted intrinsic value is equal to the current stock price and the expected total return is equal to the required rate of return. In this situation the analysis would call the stock a “Hold” and would recommend that investors not buy or sell it. However if the analyst were somewhat more optimistic and thought the growth rate would be 10.0 rather than 8.3 the forecastedintrinsicvaluewouldbebyEquation9-234.19andtheanalystwould callita“Buy.”Atg¼6theintrinsicvaluewouldbe15.83andthestockwould be a “Sell.” Changes in the required rate of return would produce similar changes in the forecasted intrinsic value and thus the equilibrium current price. 9-5b Dividends Versus Growth The discounted dividend model as expressed in Equation 9-2 shows that other things held constant a higher value for D 1 increases a stock’s price. However Equation 9-2 shows that a higher growth rate also increases the stock’s price. But now recognize the following: l Dividends are paid out of earnings. l Therefore growth in dividends requires growth in earnings. l Earnings growth in the long run occurs primarily because firms retain earn- ings and reinvest them in the business. l Therefore the higher the percentage of earnings retained the higher the growth rate. To illustrate all this suppose you inherit a business that has 1000000 of assets no debt and thus 1000000 of equity. The expected return on equity ROE 8 The dividends get quite large but the discount rate exceeds the growth rate so the PVs of the dividends become quite small. In theory you would have to go out to infinity to find the exact price of a constant growth stock but the difference between the Equation 9-2 value and the sum of the PVs can’t be seen out to 2 decimal places if you go out about 170 periods. 280 Part 3 Financial Assets

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equals 10.0 so its expected earnings for the coming year are 0.101000000 ¼ 100000. You could take out the entire 100000 of earnings in dividends or you could reinvest some or all of the 100000 in the business. If you pay out all the earnings you will have 100000 of dividend income this year but dividends will not grow because assets and therefore earnings will not grow. However suppose you decide to have the firm pay out 40 and retain 60. Now your dividend income in Year 1 will be 40000 but assets will rise by 60000 and earnings and dividends will likewise increase: Next years earnings¼ Prior earningsþROEðRetained earningsÞ ¼ 100000þ0:1ð60000Þ ¼ 106000 Next years dividends¼ 0:4 106000Þ¼ 42400 ð Moreover your dividend income will continue togrow by 6 per year thereafter: Growth rate¼ð1 Payout ratioÞROE ¼ð1 0:4Þ10:0 ¼ 0:6ð10:0Þ¼ 60 9-4 Thisdemonstratesthatinthelongrungrowthindividendsdependsprimarilyon the firm’s payout ratio and its ROE. In our example we assumed that other things remain constant. This is often but not always a logical assumption. For example suppose the firm develops a Present Values of Dividends of a Constant Growth Stock where D 0 ¼ 1.15 g ¼ 8.3 r s ¼ 13.7 FIGURE 9-2 Dividend 1.15 PV D 1 1.10 0 5 10 15 20 PV of Each Dividend D 0 1 + g t 1 + r s t Area under PV Curve 23.06 Dollar Amount of Each Dividend D 0 1 + g t Years PV D t P 0 Σ 8 t 1 ˆ Chapter 9 Stocks and Their Valuation 281

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successful new product or hires a better CEO or makes some other change that increased the ROE. Any of these actions could cause the ROE and thus the growth rate to increase. Also note that the earnings of new firms are often low or even negativeforseveralyearsthenbegintoriserapidlyfinallygrowthlevelsoffasthe firmapproachesmaturity.Suchafirmmightpaynodividendsforitsfirstfewyears then pay a low initial dividend but let it increase rapidly and finally make regular payments that grow at a constant rate once earnings have stabilized. In any such situation the nonconstant model as discussed in a later section must be used. 9-5c Which Is Better: Current Dividends or Growth We saw in the preceding section that a firm can pay a higher current dividend by increasingitspayoutratiobutthatwillloweritsdividendgrowthrate.Sothefirm can provide a relatively high current dividend or a high growth rate but not both. This being the case which would stockholders prefer The answer is not clear. As we will see in the dividend chapter some stockholders prefer current dividends while others prefer a lower payout ratio and future growth. Empirical studies have been unable to determine which strategy is optimal in the sense of max- imizing afirm’s stock price. So dividend policy is an issue that management must decide on the basis of its judgment not a mathematical formula. Logically shareholders should prefer for the company to retain more earnings hence pay less current dividends if the firm has exceptionally good investment oppor- tunities however shareholders should prefer a high payout if investment opportunities are poor. In spite of this taxes and other factors complicate the situation. We will discuss all this in detail in the dividend chapter but for now just assume that the firm’s management has decided on a payout policy and uses that policy to determine the actual dividend. 9-5d Required Conditions for the Constant Growth Model Several conditions are necessary for Equation 9-2 to be used. First the required rateofreturnr s mustbegreaterthanthelong-rungrowthrateg.Iftheequationis used in situations where g is greater than r s the results will be wrong meaningless and misleading.Forexampleiftheforecastedgrowthrateinourexamplewas15and thus exceeded the 13.7 required rate of return stock price as calculated by Equation 9-2 would be a negative 101.73. That would be nonsense—stocks can’t have negative prices. Moreover in Table 9-1 the PV of each future dividend wouldexceedthatoftheprioryear.IfthissituationwasgraphedinFigure9-2the step-function curve for the PV of dividends would be increasing not decreasing sothesumwouldbeinfinitely highwhich wouldindicate aninfinitelyhighstock price.Obviouslystockpricescannotbeeither infinite ornegativesoEquation9-2 cannot be used unless r s g. Second the constant growth model as expressed in Equation 9-2 is not appropriate unless a company’s growth rate is expected to remain constant in the future.Thisconditionalmostneverholdsfornewstart-upfirmsbutitdoesexistfor manymaturecompanies.IndeedmaturefirmssuchasAlliedandGEaregenerally expectedtogrowataboutthesamerateasnominalgrossdomesticproductthatis real GDP plus inflation. On this basis one might expect the dividends of an average or “normal” company to grow at a rate of 5 to 8 a year. Note too that Equation 9-2 is sufficiently general to handle the case of a zero growthstockwhere thedividendisexpectedtoremain constantovertime.Ifg¼ 0 Equation 9-2 reduces to Equation 9-5: Zero Growth Stock A common stock whose future dividends are not expected to grow at all that is g ¼ 0. P 0 ¼ D r s 9-5 282 Part 3 Financial Assets

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This is the same equation as the one we developed in Chapter 5 for a perpetuity and it is simply the current dividend divided by the discount rate. Finally as we discuss later in the chapter most firms even rapidly growing startups and others that pay no dividends at present can be expected to pay dividends at some point in the future at which time the constant growth model will be appropriate. For such firms Equation 9-2 is used as one part of a more complicated valuation equation that we discuss next. SELFTEST Write out and explain the valuation formula for a constant growth stock. Explain how the formula for a zero growth stock can be derived from that for a normal constant growth stock. Firm A is expected to pay a dividend of 1.00 at the end of the year. The required rate of return is r s ¼ 11. Other things held constant what would the stock’s price be if the growth rate was 5 What if g was 0 16.67 9.09 Firm B has a 12 ROE. Other things held constant what would its expected growth rate be if it paid out 25 of its earnings as dividends 75 9 3 If Firm B had a 75 payout ratio but then lowered it to 25 causing its growth rate to rise from 3 to 9 would that action necessarily increase the price of its stock Why or why not 9-6 VALUING NONCONSTANT GROWTH STOCKS Formanycompaniesitisnotappropriatetoassumethatdividendswillgrowata constant rate. Indeed most firms go through life cycles where they experience different growth rates duringdifferentparts ofthe cycle.Intheir earlyyearsmost firms grow much faster than the economy as a whole then they match the economy’s growth and finally they grow at a slower rate than the economy. 9 Automobile manufacturers in the 1920s computer software firms such as Micro- softinthe1990sandGoogleinthe2000sareexamplesoffirmsintheearlypartof theircycle.Thesefirmsaredefinedassupernormalornonconstantgrowthfirms. Figure 9-3 illustrates nonconstant growth and compares it with normal growth zero growth and negative growth. 10 In the figure the dividends of the supernormal growth firm are expected to growata30rateforthreeyearsafterwhichthegrowthrateisexpectedtofallto 8 the assumed average for the economy. The value of this firm’s stock like any other asset is the present value of its expected future dividends as determined by 9 The concept of life cycles could be broadened to product cycle which would include both small start-up companies and large companies such as Microsoft and Procter Gamble which periodically introduce new products that give sales and earnings a boost. We should also mention business cycles which alternately depress and boost sales and profits. The growth rate just after a major new product has been introduced or just after a firm emerges from the depths of a recession is likely to be much higher than the “expected long-run average growth rate” which is the proper number for use in the discounted dividend model. 10 A negative growthrate indicatesa decliningcompany.A miningcompany whoseprofitsare fallingbecauseof a decliningorebody isan example.Someonebuyingsuch acompanywouldexpect itsearningsandconsequently its dividends and stock price to decline each year which would lead to capital losses rather than capital gains. Obviously a declining company’s stock price is relatively low and its dividend yield must be high enough to offset the expected capital loss and still produce a competitive total return. Students sometimes argue that they would never be willing to buy a stock whose price was expected to decline. However if the present value of the expecteddividends exceeds the stock price the stock is still a good investment that would provide a good return. Supernormal Nonconstant Growth The part of the firm’s life cycle in which it grows much faster than the economy as a whole. Chapter 9 Stocks and Their Valuation 283

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Equation9-1. When D t is growingat aconstant rate wecansimplify Equation9-1 to Equation 9-2 P 0 ¼ D 1 /r s – g. In the supernormal case however the expected growth rate is not a constant. In our example there are two distinctly different rates. BecauseEquation9-2requiresaconstantgrowthrateweobviouslycannotuse ittovaluestocksthatarenotgrowingataconstantrate.Howeverassumingthata company currently enjoying supernormal growth will eventually slow down and become a constant growth stock we can combine Equations 9-1 and 9-2 to con- struct a new formula Equation 9-6 for valuing the stock. Firstweassumethatthedividendwillgrowatanonconstantrategenerallya relatively high rate for N periods after which it will grow at a constant rate g. N is often called the terminalor horizon date. Second we can use the constant growthformulaEquation9-2todeterminewhatthestock’shorizonorterminal value will be N periods from today: Horizon Value¼ P N ¼ D Nþ1 r s g The stock’s intrinsic value today P 0 is the present value of the dividends during the nonconstant growth period plus the present value of the horizon value: P 0 ¼ D 1 ð1þr s Þ 1 þ D 2 ð1þr s Þ 2 þþ D N ð1þr s Þ N |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflzfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl PV of dividends during the nonconstant growth Periodt¼ 1 N þ D Nþ1 ð1þr s Þ Nþ1 þþ D 1 ð1þr s Þ 1 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflzfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl Horizon value¼ PV of dividends during the constant growth Periodt¼ Nþ1 1 Illustrative Dividend Growth Rates FIGURE 9-3 Dividend 1.15 Declining Growth –8 Zero Growth 0 Normal Growth 8 Normal Growth 8 End of Supernormal Growth Period Supernormal Growth 30 0 123 4 5 Years TerminalHorizonDate The date when the growth rate becomes constant. At this date it is no longer necessary to forecast the individual dividends. Horizon Terminal Value The value at the horizon date of all dividends expected thereafter. 284 Part 3 Financial Assets

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P 0 ¼ D 1 ð1þr s Þ 1 þ D 2 ð1þr s Þ 2 þþ D N ð1þr s Þ N |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflzfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl PV of dividends during the nonconstant growth period t¼ 1 N þ P N ð1þr s Þ N |fflfflfflfflfflzfflfflfflfflffl PV of horizon value P N : ½ðD Nþ1 Þðr s gÞ ð1þr s Þ N 9-6 To implement Equation 9-6 we go through the following three steps: 1. Find the PV of each dividend during the period of nonconstant growth and sum them. 2. Find the expected stock price at the end of the nonconstant growth period at whichpointithasbecomeaconstantgrowthstocksoitcanbevaluedwiththe constant growth model and discount this price back to the present. 3. Add these two components to find the stock’s intrinsic value P 0 . Figure 9-4 illustrates the process for valuing nonconstant growth stocks. Here we use a new company Firm M and we assume that the following five facts exist: r s ¼ stockholders’ required rate of return ¼ 13.4. This rate is used to discount the cash flows. N ¼ years of nonconstant growth ¼ 3. g s ¼ rate of growth in both earnings and dividends during the nonconstant growth period ¼ 30. This rate is shown directly on the time line. Note: The growth rate during the nonconstant growth period could vary from year to year. Also there could be several different nonconstant growth periods—for example 30 for three years 20 for the next three years and a constant 8 thereafter. g n ¼ rate of normal constant growth after the nonconstant period ¼ 8.0. This rate is also shown on the time line after Period 3 when it is in effect. D 0 ¼ last dividend the company paid ¼ 1.15. Thevaluationprocessdiagrammed inFigure 9-4 isexplained inthesteps setforth below the time line. The value of the nonconstant growth stock is calculated to be 39.21. Note that in this example we assumed a relatively short 3-year horizon to keepthingssimple. Whenevaluating stocks most analystsuse a longer horizon for example 5 years to estimate intrinsic values. This requires a few more calculations but because analysts use spreadsheets the arithmetic is not a problem. In practice the real limitation is obtaining reliable forecasts for future growth. SELFTEST Explain how one would find the value of a nonconstant growth stock. Explain what is meant by terminal horizon date and horizon terminal value. Chapter 9 Stocks and Their Valuation 285

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9-7 VALUING THE ENTIRE CORPORATION 11 Thus far we have discussed the discounted dividend model for valuing a firm’s common stock. This procedure is widely used but it is based on the assumption thattheanalystcanforecastfuturedividendsreasonablywell.Thisisoftentruefor mature companies that have a history of steadily growing dividends. However dividends are dependent on earnings so a really reliable dividend forecast must be based on an underlying forecast of the firm’s future sales costs and capital requirements. This recognition has led to an alternative stock valuation approach the corporate valuation model. Finding the Value of a Nonconstant Growth Stock FIGURE 9-4 02 1 34 D 3 2.5266 D 2 1.9435 D 1 1.4950 D 4 2.7287 53.0576 P ˆ 3 50.5310 g s 30 30 13.4 13.4 13.4 30 g n 8 1.3183 1.5113 36.3838 39.2134 39.21 P ˆ 0 Notes to Figure 9-4: Step 1. Calculate the dividends expected at the end of each year during the nonconstant growth period. Calculate the first dividend D 1 ¼ D 0 1 + g s ¼ 1.151.30¼ 1.4950. Here g s is the growth rate during the 3-year nonconstant growth period 30. Show the 1.4950 on the time lineasthecashflowatTime1.CalculateD 2 ¼D 1 1+g s ¼1.49501.30¼1.9435thenD 3 ¼D 2 1+g s ¼1.94351.30¼2.5266.Show these values on the time line as the cash flows at Times 2 and 3. Note that D 0 is used only to calculate D 1 . Step 2. The price of the stock is the PV of dividends from Time 1 to infinity so in theory we could project each future dividend with the normal growth rate g n ¼ 8 used to calculate D 4 and subsequent dividends. However we know that after D 3 has been paid at Time 3 the stock becomes a constant growth stock. Therefore we can use the constant growth formula to find P 3 which is the PV of the dividends from Time 4 to infinity as evaluated at Time 3. First we determine D 4 ¼ 2.52661.08 ¼ 2.7287 for use in the formula then we calculate P 3 as follows: P 3 ¼ D 4 r s g n ¼ 2:7287 0:134 0:08 ¼ 50:5310 We show this 50.5310 on the time line as a second cash flow at Time 3. The 50.5310 is a Time 3 cash flow in the sense that the stockholder could sell the stock for 50.5310 at Time 3 and in the sense that 50.5310 is the present value of the dividend cash flows from Time 4 to infinity. Note that the total cash flow at Time 3 consists of the sum of D 3 +P 3 ¼ 2.5266 þ 50.5310 ¼ 53.0576. Step3. Now that the cash flows have been placed on the time line we can discount each cash flow at the required rate of return r s ¼ 13.4. We could discount each cash flow by dividing by 1.134 t where t¼ 1 for Time 1 t¼ 2 for Time 2 and t¼ 3 for Time 3. This produces the PVs shown to the left below the time line and the sum of the PVs is the value of the nonconstant growth stock 39.21. With a financial calculator you can find the PV of the cash flows as shown on the time line with the cash flow CFLO register of your calculator. Enter 0 for CF 0 because you receive no cash flow at Time 0 CF 1 ¼ 1.495 CF 2 ¼ 1.9435 and CF 3 ¼ 2.5266þ 50.5310¼ 53.0576. Then enter I/YR ¼ 13.4 and press the NPV key to find the value of the stock 39.21. 11 The corporate valuation model presented in this section is widely used by analysts and it is in many respects superior to the discounted dividend model. However it is rather involved as it requires the estimation of sales costs and cash flows on out into the future before the discounting process is begun. Therefore in the intro- ductory course some instructors may prefer to omit Section 9-7 and skip to Section 9-8. Corporate Valuation Model A valuation model used as an alternative to the discounted dividend model to determine a firm’s value especially one with no history of divi- dends or the value of a division of a larger firm. The corporate model first calculates the firm’s free cash flows then finds their present values to deter- mine the firm’s value. 286 Part 3 Financial Assets

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EVALUATING STOCKS THAT DON’T PAY DIVIDENDS The discounted dividend model assumes that the firm is currently paying a dividend. However many firms even highly profitable ones including Google Dell and Apple have never paid a dividend. If a firm is expected to begin payingdividendsinthefuturewecanmodifytheequations presented in the chapter and use them to determine the value of the stock. A new business often expects to have low sales during its firstfewyears ofoperationasitdevelops itsproduct. Then if the product catches on sales will grow rapidly for several years. Sales growth brings with it the need for additional assets—a firm cannot increase sales without also increasing its assets and asset growth requires an increase in liability and/or equity accounts. Small firms can generally obtain some bank credit but they must maintain a reasonable bal- ance between debt and equity. Thus additional bank bor- rowings require increases in equity and getting the equity capital needed to support growth can be difficult for small firms. They have limited access to the capital markets and even when they can sell common stock their owners are reluctant to do so for fear of losing voting control. Therefore the best source of equity for most small businesses is retained earnings for this reason most small firms pay no dividends during their rapid growth years. Eventually though successful small firms do pay dividends and those dividends generally grow rapidly at first but slow down to a sustainable constant rate once the firm reaches maturity. If a firm currently pays no dividends but is expected to pay future dividends the value of its stock can be found as follows: 1. Estimate at what point dividends will be paid the amountofthe firstdividendthegrowth rateduringthe supernormal growth period the length of the super- normal period the long-run constant growth rate and the rate of return required by investors. 2. Use the constant growth model to determine the priceof the stock after the firm reaches a stable growth situation. 3. Set out on a time line the cash flows dividends during the supernormal growth period and the stock price once the constant growth state is reached then find the present value of these cash flows. That present value represents the value of the stock today. To illustrate this process consider the situation for Marvel-Lure Inc. a company that was set up in 2007 to produce and market a new high-tech fishing lure. Marvel- Lure’s salesare currentlygrowing atarate of200 peryear. The company expects to experience a high but declining rate of growth in sales and earnings during the next 10 years after which analysts estimate that it will grow at a steady 10 per year. The firm’s management has announced that it will pay no dividends for 5 years but that if earnings materialize as forecasted it will payadividend of 0.20 pershareattheend ofYear60.30inYear70.40 in Year 8 0.45 in Year 9 and 0.50 in Year 10. After Year 10 current plans are to increase dividends by 10 per year. MarvelLure’s investment bankers estimate that invest- ors require a 15 return on similar stocks. Therefore we find the value of a share of MarvelLure’s stock as follows: P 0 ¼ 0 ð1:15Þ 1 þþ 0 ð1:15Þ 5 þ 0:20 ð1:15Þ 6 þ 0:30 ð1:15Þ 7 þ 0:40 ð1:15Þ 8 þ 0:45 ð1:15Þ 9 þ 0:50 ð1:15Þ 10 þ 0:50ð1:10Þ 0:15 0:10 1 ð1:15Þ 10 ¼ 3:30 The last term finds the expected stock price in Year 10 and then finds the present value of that price. Thus we see that the discounted dividend model can be applied to firms that currentlypaynodividendsprovidedwecanestimatefuture dividends with a fair degree of confidence. However in many cases we can have more confidence in the forecasts of free cash flows and in these situations it is better to use the corporate valuation model. Rather than starting with a forecast of dividends the corporate valuation model focuses on the firm’s future free cash flows. We discussed free cash flow FCF in Chapter 3 where we developed the following equation: FCF¼ EBITð1 TÞþ Depreciation and amortizaton Net Capital þ working expenditures capital 2 6 4 3 7 5 3 7 5 2 6 6 4 EBIT is earnings before interest and taxes and free cash flow represents the cash generated from current operations less the cash that must be spent on investments in fixedassetsandworkingcapitaltosupportfuturegrowth.ConsiderthecaseofHome Depot HD. The first term in brackets in the preceding equation represents the amount of cash that HD is generating from its existing stores. The second term Chapter 9 Stocks and Their Valuation 287

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represents the amount of cash the company plans to spend this period to construct new stores. To open a new store HD must spend cash to purchase the land and construct the building—these are the capital expenditures and they lead to a corre- spondingincreaseinthefirm’sfixedassetsasshownonthebalancesheet.ButHDalso needstoincreaseitsworkingcapitalespeciallyinventory.Puttingeverythingtogether HDgeneratespositivefreecashflowforitsinvestorsifandonlyifthemoneyfromits existing stores exceeds the money required to build and equip its new stores. 9-7a The Corporate Valuation Model In Chapter 3 we explained that a firm’s value is determined by its ability to generate cash flow both now and in the future. Therefore its market value can be expressed as follows: Market value ¼ V company ¼ PV of expected future free cash flows of company ¼ FCF 1 ð1þWACCÞ 1 þ FCF 2 ð1þWACCÞ 2 þþ FCF 1 ð1þWACCÞ 1 9-7 Here FCF t is the free cash flow in Year t and the discount rate the WACC is the weighted average cost of all the firm’s capital. When thinking about the WACC note these two points: 1. Thefirmfinanceswithdebtpreferredstockandcommonequity.TheWACC is the weighted average of these three types of capital and we discuss it in detail in Chapter 10. 2. Free cash flow is the cash generated before any payments are made to any investors so it must be used to compensate common stockholders preferred stock- holders and bondholders. Moreover each type of investor has a required rate of returnandtheweightedaverageofthosereturnsistheWACCwhichisused to discount the free cash flows. Freecashflowsaregenerallyforecastedfor5to10yearsafterwhichitisassumed that the final explicitly forecasted FCF will grow at some long-run constant rate. Once the company reaches its horizon date when cash flows begin to grow at a constant rate we can use the following formula to calculate the market value of the company as of that date: Horizon value¼ V Company at t¼N ¼ FCF Nþ1 ðWACC g FCF Þ 9-8 The corporate model is applied internally by the firm’s financial staff and by outside security analysts. For illustrative purposes we discuss an analysis con- ducted by Susan Buskirk senior food analyst for the investment banking firm MortonStaleyandCompany.HeranalysisissummarizedinTable9-2whichwas reproduced from the chapter Excel model. l BasedonAllied’shistoryandBuskirk’sknowledgeofthefirm’sbusinessplan she estimated sales costs and cash flows on an annual basis for 5 years. Growthwillvaryduringthoseyearsbutsheassumesthatthingswillstabilize andgrowthwillbeconstantafterthefifthyear.Shewouldhavemadeexplicit forecasts for more years if she thought it would take longer to reach a steady- state constant growth situation. l Buskirk next calculated the expected free cash flows FCFs for each of the 5 nonconstant growth years and she found the PV of those cash flows discounted at the WACC. l After Year 5 she assumed that FCF growth would be constant hence the constant growth model could be used to find Allied’s total market value at Year 5. This “horizon or terminal value” is the sum of the PVs of the FCFs from Year 6 on out into the future discounted back to Year 5 at the WACC. It 288 Part 3 Financial Assets

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Allied Food Products: Free Cash Flow Valuation Table 9-2 AB C D E F G H 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 Part 1. Key Inputs Forecasted Y ears 2010 2011 2012 2013 2009 2010 2011 2012 2013 2009 2008 Sales growth rate Operating costs as a of sales Growth in operating capital Deprn as a of operating capital Tax rate WACC Long-run FCF growth g LR 9.0 87.0 8.0 8.0 9.0 86.0 8.0 7.0 9.0 85.0 8.0 7.0 8.0 85.0 8.0 7.0 10.0 87.0 8.0 6.0 40.0 10.0 6.0 Part 2. Forecast of Cash Flows During Period of Nonconstant Growth Historical Forecasted Y ears 4615.5 3923.2 185.1 507.2 304.3 2644.8 195.9 108.4 67.3 Sales Operating costs Depreciation EBIT EBIT 1 - T Total operating capital Net new operating cap Free Cash Flow FCF PV of FCFs 3000.0 2616.2 100.0 283.8 170.3 1800.0 280 -109.7 N.A. 3300.0 2871.0 116.6 312.4 187.4 1944.0 144.0 43.4 39.5 3597.0 3129.4 168.0 299.6 179.8 2099.5 155.5 24.3 20.1 3920.7 3371.8 158.7 390.2 234.1 2267.5 168.0 66.1 49.7 4273.6 3632.6 171.4 469.6 281.8 2448.9 181.4 100.4 68.6 Part 3. Terminal Value and Intrinsic Value Estimation Estimated Value at the Horizon 2013 Free Cash Flow 2014 Terminal Value at 2013 TV PV of the 2013 TV Calculation of Firms Intrinsic Value Sum of PVs of FCFs 2009-2013 PV of 2013 TV Total corporate value Less: market value of debt and pfd Intrinsic value of common equity Shares outstanding millions 114.9 2872.7 1783.7 245.1 1783.7 2028.8 860.0 1168.8 50.0 Intrinsic Value Per Share 23.38 FCF 2013 1 + g LR TV / 1 + WACC N FCF 2014 WACC - g TV 2013 follows that: Horizon Value at t ¼ 5 ¼ FCF 6 /WACC – g FCF where g FCF represents the long-run growth rate of free cash flow. l Next she discounted the Year 5 terminal value back to the present to find its PV at Year 0. l She then summed all the PVs the annual cash flows during the nonconstant period plus the PV of the horizon value to find the firm’s estimated total market value. l Thenshesubtractedthevalueofthedebtandpreferredstocktofindthevalue of the common equity. l Finally she divided the equity value by the number of shares outstanding andtheresultwasherestimateofAllied’sintrinsicvaluepershare.Thisvalue wasquiteclosetothestock’smarketpricesosheconcludedthatAllied’sstock is priced at its equilibrium level. Consequently she issued a “Hold” recom- mendation on the stock. If the estimated intrinsic value had been significantly below the market price she would have issued a “Sell” recommendation if the estimated intrinsicvaluehadbeenwell abovethemarketprice shewould have called the stock a “Buy.” Chapter 9 Stocks and Their Valuation 289

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9-7b Comparing the Corporate Valuation and Discounted Dividend Models Analysts use both the discounted dividend model and the corporate valuation model when valuing mature dividend-paying firms and they generally use the corporate model when valuing divisions and firms that do not pay dividends. In OTHER APPROACHES TO VALUING COMMON STOCKS While the dividend growth and the corporate valuation models presented in this chapter are the most widely used methods for valuing common stocks they are by no means the only approaches. Analysts often use a number of dif- ferent techniques to value stocks. Two of these alternative approaches are described here. The P/E Multiple Approach Investors have long looked for simple rules of thumb to determine whether a stock is fairly valued. One such approach istolook at thestock’s price-to-earningsP/Eratio. Recall from Chapter 4 that a company’s P/E ratio shows how much investorsarewillingtopayforeachdollarofreportedearnings. As a starting point you might conclude that stocks with low P/E ratios are undervalued since their price is “low” given cur- rent earnings while stocks with high P/E ratios are overvalued. Unfortunately however valuingstocks isnotthatsimple. We should not expect all companies to have the same P/E ratio. P/E ratios are affected by risk—investors discount the earnings of riskier stocks at a higher rate. Thus all else equal riskier stocks should have lower P/E ratios. In addition when you buy a stock you have a claim not only on current earn- ings but also on all future earnings. All else equal companies with stronger growth opportunities will generate larger future earnings and thus should trade athigher P/E ratios. Therefore eBay is not necessarily overvalued just because its P/E ratio is 121.2 at a time when the median firm has a P/E of 19.7. Investors believe that eBay’s growth potential is well above average. Whether the stock’s future prospects justify its P/E ratio remains to be seen but in and of itself a high P/E ratio does not mean that a stock is overvalued. Nevertheless P/E ratios can provide a useful starting point instock valuation. If astock’s P/E ratio is well above its industry average and if the stock’s growth potential and risk are similar to other firms in the industry the stock’s price may be too high. Likewise if a company’s P/E ratio falls well below its historical average the stock may be undervalued —particularly if the company’s growth prospects and risk are unchanged and if the overall P/E for the market has remained constant or increased. One obvious drawback of the P/E approach is that it depends on reported accounting earnings. For this reason some analysts choose to rely on other multiples to value stocks. For example some analysts look at a company’s price-to-cash-flow ratio while others look at the price-to- sales ratio. The EVA Approach In recent years analysts have looked for more rigorous alternatives to the discounted dividend model. More than a quarterofallstockslistedontheNYSE paynodividends.This proportion is even higher on Nasdaq. While the discounted dividend model can still be used for these stocks see “Evaluating Stocks That Don’t Pay Dividends” this approach requires that analysts forecast when the stock will begin paying dividends what the dividend will be once it is establishedandwhatthefuturedividendgrowthratewillbe. In many cases these forecasts contain considerable errors. An alternative approach is based on the concept of Economic Value Added EVA which we discussed in Chapter 4 in “Economic Value Added EVA versus Net Income” that can be written as follows: EVA¼ðEquity capitalÞðROE Cost of equity capitalÞ This equation suggests that companies can increase their EVA by investing in projects that provide shareholders with returns that are above their cost of equity capital which is the return they could expect to earn on alternative invest- ments with the same level of risk. When you purchase stock in a company you receive more than just the book value of equity—you also receive a claim on all future value that is created by the firm’s managers the present value of all future EVAs. It follows that a company’s market value of equity can be written as follows: Marketvalueof equity¼Book valueþPVof allfutureEVAs We can find the “fundamental” value of the stock P 0 by simply dividing the preceding expression by the number of shares outstanding. As is the case with the discounted dividend model we can simplify the expression by assuming that at some point intimeannualEVAbecomesaperpetuity orgrowsatsome constant rate over time. a a What we have presented here is a simplified version of what is often referred to as the Edwards-Bell-Ohlson EBO model. For a more complete description of this technique and an excellent summary of how it can be used in practice read the article “Measuring Wealth” by Charles M. C. Lee in CA Magazine April 1996 pp. 32–37. 290 Part 3 Financial Assets

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principle we should find the same intrinsic value using either model but differ- encesareoftenobserved.Whenaconflictexiststheassumptionsembeddedinthe corporate model can be reexamined and once the analyst is convinced they are reasonabletheresultsofthatmodelareused.InourAlliedexampletheestimates were extremely close—the discounted dividend model predicted a price of 23.06 per share versus 23.38 using the corporate model both are essentially equal to Allied’s actual 23.06 price. In practice intrinsic value estimates based on the two models normally deviate from one another and from actual stock prices leading different analysts to reach different conclusions about the attractiveness of a given stock. The better the analyst the more often his or her valuations turn out to be correct but no one can make perfectpredictionsbecausetoomanythingscanchangerandomlyandunpredictably inthefuture.Givenallthisdoesitmatterwhetheryouusethecorporatemodelorthe discounted dividend model to value stocks We would argue that it does. If we had tovalueforexample100maturecompanieswhosedividendswereexpectedtogrow steadily in the future we would probably use the discounted dividend model. Here we would estimate only the growth rate in dividends not the entire set of pro forma financial statements hence it would be more feasible to use the dividend model. However if we were studying just one company or a few companies espe- cially companies still in the high-growth stage of their life cycles we would want to project future financial statements before estimating future dividends. Because we would already have projected future financial statements we would go ahead and apply the corporate model. Intel which pays a dividend of 0.56 versus earnings of about 1.17 is an example of a company where either model could be used but we think the corporate model is better. Now suppose you were trying to estimate the value of a company such as eBay that to date 2008 has never paid a dividend or a new