Introduction to time value of money

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Introduction to time value of money

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FINANCIAL MANAGEMENT:

FINANCIAL MANAGEMENT

PowerPoint Presentation:

Title: Financial Management Objective In today’s dynamic world engineers along with taking technical decisions also have to take financial decisions. So they need to understand, analyze and interpret financial data and financial issues. This course will help them in understanding the concepts and principles of accounting and finance with the support of software packages so that they can make quick informed financial decisions. Learning Outcomes At the end of the course the students will be able to understand: · basic accounting principles. · how to measure the performance of a business. · how to make and evaluate the impact of business decisions at all levels. Methodology The course will be taught with the aid of lectures, case studies, and use of computer spreadsheet programs. The students will self-learn the usage of accounting packages available in the industry.

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Text Book Financial Management by M.Y. Khan, and P.K. Jain, Tata McGraw Hill. Financial Management by Prasanna Chandra, Tata McGraw Hill. Books for Reference Principles of corporate finance by Brealey, Richard A. and Myers, Stewart C. Tata McGraw-Hill Publishing Delhi. Fundamentals of financial management by Brigham, Eugene F,Houston, Joel F. Thomson Asia Pte Ltd. Financial management by I.M. Pandey, Vikas Publishing House Pvt Ltd.

Course Contents:

Course Contents Topic- Introduction Basic Financial Concepts Long Term Sources of Finance Capital Budgeting: Principle Techniques Concept and measurement of cost of capital Cash Flows for Capital Budgeting Financial statements & analysis Leverages and Capital structure decision Working capital management Dividend Policy

Evaluation (Lecture Course):

Evaluation (Lecture Course) Exam % of Marks Duration of Examination Coverage / Scope (i) TEST-1 (T-1) 20 1 Hour Syllabus covered upto test 1 (ii) TEST -2 (T-2) 25 1 Hour 15 Minutes Mainly syllabus covered after Test-1, plus some questions from portions covered upto test 1 (iii)TEST-3 (T-3) 30 1 Hour 30 Minutes Mainly syllabus covered after Test-2, and upto Test-3 Plus some questions from portions covered Test-1 and Test-2 . (iv) Assignments, Quizzes, home work & Regularity in attendance. 25 Quizzes: 5 Attendance: 5 Assignment: 5 Project work: 10 Entire Semester As decided and announced by the teacher concerned in the class at the beginning of the course

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AN OVERVIEW

DEFINITION:

DEFINITION Financial Management is broadly concerned with the acquisition (investment), financing and management of assets by a business firm

GOALS OF THE FIRM:

GOALS OF THE FIRM Maximizing owners/shareholders’ wealth Maximizing the price per share Market price of a share serves as a barometer for business performance It indicates how well management is doing on behalf of its’ shareholders

OBJECTIVES OF FINANCIAL MANAGEMENT:

OBJECTIVES OF FINANCIAL MANAGEMENT Maximize owners' wealth Market value of equity

SCOPE OF FINANCIAL MANAGEMENT:

SCOPE OF FINANCIAL MANAGEMENT What should be the composition of the firms’ assets? What should be the mix of the firms’ financing? How should the firm analyse, plan and control its financial affairs?

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Financial Analysis, Planning and Control Balance Sheet Long Term Financing Short Term Financing Fixed Assets Current Assets Management of the Firm’s Asset Structure Management of the Firm’s Financial Structure KEY ACTIVITIES OF FINANCIAL MANAGEMENT

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Capital Budgeting Decisions Capital Structure Decisions Dividend Decisions Working Capital Decisions Return Risk Market Value of the Firm RISK RETURN TRADE OFF

FINANCE AND ECONOMICS:

FINANCE AND ECONOMICS Macro Economics Necessary for understanding the environment in which the firm operates Growth rate of economy, tax environment, availability of funds, rate of inflation, terms on which the firm can raise finances Micro Economics Helpful in sharpening the tools of decision making Principle of marginal analysis is applicable to decision making

FINANCE AND ACCOUNTING:

FINANCE AND ACCOUNTING Value Maximising vs. Score Keeping Cash Flow Method vs. Accrual Method Uncertainty vs. Certainty

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Time Value of Money

The Interest Rate:

Obviously, Rs10,000 today . You already recognize that there is TIME VALUE TO MONEY !! The Interest Rate Which would you prefer – Rs10,000 today or Rs10,000 in 5 years ?

Why TIME?:

TIME allows you the opportunity to postpone consumption and earn INTEREST A rupee today represents a greater real purchasing power than a rupee a year hence Receiving a rupee a year hence is uncertain so risk is involved Why TIME? Why is TIME such an important element in your decision?

Time Value Adjustment:

Time Value Adjustment Two most common methods of adjusting cash flows for time value of money: Compounding —the process of calculating future values of cash flows and Discounting —the process of calculating present values of cash flows.

Types of Interest:

Types of Interest Compound Interest Interest paid (earned) on any previous interest earned, as well as on the principal borrowed (lent). Simple Interest Interest paid (earned) on only the original amount, or principal borrowed (lent).

Simple Interest Formula:

Simple Interest Formula Formula SI = P 0 ( i )( n ) SI : Simple Interest P 0 : Deposit today (t=0) i : Interest Rate per Period n : Number of Time Periods

Simple Interest Example:

SI = P 0 ( i )( n ) = Rs1,000 ( .07 )( 2 ) = Rs140 Simple Interest Example Assume that you deposit Rs1,000 in an account earning 7% simple interest for 2 years. What is the accumulated interest at the end of the 2nd year?

Simple Interest (FV):

FV = P 0 + SI = Rs1,000 + Rs140 = Rs 1,140 Future Value is the value at some future time of a present amount of money, or a series of payments, evaluated at a given interest rate. Simple Interest (FV) What is the Future Value ( FV ) of the deposit?

Simple Interest (PV):

The Present Value is simply the Rs 1,000 you originally deposited. That is the value today! Present Value is the current value of a future amount of money, or a series of payments, evaluated at a given interest rate. Simple Interest (PV) What is the Present Value ( PV ) of the previous problem?

Future Value Single Deposit (Graphic):

Assume that you deposit Rs 1,000 at a compound interest rate of 7% for 2 years . Future Value Single Deposit (Graphic) 0 1 2 Rs 1,000 FV 2 7%

PowerPoint Presentation:

FV 1 = P 0 (1+ i ) 1 = Rs 1,000 (1 .07 ) = Rs 1,070 FV 2 = FV 1 (1+ i ) 1 = P 0 (1+ i )(1+ i ) = Rs1,000 (1 .07 )(1 .07 ) = P 0 (1+ i ) 2 = Rs1,000 (1 .07 ) 2 = Rs1,144.90 You earned an EXTRA Rs 4.90 in Year 2 with compound over simple interest. Future Value Single Deposit (Formula)

General Future Value Formula:

FV 1 = P 0 (1+ i ) 1 FV 2 = P 0 (1+ i ) 2 General Future Value Formula: FV n = P 0 (1+ i ) n or FV n = P 0 ( FVIF i , n ) General Future Value Formula etc.

Problem :

Reena wants to know how large her deposit of Rs 10,000 today will become at a compound annual interest rate of 10% for 5 years . Problem 0 1 2 3 4 5 Rs10,000 FV 5 10%

Solution:

Solution Calculation based on general formula: FV n = P 0 (1+ i ) n FV 5 = Rs10,000 (1+ 0 .10 ) 5 = Rs 16,105.10

Double Your Money!!!:

We will use the “ Rule-of-72 ” . Double Your Money!!! Quick! How long does it take to double Rs 5,000 at a compound rate of 12% per year (approx.)?

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Doubling Period = 72 / Interest Rate 6 years For accuracy use the “ Rule-of-69 ” . Doubling Period =0.35 +(69 / Interest Rate) 6.1 years

Present Value Single Deposit (Graphic):

Assume that you need Rs 1,000 in 2 years. Let’s examine the process to determine how much you need to deposit today at a discount rate of 7% compounded annually. 0 1 2 Rs 1,000 7% PV 1 PV 0 Present Value Single Deposit (Graphic)

Present Value Single Deposit (Formula):

PV 0 = FV 2 / (1+ i ) 2 = Rs 1,000 / (1 .07 ) 2 = FV 2 / (1+ i ) 2 = Rs 873.44 Present Value Single Deposit (Formula) 0 1 2 Rs 1,000 7% PV 0

General Present Value Formula:

PV 0 = FV 1 / (1+ i ) 1 PV 0 = FV 2 / (1+ i ) 2 General Present Value Formula: PV 0 = FV n / (1+ i ) n or PV 0 = FV n ( PVIF i , n ) General Present Value Formula etc.

Problem:

Reena wants to know how large of a deposit to make so that the money will grow to Rs 10,000 in 5 years at a discount rate of 10% . Problem 0 1 2 3 4 5 Rs 10,000 PV 0 10%

Problem Solution:

Calculation based on general formula: PV 0 = FV n / (1+ i ) n PV 0 = Rs 10,000 / (1+ 0 .10 ) 5 = Rs 6,209.21 Problem Solution

Types of Annuities:

Types of Annuities Ordinary Annuity : Payments or receipts occur at the end of each period. Annuity Due : Payments or receipts occur at the beginning of each period. An Annuity represents a series of equal payments (or receipts) occurring over a specified number of equidistant periods.

Examples of Annuities:

Examples of Annuities Student Loan Payments Car Loan Payments Insurance Premiums Retirement Savings

Parts of an Annuity:

Parts of an Annuity 0 1 2 3 Rs 100 Rs 100 Rs 100 (Ordinary Annuity) End of Period 1 End of Period 2 Today Equal Cash Flows Each 1 Period Apart End of Period 3

Parts of an Annuity:

Parts of an Annuity 0 1 2 3 Rs 100 Rs 100 Rs 100 (Annuity Due) Beginning of Period 1 Beginning of Period 2 Today Equal Cash Flows Each 1 Period Apart Beginning of Period 3

Ordinary Annuity -- FVA:

FVA n = A (1+ i ) n-1 + A (1+ i ) n-2 + ... + A (1+ i ) 1 + A (1+ i ) 0 Ordinary Annuity -- FVA A A A 0 1 2 n n+1 FVA n A = Periodic Cash Flow Cash flows occur at the end of the period i% . . .

Example of an Ordinary Annuity -- FVA:

Example of an Ordinary Annuity -- FVA Rs1,000 Rs1,000 Rs1,000 0 1 2 3 4 7% Cash flows occur at the end of the period

Example of an Ordinary Annuity -- FVA:

FVA 3 = 1,000 (1 .07 ) 2 + 1,000 (1 .07 ) 1 + 1,000 (1 .07 ) 0 = 1,145 + 1,070 + 1,000 = Rs 3,215 Example of an Ordinary Annuity -- FVA Rs1,000 Rs1,000 Rs1,000 0 1 2 3 4 Rs3,215 = FVA 3 7% Rs1,070 Rs1,145 Cash flows occur at the end of the period

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General Formula for Calculating Future Value of an Ordinary Annuity

Annuity Due -- FVAD:

FVAD n = R (1+ i ) n + R (1+ i ) n-1 + ... + R (1+ i ) 2 + R (1+ i ) 1 = FVA n (1+ i ) Annuity Due -- FVAD R R R R R 0 1 2 3 n-1 n FVAD n i% . . . Cash flows occur at the beginning of the period

Example of an Annuity Due -- FVAD:

FVAD 3 = 1,000 (1 .07 ) 3 + 1,000 (1 .07 ) 2 + 1,000 (1 .07 ) 1 = 1,225 + 1,145 + 1,070 = Rs 3,440 Example of an Annuity Due -- FVAD 1,000 1,000 1,000 1,070 0 1 2 3 4 Rs 3,440 = FVAD 3 7% Rs1,225 Rs1,145 Cash flows occur at the beginning of the period

Ordinary Annuity -- PVA:

PVA n = R /(1+ i ) 1 + R /(1+ i ) 2 + ... + R /(1+ i ) n Ordinary Annuity -- PVA R R R 0 1 2 n n+1 PVA n R = Periodic Cash Flow i% . . . Cash flows occur at the end of the period

Example of an Ordinary Annuity -- PVA:

Example of an Ordinary Annuity -- PVA Rs1,000 Rs1,000 Rs1,000 0 1 2 3 4 7% Cash flows occur at the end of the period

Example of an Ordinary Annuity -- PVA:

PVA 3 = 1,000 /(1 .07 ) 1 + 1,000 /(1 .07 ) 2 + 1,000 /(1 .07 ) 3 = 934.58 + 873.44 + 816.30 = 2,624.32 Example of an Ordinary Annuity -- PVA Rs1,000 Rs1,000 Rs1,000 0 1 2 3 4 Rs 2,624.32 = PVA 3 7% 934.58 873.44 816.30 Cash flows occur at the end of the period

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General Formula for Calculating Present Value of an Ordinary Annuity

Annuity Due -- PVAD:

PVAD n = R /(1+ i ) 0 + R /(1+ i ) 1 + ... + R /(1+ i ) n-1 = PVA n (1+ i ) Annuity Due -- PVAD R R R R 0 1 2 n-1 n PVAD n R : Periodic Cash Flow i% . . . Cash flows occur at the beginning of the period

Example of an Annuity Due -- PVAD:

PVAD n = 1,000 /(1 .07 ) 0 + 1,000 /(1 .07 ) 1 + 1,000 /(1 .07 ) 2 = Rs 2,808.02 Example of an Annuity Due -- PVAD 1,000.00 1,000 1,000 0 1 2 3 4 2,808.02 = PVAD n 7% 934.58 873.44 Cash flows occur at the beginning of the period

Mixed Flows Example:

Reena will receive the set of cash flows below. What is the Present Value at a discount rate of 10% ? Mixed Flows Example 0 1 2 3 4 5 600 600 400 400 100 PV 0 10%

Solution:

Solution 0 1 2 3 4 5 600 600 400 400 100 10% 545.45 495.87 300.53 273.21 62.09 Rs 1677.15 = PV 0 of the Mixed Flow

Shorter Discounting Periods:

General Formula: FV n = PV 0 (1 + [ i / m ]) m n Or = PV 0 * PVIF i / m , m * n n : Number of Years m : Compounding Periods per Year i : Annual Interest Rate FV n , m : FV at the end of Year n PV 0 : PV of the Cash Flow today Shorter Discounting Periods

Example:

Reena has Rs1,000 to invest for 1 year at an annual interest rate of 12% . Example Annual FV = 1,000 (1+ [ .12 / 1 ]) (1) (1) = 1,120 Semi FV = 1,000 (1+ [ .12 / 2 ]) (2) (1) = 1,123.6

Effective vs. Nominal Rate of Interest:

Effective vs. Nominal Rate of Interest Rs. 1000 Rs.1123.6 So, Rs. 1000 grows @ 12.36% annually Effective Rate of Interest r = 1 + i/m m - 1

Problem:

Basket Wonders (BW) has a Rs1,000 CD at the bank. The interest rate is 6% compounded quarterly for 1 year. What is the Effective Annual Interest Rate ( EAR )? Problem EAR = ( 1 + 6% / 4 ) 4 - 1 = 1.0614 - 1 = .0614 or 6.14%!

Perpetuity:

Perpetuity A perpetuity is an annuity with an infinite number of cash flows. The present value of cash flows occurring in the distant future is very close to zero. At 10% interest, the PV of Rs 100 cash flow occurring 50 years from today is Rs 0.85!

Present Value of a Perpetuity:

Present Value of a Perpetuity When n=  PV perpetuity = [A/(1+i)] [1-1/(1+i)] = A(1/i) = A/i

Present Value of a Perpetuity:

Present Value of a Perpetuity What is the present value of a perpetuity of Rs270 per year if the interest rate is 12% per year? PV A i perpetuity = = = Rs270 0.12 Rs 2250

Steps to Amortizing a Loan:

1. Calculate the payment per period . 2. Determine the interest in Period t. Loan balance at (t-1) x (i%) 3. Compute principal payment in Period t. ( Payment - interest from Step 2) 4. Determine ending balance in Period t. ( Balance - principal payment from Step 3) 5. Start again at Step 2 and repeat. Steps to Amortizing a Loan

Amortizing a Loan Example:

Reena is borrowing Rs10,000 at a compound annual interest rate of 12% . Amortize the loan if annual payments are made for 5 years . Amortizing a Loan Example Step 1: Payment PV 0 = A (PVIFA i% , n ) Rs10,000 = A (PVIFA 12% , 5 ) Rs10,000 = A (3.605) A = Rs10,000 / 3.605 = Rs2,774

Amortizing a Loan Example:

Amortizing a Loan Example

Amortizing a Loan Example:

Amortizing a Loan Example [Last Payment Slightly Higher Due to Rounding]

Amortizing a Loan Example:

Amortizing a Loan Example [Last Payment Slightly Higher Due to Rounding]

Usefulness of Amortization:

Usefulness of Amortization 2. Calculate Debt Outstanding -- The quantity of outstanding debt may be used in financing the day-to-day activities of the firm. 1. Determine Interest Expense -- Interest expenses may reduce taxable income of the firm.

EXERCISE:

EXERCISE Ashish recently obtained a Rs.50,000 loan. The loan carries an 8% annual interest. Amortize the loan if annual payments are made for 5 years .

SOLUTION:

SOLUTION

EXERCISE:

EXERCISE Compute the present value of the following future cash inflows, assuming a required rate of 10%: Rs. 100 a year for years 1 through 3, and Rs. 200 a year from years 6 through 15. ANS: 1011.75

Solution:

Solution 100 100 100 200 200 200 0 1 2 3 6 7 15 248.70 i% . . . Cash flows occur at the end of the period . . . 1228.9 763.05 1011.75 Till 5 th year

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