Chapter 15: Chapter 15 Investment, Time, and Capital Markets
Topics to be Discussed: Topics to be Discussed Stocks Versus Flows
Present Discounted Value
The Value of a Bond
The Net Present Value Criterion for Capital Investment Decisions
Topics to be Discussed: Topics to be Discussed Adjustments for Risk
Investment Decisions by Consumers
Intertemporal Production Decisions--- Depletable Resources
How are Interest Rates Determined?
Introduction: Introduction Capital
Choosing an input that will contribute to output over a long period of time
Comparing the future value to current expenditures
Stocks Versus Flows: Stocks Versus Flows Stock
Capital is a stock measurement.
The amount of capital a company owns
Stocks Versus Flows: Stocks Versus Flows Flows
Variable inputs and outputs are flow measurements.
An amount per time period
Present Discounted Value (PDV): Present Discounted Value (PDV) Determining the value today of a future flow of income
The value of a future payment must be discounted for the time period and interest rate that could be earned.
Present Discounted Value (PDV): Present Discounted Value (PDV) Future Value (FV)
Present Discounted Value (PDV): Present Discounted Value (PDV) Question
What impact does R have on the PDV?
PDV of $1 Paid in the Future: PDV of $1 Paid in the Future 0.01 $0.990 $0.980 $0.951 $0.905 $0.820 $0.742
0.02 0.980 0.961 0.906 0.820 0.673 0.552
0.03 0.971 0.943 0.863 0.744 0.554 0.412
0.04 0.962 0.925 0.822 0.676 0.456 0.308
0.05 0.952 0.907 0.784 0.614 0.377 0.231
0.06 0.943 0.890 0.747 0.558 0.312 0.174 Interest
Rate 1 Year 2 Years 3 Years 4 Years 5 Years 6 Years
PDV of $1 Paid in the Future: PDV of $1 Paid in the Future 0.07 0.935 0.873 0.713 0.508 0.258 0.131
0.08 0.926 0.857 0.681 0.463 0.215 0.099
0.09 0.917 0.842 0.650 0.422 0.178 0.075
0.10 0.909 0.826 0.621 0.386 0.149 0.057
0.15 0.870 0.756 0.497 0.247 0.061 0.015
0.20 0.833 0.694 0.402 0.162 0.026 0.004 Interest
Rate 1 Year 2 Years 3 Years 4 Years 5 Years 6 Years
Present Discounted Value (PDV): Present Discounted Value (PDV) Valuing Payment Streams
Choosing a payment stream depends upon the interest rate.
Two Payment Streams: Two Payment Streams Payment Stream A: $100 $100 0
Payment Stream B: $20 $100 $100 Today 1 Year 2 Years
Two Payment Streams: Two Payment Streams
PDV of Payment Streams: PDV of Payment Streams PDV of Stream A: $195.24 $190.90 $186.96 $183.33
PDV of Stream B: 205.94 193.54 182.57 172.77 R = .05 R = .10 R = .15 R = .20 Why does the PDV of A
relative to B increase as
R increases and vice versa
for B?
The Value of Lost Earnings: The Value of Lost Earnings PDV can be used to determine the value of lost income from a disability or death.
The Value of Lost Earnings: The Value of Lost Earnings Scenario
Harold Jennings died in an auto accident January 1, 1986 at 53 years of age.
Salary: $85,000
Retirement Age: 60
The Value of Lost Earnings: The Value of Lost Earnings Question
What is the PDV of Jennings’ lost income to his family?
Must adjust salary for predicted increase (g)
Assume an 8% average increase in salary for the past 10 years
The Value of Lost Earnings: The Value of Lost Earnings Question
What is the PDV of Jennings’ lost income to his family?
Must adjust for the true probability of death (m) from other causes
Derived from mortality tables
The Value of Lost Earnings: The Value of Lost Earnings Question
What is the PDV of Jennings’ lost income to his family?
Assume R = 9%
Rate on government bonds in 1983
The Value of Lost Earnings: The Value of Lost Earnings
Calculating Lost Wages: Calculating Lost Wages 1986 $ 85,000 .991 1.000 $84,235
1987 91,800 .990 .917 83,339
1988 99,144 .989 .842 82,561
1989 107,076 .988 .772 81,671
1990 115,642 .987 .708 80,810
1991 124,893 .986 .650 80,043
1992 134,884 .985 .596 79,185
1993 145,675 .984 .547 78,408 Year W0(1 + g)t (1 - mt) 1/(1 + R)t W0(1 + g)t(1 - mt)/(1 + R)t
The Value of Lost Earnings: The Value of Lost Earnings Finding PDV
The summation of column 4 will give the PDV of lost wages ($650,252)
Jennings’ family could recover this amount as compensation for his death.
The Value of a Bond: The Value of a Bond Determining the Price of a Bond
Coupon Payments = $100/yr. for 10 yrs.
Principal Payment = $1,000 in 10 yrs.
Present Value of the Cash Flow from a Bond: Present Value of the Cash Flow from a Bond Interest Rate PDV of Cash Flow
($ thousands) 0 0.05 0.10 0.15 0.20 0.5 1.0 1.5 2.0
The Value of a Bond: The Value of a Bond Perpetuities
Perpetuities are bonds that pay out a fixed amount of money each year, forever.
Effective Yield on a Bond: Effective Yield on a Bond Calculating the Rate of Return From a Bond
Effective Yield on a Bond: Effective Yield on a Bond Calculating the Rate of Return From a Bond
Effective Yield on a Bond: Effective Yield on a Bond Interest Rate 0 0.05 0.10 0.15 0.20 0.5 1.0 1.5 2.0 PDV of Payments (Value of Bond)
($ thousands) Why do yields differ
among different bonds? The effective yield is the interest
rate that equates the present
value of a bond’s payment
stream with the bond’s market price.
The Yields on Corporate Bonds: The Yields on Corporate Bonds In order to calculate corporate bond yields, the face value of the bond and the amount of the coupon payment must be known.
Assume
IBM and Polaroid both issue bonds with a face value of $100 and make coupon payments every six months.
The Yields on Corporate Bonds: The Yields on Corporate Bonds Closing prices for each July 23, 1999: IBM 53/8 09 5.8 30 92 -11/2
Polaroid 111/2 06 10.8 80 106 -5/8
a: coupon payments for one year ($5.375)
b: maturity date of bond (2009)
c: annual coupon/closing price ($5.375/92)
d: number traded that day (30)
e: closing price (92)
f: change in price from previous day (-11/2) a b c d e f
The Yields on Corporate Bonds: The Yields on Corporate Bonds The IBM bond yield:
Assume annual payments
2009 - 1999 = 10 years
The Yields on Corporate Bonds: The Yields on Corporate Bonds The Polaroid bond yield: Why was Polaroid
R* greater?
The Net Present Value Criterion for Capital Investment Decisions: The Net Present Value Criterion for Capital Investment Decisions In order to decide whether a particular capital investment is worthwhile a firm should compare the present value (PV) of the cash flows from the investment to the cost of the investment.
The Net Present Value Criterion for Capital Investment Decisions: NPV Criterion
Firms should invest if the PV exceeds the cost of the investment. The Net Present Value Criterion for Capital Investment Decisions
The Net Present Value Criterion for Capital Investment Decisions: The Net Present Value Criterion for Capital Investment Decisions
The Net Present Value Criterion for Capital Investment Decisions: The Electric Motor Factory (choosing to build a $10 million factory)
8,000 motors/ month for 20 yrs
Cost = $42.50 each
Price = $52.50
Profit = $10/motor or $80,000/month
Factory life is 20 years with a scrap value of $1 million
Should the company invest? The Net Present Value Criterion for Capital Investment Decisions
The Net Present Value Criterion for Capital Investment Decisions: Assume all information is certain (no risk)
R = government bond rate The Net Present Value Criterion for Capital Investment Decisions
Net Present Value of a Factory: Net Present Value of a Factory Interest Rate, R 0 0.05 0.10 0.15 0.20 -6 Net Present Value
($ millions) -4 -2 0 2 4 6 8 10
The Net Present Value Criterion for Capital Investment Decisions: Real versus Nominal Discount Rates
Adjusting for the impact of inflation
Assume price, cost, and profits are in real terms
Inflation = 5% The Net Present Value Criterion for Capital Investment Decisions
The Net Present Value Criterion for Capital Investment Decisions: Real versus Nominal Discount Rates
Assume price, cost, and profits are in real terms
Therefore,
P = (1.05)(52.50) = 55.13, Year 2 P = (1.05)(55.13) = 57.88….
C = (1.05)(42.50) = 44.63, Year 2 C =….
Profit remains $960,000/year The Net Present Value Criterion for Capital Investment Decisions
The Net Present Value Criterion for Capital Investment Decisions: Real versus Nominal Discount Rates
Real R = nominal R - inflation = 9 - 5 = 4 The Net Present Value Criterion for Capital Investment Decisions
Net Present Value of a Factory: Net Present Value of a Factory Interest Rate, R 0 0.05 0.10 0.15 0.20 -6 Net Present Value
($ millions) -4 -2 0 2 4 6 8 10
The Net Present Value Criterion for Capital Investment Decisions: Negative Future Cash Flows
Investment should be adjusted for construction time and losses. The Net Present Value Criterion for Capital Investment Decisions
The Net Present Value Criterion for Capital Investment Decisions: Electric Motor Factory
Construction time is 1 year
$5 million expenditure today
$5 million expenditure next year
Expected to lose $1 million the first year and $0.5 million the second year
Profit is $0.96 million/yr. until year 20
Scrap value is $1 million The Net Present Value Criterion for Capital Investment Decisions
The Net Present Value Criterion for Capital Investment Decisions: The Net Present Value Criterion for Capital Investment Decisions
Adjustments for Risk: Adjustments for Risk Determining the discount rate for an uncertain environment:
This can be done by increasing the discount rate by adding a risk-premium to the risk-free rate.
Owners are risk averse, thus risky future cash flows are worth less than those that are certain.
Adjustments for Risk: Adjustments for Risk Diversifiable Versus Nondiversifiable Risk
Diversifiable risk can be eliminated by investing in many projects or by holding the stocks of many companies.
Nondiversifiable risk cannot be eliminated and should be entered into the risk premium.
Adjustments for Risk: Adjustments for Risk Measuring the Nondiversifiable Risk Using the Capital Asset Pricing Model (CAPM)
Suppose you invest in the entire stock market (mutual fund)
rm = expected return of the stock market
rf = risk free rate
rm - rf = risk premium for nondiversifiable risk
Adjustments for Risk: Adjustments for Risk Measuring the Nondiversifiable Risk Using the Capital Asset Pricing Model (CAPM)
Calculating Risk Premium for One Stock
Adjustments for Risk: Adjustments for Risk Question
What is the relationship between the nondiversifiable risk and the value of the asset beta?
Adjustments for Risk: Adjustments for Risk Given beta, we can determine the correct discount rate to use in computing an asset’s net present value:
Adjustments for Risk: Adjustments for Risk Determining beta
Stock
Estimated statistically for each company
Adjustments for Risk: Adjustments for Risk Determining beta
Factory
Weighted average of expected return on the company’s stock and the interest on the debt
Expected return depends on beta
Caution: The investment should be typical for the company
Investment Decisions by Consumers: Investment Decisions by Consumers Consumers face similar investment decisions when they purchase a durable good.
Compare future benefits with the current purchase cost
Investment Decisions by Consumers: Benefits and Cost of Buying a Car
S = value of transportation services in dollars
E = total operating cost/yr
Price of car is $20,000
Resale value of car is $4,000 in 6 years Investment Decisions by Consumers
Investment Decisions by Consumers: Benefits and Cost Investment Decisions by Consumers
Choosing an Air Conditioner: Choosing an Air Conditioner Buying a new air conditioner involves making a trade-off.
Air Conditioner A
Low price and less efficient (high operating cost)
Choosing an Air Conditioner: Choosing an Air Conditioner Buying a new air conditioner involves making a trade-off.
Air Conditioner B
High price and more efficient
Both have the same cooling power
Assume an 8 year life
Choosing an Air Conditioner: Choosing an Air Conditioner
Choosing an Air Conditioner: Choosing an Air Conditioner Should you choose A or B?
Depends on the discount rate
If you borrow, the discount rate would be high
Probably choose a less expensive and inefficient unit
If you have plentiful cash, the discount rate would be low.
Probably choose the more expensive unit
Intertemporal Production Decisions---Depletable Resources: Intertemporal Production Decisions---Depletable Resources Firms’ production decisions often have intertemporal aspects---production today affects sales or costs in the future.
Intertemporal Production Decisions---Depletable Resources: Scenario
You are given an oil well containing 1000 barrels of oil.
MC and AC = $10/barrel
Should you produce the oil or save it? Intertemporal Production Decisions---Depletable Resources
Intertemporal Production Decisions---Depletable Resources: Scenario
Pt = price of oil this year
Pt+1 = price of oil next year
C = extraction costs
R = interest rate
Intertemporal Production Decisions---Depletable Resources
Intertemporal Production Decisions---Depletable Resources: Do not produce if you expect its price less its extraction cost to rise faster than the rate of interest.
Extract and sell all of it if you expect price less cost to rise at less than the rate of interest.
What will happen to the price of oil? Intertemporal Production Decisions---Depletable Resources
Price of an Exhaustible Resource: Price of an Exhaustible Resource Time Price Quantity Price
Price of an Exhaustible Resource: In a competitive market, Price - MC must rise at exactly the rate of interest.
Why?
How would producers react if:
P - C increases faster than R?
P - C increases slower than R? Price of an Exhaustible Resource
Price of an Exhaustible Resource: Notice
P > MC
Is this a contradiction to the competitive rule that P = MC?
Hint: What happens to the opportunity cost of producing an exhaustible resource? Price of an Exhaustible Resource
Price of an Exhaustible Resource: P = MC
MC = extraction cost + user cost
User cost = P - marginal extraction cost Price of an Exhaustible Resource
Price of an Exhaustible Resource: How would a monopolist choose their rate of production?
They will produce so that marginal revenue revenue less marginal cost rises at exactly the rate of interest, or
(MRt+1 - c) = (1 + R)(MRt - c) Price of an Exhaustible Resource
Price of an Exhaustible Resource: The monopolist is more conservationist than a competitive industry.
They start out charging a higher price and deplete the resources more slowly. Price of an Exhaustible Resource Resource Production by a Monopolist
How Depletable Are Depletable Resources?: How Depletable Are Depletable Resources? Crude oil .4 to .5
Natural gas .4 to .5
Uranium .1 to .2
Copper .2 to .3
Bauxite .05 to .2
Nickel .1 to .2
Iron Ore .1 to .2
Gold .05 to .1 Resource User Cost/Competitive Price
How Depletable Are Depletable Resources?: The market structure and changes in market demand have had a very dramatic impact on resource prices over the past few decades.
Question
Why would oil and natural gas have such a high user cost ratio compared to the other resources? How Depletable Are Depletable Resources?
How Are Interest Rates Determined?: How Are Interest Rates Determined? The interest rate is the price that borrowers pay lenders to use their funds.
Determined by supply and demand for loanable funds.
Supply and Demand for Loanable Funds: Supply and Demand for Loanable Funds Quantity of
Loanable Funds R
Interest
Rate
Changes In The Equilibrium: Changes In The Equilibrium Quantity of
Loanable Funds R
Interest
Rate
Changes In The Equilibrium: Changes In The Equilibrium Quantity of
Loanable Funds R
Interest
Rate
Changes In The Equilibrium: Changes In The Equilibrium Quantity of
Loanable Funds R
Interest
Rate
How Are Interest Rates Determined?: A Variety of Interest Rates
1) Treasury Bill Rate
2) Treasury Bond Rate
3) Discount Rate How Are Interest Rates Determined?
How Are Interest Rates Determined?: A Variety of Interest Rates
4) Commercial Paper Rate
5) Prime Rate
6) Corporate Bond Rate How Are Interest Rates Determined?
Summary: Summary A firm’s holding of capital is measured as a stock, but inputs of labor and raw materials are flows.
When a firm makes a capital investment, it spends money now, so that it can earn profits in the future.
Summary: Summary The present discounted value (PDV) of $1 paid n years from now is $1/(1 + R)n.
A bond is a contract in which a lender agrees to pay the bondholder a stream of money.
Summary: Summary Firms can decide whether to undertake a capital investment by applying the NPV criterion.
The discount rate that a firm uses to calculate the NPV for an investment should be the opportunity cost of capital.
Summary: Summary An adjustment for risk can be made by adding a risk premium to the discount rate.
Consumers are also faced with investment decisions that require the same kind of analysis as those of firms.
Summary: Summary An exhaustible resource in the ground is like money in the bank and must earn a comparable return.
Market interest rates are determined by the demand and supply of loanable funds.
End of Chapter 15: End of Chapter 15 Investment, Time, and Capital Markets