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# Chapter_02Present Value and The Opportunity Cost of Capita(公司金融,英文版)l

Principles of Corporate Finance
Seventh Edition

Chapter 2
Present Value and The Opportunity Cost of Capital

Richard A. Brealey Stewart C. Myers

Slides by Matthew Will
McGraw Hill/Irwin

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Topics Covered
? Present Value ? Net Present Value ? NPV Rule ? ROR Rule ? Opportunity Cost of Capital ? Managers and the Interests of Shareholders

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Present Value
Present Value Discount Factor

Value today of a future cash flow. Discount Rate

Present value of a \$1 future payment.

Interest rate used to compute present values of future cash flows.
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Present Value

Present Value = PV PV = discountfactor ? C1

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Present Value
Discount Factor = DF = PV of \$1

DF ?

1 (1? r ) t

Discount Factors can be used to compute the present value of any cash flow.

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Valuing an Office Building
Step 1: Forecast cash flows Cost of building = C0 = 350 Sale price in Year 1 = C1 = 400

Step 2: Estimate opportunity cost of capital If equally risky investments in the capital market offer a return of 7%, then Cost of capital = r = 7%

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Valuing an Office Building
Step 3: Discount future cash flows

PV ?

C1 (1? r )

?

400 (1?.07)

? 374

Step 4: Go ahead if PV of payoff exceeds investment

NPV ? ?350 ? 374 ? 24
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Net Present Value
NPV = PV - required investment C1 NPV = C0 ? 1? r

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Risk and Present Value
? Higher risk projects require a higher rate of return ? Higher required rates of return cause lower PVs

PV of C1 ? \$400 at 7% 400 PV ? ? 374 1 ? .07
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Risk and Present Value
PV of C1 ? \$400 at 12% 400 PV ? ? 357 1 ? .12 PV of C1 ? \$400 at 7% 400 PV ? ? 374 1 ? .07

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Rate of Return Rule
? Accept investments that offer rates of return in excess of their opportunity cost of capital

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Rate of Return Rule
? Accept investments that offer rates of return in excess of their opportunity cost of capital
Example In the project listed below, the foregone investment opportunity

is 12%. Should we do the project?
profit 400,000 ? 350,000 Return ? ? ? .143 or 14.3% investment 350,000

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Net Present Value Rule
? Accept investments that have positive net present value

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Net Present Value Rule
? Accept investments that have positive net present value
Example Suppose we can invest \$50 today and receive \$60 in one year. Should we accept the project given a 10% expected return?

60 NPV = -50 + ? \$4.55 1.10
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Opportunity Cost of Capital
Example You may invest \$100,000 today. Depending on the state of the economy, you may get one of three possible cash payoffs:

Economy Payoff

Slump

Normal

Boom

\$80,000 110,000 140,000

80,000 ? 110,000 ? 140,000 Expected payoff ? C1 ? ? \$110,000 3
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Opportunity Cost of Capital
Example - continued The stock is trading for \$95.65. Next year’s price, given a normal economy, is forecast at \$110

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Opportunity Cost of Capital
Example - continued The stocks expected payoff leads to an expected return.

expected profit 110 ? 95.65 Expected return ? ? ? .15 or 15% investment 95.65

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Opportunity Cost of Capital
Example - continued Discounting the expected payoff at the expected return leads to the PV of the project

110,000 PV ? ? \$95,650 1.15
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Investment vs. Consumption
? Some people prefer to consume now. Some prefer to invest now and consume later. Borrowing and lending allows us to reconcile these opposing desires which may exist within the firm’s shareholders.

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Investment vs. Consumption
income in period 1 100 An 80 Some investors will prefer A and others B

60

40

Bn

20

20
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40 60 income in period 0

80

100

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Investment vs. Consumption
The grasshopper (G) wants to consume now. The ant (A) wants to wait. But each is happy to invest. A prefers to invest 14%, moving up the red arrow, rather than at the 7% interest rate. G invests and then borrows at 7%, thereby transforming \$100 into \$106.54 of immediate consumption. Because of the investment, G has \$114 next year to pay off the loan. The investment’s NPV is \$106.54-100 = +6.54

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Copyright ? 2003 by The McGra

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Investment vs. Consumption
?

Dollars Later

A invests \$100 now and consumes \$114 next year

114

107

The grasshopper (G) wants to consume now. The ant (A) wants to wait. But each is happy to invest. A prefers to invest 14%, moving up the red arrow, rather than at the 7% interest rate. G invests and then borrows at 7%, thereby transforming \$100 into \$106.54 of immediate consumption. Because of the investment, G has \$114 next year to pay off the loan. The investment’s NPV is \$106.54100 = +6.54

G invests \$100 now, borrows \$106.54 and consumes now. Dollars Now

100
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106.54

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Managers and Shareholder Interests
? Tools to Ensure Management Pays Attention to the Value of the Firm
Manger’s actions are subject to the scrutiny of the board of directors. ? Shirkers are likely to find they are ousted by more energetic managers. ? Financial incentives such as stock options
?

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