Principles of Corporate Finance_ 12th Edition

Chapter 9 Risk and the Cost of Capital 237

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When to Use a Single Risk-Adjusted Discount Rate

for Long-Lived Assets

We are now in a position to examine what is implied when a constant risk-adjusted discount

rate is used to calculate a present value.

Consider two simple projects. Project A is expected to produce a cash flow of $100 mil-

lion for each of three years. The risk-free interest rate is 6%, the market risk premium is 8%,

and project A’s beta is .75. You therefore calculate A’s opportunity cost of capital as follows:

r = rf + β(rm − rf)

= 6 + .75(8) = 12%

Discounting at 12% gives the following present value for each cash flow:

◗ FIGURE 9.3

Two ways to calculate

present value. “Hair-

cut for risk” is finan-

cial slang referring to

the reduction of the

cash flow from its

forecasted value to its

certainty equivalent.

Risk-Adjusted Discount Rate Method

Certainty-Equivalent Method

Discount for time and risk

Present

value

Future

cash

flow

C 1

Discount for time

value of money

Haircut

for risk

Project A

Year Cash Flow PV at 12%

1 100 89.3

2 100 79.7

3 100 71.2

Total PV 240.2

Project B

Year Cash Flow PV at 6%

1 94.6 89.3

2 89.6 79.7

3 84.8^ 71.2

Total PV 240.2

Now compare these figures with the cash flows of project B. Notice that B’s cash flows are

lower than A’s; but B’s flows are safe, and therefore they are discounted at the risk-free inter-

est rate. The present value of each year’s cash flow is identical for the two projects.