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# CAPM, Expected Return, Valuation, Cost of Capital for Project

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1. You are a consultant to a firm evaluating an expansion of its current business. The cash-flow forecasts (in millions of dollars) for the project are:

Years Cash Flow

0 -100
1 - 10 +15

On the basis of the behavior of the firm's stock, you believe that the beta of the firm is 1.4. Assuming that the rate of return available on risk-free investments is 4% and that the expected rate of return on the market portfolio is 12%, what is the NPV of the project.

2. Reconsider the project in the preceding problem. What is the project IRR? What is the cost of capital for the project? Does the accept-reject decision using IRR agree with the decision using NPV?

3, A share of stock with a beta of .75 now sells for \$50. Investors expect the stock to pay a year-end dividend of \$2. The T-bill rate is 4%, and the market risk premium is 7%. If the stock is perceived to be fairly priced today, what must be investors' expectation of the price of the stock at the end of the year?

4. Reconsider the stock in the preceding problem. Suppose investors actually believe the stock will sell for \$52 at year-end. Is the stock a good or bad buy? What will investors do? At what point will the stock reach an "equilibrium" at which it again is perceived as fairly priced?

#### Solution Preview

See attached Excel file.

1. NPV = PV of cash flows - initial investment.
To find the PV of cash flows we need the discounting rate. From the details given, we calculate the cost of equity and use that to discount the cash flows.
Using CAPM,
Cost of equity = Rf + (Rm-Rf) beta = 4% + (12%-4%) 1.4 = 15.2%
The cash flows are an annuity and so the PV is calculated as
PV of cash flows = 15 X PVIFA (10 years,15.2%) = 15 X 4.9807 = 74.71
NPV = 74.71 - 100 = -25.29
Since the NPV is negative, the project should not be accepted.

2. IRR is the discounting rate at which the NPV is zero ...

#### Solution Summary

The solution determines the CAPM, expected return, valuation, and cost of capital for expansion project.

\$2.19