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

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?

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#### 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.

1) Currently, the risk-free rate is 6% and the market risk premium is 5%. Given this information, which of the following statements is CORRECT?

2) A stock has an expected return of 12.60%. Its beta is 1.49 and the risk-free rate is 5.00%. What is the market risk premium?

3) For the purpose of Millar's cash flows, what is your estimate of the company cost of equity?

4) If the company's weighted average cost of capital is 11 percent, what is the current value of operations, to the nearest million.

5) If Target sells the old machine at market value, what is the initial after-tax outlay for the new printing machine?

1) Currently, the risk-free rate is 6% and the market risk premium is 5%. Given this information, which of the following statements is CORRECT?

a) An index fund with beta =1.0 should have a required return of 11%

b) If a stock has a negative beta, its required return must also be negative

c) An index fund with beta =1.0 should have a required return less than 11%

d) If a stock's beta doubles, its required return must also double

e) An index fund with beta = 1.0 should have a required return greater than 11%

2) A stock has an expected return of 12.60%. Its beta is 1.49 and the risk-free rate is 5.00%. What is the market risk premium?

a) 5.10%

b) 5.23%

c) 5.36%

d) 5.49%

e) 5.63%

3) Millar Motors is a relatively small company and its beta is 1.30. The current 1-year T-Bill rate and 10-year T-bond rate are 2.00% and 4.00% respectively. In the past 10 years, the average rate on the 10-year T-bond rate has been 6.00%. For the same period the annual return on market indices for large stocks and small stocks have been 13.00% and 15.00% respectively. Investors expect Millar Motors' revenues to growth at 5% next year and the annual future stock market return to be 12.00%. For the purpose of Millar's cash flows, what is your estimate of the company cost of equity?

a) 13.0%

b) 18.9%

c) 13.1%

d) 15.7%

e) 15.1%

4) Suppose a company's projected free cash flow for next year is $500 million and it is expected to grow at a constant rate of 6 percent. If the company's weighted average cost of capital is 11 percent, what is the current value of operations, to the nearest million.

a) $530 million

b) $4,545 million

c) $8,333 million

d) $10,000 million

e) $10,600 million

5) The Target Copy Company is contemplating the replacement of its old printing machine with a new model costing $60,000. The old machine, which originally cost $40,000, has 6 years expected life remaining and a current book value of $30,000 versus a current market value of $24,000. Target's corporate tax rate is 40 percent. If Target sells the old machine at market value, what is the initial after-tax outlay for the new printing machine?

a) -$22,180

b) -$30,000

c) -$33,600

d) -$36,000

e) -$40,000