Question

principles of corporate finance chapter 9

1. Suppose a firm uses its company cost of capital to evaluate all projects. Will it underestimate or overestimate the value of high-risk projects?

2. A company is 40% financed by risk-free debt. The interest rate is 10%, the expected market risk premium is 8%, and the beta of the company’s common stock is .5. What is the company cost of capital? What is the after-tax WACC, assuming that the company pays tax at a 35% rate?

4. Define the following terms: a. Cost of debt b. Cost of equity c. After-tax WACC d. Equity beta e. Asset beta f. Pure-play comparable g. Certainty equivalent

5. Asset betas EZCUBE Corp. is 50% financed with long-term bonds and 50% with common equity. The debt securities have a beta of .15. The company’s equity beta is 1.25. What is EZCUBE’s asset beta?

9. True or false?

a. The company cost of capital is the correct discount rate for all projects because the high risks of some projects are offset by the low risk of other projects.

b. Distant cash flows are riskier than near-term cash flows. Therefore long-term projects require higher risk-adjusted discount rates.

c. Adding fudge factors to discount rates undervalues long-lived projects compared with quick-payoff projects.

10. A project has a forecasted cash flow of $110 in year 1 and $121 in year 2. The interest rate is 5%, the estimated risk premium on the market is 10%, and the project has a beta of .5. If you use a constant risk-adjusted discount rate, what is a. The PV of the project? b. The certainty-equivalent cash flow in year 1 and year 2? c. The ratio of the certainty-equivalent cash flows to the expected cash flows in years 1 and 2?

12. Nero Violins has the following capital structure:

security	beat	total market value(sillions)
debt	0	100
preferred stock	0.2	40
common stock	1.2	299

a. What is the firm’s asset beta? (Hint: What is the beta of a portfolio of all the firm’s securities?) b. Assume that the CAPM is correct. What discount rate should Nero set for investments that expand the scale of its operations without changing its asset beta? Assume a risk-free interest rate of 5% and a market risk premium of 6%.

16. What types of firms need to estimate industry asset betas? How would such a firm make the estimate? Describe the process step by step.

17. Binomial Tree Farm’s financing includes $5 million of bank loans. Its common equity is shown in Binomial’s Annual Report at $6.67 million. It has 500,000 shares of common stock outstanding, which trade on the Wichita Stock Exchange at $18 per share. What debt ratio should Binomial use to calculate its WACC or asset beta? Explain.

Answer 1

1)

Suppose the company uses the cost of capital to evaluate high risk projects, this would end up in overestimating the value of projects since the discount rate needed to discount the cash flows need to be higher owing to higher risk premium and hence the value will be smaller.

2)

Cost of Equity = Risk free rate + Beta * MRP = 10% + 0.5* 8% = 14%

Cost of debt, kd = 10%

Wd = 0.4

We = 0.6

After tax WACC= kd* Wd*(1-t) + Ke * We = 10% * 0.4* 0.65 + 14%* 0.6 = 11%

5)

Asset Beta of EZ cube = Equity beta/[(1+D/E(1-t)] or (E/V* Equity beta)+(D/V* Debt beta)

Asset Beta = 0.5 * 0.15 + 0.5* 1.25 = 0.7

9)

a)

The company cost of capital shall not be used as the cost of capital for all projects as some projects of higher risk need to use a higher cost of capital while those of lower risk must use lower cost of capital. It is impossible to assume that risk of projects cancel each other. So false

b)

Distant cash flows have term premium as there is more uncertainty with respect to cash flows. So ceterus paribus, distant cash flows require higher risk adjusted discount rates

So True

c)

As uncertainty is more for long lived projects, the fudge factors included can be more. As a result the long lived projects can end up with a lower valuation than actual

Hence True