1.In year 1, AMC will earn $2000 before interest and taxes. The market expects these earnings to grow at a rate of 3% per year. The firm will make no net investments (i.e., capital expenditures will equal depreciation) or changes to net working capital. Assume that the corporate tax rate equals 40%. Right now, the firm has $5000 in risk-free debt. It plans to keep a constant ratio of debt to equity every year, so that on average the debt will also grow by 3% per year. Suppose the risk-free rate equals 5%, and the expected return on the market equals 11%. The asset beta for this industry is 1.11.

a. If AMC were an all-equity (unlevered) firm, what would its market value be?

b. Assuming the debt is fairly priced, what is the amount of interest AMC will pay next year? If AMC’s debt is expected to grow by 3% per year, at what rate are its interest payments expected to grow?

c. Even though AMC’s debt is riskless (the firm will not default), the future growth of AMC’s debt is uncertain, so the exact amount of the future interest payments is risky. Assuming the future interest payments have the same beta as AMC’s assets, what is the present value of AMC’s interest tax shield?

d. Using the APV method, what is AMC’s total market value, V L? What is the market value of AMC’s equity?

e. What is AMC’s WACC? (Hint: Work backward from the FCF and V L.)

f. Using the WACC method, what is the expected return for AMC equity?

g. Show that the following holds for AMC: .[SHERYL: there’s an equation that should be set here, but I can’t get it out of the PDF in correct for. It’s on page 631].

h. Assuming that the proceeds from any increases in debt are paid out to equity holders, what cash flows do the equity holders expect to receive in one year? At what rate are those cash flows expected to grow? Use that information plus your answer to part (f ) to derive the market value of equity using the FTE method. How does that compare to your answer in part (d)?

2.Prokter and Gramble (PG) has historically maintained a debt-equity ratio of approximately 0.20. Its current stock price is $50 per share, with 2.5 billion shares outstanding. The firm enjoys very stable demand for its products, and consequently it has a low equity beta of 0.50 and can borrow at 4.20%, just 20 basis points over the risk-free rate of 4%. The expected return of the market is 10%, and PG’s tax rate is 35%.

a. This year, PG is expected to have free cash flows of $6.0 billion. What constant expected growth rate of free cash flow is consistent with its current stock price?

b. PG believes it can increase debt without any serious risk of distress or other costs. With a higher debt-equity ratio of 0.50, it believes its borrowing costs will rise only slightly to 4.50%. If PG announces that it will raise its debt-equity ratio to 0.5 through a leveraged recap, determine the increase in the stock price that would result from the anticipated tax savings.

3.Amarindo, Inc. (AMR), is a newly public firm with 10 million shares outstanding. You are doing a valuation analysis of AMR. You estimate its free cash flow in the coming year to be $15 million, and you expect the firm’s free cash flows to grow by 4% per year in subsequent years. Because the firm has only been listed on the stock exchange for a short time, you do not have an accurate assessment of AMR’s equity beta. However, you do have beta data for UAL, another firm in the same industry:

AMR has a much lower debt-equity ratio of 0.30, which is expected to remain stable, and its debt is risk free. AMR’s corporate tax rate is 40%, the risk-free rate is 5%, and the expected return on the market portfolio is 11%.

a. Estimate AMR’s equity cost of capital.

b. Estimate AMR’s share price.

4.Remex (RMX) currently has no debt in its capital structure. The beta of its equity is 1.50. For each year into the indefinite future, Remex’s free cash flow is expected to equal $25 million. Remex is considering changing its capital structure by issuing debt and using the proceeds to buy back stock. It will do so in such a way that it will have a 30% debt-equity ratio after the change,and it will maintain this debt-equity ratio forever. Assume that Remex’s debt cost of capital will be 6.5%. Remex faces a corporate tax rate of 35%. Except for the corporate tax rate of 35%,there are no market imperfections. Assume that the CAPM holds, the risk-free rate of interest is 5%, and the expected return on the market is 11%.

a. Using the information provided, complete the following table:

b. Using the information provided and your calculations in part (a), determine the value of the tax shield acquired by Remex if it changes its capital structure in the way it is considering.

5.You are evaluating a project that requires an investment of $90 today and provides a single cash flow of $115 for sure one year from now. You decide to use 100% debt financing, that is, you will borrow $90. The risk-free rate is 5% and the tax rate is 40%. Assume that the investment is fully depreciated at the end of the year, so without leverage you would owe taxes on the difference between the project cash flow and the investment, that is, $15.

a. Calculate the NPV of this investment opportunity using the APV method.

b. Using your answer to part (a), calculate the WACC of the project.

c. Verify that you get the same answer using the WACC method to calculate NPV.

d. Finally, show that flow-to-equity also correctly gives the NPV of this investment opportunity.

6.Tybo Corporation adjusts its debt so that its interest expenses are 20% of its free cash flow. Tybo is considering an expansion that will generate free cash flows of $2.5 million this year and is expected to grow at a rate of 4% per year from then on. Suppose Tybo’s marginal corporate tax rate is 40%.

a. If the unlevered cost of capital for this expansion is 10%, what is its unlevered value?

b. What is the levered value of the expansion?

c. If Tybo pays 5% interest on its debt, what amount of debt will it take on initially for the expansion?

d. What is the debt-to-value ratio for this expansion? What is its WACC?

e. What is the levered value of the expansion using the WACC method?

7.You are on your way to an important budget meeting. In the elevator, you review the project valuation analysis you had your summer associate prepare for one of the projects to be discussed:

Looking over the spreadsheet, you realize that while all of the cash flow estimates are correct, your associate used the flow-to-equity valuation method and discounted the cash flows using the company’s equity cost of capital of 11%. However, the project’s incremental leverage is very different from the company’s historical debt-equity ratio of 0.20: For this project, the company will instead borrow $80 million upfront and repay $20 million in year 2, $20 million in year 3, and $40 million in year 4. Thus, the project’s equity cost of capital is likely to be higher than the firm’s, not constant over time—invalidating your associate’s calculation. Clearly, the FTE approach is not the best way to analyze this project. Fortunately, you have your calculator with you, and with any luck you can use a better method before the meeting starts.

a. What is the present value of the interest tax shield associated with this project?

b. What are the free cash flows of the project?

c. What is the best estimate of the project’s value from the information given?

8.Your firm is considering building a $600 million plant to manufacture HDTV circuitry. You expect operating profits (EBITDA) of $145 million per year for the next 10 years. The plant will be depreciated on a straight-line basis over 10 years (assuming no salvage value for tax purposes). After 10 years, the plant will have a salvage value of $300 million (which, since it will be fully depreciated, is then taxable). The project requires $50 million in working capital at the start, which will be recovered in year 10 when the project shuts down. The corporate tax rate is 35%. All cash flows occur at the end of the year.

a. If the risk-free rate is 5%, the expected return of the market is 11%, and the asset beta for the consumer electronics industry is 1.67, what is the NPV of the project?

b. Suppose that you can finance $400 million of the cost of the plant using 10-year, 9% coupon bonds sold at par. This amount is incremental new debt associated specifically with this project and will not alter other aspects of the firm’s capital structure. What is the value of the project, including the tax shield of the debt?