1.DFS Corporation is currently an all-equity firm, with assets with a market value of $100 million and 4 million shares outstanding. DFS is considering a leveraged recapitalization to boost its share price. The firm plans to raise a fixed amount of permanent debt (i.e., the outstanding principal will remain constant) and use the proceeds to repurchase shares. DFS pays a 35% corporate tax rate, so one motivation for taking on the debt is to reduce the firm’s tax liability. However, the upfront investment banking fees associated with the recapitalization will be 5% of the amount of debt raised. Adding leverage will also create the possibility of future financial distress or agency costs; shown below are DFS’s estimates for different levels of debt:

a. Based on this information, which level of debt is the best choice for DFS?

b. Estimate the stock price once this transaction is announced.

2.Your firm is considering a $150 million investment to launch a new product line. The project is expected to generate a free cash flow of $20 million per year, and its unlevered cost of capital is 10%. To fund the investment, your firm will take on $100 million in permanent debt.

a. Suppose the marginal corporate tax rate is 35%. Ignoring issuance costs, what is the NPV of the investment?

b. Suppose your firm will pay a 2% underwriting fee when issuing the debt. It will raise the remaining $50 million by issuing equity. In addition to the 5% underwriting fee for the equity issue, you believe that your firm’s current share price of $40 is $5 per share less than its true value. What is the NPV of the investment including any tax benefits of leverage? (Assume all fees are on an after-tax basis.)

3.Consider Avco’s RFX project from Section 18.3. Suppose that Avco is receiving government loan guarantees that allow it to borrow at the 6% rate. Without these guarantees, Avco would pay 6.5% on its debt.

a. What is Avco’s unlevered cost of capital given its true debt cost of capital of 6.5%?

b. What is the unlevered value of the RFX project in this case? What is the present value of the interest tax shield?

c. What is the NPV of the loan guarantees? (Hint : Because the actual loan amounts will fluctuate with the value of the project, discount the expected interest savings at the unlevered cost of capital.)

d. What is the levered value of the RFX project, including the interest tax shield and the NPV of the loan guarantees?

4.Arden Corporation is considering an investment in a new project with an unlevered cost of capital of 9%. Arden’s marginal corporate tax rate is 40%, and its debt cost of capital is 5%.

a. Suppose Arden adjusts its debt continuously to maintain a constant debt-equity ratio of 50%. What is the appropriate WACC for the new project?

b. Suppose Arden adjusts its debt once per year to maintain a constant debt-equity ratio of 50%. What is the appropriate WACC for the new project now?

c. Suppose the project has free cash flows of $10 million per year, which are expected to decline by 2% per year. What is the value of the project in parts (a) and (b) now?

5.XL Sports is expected to generate free cash flows of $10.9 million per year. XL has permanent debt of $40 million, a tax rate of 40%, and an unlevered cost of capital of 10%.

a. What is the value of XL’s equity using the APV method?

b. What is XL’s WACC? What is XL’s equity value using the WACC method?

c. If XL’s debt cost of capital is 5%, what is XL’s equity cost of capital?

d. What is XL’s equity value using the FTE method?

6.Propel Corporation plans to make a $50 million investment, initially funded completely with debt. The free cash flows of the investment and Propel’s incremental debt from the project follow:

Propel’s incremental debt for the project will be paid off according to the predetermined schedule shown. Propel’s debt cost of capital is 8%, and its tax rate is 40%. Propel also estimates an unlevered cost of capital for the project of 12%.

a. Use the APV method to determine the levered value of the project at each date and its initial NPV.

b. Calculate the WACC for this project at each date. How does the WACC change over time? Why?

c. Compute the project’s NPV using the WACC method.

d. Compute the equity cost of capital for this project at each date. How does the equity cost of capital change over time? Why?

e. Compute the project’s equity value using the FTE method. How does the initial equity value compare with the NPV calculated in parts (a) and (c)?

7.Gartner Systems has no debt and an equity cost of capital of 10%. Gartner’s current market capitalization is $100 million, and its free cash flows are expected to grow at 3% per year. Gartner’s corporate tax rate is 35%. Investors pay tax rates of 40% on interest income and 20% on equity income.

a. Suppose Gartner adds $50 million in permanent debt and uses the proceeds to repurchase shares. What will Gartner’s levered value be in this case?

b. Suppose instead Gartner decides to maintain a 50% debt-to-value ratio going forward. If Gartner’s debt cost of capital is 6.67%, what will Gartner’s levered value be in this case?

8.Revtek, Inc., has an equity cost of capital of 12% and a debt cost of capital of 6%. Revtek maintains a constant debt-equity ratio of 0.5, and its tax rate is 35%.

a. What is Revtek’s WACC given its current debt-equity ratio?

b. Assuming no personal taxes, how will Revtek’s WACC change if it increases its debt-equity ratio to 2 and its debt cost of capital remains at 6%?

c. Now suppose investors pay tax rates of 40% on interest income and 15% on income from equity. How will Revtek’s WACC change if it increases its debt-equity ratio to 2 in this case?

d. Provide an intuitive explanation for the difference in your answers to parts (b) and (c).