# Finance three exercises 21-1, 21-2, 21-5

Ex 21-1

Vandell’s free cash flow (FCF0) is $2 million per year and is expected to grow at a constant rate of 5% a year; its beta is 1.4. What is the value of Vandell’s operations?

If Vandell has $10.82 million in debt, what is the current value of Vandell’s stock?

(Hint: Use the corporate valuation model from Chapter 13.)

Ex 21-2

Hastings estimates that if it acquires Vandell, interest payments will be $1,500,000 per year for 3 years, after which the current target capital structure of 30% debt will be maintained. Interest in the fourth year will be $1.472 million, after which interest and the tax shield will grow at 5%. Synergies will cause the free cash flows to be $2.5 million, $2.9 million, $3.4 million, and $3.57 million in Years 1 through 4, respectively, after which the free cash flows will grow at a 5% rate. What is the unlevered value of Vandell, and what is the value of its tax shields? What is the per share value of Vandell to Hastings Corporation? Assume that Vandell now has $10.82 million in debt.

Ex 21-5

Marston Marble Corporation is considering a merger with the Conroy Concrete Company. Conroy is a publicly traded company, and its beta is 1.30. Conroy has

been barely profitable, so it has paid an average of only 20% in taxes during the last several years. In addition, it uses little debt; its target ratio is just 25%, with the cost of debt 9%.

If the acquisition were made, Marston would operate Conroy as a separate, wholly owned subsidiary. Marston would pay taxes on a consolidated basis, and the tax rate would therefore increase to 35%. Marston also would increase the debt capitalization in the Conroy subsidiary to wd = 40%, for a total of $22.27 million in debt by the end of Year 4, and pay 9.5% on the debt. Marston’s acquisition department estimates that Conroy, if acquired, would generate the following free cash flows and interest expenses (in millions of dollars) in Years 1–5:

Year

1

2

3

4

5

In Year 5, Conroy’s interest expense would be based on its beginning-of-year (that is, the end-of-Year-4) debt, and in subsequent years both interest expense and free cash flows are projected to grow at a rate of 6%.

These cash flows include all acquisition effects. Marston’s cost of equity is 10.5%, its beta is 1.0, and its cost of debt is 9.5%. The risk-free rate is 6%, and the market risk premium is 4.5%.

a. What is the value of Conroy’s unlevered operations, and what is the value of Conroy’s tax shields under the proposed merger and financing arrangements?

b. What is the dollar value of Conroy’s operations? If Conroy has $10 million in debt outstanding, how much would Marston be willing to pay for Conroy?