Question: Nadir, Inc., an unlevered firm, has expected earnings before interest and taxes of $2 million per year. Nadir's tax rate is 40%, and the market value is V=E=$12 million. The stock has a beta of 1, and the risk free rate is 9%. [Assume that E(Rm)-Rf=6%] Management is considering the use of debt; debt would be issued and used to buy back stock, and the size of the firm would remain constant. The default free interest rate on debt is 12%. Since interest expense is tax deductible, the value of the firm would tend to increase as debt is added to the capital structure, but there would be an offset in the form of the rising cost of bankruptcy. The firm's analysts have estimated, approximately, that the present value of any bankruptcy cost is $8 million and the probability of bankruptcy will increase with leverage according to the following schedule:

Value of debt               Probability of failure

$ 2,500,000                       0.00%

$ 5,000,000                       8.00%

$ 7,500,000                       20.5%

$ 8,000,000                       30.0%

$ 9,000,000                       45.0%

$10,000,000                       52.5%

$12,500,000                       70.0%

a. What is the cost of equity and WACC at this time?

b. What is the optimal capital structure when bankruptcy costs are considered?

c. What will the value of the firm be at this optimal capital structure?