ABC, Inc. is a company that so far has not taken on any debt at all. ABC has 3 million shares outstanding, each trading at $25 per share. The corporate tax rate is 40%.

Suddenly ABC management decides that they should take on some debt. ABC is considering three possible debt levels: $20 million of debt, $40 million of debt or $60 million of debt. In either case, ABC will use the proceeds from the debt issue to buy back shares, and expects to keep the debt at a constant level forever. Capital markets are efficient and the yield that ABC have to promise investors for the different debt levels is equal to 5% for the lowest debt level, 7% for the intermediate debt level, and 9% for the highest debt level.

A disadvantage of ABC taking on debt is that it may enter financial distress at any point in the future. If distress happened, it would cost the company $6 million. ABC estimates that the likelihood of financial distress would be 2% for the lowest debt level, 6% for the intermediate debt level and 8% for the highest debt level. The discount rate to be used for these distress costs has been estimated to be 2%.

a. What is the present value of financial distress costs for each of the three scenarios?

b. Compute the firm value of ABC under each of the three scenarios. What debt level should ABC choose?

c. Assume ABC decides to take on the level of debt you came up with for question b). What will happen to ABC’s share price when the market learns about this decision to recapitalize?

d. After having settled on the optimal amount of debt, what will the total market value of equity of ABC be once the company has used the proceeds from the new debt to repurchase their shares? What is the total gain to equity holders from the repurchase?