Spectreman Ltd. is a levered firm with $4M of permanent debt outstanding, and 1 million shares priced at $15 each. The company faces a marginal tax rate of 30%, and its management is considering to permanently increase the company's leverage in line with other firms in its sector. To this aim, the firm will issue debt to buy back stock. The management has estimated that the present value of any bankruptcy costs is $1M, and the probability of bankruptcy increases with leverage according to the following schedule: 

Value of debt .................Probability of failure 

 $4,000,000 .....................................0% 

$5,000,000..................................... 10%

 $7,500,000 ..................................... 25%

$8,000,000 .....................................30% 

$9,000,000 .....................................50%

$10,000,000 ..................................... 70.5% 

When choosing its capital structure, the firm restricts its choice to the above levels of debt. 

1.  Estimate the optimal level of debt for the firm using the APV method. 

2. How many shares will the firm buy if it issues the optimal amount of debt? What will the share price be after the recapitalization? How many shares will there be after the recapitalization? 

3. Summarise your answers to question (2) by drawing the market value balance sheet after the recap announcement, after the debt issue, and after the stock buyback.