Progressive Home Health Care Inc. is a for-profit provider of home health care services in the Pacific Northwest. At present, it has EBIT of $2 million per year, no debt, and a market value of approximately $12 million. Although management is pleased with the good financial condition of Progressive, they are also concerned that the firm might be the target of a potential hostile takeover by a large competitor. Therefore, Progressive is considering issuing debt to buy back shares, the interest on which would be tax deductible (its tax rate is 40 percent). Management recognizes that as the amount of debt increases, both the value of the firm and the risk of financial distress increase. The CFO estimates that the present value of any future financial distress costs is $8 million, and that the probability of distress increases with the amount of debt in the following steps:

Probability of financial   Value of debt distress
0                                       0%
$2,500,000                          1%
$5,000,000                          2%
$7,500,000                          4%
$10,000,000                         8%
$12,500,000                        16%
$15,000,000                        32%
$20,000,000                        64%

a. What is Progressive's cost of equity and corporate cost of capital now?

b. According to MM with corporate taxes, what is the optimal level of debt?

c. According to MM with corporate taxes and financial distress, what is the optimal level of debt?

d. Plot the value of Progressive, with and without the costs of financial distress, as a function of the amount of debt. Why do the lines differ in shape?