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 about $12 million. Although management is pleased with the good financial condition of Progressive, they are also concerned that firm may be the target of a potential hostile takeover by a large competitor.
Thus, Progressive is considering issuing debt to buy back shares, the interest on which would be tax deductible (its tax rate is 40%). Management identifies 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 show value of any future financial distress costs is $8 million, and that the probability of distress increases with the amount of debt in the subsequent 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. Evaluate what is Progressive's cost of equity and corporate cost of capital now?

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

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

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