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%	$12,000,000.0
	$2,500,000	1%	$13,000,000.0
	$5,000,000	2%	$14,000,000.0
	$7,500,000	4%	$15,000,000.0
	$10,000,000	8%	$16,000,000.0
	$12,500,000	16%	$17,000,000.0
	$15,000,000	32%	$18,000,000.0
	$20,000,000	64%	$20,000,000.0
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?