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Progressive Inc

Finance

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Progressive Inc. is a for-profit provider of home health services. It has EBIT of $2 million per year, no debt, and a market value of approximately $12 million. Progressive is considering issuing debt to buy back shares, the interest on which would be tax deductible (tax rate = 40%). 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:

Value of debt Probability of financial 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%

Progressive does not have any debt and the unlevered value of the firm is $12,000,000

The corporate cost of capital is 10%.

QUESTION

What would be the value of the firm be if Progressive borrowed the following -

1. 2,500,000

2. 10,000,000

3. 20,000,000