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Progressive Inc
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
Expert Solution
| Unlevered Market Value of Progressive Inc = | $ 12,000,000 |
| Tax rate = | 40% |
| PV of Future Financial Distress cost = | $ 8,000,000 |
| Now Enterpeise Value of a Levered Firm =Unlevered Firm Value + Debt *Tax Rate - (Pv of Future Financial Distress cost)*Probability of Fincial Distress ; | ||||||
| We shall use the given details to find the EV : |
| a | b. | c. | d. | e | f. | g | h | |
| Sr No | Debt Amount | Unlvered Market Value | Tax Rate | Debt *Tax Rate=a*c | PV of future Financial Distress | Probaility of Financial Distress | PV of Financial Distress*Probability of Financial distress=e*f | Enterprise Value=Value of The Firm =b+d-g |
| 1 | $ 2,500,000 | $ 12,000,000 | 40% | $ 1,000,000 | $ 8,000,000 | 1% | $ 80,000 | $ 12,920,000 |
| 2 | $ 10,000,000 | $ 12,000,000 | 40% | $ 4,000,000 | $ 8,000,000 | 8% | $ 640,000 | $ 15,360,000 |
| 3 | $ 20,000,000 | $ 12,000,000 | 40% | $ 8,000,000 | $ 8,000,000 | 64% | $ 5,120,000 | $ 14,880,000 |
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