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Your firm is considering issuing one-year debt, and has come up with the following estimates of the value of the interest tax shield and the probability of distress for different levels of debt: Debt Level ($ million) 0405060708090PV(Interest Tax Shield)0.000.760.951.141.331.521.71Probability of Financial Distress0%0%1%2%7%16%31%Suppose the appropriate discount rate for financial distress costs is 5%. Which level of debt above is optimal if, in the event of distress, the firm will have distress costs equal to 10 million?A.80B.60C.40D.None of the options

Question

Your firm is considering issuing one-year debt, and has come up with the following estimates of the value of the interest tax shield and the probability of distress for different levels of debt: Debt Level ($ million) 0405060708090PV(Interest Tax Shield)0.000.760.951.141.331.521.71Probability of Financial Distress0%0%1%2%7%16%31%Suppose the appropriate discount rate for financial distress costs is 5%. Which level of debt above is optimal if, in the event of distress, the firm will have distress costs equal to 10 million?A.80B.60C.40D.None of the options

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Solution

The optimal level of debt is the one that maximizes the firm's value, which is the sum of the present value of the interest tax shield and the present value of the distress costs.

The present value of the distress costs can be calculated as the product of the probability of financial distress and the distress costs, discounted at the appropriate rate. In this case, the distress costs are $10 million and the discount rate is 5%.

For each level of debt, we can calculate the present value of the distress costs, subtract this from the present value of the interest tax shield, and choose the level of debt that gives the highest value.

  1. Debt Level = 40million:PV(DistressCosts)=040 million: PV(Distress Costs) = 0% * 10 million / (1 + 5%) = 0millionValue=0 million Value = 0.76 million - 0million=0 million = 0.76 million

  2. Debt Level = 50million:PV(DistressCosts)=150 million: PV(Distress Costs) = 1% * 10 million / (1 + 5%) = 0.95millionValue=0.95 million Value = 0.95 million - 0.95million=0.95 million = 0 million

  3. Debt Level = 60million:PV(DistressCosts)=260 million: PV(Distress Costs) = 2% * 10 million / (1 + 5%) = 1.90millionValue=1.90 million Value = 1.14 million - 1.90million=−1.90 million = -0.76 million

  4. Debt Level = 70million:PV(DistressCosts)=770 million: PV(Distress Costs) = 7% * 10 million / (1 + 5%) = 6.67millionValue=6.67 million Value = 1.33 million - 6.67million=−6.67 million = -5.34 million

  5. Debt Level = 80million:PV(DistressCosts)=1680 million: PV(Distress Costs) = 16% * 10 million / (1 + 5%) = 15.24millionValue=15.24 million Value = 1.52 million - 15.24million=−15.24 million = -13.72 million

  6. Debt Level = 90million:PV(DistressCosts)=3190 million: PV(Distress Costs) = 31% * 10 million / (1 + 5%) = 29.52millionValue=29.52 million Value = 1.71 million - 29.52million=−29.52 million = -27.81 million

The highest value is achieved with a debt level of $40 million.

Therefore, the optimal level of debt is $40 million, so the correct answer is C. 40.

This problem has been solved

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