Your firm is considering issuing one-year debt, and has come up with the followi

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:

Suppose the firm has a beta of zero, so that the appropriate discount rate for financial distress costs is the risk-free rate of 5%.

Which level of debt above is optimal if, in the event of distress, the firm will have distress costs equal to:

a. $2 million?

If Distress costs are equal to $2 million, the optimal level of debt is $___ million (Round to the nearest integer.)

b. $5 million?

If Distress costs are equal to $5 million, the optimal level of debt is $___ million (Round to the nearest integer.)

c. $25 million?

If Distress costs are equal to $25 million, the optimal level of debt is $___ million (Round to the nearest integer.)

Debt Level (in $ million) 0 40 50 60 70 80 90 PV (Interest tax shield, $ million) 0.00 0.76 0.95 1.14 1.33 1.52 1.71 Probability of financial distress 0% 0% 1% 2% 7% 16% 31%

Explanation / Answer

Hence for 2 million distress cost, the optimum level of Debt should be $70 million

For 5 million distress cost, the optimum level of Debt should be $80 million and similarly for 25 million distress cost, the optimum debt should be 90 million dollars.

Debt 0 40 50 60 70 80 90 Interest @ 5% 0 2 2.5 3 3.5 4 4.5 Total Obligation 0 42 52.5 63 73.5 84 94.5 PV tax sheild 0 0.76 0.95 1.14 1.33 1.52 1.71 Probability 0% 0% 1% 2% 7% 16% 31% Gross Financial Distress 0 0 0.525 1.26 5.145 13.44 29.295 Net Financial Distress (Gross - Tax shield) 0 -0.76 -0.425 0.12 3.815 11.92 27.585

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