# Estimate the effect of the change in the cost of

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Estimate the effect of the change in the cost of capital on firm value Estimate the effect on the stock price n In terms of the mechanics, what would you need to do to get to the optimal immediately?

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Aswath Damodaran 68 III. The APV Approach to Optimal Capital Structure n In the adjusted present value approach, the value of the firm is written as the sum of the value of the firm without debt (the unlevered firm) and the effect of debt on firm value Firm Value = Unlevered Firm Value + (Tax Benefits of Debt - Expected Bankruptcy Cost from the Debt) n The optimal dollar debt level is the one that maximizes firm value
Aswath Damodaran 69 Implementing the APV Approach n Step 1: Estimate the unlevered firm value. This can be done in one of two ways: Estimating the unlevered beta, a cost of equity based upon the unlevered beta and valuing the firm using this cost of equity (which will also be the cost of capital, with an unlevered firm) Alternatively, Unlevered Firm Value = Current Market Value of Firm - Tax Benefits of Debt (Current) + Expected Bankruptcy cost from Debt n Step 2: Estimate the tax benefits at different levels of debt. The simplest assumption to make is that the savings are perpetual, in which case Tax benefits = Dollar Debt * Tax Rate n Step 3: Estimate a probability of bankruptcy at each debt level, and multiply by the cost of bankruptcy (including both direct and indirect costs) to estimate the expected bankruptcy cost.

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Aswath Damodaran 70 Estimating Expected Bankruptcy Cost n Probability of Bankruptcy Estimate the synthetic rating that the firm will have at each level of debt Estimate the probability that the firm will go bankrupt over time, at that level of debt (Use studies that have estimated the empirical probabilities of this occurring over time - Altman does an update every year) n Cost of Bankruptcy The direct bankruptcy cost is the easier component. It is generally between 5-10% of firm value, based upon empirical studies The indirect bankruptcy cost is much tougher. It should be higher for sectors where operating income is affected significantly by default risk (like airlines) and lower for sectors where it is not (like groceries)
Aswath Damodaran 71 Tax Benefits at Debt Ratios Debt Ratio \$ Debt Tax Rate Tax Benefits 0% \$0 35.00% \$0 10% \$4,079 35.00% \$1,428 20% \$8,158 35.00% \$2,855 30% \$12,237 35.00% \$4,283 40% \$16,316 35.00% \$5,710 50% \$20,394 30.05% \$6,128 60% \$24,473 22.76% \$5,571 70% \$28,552 17.17% \$4,903 80% \$32,631 15.02% \$4,903 90% \$36,710 13.36% \$4,903 Tax Benefits capped when interest expenses exceed EBIT

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Aswath Damodaran 72 Expected Bankruptcy Costs Debt Ratio Bond Rating Probability of Default Expected Bankruptcy Cost 0% AA 0.28% \$32 10% AA 0.28% \$32 20% A- 1.41% \$161 30% BB 12.20% \$1,389 40% CCC 50.00% \$5,693 50% CCC 50.00% \$5,693 60% CC 65.00% \$7,401 70% C 80.00% \$9,109 80% C 80.00% \$9,109 90% C 80.00% \$9,109
Aswath Damodaran 73 Boeing: APV at Debt Ratios Debt Ratio Unlevered Value Tax Benefits Bankruptcy Value of Costs Levered Firm 0% \$37,953 \$0 \$32 \$37,921 10% \$37,953 \$1,428 \$32 \$39,349 20% \$37,953 \$2,855 \$161 \$40,648 30% \$37,953 \$4,283 \$1,389 \$40,847 40% \$37,953 \$5,710 \$5,693 \$37,970 50% \$37,953 \$6,128 \$5,693 \$38,388 60% \$37,953 \$5,571 \$7,401 \$36,123 70% \$37,953 \$4,903 \$9,109 \$33,747 80% \$37,953 \$4,903 \$9,109 \$33,747 90% \$37,953 \$4,903 \$9,109 \$33,747 Exp. Bk. Cst: Expected Bankruptcy cost
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