 # Optimal Capital Structure The Cost of Capital Approach P.V. Viswanath Based on Damodaran’s Corporate Finance.

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Optimal Capital Structure The Cost of Capital Approach P.V. Viswanath Based on Damodaran’s Corporate Finance

P.V. Viswanath2 Cost of Capital Approach  We have already seen that FCFF = EBIT(1-t) – (Capital Expenditures – Dep) – Change in Noncash Working Capital  The Value of the firm is the sum of the discounted present values of FCFF plus current cash.  If we can assume that the cashflows are unaffected by the choice of financing mix, then Max Firm Value = Min WACC

P.V. Viswanath3 Cost of Equity Capital  We compute WACC at different debt/capital ratios and pick the lowest WACC.  Three inputs needed: Cost of equity After-tax cost of debt Weights on debt and equity  Start with the current equity beta and compute the firm’s asset beta.  Compute the firm’s levered beta for different debt ratio levels and use this to figure out the cost of equity capital at the different debt ratio levels.

P.V. Viswanath4 Cost of debt capital  Estimate the firm’s dollar debt and interest exp at each debt ratio.  At each debt ratio, compute a financial ratio(s) such as the interest coverage ratio (EBIT/Interest expenses) to measure default risk; use that ratio(s) to estimate a synthetic bond rating for the firm. Add on a default spread based on the estimated rating to the risk-free rate to get the pre-tax cost of debt. Apply the marginal tax rate to get the after-tax cost of debt, keeping in mind that the marginal tax rate might decrease as we increase the amount of debt-related income deductions for tax purposes.  Weight the costs of debt and equity based on the proportions used of each type.  Choose the debt ratio that minimizes the WACC.

P.V. Viswanath5 Interest Coverage Ratios and Spreads If interest coverage ratio is >≤ toRating isSpread is -1000000.199999D20.00% 0.20.649999C12.00% 0.650.799999CC10.00% 0.81.249999CCC8.00% 1.251.499999B-6.00% 1.51.749999B4.00% 1.751.999999B+3.25% 22.2499999BB2.50% 2.252.49999BB+2.00% 2.52.999999BBB1.50% 34.249999A-1.00% 4.255.499999A0.85% 5.56.499999A+0.70% 6.58.499999AA0.50% 8.50100000AAA0.35%

P.V. Viswanath6 Constrained Approach  The unconstrained approach is problematic because agency costs are going to increase as the debt ratio goes up and as the bond rating goes down.  To keep a limit on these costs, the firm might want to put a constraint on the lowest bond rating allowed.  Use normalized operating income to estimate bond ratings so that temporarily depressed income does not yield an overly low optimal debt ratio.  Lower estimates of operating income for higher debt ratios due to indirect bankruptcy costs.

P.V. Viswanath7 Example  Problem 12, Chapter 19 from Damodaran, Corporate Finance, Theory and Practice  You have been asked by JJ Corporation, a California-based firm that manufactures and services digital satellite television systems, to evaluate its capital structure. They currently have 70 million shares outstanding trading at \$10 per share. In addition, it has 500,000 ten-year convertible bonds, with a coupon rate of 8%, trading at \$1000 per bond. JJ Corporation is rated BBB, and the interest rate on BBB straight bonds is currently 10%. The beta for the company is 1.2, and the current risk-free rate is 6%. The tax rate is 40%.

P.V. Viswanath8 Debt-Equity Ratio computation  a. What is the firm's current debt-equity ratio?  Solution: The market value of the common stock is 70m. x \$10 = \$700m. The 500,000 convertible bonds would sell at a yield of 10% if they were straight. Hence the straight bond component of the convertibles =  Since the convertibles trade at \$1000 per bond, the equity component = \$124.63 per convertible bond. Hence total equity = 700+124.63(0.5m.) = 762.32m. The market value of the debt component of the convertibles = 875.37(0.5) = 437.69m. Hence the debt-equity ratio = 437.69/762.32 = 57.41%.

P.V. Viswanath9 WACC Computation  b. What is the firm's current weighted average cost of capital?  Solution: The required rate of return on the equity, using the CAPM is.06 + 1.2(0.055) = 12.6%.  The WACC = (.5741/1.5741)(1-0.4)10% + (1/1.5741)12.6% = 10.192%, using the data from the previous section.

P.V. Viswanath10 Cost of equity after borrowing  JJ Corporation is proposing to borrow \$250 million to use for the following purposes: Buy back \$100 million Pay \$100 million in dividends Invest \$50 million in a project with a NPV of \$25 million. The effect of this additional borrowing will be a drop in the bond rating to B, which currently carries an interest rate of 11%.  c. What will be the firm's cost of equity after this additional borrowing?

P.V. Viswanath11 Cost of equity after borrowing  Solution: After this borrowing, the market value of equity will be \$762.32m - \$200m + \$25m. = \$586.5m. The market value of debt will be 437.69+250=687.69m.  Hence the debt-equity ratio will be 1.17. The unlevered beta = Hence the levered beta will be equal to 0.89(1+(1-0.4)1.17) = 1.52.  Hence, the cost of equity =.06+1.52(0.055) = 14.36%.

P.V. Viswanath12 WACC after borrowing  d. What will the firm's weighted average cost of capital be after this additional borrowing?  Solution: The WACC =

P.V. Viswanath13 Value of firm after borrowing  e. What will the value of the firm be after this additional borrowing?  Solution: The original firm value was \$1200. The WACC has decreased from 10.192% to 10.17%; hence the annual savings in financing costs equal (1200)(.10192-.1017).  Discounting these at the new cost of capital of 10.17%, we get (762.32+437.68)(.10192-.1017)/(0.1017) = \$2.36m.  New Firm Value= \$ 1,200 (original firm value) + \$ 50 (net increase in capital after capital structure changes)+ \$ 25 (NPV of new project) + \$ 2.36 (increase in firm value due to capital structure change) = \$ 1277.36 million.

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