Can you please tell me where I\'m going wrong with my WACC calculation? Tax rate

Question

Can you please tell me where I'm going wrong with my WACC calculation? Tax rate = 35%, Risk free rate = 4%, risk prem = 7%, unlevered beta = 1.5. Using the CAPM to estimate the cost of common equity and estimates that the risk-free rate is 4%, the market risk prem is 7%, and tax rate is 35%. The company estimates that if it had no debt, its "unlevered" beta would be 1.5 1) What would be the WACC at the optimal capital structure? What would teh firm's optimal capital structure be? My professor says WACC should be 13.77, but my calcuation at 60/40 is coming out to 3.836. Help please.

Debt-to-Capital Ratio Equity-to-Capital Ratio Debt-to-Equity Ratio Bond Rating Before-Tax Cost of Debt Rate of Interest Cost of Equity Weighted cost of capital (wd) (we) (D/E) (rd) ((rd(1-T)) re 0.0 1.0 0.00 A 6.0% 3.9 9.425 9.425 0.2 0.8 0.25 BBB 7.0% 4.55 9.425 7.554 0.4 0.6 0.67 BBB 9.0% 5.85 9.425 5.691 0.6 0.4 1.50 C 11.0% 7.15 9.425 3.836 0.8 0.2 4.00 D 14.0% 9.1 9.425 1.997

Explanation / Answer

based on CAPM the cost of equity= Rf + Beta ( Rm- Rf)

= 4+ 1.5X 7 (- tax)

=14.5 - 35% (tax rate is 35% and 35% on 14.5 is 5.075)

= 14.5 - 5.075= 9.425

csot of debt= I (1- tax rate), i.e. for 6% intersest= 6(1- 35%)=

the optimum combination of debt and equity is 40% of debt and 60% equity, it provides lower cost of capital than any other combination.

% of debt rate of interest % of equity cost of equity weghted cost of capital 0 3.9 1.0 9.25 9.25 0.2 4.55 0.8 9.25 8.31 0.4 5.85 0.6 9.25 7.89 0.6 7.15 0.4 9.25 7.99 0.8 9.1 0.2 9.25 9.13

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