WACC and Optimal Capital Structure: using CAPm to estimate cost of common equity

Question

WACC and Optimal Capital Structure: using CAPm to estimate cost of common equity and estimates of risk-free rate is 4%, market risk premium is 7%, and tax rate is 35%. The company estimates that if it had no debt, its "unlevered" beta would be 1.5. What would be the WACC at the optimal capital structure? What would be the firm's optimal capital structure be? Please show calculations.

14.0%

Debt-to-Capital Ratio Equity-to-Capital Ratio Debt-to-Equity Ratio Bond Rating Before-Tax Cost of Debt (wd) (we) (D/E) (rd) ((rd(1-T)) 0.0 1.0 0.00 A 6.0% 0.2 0.8 0.25 BBB 7.0% 0.4 0.6 0.67 BBB 9.0% 0.6 0.4 1.50 C 11.0% 0.8 0.2 4.00 D

14.0%

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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