Blue Ribbon, Inc. wants to have a weighted average cost of capital of 10 %. The firm has an after-tax cost of debt of 4 % and a cost of equity of 12 %. What debt-equity ratio is needed for the firm to achieve their targeted weighted average cost of capital?

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Quizplus · Accepted Answer

The weighted average cost of capital (WACC) is calculated as follows: WACC = E/V * Re + D/V * Rd * (1 - Tc), where E is the market value of the equity, D is the market value of the debt, V = E + D is the total market value of the firm's financing (equity and debt), Re is the cost of equity, Rd is the cost of debt, and Tc is the corporate tax rate. However, since the after-tax cost of debt is already given, we don't need to adjust Rd for taxes in this calculation.Given that the firm wants a WACC of 10%, the after-tax cost of debt (Rd) is 4%, and the cost of equity (Re) is 12%, we can set up the equation to solve for the debt-equity ratio (D/E), which is D/V divided by E/V.Let's denote the debt-equity ratio as x. Therefore, D/E = x, which implies D/V = x / (1 + x) and E/V = 1 / (1 + x).The equation to achieve a WACC of 10% is:10% = (1 / (1 + x)) * 12% + (x / (1 + x)) * 4%Solving for x gives us a debt-equity ratio of 0.333..., which is approximately 0.33 or 33%.