Phil's Carvings wants to have a weighted average cost of capital of 9.5 percent.The firm has an aftertax cost of debt of 6.5 percent and a cost of equity of 12.75 percent.What debt-equity ratio is needed for the firm to achieve its targeted weighted average cost of capital?

Question

Quizplus · Accepted Answer

The weighted average cost of capital (WACC) is calculated as 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, in this question, the after-tax cost of debt is already given, so we don't need to adjust for taxes.Given that the firm wants a WACC of 9.5%, the after-tax cost of debt is 6.5%, and the cost of equity is 12.75%, we can set up the equation for WACC and solve for the debt-equity ratio (D/E).Let E = equity, D = debt, then D/E = debt-equity ratio.WACC = (E/(D+E)) * Re + (D/(D+E)) * RdGiven WACC = 9.5%, Rd = 6.5%, and Re = 12.75%, we need to find D/E.Rearranging the equation to solve for D/E, we get:9.5 = (1/(1+D/E)) * 12.75 + (D/E/(1+D/E)) * 6.5Solving this equation for D/E gives us the debt-equity ratio required to achieve the targeted WACC. The correct answer is the ratio that satisfies this equation, which is approximately 1.08. This means the firm needs a debt-equity ratio of about 1.08 to achieve its targeted WACC of 9.5%.

Phil's Carvings Wants to Have a Weighted Average Cost of Capital