A firm has an expected return on equity of 14% and an after-tax cost of debt of 6%.What debt-equity ratio should be used in order to keep the WACC at 10%?
A)1.00
B)0.75
C)0.50
D)0.25

Question

Quizplus · Accepted Answer

The Weighted Average Cost of Capital (WACC) is calculated using the formula: 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 (the total market value of the firm's financing), Re is the cost of equity, Rd is the cost of debt, and Tc is the corporate tax rate. In this scenario, we are not given a corporate tax rate, but we are told the after-tax cost of debt, so we can simplify the formula to WACC = (E/V) * Re + (D/V) * Rd. We are asked to find the debt-equity ratio (D/E) that results in a WACC of 10%, with Re = 14% and Rd = 6%.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). Plugging these into the WACC formula and setting WACC to 10% gives us:10% = (1 / (1 + x)) * 14% + (x / (1 + x)) * 6%Solving for "x" in this equation gives us a debt-equity ratio of 1.00, meaning the firm should have equal amounts of debt and equity to maintain a WACC of 10%.

A Firm Has an Expected Return on Equity of 14