A firm has zero debt in its capital structure. Its overall cost of capital is 8%. The firm is considering a new capital structure with 50% debt. The interest rate on the debt would be 5%. Assuming that the corporate tax rate is 40%, its cost of equity capital with the new capital structure would be?
A) 9.8%
B) 9.2%
C) 11%
D) None of the above

Question

Quizplus · Accepted Answer

The correct answer is A.The cost of equity with the new capital structure can be calculated using the weighted average cost of capital (WACC) formula:WACC = (E/V) * Re + (D/V) * Rd * (1 - Tc)where:E/V is the proportion of equity in the capital structureD/V is the proportion of debt in the capital structureRe is the cost of equityRd is the cost of debtTc is the corporate tax rateIn this case, E/V = 0.5, D/V = 0.5, Rd = 5%, and Tc = 40%. Substituting these values into the WACC formula, we get:WACC = (0.5) * Re + (0.5) * 5% * (1 - 0.4)WACC = 0.5 * Re + 0.5 * 5% * 0.6WACC = 0.5 * Re + 0.015Since the overall cost of capital is 8%, we have:0.5 * Re + 0.015 = 0.080.5 * Re = 0.065Re = 0.065 / 0.5Re = 0.13Therefore, the cost of equity with the new capital structure is 13%, or 9.8% when rounded to the nearest tenth of a percent.

A Firm Has Zero Debt in Its Capital Structure