Question

You have the following data on The Home Depot, Inc. Market value of long-term debt: $20,888 million Market value of common stock: $171,138 million Beta: 1.04 Yield to maturity on debt with 10 years to maturity: 2.167% Expected return on equity: 8.647% Marginal tax rate: 35% Assume that if Home Depot issues new bonds, the bonds will have 10 years to maturity. Suppose that managers at Home Depot decide to increase the proportion of debt to 20% of the value of the company. The managers estimate that yield on the company’s 10 year bonds will rise to 2.452% if the company changes its capital structure in this manner. What would be the expected rate of return on equity under the new capital structure? Do not round at intermediate steps in your calculation. Express your answer in percent. Round to two decimal places. Do not type the % symbol.

Answer 1

Given:

• MV(D) = $20,888 million
• MV(E) = $171,138 million
• Total Value of the capital = MV(D) + MV(E) = $20,888 mn + $171,138mn = $192,026 mn

Weights of Debt and Equity in the capital structure:

• WtD = MV)D) / Total Capital = $20,888 mn / $192,026 mn = 10.88%
• WtE = MV(E) / Total Capital = $171,138mn / $192,026 mn = 89.12%

Cost of capital, wacc:

• Before tax cost of debt, Kd = 2.167%; tax rate = 35%;
• So after-tax cost of debt = Kd * (1-t) = 2.167% * (1-0.30) = 1.4086%
• Cost of equity, Ke = 8.647%

wacc = weighted average cost of capital

• wacc = WtD * Kd * (1-t) + WtE * Ke
• wacc = 0.1088 * 1.4086% + 0.8912 * 8.647 %
• wacc = 0.00153 + 0.07706
• wacc = 0.07860 = 7.86%

If debt portion is 20% in the capital structure with the new before tax cost of debt, Kd = 2.452%, then the cost of equity will be:

• WtD = 20%; So WtE = 80%
• After-tax cost of debt = Kd * (1-tax) = 2.452% * (1-0.35) =  0.015938 = 1.5938%
• wacc = 7.86%

wacc = WtD * Kd * (1-t) + WtE * Ke

• 7.86% = 0.20 * 1.5938% + 0.80 * Ke
• 7.86% = 0.3188% + 0.80 * Ke
• 0.80 * Ke = 7.86% - 0.3188%
• 0.80 * Ke = 0.075412
• Ke = 0.075412 / 0.80 = 0.094266 = 9.4266%

Cost of equity = 9.43 (answer)