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: 8.771%

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 2.413% 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

Market value of long-term debt: $20,888 million
Market value of common stock: $171,138 million
Total value = 20,888 + 171,138 = 192,026
Under Capm new Cost of equity = risk free rate + beta * (Market return - Risk free rate )
Market return =( 8.771% - 2.617%)/1.04 + 2.167% = 0.080843 or 8.0843%
Beta levered = 1.04
Beta Unlevered = Beta Levered /(1 + (1 -tax rate )*D/E) = 1.04/(1+(1-35%)*20888/171,138) = 0.96355643715
After new Capital Structure
Debt / Equity = 20%/80% = 1/4
Beta Levered New = Beta unlevered* ( 1+ (1 -tax rate)*D/E) = 0.96355643715* (1+(1-35%)*1/4) = 1.1201343
New Cost of Equity = New Risk free Rate + Betanew * ( Market return - new risk free rate) =
2.413% + 1.1201343 *(  8.0843% - 2.413%) = 0.0877 or 8.77

Best of Luck. God Bless