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: 8.895% 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 2.376% 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?

Expected rate of return on equity under the new capital structure is 9.75 %

Explanation:

given data

Market value of long-term debt =  $20,888 million

Market value of common stock =  $171,138 million

Beta =  1.04

Yield to maturity at 10 year t = 2.167%

Expected return on equity = 8.895%

Marginal tax rate t =  35%

solution

we get here cost of unlevered equity  by the cost of levered equity formula that is  

cost of levered equity  = rSU + (rSU-rD) ×  (1-t) × (D÷S)    1

here rSL is cost of levered equity and  rSU is cost of unlevered equity and rD is before tax cost of debt and D is  value of debt and S is value of equity.

put here value and we will get  

8.895% = rSU + (rSU-2.167%) ×  (1-35%) × (20,888÷171,138)

solve it we get

rSU = 0.084005

cost of unlevered equity  = 8.40 %

and

cost of levered equity for new capital structure will be

put here value in equation 1

cost of levered equity  = 8.40 + (8.40-2.376%) × (1-35%) × ( 20 ÷ 80 )

cost of levered equity = 9.75 %

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