Question

Holland Auto Parts is considering a merger with Workman Car Parts. Workman's market-determined beta is 0.9, and the firm currently is financed with 20% debt, at an interest rate of 8%, and its tax rate is 25%. If Holland acquires Workman, it will increase the debt to 60%, at an interest rate of 9%, and the tax rate will increase to 35%. The risk-free rate is 6% and the market risk premium is 4%. What will Workman's required rate of return on equity be after it is acquired?

Answer 1

Answer:

0.097 OR 9.7%

Explanation:

Cost of Equity using CAPM-

Re = Rf + Beta (Rpm)

where,

Rf = Risk free return = 6%,

Rpm = Risk premium = 4%,

Beta = 0.9

Therefore,

Re = .06 + .9 (.04)

    = 9.6%

Unlevered cost of equity:

ReU = Wd × rd + We × re

where,

ReU = Unlevered cost of equity,

Wd = Debt = 20%

rd = cost of debt = 8%

We = equity = 80%

re = cost of equity  = 9.6%

Therefore,

ReU = 0.20 × 8% + .80 × 9.6%

       = 9.28%

Levered cost of Equity:

New Debt = 60%,

New Equity = 40%,

New rd = 9%

ReL = ReU + (ReU - rd) (D ÷ E)

= 9.28% + (9.28% - 9%) (0.60 ÷ 0.40)

= 0.097 OR 9.7%