Question

Optimal Capital Structure with Hamada

Beckman Engineering and Associates (BEA) is considering a change in its capital structure. BEA currently has $20 million in debt carrying a rate of 6%, and its stock price is $40 per share with 2 million shares outstanding. BEA is a zero growth firm and pays out all of its earnings as dividends. The firm's EBIT is $13.257 million, and it faces a 30% federal-plus-state tax rate. The market risk premium is 6%, and the risk-free rate is 5%. BEA is considering increasing its debt level to a capital structure with 35% debt, based on market values, and repurchasing shares with the extra money that it borrows. BEA will have to retire the old debt in order to issue new debt, and the rate on the new debt will be 8%. BEA has a beta of 0.8.

1. What is BEA's unlevered beta? Use market value D/S (which is the same as w_d/w_s) when unlevering. Round your answer to two decimal places.
   
   
2. What are BEA's new beta and cost of equity if it has 35% debt? Do not round intermediate calculations. Round your answers to two decimal places.

   Beta
   Cost of equity	%

   
   
3. What are BEA’s WACC and total value of the firm with 35% debt? Do not round intermediate calculations. Round your answer to two decimal places.
   %
   
   What is the total value of the firm with 35% debt? Do not round intermediate calculations. Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answer to three decimal places.
   $ million

Answer 1

A.

Calculation of unlevered beta

βU = βL/[(1+(1−T)(D/E)] = 0.8/[1 + (1−.30)(20/80)] = 0.8 / 1.175 = 1.47

B.

Calculation of new beta after releveraging and cost of equity if it has 30% debt:

βL = βU[(1+(1−T)(D/E)]

At 35% debt,

βL = 1.47[1 + (1 - 0.3)(35/65) = 1.47 x 1.3769 = 2.02

With CAPM, cost of equity can be calculated as

Ke = Rf+β(Rm−Rf)

= 5% + 2.02 x 6%= 5% + 12.13% = 17.13%

c.

Calculation of WACC:

WACC = [wD x kD x (1 - t)] + [wE x kE]

= [0.35 x 8% x (1 - 0.30)] + [0.65 x 17.13%] = 1.96% + 11.14% = 13.10%

Calculation of total value of firm with 35% debt:

V = FCF/WACC

= EBIT(1 - T)/WACC

= 13.357(1-0.3)/0.1310 = $71.39 million