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 $12.263 million, and it faces a 30% federal-plus-state tax rate. The market risk premium is 4%, and the risk-free rate is 5%. BEA is considering increasing its debt level to a capital structure with 40% 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 1.2.

A. What is BEA's unlevered beta? Use market value D/S (which is the same as wd/ws) when unlevering. Do not round intermediate calculations. Round your answer to two decimal places.

B. What are BEA's new beta and cost of equity if it has 40% debt? Do not round intermediate calculations. Round your answers to two decimal places.

Beta:

Cost of equity: %

C. What are BEA’s WACC and total value of the firm with 40% debt? Do not round intermediate calculations. Round your answer to two decimal places.

%

What is the total value of the firm with 40% debt? Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. Do not round intermediate calculations. Round your answer to three decimal places.

$ million

Answer 1

Calculation of Unlevered Beta

Given

Total Debt : $ 20000000

Total Equity :$2 million * $40 = $80000000

Unlevered Beta = Levered Beta/ {1+[(1-tax)*D/E ratio]}

= 1.2 / {1+ [(1-0.30) x 2/8]} = 1.2/ (1+{0.7 x 0.25}) = 1.2/ (1+ 0.175) = 1.02

Calculation of New Beta if debt increased to 40%

Beta = unlevered Beta * {1+[(1-tax)*D/E ratio]}

= 1.02 x {1+ [(1-0.30) * 0.40]} = 1.02 x {1 + (0.7 * 0.4)} = 1.02 x (1 + 0.28) = 1.02 * 1.28 = 1.31

Cost of equity

Given

Market Risk premium (R_m - R_f) = 4%

K_e = R_f + Beta (R_m - R_f) = 5% + 1.31 (4%) = 5% + 5.24% = 10.24%

Calculation of WACC

Cost of debt = 8% * (1 -0.30) = 5.6%

WACC = 60% X 10.24% + 40% X 5.6% = 6.144 % + 2.24% = 8.384 %

Particulars	Value in $ million
EBIT	12.263
Interest (@8% on $32 million)	2.56
Equity earning	9.703
Cost of Equity	10.24
Market Value of Equity A	94.755
Cost of debt	8%
Market value of debt B	32.00
Market value of the firm (A+B)	126.755