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 $14.379 million, and it faces a 40% 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 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 1.0.

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

0.87

b. 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: 1.15

Cost of Equity: 9.6

c. 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.

%

d. What is the total value of the firm with 35% 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.

Answer 1

a Total current debt = D = $20 million

Total Equity = E = no of shares x price per share = 2 million share x $40 per share = $80 million

Debt/Total Equity = D/E = 20miilion / 80 million = 0.25

Current Beta = Current Levered Beta = 1, Tax rate = 40%

Unlevered Beta = 1 / 1.15 = 0.8695 = 0.87 (rounded to 2 decimal places)

Hence Unvlevered Beta = 0.87

b. To find the BEA's new Beta when debt is 35% of capital structure, we need to calculate levered Beta

Equity percentage = 1 - percentage of Debt = 1 - 35% = 1-0.35 = 0.65 = 65%

So New (Debt/Equity) = D/E = 35%/65% = 0.5384

We know that

BEA's new Beta = Levered Beta = Unlevered Beta [ 1 + (1-tax rate) (D/E)]

= 0.87[1 + (1-40%)(0.5384)] = 0.87[1 + 60% x 0.5384] = 0.87 [1 + 0.32304] = 0.87 x 1.32304 = 1.1510 = 1.15 (rounded to two decimal places

BEA's New Beta = 1.15

According to CAPM

Cost of Equity = Risk free rate + Beta x market risk premium

= 5% + 1.15 x 4% = 5% + 4.60% = 9.60%

c. Company retires old debt and then issues new debt to repurchase shares such that

Debt/Total Capital = D/T = 35%

Equity/Total capital = E/T = (1 - D/T) = (1-35%) = 65%

Cost of new debt = r_d = 8% and Cost of Equity when debt is 35% = r_e = 9.60%

WACC = r_d (D/T)(1-tax rate) + r_e (E/T)

WACC = 8%(35%)(1-40%) + 9.60%(65%)

WACC = 8% x 35% x 60% + 9.60% x 65%

WACC = 1.68% + 6.24% = 7.92%

Since BEA is a no growth firm and pays all its earnings as dividends, therefore after tax operating profit i.e. EBIT(1-tax rate) will distributed between debt holders and shareholders

Hence EBIT(1-tax rate) can be used to find Value of the firm

EBIT = 14.379 million = 14379000

Let Value of the firm be V

V = 86274000 / 7.92% = 108931818.18

V = (108931818.18 / 1000000) million = 108.93181818 million = 108.93 million (rounded to 2 places off decimal)

d. Value of firm = 108.93181818 million = 108.932 million (rounded to 3 places off decimal)