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 $13.565 million, and it faces a 40% federal-plus-state tax rate. The market risk premium is 6%, and the risk-free rate is 6%. BEA is considering increasing its debt level to a capital structure with 30% 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 10%. BEA has a beta of 1.0.

What is the total value of the firm with 30% 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

1. 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.
2. What are BEA's new beta and cost of equity if it has 30% 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 30% debt? Do not round intermediate calculations. Round your answer to two decimal places.
     %

Answer 1

a. Current Equity = E = price per share x number of shares outstanding = $40 per share x 2 million share = $80 million

Current debt = D = $20 million , Tax rate = 40%

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

Current Beta = Current Levered Beta = 1

$Unlevered\ Beta = \frac{Levered\ Beta}{1 + (1-tax\ rate) \frac{D}{E}}$

$Unlevered\ Beta = \frac{1}{1 + (1 - 40\%) (0.25)}$

$Unlevered\ Beta = \frac{1}{1 + (60\%) (0.25)}$

$Unlevered\ Beta = \frac{1}{1 + 0.15}$

Unlevered Beta = 1/1.15

Unlevered Beta = 0.8695 = 0.87 (rounded to two places off decimal)

b. BEA's new Beta will be equal to levered beta with capital structure consisting of 30% debt

New Percentage of Debt = D_new = 35%, New percentage of Equity = E_mew = 1 - D_new = 1 - 30% = 70%

So D_new / E_new = 30%/70% = 3/7 = 0.42857

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

= 0.87 [ 1 + (1-40%) (0.42857)] = 0.87[1 + 60% x 0.42857] = 0.87 (1 + 0.257142) = 0.87 x 1.257142 = 1.0937142 = 1.09 (rounded to two places off decimal)

Hence BEA's New Beta = 1.09

Risk free rate = 6%, Risk premium = 6%

According to capital asset pricing model

Cost of Equity = Risk free rate + BEA's new Beta x Risk premium = 6% + 1.09 x 6% = 6% + 6.54% = 12.54%

c. It is known that company retires its old debt to issue new debt and repurchases shares with extra money it borrows such that

Debt / Total capital = w_d = 30% and Equity / Total Capital = w_e = 1 - w_d = 1 - 30% = 70%

Cost of new debt = r_d = 10% and Cost of Equity = r_e = 12.54%

WACC = r_d (w_d)(1-tax rate) + r_e (w_e)

= 10%(30%)(1-40%) + 12.54%(70%) = 10% x 30% x 60% + 12.54% x 70% = 1.80% + 8.778% = 10.578 = 10.58%

BEA' s WACC when debt is 30% = 10.58%

After tax profit of BEA i.e. EBIT(1-tax rate) will be distributed between the bondholders and shareholders and also BEA is a no growth firm and pays all its earnings as dividends, hence EBIT will remain constant and hence can be used to find the value of firm

EBIT = 13.565 million = 13.565 x 1000000 = 13565000

Let Value of the firm be V

$V=\frac{EBIT(1-tax\ rate)}{WACC}$

$V=\frac{13565000(1-40\%)}{10.58\%}$

V = 8139000 / 10.58% = 76928166.351

Value of firm rounded to two places of decimal = 76928166.35

Value of firm rounded to two places of decimal in millions = 76928166.351 / 1000000 = 76.928166351 million = 76.92 million

Value of firm rounded to three places of decimal in millions = 76928166.351 / 1000000 = 76.928166352 million = 76.928 million