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 8%, 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 $14.131 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 45% 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 12%. BEA has a beta of 1.2.

1. What is BEA's unlevered beta before restructuring? 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 after releveraging and cost of equity if it has 45% debt? Round your answers to two decimal places.

   Beta
   Cost of equity	%

   
   
3. What is BEA's WACC after releveraging? Round your answer to two decimal places.
     %
   
   What is the total value of the firm with 45 % debt? 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. 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 = 1.2, Tax rate = 30%

Unlevered Beta before restructuring = (Levered Beta) / [1 + (D/E)(1-tax rate)] = (1.2) / [1 + (0.25)(1-30%)] = (1.2) / [1 + 0.25 x 70%] = 1.2 / (1 + 0.175) = 1.2 / 1.175 = 1.0212 = 1.02 (rounded to two decimal places)

Unlevered Beta = 1.02

b. Since after restructuring capital structure consists of 45% debt,

Percentage of debt = 45% , percentage of equity = 1 - debt percentage = 1 - 45% = 55%

New debt to equity ratio = D/E = 45%/55%

BEA's new Beta after releveraging = Levered Beta with 45% debt = Unlevered Beta [ 1 + (1-tax rate) (D/E)]

Levered Beta with 45% debt = 1.02 [ 1 + (1-30%) (45%/55%)] = 1.02 [ 1 + (70%) (45%/55%)] = 1.02 (1 + 0.572727) = 1.02 x 1.572727 = 1.6041 = 1.60 (rounded to two decimal places)

Hence BEA's New beta after releveraging = 1.60

According to CAPM

Cost of Equity with 45% debt = Risk free rate + BEA's new Beta x market risk premium

= 5% + 1.60 x 6% = 5% + 9.60% = 14.60%

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

Debt/Total Capital = D/T = 45%

Equity/Total capital = E/T = (1 - D/T) = (1-35%) = 55%

Cost of new debt = r_d = 12% and Cost of Equity when debt is 45% = r_e = 14.60%

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

WACC = 12%(45%)(1-30%) + 14.60%(55%)

WACC = 12% x 45% x 70% + 14.60% x 55%

WACC = 3.78% + 8.03% = 11.81%

Hence WACC = 11.81%

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 = $14.131 million = $14.131 x 1000000 = $14131000

Let V = Value of BEA with 45% debt

V = [EBIT(1-tax rate)] / (WACC) = [14131000(1-30%)] / (11.81%) = 9891700 / 11.81% = 83756985.6054

Value of firm with 45% debt (in millions) = 83756985.6054 / 1000000 = 83.7569856054 million = 83.757 million (rounded to three places of decimal)

Hence Value of firm = 83.757 million