Question

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 $12.427 million, and it faces a 35% 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 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 1.0.

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 45% 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 45% debt? Do not round intermediate calculations. Round your answer to two decimal places.
   %
   
   What is the total value of the firm with 45% 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). levered beta = 1

unlevered beta = levered beta/(1+(1-T)D/E) =

where T = tax-rate

D = weight of debt

E = weight of equity

Debt = 20 million

Equity = share per price* number of shares = 40*2 million = 80 million

unlevered beta = 1/(1+(1-35%)*(20/80) = 0.86

b). Now debt becomes 45% of the capital structure, so equity is 55%

Therefore, new debt amount is 45%*80 million/55% = 65.45 million (cost of this debt is 12%, as given in the question)

New beta will be the unlevered beta which is relevered as per this new capital structure

beta = unlevered beta*(1+(1-T)D/E)

= 0.86*(1+(1-35%)*(45%/55%)) = 1.317

Cost of equity = risk-free rate + beta*market risk premium = 6% + 1.317*6% = 13.9%

c). WACC = after-tax cost of debt*(D/V) + cost of equity*(E/V)

D/V = 45%; E/V = 55%

cost of equity = 13.9%

after-tax cost of debt = (1-35%)*12% = 7.8%

WACC = (7.8%*45%)+(13.9%*55%) = 11.16%

Value of the firm with 45% debt:

Value of the unlevered firm = EBIT(1-T)/unlevered cost of equity = 12.247*(1-35%)/0.1116 = 72.37 million

(unlevered cost of equity = risk-free rate + unlevered beta*market risk premium = 6% + (0.860*6%) = 0.1116)

Tax shield due to the debt = tax-rate*debt = 35%*65.45 = 22.91 million

Value of the firm = unlevered firm + tax shield = 72.37 + 22.91 = 95.28 million.