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 $17 million, and it faces a 25% federal-plus-state tax rate. The market risk premium is 5%, and the risk-free rate is 7%. 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 11%. BEA has a beta of 0.9. 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. 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: Cost of equity:   % What is BEA's WACC with 35% debt? Do not round intermediate calculations. Round your answer to two decimal places.   % What is the total value of the firm with 35% debt? Do not round intermediate calculations. Enter your answer in millions. For example, an answer of $1.234 million should be entered as 1.234, not 1,234,000. Round your answer to three decimal places. $   million

Answer 1

Solution:

1. Given:

Debt = D = $20 Million

Equity = E = $40 * 2 Million = $80 Million

Tax = T = 25% = 0.30

Beta Levered = β_L = 0.9

Unlevered Beta       = β_U      = β_L /(1+((1-T)*(D/E))) = 0.9/(1+((1-.25)*(20/80)))

                                                         = 0.9/(1+(0.75*(20/80))) = 0.9/(1+(0.75*0.25))

                                                         = 0.9/(1+0.1875) = 0.9/1.1875 = 0.75789 = .76

1. Given,

Beta Unlevered β_{U =} 0.76

D/E = 35% = 0.35

Beta Levered = β_L = β_U (1+((1-T)*(D/E))) = 0.76(1+((1-0.25)*(0.35)))

= 0.76(1+(0.75*0.35))         = 0.76(1+0.2625) = 0.76 * 1.2625

= 0.9595 =0.96

Cost of Equity = Rf + β_L(E(Rm) – Rf)

Where

Rf = Risk-free rate of return = 7%

E(Rm) = Expected market return = Risk-free rate of return + Market Risk Premium

                                                            = 7% + 5% = 12%

Therefore, Cost of Equity = 0.07 + (0.96 * (0.12 – 0.07)) = 0.07 + (0.96 * 0.05)

                                                = 0.07 + 0.048 =0.118 = 11.8%