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 $13.261 million, and it faces a 40 % 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 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 11 %. BEA has a beta of 1.2. a. 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 b. 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: % c. 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 % 30 % debt? Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. Do not round What is the total value of the firm with intermediate calculations. Round your answer to three decimal places. million

Answer 1

(a) Debt Value = D = $ 20 million, Price per Share = $ 40 and Number of Shares Outstanding = N = 2 million

Equity Value = E = 40 x 2 = $ 80 million

Debt-to-Equity Ratio = DE = 20/80 = 0.25, Tax Rate = 40%, Equity Beta at existing level of Debt = B(e1) = 1.2

B(a) = B(e1) / [1+(1-Tax Rate) x (DE)] = 1.2/[1+(1-0.4) x (0.25)] = 1.0435

(b) New Debt Level = 30%, New DE Ratio = [0.3/(1-0.3)] = 3/7

New Equity Beta = B(e2) = B(a) x [1+(1-Tax Rate) x (New DE Ratio)] = 1.0435 x [1+(1-0.4) x (3/7)] = 1.3118 ~ 1.312

Risk-Free Rate = Rf = 7% and Market Risk Premium = MRP = 5 %

New Cost of Equity = ke = Rf + MRP x B(e2) = 7 + 1.312 x 5 = 13.559 % ~ 13.56 %

(c) The firm retires the old debt and raises new debt at a cost of 11%, New Debt Level = 30% or 0.3 and New Equity Level = 70% or 0.7, Tax Rate = t = 40%, ke = 13.56 %

WACC = 0.3 x (1-0.4) x 11 + 0.7 x 13.56 = 11.47 %

Perpetual EBIT = $ 13.261 million and Tax Rate = 40%

NOPAT = (1-Tax Rate) x EBIT = (1-0.4) x 13.261 = $ 7.9566 million

The firm is no-growth and pays out all of its earnings post tax (NOPAT) as dividends.

Therefore, Total Firm Value = NOPAT / WACC = 7.9566 / (0.1147) = $ 69.36 million