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 $12.168 million, and it faces a 35% federal-plus-state tax rate. The market risk premium is 6%, and the risk-free rate is 7%. 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 11%. BEA has a beta of 0.8. 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 45% 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 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? 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

Answer 1

(a) Existing Capital Structure: Debt = $ 20 million, Stock Price = $ 40, Number of Shares Outstanding = N = 2 million

Value of Equity = Stock Price x N = 40 x 2 = $ 80 million

Debt to Equity Ratio (DE) = DE1 = 20/80 = 0.25

Cost of Existing Debt = kd1 = 8%

Initial Equity Beta = B(e1) = 0.8

Tax Rate = t = 35 %

Therefore, the Unlevered Beta = Asset Beta = B(a) = B(e1) / [1+(1-t) x (DE1)] = 0.8 / [1+(1-0.35) x (0.25)] = 0.68817

(b) New Debt Level = 45 %, New Debt-to-Equity Ratio = DE2 = [0.45/(1-0.45)] = 0.81818

New Levered Beta = B(e2) = B(a) x [1+(1-t) x (DE2)] = 0.68817 x [1+(1-0.35) x (0.81818)] = 1.05415

Risk-Free Rate = Rf = 7 % and Market Risk Premium = MRP = 6 %

Therefore, Cost of Equity = ke = Rf + B(e2) x (MRP) = 7 + 1.05415 x 6 = 13.3249 % ~ 13.325 %

(c) EBIT = $ 12.168 million and Tax Rate = 35 %, as the firm pays out all of its earnings as dividends, the firm is a no-growth firm, thereby implying that the EBIT will remain constant at the existing level forever.

NOPAT = EBIT x (1-Tax Rate) = 12.168 x (1-0.35) = $ 7.9092 million

Debt Value = D = 45 % or 0.45 and Equity Value = E = 1 - 0.45 = 0.55, New Cost of Debt = kd2 = 11%,

Therefore, New WACC = kd2 x D x (1-t) + ke x E = 11 x 0.45 x (1-0.35) + 13.325 x 0.55 = 10.546 %

Firm Value = NOPAT / WACC = 7.9092 / 0.10546 = $ 74.99566 million ~ $ 74.99 million