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 $13.260 million, and it faces a 35% federal-plus-state tax rate. The market risk premium is 4%, 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 10%. BEA has a beta of 1.1.

What is BEA's unlevered beta before restructuring? Use market value D/S (which is the same as wd/ws) when unlevering. Round your answer to two decimal places.
________

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 _______%

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

1)

Market value of debt = 20,000,000

Market value of equity = 2,000,000 * 40 = 80,000,000

Debt-to-equity ratio = 20,000,000 / 80,000,000

Debt-to-equity ratio = 0.25

BEA's unlevered beta = BEAs levered beta / ( 1 + (1 - tax) debt/equity

BEA's unlevered beta = 1.1 / ( 1 + ( 1 - 0.35)0.25

BEA's unlevered beta = 1.1 / 1.1625

BEA's unlevered beta = 0.9462 or 0.95

2)

BEA's levered beta = BEA's unlevred beta * ( 1 + (1 - tax) debt/equity

BEA's levered beta = 0.95 * ( 1 + ( 1 - 0.35) 45%/55%

BEA's levered beta = 0.95 * (1.65)0.818182

BEA's levered beta = 1.28

Cost of equity using CAPM method = risk free rate + beta ( market risk premium)

Cost of equity = 0.06 + 1.28 ( 0.04)

Cost of equity = 0.1112 or 11.12%

3)

WACC after releveraging = Weigth of debt * cost of debt( 1- tax) + weight of equity * cost of equity

WACC after releveraging = 0.45 * 0.1 ( 1 - 0.35) + 0.55 * 0.1112

WACC after releveraging = 0.02925 + 0.06116

WACC after releveraging = 0.09041 or 9.04%

4)

Value of firm = EBIT ( 1 - tax) / WACC

Value of firm = 13,260,000 ( 1 - 0.35) / 0.09041

Value of firm = 8,619,000 / 0.09041

Value of firm = $95,332,374.74 or 95.332 million