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 7%, 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 $12.535 million, and it faces a 30% 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 50% 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 9%. 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 50% 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 50% debt? Do not round intermediate calculations. Round your answer to two decimal places. %

What is the total value of the firm with 50% 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

Beta (leavered) = 0.8

Tax rate = 30% = 0.3

Debt = $20 m

Equity = $40/share * 2 m shares = $80 m

Firm value = Debt + equity = $20m + $80m = $100m

Debt/equity = $20m/$80m = 0.25

(A) Beta(unleavered) = 0.8/(1+(1-0.3)*0.25) = 0.6809 = 0.68 (rounded to 2 decimal places)

New debt = 50%, therefore equity = (100% - 50%) = 50%

debt/equity = 50%/50% = 1

Beta(leavered) = beta(unleavered) * (1 + (1 - tax)*debt/equity)

Beta(leavered) = 0.6809*(1+(1-0.3)*1) = 1.1575 = 1.16

Ke cost of equity

Ke = Rf + beta(leavered)*(Rm - Rf)

Rf risk free rate = 6%

Rm - Rf: market risk premium = 4%

Ke = 6%+1.1575*4% = 10.63%

WACC: weighted average cost of capital

WACC = %debt*(cost of debt)*(1 - tax rate) + %equity*(cost of equity)

Cost of debt = 9%

WACC = 50%*9%*(1-0.3)+50%*10.63% = 0.08465 = 8.465% = 8.47%

EBIT = $12.535m

New debt = 50% of firm value = 50% * $100m = $50m

Interest cost (=9%) = 9%*$50m = $4.5m

EBT = $12.535m - $4.5m = $8.035m

Tax(30%) = 30%*$8.035m = $2.4105m

EAT (earning after tax) = $8.035m - $2.4105m = $5.6245m

Dividend (Do) = 100% of EAT = $5.6245m

Value(equity) = Do * (1 + g)/(Ke - g)

g: is the growth rate = 0%

Ke: cost of equity = 10.63%

Value(equity) = $5.6245m * (1 + 0)/(10.63% - 0) = $52.91m

Total value of firm = Value(equity) + Value(debt) = $52.91m + $50m = $102.91m