Problem 1510 Optimal Capital Structure with Hamada Beckman E

Problem 15-10
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 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 $13.327 million, and it faces a 40% federal-plus-state tax rate. The market risk premium is 5%, and the risk-free rate is 4%. 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 8%. 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. Round your answer to two decimal places.

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.

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? Do not round intermediate calculations. 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

Solution

At present, the firm\'s debt is $ 20 million and equity value is (2 million shares * 40) = $ 80 million. Hence its Ddebt/Equity ratio is (20/80) = 0.25 and its beta is 0.9.

Unlevered Beta = Levered Beta / [1+((1-tax rate)*(D/E))] = 0.9/[1+((1-40%)*0.25))] = 0.78

SInce we now have the unlevered beta, we can calculate the levered beta at 45% debt level using the same equation as above:

New Beta = Unlevered Beta * [1+((1-tax rate)*(D/E))] = 0.78 * [1+((1-40%)*45%/55%))] = 1.17

At this new beta of 1.17, as per CAPM, the cost of equity will be :

risk free rate + Beta * market risk premium = 4% + 1.17*5% = 9.85%

WACC = w_d * new debt cost * (1-40%) + w_e * equity cost; where w_d and w_e are respective debt and equity weightage in capital structure.

WACC = 45% * 8% * (1-40%) + 55% * 9.85% = 7.58%

Total value of firm (given it is zero growth) = EBIT * (1-tax rate) / WACC = [13.327 * (1-40%)]/7.58% = 105.491 million