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 $14.276 million, and it faces a 40% 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 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 15%. BEA has a beta of 1.2.

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

1. What is BEA's unlevered beta? Use market value D/S (which is the same as w_d/w_s) when unlevering. Do not round intermediate calculations. Round your answer to two decimal places.
2. 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:   %
3. 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.
     %

Answer 1

- Value of Debt = $20 million

- Value of Equity = $40*2 million shares

= $80 million

BEA beta = 1.2

a). Calculating unlevered Beta:-

Unlevered Beta = Equity Beta/[1+(1-Tax rate)*Debt/Equity]

= 1.2/[1+(1-0.40)*20/80]

= 1.043478

So, unlevered beta is 1.04

b). Calculating Equity beta with new debt of 50%:-

Levered Beta = Unlevered Beta*[1+(1-Tax rate)*Debt/Equity]

= 1.043478*[1+(1-0.40)*0.50/0.50]

= 1.6695648

So, Levered Beta is 1.67

As per CAPM,

Rf = Risk free Return = 7%

Rmp = Market Risk Premium = 6%

Beta = 1.6695648

Expected Return = 7% + 1.6695648(6%)

= 17.0173888%

So, Cost of Equity is 17.02%

c). Calculating BEA's WACC with 50% debt amount:-

Before-tax Cost of Debt of new debt is 15%

WACC= (Weight of Debt)(Before-tax Cost of Debt)(1-Tax Rate) + (Weight of Equity)(Cost of Equity)

WACC = (0.50)(15%)(1-0.40) + (0.50)(17.0173888%)

WACC = 4.5% + 8.5086944%

WACC = 13.0086944%

SO, WACC is 13.01%

d). Total Value of Firm with 50% Debt = EBIT(1-Tax rate)/WACC

= $14.276 million(1- 0.40)/13.0086944%

= $65.845 million

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