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 6%, 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 $14.418 million, and it faces a 40% federal-plus-state tax rate. The market risk premium is 5%, and the risk-free rate is 5%. BEA is considering increasing its debt level to a capital structure with 30% 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 1.2. Unlevered Beta is 1.043.

What are BEA's new beta and cost of equity if it has 30% debt? Do not round intermediate calculations. Round your answers to two decimal places.

Beta
Cost of equity	%

What are BEA’s WACC and total value of the firm with 30% debt? Do not round intermediate calculations. Round your answer to two decimal places.
%

What is the total value of the firm with 30% 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

Answer 1

Unlevered Beta = 1.043, Tax Rate = 40%, Debt to Equity Ratio = (3/7)

Therefore, New Beta = 1.043 x [1+(1-0.4) x (3/7)] = 1.30014 ~ 1.3

Current Capital Structure:

Debt = $ 20 million, Interest Rate = 6 % Stock Price = $ 20, Number of Shares Outstanding = 2million

Equity = 2 x 40 = $ 80 mllion

Debt to Equity Ratio = DE = 20 / 80 = 0.25 and Tax Rate = 40 %

Current Beta = 1.2

Asset Beta (Unlevered Beta) = Current Beta / [1+(1-Tax Rate) x DE] = 1.2 / [1+(1-0.4) x (0.25)] = 1.043

Market Risk Premium = MRP = 5 % and Risk-Free Rate = Rf = 5 %

Unlevered Cost of Equity = Ru = 5 + 1.043 x 5 = 10.215 %

New Capital Structure:

Debt = 30 % and Equity = 100 - 30 = 70%

DE = 30/70 = 3/7 and New Cost of Debt = 9 % = Rd

Therefore, New Cost of Equity = Rl = Ru + (1-Tax Rate) x De x (Ru - Rd) = 10.215 + (1-0.4) x (3/7) x (10.215 - 9) = 10.53 %

New WACC = (1-0.4) x 9 + 0.3 + 10.53 x 0.7 = 8.991 %

EBIT = $ 14.418 million

NOPAT = EBIT x (1-Tax Rate) = 14.418 x (1-0.4) = $ 8.651 million

Therefore, Firm Value = NOPAT / New WACC = 8.651 / 0.08991 = $ 96.22 million