Question

An all equity firm is expected to generate perpetual EBIT of $100 million per year forever. The corporate tax rate is 35%. The firm has an unlevered (asset or EV) Beta of 0.8. The risk-free rate is 4% and the market risk premium is 6%. The number of outstanding shares is 10 million.

1. a. Calculate the existing WACC of the unlevered firm. Calculate the total value of this all

equity firm and the share price.

b. The firm decides to replace part of the equity financing with perpetual debt. The firm will

issue $100 million of permanent debt at the riskless interest rate of 4%, and use this $100 million of proceeds to repurchase the same amount of common stock.

c. Find the new value of the levered firm following this capital structure change. B. Find the new number of shares outstanding, and the new share price.

d. Calculate the new cost of equity, and the new WACC following this capital structure change.

Also calculate the new equity Beta (see files “Old Final Exam problems”, and “Chapter 15 example” for the formula; use the tax version of the formula, and assu

Answer 1

HI

1.a) AS per CAPM

WACC of unlevered firm = risk free rate +beta*market risk premium

WACC = 4+0.8*6 = 8.8%

EBIT = $100 million

tax rate = 35%

Value of unlevered firm = EBIT*(!-tax rate)/WACC

= 100,000,000*(1-35%)/8.8%

= $738,636,363.64

number of shares outstanding = 10,000,000

So price per share= 738,636,363.64/10,000,000

= $73.86 per share

b) total debt taken = $100,000,000

rate = 4%

total value of levered firm before purchase of shares = 100,000,000*0.35 + 738636363.64

= $773,636,363.64

number of shares to be repurchased = 100,000,000/73.86 = 1,353,846.15

Value of levered firm after purchase = value of levered firm before purchase - debt

= 773636363.64 - 10,000,000

= $673,636,363.64

Total shares remaining = 10,000,000 - 1353846.15 = 8,646,153.85

Value of equity = 673636363.64 - 100,000,000

= $573 ,636,363.64

Price per share = 573,636,363.64/ 8646153.85 = $66.35 per share

c) Debt to equity = 100,000,000 / 573636,363.64 = 0.17

Levered beta= 0.8*(1+(1-35%)*0.17)

= 0.89

Levered Cost of equity = 4+ 0.89*6 = 9.34%

New WACC = 9.34*(1/(1+0.17) + 0.04*(0.17/(1+0.17)*(1-35%)

= 7.96%

Thanks