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

2) 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. A. 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.

Answer 1

1. CAPM return = Risk Free + Beta * Market Risk Premium

CAPM return = 4% + 0.80 * 6%

CAPM return = 8.80%

2. Value of Unlevered Company = EBIT * (1 - Tax) / CAPM return = $100 M * 0.65 / 8.80% = $738.64 Million

A. Value of Levered Company = Value of Unlevered Company + Value of Debt * Tax = $738.65 M + 100 M * 0.35

Value of Levered Company = $773.64 Million

B. New Share Price = (Value of Company - Value of Debt) / Shares O/s

New Share Price = ($773.64 M - $100 M) / 10 M

New Share Price = $67.36

B-1. Number of Shares O/s after repurchase = Current Shares - Share Repurchased

Number of Shares O/s = 10 M - (100 M / 67.36)

Number of Shares O/s = 8.52 Million Shares