In: Finance
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. 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.
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.
A. Find the new value of the levered firm following this capital structure change
Unlevered Beta = 0.8
Risk Free Rate = 4%
Market Risk Premium = 6%
Required Return = Risk Free Rate + (Beta*Market Risk Premium) = 4% + (0.8*6%) = 4%+4.8% = 8.8%
Perpetual EBIT = $100 Million
Tax rate = 35%
Free Cash Flows (Earnings after tax) = $100 Million * (1-35%) = $65 Million
Value of the firm (unlevered firm) = Free Cash Flows / Required return = $65 Million / 8.8% = $738.64 Million
Under Modigliani Miller Theory, Value of the unlevered firm equals value of the levered firm and capital structure does not change the value of the firm.
Thus, value of the firm after the capital structure change= $738.64 Million
B. Find the new number of shares outstanding, and the new share price.
New number of shares outstanding = Number of shares of unlevered firm - Shares repurchased
Number of shares of unlevered firm = 10 Million
Shares Repurchased = $100 Million / Value per share
Value per share = Value of the firm (unlevered) / shares outstanding = $738.64 Million / 10 Million = $73.86 per share
Thus, Shares repurchased = $100 Million / $73.86 = 1,353,913 shares
Hence, New number of shares outstanding = 10 Million - 1,353,913 = 8,646,087 shares
New share price:
Value of the firm = $738.64 Million
Value of Debt = $100 Million
Thus, value of equity = $738.64 Million - $100 Million = $638.64 Million
New Share Price = Value of Equity / New number of shares outstanding = $638.64 Million/8,646,087 shares = $73.86