Question

An all equity firm is expected to generate perpetual EBIT of $50 million per year forever. The corporate tax rate is 0% in a fantasy no tax world. The firm has an unlevered (asset or EV) Beta of 1.0. The risk-free rate is 5% and the market risk premium is 6%. The number of outstanding shares is 10 million.

2.   The firm decides to replace part of the equity financing with perpetual debt. The firm issues $100 million of permanent debt at the riskless interest rate of 5%, and repurchases $100 million of equity.

      A. Find the new value of the levered firm.

      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 = 5% + 1.0* 6%

CAPM return = 11.00%

2. Value of Unlevered Company = EBIT * (1 - Tax) / CAPM return = $50 M * 1 / 11.00% = $909.09 Million

A. Value of Levered Company = Value of Unlevered Company = $909.09 Million

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

New Share Price = ($909.09 M - $100 M) / 10 M

New Share Price = $80.91

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

Number of Shares O/s = 10 M - (100 M / 80.91)

Number of Shares O/s = 8.76 Million Shares