Hi i was little confused about the (b) i have calcluate the Market value of Levered firm, but how can we calculate the new share price?

Question 1: a)(4 marks) There is an unlevered firm that is all equity financed, it expects a 30 million cashflow before tax in perpetuity. All its earnings are distributed to the shareholders by dividends. There are currently 2.8 million shares outstanding. The required return on equity is 15%. Corporate tax rate is 30%. Find the firm value and the stock price. Earnings after tax = 30*(1-0.3) = 21 million Earnings per share = $21 million / 2.8 million stocks = $7.5 per stock Equity price = expected income on equity/return on equity = 7.5/0.15 = $50.00 Firm value = 50 * 2.8 = $140.00 million b)(6 marks) Now the firm wants to recapitalize by borrowing $50.00 million of debt at a perpetual rate of 6.00%. How does this affect the share price and firm value? (a ) Free cash flow=30(1-0.3)=21m Firm's value=21m/0.15=140m Share price=140/2.8=$50 (b) the value of levered firm= Vu+PV of tax shield=140m+ 50*0.3=$155m Shares repurchased=50m/50=1m The number of shares remaining=2.8-1=1.8m The market value of equity=155-50=105m Therefore, the share price=105m/1.8=