Question

An all-equity firm with 200,000 shares outstanding, Antwerther Inc., has $2,000,000 of EBIT, which is expected to remain constant in the future. The company pays out all of its earnings, so earnings per share (EPS) equal dividends per shares (DPS). Its tax rate is 40%.

The company is considering issuing $5,000,000 of 10.0% bonds and using the proceeds to repurchase stock. The risk-free rate is 6.5%, the market risk premium is 5.0%, and the beta is currently 0.95, but the CFO believes beta would rise to 1.10 if the recapitalization occurs.

Assuming that the shares can be repurchased at the price that existed prior to the recapitalization, what would the price be following the recapitalization?

		$65.77
		$69.23
		$70.59
		$71.33
		$74.14

Answer 1

Initially we have to find the earnings per share of an all equity firm.

Interest expenses are zero. So Total Earnings=EBIT*(1-tax rate)=$2,000,000*(1-40%)=$1,200,000

Earnings per share (EPS)=Total earnings/Shares Outstanding=$1,200,000/200,000=$6

EPS=DPS

Cost of equity=risk free rate+(beta*market risk premium)=6.5%+(0.95*5%)=11.25%

Value of the Stock before recapitalization=DPS/Cost of equity (anyway growth rate=0)

=$6/11.25%=$53.33

==> Now company has issued $5,000,000 bonds to repurchase the shares.

With $5,000,000 worth, he can repurchase the shares of=$5,000,000/$53.33=93,750

Then the total outstanding shares=200,000-93,750=106,250

Now, The Earnings before taxes=EBIT-Interest expenses=$2,000,000-(10%*5000000)=1,500,000

Total earnings=Earnings before taxes*(1-tax rate)=$1,500,000*(1-40%)=$900,000

EPS=Total earnings/Outstanding shares=900,000/106250=8.47

EPS=DPS

Cost of equity after recapitalization=risk free rate+(beta*market risk premium)=6.5%+(1.1*5%)=12%

Value of the stock after recapitaalization=DPS/12%=8.47/12%=$70.59

Option c is correct