Question

An all-equity firm just paid $4 per share dividend and for foreseeable future, will reinvest 65% of its earnings in projects that are expected to provide 10% RoR forever. If the treasury yield is 1.5%, the market risk premium is 7% and the firm’s beta is 1.5, then calculate the firm’s EPS and Share Price. What is the present value of the growth opportunities for the firm? If the growth can be achieved with debt at 5%, such that D:E ratio = 1:2, then what would the share price be? If needed, then assume that the firm’s income is subject to a 30% tax rate.

Answer 1

	Rate of Return	10%
	Plow back(Reinvestment) rate	0.65
	g=Growth rate of the earnings=0.65*10%	0.065	.(6.5%)
	D0= Current Dividend	$4
	Earning Per Share *(1-0.65)=$4
	Earning Per Share =4/0.35=	$11
	D1=Next years dividend=4*(1+g)=4*1.065	$4.26
	Calculation of required return on equity:
	Risk Free Rate=Treasury yield=1.5%
	Beta =1.5
	Market Risk Premium =7%
	R=Required Return=Risk free Rate+Beta*Market Risk Premium
	R=Required Return=1.5+1.5*7=12%	0.12
	Current Price =4.26/(0.12-0.065)=	$77.45
	EPS	$11
	Share Price	$77.45
	If D:E ratio =1:2
	D=0.5E
	Total Capital =E+0.5E=1.5E
	Weight of Debt   in total Capital=0.5E/1.5E=	0.333333
	Weight of Equity in total Capital=E/1.5E=	0.666667
	Cost of Equity =12%
	Cost of Debt =5%*(1-tax rate)=5*(1-0.3)=	3.50%
	Weighted Average Cost of Capital (WACC)
	0.333333*3.5+0.666667*12=	9.17%	0.0917
	Share Price =4.26/(0.0917-0.065)=	$159.55