Question

A company currently pays a dividend of $3 per share (D0 = $3). It is estimated that the company's dividend will grow at a rate of 25% per year for the next 2 years, and then at a constant rate of 8% thereafter. The company's stock has a beta of 1.6, the risk-free rate is 8%, and the market risk premium is 4%. What is your estimate of the stock's current price? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

first let us know the required rate of return using CAPM;

risk free rate + beta *(market risk premium)

=>8%+ 1.60*(4%)

=>14.40%.

PV factor formula = 1/(1+r)^n

r=14.40%=>0.1440.

year	cash flow	PV factor @14.40%	cash flow *PV factor
1	$3+25%=>$3.75	1/(1.144)^1=>0.874126	($3.75*0.874126)=>$3.2779725
2	$3.75+25%=>$4.6875	1/(1.144)^2=>0.764096	($4.6875*0.764096)=>$3.5817
2	(see note)$79.1015625	1/(1.144)^2=>0.764096	($79.1015625*0.764096)=>$60.4411875
		Current price	$67.30

note;

horizon value at end of year 2 = dividend of year 2*(1+growth rate) / (required return - growth rate)

=>$4.6875*(1+0.08) / (0.144-0.08)

=>5.0625/0.064

=>$79.1015625