Question

A company is presently enjoying relatively high growth because of a surge in the demand for its new product management expects earnings and dividends to grow at a rate of 34% for the next two years 20.85% in year three and four and after which competition will probably reduce the growth rate in earnings and dividends to constant growth rate of 6.00% the company's last dividend was a $1.75 it's beta is 1.75 the market risk premium is 10.60% and the risk-free rate is 5.25% what is the current price of the common stock

Answer 1

Current price of Stock is $ 19.54

Working:

Step-1:Calculation of cost of Equity
	As per Capital Asset Pricing Model,
	Required rate of return			=	Risk Free rate + Beta *market risk premium
				=	5.25%	+	1.75	*	10.60%
				=	23.80%
Step-2:Calculation of Present Value of four years dividend
	Year	Dividend	Discount factor @ 23.80%			Present Value
	1	$       2.35		0.8078		$       1.89
	2	$       3.14		0.6525		$       2.05
	3	$       3.80		0.5270		$       2.00
	4	$       4.59		0.4257		$       1.95
	Total					$       7.90
	Working:
	Year	Last years dividend			Growth rate		Current Years dividend
	1		$       1.75		34.00%		$       2.35
	2		$       2.35		34.00%		$       3.14
	3		$       3.14		20.85%		$       3.80
	4		$       3.80		20.85%		$       4.59
Step-3:Calculation of terminal value of dividend
	Terminal Value of dividend			=	D4*(1+g)/(Ke-g)			Where,
				=	4.59*(1+0.06)/(0.238-0.06)			D4	$       4.59
				=	$    27.33			g	6.00%
								Ke	23.80%
Step-4:Calculation of present value of terminal value
	Present Value of terminal value of dividend					=	$    27.33	x	0.4257
						=	$    11.64
Step-5:Calculation of present value of all dividends
	Present Value of all dividend			=	$       7.90	+	$    11.64
				=	$    19.54
As per dividend discount model, price of stock is the present value of all dividends. Thus, Price of Common Stock is $ 19.54