Question

A company recently paid a dividend of $1.20 per share. It is estimated that the company's dividend will grow at the rate of 15% per year for the next 5 years, then at a constant rate of 7% a year thereafter. The required return on this company is 8.80%. What is the estimated stock price today?

Answer 1

As per dividend discount model, current price of stock is the present value of future dividends.
Step-1:Calculate present value of dividend of next 5 years
	Year	Dividend	Discount factor	Present value
	a	b	c=1.088^-a	d=b*c
	1	$       1.38	0.919118	$       1.27
	2	$       1.59	0.844777	$       1.34
	3	$       1.83	0.77645	$       1.42
	4	$       2.10	0.713649	$       1.50
	5	$       2.42	0.655927	$       1.58
	Total			$       7.11
	Working:
	Year			Dividend
	1	1.20*1.15		1.38
	2	1.38*1.15		1.59
	3	1.59*1.15		1.83
	4	1.83*1.15		2.10
	5	2.10*1.15		2.42
Step-2:Calculate present value of after year 5's dividend
	Present value		=	Present value of future dividends at 5 years from now * Present value of 1
			=	(D5*(1+g)/Ke-g))*(1+Ke)^-n
			=	(2.42*(1+0.07)/(0.088-0.07))*(1+0.088)^-5
			=	$    94.36
	Where,
	D5	Dividend of year 5			$       2.42
	g	Growth rate in dividend			0.0700
	Ke	Required rate of return			0.0880
Step-3:Calculation of present value of all dividend
	Present value of all dividends			=	$       7.11	+	$    94.36
				=	$ 101.47
So, estimated stock price today is			$ 101.47