Question

A stock just paid annual dividends of $3.55 per share. The dividends are expected to grow at 20 per cent per year for 4 years, and then remain constant in perpetuity. If the investors' required return for the stock is 11.8 percent, what should be the price of the stock today?

Answer 1

As per dividend discount method, current share price is the present value of future dividends.
Step-1:Present value of dividend of non-constant growth years
Year	Dividend	Discount factor	Present value
a	b	c=1.118^-a	d=b*c
1	$       4.26	0.8945	$       3.81
2	$       5.11	0.8000	$       4.09
3	$       6.13	0.7156	$       4.39
4	$       7.36	0.6401	$       4.71
Total			$    17.00
Working;
Dividend of Year :
1	=	$       3.55	*	1.20	=	$       4.26
2	=	$       4.26	*	1.20	=	$       5.11
3	=	$       5.11	*	1.20	=	$       6.13
4	=	$       6.13	*	1.20	=	$       7.36
Step-2:Calculation of terminal value of dividend at the end of non-constant growth years
Terminal value	=	(D5/Ke)*DF4		Where,
	=	$    39.93		D5(Dividend of year 5)	=	$       7.36
				Ke (Required return)	=	11.80%
				DF4 (Discount factor of year 4)	=	0.6401
Step-3:Sum of present value of future dividends
Sum of present value of future dividends	=	$    17.00	+	$    39.93
	=	$    56.93
So, Price of stock is		$    56.93