Question

XYZ company presently pays a dividend of $ 1.50 per share on its common
stock. The company expects to increase the dividend at a 20% annual rate the
first four years and at the rate of 13% at the next four years then the growth on
the dividend at a 7% thereafter. This phased growth patterns is in keeping with
the expected life cycle of earnings. You are required a 16% return to invest in
this stock. What value should you place on a share of this Stock?

Answer 1

$ 31.36

As per dividend discount model, current value per share is the present value of dividends which is calculated as follows:
Step-1:Present value of dividend of non-constant growth stage
Year	Dividend	Discount factor	Present value
a	b	c=1.16^-a	d=b*c
1	1.80	0.8621	1.55
2	2.16	0.7432	1.61
3	2.59	0.6407	1.66
4	3.11	0.5523	1.72
5	3.51	0.4761	1.67
6	3.97	0.4104	1.63
7	4.49	0.3538	1.59
8	5.07	0.3050	1.55
Total			12.97
Working:
Dividend of Year:
1	=	1.50	*	1.20	=	1.80
2	=	1.80	*	1.20	=	2.16
3	=	2.16	*	1.20	=	2.59
4	=	2.59	*	1.20	=	3.11
5	=	3.11	*	1.13	=	3.51
6	=	3.51	*	1.13	=	3.97
7	=	3.97	*	1.13	=	4.49
8	=	4.49	*	1.13	=	5.07
Step-2:Present value of dividend of growth stage
Present Value	=	D8*(1+g)/(Ke-g)*DF8
	=	18.39
Where,
D8	=	Year 8 dividend	=	5.07
g	=	growth after 8 years	=	7%
Ke	=	Discount rate	=	16%
DF8	=	Discount factor of year 8	=	0.3050
Step-3:Calculation of price of each share
Current value of each share	=	Sum of present value of dividends
	=	12.97	+	18.39
	=	31.36