Question

Nonconstant growth rate:

d0= $1.75
g1= 4% for 3 years
g2= 5% for 4 years
g3= 3% thereafter
r= 8.5%
P=?

If you could include a timeline as well as the steps that would be great.

Answer 1

As per dividend growth model, current price of stock is the present value of future dividends.
Step-1:Present value of dividend of next 7 years
Year	Dividend	Discount factor	Present value
a	b	c=1.085^-a	d=b*c
1	$       1.82	0.921659	$       1.68
2	$       1.89	0.849455	$       1.61
3	$       1.97	0.782908	$       1.54
4	$       2.07	0.721574	$       1.49
5	$       2.17	0.665045	$       1.44
6	$       2.28	0.612945	$       1.40
7	$       2.39	0.564926	$       1.35
Total			$    10.51
Working:
Dividend of year:
1	=	$       1.75	x	1.04	=	$       1.82
2	=	$       1.82	x	1.04	=	$       1.89
3	=	$       1.89	x	1.04	=	$       1.97
4	=	$       1.97	x	1.05	=	$       2.07
5	=	$       2.07	x	1.05	=	$       2.17
6	=	$       2.17	x	1.05	=	$       2.28
7	=	$       2.28	x	1.05	=	$       2.39
Step-2:Present value of dividends after year 7
Present value		=	D7*(1+g)/(K-g)*DF7			Where,
		=	$    25.31			D7	Dividend of year 7		$       2.39
						g	Growth after year 7		3%
						K	Required rate of return		8.50%
						DF7	Discount factor of year 7		0.564926
Step-3:Present value of all dividends
Present value of all dividends			=	$    10.51	+	$    25.31
			=	$    35.82
Present value of all dividends is $ 35.82.
So, current price(P) of stock is			$    35.82