Question

Company CT will have a growth rate of 30 percent for 3 years. after that, the company will grow at 25 percent for five years. The company will have a growth rate for 15 percent for ten years. Then the company will have a constant growth rate of 10 percent. The required rate of return of investors for this company is 15 percent. if the company just paid a a dividend of 0.50 , what should be the stock price of this company

Answer 1

Stock price of company should be $ 41.67

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=1.15^-a	d=b*c
1	$       0.65	0.8696	$       0.57
2	$       0.85	0.7561	$       0.64
3	$       1.10	0.6575	$       0.72
4	$       1.37	0.5718	$       0.79
5	$       1.72	0.4972	$       0.85
6	$       2.15	0.4323	$       0.93
7	$       2.68	0.3759	$       1.01
8	$       3.35	0.3269	$       1.10
9	$       3.86	0.2843	$       1.10
10	$       4.43	0.2472	$       1.10
11	$       5.10	0.2149	$       1.10
12	$       5.86	0.1869	$       1.10
13	$       6.74	0.1625	$       1.10
14	$       7.75	0.1413	$       1.10
15	$       8.92	0.1229	$       1.10
16	$    10.25	0.1069	$       1.10
17	$    11.79	0.0929	$       1.10
18	$    13.56	0.0808	$       1.10
Total			$    17.56
Working;
Dividend of Year :
1	=	$       0.50	*	1.30	=	$       0.65
2	=	$       0.65	*	1.30	=	$       0.85
3	=	$       0.85	*	1.30	=	$       1.10
4	=	$       1.10	*	1.25	=	$       1.37
5	=	$       1.37	*	1.25	=	$       1.72
6	=	$       1.72	*	1.25	=	$       2.15
7	=	$       2.15	*	1.25	=	$       2.68
8	=	$       2.68	*	1.25	=	$       3.35
9	=	$       3.35	*	1.15	=	$       3.86
10	=	$       3.86	*	1.15	=	$       4.43
11	=	$       4.43	*	1.15	=	$       5.10
12	=	$       5.10	*	1.15	=	$       5.86
13	=	$       5.86	*	1.15	=	$       6.74
14	=	$       6.74	*	1.15	=	$       7.75
15	=	$       7.75	*	1.15	=	$       8.92
16	=	$       8.92	*	1.15	=	$    10.25
17	=	$    10.25	*	1.15	=	$    11.79
18	=	$    11.79	*	1.15	=	$    13.56
Step-2:Calculation of terminal value of dividend at the end of non-constant growth years
Terminal value	=	D18*(1+g)/(Ke-g)*DF18		Where,
	=	$    24.11		D18(Dividend of year 18)	=	$    13.56
				g (Growth rate in dividend)	=	10%
				Ke (Required return)	=	15%
				DF18 (Discount factor of year 18)	=	0.0808
Step-3:Sum of present value of future dividends
Sum of present value of future dividends	=	$    17.56	+	$    24.11
	=	$    41.67
So, Price of stock is		$    41.67