D0=1.00 Dividend is expected to grow at 8% for 10 years, then 5% indefinitely. R=8% for...

D0=1.00

Dividend is expected to grow at 8% for 10 years, then 5% indefinitely. R=8% for the next 4 years, R=7% for the following 3 years, then 6% indefinitely.

What is today's expected stock price?

Expert Solution

As pe dividend discount model, current price of stock is the present value of future dividends.

Step-1:Calculation of present value of dividends for first 10 years

Year	Dividend	Discount factor	Present value
	a	b	c=a*b
1	$ 1.08	0.925926	$ 1.00
2	$ 1.17	0.857339	$ 1.00
3	$ 1.26	0.793832	$ 1.00
4	$ 1.36	0.73503	$ 1.00
5	$ 1.47	0.686944	$ 1.01
6	$ 1.59	0.642004	$ 1.02
7	$ 1.71	0.600003	$ 1.03
8	$ 1.85	0.566041	$ 1.05
9	$ 2.00	0.534001	$ 1.07
10	$ 2.16	0.503774	$ 1.09

Total			$ 10.26

Working:

Dividend of year:
1	=	$ 1.00	*	1.08	=	$ 1.08
2	=	$ 1.08	*	1.08	=	$ 1.17
3	=	$ 1.17	*	1.08	=	$ 1.26
4	=	$ 1.26	*	1.08	=	$ 1.36
5	=	$ 1.36	*	1.08	=	$ 1.47
6	=	$ 1.47	*	1.08	=	$ 1.59
7	=	$ 1.59	*	1.08	=	$ 1.71
8	=	$ 1.71	*	1.08	=	$ 1.85
9	=	$ 1.85	*	1.08	=	$ 2.00
10	=	$ 2.00	*	1.08	=	$ 2.16

Discount factor of year:
1	=	1.08^-1					=	0.925926
2	=	1.08^-2					=	0.857339
3	=	1.08^-3					=	0.793832
4	=	1.08^-4					=	0.73503
5	=	1.07^-1	*	1.08^-4			=	0.686944
6	=	1.07^-2	*	1.08^-4			=	0.642004
7	=	1.07^-3	*	1.08^-4			=	0.600003
8	=	1.06^-1	*	1.07^-3	*	1.08^-4	=	0.566041
9	=	1.06^-2	*	1.07^-3	*	1.08^-4	=	0.534001
10	=	1.06^-3	*	1.07^-3	*	1.08^-4	=	0.503774

Step-2:Calculation of present value of dividend after year 10

Present value of dividends	=	D10(1+g)/(Ke-g)DF10		Where.
	=	$ 114.20		D10	$ 2.16
				g	5%
				Ke	6%
				DF10	0.503774

Step-3:Calculation of value of stock today

Value of stock today	=	Sum of present value of future dividends
	=	$ 10.26	+	$ 114.20
	=	$ 124.46

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