Question

The current price of a stock is $102.00. If dividends are expected to be $10 per share for the next 5 years, and the required return is 12%, then what should price of the stock be in 5 years when you plan to sell it? If the dividend and required return is expected to increase by $5 five years from now, does the current stock price also increase by $5? Why or why not?

Answer 1

Formula sheet

A	B	C	D	E	F	G	H	I	J	K
2
3		Current price of share is the present value of future dividends.
4		Assuming the price of share at the end of 5th year is P, then terminal value of dividends in 5th year is P.
5
6		Year	0	1	2	3	4	5
7		Dividends		10	10	10	10	10
8		Terminal Value						P
9
10		Required Rate of return	0.12
11
12		Current Price of Share	=Present Value of future dividends
13			=10*(P/A,12%,5)+P*(P/F,12%,5)
14
15		(P/A,12%,5)	=PV(D10,I6,-1,0)
16		(P/F,12%,5)	=1/((1+D10)^I6)
17
18		Current Price of Share	=10*(P/A,12%,5)+P*(P/F,12%,5)
19			=10*3.60+P*0.56
20
21		Since Current Price of share is	102
22		Therefore above equation can be written as follows:
23		$102 = $36 + P*0.56
24
25		Solving the above equation,
26		P=	=(D21-E7*D15)/D16	=(D21-E7*D15)/D16
27
28		Hence Price of share in 5 Years will be	=D26
29
30		Since price of share is the present value of future dividends,
31		therefore increase in dividends by $5 will increase the share price by present value of $5 which will be less than $5.
32
33		Hence increase in dividend by $5 will not increase the share price by $5.
34