Question

1. The current price of a stock is $55.68. If dividends are expected to be $0.80 per share for the next five years, and the required return is 6%, then what should the price of the stock be in 5 years when you plan to sell it? If the dividend and required return remain the same, and the stock price is expected to increase by $1 five years from now, does the current stock price also increase by $1? Why or why not?

Answer 1

Answer to (a)

The current price of stock is $ 55.68 and dividend are expected to be 0.80 for next 5 years.

So first of all present value of dividend is calculated, then it is deducted from current stock price to determine net price of stock. Then compounding of that amount is made to determine value of stock after five years.

Value will be as follow:

Year	Dividend	Present Value Factor @ 6%	Present Value of Dividend
1	0.8	0.943	0.755
2	0.8	0.890	0.712
3	0.8	0.840	0.672
4	0.8	0.792	0.634
5	0.8	0.747	0.598
	Present Value of Dividend (a)	3.37
Current Price of Stock(b)	55.68
Total (b-a)=c	52.31
Future compounding (1.06)^5 (d)	1.34
Future Value(c*d)	70.00

Therefore future price of stock is $ 70. Alternative solution is that compounding of dividend is done instead of discounting and then such value is deducted from future value of (55.68)*(1.06)^5 and answer will be same.

CALCULATION IS AS FOLLOW:

Year	Future Compound Factor	Dividend	Future Value
1	1.26	0.8	1.01
2	1.19	0.8	0.95
3	1.12	0.8	0.90
4	1.06	0.8	0.85
5	1.00	0.8	0.80
		Future Value of Dividend (a)	4.51
	Future value of current price of stock i.e. 55.68*(1.06)^5          (b)	74.51
	Future price of stock (b-a)	$ 70.00

Answer to (b):

If price is increase b $1 five years, from now, current price does not increase by same amount, because of discounting factor as present value of $ 1 received after five year from now is (1/(1.06)^5)=0.747. Therefore current price will not increase by same amount rather by $0.747 after considering effect of time value.