Question

Greentop Inc. plans on increasing its annual dividend by 15 percent a year for the next four years and then decreasing the growth rate to 2.5 percent per year. The company just paid its annual dividend in the amount of $.20 per share. The required rate of return is 17.4 percent.

(a) What is the current value of one share of this stock?

(b) What is the expected stock price of this stock for next year?

(c) What is the expected stock price of this stock in 10 years?

I need explanation. thanks!

Answer 1

a)	The fair price of a stock is the PV of the expected dividends when discounted at the
	required rate of return. The dividends for the first four years have a growth rate of 15% and the growth
	rate is constant from the fifth year at 2.5% per year. Hence, PVs of dividends have to be worked out separately for t1 to t4.
	However, the continuing value of dividends from t5 can be valued as a growing perpetuity having growth
	rate of 17.4% and then discounted to get the PV.
	Year	Expected Dividends	PVIF at 17.4%	PV at 17.4%
	1	0.2300	0.85179	$           0.20
	2	0.2645	0.72554	$           0.19
	3	0.3042	0.61801	$           0.19
	4	0.3498	0.52641	$           0.18
	PV of expected dividends t1 to t4			$           0.76
	Terminal value of dividends = 0.3498*1.025/(0.174-0.025)=				$          2.41
	PV of terminal value = 2.41*0.52641 =			$           1.27
	Current value of one share			$           2.03
b)	Year	Expected Dividends	PVIF at 17.4%	PV at 17.4%
	2	0.2645	0.85179	$           0.23
	3	0.3042	0.72554	$           0.22
	4	0.3498	0.61801	$           0.22
	PV of expected dividends t2 to t4			$           0.66
	Terminal value of dividends = 0.3498*1.025/(0.174-0.025)=				$          2.41
	PV of terminal value = 2.41*0.61801 =			$           1.49
	Expected stock price for next year			$           2.15
c)	Expected stock price in 10 years = D11/(0.174-0.025) = 0.3498*1.025^7/(0.174-0.025) =			$           2.79