Question

Five years ago a XYZ stock paid a $1.15 dividend. Since then it has split two for one once and three for two twice. XYZ current earnings per share are $1.15, and the plowback ratio is 50%. The dividends are expected to grow with their historical rate for the next three years. Beginning year four, XYZ return on equity is expected to be 9%. If the firm’s appropriate discount rate is 13.5% what the stock price should be? (40 points)

Answer 1

1)	Dividend paid 5 years ago converted to per share as of
	today (that is after adjustment for stock splits) =
	= 1.15*(1/2)*(2/3)*(2/3) =	$           0.26
2)	Current dividend = 1.15*50% =	$           0.58
3)	Growth rate in dividends for next 3 years = (0.58/0.26)^(1/5)-1 =	17.41%
4)	Perpetual growth rate form year 4 = 9%*50% =	4.50%
5)	PV of dividends for t1 to t3:
	Year	Dividend	PVIF at 13.5%	PV at 13.5%
	0	$           0.58	1
	1	$           0.68	0.88106	$              0.60
	2	$           0.80	0.77626	$              0.62
	3	$           0.94	0.68393	$              0.64
	PV of dividends for t1 to t3			$              1.86
	Terminal value of dividends at t3 = 0.94*1.045/(0.135-0.045) =				$           10.91
	PV of terminal value = 10.91*0.68393 =			$              7.46
	Stock price should be			$              9.33