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?

Answer 1

Current dividend = EPS*(1-plowback ratio) = 1.15*(1-0.5) = 0.575

Split adusted dividend 10 years ago = 1.15*0.5*0.66*0.66=0.25047

Short term growth rate

Annual average growth rate

=((last value/First value)^(1/Time between 1st and last value)-1)*100

=((1.15/0.25047)^(1/5)-1)*100

Annual Growth rate% = 35.64

Long term growth rate

Growth rate=ROE*(1-payout ratio)

growth rate=9*(1-0.5)

growth rate = 4.5

	Required rate=	13.50%
Year	Previous year dividend	Dividend growth rate	Dividend current year	Horizon value	Total Value	Discount factor	Discounted value
1	1.15	35.64%	1.55986		1.55986	1.135	1.3743
2	1.55986	35.64%	2.115794104		2.115794104	1.288225	1.64241
3	2.115794104	35.64%	2.869863123	33.322	36.19186312	1.462135375	24.75274
	Long term growth rate (given)=	4.50%			Value of Stock =	Sum of discounted value =	27.77

Where
Current dividend =Previous year dividend*(1+growth rate)^corresponding year
Total value = Dividend + horizon value (only for last year)
Horizon value = Dividend Current year 3 *(1+long term growth rate)/( Required rate-long term growth rate)
Discount factor=(1+ Required rate)^corresponding period
Discounted value=total value/discount factor