Question

Ten years ago a XYZ stock paid a $0.30 dividend. Since then it has split two for one three times and three for two twice. XYZ current earnings per share are $1.40, and the payout ratio is 30%. 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 12%. If the firm’s appropriate discount rate is 10.8% what the stock price should be?

Answer 1

Current dividend = EPS*payout ratio = 1.4*0.3=0.42

Dividend 10 years ago adjusted for splits = 0.3*0.5*0.5*0.5*0.66*0.66 = 0.016335

Annual average growth rate

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

=((0.3/0.016335)^(1/10)-1)*100

Annual Growth rate% = 33.78 =short term growth rate

Long term growth rate :

Growth rate=ROE*(1-payout ratio)

growth rate=12*(1-0.3)

growth rate = 8.4

	Required rate=	10.80%
Year	Previous year dividend	Dividend growth rate	Dividend current year	Horizon value	Total Value	Discount factor	Discounted value
1	0.42	33.78%	0.561876		0.561876	1.108	0.5071
2	0.561876	33.78%	0.751677713		0.751677713	1.227664	0.61228
3	0.751677713	33.78%	1.005594444	45.419	46.42459444	1.360251712	34.12941
	Long term growth rate (given)=	8.40%			Value of Stock =	Sum of discounted value =	35.25

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