Question

Consider a stock that most recently paid a dividend of $0.75. The company plans to increase dividends by 50% each year for the next 3 years, then by 20% each year for 4 years, and then level off to a permanent growth rate in dividends of 6%. If the actual stock price today is $100, what is the implied required rate of return

Answer 1

	Required rate=	9.45%
Year	Previous year dividend	Dividend growth rate	Dividend current year	Horizon value	Total Value	Discount factor	Discounted value
1	0.75	50%	1.125		1.125	1.094	1.0283
2	1.125	50%	1.6875		1.6875	1.198	1.4086
3	1.6875	50%	2.53125		2.53125	1.311	1.93078
4	2.53125	20%	3.0375		3.0375	1.435	2.11672
5	3.0375	20%	3.645		3.645	1.57	2.32166
6	3.645	20%	4.374		4.374	1.719	2.5445
7	4.374	20%	5.2488	161.497	166.7458	1.881	88.64742
	Long term growth rate (given)=	6%			Value of Stock =	Sum of discounted value =	100

Where
Current dividend =	Previous year dividend*(1+growth rate)^corresponding year
Unless dividend for the year provided
Total value = Dividend	+ horizon value (only for last year)
Horizon value =	current Dividend year 7 *(1+long term growth rate)/( required rate-long term growth rate)
Discount factor=	(1+ required rate)^corresponding period
Discounted value=	total value/discount factor

implied rate = 9.45%