Question

Rochelle, Rochelle Partners stock currently trades at $23.27. It will pay dividends for the next four years of $0.75 each year. In year 5 the dividend will grow by 20%, and it will grow by an additional 20% per year compounded for the three years after that (years 6-8) as well. Starting in year 9, the dividend growth rate will settle into a steady rate of growth which you forecast to remain constant indefinitely from that point forward. Assuming your discount rate is 9%, what is the minimum rate of growth in the dividend you need to have from year 9 onward in order to justify the current price of the shares?

Answer 1

The price of a share is the discounted value of the expected dividends.
The PV of the dividends for the 1st 8 years is calculated below:
Year	Expected Dividend	PVIF at 9%	PV at 9%
1	$               0.75	0.91743	$             0.69		`
2	$               0.75	0.84168	$             0.63
3	$               0.75	0.77218	$             0.58
4	$               0.75	0.70843	$             0.53
5	$               0.90	0.64993	$             0.58
6	$               1.08	0.59627	$             0.64
7	$               1.30	0.54703	$             0.71
8	$               1.56	0.50187	$             0.78
PV of dividends t1 to t8			$             5.15
PV of continuing value of dividends
when perpetual growth rate starts = 23.27-5.15 =				$      18.12
Continuing value of dividends at t8 = 18.12/0.50187 =				$      36.10
Now, applying the formula for PV of perpetuity,
36.10 = 1.56*(1+g)/(0.09-g), where g is the perpetual
growth rate.
Solving for g
(36.10/1.56)*(0.09-g) = 1+g
23.141*(0.09-g) = 1+g
2.0827-23.14*g = 1+g
24.14*g = 1.0827
g = 1.0827/24.14 =		4.49%
Minimum growth rate from year 9 = 4.49%