Question

The Duo Growth Company just paid a dividend of $1 per share. The dividend is expected to grow at a rate of 25% per year for the next three years and then level off to 5% per year forever. You think the appropriate market capitalization rate is 20% per year.

a. What is your estimate of the intrinsic value of a share of stock?

b. If the market price of a share is equal to the intrinsic value, what is the expected dividend yield?

c. What do you expect its price to be one year from now?

d. Is the implied capital gain consistent with your estimate of the dividend yield and the market capitalization rate?

Answer 1

a]	Intrinsic value of the share is the PV of the
	expected dividends. It is calculated below:
	Year	Dividend	PVIF at 20%	PV at 20%
	0	1.00
	1	1.25	0.83333	$             1.04
	2	1.56	0.69444	$             1.08
	3	1.95	0.57870	$             1.13
	Cumulative PV of dividends t1 tp t3			$             3.25
	Terminal value of dividends = 1.95*1.05/(0.20-0.05) =		$             13.65
	PV of terminal value = 13.65*0.57870 =			$             7.90
	Intrinsic value of the share			$           11.15
b]	Expected dividend yield = 1.25/11.15 =	11.21%
c]	Price 1 year from now:
	Year	Dividend	PVIF at 20%	PV at 20%
	2	1.56	0.83333	$             1.30
	3	1.95	0.69444	$             1.35
	Cumulative PV of dividends t1 tp t3			$             2.65
	Terminal value of dividends = 1.95*1.05/(0.20-0.05) =		$             13.65
	PV of terminal value = 13.65*0.69444 =			$             9.48
	Price one year from now			$           12.13
d]	Implied capital gain = 12.13/11.15-1 =	8.79%
	Total yield = Dividend yield+Capital gains yield = 11.21%+8.79% =	20.00%
	As the total yield equals the market capitalization
	rate, the implied capital gain yield is consistent
	with the estimate of the dividend yield.