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Ch 10-22 Build a Model Solution

Ch 10-22 Build a Model Solution							3/4/01
Chapter 10. Solution for Ch 10-22 Build a Model
Rework Problem 10-19. Taussig Technologies Corporation (TTC) has been growing at a rate of 20% per
year in recent years. This same growth rate is expected to last for another 2 years.
a. If D0 = $1.60, k = 10%, and gn = 6%, what is TTC's stock worth today? What are its expected dividend
yield and capital gains yield at this time?
1. Find the price today.
D 0	$1.60
k s	10.0%
gS	20%	Short-run g; for Years 1-2 only.
gL	6%	Long-run g; for Year 3 and all following years.
	20%			6%
Year	0	1	2	3
Dividend	$1.60	1.92	2.304	2.44224
PV of dividends
$1.7455
1.9041						2.4422
$50.4595			61.0560	= Terminal value = P2 =
						4.0%	= k - gL
$54.1091	= P0
2. Find the expected dividend yield.
Recall that the expected dividend yield is equal to the next expected annual dividend divided by the price at
the beginning of the period.
Dividend yield =	D 1	/	P 0
Dividend yield =	$1.920	/	$54.109
Dividend yield =	3.55%
3. Find the expected capital gains yield.
The capital gains yield can be calculated by simply subtracting the dividend yield from the total
expected return.
Cap. Gain yield=	Expected return	-	Dividend yield
Cap. Gain yield=	10.0%	-	3.55%
Cap. Gain yield=	6.45%
Alternatively, we can recognize that the capital gains yield measures capital appreciation, hence solve for
the price in one year, then divide the change in price from today to one year from now by the current price.
To find the price one year from now, we will have to find the present values of the terminal value and second
year dividend to time period one.
P 1	=	P 2	+	D 2
		(1 + k)
P 1	=	61.0560	+	2.304
		1.10
P 1	=	$57.60
Cap. Gain yield=	(P1 - P0)	/	P0
Cap. Gain yield=	$3.49	/	$54.1091
Cap. Gain yield=	6.45%
b. Now assume that TTC's period of supernormal growth is to last for 5 years rather than 2 years.
How would this affect its price, dividend, yield, and capital gains yield?
1. Find the price today.
D 0	$1.60
k s	10.0%
gS	20%	Short-run g; for Years 1-5 only.
gL	6%	Long-run g; for Year 6 and all following years.
	20%						6%
Year	0	1	2	3	4	5	6
Dividend	$1.60	1.92	2.304	2.7648	3.31776	3.981312	4.22019072
PV of dividends
$1.7455
1.9041
2.0772
2.2661
2.4721
						4.2202
$65.5102			105.5048	= Terminal value = P5 =
$75.9751	= P0					4.0%	= k - gL
Part 2. Finding the expected dividend yield.
Dividend yield =	D 1	/	P 0
Dividend yield =	$1.920	/	$75.975
Dividend yield =	2.53%
Part 3. Finding the expected capital gains yield.
Cap. Gain yield=	Expected return	-	Dividend yield
Cap. Gain yield=	10.0%	-	2.53%
Cap. Gain yield=	7.47%
c. What will be TTC's dividend yield and capital gains yield once its period of supernormal growth ends?
We used the 5 year supernormal growth scenario for this calculation, but ultimately it does not matter
which example you use, as they both yield the same result.
Dividend yield =	D n+1	/	P n
Dividend yield =	4.22019072	/	105.5048
Dividend yield =	4.0%
Cap. Gain yield=	Expected return	-	Dividend yield
Cap. Gain yield=	10.0%	-	4.0%
Cap. Gain yield=	6.0%
Upon reflection, we see that these calculations were unnecessary because the constant growth assumption
holds that the long-term growth rate is the dividend growth rate and the capital gains yield, hence we could
have simply subtracted the long-run growth rate from the required return to find the dividend yield.

Discounted two years

Discounted 5 years