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09problem
3/22/2010 7:09
12/14/2005
Chapter 9.
Solution for EndofChapter Comprehensive/Spreadsheet problem
Problem 925
Taussig Technologies Corporation (TTC) has been growing at a rate of 20% per year in recent years. This
and capital gains yields at this time, that is, during Year 1?
1.
Find the price today.
$1.60
10.0%
20%
Shortrun g; for Years 12 only.
6%
Longrun g; for Year 3 and all following years.
20%
6%
Year
0
1
2
3
Dividend
$1.60
1.92
2.3
2.44
PV of dividends
$1.7455
1.9041
2.4422
$50.4595
61.0560
4.0%
$54.1091
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 =
/
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.
=
+
=
61.0560
+
2.3
1.10
=
$57.60
Cap. Gain yield=
/
Cap. Gain yield=
$3.49
/
$54.1091
Cap. Gain yield=
6.45%
same growth rate is expected to last for another 2 years, then to decline to g
n
= 6%.
a.
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