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FI 311H Financial Management Professor Hadlock
Problem Set #2 Answer Key
Chapter 5 Problems
#1.
(a) PV = 1,000/ (1.06)
12
= 1,000/2.012 =
$496.97
(b) PV = 1,000/ (1.12)
12
= 1,000 /3.986 =
$256.68
(c) If the bond price equals $256.68 then we know that 12% is the discount rate that
equates this price with the present value.
Thus, the answer is
12%.
#2.
The bond will pay 4% x 1,000 = $40 every six months.
Each of these $40 payments
should be discounted at 5%.
There will be 20 such payments, along with the principal
repayment at period 20.
Using our formulas, the value of the bond is:
($40/.05) x [1 – (1/(1.05)
20
)] + $1,000/(1.05)
20
= $498.49 + $376.89 =
$875.38
#3.
(a)
Next year’s dividend (D
1
) should be $4 x (1.06) = $4.24.
Thus, the price of the stock
given by our constant growth formula should be P = $4.24/(rg) = $4.24/(.12.06) =
$4.24/.06 =
$70.67.
(b)
The price in year five should be determined by the dividend one year thereafter (i.e.,
D
6
) and the same constant growth formula.
Note that D
6
= $4 x (1.06)
6
= $5.67 and thus
P
5
= D
6
/(.1206) = $5.67/.06 =
$94.57
.
#4.
Dividend in year 1
$1.00 x 1.12 = $1.12, present value of 1.12/(1.10) = $1.018
Dividend in year 2
$1.12 x 1.12 = $1.25, present value of 1.25/(1.10)
2
= $1.037
Dividend in year 3
$1.25 x 1.12 = $1.40, present value of 1.40/(1.10)
3
= $1.055
Dividend in year 4
$1.40 x 1.12 = $1.57, present value of 1.57/(1.10)
4
= $1.075
Dividend in year 5
$1.57 x 1.05 = $1.65, grows at a 5% rate thereafter, this stream
of dividends can be viewed as a growing perpetuity.
Its value as of
date 4 will be D
5
/(rg) = $1.65/(.10.05) = $33.04.
Its value as of
date 0 will then be $33.04/(1.10)
4
= $22.57.
Total present value = $1.018 + $1.037 + $1.055 + $1.075 + $22.569 =
$26.75
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View Full Document#5.
Growth rate g = retention ratio x ROE = .50 x .12 =
6.0%
Next year earnings = $40 million x 1.06 =
$42.40 million
#6.
g = retention ratio x ROE = 0.75 x 0.12 = 0.09 = 9%
Current Dividend per share = $20 million (1  0.75) / 1.25 million
= $4
Next year’s expected dividend = $4 x (1 + g) = $4 x 1.09 = $4.36
(a) r = D
1
/P
0
+ g = $4.36/$60 + 0.09 = 0.1627 =
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 Spring '11
 Thompson

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