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Chapter 7 CFIN5
Chapter 7 Solutions
7-1 Total dollar return per share = ($19 - $20) + 4($0.20) = -$0.20
a.
$19 - $20 $0.80 -$0.20
Rate of = 0.01 1.0%
return $20 $20 $20
+ = =- =-
b.
$19 - $20 $0.80
Rate of Dividend
Capital
= 0.05 0.04 5.0% 4.0% gains yield
return $20 $20
+ =- + =- + = +
7-2 a.
$988 - $950 $47.50 $85.50
Rate of = 0.09 9.0%
return $950 $950 $950
+ = = =
b.
$988 - $950 $47.50
Rate of Dividend
Capital
= 0.04 0.05 4.0% 5.0% gains yield
return $950 $950
+ = + = + = +
7-3 Dividend = 0.09($110) = $9.90
0
ps
D $110(0.09) $9.90
ˆ = $66
P0.15 0.15
r
= = =
7-4 Dividend = $16.50
0
ps
D $16.50
ˆ = $150
P0.11
r
= =
7-5 Dividend = 0.05($40) = $2
a. rps = 10%:
0
ps
D $2
ˆ = $20
P0.10
r
= =
b. rps = 8%:
0
ps
D $2
ˆ = $25
P0.08
r
= =
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
Chapter 7 CFIN5
7-6
1
ˆ
D $2(1.05) $2.10= =
0
1
0
s s
ˆ(1 + g) $2.00(1.05) $2.10
D
D
ˆ = = $30
P - g - g 0.12 .05 0.07
r r
= = =
-
7-7
1
ˆ
D $3(1.04) $3.12= =
0
1
0
s s
ˆ(1 + g) $3.00(1.04) $3.12
D
D
ˆ = = $52
P - g - g 0.10 .04 0.06
r r
= = =
-
7-8
1
ˆ
D $1.20(1.025) $1.23= =
0
1
0
s s
ˆ(1 + g) $1.20(1.025) $1.23
D
D
ˆ = = $9.84
P - g - g 0.15 .025 0.125
r r
= = =
-
7-9 rs = Dividend yield + Capital gains yield
= 8% + 6% = 14%
1
0
s
ˆ$1.06
D
ˆ = = $13.25
P - g 0.14 0.06
r
=
-
Alternative solution:
1
0
0
0
ˆ
D
Dividend
yield P
$1.06
0.08 P
$1.06
P $13.25
0.08
=
=
= =
7-10 rs = 16%
g = ?, but we know the price of the stock is P0 = $19.50
1
ˆ
D $2.34=
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
Chapter 7 CFIN5
We can solve for g as follows:
1
0
s
ˆ
D
Pr g
$2.34
$19.50 0.16 g
=-
=-
Solving for g, we find the growth rate to be 4 percent:
Chapter 7 CFIN5
Cash flow time line for this scenario:
0123∞
0.000.500.530.50(1.06)∞-2
rs = 14%
gnorm = 6% …
2
1
s norm
ˆ
D0.50
ˆ
6.25 P r g 0.14 .06
= = =
- -
6.255.4825
Alternative Solution:
Students might solve the problem by computing the price at the end of Year 2, because they believe that
the first year of constant growth is in Year 3. The solution in this case would be:
Chapter 7 CFIN5
Chapter 7 CFIN5
Chapter 7 CFIN5
Chapter 7 CFIN5
1 2 2
01 2 1 2
s s
ˆ ˆ ˆ
D D P $1.50 $2.00 $35.00
P(1 r ) (1 r ) (1.11) (1.11)
$1.50(0.90090) $37.00(0.81162) $31.38
++
= + = +
+ +
= + =
Cash flow time line:
0123∞
1.502.002.102.00(1.05)∞-2
rs = 11%
gnorm = 5% …
3
2
s norm
ˆ
D2.10
ˆ
35.00 P r g 0.11 .05
= = =
- -
37.00
1.3514
30.0300
31.3814
Alternative solution: Because the $2 dividend actually represents the first constant-growth dividend (the
starting basis for constant growth), the constant growth model can be used to compute the value of the
stock at the end of Year 1 as follows:
2
1
s norm
ˆ
D$2.00
ˆ
P $33.33
r g 0.11 0.05
= = =
- -
Thus, if the stock is sold in one year, the investor would have received one dividend payment equal to
$1.50 and the $33.33 stock price. The PV of $34.83 one year from today is: PV = P0 = $34.83/1.11 =
$31.38
7-16
1
ˆ
D
= $0.60
2
ˆ
D
3
ˆ
D
= $2.40
4
ˆ
D
= $3.50
5
ˆ
D
= $3.50(1.04) = $3.64; Because this is affected by constant growth (gnorm = 4%), it can be used to
compute the price of the stock at the end of Year 4.
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
Chapter 7 CFIN5
5
4
s norm
ˆ
D$3.64 $3.64
ˆ
P $22.75
r g 0.20 0.04 0.16
= = = =
- -
Thus, the current price of the stock is
3
1 2 4 4
01 2 3 4
s s s s
1 2 3 4
ˆ
ˆ ˆ ˆ ˆ
D
D D D P
P(1 r ) (1 r ) (1 r ) (1 r )
$0.60 $0.90 $2.40 $3.50 $22.75
(1.20) (1.20) (1.20) (1.20)
$0.60(0.83333) $0.90(0.69444) $2.40(0.57870) $26.25(0.48225) $15.17
+
= + + +
+ + + +
+
= + + +
= + + + =
Cash flow time line:
Alternative solution: Because the $3.50 dividend actually represents the first constant-growth dividend
(the starting basis for constant growth), the constant growth model can be used to compute the value of
the stock at the end of Year 3 as follows:
4
3
s norm
ˆ
D$3.50
ˆ
P $21.875
r g 0.20 0.04
= = =
- -
Thus, if the stock is sold in three years, the investor would have received three dividend payments equal
to $0.60, $0.90, and $2.40, respectively, and the $21.875 stock price at the end of Year 3. The PV of this
cash flow stream is:
3 3
1 2
01 2 3 1 2 3
s s s
ˆ ˆ
ˆ ˆ D P
D D $0.60 $0.90 $2.40 $21.875
P(1 r ) (1 r ) (1 r ) (1.20) (1.20) (1.20)
$0.60(0.83333) $0.90(0.69444) $24.275(0.57870) $15.17
++
= + + = + +
+ + +
= + + =
7-17 P0 19 x $3.70 = $70.30
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
0 1 2 3 4 5 ∞
rs = 11%
gnorm = 4% …
Chapter 7 CFIN5
7-18 Price range: 28 x $4 = $112 to 30 x 4 = $120
7-19 NI = $65,000
T = 35%
Interest expense = $40,000
Invested capital = $800,000
7-20 Net income = $1.2 million = (Taxable income)(1 - 0.40)
Taxable income = ($1.2 million)/(1 - 0.40) = $2.0 million
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
