Chapter 7 CFIN6
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
= = − = −
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
7-5 Dividend = 0.05($40) = $2
a. rps = 10%:
0ps
D $2
ˆ = $20
P0.10
r==
0ps
D $2
ˆ = $25
P0.08
r==
Chapter 7 CFIN6
7-7
7-8
1
ˆ
D $1.20(1.025) $1.23==
0
1
0ss
ˆ(1 + g) $1.20(1.025) $1.23
D
D
ˆ = = $9.84
P – g – g 0.15 .025 0.125
rr
= = =
−
Alternative solution:
1
0
ˆ
D
Dividend
yield P
=
7-10 rs = 16%
g = ?, but we know the price of the stock is P0 = $19.50
1
ˆ
D $2.34=
Chapter 7 CFIN6
1
0s
ˆ
D
Prg
=−
The next step is to use the growth rate to project the stock price five years hence:
65
01
5ss
5
D (1 g) D (1 g)
ˆ
Pr g r g
$2.34(1.04) $2.847 $23.72
0.16 0.04 0.12
++
==
−−
= = =
−
P
ˆ
7-11 D0 =
1
ˆ
D
= $0
2
ˆ
D
= $0.50; this actually is the first dividend that is affected by constant growth (gnorm = 6%), thus it can
be used to compute the price of the stock at the end of the non-constant growth period.
0 1 2 3 ∞
0.00 0.50 0.53 0.50(1.06)∞-2
rs = 14%
gnorm = 6%
5.4825
Chapter 7 CFIN6
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:
3
ˆ
D
= $0.50(1.06) = $0.53
7.125
5.4825
Cash flow time line for this scenario:
7-12 D0 = $0
1 2 3
ˆ ˆ ˆ
D D D===
$0
0 1 2 3 ∞
0.00 0.50 0.53 0.50(1.06)∞-2
rs = 14%
gnorm = 6%
…
Chapter 7 CFIN6
4
3s norm
ˆ
D$3.00
ˆ
P $30.00
r g 0.10 0
= = =
−−
Thus, the current price of the stock is
Alternative Solution:
Students might solve the problem by computing the price at the end of Year 4, because they believe
that the first year of constant growth is in Year 4. The solution in this case would be:
4
ˆ
D
= $3.00
5
4s norm
ˆ
D$3.00
ˆ
P $30
r g 0.10 0
= = =
−−
7-13 D0 = $1.00
1
ˆ
D
=
2
ˆ
D
= $1.00
0 1 2 3 4 ∞
0.00 0.00 0.00 3.00 3.00
rs = 10%
gnorm = 0%
…
30.00
3
ˆ
D
Chapter 7 CFIN6
Thus, the current price of the stock is
13.00
10.3513
Cash flow time line:
Alternative Solution:
Some students might recognize that the last $1 dividend that is paid is the base dividend that will grow
by 8 percent each year thereafter for the remainder of the company’s life. As a result, the $ dividend
paid in Year 2 can be considered the first constant growth dividend, and it can be used to compute the
price of the stock at the end of Year 1.
0 1 2 3 ∞
1.00 1.00 1.08 1.00(1.08)∞-2
rs = 17%
gnorm = 8%
…
0.8547
Chapter 7 CFIN6
7-14 D0 = $0
1
ˆ
D
2
ˆ
D
= $0
20.00
0.0000
17.3913
The PV of $20 one year from today is: PV = P0 = $20/1.15 = $17.39
Cash flow time line:
Alternative solution:
3
ˆ
D
= $2.00(1.05) = $2.10; Because this is affected by constant growth (gnorm = 5%), it can be used to
compute the price of the stock at the end of Year 2.
0 1 2 3 ∞
rs = 15%
gnorm = 5%
…
0.00 2.00 2.10 2.00(1.05)∞-2
0.0000
17.3913
Chapter 7 CFIN6
Cash flow time line:
7-15 D0 = $0
1
ˆ
D
= $1.50
3
2s norm
ˆ
D$2.10 $2.10
ˆ
P $35
r g 0.11 0.05 0.06
= = = =
−−
Thus, the current price of the stock is
37.00
31.3814
Cash flow time line:
0 1 2 3 ∞
1.50 2.00 2.10 2.00(1.05)∞-2
rs = 11%
gnorm = 5%
…
1.3514
0 1 2 3 ∞
rs = 15%
gnorm = 5%
…
Chapter 7 CFIN6
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:
7-16
1
ˆ
D
= $0.60
2
ˆ
D
3
ˆ
D
5
ˆ
D
= $0.90
5
4s 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
26.25
15.1730
Chapter 7 CFIN6
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
3s 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:
7-17 P0 19 x $3.70 = $70.30
0 1 2 3 4 5 ∞
0.60 0.90 2.40 3.50 3.64 3.50(1.05)∞-4
rs = 11%
gnorm = 4%
…
0.5000
0.6250
Chapter 7 CFIN6
Net income = $65,000 = (Taxable income)(1 – 0.40)
Taxable income = ($65,000)/(1 – 0.35) = $100,000
7-20 Net income = $1.2 million = (Taxable income)(1 – 0.40)
Taxable income = ($1.2 million)/(1 – 0.40) = $2.0 million
EBIT = Taxable income + Interest