# solutions-chapter-018-equity-valuation-models

```lOMoARcPSD|13865176
Solutions Chapter 018 - Equity Valuation Models
Security Analysis/Port Mgmt (University of Memphis)
StuDocu is not sponsored or endorsed by any college or university
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
CHAPTER18
:EQUI
TYVALUATI
ONMODELS
PROBLEM SETS
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. k=D1/
P0+g
0.
16=\$2/
\$50+g g=0.
12=12%
b
. P0=D1/
(
k–g
)=\$2/
(
0.
16–0.
05)=\$18.
18
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18-1
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
5. a
. g=ROE b=16%  0.
5=8%
D1=\$2(
1–b)=\$2(
1–0.
5)=\$1
P0=D1/
(
k–g
)=\$1/
(
0.
12–0.
08)=\$25
3=\$
3=\$
b
. P3=P0(
1+g
)
25(
1.
08)
31.
49
6. a
. k=r
r
–r
=6% +1.
25(
14% –6%)=16%
f+(
M)
f]
g=2/
39% =6%
D1=E0(
1+g
)(
1–b)=\$3(
1.
06)(
1/
3)=\$1.
06
P0 
D1
\$1.06

\$10.60
k  g 0.16  0.06
b
. Le
a
di
n
gP0/
E1=\$10.
60/
\$3.
18=3.
33
Tr
a
i
l
i
n
gP0/
E0=\$10.
60/
\$3.
00=3.
53
c
.
E1
\$3.18
\$10.60 
 \$9.275
k
0.16
Th
el
o
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Er
a
t
i
osa
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g
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t
i
v
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oorROE(
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PVGO P0 
d.No
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ur
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vi
s
ebt
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3,gt
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3 9% =3%,a
ndD1t
o:
E0 1.
03 (
2/
3)=\$2.
06
Thus
:
V0=\$2.
06/
(
0.
16–0.
03)=\$15.
85
V0i
nc
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ty
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.
7. Si
nc
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t
a=1.
0,t
he
nk=ma
r
k
e
tr
e
t
ur
n=15%
The
r
e
f
o
r
e
:
15% =D1/
P0+g=4% +g g=11%
18-2
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
8. a
. P0 
D1
\$8

\$160
k  g 0.10  0.05
b
. Th
ed
i
vi
de
ndpa
y
o
utr
a
t
i
oi
s8/
12=2/
3,s
ot
hep
l
o
wba
c
kr
a
t
i
oi
sb=1/
3.The
i
mpl
i
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dv
a
l
ueofROEonf
ut
ur
ei
n
v
e
s
t
me
nt
si
sf
oundb
ys
ol
vi
n
g
:
g=b ROEwi
t
hg=5% a
ndb=1/
3 ROE=15%
c
.
As
s
umi
n
gROE=k,pr
i
c
ei
se
q
ua
lt
o:
E1
\$12

\$120
k
0.10
Th
e
r
e
f
or
e
,t
hema
r
k
e
ti
sp
a
yi
n
g\$40pe
rs
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a
r
e(
\$160–\$120)f
orgr
o
wt
h
oppor
t
uni
t
i
e
s
.
P0 
9. a
. k=D1/
P0+g
D1=0.
5 \$2=\$1
g=b ROE=0.
5 0.
20=0.
10
Th
e
r
e
f
or
e
:k=(
\$1/
\$10)+0.
10=0.
20=20%
b
. Si
nc
ek=ROE,t
heNPVoff
ut
ur
ei
n
v
e
s
t
me
ntoppor
t
uni
t
i
e
si
sz
e
r
o:
PVGO P0 
E1
\$10  \$10 0
k
c
. Si
nc
ek=ROE,t
hes
t
oc
kpr
i
c
ewoul
dbeuna
ffe
c
t
e
db
yc
u
t
t
i
n
gt
hedi
vi
de
nda
nd
i
n
v
e
s
t
i
n
gt
hea
ddi
t
i
ona
le
a
r
ni
n
g
s
.
10. a
. k=r
[
E(
r
–r
=8% +1.
2(
15% –8%)=16.
4%
f+
M)
f]
g=b ROE=0.
6 20% =12%
V0 
D 0 (1  g )
\$4 1.12

\$101.82
k g
0.164  0.12
b
. P1=V1=V0(
1+g
)=\$101.
82 1.
12=\$114.
04
E(r ) 
D1  P1  P0 \$4.48  \$114.04  \$100

0.1852 18.52%
P0
\$100
18-3
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
11.
Ti
me
:
0
Et
\$10.
000
Dt
\$0.
000
b
1.
00
g
20.
0%
a
. V5 
V0 
1
\$12.
000
\$0.
000
1.
00
20.
0%
5
\$24.
883
\$0.
000
1.
00
20.
0%
6
\$29.
860
\$11.
944
0.
60
9.
0%
D6
\$11 .944

\$199.07
k  g 0.15  0.09
V5
\$199.07

\$98.97
5
(1  k )
1.15 5
b
.Thepr
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c
es
ho
ul
dr
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s
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ry
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a
run
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i
ly
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a
r6:be
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a
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et
he
r
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snod
i
vi
de
nd,t
he
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nt
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r
er
e
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ur
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nc
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pi
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a
lg
a
i
ns
.
c
. Th
ep
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y
outr
a
t
i
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enoe
ffe
c
toni
n
t
r
i
ns
i
cv
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l
u
eb
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c
a
us
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12. a
. Th
es
ol
u
t
i
oni
ss
ho
wni
nt
heEx
c
e
ls
pr
e
a
d
s
h
e
e
tb
e
l
o
w:
Inputs
be
t
a
mkt_prem
rf
k_equity
plowback
roe
term_gwt
h
.90
0.08
0.045
0.117
0.74
0.13
0.0962
Value line
forecasts of
annual dividends
Transitional period
with slowing dividend
growth
Beginning of constant
growth period
Year
2008
2009
2010
2011
2012
2013
2014
Dividend
0.77
0.88
0.99
1.10
1.24
1.39
1.56
2015
2016
2017
2018
2019
2020
2021
2022
2023
1.74
1.94
2.16
2.39
2.64
2.91
3.20
3.51
3.85
Div growth Term value
0.1262
0.1232
0.1202
Investor CF
0.77
0.88
0.99
1.10
1.24
1.39
1.56
0.1172
0.1142
0.1112
0.1082
0.1052
0.1022
0.0992
0.0962
0.0962
1.74
1.94
2.16
2.39
2.64
2.91
3.20
3.51
206.50
202.65
45.71 = PV of CF
E17 * (1+ F17)/(B5 - F17)
NPV(B5,H2:H17)
b
.
,c
.Us
i
n
gt
heEx
c
e
ls
pr
e
a
ds
he
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t
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ha
tt
hei
nt
r
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ns
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l
ue
sa
r
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71a
nd
\$17.
39,r
e
s
pe
c
t
i
v
e
l
y
.
18-4
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
13. Thes
o
l
ut
i
on
sde
r
i
v
e
df
r
om Spr
e
a
d
s
h
e
e
t18.
2a
r
ea
sf
ol
l
o
ws
:
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n
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cv
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e
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nt
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ue I
n
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FCFF
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pe
rs
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rs
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a
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81,
171
68,
470
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83
b
.
59,
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49,
185
24.
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27.
17
c
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32.
00
14.
Ti
me
:
0
1
2
3
Dt
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0000
\$1.
2500
\$1.
5625
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g
25.
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25.
0%
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0%
5.
0%
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. Th
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e
a
r
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r
om no
wi
s
:
P2=D3/
(
k–g
)=\$1.
953125/
(
0.
20–0.
05)=\$13.
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Th
ePVoft
hi
se
xpe
c
t
e
dpr
i
c
ei
s
:\$13.
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1.
202=\$9.
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ePVofe
xpe
c
t
e
dd
i
vi
de
nd
si
ny
e
a
r
s1a
nd2i
s
:
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
\$2.13
1.20
1.20 2
Thu
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18-5
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
15.
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me
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18-6
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
b
. Ti
me
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18-7
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
3. a
. Thi
sdi
r
e
c
t
ori
sc
onf
us
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d
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18-8
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
5. a
. Fr
e
ec
a
s
hflo
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oe
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y(
FCFE)i
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18-9
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
Fr
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om r
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a
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ni
n
g
s
.
18-10
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
i
i
.Bo
t
ht
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a
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h
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outr
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t
i
o
.
P/E on trailing earnings:
P/E = [payout ratio  (1 + g)]/(r  g) = [0.30  1.13]/(0.14  0.13) = 33.9
P/
Eonne
xty
e
a
r
'
se
a
r
ni
n
g
s
:
P/E = payout ratio/(r  g) = 0.30/(0.14  0.13) = 30.0
b
. Th
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rSunda
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'
sP/
Er
a
t
i
o
.
18-11
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
7.
a.
The sustainable growth rate is equal to:
plowback ratio &times; return on equity = b &times; ROE
where
b = [Net Income – (Dividend per share &times; shares outstanding)]/Net Income
ROE = Net Income/Beginning of year equity
In 2005:
b = [208 – (0.80 &times; 100)]/208 = 0.6154
ROE = 208/1380 = 0.1507
Sustainable growth rate = 0.6154 &times; 0.1507 = 9.3%
In 2008:
b = [275 – (0.80 &times; 100)]/275 = 0.7091
ROE = 275/1836 = 0.1498
Sustainable growth rate = 0.7091 &times; 0.1498 = 10.6%
b.
i. The increased retention ratio increased the sustainable growth rate.
Retention ratio = [Net Income – (Dividend per share &times; shares outstanding)]/Net Income
Retention ratio increased from 0.6154 in 2005 to 0.7091 in 2008.
This increase in the retention ratio directly increased the sustainable growth rate
because the retention ratio is one of the two factors determining the sustainable
growth rate.
ii. The decrease in leverage reduced the sustainable growth rate.
Financial leverage = (Total Assets/Beginning of year equity)
Financial leverage decreased from 2.34 (= 3230/1380) at the beginning of 2005 to 2.10
at the beginning of 2008 (= 3856/1836)
This decrease in leverage directly decreased ROE (and thus the sustainable growth rate)
because financial leverage is one of the factors determining ROE (and ROE is one of
the two factors determining the sustainable growth rate).
8.
a.
The formula for the Gordon model is:
V0 = [D0 &times; (1 + g)]/(r – g)
where:
D0 = dividend paid at time of valuation
g = annual growth rate of dividends
r = required rate of return for equity
In the above formula, P0, the market price of the common stock, substitutes for V0
and g becomes the dividend growth rate implied by the market:
P0 = [D0 &times; (1 + g)]/(r – g)
Substituting, we have:
58.49 = [0.80 &times; (1 + g)]/(0.08 – g)  g = 6.54%
18-12
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
b.
Use of the Gordon growth model would be inappropriate to value Dynamic’s
common stock, for the following reasons:
i. The Gordon growth model assumes a set of relationships about the growth rate for
dividends, earnings, and stock values. Specifically, the model assumes that
dividends, earnings, and stock values will grow at the same constant rate. In valuing
Dynamic’s common stock, the Gordon growth model is inappropriate because
management’s dividend policy has held dividends constant in dollar amount
although earnings have grown, thus reducing the payout ratio. This policy is
inconsistent with the Gordon model assumption that the payout ratio is constant.
ii. It could also be argued that use of the Gordon model, given Dynamic’s current
dividend policy, violates one of the general conditions for suitability of the model,
namely that the company’s dividend policy bears an understandable and consistent
relationship with the company’s profitability.
9. a
. Th
ei
ndus
t
r
y
’
se
s
t
i
ma
t
e
dP/
Ec
a
nbec
omput
e
du
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i
n
gt
hef
ol
l
o
wi
n
gmode
l
:
P0/
E1=p
a
y
outr
a
t
i
o/
(
r g
)
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we
v
e
r
,s
i
nc
era
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eno
te
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c
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t
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he
ymus
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o
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e
dus
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n
gt
he
f
ol
l
o
wi
n
gf
or
mul
a
s
:
gind=ROE r
e
t
e
nt
i
onr
a
t
e=0.
25 0.
40=0.
10
r
o
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a e
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ui
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nd=g
=0.06 + (1.2  0.05) = 0.12
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e
r
e
f
or
e
:
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E1=0.
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(
0.
12 0.
10)=30.
0
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18-13
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
10. a
. k=r
r
–r
=4.
5% +1.
15(
14.
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Chapter 18 - Equity Valuation Models
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lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
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Chapter 18 - Equity Valuation Models
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18-17