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Solutions Chapter 018 - Equity Valuation Models
Security Analysis/Port Mgmt (University of Memphis)
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Chapter 18 - Equity Valuation Models
CHAPTER18
:EQUI
TYVALUATI
ONMODELS
PROBLEM SETS
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4. a
. 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
Th
epr
i
c
ef
a
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si
nr
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pon
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r
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hp
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os
pe
c
t
s
.
18-1
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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
wP/
Er
a
t
i
osa
ndn
e
g
a
t
i
v
ePVGOa
r
eduet
oap
oorROE(
9%)t
ha
ti
sl
e
s
s
t
ha
nt
hema
r
k
e
tc
a
pi
t
a
l
i
z
a
t
i
onr
a
t
e(
16%)
.
PVGO P0 
d.No
w,y
o
ur
e
vi
s
ebt
o1/
3,gt
o1/
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
r
e
a
s
e
sb
e
c
a
us
et
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m pa
y
soutmor
ee
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r
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g
si
ns
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e
a
dofr
e
i
n
v
e
s
t
i
n
gapoor
ROE.Thi
si
nf
or
ma
t
i
oni
sno
ty
e
tkn
o
wnt
ot
her
e
s
toft
hema
r
k
e
t
.
7. Si
nc
ebe
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
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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
e
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
h
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
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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
i
c
es
ho
ul
dr
i
s
eb
y15% pe
ry
e
a
run
t
i
ly
e
a
r6:be
c
a
u
s
et
he
r
ei
snod
i
vi
de
nd,t
he
e
nt
i
r
er
e
t
ur
nmus
tbei
nc
a
pi
t
a
lg
a
i
ns
.
c
. Th
ep
a
y
outr
a
t
i
owoul
dha
v
enoe
ffe
c
toni
n
t
r
i
ns
i
cv
a
l
u
eb
e
c
a
us
eROE=k.
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
e
t
,wefindt
ha
tt
hei
nt
r
i
ns
i
cv
a
l
ue
sa
r
e$29.
71a
nd
$17.
39,r
e
s
pe
c
t
i
v
e
l
y
.
18-4
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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
:
I
n
t
r
i
ns
i
cv
a
l
u
e
: I
n
t
r
i
ns
i
cv
a
l
u
e
: I
nt
r
i
ns
i
cv
a
l
ue I
n
t
r
i
ns
i
cv
a
l
ue
FCFF
FCFE
pe
rs
ha
r
e
:FCFF pe
rs
ha
r
e
:FCFE
a
.
81,
171
68,
470
36.
01
37.
83
b
.
59,
961
49,
185
24.
29
27.
17
c
.
69,
813
57,
913
29.
73
32.
00
14.
Ti
me
:
0
1
2
3
Dt
$1.
0000
$1.
2500
$1.
5625
$1.
953125
g
25.
0%
25.
0%
25.
0%
5.
0%
a
. Th
ed
i
vi
de
ndt
obepa
i
da
tt
h
ee
ndofy
e
a
r3i
st
h
efir
s
ti
ns
t
a
l
l
me
ntofadi
vi
de
nd
s
t
r
e
a
mt
ha
twi
l
li
nc
r
e
a
s
ei
nde
fini
t
e
l
ya
tt
h
ec
ons
t
a
ntgr
o
wt
hr
a
t
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e
r
e
f
or
e
,we
c
a
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et
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ons
t
a
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o
wt
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ul
a
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ddi
n
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s
e
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l
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de
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ep
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a
l
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c
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t
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ka
tt
h
ee
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e
a
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Th
ee
xpe
c
t
e
dpr
i
c
e2y
e
a
r
sf
r
om no
wi
s
:
P2=D3/
(
k–g
)=$1.
953125/
(
0.
20–0.
05)=$13.
02
Th
ePVoft
hi
se
xpe
c
t
e
dpr
i
c
ei
s
:$13.
02/
1.
202=$9.
04
Th
ePVofe
xpe
c
t
e
dd
i
vi
de
nd
si
ny
e
a
r
s1a
nd2i
s
:
$1.25 $1.5625

$2.13
1.20
1.20 2
Thu
st
hec
ur
r
e
ntpr
i
c
es
h
oul
db
e
:$9.
04+$2.
13=$11.
17
b
.Expe
c
t
e
ddi
vi
de
ndyi
e
l
d=D1/
P0=$1.
25/
$11.
17=0.
112=11.
2%
c
. Th
ee
xpe
c
t
e
dpr
i
c
eoney
e
a
rf
r
om n
o
wi
st
hePVa
tt
ha
tt
i
meofP2a
ndD2:
P1=(
D2+P2)
/
1.
20=(
$1.
5625+$13.
02)
/
1.
20=$12.
15
Th
ei
mpl
i
e
dc
a
pi
t
a
lg
a
i
ni
s
:
(
P1–P0)
/
P0=(
$12.
15–$11.
17)
/
$11.
17=0.
088=8.
8%
Th
es
um oft
h
ei
mpl
i
e
dc
a
pi
t
a
lg
a
i
nsyi
e
l
da
ndt
hee
xpe
c
t
e
dd
i
vi
de
ndyi
e
l
di
se
q
ua
l
t
ot
h
ema
r
k
e
tc
a
pi
t
a
l
i
z
a
t
i
onr
a
t
e
.Thi
si
sc
on
s
i
s
t
e
ntwi
t
ht
heDDM.
18-5
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lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
15.
Ti
me
:
0
1
4
5
Et
$5.
000
$6.
000 $10.
368 $12.
4416
Dt
$0.
000
$0.
000
$0.
000 $12.
4416
Di
vi
d
e
nds=0f
ort
hene
xtf
oury
e
a
r
s
,s
ob=1.
0(
100% pl
o
wba
c
kr
a
t
i
o)
.
a
. P4  D 5  $12.4416 $82.944
k
0.15
V0 
P4
$82.944

$47.42
4
(1  k )
1.15 4
b
. Pr
i
c
es
h
oul
di
nc
r
e
a
s
ea
tar
a
t
eof15% o
v
e
rt
hene
xty
e
a
r
,s
ot
ha
tt
heHPRwi
l
l
e
q
u
a
lk.
16. Be
f
o
r
e
t
a
xc
a
s
hflo
wf
r
om op
e
r
a
t
i
ons
$2,
100,
000
De
pr
e
c
i
a
t
i
on
210,
000
Ta
x
a
bl
eI
nc
ome
1,
890,
000
Ta
x
e
s(
@ 35%)
661,
500
Af
t
e
r
t
a
xunl
e
v
e
r
a
g
e
di
nc
ome
1,
228,
500
Af
t
e
r
t
a
xc
a
s
hflo
wf
r
om op
e
r
a
t
i
ons
(
Af
t
e
r
t
a
xunl
e
v
e
r
a
g
e
di
nc
ome+de
pr
e
c
i
a
t
i
on)
1,
438,
500
Ne
wi
n
v
e
s
t
me
nt(
20% ofc
a
s
hflo
wf
r
om op
e
r
a
t
i
ons
)
420
,
000
Fr
e
ec
a
s
hflo
w
(
Af
t
e
r
t
a
xc
a
s
hflo
wf
r
om ope
r
a
t
i
ons–ne
wi
n
v
e
s
t
me
n
t
) $1,
018,
500
Th
ev
a
l
ueoft
hefir
m(
i
.
e
.
,de
btpl
use
q
ui
t
y)i
s
:
V0 
C1
$1,018,500

$14,550,000
k g
0.12  0.05
Si
nc
et
hev
a
l
u
eoft
hede
bti
s$4mi
l
l
i
on,t
hev
a
l
u
eoft
h
ee
q
ui
t
yi
s$10,
550,
000.
17. a
. g=ROE b=20%  0.
5=10%
P0 
D (1  g ) $0.50 1.10
D1
 0

$11
k g
k g
0.15  0.10
18-6
Downloaded by Vi Nguy?n T??ng (vint19404b@st.uel.edu.vn)
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
b
. Ti
me
EPS
Di
vi
d
e
nd Comme
nt
0
$1.
0000 $0.
5000
1
$1.
1000 $0.
5500 g=10%,pl
o
wba
c
k=0.
50
2
$1.
2100 $0.
7260 EPSha
sgr
o
wnb
y10% ba
s
e
donl
a
s
t
y
e
a
r
’
se
a
r
ni
n
g
spl
o
wba
c
ka
ndROE;t
hi
s
y
e
a
r
’
se
a
r
ni
n
g
spl
o
wba
c
kr
a
t
i
on
o
wf
a
l
l
s
t
o0.
40a
ndpa
y
outr
a
t
i
o=0.
60
3
$1.
2826 $0.
7696 EPSgr
o
wsb
y(
0.
4)(
15%)=6% a
nd
pa
y
o
utr
a
t
i
o=0.
60
Att
i
me2:P2 
D3
$0.7696

$8.551
k  g 0.15  0.06
Att
i
me0:V0 
$0.55 $0.726  $8.551

$7.493
1.15
(1.15) 2
c
. P0=$11a
ndP1=P0(
1+g
)=$12.
10
(
Be
c
a
us
et
hema
r
k
e
ti
suna
wa
r
eoft
h
ec
ha
n
g
e
dc
o
mpe
t
i
t
i
v
es
i
t
ua
t
i
on,i
tb
e
l
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e
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e
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he
s
t
oc
kpr
i
c
es
ho
ul
dgr
o
wa
t10% pe
ry
e
a
r
.
)
P2=$8.
551af
t
e
rt
hema
r
k
e
tbe
c
ome
sa
wa
r
eoft
hec
h
a
n
g
e
dc
ompe
t
i
t
i
v
es
i
t
ua
t
i
on.
P3=$8.
551 1.
06=$9.
064(
Thene
wgr
o
wt
hr
a
t
ei
s6%.
)
Ye
a
r
1
2
3
Re
t
ur
n
($12.10  $11)  $0.55
0.150 15.0%
$11
($8.551  $12.10)  $0.726
 0.233  23.3%
$12.10
($9.064  $8.551)  $0.7696
0.150 15.0%
$8.551
Mor
a
l
:I
n"
nor
ma
lpe
r
i
ods
"whe
nt
h
e
r
ei
snos
pe
c
i
a
li
nf
or
ma
t
i
on,
t
hes
t
oc
kr
e
t
ur
n=k=15%.Wh
e
ns
pe
c
i
a
li
nf
or
ma
t
i
o
na
r
r
i
v
e
s
,a
l
lt
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bnor
ma
l
r
e
t
ur
na
c
c
r
ue
si
nt
hatpe
r
i
od,a
sonewoul
de
xpe
c
ti
na
ne
ffic
i
e
ntma
r
k
e
t
.
CFAPROBLEMS
1. P0=D1/
(
k–g
)=$2.
10/
(
0.
11–0)=$19.
09
2. Ia
ndI
I
18-7
Downloaded by Vi Nguy?n T??ng (vint19404b@st.uel.edu.vn)
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
3. a
. Thi
sdi
r
e
c
t
ori
sc
onf
us
e
d
.I
nt
h
ec
ont
e
xtoft
h
ec
ons
t
a
ntgr
o
wt
hmode
l
[
i
.
e
.
,P0=D1/
(
k–g
)
]
,i
ti
st
r
uet
ha
tpr
i
c
ei
shi
ghe
rwh
e
ndi
vi
de
ndsa
r
eh
i
g
he
r
hol
di
n
ge
v
e
r
y
t
hi
n
ge
l
s
ei
nc
l
udi
n
gdi
v
i
de
ndg
r
o
wt
hc
ons
t
ant
.Bute
v
e
r
yt
hi
n
ge
l
s
ewi
l
l
no
tbec
ons
t
a
nt
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ft
hefir
mi
nc
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e
a
s
e
st
h
ed
i
vi
de
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y
o
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a
t
e
,t
hegr
o
wt
hr
a
t
egwi
l
l
f
a
l
l
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nf
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c
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,i
fROE>k
,pr
i
c
ewi
l
lf
a
l
l
.
b
. (
i
)Ani
nc
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e
a
s
ei
ndi
vi
de
ndp
a
y
outwi
l
lr
e
duc
et
h
es
us
t
a
i
na
bl
egr
o
wt
hr
a
t
ea
sl
e
s
s
f
undsa
r
er
e
i
n
v
e
s
t
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di
nt
h
efir
m.Th
es
us
t
a
i
n
a
bl
egr
o
wt
hr
a
t
e
(
i
.
e
.
,ROEpl
o
wba
c
k)wi
l
lf
a
l
la
spl
o
wba
c
kr
a
t
i
of
a
l
l
s
.
(
i
i
)Thei
nc
r
e
a
s
e
dd
i
vi
de
ndpa
y
o
utr
a
t
ewi
l
lr
e
duc
et
hegr
o
wt
hr
a
t
eofbookv
a
l
ue
f
ort
hes
a
mer
e
a
s
o
n-l
e
s
sf
undsa
r
er
e
i
n
v
e
s
t
e
di
nt
h
efir
m.
4. Us
i
n
gat
wo
s
t
a
g
ed
i
vi
de
nddi
s
c
ountmode
l
,t
h
ec
u
r
r
e
ntv
a
l
ueofas
ha
r
eofSunda
n
c
ii
s
c
a
l
c
ul
a
t
e
da
sf
ol
l
o
ws
.
D3
D1
D2
(k  g)
V0 


1
2
(1  k ) (1  k )
(1  k ) 2
$0.5623
$0.3770 $0.4976 (0.14  0.13)



$43.98
1.141
1.14 2
1.14 2
wh
e
r
e
:
E0=$0.
952
D0=$0.
286
1=$
E1=E0(
1.
32)
0.
952 1.
32=$1.
2566
D1=E1 0.
30=$1.
2566 0.
30=$0.
3770
2=$
2=$
E2=E0(
1.
32)
0.
952 (
1.
32)
1.
6588
D2=E2 0.
30=$1.
6588 0.
30=$0.
4976
2 1
3 1
E3=E0 (
1.
32)
.
13=$0.
952 (
1.
32)
.
13=$1.
8744
D3=E3 0.
30=$1.
8743 0.
30=$0.
5623
18-8
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lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
5. a
. Fr
e
ec
a
s
hflo
wt
oe
q
ui
t
y(
FCFE)i
sde
fine
da
st
hec
a
s
hflo
wr
e
ma
i
ni
n
ga
f
t
e
r
me
e
t
i
n
ga
l
lfina
n
c
i
a
lobl
i
g
a
t
i
ons(
i
nc
l
udi
n
gde
btpa
yme
nt
)a
nda
f
t
e
rc
o
v
e
r
i
n
g
c
a
pi
t
a
le
xpe
ndi
t
ur
ea
ndwor
ki
n
gc
a
pi
t
a
lne
e
d
s
.TheFCFEi
same
a
s
ur
eofho
w
muc
ht
hefir
mc
a
na
ffo
r
dt
opa
youta
sd
i
vi
de
nd
s
,buti
nag
i
v
e
ny
e
a
rma
ybemor
e
orl
e
s
st
h
a
nt
hea
mounta
c
t
ua
l
l
ypa
i
dout
.
Sunda
nc
i
'
sFCFEf
ort
hey
e
a
r2008i
sc
o
mput
e
da
sf
ol
l
o
ws
:
FCFE =
Earnings after tax + Depreciation expense  Capital expenditures  Increase in NWC
=$80mi
l
l
i
on+$23mi
l
l
i
on $38mi
l
l
i
on $41mi
l
l
i
on=$24mi
l
l
i
on
FCFEpe
rs
ha
r
e=FCFE/
numbe
rofs
ha
r
e
sout
s
t
a
ndi
n
g
=$24mi
l
l
i
on/
84mi
l
l
i
ons
ha
r
e
s=$0.
286
Att
h
eg
i
v
e
nd
i
vi
de
ndpa
y
o
utr
a
t
i
o
,Sunda
nc
i
'
sFCFEpe
rs
h
a
r
ee
q
ua
l
sd
i
vi
de
nd
sp
e
r
s
h
a
r
e
.
b
. Th
eFCFEmode
lr
e
q
ui
r
e
sf
o
r
e
c
a
s
t
sofFCFEf
ort
heh
i
ghgr
o
wt
hy
e
a
r
s(
2009a
nd
2010)pl
usaf
o
r
e
c
a
s
tf
ort
hefir
s
ty
e
a
rofs
t
a
bl
egr
o
wt
h(
2011)i
nor
de
rt
ot
oa
l
l
o
w
f
ora
ne
s
t
i
ma
t
eoft
het
e
r
mi
na
lv
a
l
uei
n2010ba
s
e
donpe
r
pe
t
ua
lgr
o
wt
h.Be
c
a
u
s
e
a
l
loft
hec
o
mpone
n
t
sofFCFEa
r
ee
xpe
c
t
e
dt
ogr
o
wa
tt
hes
a
mer
a
t
e
,t
hev
a
l
ue
s
c
a
nbeobt
a
i
ne
db
ypr
o
j
e
c
t
i
n
gt
heFCFEa
tt
hec
ommonr
a
t
e
.(
Al
t
e
r
na
t
i
v
e
l
y
,t
he
c
ompone
nt
sofFCFEc
a
nbepr
o
j
e
c
t
e
da
nda
ggr
e
g
a
t
e
df
ore
a
c
hy
e
a
r
.
)
Th
ef
ol
l
o
wi
n
gt
a
bl
es
ho
wst
hepr
oc
e
s
sf
ore
s
t
i
ma
t
i
n
gSunda
nc
i
'
sc
ur
r
e
ntv
a
l
ueona
pe
rs
h
a
r
eba
s
i
s
.
18-9
Downloaded by Vi Nguy?n T??ng (vint19404b@st.uel.edu.vn)
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
Fr
e
eCa
s
hFl
o
wt
oEq
ui
t
y
Ba
s
eAs
s
u
mp
t
i
ons
Sha
r
e
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t
s
t
a
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n
g
:84mi
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l
i
on
Re
q
ui
r
e
dr
e
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ur
none
q
ui
t
y(
r
)
:14%
Ac
t
ua
l
2008
Gr
o
wt
hr
a
t
e(
g
)
Ea
r
ni
n
g
sa
f
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e
rt
a
x
Pl
us
:De
p
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e
c
i
a
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a
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ki
n
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a
pi
t
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l
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l
s
:FCFE
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r
mi
na
lv
a
l
ue
To
t
a
lc
a
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hflo
wst
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Di
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ount
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l
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$38
$41
$24
Pe
rs
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e
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$0.
452
$0.
488
$0.
286
Pr
o
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e
c
t
e
d
2009
27%
Pr
o
j
e
c
t
e
d
2010
27%
Pr
o
j
e
c
t
e
d
2011
13%
$1.
2090
$0.
3480
$0.
5740
$0.
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98
$0.
3632
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7351
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4419 $0
.
4994
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.
8238
$0.
7871 $0.
8894
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1300*
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3632
$52.
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$0.
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4673***
$40.
7859****
*Pr
o
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c
t
e
d2010Te
r
mi
na
lv
a
l
ue=(
Pr
o
j
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c
t
e
d2011FCFE)
/
(
r g
)
**Pr
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d2010To
t
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lc
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***Di
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****Cur
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e=
Sum ofDi
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ount
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t
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le
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o
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e
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ni
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r
e
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o
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et
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s
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l
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t
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a
n
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n
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vi
de
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lpr
o
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de
sabe
t
t
e
re
s
t
i
ma
t
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a
l
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sbi
a
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e
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o
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r
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n
g
l
o
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Er
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t
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gh
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o
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d
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ti
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ons
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d
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r
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da
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ons
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a
t
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emode
li
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e
ndst
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f
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e
we
runde
r
v
a
l
ue
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k
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i
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er
e
l
a
t
i
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et
of
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me
n
t
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s
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eDDM doe
sno
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o
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ort
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e
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d
v
a
n
t
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g
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l
a
t
i
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et
ot
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a
pi
t
a
lg
a
i
nsa
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hi
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a
bl
ef
r
om r
e
t
e
nt
i
onof
e
a
r
ni
n
g
s
.
18-10
Downloaded by Vi Nguy?n T??ng (vint19404b@st.uel.edu.vn)
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
i
i
.Bo
t
ht
wos
t
a
g
ev
a
l
ua
t
i
onmode
l
sa
l
l
o
wf
ort
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s
t
i
nc
tpha
s
e
sofgr
o
wt
h,a
ni
ni
t
i
a
l
fini
t
ep
e
r
i
odwhe
r
et
h
egr
o
wt
hr
a
t
ei
sa
bnor
ma
l
,f
ol
l
o
we
db
yas
t
a
bl
egr
o
wt
hpe
r
i
odt
ha
t
i
se
xpe
c
t
e
dt
ol
a
s
ti
nde
fini
t
e
l
y
.The
s
et
wos
t
a
g
emode
l
ss
h
a
r
et
hes
a
mel
i
mi
t
a
t
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on
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h
r
e
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pe
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o
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ha
s
s
u
mp
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ons
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r
s
t
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he
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ei
st
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n
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h
edur
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xt
r
a
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na
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o
wt
hpe
r
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od
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x
a
mpl
e
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on
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e
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o
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a
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rv
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l
ua
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e
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ei
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yl
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pe
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i
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om hi
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o
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o
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v
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nt
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ume
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z
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f
t
(
i
.
e
.
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si
nfini
t
e
)
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het
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es
hi
f
tf
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om hi
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r
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ump
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om s
ub
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.
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. Th
ef
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mul
af
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a
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a
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t
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o(
P/
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oras
t
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vi
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yt
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e
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r
e
t
ur
na
ndt
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o
wt
hr
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t
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vi
de
nds
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ft
heP/
Ei
sc
a
l
c
ul
a
t
e
dba
s
e
dont
r
a
i
l
i
n
g
e
a
r
ni
n
g
s(
y
e
a
r0)
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y
o
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si
nc
r
e
a
s
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db
yt
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wt
hr
a
t
e
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ft
heP/
Ei
s
c
a
l
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ul
a
t
e
dba
s
e
donne
xty
e
a
r
’
se
a
r
ni
n
g
s(
y
e
a
r1)
,t
henume
r
a
t
ori
st
h
ep
a
y
outr
a
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
eP/
Er
a
t
i
oi
sade
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r
e
a
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n
gf
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is
t
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kwoul
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t
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o
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rt
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P/
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t
i
o
.
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t
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o
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rt
heP/
Er
a
t
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o
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nc
iwoul
dc
omma
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f
a
na
l
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t
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e
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s
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o
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hr
a
t
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.
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Er
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t
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um.Ani
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d
ma
r
k
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tr
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a
s
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st
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a
t
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t
ur
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o
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r
i
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gt
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ni
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gh
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mi
um woul
db
ee
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t
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dt
o
l
o
we
rSunda
nc
i
'
sP/
Er
a
t
i
o
.
18-11
Downloaded by Vi Nguy?n T??ng (vint19404b@st.uel.edu.vn)
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
7.
a.
The sustainable growth rate is equal to:
plowback ratio × return on equity = b × ROE
where
b = [Net Income – (Dividend per share × shares outstanding)]/Net Income
ROE = Net Income/Beginning of year equity
In 2005:
b = [208 – (0.80 × 100)]/208 = 0.6154
ROE = 208/1380 = 0.1507
Sustainable growth rate = 0.6154 × 0.1507 = 9.3%
In 2008:
b = [275 – (0.80 × 100)]/275 = 0.7091
ROE = 275/1836 = 0.1498
Sustainable growth rate = 0.7091 × 0.1498 = 10.6%
b.
i. The increased retention ratio increased the sustainable growth rate.
Retention ratio = [Net Income – (Dividend per share × 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 × (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 × (1 + g)]/(r – g)
Substituting, we have:
58.49 = [0.80 × (1 + g)]/(0.08 – g)  g = 6.54%
18-12
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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
s
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
ndga
r
eno
te
xpl
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c
i
t
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he
ymus
tbec
o
mput
e
dus
i
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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=0.06 + (1.2  0.05) = 0.12
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e
r
e
f
or
e
:
P0/
E1=0.
60/
(
0.
12 0.
10)=30.
0
b
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18-13
Downloaded by Vi Nguy?n T??ng (vint19404b@st.uel.edu.vn)
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
10. a
. k=r
r
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=4.
5% +1.
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14.
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18-14
Downloaded by Vi Nguy?n T??ng (vint19404b@st.uel.edu.vn)
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
11. a
. Th
ev
a
l
ueofas
h
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r
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l
:
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)=4% +1.
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om CFOt
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18-15
Downloaded by Vi Nguy?n T??ng (vint19404b@st.uel.edu.vn)
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
Not
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18-16
Downloaded by Vi Nguy?n T??ng (vint19404b@st.uel.edu.vn)
lOMoARcPSD|13865176
Chapter 18 - Equity Valuation Models
c
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18-17
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