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4-1
Fin
an
cial
Sta
tem
ent
An
aly
sis
MS
c. i
n F
ina
nci
al
An
aly
sis
for
Exec
uti
ves
Dep
art
men
t o
f B
an
kin
g &
Fin
an
cia
l M
an
ag
emen
t
Un
iver
sity
of
Pir
aeu
s
Dr.
Geo
rgio
s A
. P
ap
an
ast
aso
po
ulo
s
4-2
4-3
4-4
Sim
ple
(a
nd
Ch
eap
) A
pp
roa
ches
to
Va
lua
tio
n
•F
undam
enta
l an
alysi
s is
det
aile
d a
nd c
ost
ly.
•S
imple
appro
aches
avoid
fore
cast
ing a
nd m
inim
ize
info
rmat
ion a
nal
ysi
s. B
ut
they
lose
pre
cisi
on.
•S
imple
met
hods:
�M
etho
d o
f C
om
par
able
s
�S
cree
nin
g o
n M
ult
iple
s
�A
sset
-Bas
ed V
alu
atio
n
4-5
Th
e M
eth
od
of
Co
mp
ara
ble
s
1.
Iden
tify
com
par
able
fir
ms
that
hav
e si
mil
ar o
per
atio
ns
to
the
firm
wh
ose
val
ue
is i
n q
ues
tion (
the
“tar
get
”).
2.
Iden
tify
mea
sure
s fo
r th
e co
mpar
able
fir
ms
in t
hei
r
finan
cial
sta
tem
ents
–ea
rnin
gs,
book v
alue,
sal
es, ca
sh
flow
–an
d c
alcu
late
mult
iple
s of
those
mea
sure
s at
whic
h t
he
firm
s tr
ade.
3.
Apply
thes
e m
ult
iple
s to
the
corr
espondin
g m
easu
res
for
the
targ
et t
o g
et t
hat
fir
m’s
val
ue.
4-6
Th
e M
eth
od
of
Co
mp
ara
ble
s:
Del
l, G
ate
wa
y a
nd
Hew
lett
Pa
cka
rd,
20
02
Aver
age
Mult
iple
for
Com
par
able
s
Del
l's
Num
ber
D
ell's
V
aluat
ion
Sal
es
0.5
3
$31,1
68
$16,5
19
Ear
nin
gs
52.8
1,2
46
65,7
89
Book V
alu
e
1.8
4,6
94
8,4
49
Aver
age
of
Val
uat
ions
30,2
52
S
ales
E
arnin
gs
Bo
ok
Val
ue
Mar
ket
V
alue
P/S
P
/E
P/B
Hew
lett
Pac
kar
d C
o.
$
45
,22
6
$
62
4
$
13
,95
3
$
32
,96
3
0
.73
52
.8
2
.4
Gat
eway
20
00
Inc.
6,0
80
(1
,290
) 1
,56
5
1,9
44
0
.32
-
1.2
Del
l C
om
pute
r C
orp
.
31
,168
1
,24
6
4,6
94
?
? ?
?
4-7
Ho
w C
hea
p i
s th
is M
eth
od
?
Conce
ptu
al p
roble
ms:
•C
ircu
lar
reas
onin
g:
Pri
ce i
s as
cert
ain
ed f
rom
pri
ce (
of
the
com
ps)
•V
iola
tes
the
ten
et:
“When
cal
cula
ting
val
ue
to c
hal
leng
e p
rice
, d
on’t
le
t pri
ce e
nte
r th
e ca
lcu
lati
on
”
•If
th
e m
arket
is
effi
cien
t fo
r th
e co
mp
arab
le c
om
pan
ies.
...W
hy i
s it
no
t fo
r th
e ta
rget
co
mp
any ?
Imple
men
tati
on p
roble
ms:
•F
ind
ing t
he
com
par
able
s th
at m
atch
pre
cise
ly
•D
iffe
rent
acco
unti
ng
met
ho
ds
for
com
ps
and
tar
get
•D
iffe
rent
pri
ces
fro
m d
iffe
rent
mu
ltip
les
•W
hat
ab
ou
t n
egat
ive
den
om
inat
ors
?
Appli
cati
ons:
•IP
Os;
fir
ms
that
are
no
t tr
aded
(to
app
rox
imat
e pri
ce, n
ot
val
ue)
4-8
Un
lev
ered
(or
En
terp
rise
) M
ult
iple
s (t
ha
t a
re
Un
aff
ecte
d b
y t
he
Fin
an
cin
g o
f O
per
ati
on
s)
Deb
tN
et
E
qu
ity
of
V
alu
eB
oo
k
Deb
tN
et
E
qu
ity
of
V
alu
eM
ark
et
BP
En
terp
rise
ebit
da
Deb
tN
et
Eq
uit
y
of
V
alu
eM
ark
et
da
Pri
ce/e
bit
U
nle
ver
ed
ebit
Deb
tN
et
E
qu
ity
o
f
Val
ue
Mar
ket
P
rice
/eb
it
Un
lev
ered
Sal
es
Deb
tN
et
Eq
uit
y
of
V
alu
eM
ark
et
Rat
io s
Pri
ce/S
ale
U
nle
ver
ed
++=
+=
+=
+=
4-9
Va
ria
tio
ns
of
the
P/E
Ra
tio E
ps
sy
ear'
nex
t
of
Fo
reca
st
shar
ep
er
P
rice
P/E
F
orw
ard
qu
arte
rsfo
ur
rece
nt
mo
st
for
E
ps
o
f
Su
m
shar
ep
er
P
rice
P/E
R
oll
ing
Ep
s
ann
ual
Las
t
shar
ep
er
P
rice
P
/E
Tra
ilin
g
=
=
=
4-1
0
Div
iden
d–
Ad
just
ed P
/E earn
ing
sn
ot
bu
t
pri
ces
af
fect
s
Div
iden
d :
Rat
ion
ale
Ep
s
Dp
s
An
nu
alsh
are
per
Pri
ceP
/E
Ad
just
ed-
Div
iden
d+
=
4-1
1
Ty
pic
al
Va
lues
fo
r C
om
mo
n M
ult
iple
s
En
terp
rise
Tra
ilin
gF
orw
ard
Un
leve
red
Un
leve
red
Un
leve
red
Pe
rce
nti
leP
/BP
/BP
/EP
/EP
/SP
/SP
/CF
OP
/eb
itd
aP
/eb
it
95
7.9
12.7
Negative
49.2
8.9
8.1
Negative
30.1
Negative
earn
ings
cash flo
webit
75
2.9
2.7
23.5
19.1
1.7
2.0
18.8
10.6
15.3
50
1.7
1.5
15.2
13.1
0.8
0.9
9.9
7.0
9.9
25
1.0
1.0
10.3
9.2
0.3
0.5
5.6
4.8
6.6
50.5
0.6
5.9
5.6
0.1
0.2
2.3
2.5
3.3
Mu
ltip
le
4-1
2
Scr
een
ing
An
aly
sis
•T
echnic
al s
cree
ns:
iden
tify
posi
tions
bas
ed o
n t
radin
g i
ndic
ators
�P
rice
scr
eens
�S
mal
l st
ock
scr
eens
�N
egle
cted
sto
cks
scre
ens
�S
easo
nal
scr
eens
�M
om
entu
m s
cree
ns
�In
sider
tra
din
g s
cree
ns
•F
undam
enta
l sc
reen
s: i
den
tify
posi
tions
bas
ed o
n f
undam
enta
l in
dic
ators
of
the
firm
’s o
per
atio
ns
rela
tive
to p
rice
�P
rice
/Ear
nin
gs
(P/E
) ra
tios
�M
arket
/Book V
alue
(P/B
) ra
tios
�P
rice
/Cas
h F
low
(P
/C)
rati
os
�P
rice
/Div
iden
d (
P/d
) ra
tios
•A
ny
com
bin
atio
n o
f th
ese
met
hods
is p
oss
ible
4-1
3
Ho
w M
ult
iple
Scr
een
ing
Wo
rks
1.
Iden
tify
a m
ult
iple
on
wh
ich
to s
cree
n s
tock
s.
2.
Ran
k s
tock
s o
n t
hat
mu
ltip
le, fr
om
hig
hes
t to
low
est.
3.
Bu
y s
tock
s w
ith
th
e lo
wes
t m
ult
iple
s an
d (
sho
rt)
sell
sto
cks
wit
h t
he
hig
hes
t m
ult
iple
s.
4-1
4
Fu
nd
am
enta
l S
cree
nin
g:
Ret
urn
to
Pri
ce-t
o-B
oo
k
Mean
Pri
ce/B
oo
kM
onth
lyM
ean
Gro
up
Retu
rn (
%)
Beta
1 (
Hig
h)
0.4
91.3
5
20
.87
1.3
2
30
.97
1.3
0
41
.04
1.2
8
51
.17
1.2
7
61
.30
1.2
7
71
.44
1.2
7
81
.50
1.2
7
91
.59
1.2
9
10 (
Lo
w)
1.8
81.3
4
So
urc
e: F
ama
and
Fre
nch
(1
99
2)
4-1
5
Aver
age
Mon
thly
Ret
urn
s an
d E
stim
ate
d B
etas
from
Ju
ly 1
963
to D
ecem
ber
1990 f
or
Ten
Siz
e G
rou
ps
Tec
hn
ica
l S
cree
nin
g:
Ret
urn
s to
Siz
e
Mean
Siz
eM
ean
Mo
nth
ly
Grou
pB
eta
Retu
rn (
%)
1 (
Large)
0.9
30
.89
21
.02
0.9
5
31
.08
1.1
0
41
.16
1.0
7
51
.22
1.1
7
61
.24
1.2
9
71
.33
1.2
5
81
.34
1.2
4
91
.39
1.2
9
10 (
Sm
all
)1
.44
1.5
2
So
urc
e: F
ama
and
Fre
nch
(1
99
2)
4-1
6
Aver
age
Mon
thly
Ret
urn
s an
d E
stim
ate
d B
etas
from
Ju
ly 1
963
to D
ecem
ber
1990 f
or
Ten
Bet
a G
rou
ps
Ret
urn
s to
Bet
a:
Is
Bet
a D
ead
?
Mean
Beta
Mon
thly
Mean
Gro
up
R
etu
rn
(%
)B
eta
1 (
Hig
h)
1.2
61
.68
21.3
31
.52
31.2
31
.41
41.2
31
.32
51.3
01
.26
61.3
01
.19
71.3
11
.13
81.2
61
.04
91.3
20
.92
10 (
Lo
w)
1.2
00
.80
So
urc
e: F
ama
and
Fre
nch
(1
99
2)
4-1
7
Ret
urn
s to
tw
o f
un
da
men
tal
scre
ens
So
urc
e: L
ako
nis
ho
k, S
hle
ifer
, &
Vis
hn
y, “C
on
trar
ian
In
ves
tmen
t, E
xtr
apo
lati
on
,
and
Ris
k,”
Jou
rna
l o
f F
ina
nce
, V
ol.
49
, N
o. 5
. (D
ec., 1
99
4),
p 1
55
4.
Gla
mour
Val
ue
4-1
8
Yea
r b
y Y
ear
Ret
urn
s:
Va
lue
Min
us
Gla
mo
ur
So
urc
e: L
ako
nis
ho
k, S
hle
ifer
, &
Vis
hn
y, “C
on
trar
ian
In
ves
tmen
t, E
xtr
apo
lati
on
,
and
Ris
k,”
Jou
rna
l o
f F
ina
nce
, V
ol.
49
, N
o. 5
. (D
ec., 1
99
4),
p 1
56
6.
4-1
9
P/B
an
d P
/V
Ra
tio
s: T
he
Do
w S
tock
s
19
79
-96
So
urc
e: L
ee,
Myer
s &
Sw
amin
ath
an,
“Wh
at i
s th
e In
trin
sic
Val
ue
of
the
Do
w,”
Jou
rna
l o
f F
ina
nce,
(O
ct.,
19
99
).
4-2
0
Pro
ble
ms
wit
h S
cree
nin
g
•Y
ou
cou
ld b
e lo
ad
ing u
p o
n a
ris
k f
act
or
�Y
ou
nee
d a
ris
k m
od
el
•Y
ou
are
in
dan
ger
of
trad
ing w
ith
som
eon
e w
ho
kn
ow
s m
ore
th
an
you
�Y
ou
nee
d a
mo
del
th
at a
nti
cipat
es f
utu
re p
ayo
ffs
•A
fu
ll-b
low
n f
un
dam
enta
l an
aly
sis
suppli
es t
his
4-2
1
Ass
et B
ase
d V
alu
ati
on
•V
alu
es t
he
firm
’s a
sset
s an
d t
hen
sub
trac
ts t
he
val
ue
of
deb
t:
•T
he
bal
ance
shee
t do
es t
his
cal
cula
tion
, bu
t im
per
fect
ly:
�S
har
eho
lder
s’E
qu
ity =
To
tal
Ass
ets
-Tota
l L
iab
ilit
ies
•P
roble
ms
wit
h t
his
appro
ach:
�G
etti
ng
th
e v
alu
e of
op
erat
ing a
sset
s w
hen
ther
e is
not
a m
arket
for
them
�Id
enti
fyin
g v
alu
e in
use
for
a p
arti
cula
r fi
rm
�G
etti
ng
th
e v
alu
e of
inta
ng
ible
ass
ets
(bra
nd n
ames
, R
&D
)
�G
etti
ng
th
e v
alu
e of
“syn
erg
ies”
of
asse
ts b
ein
g u
sed t
og
ether
•A
pp
lica
tion
s:
�“A
sset
-bas
ed”
firm
s su
ch a
s oil
and
gas
an
d m
iner
al p
rodu
cts
�C
alcu
lati
ng l
iqu
idat
ion v
alu
e
4-2
2
4-2
3
Bu
sin
ess
Act
ivit
ies
Bu
sin
ess
Act
ivit
ies
•F
inan
cing
Act
ivit
ies:
Rai
sin
g c
ash
fro
m i
nv
esto
rs
and
ret
urn
ing
cas
h t
o i
nv
esto
rs
•In
ves
tin
g A
ctiv
itie
s: I
nv
esti
ng
cas
h r
aise
d f
rom
inv
esto
rs i
n o
per
atio
nal
ass
ets
•O
per
atin
g A
ctiv
itie
s: U
tili
zing
in
ves
tmen
ts t
o
pro
du
ce a
nd
sel
l p
rod
uct
s
4-2
4
Wh
at
Cre
ate
s V
alu
e in
a F
irm
?W
ha
t C
rea
tes
Va
lue
in a
Fir
m ?
•E
qu
ity F
inan
cin
g A
ctiv
itie
s ?
�S
har
e Is
sues
?
�S
har
e R
epurc
has
es ?
�D
ivid
ends
?
•D
ebt
Fin
anci
ng
Act
ivit
ies
?
•In
ves
ting
an
d O
per
atin
g A
ctiv
itie
s?
�D
isti
ngu
ish a
nti
cip
ated
(ex
ante
) v
alu
e in
inves
ting
act
ivit
ies
fro
m
real
ized
(ex
post
) v
alu
e in
op
erat
ion
s
•V
alu
e is
cre
ated
in
pro
du
ct a
nd f
acto
r m
arket
s
4-2
5
•If
th
e p
rice
paid
fo
r a s
tock
is
(ex
pec
ted
payo
ff d
isco
un
ted
at
the
req
uir
ed p
ayoff
per
do
lla
r, ρ ρρρ
), t
he
sto
ck i
s a
pp
rop
riate
ly p
rice
d:
the
ma
rket
pri
ce i
s ef
fici
ent
Th
e N
o A
rbit
rag
e C
on
dit
ion
(N
A)
Th
e N
o A
rbit
rag
e C
on
dit
ion
(N
A)
•O
r, p
rice
is
effi
cien
t if
it
equ
als
th
e ex
pec
ted
ret
urn
ca
pit
ali
zed
at
the
req
uir
ed r
ate
-of-
retu
rn:
•O
r, t
od
ay
’s p
rice
(P
0)
mu
st b
e su
ch t
hat
the
req
uir
ed r
ate
-of-
retu
rn,
ρ ρρρ-
1,
wil
l eq
ua
l th
e (e
xp
ecte
d)
rate
-of-
retu
rn:
Req
uir
ed R
ate
-of
Ret
urn
=
E
xp
ecte
d R
ate
-of-
Ret
urn
E
dP
Pρ
11
0
+=
10
11
0−−
+=
E
Pd
PP
ρ
0
01
11
P
Pd
PE
−+
=−
ρ
4-2
6
•If
NA
ho
lds,
th
e m
ark
et i
s ef
fici
ent
for
tha
t st
ock
: th
ere
is n
o a
rbit
rage
op
po
rtu
nit
y
•A
ny
dis
crep
an
cy b
etw
een
ex
pec
ted
an
d r
equ
ired
rate
-of-
retu
rn,
is a
n
arb
itra
ge
op
port
un
ity
that,
if
exp
loit
ed,
wil
l p
rofi
t th
e a
rbit
rag
e tr
ad
er.
•A
n a
rbit
rag
e o
pp
ort
un
ity
ari
ses
if
Arb
itra
ge
Tra
din
g S
tra
teg
ies
Arb
itra
ge
Tra
din
g S
tra
teg
ies
•If
then
BU
Y
Th
e d
iffe
ren
ce i
s ca
lled
th
e ex
pec
ted
ab
norm
al
retu
rna
nd
th
e ru
le c
an
be
rest
ate
d a
s: B
UY
if
the
exp
ecte
d a
bn
orm
al
retu
rn i
s p
osi
tiv
e, a
nd
SE
LL
if
neg
ati
ve.
If
it i
s ze
ro, d
o n
oth
ing (
HO
LD
)
•If
then
SE
LL
10
01
1−
>−
+E
P
Pd
Pρ
10
01
1−
<−
+E
P
Pd
Pρ
4-2
7
Mea
suri
ng R
etu
rns
Mea
suri
ng R
etu
rns
Hew
lett
Hew
lett
-- Pack
ard
: R
etu
rns
for
1991
Pack
ard
: R
etu
rns
for
1991
__________________________________________________________
Hew
lett
-Pac
kar
d C
om
pan
y:
Ret
urn
s fo
r 1991
Req
uir
ed r
eturn
is
12%
Pri
ce a
t en
d o
f 1991
$50.3
75
1991 D
ivid
end
.480
1991 P
ayoff
50.8
55
Pri
ce a
t en
d o
f 1990
26.0
00
1991 R
eturn
24.8
55
Rat
e of
retu
rn =
$24.8
55 /
26.0
= 9
5.6
%
Log
o u
sed
wit
h p
erm
issi
on
of
Hew
lett
Pac
kar
d
4-2
8
Hew
lett
Hew
lett
-- Pa
cka
rd:
Ret
urn
s fo
r 1
99
1P
ack
ard
: R
etu
rns
for
19
91
____________________________________________________________
Req
uir
ed r
eturn
is
12%
Pri
ce a
t en
d o
f 1991
$50.3
75
1991 D
ivid
end
.480
1991 P
ayoff
50.8
55
Pri
ce a
t en
d o
f 1990
26.0
00
1991 R
eturn
24.8
55
Rat
e of
retu
rn =
$24.8
55/2
6.0
00
= 95.6
%N
orm
al r
eturn
: $
26 x
.12
3.1
20
Abnorm
al r
eturn
21.7
35
Abnorm
al r
ate
of
retu
rn =
21.7
35/2
6.0
0 =
83.6
%
Rat
e of
retu
rn
95.6
%−
Norm
al r
eturn
12.0
%A
bnorm
al r
ate
of
retu
rn83.6
%____________________________________________________________
Log
o u
sed
wit
h p
erm
issi
on
of
Hew
lett
Pac
kar
d
4-2
9
Th
e P
roce
ss o
f F
un
da
men
tal
An
aly
sis
Th
e P
roce
ss o
f F
un
da
men
tal
An
aly
sis
•A
val
uat
ion m
odel
guid
es t
he
pro
cess
•F
ore
cast
ing i
s at
the
hea
rt o
f th
e pro
cess
and a
val
uat
ion m
odel
spec
ifie
s w
hat
is
to b
e
fore
cast
ed (
Ste
p 3
) a
nd h
ow
a f
ore
cast
is
conver
ted t
o a
val
uat
ion (
Ste
p 4
). W
hat
is
to b
e
fore
cast
ed (
Ste
p 3
) dic
tate
s th
e in
form
atio
n a
nal
ysi
s (S
tep 2
)
Ste
p 1
-K
now
ing
th
e B
usi
nes
s
•Th
e P
rod
uct
s
•Th
e K
no
wle
dg
e B
ase
•Th
e C
om
pet
itio
n
•Th
e R
egu
lato
ry C
on
stra
ints
Ste
p 2
-A
na
lyzi
ng
In
form
ati
on
•In
Fin
anci
al S
tate
men
ts
•Ou
tsid
e o
f F
inan
cial
Sta
tem
ents
•Ste
p3
-F
ore
cast
ing
Pay
off
s
•Mea
suri
ng
Val
ue
Add
ed
•Fore
cast
ing
Val
ue
Ad
ded
•Ste
p 4
-C
on
ver
t F
ore
cast
s to
a V
alu
ati
on
Ste
p 5
-T
rad
ing
on
th
e V
alu
ati
on
•Ou
tsid
e In
ves
tor
Co
mp
are
Val
ue
wit
h P
rice
to
BU
Y,
SE
LL
, or
HO
LD
•In
sid
e In
ves
tor
Co
mp
are
Val
ue
wit
h C
ost
to
AC
CE
PT
or
RE
JEC
T S
trat
egy
Str
ateg
y
4-3
0
Va
lua
tio
n M
od
els:
Go
ing
Co
nce
rns
Va
lua
tio
n M
od
els:
Go
ing
Co
nce
rns
CF
1C
F 2C
F3
CF4
CF
5
A F
irm
12
34
50
d1
d2
d3
d4
d5
Div
iden
d
Flo
w
12
34
50
TV
T
T d T
Eq
uit
y
Th
e te
rmin
al v
alu
e, T
VT
is t
he
pri
ce p
ayo
ff,
PT
wh
en t
he
shar
e is
so
ld
Val
uat
ion
iss
ues
:T
he
fore
cast
tar
get
: div
iden
ds,
cas
h f
low
, ea
rnin
gs?
Th
e ti
me
ho
rizo
n:
T =
5,
10,
?
Th
e te
rmin
al v
alue
Th
e dis
coun
t ra
te
∞
4-3
1
Th
e D
ivid
end
Dis
cou
nt
Mo
del
: T
arg
etin
g
Th
e D
ivid
end
Dis
cou
nt
Mo
del
: T
arg
etin
g
Div
iden
ds
Div
iden
ds
•D
DM
:
Pro
ble
ms:
How
far
does
one
pro
ject
?
•D
oes
pro
vid
e a
good e
stim
ate
of
VE
0?
(i)
D
ivid
end p
oli
cy c
an b
e ar
bit
rary
and n
ot
linked
to v
alue
added
.
(ii)
T
he
firm
can
borr
ow
to p
ay d
ivid
ends;
this
does
not
crea
teval
ue
(iii
) T
hin
k o
f a
firm
that
“pay
s no d
ivid
ends”
•T
he
div
idend i
rrele
vancy
conce
pt
•T
he
div
idend c
onundru
m:
�E
quit
y v
alue
is b
ased
on f
utu
re d
ivid
ends,
but
fore
cast
ing d
ivid
ends
over
fin
ite
hori
zons
does
not
giv
e an
indic
atio
n o
f th
is v
alue
•C
oncl
usi
on:
Focu
s on c
reat
ion o
f w
ealt
h r
ather
than
dis
trib
uti
on
of
wea
lth.
31
20
23
E
EE
E
dd
dV
ρρ
ρ=
++
+⋯
31
20
23
ET T
EE
EE
dd
dd
Vρ
ρρ
ρ=
++
++
⋯
4-3
2
Som
e M
ath
: T
he
Valu
e of
a P
erp
etu
ity a
nd
a
Som
e M
ath
: T
he
Valu
e of
a P
erp
etu
ity a
nd
a
Per
pet
uit
y w
ith
Gro
wth
Per
pet
uit
y w
ith
Gro
wth
Th
e V
alu
e of
a P
erp
etu
ity
A p
erp
etuit
y i
s a
con
stan
t st
ream
th
at c
onti
nu
es w
itho
ut
end
. A
co
nst
ant
stre
am i
s so
met
imes
ref
erre
d t
o a
s an
annuit
y, so
a p
erp
etuit
y i
s an
ann
uit
y t
hat
co
nti
nu
es f
ore
ver
. T
o v
alu
e th
at s
trea
m, o
ne
cap
ital
izes
th
e co
nst
ant
amo
unt
exp
ecte
d. If
th
e div
iden
d e
xp
ecte
d n
ext
yea
r is
exp
ecte
d t
o b
e a
per
pet
uit
y, th
e v
alu
e of
the
div
iden
d
stre
am i
s
Va
lue
of
a p
erp
etu
al
div
iden
d s
trea
m =
Th
e V
alu
e of
a P
erp
etu
ity w
ith
Gro
wth
If a
n a
mo
unt
is f
ore
cast
ed t
o g
row
at
a co
nst
ant
rate
, it
s v
alu
eca
n b
e ca
lcula
ted
by c
apit
aliz
ing
th
e am
ou
nt
at t
he
requ
ired
ret
urn
ad
just
ed f
or
the
gro
wth
rat
e:
Va
lue
of
a d
ivid
end
gro
win
g a
t a
co
nst
an
t ra
te=
1
10
−=
E
Ed
Vρ
g
dV
E
E
−=
ρ1
0
4-3
3
Ter
min
al
Va
lues
fo
r th
e D
DM
Mo
del
Ter
min
al
Va
lues
fo
r th
e D
DM
Mo
del
A.
Cap
ital
ize
exp
ecte
d t
erm
inal
div
iden
ds
B.
Cap
ital
ize
exp
ecte
d t
erm
inal
div
iden
ds
wit
h g
row
th
Wil
l it
wo
rk?
T1
TT
EdT
VP
1ρ
+=
=−
T1
TT
EdT
VP
gρ
+=
=−
4-3
4
Div
iden
d D
isco
un
t A
na
lysi
s:
Div
iden
d D
isco
un
t A
na
lysi
s:
Ad
va
nta
ges
an
d D
isa
dv
an
tages
Ad
va
nta
ges
an
d D
isa
dv
an
tages
Adva
nta
ges
Adva
nta
ges
•E
asy
co
nce
pt:
div
iden
ds
are
wh
at s
har
eho
lder
s g
et, so
fore
cast
th
em
•P
red
icta
bil
ity:
div
iden
ds
are
usu
ally
fai
rly s
tab
le i
n t
he
short
run
so
div
iden
ds
are
easy
to
fore
cast
(in
th
e sh
ort
run
)
Dis
adva
nta
ges
Dis
adva
nta
ges
•R
elev
an
ce:
div
iden
ds
pay
ou
t is
n
ot
rela
ted
to
val
ue,
at
leas
t in
th
e sh
ort
ru
n;
div
iden
d
fore
cast
s ig
nore
th
e ca
pit
al
gai
n c
om
po
nen
t of
pay
off
s.
Wh
en I
t W
ork
s B
est
Wh
en I
t W
ork
s B
est
•W
hen
pay
ou
t is
per
man
entl
y t
ied
to t
he
val
ue
gen
erat
ion i
n t
he
firm
. F
or
exam
ple
, w
hen
a f
irm
has
a f
ixed
pay
out
rati
o (
div
iden
ds/
earn
ing
s).
4-3
5
Ca
sh F
low
s fo
r a
Go
ing
Co
nce
rnC
ash
Flo
ws
for
a G
oin
g C
on
cern
Cash
flo
w f
rom
op
erati
on
s (i
nfl
ow
s)
Cash
in
ves
tmen
t (o
utf
low
s)
Fre
e ca
sh f
low
Tim
e, t
C1
C2
C3
C4
I 1I 2
I 3I 4
C1-I
1C
2-I
2C
3-I
3C
4-I
4
C5
I 5
C5-I
5
12
43
5
Fre
e ca
sh f
low
is
cash
flo
w f
rom
op
erat
ion
s th
at r
esu
lts
fro
m i
nv
estm
ents
min
us
cash
use
d t
o m
ake
inv
estm
ents
.
4-3
6
Th
e D
isco
un
ted
Cash
Flo
w (
DC
F)
Mod
elT
he
Dis
cou
nte
d C
ash
Flo
w (
DC
F)
Mod
el
Cas
h f
low
fro
m
op
erat
ions
(infl
ow
s)
C
1
C
2
C
3
C4
C
5
--->
C
ash
in
ves
tmen
t
I
1
I2
I 3
I 4
I
5
--
->
(outf
low
s)
Fre
e ca
sh f
low
C
1 −
I1
C2 −
I2
C3 −
I3
C4
−
I4
C
5 −
I5 -
-->
__
__
__
__
___
__
__
__
__
__
___
__
__
__
__
___
__
__
__
__
__
___
--->
Tim
e, t
1
2
3
4
5
D 0T F
T
T F
TT
3 F
33
2 F
22
F
11
E 0V
VC
IC
IC
IC
IC
V−
ρ+
ρ−−
−−
+ρ−
+ρ−
+ρ−
=
F OV
D 0F 0
E 0V
VV
−=
4-3
7
Th
e C
on
tin
uin
g V
alu
e fo
r th
e D
CF
Mod
elT
he
Co
nti
nu
ing V
alu
e fo
r th
e D
CF
Mod
el
A.
Cap
ital
ize
term
inal
fre
e ca
sh f
low
B. C
apit
aliz
e te
rmin
al f
ree
cash
flo
w w
ith
gro
wth
Wil
l it
wo
rk?
1ρ
IC
CV
F
1T
1T
T−−
=+
+
gρ
IC
CV
F
1T
1T
T−−
=+
+
4-3
8
DC
F V
alu
ati
on
: T
he
Coca
DC
F V
alu
ati
on
: T
he
Coca
-- Cola
Com
pan
yC
ola
Com
pan
y
1999
2000
2001
2002
2003
2004
Cas
h f
rom
oper
atio
ns
3,6
57
4,0
97
4,7
36
5,4
57
5,9
29
Cas
h i
nves
tmen
ts947
1,1
87
1,1
67
906
618
Req
uir
ed r
eturn
is
9%
Book v
alue
of
net
deb
t is
4,4
35
Shar
es o
uts
tandin
g a
re 2
,472
Ass
um
e gro
win
g F
CF
at
5%
aft
er p
erio
d T
Val
ue
per
shar
e ?
4-3
9
DC
F V
alu
ati
on
: T
he
Coca
DC
F V
alu
ati
on
: T
he
Coca
-- Cola
Com
pan
yC
ola
Com
pan
y
In m
illi
on
s of
doll
ars
exce
pt
shar
e an
d p
er-s
har
e n
um
ber
s. R
equir
ed r
eturn
for
the
firm
is
9%
19
99
2000
2001
2002
2003
2004
Cas
h f
rom
op
erat
ion
s3
,657
4,0
97
4,7
36
5,4
57
5,9
29
Cas
h i
nv
estm
ents
947
1,1
87
1,1
67
906
618
Fre
e ca
sh f
low
2,7
10
2,9
10
3,5
69
4,5
51
5,3
11
Dis
cou
nt
rate
(1
.09)t
1.0
9 1
.188
1 1
.29
50
1.4
11
6 1
.538
6
Pre
sen
t v
alu
e of
free
cas
h f
low
s2
,486
2,4
49
2,7
56
3,2
24
3,4
52
Tota
l p
rese
nt
val
ue
to 2
004
14
,367
Co
nti
nuin
g v
alu
e (C
V)*
13
9,4
14
Pre
sen
t v
alu
e of
CV
90
,611
Ente
rpri
se v
alu
e1
04
,978
Bo
ok
val
ue
of
net
deb
t4
,435
Val
ue
of
equit
y (
)1
00
,543
Sh
ares
ou
tsta
nd
ing
2,4
72
Val
ue
per
sh
are
$40
.67
*C
V =
5
,311
x 1
.05
= 1
39
,414
1.0
9 -
1.0
5
Pre
sen
t v
alu
e of
CV
=
13
9,4
14
= 90
,611
1.5
386
4-4
0
Th
e D
CF
Mod
el:
Th
e D
CF
Mod
el:
Wil
l it
work
for
Wal
Wil
l it
work
for
Wal --
Mart
Sto
res?
Mart
Sto
res?
Wal
-Mar
t S
tore
s, I
nc.
(Fis
cal
yea
rs e
ndin
g J
anu
ary 3
1. A
mounts
in m
illi
ons
of
doll
ars.
)
19
88
1989
1990
1991
1992
1993
19
94
19
95
19
96
Cas
h f
rom
op
erat
ions
53
6828
968
1,4
22
1,5
53
1,5
40
2,5
73
3,4
10
2,9
93
Cas
h i
nves
tmen
ts62
7541
894
1,5
26
2,1
50
3,5
06
4,4
86
3,7
92
3,3
32
Fre
e ca
sh f
low
(91)
287
74
(104)
(597)
(1,9
66)
(1,9
13
)(3
82)
(33
9)
Div
iden
ds
per
shar
e0.0
30.0
40.0
60.0
70.0
90.1
10
.13
0.1
70
.20
Pri
ce p
er s
har
e6⅞
8½
10⅝
16½
27
32½
26
½2
5⅞
24⅜
4-4
1
Wh
y F
ree
Cash
Flo
w i
s n
ot
a V
alu
eW
hy F
ree
Cash
Flo
w i
s n
ot
a V
alu
e-- A
dd
ed C
on
cep
tA
dd
ed C
on
cep
t
•C
ash f
low
fro
m o
per
atio
ns
(val
ue
added
) is
red
uce
d b
y
inves
tmen
ts (
whic
h a
lso a
dd v
alue)
: in
ves
tmen
ts a
re
trea
ted a
s val
ue
loss
es
•V
alue
rece
ived
is
not
mat
ched
agai
nst
val
ue
surr
ender
ed
to g
ener
ate
val
ue
A f
irm
red
uce
s fr
ee c
ash f
low
by i
nves
ting a
nd i
ncr
ease
s
free
cas
h f
low
by r
educi
ng i
nves
tmen
ts:
free
cas
h f
low
is
par
tial
ly a
liq
uid
atio
n c
once
pt
Note
: an
alyst
s fo
reca
st e
arnin
gs,
not
cash
flo
ws
4-4
2
Dis
cou
nte
d C
ash
Flo
w A
na
lysi
s:
Dis
cou
nte
d C
ash
Flo
w A
na
lysi
s:
Ad
va
nta
ges
an
d D
isa
dv
an
tages
Ad
va
nta
ges
an
d D
isa
dv
an
tages
Ad
van
tag
esA
dva
nta
ges
•E
asy
con
cept:
cash
fl
ow
s ar
e “r
eal”
and
easy
to t
hin
k a
bout;
th
ey a
re n
ot
affe
cted
by
acc
ounti
ng r
ule
s•
Fam
ilia
rity
:is
a
stra
ight
appli
cati
on o
f fa
mil
iar
net
pre
sent
val
ue
tech
niq
ues
Dis
adva
nta
ges
Dis
adva
nta
ges
•S
usp
ect
con
cept:
�fr
ee c
ash
flo
w d
oes
no
t m
easu
re v
alu
e ad
ded
in
th
e sh
ort
run;
val
ue
gai
ned
is
not
mat
ched
wit
h v
alu
e g
iven
up
.
�fr
ee c
ash
flo
w f
ails
to r
eco
gniz
e v
alu
e g
ener
ated
th
at d
oes
not
invo
lve
cash
flo
ws
�in
ves
tmen
t is
tre
ated
as
a lo
ss o
f v
alu
e
�fr
ee c
ash
flo
w i
s p
artl
y a
liq
uid
atio
n c
on
cep
t; f
irm
s in
crea
se f
ree
cash
flo
w b
y c
utt
ing
bac
k o
n i
nv
estm
ents
.
•F
ore
cast
hori
zon
s:ty
pic
ally
req
uir
es f
ore
cast
s fo
r lo
ng
per
iods;
ter
min
al v
alues
for
sho
rter
per
iod
s ar
e har
d t
o
calc
ula
te w
ith a
ny r
elia
bil
ity
•V
ali
dati
on
:it
is
har
d t
o v
alid
ate
free
cas
h f
low
fore
cast
s •
Not
ali
gn
ed w
ith
wh
at
peo
ple
fo
reca
st:
anal
yst
s fo
reca
st
earn
ings,
not
free
cas
h f
low
; ad
just
ing
ear
nin
gs
fore
cast
s to
fr
ee
cash
fo
reca
sts
req
uir
es
furt
her
fo
reca
stin
g
of
accr
ual
s.
Wh
en I
t W
ork
s B
est
Wh
en I
t W
ork
s B
est
•W
hen
th
e in
ves
tmen
t p
atte
rn i
s su
ch a
s to
pro
du
ce c
on
stan
t fr
ee c
ash
flo
w o
r fr
ee c
ash
flo
w g
row
ing
at
a co
nst
ant
rate
.
4-4
3
Fea
ture
s o
f th
e In
com
e S
tate
men
tF
eatu
res
of
the
Inco
me
Sta
tem
ent
1. D
ivid
ends
don’t
aff
ect
inco
me
2. In
ves
tmen
t does
n’t
aff
ect
inco
me
3. T
her
e is
a m
atch
ing o
f
�V
alu
e ad
ded
(rev
enu
es)
�V
alu
e lo
st (
expen
ses)
�N
et v
alu
e ad
ded
(net
in
com
e)
4. A
ccru
als
adju
st c
ash f
low
s
Acc
rual
s
Val
ue
add
ed t
hat
is n
ot
cash
flo
w
Adju
stm
ents
to c
ash i
nfl
ow
s
that
are
not
val
ue
add
ed
4-4
4
Ea
rnin
gs
an
d C
ash
Flo
ws
Ea
rnin
gs
an
d C
ash
Flo
ws
Ear
nin
gs
= [
C -
I] -
i +
I +
acc
rual
s
= C
-i
+ a
ccru
als
•T
he
earn
ing
s ca
lcu
lati
on
ad
ds
bac
k i
nv
estm
ents
and
pu
ts t
hem
bac
k i
n t
he
bal
ance
sh
eet.
It
also
add
s ac
cru
als.
4-4
5
Th
e a
rtic
ula
tio
n o
f th
e fi
na
nci
al
sta
tem
ents
T
he
art
icu
lati
on
of
the
fin
an
cia
l st
ate
men
ts
thro
ug
h t
he
reco
rdin
g o
f ca
sh f
low
s a
nd
acc
rua
lsth
rou
gh
th
e re
cord
ing
of
cash
flo
ws
an
d a
ccru
als
Inves
tmen
t an
d d
isin
ves
tmen
t b
y o
wn
ers
Ear
nin
gs
N
et c
ha
ng
e in
ow
ner
s’ e
qu
ity
SStt aa
tt eemm
eenn
tt ooff
SShh
aarreehh
ooll dd
eerrss ’’
EEqq
uuii tt
yy ––
yy
eeaarr 11
Cas
h f
rom
op
erat
ion
s
+ A
ccru
als N
et i
nco
me
II nnccoo
mmee SS
tt aatt ee
mmeenn
tt ––
yyeeaa
rr 11
Cas
h f
rom
op
erat
ion
s C
ash
fro
m i
nves
tin
g
Deb
t fi
nan
cin
g
Net
ch
an
ge
in c
ash
CCaa
ss hh FF
ll ooww
SStt aa
tt eemm
eenn
tt ––
yyeeaa
rr 11
Cas
h0
+ O
ther
Ass
ets 0
Tota
l A
sset
s 0
- L
iab
ilit
ies 0
Ow
ner
s’ e
qu
ity
0
Cas
h1
+ O
ther
Ass
ets 1
Tota
l A
sset
s 1
- L
iab
ilit
ies 1
Ow
ner
s’ e
qu
ity
1
EEnn
ddii nn
gg BB
aall aa
nnccee SS
hheeeett
––
yyeeaa
rr 11
Beg
inn
ing
sto
cks
Flo
ws
En
din
g s
tock
s
EEnn
ddii nn
gg BB
aall aa
nnccee SS
hheeeett
––
yyeeaa
rr 00
E
qu
ity f
inan
cin
g
Net
ca
sh f
low
s fr
om
all
act
ivit
ies
incr
ease
s ca
sh i
n t
he
bala
nce
shee
t
Ca
sh f
rom
op
erati
on
s in
crea
ses
net
in
com
e a
nd
sh
are
ho
lder
s’eq
uit
y
Ca
sh i
nve
stm
ents
in
crea
se o
ther
ass
ets
Ca
sh f
rom
deb
t fi
na
nci
ng
in
crea
ses
liab
ilit
ies
Ca
sh f
rom
eq
uit
y fi
nan
cing
in
crea
ses
sha
reh
old
ers’
equ
ity
Acc
rua
ls i
ncr
ease
net
in
com
e, s
ha
rehold
ers’
equ
ity,
ass
ets
an
d l
iabil
itie
s
5-4
6
5-4
7
Va
lua
tio
n o
f In
ves
tmen
tsV
alu
ati
on
of
Inv
estm
ents
Va
lue
of
Inv
estm
ent
= B
oo
k V
alu
e of
Inv
estm
ent
+ V
alu
e a
dd
ed f
rom
Inv
estm
ent
Va
lue
ad
ded
fro
m I
nv
estm
ent
is e
xp
ress
ed t
hou
gh
Res
idu
al
Earn
ings
Res
idu
al
Ea
rnin
gs:
Ea
rnin
gs
ab
ov
e o
r b
elo
w a
no
rma
l le
vel
.
Q:
No
rma
l L
evel
?
A:
Req
uir
ed r
etu
rn X
In
ves
tmen
t
5-4
8
Va
luin
g a
On
eV
alu
ing
a O
ne-- P
erio
d P
roje
ct (
1)
Per
iod
Pro
ject
(1
)
Inv
estm
ent
$
400
Req
uir
ed r
etu
rn 1
0%
Rev
enu
e fo
reca
st $
440
Ex
pen
se f
ore
cast
$
400
Fo
reca
sted
ea
rnin
gs
$ 40
(Rev
enu
e $4
40
-D
epre
ciati
on
$4
00
)
Th
is i
s a Z
ero
-RE
pro
ject
Th
is i
s a z
ero N
PV
pro
ject
:
DC
F V
alu
ati
on
:
40
0
1.1
0
0
4
00
Val
ue
0
40
0)
x
(0.1
0 -
40
)In
ves
tmen
tre
turn
x
R
equ
ired
(E
arn
ing
sea
rnin
gs
R
esid
ual
11
=
+===
−=
40
01
0.
144
0=
=V
5-4
9
Va
luin
g a
On
eV
alu
ing
a O
ne-- P
erio
d P
roje
ct (
2)
Per
iod
Pro
ject
(2
)
Inves
tmen
t $400
Req
uir
ed r
eturn
10%
Rev
enue
fore
cast
$448
Expen
se f
ore
cast
$
400
Ear
nin
gs
fore
cast
$ 48 (
Rev
enue
$448-
Dep
reci
atio
n $
400)
1R
esid
ual
ear
nin
gs
48
- (
0.1
0 x
40
0)
= 8
8V
alu
e
Pro
ject
40
0
4
07
.27
1.1
0
= =+
=
Th
e p
roje
ct a
dd
s v
alu
e
==
27
.407
1.1
0
448
val
ue
DC
F
5-5
0
Va
luin
g a
Sa
vin
gs
Acc
ou
nt
Va
luin
g a
Sa
vin
gs
Acc
ou
nt
Forecast
Year
__
__
___
___
___
___
__
__
__
___
___
___
__
__
__
___
2
00
0
200
1
2
00
2
20
03
20
04
200
5
Earn
ing
s w
ith
draw
n e
ach
yea
r (f
ull
payo
ut)
Earn
ings
5
5
5
5
5
Div
iden
ds
5
5
5
5
5
Bo
ok
valu
e
10
0
1
00
10
0
1
00
10
0
100
R
esi
dual
earn
ing
s
0
0
0
0
0
__
__
__
__
___
___
___
__
__
__
___
___
___
__
__
__
___
___
___
__
__
__
___
__
__
__
___
___
___
__
__
__
___
___
___
No w
ith
dra
wa
ls (
zero
payo
ut)
Earn
ings
5
5
.25
5.5
1
5.7
9
6.0
8
Div
iden
ds
0
0
0
0
0
B
oo
k v
alu
e
10
0
10
5
11
0.2
5
11
5.7
6
121
.55
1
27.6
3
Resi
dual
earn
ing
s
0
0
0
0
0
__
__
__
__
___
___
___
__
__
__
___
___
___
__
__
__
___
___
___
__
__
__
___
__
__
__
___
___
___
__
__
__
___
___
___
Val
ue
= B
ook
Val
ue
+ P
rese
nt
Val
ue
of
Res
idu
al E
arnin
gs
= 1
00
+ 0
= 1
00
5-5
1
Les
son
s fr
om
th
e S
av
ing
s A
cco
un
tL
esso
ns
fro
m t
he
Sa
vin
gs
Acc
ou
nt
1.
An a
sset
is
wort
h a
pre
miu
m o
r dis
count
to i
ts b
ook v
alue
only
if
the
book v
alue
is
expec
ted t
o e
arn n
on-z
ero r
esid
ual
ear
nin
gs.
2.
Res
idual
ear
nin
gs
tech
niq
ues
rec
ogniz
e th
at e
arnin
gs
gro
wth
does
not
add v
alue
if
that
gro
wth
com
es f
rom
inves
tmen
t ea
rnin
g a
t th
e re
quir
ed r
eturn
.
3.
Even
though a
n a
sset
does
not
pay
div
iden
ds,
it
can b
e val
ued
fro
m i
ts b
ook v
alue
and e
arnin
gs
fore
cast
s.
4.
The
val
uat
ion o
f th
e sa
vin
gs
acco
unt
does
not
dep
end o
n d
ivid
end
pay
out.
T
he
two
scen
ario
s hav
e dif
fere
nt
expec
ted d
ivid
ends,
but
the
sam
e val
ue.
5.
The
val
uat
ion o
f a
savin
gs
acco
unt
is u
nre
late
d t
o f
ree
cash
flo
ws:
T
he
two
acco
unts
hav
e th
e sa
me
val
ue,
but
dif
fere
nt
free
cas
h f
low
.
5-5
2
Pri
ceP
rice
-- toto
-- Bo
ok
Ra
tio
Bo
ok
Ra
tio
P/B
rat
io i
s bas
ed o
n e
xpec
ted f
utu
re e
arnin
gs
that
hav
e bee
n n
ot
yet
rec
ogniz
ed t
o t
he
book v
alue.
Thus,
if
�ex
pec
ted f
utu
re e
arnin
gs
are
equal
to r
equir
ed e
arnin
gs
(i.e
., n
orm
al e
arnin
gs)
then
we
get
“n
orm
al”
P/B
= 1
.
�ex
pec
ted f
utu
re e
arnin
gs
are
above
requir
ed e
arnin
gs
(i.e
., p
osi
tive
abnorm
al e
arnin
gs)
then
we
get
P
/B >
1.
�ex
pec
ted f
utu
re e
arnin
gs
are
bel
ow
req
uir
ed e
arnin
gs
(i.e
., n
egat
ive
abnorm
al e
arnin
gs)
then
we
get
P
/B <
1.
5-5
3
A M
od
el f
or
An
cho
rin
g V
alu
e o
n B
oo
k V
alu
eA
Mo
del
fo
r A
nch
ori
ng
Va
lue
on
Bo
ok
Va
lue
()
E1
20
02
3
EE
E
RE
RE
RE
Val
ue o
f co
mm
on
eq
uit
y
V..
.ρ
ρρ
wh
ere
RE
is
resi
du
al e
arn
ing
s fo
r eq
uit
y:
Resi
du
al
earn
ing
s c
om
pre
hen
siv
e earn
ing
s -
(req
uir
ed
r
etu
rn f
or
eq
uit
B=
++
++
=
tt
Et
1
y x
beg
inn
ing
of
peri
od
bo
ok
valu
e)
RE
Earn
(ρ1
)B
--
−=
−−
5-5
4
Der
iva
tion
of
the
Eq
uit
y V
alu
ati
on
Mo
del
: O
ne
Per
iod
Der
iva
tion
of
the
Eq
uit
y V
alu
ati
on
Mo
del
: O
ne
Per
iod
Val
uin
g a
one-
per
iod p
ayoff
equat
ion:
Subst
itute
for
the
expec
ted d
ivid
end
to g
et
or
The
amount,
i
s ca
lled
Res
idu
al
Earn
ings
E
10
11
0ρ
P)
B(B
Ear
nin
gs
P+
−−
=
)B
(BE
arn
ing
sd
01
11
−−
=
E
11
E
0E
10
0ρ
BP
ρ
1)B
(ρE
arnin
gs
BP
−+
−−
+=
()
0E
1B
1ρ
Ear
nin
gs
−−
()
E
11
0ρ
dP
P+
=
5-5
5
Der
iva
tion
of
the
Eq
uit
y V
alu
ati
on
Mo
del
: D
eriv
ati
on
of
the
Eq
uit
y V
alu
ati
on
Mo
del
: M
ult
iper
iod
Mu
ltip
erio
d
Su
bst
itu
tin
g c
om
pre
hen
sive
earn
ings
an
d b
ook
valu
e fo
r d
ivid
end
s in
each
per
iod
,
If w
e se
t
As
effi
cien
t pri
ces
equal
intr
insi
c val
ues
, th
en
()
()
()
T E
TT
T E
1T
ET
2 E
1E
2
E
0E
10
0
ρ
BP
ρ
B1
ρE
arn
ing
s..
.
...
ρ
B1
ρE
arn
ing
s
ρ
B1
ρE
arn
ing
sB
P
−+
−−
+
+−
−+
−−
+=
−
()
1t
Et
tB
1ρ
Ear
nin
gs
RE
−−
−=
T E
TT
T E
T
2 E
2
E
10
0ρ
BP
ρRE
....
ρRE
ρRE
BP
−+
++
++
=
T E
TE T
T E
T
2 E
2
E
10
E 0ρ
BV
ρRE
.....
ρRE
ρRE
BV
−+
++
++
=
5-5
6
Th
e C
on
tin
uin
g V
alu
e fo
r th
e R
E M
od
el
Th
e C
on
tin
uin
g V
alu
e fo
r th
e R
E M
od
el
Pre
miu
m
i
s ass
esse
d t
hro
ug
h t
he
pre
sen
t valu
e of
resi
du
al
earn
ings:
i.e.
, th
e c
on
tin
uin
g v
alu
e o
f th
e m
od
el.
Case
1:
RE
is
fore
cast
ed t
o b
e ze
ro i
n p
erp
etu
ity a
fter
T
So
Case
1I:
RE
is
fore
cast
ed t
o b
e co
nst
an
t in
per
pet
uit
y a
fter
T
So
Case
1II
: R
E i
s fo
reca
sted
to g
row
at
con
stan
t ra
te i
n p
erp
etu
ity a
fter
T
So
0C
VT=(
)T
E TB
V− 1
RE
CV
E
1+
TT
−=
ρ
gρRE
CV
E
1+
TT
−=
()
TC
V
5-5
7
Alt
ern
ati
ve
Mea
sure
of
Res
idu
al
Ea
rnin
gs
Alt
ern
ati
ve
Mea
sure
of
Res
idu
al
Ea
rnin
gs
Res
idual
ear
nin
gs
is t
he
rate
of
retu
rn o
n e
quit
y, R
OC
E,
expre
ssed
as
a doll
ar e
xce
ss r
eturn
on e
quit
y r
ather
than
a r
atio
. B
ut
it c
an b
e ex
pre
ssed
in r
atio
form
:
()
()
[]
1t
Et
1t
Et
B1
RO
CE
B1
Ear
nin
gs
−−
−ρ
−=
−ρ
−
tt
t-1
Co
mp
reh
ensi
ve
earn
ing
s to
com
mon
RO
CE
Boo
k v
alu
e=
5-5
8
Dri
ver
s o
f R
esid
ua
l E
arn
ing
sD
riv
ers
of
Res
idu
al
Ea
rnin
gs
Tw
o D
riv
ers:
1.
RO
CE
•If
fore
cast
ed R
OC
E e
qu
als
the
requ
ired
ret
urn
, th
en R
E w
ill
be
zero
,
and V
= B
•If
fore
cast
ed R
OC
E i
s g
reat
er t
han
th
e re
qu
ired
ret
urn
, th
en V
> B
•If
fore
cast
ed R
OC
E i
s le
ss t
han
th
e re
quir
ed r
eturn
, th
en V
< B
2. G
row
th i
n b
ook
val
ue
(net
ass
ets)
pu
t in
pla
ce t
o e
arn t
he
RO
CE
RE
wil
l ch
ange
wit
h c
han
ge
wit
h R
OC
E a
nd
gro
wth
in b
oo
k v
alu
e
5-5
9
P/B
, R
OC
E a
nd
Gro
wth
in
Bo
ok
Va
lue
P/B
, R
OC
E a
nd
Gro
wth
in
Bo
ok
Va
lue
P/B
in
2
00
3R
OC
E i
n 2
00
4G
row
th R
ate
fo
r
Bo
ok
Va
lue
in 2
00
4
Th
e G
ap
In
c.4
.23
28
.1%
30
.7%
Gen
era
l E
lect
ric
Co
.4
.16
22
.3%
39
.3%
Ver
izo
n C
om
mu
nic
ati
on
s In
c.3
.32
23
.4%
12
.2%
Cit
igro
up
In
c.2
.79
17
.4%
11
.5%
Ho
me
Dep
ot
Inc.
2.6
21
9.2
%1
3.2
%
Gen
era
l M
oto
rs C
orp
.1
.19
11
.1%
9.7
%
Fed
era
ted
Dep
art
men
t S
tore
s0
.92
12
.0%
3.1
%
5-6
0
Va
luin
g
Va
luin
g F
lan
iga
nF
lan
iga
n’’ ss
En
terp
rise
s
En
terp
rise
s
Ca
se 1
: Z
ero
RE
aft
er T
Ca
se 1
: Z
ero
RE
aft
er T
Fo
reca
st Y
ear
19
99
20
00
20
01
2
00
2
20
03
Ep
s0
.73
0.8
0
0
.71
0.4
7
Dp
s0
.11
0
.24
0
.25
0
.27
Bp
s3
.58
Req
uir
ed r
ate
of
retu
rn i
s 9
%.
Ass
um
e ze
ro R
E a
fter
per
iod
T (
zero
pre
miu
m a
t T
).
?V
E 0
5-6
1
Va
luin
g
Va
luin
g F
lan
iga
nF
lan
iga
n’’ ss
En
terp
rise
s
En
terp
rise
s
Ca
se 1
: Z
ero
RE
aft
er T
Ca
se 1
: Z
ero
RE
aft
er T
53
.4
95
.0
58
.3
VE 0
=+
=Fo
reca
st Y
ear
19
99
20
00
20
01
2
00
2
20
03
Ep
s0
.73
0.8
0
0
.71
0.4
7
Dp
s0
.11
0
.24
0
.25
0
.27
Bp
s3
.58
4.2
0
4.7
6
5
.22
5.4
1
RO
CE
20
.4%
19
.0%
1
4.9
%
9
.0%
RE
(9
% c
har
ge)
0
.40
8
0.4
22
0.2
82
0
.00
0
Dis
cou
nt
rate
(1
.09
)1
.09
1
.18
8 1
.29
5
1
.41
2
Pre
sen
t v
alu
e o
f R
E0
.37
4
0
.35
5 0
.21
7
0
.00
0
To
tal
pre
sen
t v
alu
e o
f R
E t
o 2
00
3
0.9
5
Val
ue
per
sh
are
4.5
3
Ass
um
ing z
ero R
E a
fter
per
iod T
(ze
ro p
rem
ium
at
T):
5-6
2
Va
luin
g G
ener
al
Ele
ctri
c V
alu
ing
Gen
era
l E
lect
ric
Ca
se 2
: C
on
sta
nt
RE
aft
er T
Ca
se 2
: C
on
sta
nt
RE
aft
er T
Fo
reca
st Y
ear
1999
2000
2001
2002
2003
2004
Ep
s1
.29
1.3
8
1.4
2
1.5
01
.60
Dp
s0
.57
0.6
6
0.7
3
0.7
7
0.8
2
Bp
s4
.32
Req
uir
ed r
ate
of
retu
rn i
s 10
%.
Ass
um
e co
nst
ant
RE
aft
er p
erio
d T
:
?V
E 0
5-6
3
Va
luin
g G
ener
al
Ele
ctri
c V
alu
ing
Gen
era
l E
lect
ric
Ca
se 2
: C
on
sta
nt
RE
aft
er T
Ca
se 2
: C
on
sta
nt
RE
aft
er T 0
7.
13
48
.5
27
.3
32
.4
VE 0
=+
+=
Fo
reca
st Y
ear
1999
2000
2001
2002
2003
2004
Ep
s1
.29
1.3
8
1.4
2
1.5
01
.60
Dp
s0
.57
0.6
6
0.7
3
0.7
7
0.8
2B
ps
4.3
25
.04
5.7
6
6.4
5
7.1
8
7.9
6
RO
CE
29
.9%
27
.4%
24
.7%
23
.3%
22
.3%
RE
(1
0%
ch
arg
e)0
.858
0.8
76
0.8
44
0.8
55
0.8
82
Dis
cou
nt
rate
(1
.10)
1.1
00
1.2
10
1.3
31
1.4
64
1.6
11
Pre
sen
t valu
e o
f R
E0
.780
0.7
24
0.6
34
0.5
84
0.5
48
To
tal
pre
sen
t va
lue
of
RE
to
20
04
3.2
7C
on
tin
uin
g v
alu
e (C
V)
8.8
2
Pre
sen
t valu
e o
f C
V5
.48
Va
lue
per
sh
are
13
.07
Th
e co
nti
nu
ing
valu
e:
CV
=
= 8
.82
Pre
sen
t valu
e o
f co
nti
nu
ing
valu
e =
=
5.4
8
Ass
um
ing
co
nst
ant
RE
aft
er p
erio
d T
:
10
.0
88
2.
0
61
05
.1
82
.8
5-6
4
Va
luin
g D
ell
Inc.
Va
luin
g D
ell
Inc.
Ca
se 3
: G
row
ing
RE
aft
er T
Ca
se 3
: G
row
ing
RE
aft
er T
Fore
cast
Yea
r
2000
2001
2002
2003
2004
2005
Ep
s0
.84
0.4
8
0.8
2
1.0
3
1.1
8
Dp
s0
.0
0.0
0.0
0.0
0.0
Bp
s2
.06
Req
uir
ed r
ate
of
retu
rn i
s 1
1 %
.
Ass
um
e g
row
ing
RE
at
6.5
% af
ter
per
iod
T :
?V
E 0
5-6
5
Va
luin
g D
ell
Inc.
Va
luin
g D
ell
Inc.
Ca
se 3
: G
row
ing
RE
aft
er T
Ca
se 3
: G
row
ing
RE
aft
er T
Fore
cast
Yea
r
2000
2001
2002
2003
2004
2005
Ep
s0
.84
0.4
8
0.8
2
1.0
3
1.1
8
Dp
s0
.0
0.0
0.0
0.0
0.0
Bp
s2
.06
2.9
0
3.3
8
4.2
0
5.2
3
6.4
1
RO
CE
40
.8%
16
.6%
24
.3%
24
.5%
22
.6%
RE
(11
% c
har
ge)
0.6
13
0.1
61
0.4
48
0.5
68
0.6
05
Dis
cou
nt
rate
(1
.11)t
1.1
10
1.2
32
1.3
68
1.5
18
1.6
85
Pre
sen
t v
alu
e of
RE
0.5
53
0.1
31
0.3
28
0.3
74
0.3
59
Tota
l p
rese
nt
val
ue
of
RE
to
2005
1.7
5
Co
nti
nuin
g v
alu
e (C
V)
14
.32
Pre
sen
t v
alu
e of
CV
8.5
0
Val
ue
per
sh
are
12
.31
Th
e co
nti
nu
ing
val
ue
(wit
h g
row
th a
t 6
.5%
):
CV
=
=
14
.32
Pre
sent
val
ue
of
con
tin
uin
g v
alu
e =
=
8.5
0
Ass
um
ing
gro
win
g R
E a
fter
per
iod
T :
31
.1
25
0.
87
5.
10
6.
20
=+
+=
EV
06
5.
11
1.
1
06
5.
16
05
.0
−×
68
5.
1
32
.1
4
5-6
6
Fo
reca
stin
g T
arg
et P
rice
s b
y A
naly
sts
Fo
reca
stin
g T
arg
et P
rice
s b
y A
naly
sts
TT
TC
VB
P
rice
Tar
get
+
=41
.5
20
03
20
03
==
BV
E
73
.20
32
.14
41
.6
20
05
20
05
20
05
=+
=+
=C
VB
VE
Cas
e 1 (
Fla
nnig
an’s
):
Cas
e 2 (
GE
):
Cas
e 3 (
Del
l):
16.7
8
82
.8
96
.7
2
00
42
00
42
00
4=
+=
+=
CV
BV
E
5-6
7
Con
ver
tin
g a
n A
naly
stC
on
ver
tin
g a
n A
naly
st’’ s
Fore
cast
to a
Valu
ati
on
: s
Fore
cast
to a
Valu
ati
on
:
Nik
e In
c.N
ike
Inc.
1)
Bp
s (2
004
): $
18
.17
2)
Con
stan
t P
ay
ou
t R
ati
o (
div
iden
ds
to e
arn
ings)
: 0
.20
6
3)
Ea
rnin
gs
Fo
reca
sts:
2005
$4.4
5
2006
$5.0
4
Fiv
e-y
ear
eps
gro
wth
rate
: 14
%
4)
Req
uir
ed R
ate
of
Ret
urn
: 10
%
5)
Ass
um
e g
row
ing
RE
at
GD
P g
row
th r
ate
of
4%
aft
er T
Pri
ce =
$75
?V
E 0
5-6
8
Con
ver
tin
g a
n A
naly
stC
on
ver
tin
g a
n A
naly
st’’ s
Fore
cast
to a
Valu
ati
on
: s
Fore
cast
to a
Valu
ati
on
:
Nik
e In
c.N
ike
Inc.
20
04A
2
00
5E
20
06
E 2
00
7E
20
08
E
20
09
E
Ep
s4
.45
5.0
4
5.7
5
6
.55
7.4
7D
ps
0.9
2
1.0
4
1.1
8
1
.35
1.5
4B
ps
18
.17
21
.70
25
.71
30
.27
3
5.4
7
41
.40
RO
CE
24
.49
%
23
.23
%
22
.36
%
2
1.6
4%
21
.06
%R
E (
10
% c
ha
rge)
2.6
33
2.8
70
3.1
75
3
.52
3
3
.92
0
Dis
cou
nt
rate
(1
.10
)t
1
.11
0
1.2
10
1.3
31
1
.46
4
1
.61
1P
rese
nt
va
lue
of
RE
2.3
94
2.3
72
2.3
86
2
.40
6
2
.43
4T
ota
l P
V t
o 2
00
9
1
1.9
9C
on
tin
uin
g v
alu
e (C
V)
6
7.9
5P
rese
nt
va
lue
of
CV
42
.19
Va
lue
per
sh
are
72
.35
Th
e co
nti
nu
ing
va
lue
(wit
h g
row
th a
t G
DP
gro
wth
ra
te o
f 4
%):
CV
=
=
67
.95
04
.1
10
.1
04
.1
92
0.
3
−×
5-6
9
Res
idu
al
Ea
rnin
gs
Mo
del
:
Res
idu
al
Ea
rnin
gs
Mo
del
:
Ad
va
nta
ges
an
d D
isa
dv
an
tages
Ad
va
nta
ges
an
d D
isa
dv
an
tages
Adva
nta
ges
Adva
nta
ges
•F
ocu
s o
n v
alu
e d
rive
rs:
focu
ses
on
pro
fita
bil
ity o
f
inv
estm
ent
and
gro
wth
in
in
ves
tmen
t th
at d
riv
e v
alu
e;
dir
ects
str
ateg
ic t
hin
kin
g t
o t
hes
e d
riv
ers
•In
corp
ora
tes
the
fin
an
cia
l st
ate
men
ts:
inco
rpo
rate
s th
e
val
ue
alre
ady r
eco
gn
ized
in
th
e b
alan
ce s
hee
t (t
he
bo
ok
val
ue)
; fo
reca
sts
the
inco
me
stat
emen
t an
d b
alan
ce s
hee
t
rath
er t
han
th
e ca
sh f
low
sta
tem
ent
•U
ses
acc
rua
l a
cco
un
tin
g:
use
s th
e p
rop
erti
es o
f ac
cru
al
acco
un
tin
g t
hat
rec
og
niz
e v
alu
e ad
ded
ah
ead
of
cash
flo
ws,
mat
ches
val
ue
add
ed t
o v
alu
e g
iven
up
an
d t
reat
s
inv
estm
ent
as a
n a
sset
rat
her
th
an a
lo
ss o
f v
alu
e
•V
ersa
tili
ty:
can
be
use
d w
ith
a w
ide
var
iety
of
acco
un
tin
g
pri
nci
ple
s.
•A
lig
ned
wit
h w
ha
t p
eop
le f
ore
cast
:an
alyst
s fo
reca
st
earn
ing
s (f
rom
wh
ich
fo
reca
sted
res
idu
al e
arn
ing
s ca
n b
e
calc
ula
ted
)
•V
ali
da
tio
n:
fore
cast
s o
f re
sid
ual
ear
nin
gs
can
be
val
idat
ed
in s
ub
seq
uen
t au
dit
ed f
inan
cial
sta
tem
ents
•P
red
icta
bil
ity:
div
iden
ds
are
usu
ally
fai
rly s
tab
le i
n t
he
sho
rt r
un
so
div
iden
ds
are
easy
to
fo
reca
st (
in t
he
sho
rt
run
)
Dis
adva
nta
ges
Dis
adva
nta
ges
•A
cco
un
tin
g c
om
ple
xit
y:
req
uir
es a
n u
nd
erst
and
ing
of
ho
w a
ccru
al a
cco
un
tin
g w
ork
s•
Su
spec
t a
cco
un
tin
g:
reli
es o
n
acco
un
tin
g n
um
ber
s th
at c
an b
e su
spec
t.
5-7
0
A S
imp
le D
emo
nst
rati
on
A S
imp
le D
emo
nst
rati
on
In m
illi
on
s of
doll
ars
. R
equ
ired
ret
urn
is
10%
per
yea
r.
Fo
reca
st Y
ear
0
1
2
3
4
5
Ear
nin
gs
12
.00
12
.36
12
.73
13
.11
13
.51
13
.91
Div
iden
ds
9.0
99
.36
9.6
49
.93
10
.23
10
.53
Bo
ok
val
ue
10
0.0
01
03
.00
106
.09
109
.27
112
.55
115
.93
RE
(10
% c
har
ge)
2.3
62
.43
2.5
02
.58
2.6
6
RE
gro
wth
rat
e3
%3
%3
%3
%
.
Th
e in
trin
sic
pri
ce-t
o-b
oo
k r
ati
o (
P/B
) is
$133
.71
/ $
100
= 1
.34
.
mil
lion
g
RE
BV
E71
.133
$03
.1
10
.1
36
.2
$100
$1
00
=−
+=
−+
=ρ
5-7
1
Pro
tect
ion
fro
m P
ay
ing
To
o M
uch
fo
r P
rote
ctio
n f
rom
Pay
ing
To
o M
uch
fo
r
Ea
rnin
gs
Gen
erate
d b
y I
nv
estm
ent
Ea
rnin
gs
Gen
erate
d b
y I
nv
estm
ent
Inves
t $50 m
illi
on
in
Yea
r 1 w
ith
pro
ceed
s fr
om
a s
hare
iss
ue:
Fo
reca
st Y
ear
0
1
2
3
4
5
Ear
nin
gs
12
.00
12
.36
17
.73
18
.61
19
.56
20
.57
Net
div
iden
ds
9.0
9(4
0.6
4)
9.6
49
.93
10
.23
10
.53
Bo
ok
val
ue
10
0.0
01
53
.00
16
1.0
91
69
.77
17
9.1
01
89
.14
RE
(1
0%
ch
arg
e)2
.36
2.4
32
.50
2.5
82
.66
RE
gro
wth
rat
e3
%3
%3
%3
%
mil
lion
VE
71
.133
$03
.1
10
.1
36
.2
$100
$0
=−
+=
Bew
are
!
5-7
2
Cre
ati
ve
Acc
ou
nti
ng
Cre
ati
ve
Acc
ou
nti
ng
�S
up
po
se t
hat
th
e m
anag
er o
f th
e fi
rm d
ecid
ed t
o c
reat
e m
ore
ear
nin
gs
for
Yea
r 1
by w
riti
ng d
ow
n i
nv
ento
ry b
y $
8 i
n y
ear
0.
�lo
ss f
rom
in
ven
tory
wil
l b
e $8
in
yea
r 0
, w
hil
e co
st o
f g
ood
s w
ill
be
und
erst
ated
by t
he
sam
e am
ou
nt
in Y
ear
1.
�E
arnin
gs
wil
l be
$4
(1
2-8
) i
n y
ear
0 a
nd $
20.3
6 (
12
.36
+8)
in
Yea
r 1.
�C
lean
surp
lus
acco
un
ting
im
pli
es t
hat
bo
ok
val
ue
wil
l b
e $
92
(1
00-8
) in
yea
r 0
.
:
5-7
3
Pro
tect
ion
fro
m P
ayin
g T
oo M
uch
for
Earn
ings
Cre
ate
d
Pro
tect
ion
fro
m P
ayin
g T
oo M
uch
for
Earn
ings
Cre
ate
d
by t
he
Acc
ou
nti
ng:
the
Sim
ple
Exam
ple
by t
he
Acc
ou
nti
ng:
the
Sim
ple
Exam
ple
Wri
tin
g i
nv
ento
ry d
ow
n b
y $
8 m
illi
on
in
Yea
r 0
cre
ate
s lo
wer
\
cost
-of-
go
od
s so
ld i
n Y
ear
1:
Fo
reca
st Y
ear
0
1
2
3
4
5
Ear
nin
gs
4.0
02
0.3
61
2.7
31
3.1
11
3.5
11
3.9
1
Div
iden
ds
9.0
99
.36
9.6
49
.93
10
.23
10
.53
Bo
ok
val
ue
92
.00
103
.00
106
.09
109
.27
112
.55
115
.93
RE
(10
% c
har
ge)
11
.16
2.4
32
.50
2.5
82
.66
RE
gro
wth
rat
e3
%3
%3
%
mil
lio
nV
E7
1.
11
3$
10
.1
03
.1
10
.1
43
.2
10
.1
16
.1
19
2$
0=
−
++
=
Bew
are
!
6-7
4
6-7
5
Th
e C
on
cep
t B
ehin
d t
he
P/E
Ra
tio
Th
e C
on
cep
t B
ehin
d t
he
P/E
Ra
tio
•P
rice
in
num
erat
or
of
P/E
is
bas
ed o
n e
xp
ecte
d f
utu
re
earn
ing
s
•E
arn
ing
s in
den
om
inat
or
is c
urr
ent
(or
forw
ard
) ea
rnin
gs
•P
/E i
s th
us
bas
ed o
n e
xp
ecte
d g
row
th i
n e
arn
ings
6-7
6
Th
e T
rail
ing
P/E
an
d F
orw
ard
P/E
Th
e T
rail
ing
P/E
an
d F
orw
ard
P/E
1P
/E
Tra
ilin
g
No
rmal
P/E
F
orw
ard
N
orm
al
retu
rn
req
uir
ed
retu
rn
req
uir
ed
1
P/E
T
rail
ing
N
orm
al
retu
rn
req
uir
ed1
P
/E
Fo
rwar
d
No
rmal
earn
ing
s]cu
rren
t n
ot
bu
t
pri
ce,
curr
ent
re
du
ce
[Div
iden
ds
Ear
nin
gs
Div
iden
d
Pri
ce
P
/E
Tra
ilin
g
Ear
nin
gs
Pri
ce
P
/E
Fo
rwar
d
0
00
1
0
−=
+==+
==
6-7
7
Va
lua
tio
n w
ith
Ea
rnin
gs
Va
lua
tio
n w
ith
Ea
rnin
gs
Gro
wth
E
arn
ing
s
Ab
no
rmal
F
ore
cast
edfo
r
Val
ue
E
xtr
a1-
Ear
n
V
1+
=Eρ
Gro
wth
E
arn
ing
s
Fo
reca
sted
for
V
alu
e
Ex
tra
E
arn
ing
s
Fo
rwar
d
dC
apit
aliz
e
Val
ue
+=
6-7
8
Th
e P
roto
typ
e S
av
ing
s A
cco
un
tT
he
Pro
toty
pe
Sav
ing
s A
cco
un
t
2
000
2001
2
002
2003
2
004
20
05
Ea
rnin
gs
wit
hd
raw
n e
ach
yea
r (f
ull
pa
yout)
Ear
nin
gs
5
5
5
5
5
D
ivid
end
s
5
5
5
5
5
B
oo
k v
alu
e
10
0
10
0
1
00
100
1
00
1
00
E
arn
ing
s g
row
th r
ate
0
0
0
0
0
No
wit
hd
raw
als
(ze
ro p
ayo
ut)
Ear
nin
gs
5
5
.25
5.5
1
5.7
9
6.0
8
Div
iden
ds
0
0
0
0
0
B
oo
k v
alu
e
10
0
10
5
11
0.2
5
1
15
.76
12
1.5
5 1
27
.63
E
arn
ing
s g
row
th r
ate
5
%
5
%
5
%
5%
6-7
9
Va
lue
of
the
Sa
vin
gs
Acc
ou
nt
Va
lue
of
the
Sa
vin
gs
Acc
ou
nt
Fu
ll P
ayou
t S
cen
ari
o:
�L
ogic
al?
Yes
, th
ere
is n
o e
arnin
gs
gro
wth
for
the
savin
gs
acco
unt.
Zer
o P
ayou
t S
cen
ari
o:
�D
oes
not
work
for
the
savin
gs
acco
unt,
but
why?
Yes
, it
is
a bad
P/E
model
, si
nce
it
focu
ses
only
on norm
al e
arnin
gs
gro
wth
(i.e
., g
row
th r
ate
equal
s re
quir
ed r
eturn
: g=ρ
=1.0
5)
and i
gnore
s
abnorm
al e
arnin
gs
gro
wth
(w
hat
if
g>ρ
?).
�B
ut
what
do w
e m
ean w
ith “
abnorm
al e
arnin
gs
gro
wth
”? T
o
answ
er t
he
ques
tion, re
call
that
the
only
dif
fere
nce
bet
wee
n t
he
two s
avin
gs
acco
unts
is
bas
ed o
n t
he
pay
out
rati
o.
100
$0.0
5
5
1-
Ear
n
V
alue
1=
==ρ
?05
.1
05
.1
5
g-
Ear
n
V
alue
1=
−=
=ρ
6-8
0
Cu
mC
um
-- Div
iden
d E
arn
ing
sD
ivid
end
Ea
rnin
gs
For
the
zero
-payo
ut
acco
unt:
2001
2002
2003
2004
2005
Cum
-div
iden
d e
arnin
gs
5.0
05.2
55.5
15.7
96.0
8
For
the
full
-payo
ut
acco
unt:
Ear
nin
gs
in t
he
acco
unt
5.0
05.0
05.0
05.0
05.0
0
Div
iden
d r
einves
ted @
5%
0.2
50.5
10.7
91.0
8
Cum
-div
iden
d e
arnin
gs
5.0
05.2
55.5
15.7
96.0
8
[]
Cum
-div
iden
d e
arnin
gs
(2002)
Ear
nin
gs
(2002)
0.0
5
Div
iden
d (
2001)
=
+×
Th
e tw
o a
ccoun
ts h
ave
dif
fere
nt
(ex-d
ivid
end
) ea
rnin
gs
gro
wth
, bu
t th
e sa
me
cum
-div
iden
d e
arn
ing
s gro
wth
6-8
1
No
rma
l E
arn
ing
sN
orm
al
Ea
rnin
gs
No
rmal
Ea
rnin
gs
is e
arn
ings
gro
win
g a
t th
e re
qu
ired
rat
e of
retu
rn:
t1
No
rmal
Ear
nin
gs
Ear
nin
gs
For
the
savin
gs
acco
unt:
No
rmal
Ear
nin
gs
(200
2)
1.0
5
Ear
nin
gs
(200
1)
= 1
.05
x 5
.00=
5.2
5
No
rmal
Ear
nin
gs
(200
3)
1.05
5
.25
Eρ
−=
=×
=×
= 5
.5125
6-8
2
Ab
no
rma
l E
arn
ing
s G
row
th (
AE
G)
Ab
no
rma
l E
arn
ing
s G
row
th (
AE
G)
Abnorm
al
Earn
ings
Gro
wth
is g
row
th o
ver
norm
al e
arnin
gs
gro
wth
AE
G =
Cu
m-d
ivid
end e
arnin
gs
–N
orm
al e
arnin
gs
For
the
Sav
ings
acco
unt:
()
()
05
12
5.
55
12
5.
52
00
3
02
5.
52
5.
52
00
2
=−
=
=−
=
AE
G
AE
G
6-8
3
Les
son
s fr
om
th
e S
av
ing
s A
ccou
nt
Les
son
s fr
om
th
e S
av
ing
s A
ccou
nt
1. A
n a
sset
is
wort
h c
apit
aliz
ed f
orw
ard e
arnin
gs
if a
bnorm
al e
arnin
gs
gro
wth
is
expec
ted t
o b
e ze
ro.
2. A
n a
sset
has
a n
orm
al P
/E r
atio
if
abnorm
al e
arnin
gs
gro
wth
is
expec
ted t
o b
e ze
ro.
3. E
arnin
gs
com
es f
rom
tw
o s
ourc
es:
�ea
rnin
gs
fro
m t
he
asse
t
�ea
rnin
gs
fro
m r
ein
ves
tin
g d
ivid
ends
4. E
x-d
ivid
end g
row
th r
ates
are
aff
ecte
d b
y d
ivid
ends:
div
iden
ds
reduce
as
sets
whic
h t
hen
ear
n l
ow
er e
arnin
gs.
5. C
um
-div
iden
d g
row
th r
ates
are
not
affe
cted
by d
ivid
ends
(sin
ce t
hey
re
flec
t ea
rnin
gs
fro
m d
ivid
ends)
: t
hey
are
eff
ecti
vel
y t
he
rate
s th
at
firm
s w
ould
hav
e if
they
did
not
pay
div
iden
ds
6-8
4
A M
od
el o
f th
e F
orw
ard
P/E
A M
od
el o
f th
e F
orw
ard
P/E
Th
e m
od
el:
Val
ue
of
equ
ity =
Cap
ital
ized
forw
ard e
arn
ings
+ E
xtr
a v
alu
e fo
rab
norm
al
earn
ing
s gro
wth
+
++
−+
−=
⋯3
4
2
32
10
1
1
1E
EE
EE
EA
EG
AE
GA
EG
Ea
rnV
ρρ
ρρ
ρ
++
++
−=
⋯3
4
2
32
11
1
EE
EE
AE
GA
EG
AE
GE
arn
ρρ
ρρ
The
intr
insi
c P
/E
1
E 0
Ear
n
Vis
giv
en b
y d
ivid
ing t
hro
ugh b
y E
arn
1
6-8
5
Mea
suri
ng
Ab
no
rma
l E
arn
ing
s G
row
th f
or
Eq
uit
ies
Mea
suri
ng
Ab
no
rma
l E
arn
ing
s G
row
th f
or
Eq
uit
ies
Abn
orm
al e
arnin
gs
gro
wth
t (A
EG
t) =
Cu
m-d
ivid
end
ear
nt
-N
orm
al e
arn
t
= [
Ear
nt+
(ρ
E–
1)
dt-
1]
–ρ
Ear
nt-
1D
ell:
R
equir
ed r
eturn
= 1
1%
E
ps
2004 =
$1.0
3
Nik
e: R
equir
ed r
eturn
= 1
0%
E
ps
2004 =
$3.5
9
Del
l C
om
pute
rN
ike
Inc.
Eps
2005
Dps
2004
Ear
nin
gs
on r
einves
ted d
ivid
ends
Cum
-div
iden
d e
arnin
gs
2005
Norm
al e
arnin
gs
from
2004:
Del
l: 1
.03 x
1.1
1;
Nik
e: 3
.59 x
1.1
0
Abnorm
al e
arnin
gs
gro
wth
(A
EG
) 2005
$0.0
0
$1.1
8
$0.0
0
1.1
8
1.1
43
$0.0
37
$0.7
4
$4.4
5
0.0
74
4.5
24
3.9
49
$0.5
75
6-8
6
Alt
ern
ati
ve
Ca
lcu
lati
on
of
AE
GA
lter
nati
ve
Ca
lcu
lati
on
of
AE
G
Abnorm
al e
arnin
gs
gro
wth
t =
[G
t–ρ
E]
x E
arnin
gs t
-1
Wher
e
For
Nik
e:
G2005
= 4
.52
4/3
.59
= 1
.260
2%
(a
26
.02%
gro
wth
rat
e)
AE
G2005=
[1
.26
02
–1
.10
] x 3
.59
= $
0.5
75
1−
−=
t
tt
Ea
rnin
gsea
rnin
gs
div
iden
dC
um
G
6-8
7
Ab
no
rma
l E
arn
ing
s G
row
th i
s E
qu
al
to t
he
Ab
no
rma
l E
arn
ing
s G
row
th i
s E
qu
al
to t
he
Ch
an
ge
in R
esid
ua
l E
arn
ing
sC
ha
ng
e in
Res
idu
al
Ea
rnin
gs
AE
Gt=
[ e
arn
t +
(ρ
E–
1)d
t-1]
-ρ
Eea
rnt-
1
By t
he
sto
cks
and
flo
ws
equ
atio
n f
or
acco
unti
ng
for
the
bo
ok
val
ue
of
equit
y (
Ch
apte
r 2
),
Bt-
1=
Bt-
2 +
ear
nt-
1–
dt-
1, so
ear
nt-
1–
dt-
1=
Bt-
1 –
Bt-
2. T
hu
s,
AE
Gt=
ear
nt
–ea
rnt-
1 -
(ρE
–1
)[B
t-1
–B
t-2]
= [ e
arn
t-
(ρE
–1
)Bt-
1]
-[ e
arn
t-1
-(ρ
E–
1)B
t-2]
= R
Et–
RE
t-1
]d
1)[
earn
(ρea
rnea
rn1
t1
tE
1t
t−
−−
−−
−−
=
+∆
+∆
+∆
+−
=..
..
R
E
R
E
R
E
E
arn
1
VE
EE
2
E
E
3
4
2
31
01
ρρ
ρρ
So
, th
e A
EG
mo
del
can
be
wri
tten
as:
6-8
8
Th
e C
on
tin
uin
g V
alu
e fo
r th
e A
EG
Mo
del
T
he
Co
nti
nu
ing
Va
lue
for
the
AE
G M
od
el
Ca
se 1
: A
EG
is
fore
cast
ed t
o b
e ze
ro i
n p
erp
etu
ity
aft
er T
So
Ca
se 1
I: A
EG
is
fore
cast
ed t
o b
e co
nst
an
t in
per
pet
uit
y a
fter
T
So
Ca
se 1
II:
AE
G i
s fo
reca
sted
to
gro
w a
t co
nst
an
t ra
te i
n p
erp
etu
ity
aft
er T
So
0C
VT=
1
AE
GC
VE
1+
TT
−=
ρ
gρ
AE
GC
VE
1+
TT
−=
6-8
9
Va
luin
g G
ener
al
Ele
ctri
c V
alu
ing
Gen
era
l E
lect
ric
Ca
se 1
: Z
ero
AE
G a
fter
TC
ase
1:
Zer
o A
EG
aft
er T
Fo
reca
st Y
ear
1999
2000
2001
2002
2003
2004
Dp
s0
.57
0.6
6
0.7
3
0.7
7
0.8
2E
ps
1.2
91
.38
1.4
2
1.5
01
.60
Req
uir
ed r
ate
of
retu
rn i
s 10
%.
Ass
um
e ze
ro A
EG
(i.
e.,
con
stan
t R
E)
afte
r p
erio
d T
:
?V
E 0
6-9
0
Valu
ing G
ener
al
Ele
ctri
c V
alu
ing G
ener
al
Ele
ctri
c
Case
1:
Zer
o A
EG
aft
er T
Case
1:
Zer
o A
EG
aft
er T
Fore
cast
Yea
r
1
999
2
00
0
200
1
200
2
200
3
200
4
D
ps
0
.57
0.6
6
0.7
3
0.7
7
0.8
2
Eps
1
.29
1.3
8
1.4
2
1.5
0
1.6
0
Dps
rein
vest
ed a
t 10%
0.0
57
0.0
66
0
.07
3
0.0
77
Cu
m-d
ivid
en
d e
arn
ings
(
eps
+ d
ps
rein
vest
ed)
1.4
37
1.4
86
1
.57
3
1.6
77
Norm
al
earn
ings
(1.1
0 x
eps t
-1)
1.4
19
1.5
18
1
.56
2
1.6
50
Abn
orm
al e
arn
ings
gro
wth
(A
EG
) 0
.018
-0.0
32
0
.01
1
0.0
27
Dis
coun
t ra
te (
1.1
0t )
1.1
00
1.2
10
1
.33
1
1.4
64
PV
of
AE
G
0.0
16
-0.0
26
0
.00
8
0.0
18
Tota
l P
V o
f A
EG
0
.01
7
Tota
l earn
ing
s to
be c
apit
ali
zed
1.3
07
Capit
aliz
ati
on r
ate
0.1
0
Valu
e per
share
1
0.
030
7.
1
13.0
7
[]
13.0
7
0.0
17
1.2
9
10
0
1
V1
99
9=
+=
.
E
Sam
e as
res
idu
al e
arn
ing
s v
alu
atio
n
6-9
1
Va
luin
g D
ell
Inc.
Va
luin
g D
ell
Inc.
Ca
se 3
: G
row
ing
AE
G a
fter
TC
ase
3:
Gro
win
g A
EG
aft
er T
Fore
cast
Yea
r
2000
2001
2002
2003
2004
2005
Ep
s0
.84
0.4
8
0.8
2
1.0
3
1.1
8
Dp
s0
.0
0.0
0.0
0.0
0.0
Bp
s2
.06
Req
uir
ed r
ate
of
retu
rn i
s 1
1 %
.
Ass
um
e g
row
ing
AE
G a
t 6
.5%
af
ter
per
iod
T
:
?V
E 0
6-9
2
Valu
ing D
ell
Inc.
Valu
ing D
ell
Inc.
Case
3:
Gro
win
g A
EG
aft
er T
Case
3:
Gro
win
g A
EG
aft
er T
Fore
cast
Yea
r
2000
2001
2002
2003
2004
2005
2006
Dps
0.0
0.0
0.0
0.0
0.0
0.0
Eps
0.8
40.4
8
0.8
2
1.0
3
1.1
8
1.3
5
Dps
rein
ves
ted (
0.1
1 ×
dps t
-1)
0.0
00.0
00.0
00.0
0
0.0
0C
um
-div
iden
d e
arnin
gs
0.4
8
0.8
2
1.0
3
1.1
8
1.3
49
Norm
al e
arnin
gs
(1.1
1 ×
eps t
-1)
0.9
32
0.5
33
0.9
10
1.1
43
1.3
10
Abnorm
al e
arnin
gs
gro
wth
-0
.452
0.2
87
0.1
20 0
.037
0.0
39
Dis
count
rate
(1.1
1t )
1.1
10
1.2
32
1.3
68 1
.518
Pre
sent
val
ue
of
AE
G-0
.408
0.2
33
0.0
88 0
.025
Tota
l P
V o
f A
EG
-0.0
62
Conti
nuin
g v
alu
e (C
V)
0.8
73
PV
of
CV
0.5
76
Tota
l ea
rnin
gs
to b
e ca
pit
aliz
ed
1.3
54
Cap
ital
izat
ion r
ate
0.1
1
Val
ue
per
shar
e
12.3
1
The
conti
nuin
g v
alu
e ca
lcula
tion:
CV
= =
0.8
73
Pre
sent
val
ue
of
CV
=
=
0.5
76
11
.03
54
.1 0
65
.1
11
.1
03
93
.0
−
51
81
.1
87
3.
0 []
31
.12
576
.0
062
.0
84
.0
11
.0
12
00
0=
+−
=E
V Sam
e as
res
idu
al e
arnin
gs
val
uat
ion
6-9
3
Con
ver
tin
g a
n A
naly
stC
on
ver
tin
g a
n A
naly
st’’ s
Fore
cast
to a
Valu
ati
on
: s
Fore
cast
to a
Valu
ati
on
:
Nik
e In
c.N
ike
Inc.
1)
Con
stan
t P
ayo
ut
Rati
o (
div
iden
ds
to e
arn
ings)
: 0
.08
7
2)
Ea
rnin
gs
Fo
reca
sts:
2005
$3.4
3
2006
$3.8
1
Fiv
e-y
ear
eps
gro
wth
rate
: 14
%
3)
Req
uir
ed R
ate
of
Ret
urn
: 10
%
4)
Ass
um
e g
row
ing
AE
G a
t G
DP
gro
wth
rate
of
4%
aft
er T
Pri
ce =
$41
?V
E 0
6-9
4
Co
nv
erti
ng
An
aly
sts
Co
nv
erti
ng
An
aly
sts ’’
Fo
reca
sts
to a
Va
lua
tion
: R
eboo
k I
nte
rnati
on
al
Fo
reca
sts
to a
Va
lua
tion
: R
eboo
k I
nte
rnati
on
al
20
04
20
05E
20
06E
20
07E
20
08E
20
09E
Dp
s0
.30
0.3
30
.38
0.4
30
.49
Ep
s3
.43
3.8
14
.34
4.9
55
.65
Dp
s r
ein
veste
d (
0.1
0 x
dp
s t-1
)0
.03
00
.033
0.0
38
0.0
43
Cum
-div
iden
d e
arn
ings
3.8
40
4.3
73
4.9
88
5.6
93
No
rma
l ea
rnin
gs (
1.1
0 x
ep
st-
1)
3.7
73
4.1
91
4.7
74
5.4
45
Abno
rma
l ea
rnin
gs g
row
th0
.067
0.1
82
0.2
14
0.2
48
Cum
-div
ep
s g
row
th r
ate
11
.95
%1
4.7
8%
14
.93
%1
5.0
0%
Dis
coun
t ra
te (
1.1
0t )
1.1
00
1.2
10
1.3
31
1.4
64
Pre
sen
t va
lue
of
AE
G0
.061
0.1
50
0.1
61
0.1
69
To
tal P
V o
f A
EG
0.5
4C
on
tinu
ing v
alu
e (
CV
)4
.299
PV
of
CV
2.9
4T
ota
l ea
rnin
gs t
o b
e c
ap
italiz
ed
6.9
1C
ap
italiz
atio
n r
ate
0.1
0
Va
lue
pe
r sh
are
$6
9.1
0
The
con
tinu
ing v
alu
e c
alc
ula
tion
:
Pre
se
nt
valu
e o
f C
V
=
10
.0
91
.6
4.2
99
04
.1
10
.1
1.0
4 x
2
48
.0
C
V=
−=
2.9
4
4641
.1
299
.4
=
6-9
5
Ap
ply
ing
th
e M
od
el:
A S
imp
le E
xa
mp
leA
pp
lyin
g t
he
Mo
del
: A
Sim
ple
Ex
am
ple
Fore
cast
for
a fi
rm w
ith
ex
pec
ted
ear
nin
gs
gro
wth
of
3 p
erce
nt
per
yea
r (i
n d
oll
ars)
. R
equir
ed r
eturn
is
10%
p
er y
ear.
Res
idu
al e
arn
ing
s v
alu
atio
n:
71
.1
33
03
.1
10
.1
36
.2
10
0V
E 2000
=−
+=
AE
G v
alu
atio
n:
71
.1
33
03
.1
10
.1
07
1.
03
6.
12
10
.0
12
00
0=
−+
=E
V
2
000
2
001
2
002
2
003
2
004
2005
Earn
ings
12.0
0
12.3
6
12.7
3
13
.11
13.5
1
1
3.9
1
D
ivid
ends
9.0
9
9.3
6
9.6
4
9
.93
10.2
3
1
0.5
3
Bo
ok v
alu
e
1
00.0
0
103.0
0
106.0
9
109
.27
112.5
5
11
5.9
3
R
E (
0.1
0)
2.3
6
2.4
3
2
.50
2.5
8
2.6
6
R
E g
row
th r
ate
3%
3%
3%
3%
E
arn
ings
on r
ein
vest
ed d
ivid
ends
0.9
36
0.9
64
0.9
93
1.0
23
C
um
-div
iden
d e
arnin
gs
13.6
67
14.0
77
14.4
99
14
.934
Norm
al e
arnin
gs
13.5
96
14.0
04
14.4
24
14
.857
Abnorm
al
earn
ings
gro
wth
0.0
71
0.0
73
0.0
75
0
.077
E
arn
ings
gro
wth
rate
3%
3%
3%
3%
Cu
m-d
ivid
end
earn
ings
gro
wth
rate
10.6
%
10.6
%
10.6
%
10.6
%
A
bnorm
al
earn
ings
gro
wth
rat
e
3
%
3%
3%
6-9
6
Pro
tect
ion
Fro
m E
arn
ing
s C
rea
ted
by
Acc
ou
nti
ng
: P
rote
ctio
n F
rom
Ea
rnin
gs
Cre
ate
d b
y A
cco
un
tin
g:
A R
estr
uct
uri
ng
Ch
arg
eA
Res
tru
ctu
rin
g C
ha
rge
20
00
20
01
20
02
200
3
2
00
4
2
00
5
E
arn
ing
s
4.0
0
2
0.3
6
1
2.7
3
1
3.1
1
1
3.5
1
1
3.9
1
D
ivid
ends
9
.09
9.3
6
9
.64
9.9
3
1
0.2
3
1
0.5
4
Bo
ok
val
ue
9
2.0
0
1
03
.00
10
6.0
9
1
09
.27
11
2.5
5
1
15
.93
E
arn
ing
s o
n r
ein
ves
ted
d
ivid
end
s
0.9
36
0
.96
4
0.9
93
1.0
23
Cum
-div
iden
d e
arnin
gs
13
.667
14.0
77
14
.49
9
1
4.9
34
N
orm
al e
arnin
gs
2
2.3
96
14.0
04
14
.42
4
1
4.8
57
Ab
norm
al e
arn
ings
gro
wth
(8.7
29
)
0.0
73
0.0
75
0.0
77
A
bn
orm
al e
arn
ings
gro
wth
rat
e
3
%
3
%
3
%
71
.1
33
10
.1
03
.1
10
.1
07
3.
0
10
.1
72
9.
83
6.
20
10
.0
12
00
0=
−+
−=
EV
6-9
7
Ab
no
rma
l E
arn
ing
s G
row
th A
na
lysi
s:
Ab
no
rma
l E
arn
ing
s G
row
th A
na
lysi
s:
Ad
va
nta
ges
an
d D
isa
dv
an
tages
Ad
va
nta
ges
an
d D
isa
dv
an
tages
Adva
nta
ges
Adva
nta
ges
•E
asy
to u
nder
stan
d:
Inves
tors
thin
k i
n t
erm
s of
futu
re e
arnin
gs;
inves
tors
buy
ear
nin
gs.
Focu
ses
dir
ectl
y o
n t
he
most
co
mm
on m
ult
iple
use
d, th
e P
/E r
atio
.•
Use
s acc
rual
acc
ou
nti
ng:
Em
bed
s th
e pro
per
ties
of
accr
ual
acc
ounti
ng b
y
whic
h r
even
ues
are
m
atch
ed w
ith e
xpen
ses
to
mea
sure
val
ue
added
fro
m
sell
ing p
roduct
s.•
Ver
sati
lity
:C
an b
e use
d
under
a v
arie
ty o
f ac
counti
ng p
rinci
ple
s.•
Ali
gn
ed w
ith
wh
at
peo
ple
fo
reca
st:
Anal
yst
s fo
reca
st
earn
ings
and e
arnin
gs
gro
wth
.
Dis
ad
van
tag
esD
isad
van
tag
es•
Acc
ou
nti
ng c
om
ple
xit
y:R
equir
es a
n u
nder
stan
din
g
of
how
acc
rual
acc
ounti
ng w
ork
s.
•C
on
cept
com
ple
xit
y:R
equir
es a
n a
ppre
ciat
ion o
f
the
conce
pt
of
cum
-div
iden
d e
arnin
gs;
that
is,
val
ue
is b
ased
on e
arnin
gs
to b
e ea
rned
wit
hin
the
firm
and f
rom
ear
nin
gs
from
the
rein
ves
tmen
t of
div
iden
ds.
•S
usp
ect
acc
ou
nti
ng:
Rel
ies
on e
arnin
gs
num
ber
s
that
can
be
susp
ect.