Financial Equations - International Due Diligence Organization€¦ · Due Diligence For The...
Transcript of Financial Equations - International Due Diligence Organization€¦ · Due Diligence For The...
From Due Diligence For The Financial Professional, 2nd Ed.Published 2010, Aegis Journal ISBN 9780982372333
By L. Burke Files, CACM, DDP PresidentInternational Due Diligence Organziation
Financial Equations
IDDO(877) 343-1600 | [email protected] | www.id-d.org
I N T E R N A T I O N A L
D U E D I L I G E N C EORGAN I Z A T I O N
443
Th
e T
ime
Valu
e o
f M
on
ey
Eq
ua
tion
sN
am
eE
qu
atio
nIn
form
atio
nE
xam
ple
Calc
ula
ting
Pre
se
nt
Valu
e a
nd
Futu
re V
alu
eNi
PV
FV
)1(
FV
=F
utu
re V
alu
eP
V=
Pre
se
nt
Valu
ei=
the inte
rest
rate
p
er
peri
od
N=
the n
um
ber
of
com
pou
ndin
g
peri
ods
What is
th
e f
utu
re v
alu
e o
f $4
0 in
5 y
rs @
5%
inte
rest?
FV
=$4
0(1
+.0
5)5
FV
=$4
0(1
.27
62
81
5)
FV
=$5
1.0
5
Pre
se
nt
Valu
e o
f a
futu
re c
ash
flow
, a
nn
ual
com
po
un
din
gt
t r
CF
PV
)1(
PV
=P
rese
nt
Valu
eC
Ft=
Futu
re C
ash
Flo
w w
hic
h o
ccurs
t
years
fro
m n
ow
r=th
e inte
rest
or
dis
cou
nt
rate
t=th
e n
um
ber
of
years
Pre
se
nt
Valu
e o
f $1
00
to
be
receiv
ed
4 y
ears
fro
m to
da
y @
10%
30.
68
$)
10.
1(
100
4PV
Futu
re V
alu
e
of
a c
ash
flow
, a
nn
ual
com
po
un
din
gt
tr
CF
FV
)1(
0
FV
t=th
e F
utu
re
Valu
e a
t th
e e
nd o
f year
tC
Fo=
the initia
l in
vestm
en
tr=
the
ann
ual
com
pou
nd
ed
in
tere
st
rate
t=th
e n
um
ber
of
years
FV
at
the e
nd o
f 3
years
of
$10
0 investe
d t
od
ay @
10%
10.
133
$)
10.
1(100
3
3FV
Pre
se
nt
Valu
e o
f a
cash
flo
w
str
eam
, an
nu
al
com
po
un
din
g
n
t
t
t r
CF
PV
0)
1(
PV
=P
rese
nt
Valu
e o
f th
e c
ash
flo
w s
tre
am
CF
t=th
e c
ash f
low
w
hic
h o
ccurs
at
the
end
of
year
tr=
the
dis
co
un
t ra
tet=
the
ye
ar,
0 t
o n
n=
the
last
year
a
cash f
low
occurs
PV
of
cash
flo
w y
r1=
$10
0,
yr2=
$1
00
, yr
3=
$10
0,
yr4=
$1
00
@1
0
99.
316
$)
10.
1(
100
)10.
1(
100
)10.
1(
100
)10.
1(
100
43
21
PV
444 Futu
re V
alu
e
of
a C
ash
Flo
w s
tream
, an
nu
al
com
po
un
din
gt
nn
t
tt
)r
(CF
FV
10
FV
t=th
e F
utu
re
Valu
e o
f th
e C
ash
Flo
w s
tre
am
at
the
end
of
year
tC
Ft=
the C
ash F
low
w
hic
h o
ccurs
at
the
end
of
year
tr=
the
dis
co
un
t ra
tet=
the
ye
ar
0 t
o n
n=
the
last
year
a
cash f
low
occurs
FV
of
cash f
low
yr1
=$1
00
, yr2
=$
10
0,
yr3=
$1
00,
yr4=
$10
0 @
10%
10.
464
$100
)10.
1(100
)10.
1(100
)10.
1(100
12
3
4FV
Pre
se
nt
Valu
e o
f an
A
nnuity,
an
nu
al
com
po
un
din
g
rrPMT
PVA
t)
1(1
PV
A=
the P
rese
nt
Valu
e o
f th
e A
nn
uity
PM
T=
the A
nnuity
paym
en
tr=
the
inte
rest
or
dis
cou
nt
rate
t=th
e n
um
ber
of
years
(th
e n
um
ber
of
paym
en
ts)
An
nuity o
f $1
00
for
3 y
ears
with
a d
iscou
nt
rate
of
10%
69.
248
$10.
)10.
1(1
100
3
PVA
Futu
re V
alu
e
of
an
Ann
uity,
an
nu
al
com
po
un
din
g
rrPMT
FVA
t
t
1)
1(
FV
A=
the
Futu
re
Valu
e o
f th
e A
nn
uity
PM
T=
the a
nn
uity
paym
en
tr=
the
inte
rest
or
dis
cou
nt
rate
t=th
e n
um
ber
of
years
(th
e n
um
ber
of
paym
en
ts)
An
nuity o
f $1
00
for
3 y
ears
with
a d
iscou
nt
rate
of
10%
00.
331
$10.
1)
10.
1(100
3
3FVA
Inte
rest
rate
qu
ote
d
an
nu
ally
com
po
un
de
d
more
tha
n
once a
year
mrr
nom
r=th
e r
ate
per
peri
od
r n
om
=th
e n
om
inal
rate
m=
the
num
ber
of
com
pou
ndin
g
peri
ods p
er
year
A 1
2%
nom
inal ra
te c
om
pou
nd
ed
month
ly is e
quiv
ale
nt to
a p
erio
dic
rate
of
1%
per
month
.
445
EA
RE
quiv
ale
nt
An
nu
al R
ate
(sam
e a
s
usin
g
nom
inal ra
te)
11
m
nom
m
rEAR
EA
R=
the
Eq
uiv
ale
nt
Ann
ual R
ate
r n
om
=th
e n
om
inal
rate
m=
the
num
ber
of
com
pou
ndin
g
peri
ods p
er
year
(com
pari
ng
inte
rest
rate
s w
ith
a c
ert
ain
fr
equ
ency r
ate
with
those t
hat
have
a
diff
ere
nt fr
equ
ency
rate
)
EA
R f
or
10%
com
po
un
de
d s
em
iann
ually
%25.
10
1025
.0
1210.
1
2
EAR
EA
R f
or
10%
com
po
un
de
d q
uart
erl
y
%38.
10
1038
.0
1410.
1
4
EAR
Pre
se
nt
Valu
e o
f a
futu
re C
ash
Flo
w w
hen
th
e inte
rest
rate
is
com
po
un
de
d
m t
imes p
er
year
mt
nomt
m
rCF
PV
1
PV
=P
rese
nt
Valu
eC
Ft=
the C
ash F
low
w
hic
h o
ccurs
at
the
end
of
year
tr
nom
=th
e n
om
inal
inte
rest
rate
m=
the
num
ber
of
com
pou
ndin
g
peri
ods p
er
year
t=th
e n
um
ber
of
years
mt=
the n
um
ber
of
com
pou
ndin
g
peri
ods in t
ye
ars
Pre
se
nt
Valu
e o
f $1
00
to
be
receiv
ed
3 y
ears
fro
m to
da
y if
th
e inte
rest ra
te is 1
0%
com
po
un
de
d q
uart
erl
y
14.
74
$
410.
1
100
)3(
4PV
446
Futu
re V
alu
e
of
an
Ann
uity
wh
en
pa
yme
nts
occur
m
times p
er
year
an
d t
he
in
tere
st ra
te
is
com
po
un
de
d
m t
imes a
ye
ar
m
r
rPMT
FVA
nom
mt
nom
t
1)
1(
FV
At=
the
Futu
re
Valu
e o
f th
e
An
nuity a
t th
e e
nd
of
year
tP
MT
=th
e A
nn
uity
pa
yme
nt
whic
h
occurs
m t
imes a
ye
ar
r nom
=th
e n
om
inal
inte
rest ra
tem
=th
e n
um
ber
of
com
po
un
din
g
peri
ods p
er
yea
rt=
the n
um
ber
of
years
mt=
the
num
ber
of
com
po
un
din
g
peri
ods in
t y
ea
rs
Futu
re V
alu
e a
t th
e e
nd o
f 3
years
of
an a
nn
uity o
f $1
00
per
qu
art
er
for
3 y
ears
if th
e
inte
rest ra
te is 8
% c
om
po
un
de
d q
uart
erl
y
21.
1341
$
408.
1)
408.
1(
100
)3(
4
3FVA
447
Sto
ck V
alu
atio
n E
qu
atio
ns
Nam
e
Equation
Info
rmatio
n
Exa
mple
C
onsta
nt
Gro
wth
S
tock
Valu
ation
gr
D
gr
gD
P1
00
)1(
Po=
the S
tock p
rice a
t tim
e 0
D
o=
the c
urr
ent div
idend
D1=
the n
ext
div
idend (
at
tim
e 1
) g=th
e g
row
th r
ate
in
div
idends
r=th
e r
equired r
etu
rn o
n
the S
tock a
nd g
<r
The S
tock
price g
iven that th
e c
urr
ent
div
idend is
$3 p
er
share
, div
idends
are
exp
ecte
d t
o g
row
at
a r
ate
of 5%
in the f
ore
seeable
futu
re,
and the
required r
etu
rn is 1
0%
.
00
.63
$05
.10
.
)05
.1(
30P
Non-
Consta
nt
Gro
wth
S
tock
Valu
ation
T
c
TT t
t
Tr
grD
r
DP
11
11
0
Po=
the S
tock p
rice a
t tim
e 0
D
t=th
e e
xpecte
d
div
idend a
t tim
e t
T
=th
e n
um
ber
of years
of non-c
onsta
nt gro
wth
gc=
the lo
ng t
erm
const
ant gro
wth
rate
in
div
idends
r=th
e r
equired r
etu
rn o
n
the S
tock a
nd
gc<
r
The S
tock
price g
iven that th
e c
urr
ent
div
idend is
$3 p
er
share
, div
idends
are
exp
ecte
d t
o g
row
at
a r
ate
of 20%
per
year
for
2 y
rs a
nd then a
t a r
ate
of 5%
per
year
from
that
poin
t on, and the r
equired r
etu
rn is
10%
. T
here
are
2 y
rs o
f non-c
onst
ant gro
wth
, so T
=2. It is
necess
ary
to
calc
ula
te e
xpecte
d d
ivid
ends f
or
year
1 thru
3 u
sin
g p
rovi
ded g
row
th r
ate
s.
60
.3
$2
0.
13
1D
32
.4
$2
0.
16
0.
32D
53
6.
4$
05
.1
32
.4
3D
82
.8
1$
10
.1
05
.1
0.
53
6.4
10
.1
32
.4
10
1
60
.3
2
21
0P
Pre
ferr
ed
Sto
ck
Valu
ation
rDP
p
p
Pp=
the P
refe
rred S
tock
Dp=
the p
refe
rred
div
idend
r=th
e r
equired r
etu
rn o
n
the S
tock
The S
tock
price o
f a P
refe
rred S
tock g
iven that th
e p
ar
valu
e is
$100 p
er
share
, th
e p
refe
rred d
ivid
end r
ate
is 5
%, and the r
equired r
etu
rn is
10%
.
50
$1
0.5
10
.
)1
00
(0
5.
pP
448
Bo
nd
Valu
ation
Eq
ua
tion
sN
am
eE
qu
atio
nIn
form
ation
Exam
ple
Bon
d
Pri
ce
t
t
rF
r
r
CB
2
2
0
21
2
21
1
2
Bo=
the
Bon
d V
alu
eC
=th
e a
nn
ual
coup
on
pa
yment
F=
the
face
valu
e o
f th
e B
ond
r=th
e r
equir
ed
re
turn
of
the
Bond
t=th
e n
um
ber
of
years
rem
ain
ing
until m
atu
rity
Face
valu
e o
f sem
iannu
al coup
on
Bond
with
face
valu
e o
f $1,0
00,
a 5
% c
oupo
n
rate
, and
10
years
rem
ain
ing
until m
atu
rity
giv
en t
hat
the
requir
ed
retu
rn is 1
0%
.
44
688
210
1
000
1
210210
11
250
10
2
10
2
0.
$.
,$
..
B
)(
Bon
dY
ield
to
M
atu
rity
t
t
YTM
F
YTMYTM
CB
2
2
0
21
2
21
1
2
Bo=
the
Bon
d p
rice
C=
the
annu
al
coup
on
pa
yment
F=
the
face
valu
e o
f th
e B
ond
YT
M=
the
Yie
ld to
M
atu
rity
on
the
B
on
dt=
the
num
ber
of
years
rem
ain
ing
until m
atu
rity
Yie
ld to
matu
rity
on
a s
em
iann
ual coupo
n b
on
d w
ith
a f
ace v
alu
e o
f $1,0
00,
a 5
%
coup
on
rate
, and
10
ye
ars
rem
ain
ing
until m
atu
rity
giv
en
the
bond
pri
ce o
f $68
8.4
4.
%YTM
YTM,
$
YTM
YTM
.$
)(
)(
10
21
000
1
221
1
250
44
688
10
2
10
2
Bon
dY
ield
to
Call
d
d
YTC
CP
YTCYTC
CB
2
2
0
21
2
21
1
2
Bo=
the
Bon
d p
rice
C=
the
ann
ual
coup
on
pri
ce
CP
=th
e C
all
pri
ce
YT
C=
the
Yie
ld t
o
Call
on
the
bon
dd=
the
num
ber
of
years
rem
ain
ing
until th
e C
all
date
Yie
ld to
Call
on
a s
em
iann
ual B
ond
with
a f
ace v
alu
e o
f $1,0
00
, a
10%
coupo
n
rate
, 10
years
rem
ain
ing
until m
atu
rity
giv
en
that
the
Bond
pri
ce
is $
1,1
00
and
it
can
be
calle
d 5
years
fro
m n
ow
at
a c
all
pri
ce o
f $1,0
00.
%.
YTM
YTC,
$
YTC
YTC
,$
)(
)(
56
7
21
000
1
221
1
2
100
100
15
2
52
449
Cap
ita
l B
udg
etin
g E
qua
tio
ns
Nam
eE
qu
atio
nIn
form
ation
Exam
ple
Net
Pre
sen
t V
alu
e(N
PV
)
T
T
T
t
tr
CF
r
CF
CF
r
CFt
NPV
1...
11
1
10
0
NP
V=
Net
Pre
sent
Valu
eC
Ft=
the
Cash
F
low
at
tim
e t
r=th
e C
ost of
Capital
Pro
ject
A C
ash F
low
--yr
0=
-$500
, yr
1=
$30
0,
yr 2
=$20
0,
yr 3
=$200
Pro
ject
B C
ash F
low
--yr
0=
-$500
, yr
1=
$20
0,
yr 2
=$20
0,
yr 3
=$300
The
calc
ula
tion
of
NP
V u
sin
g P
roje
ct
A a
nd
B—
Cost
of
Capital is
10%
.P
roje
ct
A
28.
88
$10.
1
200
10.
1
200
10.
1
300
500
32
1NPV
Pro
ject
B
50.
72
$10.
1
300
10.
1
200
10.
1
200
500
32
1NPV
Inte
rnal
Rate
of
Retu
rn(I
RR
)
T
T
T t
t
t
IRR
CF
IRR
CF
CF
IRR
CF
NPV
1...
11
01
10
0
NP
V=
Net
Pre
sent
Valu
eC
Ft=
the
Cash
F
low
at
tim
e t
IRR
=In
tern
al
Rate
of
Retu
rn
The
calc
ula
tion
of
IRR
usin
g P
roje
ct
A a
nd
B f
rom
above.
Pro
ject
A
%64.
20
1
200
1
200
1
300
500
03
21
IRR
IRR
IRR
IRR
Pro
ject
B
%5.
17
1
300
1
200
1
200
500
03
21
IRR
IRR
IRR
IRR
Pa
y-B
ack
Peri
od
Payb
ack P
eri
od=
[Last
year
with
a n
eg
ative
NC
F]+
[A
bsolu
te V
alu
e o
f N
CF
in that
year
T
ota
l C
ash F
low
in the
follo
win
g y
ear]
NC
F=
Net
Cash
Flo
wP
roje
ct
AY
r 1=
-200
Yr
2=
0P
roje
ct
BY
r 1=
-300
Yr
2=
-100
The
Payback P
eri
od
of
Pro
ject
A a
nd
B f
rom
above.
Pro
ject
AP
ayback P
eri
od=
1+
200
=2 y
ears
2
00
Pro
ject
BP
ayback P
eri
od=
2+
100
=2.3
3 y
ears
3
00
450
Fin
an
cia
l C
ash
Flo
wN
am
eE
quation
Info
rmation
Exam
ple
($ in M
illio
ns)
Opera
tin
g
Cash
Flo
wO
CF
= E
BIT
+ D
- T
OC
F=
Opera
ting
Cash
F
low
EB
IT=
Earn
ings B
efo
re
Inte
rest
& T
axes
D=
Depre
cia
tio
nT
=T
axes
$42
3 +
$77
- $
30
= $
470
Capital
Spen
din
gC
S =
EN
FA
– B
NF
A +
D
CS
=C
apital S
pen
din
gE
NF
A =
Endin
g N
et
Fix
ed A
ssets
BN
FA
=B
egin
nin
g N
et
Fix
ed A
ssets
D=
Depre
cia
tio
n
$853
- $
920
+ 7
7 =
$10
Additio
ns
To
Net
Work
ing
Capital
AN
WC
= E
NW
C -
BN
WC
AN
WC
=A
dditio
ns to
Net
Work
ing C
apital
EN
WC
=E
ndin
g N
et
Fix
ed A
ssets
BN
WC
=B
egin
nin
g N
et
Work
ing C
apital
$380
- 3
00
= $
80
Net
Work
ing
C
apital
NW
C =
CA
- C
L
NW
C=
Net W
ork
ing
C
apital
CA
=C
urr
ent
Assets
CL=
Curr
ent
Lia
bili
ties
$1,1
50
- $
77
0 =
$38
0
Cash
Flo
wF
rom
A
ssets
CF
A =
OC
F –
CS
+ A
NW
C
CF
A =
Cash
Flo
w fro
m
Assets
OC
F=
Opera
ting
Cash
F
low
CS
=C
apital S
pen
din
gA
NW
C=
Additio
ns to
Net
Work
ing C
apital
$47
0 -
$10
+ $
80
= $
540
451
Cash
Flo
w to
D
ebth
old
ers
CF
D=
IE
– E
LT
D +
BLT
D
CF
D=
Cash
Flo
w to
D
ebth
old
ers
IE=
Inte
rest
Expense
E
LT
D=
Endin
g L
on
g-
Term
Debt
BLT
D=
Begin
nin
g L
on
g-
Term
Debt
$50
- $
571
+ $
71
0 =
$18
9
Cash
Flo
w to
C
om
mon
Sto
ckh
old
ers
CF
CS
= D
P –
(E
CS
–B
CS
) –
(E
CaS
– B
CaS
) -
(ET
S-B
TS
)
CF
CS
=C
ash
Flo
w to
C
om
mon
Sto
ckhold
ers
DP
=D
ivid
ends P
aid
EC
S =
Endin
g C
om
mon
S
tocks
BC
S=
Begin
nin
g
Com
mon
Sto
cks
EC
aS
=E
ndin
g C
apital
Surp
lus
BC
aS
=B
egin
nin
g
Capital S
urp
lus
ET
S=
Endin
g T
reasury
S
tock
BT
S=
Begin
nin
g
Tre
asury
sto
ck
$20
1 -
($12
2 -
$12
0)
- ($
218
- $
210)
+ (
$0
- $
0)
=$19
1
Cash
Flo
wT
oP
refe
rred
Sto
ckh
old
ers
CF
PS
= P
DP
– (
EP
S –
BP
S)
CF
PS
=C
ash
Flo
w to
P
refe
rred
Sto
ckhold
ers
PD
P=
Pre
ferr
ed
D
ivid
en
ds P
aid
EP
S=
Endin
g P
refe
rred
S
tock
BP
S=
Begin
nin
g
Pre
ferr
ed
Sto
ck
$0
(t
his
com
pan
y h
as n
o P
refe
rred
Sto
ck)
452
Cash
Flo
w
To
Investo
rs
CF
I =
CF
D +
CF
CS
+ C
FP
S
CF
I=C
ash
Flo
w to
Investo
rs
CF
D=
Cash
Flo
w to
Debth
old
ers
CF
CS
=C
ash
Flo
w to
Com
mon
Sto
ckhold
ers
CF
PS
=C
ash
Flo
w to
Pre
ferr
ed
Sto
ckhold
ers
$18
9 +
$191
+ $
0 =
$38
0
453
Ra
tio E
qu
atio
ns
Nam
eE
quation
Info
rmation
Exam
ple
($ in M
illio
ns)
Short
-term
Solv
ency
Ratios
Curr
ent
Ratio:
TCL
TCA
CR
Quic
k R
atio:
TCL
ITCA
QR
CR
=C
urr
ent
Ratio
TC
A=
Tota
l C
urr
ent
Assets
TC
L=
Tota
l C
urr
ent
Lia
bili
ties
QR
=Q
uic
k R
atio
TC
A=
Tota
l C
urr
ent
Assets
I=
Invento
ryT
CL=
Tota
l C
urr
ent
Lia
bili
ties
000
1
500
151
,$
,$
.
1000
$
)500
$500
,1($
1
Asset
Managem
ent
Ratios
Receiv
able
s T
urn
over:
ARS
RT
Days
’ R
eceiv
able
s:
RT
DR
365
Invento
ry T
urn
over:
I
COGS
IT
Days
’ In
vento
ry:
IT
DI365
Fix
ed A
ssets
Turn
over:
NFA
SFAT
Tota
l A
ssets
Turn
over:
TAS
RT
=R
eceiv
able
s T
urn
over
S=
Sale
sA
R=
Accoun
t R
eceiv
able
s
DR
=D
ays
’ R
eceiv
able
sR
T=
Receiv
able
s T
urn
over
IT=
Invento
ry T
urn
over
CO
GS
=C
ost
of
Goo
ds S
old
I=
Invento
ry
DI=
Days
’ In
vento
ryIT
=In
vento
ry T
urn
over
FA
T=
Fix
ed
Asset
Turn
over
S=
Sale
sN
FA
=N
et
Fix
ed A
ssets
S=
Sale
sT
A=
Tota
l assets
150
$
500
,1$
10
10
365
5.36
500
$
500
,1$
3
3
365
67.
121
000
1
500
151
,$
,$
.
500
,1$
500
,1$
1
454
Debt
Manag
em
ent
Ratios
Tim
es Inte
rest
Earn
ed
:
IE
EBIT
TIE
Debt
Ratio:
TATOE
TA
TA
TD
DR
Debt
to E
quity R
atio:
TOETOE
TA
TOD
TD
DER
Equity M
ultip
lier:
TOE
TA
EM
TIE
=T
imes inte
rest
Earn
ed
EB
IT=
Earn
ings B
efo
re Inte
rest
and
Taxes
IE=
Inte
rest
Expense
DR
=D
ebt
Ratio
TD
=T
ota
l D
ebt
TA
=T
ota
l A
ssets
TO
E=
Tota
l O
wners
Equity
DE
R=
Debt
to E
quity R
atio
TD
=T
ota
l D
ebt
TO
D=
Tota
l O
wners
’ D
ebt
TA
=T
ota
l A
ssets
TO
E=
Tota
l O
wners
’ E
quity
EM
=E
quity M
ultip
lier
TA
=T
ota
l A
ssets
TO
E=
Tota
l O
wners
’ E
quity
10
$432
$2.
43
000
2
000
1000
250
,$
,$
,$
%
000
1
000
1000
21
,$
,$
,$
000
1
000
22
,$
,$
Pro
fita
bili
tyR
atio
Pro
fit
Marg
in:
SNI
PM
Retu
rn o
n A
ssets
:
TA
NI
ROA
Retu
rn o
n E
quity:
TOE
NI
ROE
PM
=P
rofit M
arg
inN
I=N
et
Incom
e
S=
Sale
s
RO
A=
Retu
rn O
n A
ssets
NI=
Net
Incom
eT
A=
Tota
l A
ssets
RO
E=
Retu
rn O
n E
quity
NI=
Net
incom
eT
OE
= T
ota
l O
wners
Equity
000
2500
25
,$$
%
500
,1$
500
$%
33.
33
000
,1$
500
$%
50
455
Mark
et
Valu
eR
atios
Pri
ce/
Earn
ing
Ratio:
EPS
PPS
PER
Mark
et-
to-B
ook R
atio:
BVPS
PPS
MTB
PE
R=
Pri
ce/E
arn
ing
Ratio
PP
S=
Pri
ce
Per
Share
EP
S=
Earn
ings P
er
Share
MT
B=
Mark
et-
to-B
ook R
atio
PP
S=
Pri
ce
Per
Share
BV
PS
=B
ook V
alu
e P
er
Share
2$25
$5.
12
5$25
$5
Div
iden
dR
atios
Payout
Ratio:
NI
DP
PR
Rete
ntio
n R
atio:
NI
ARE
RR
PR
=P
ayou
t R
atio
DP
=D
ivid
ends P
aid
NI=
Net
Incom
e
RR
=R
ete
ntio
n R
atio
AR
E=
Additio
n to
Reta
ine
d
Earn
ings
NI=
Net
Incom
e
223
$
11
$%
93.4
223
$
212
$%
07.
95
Oth
er
Ratio
Equations
Earn
ings P
er
Share
:
NSO
NI
EPS
Book V
alu
e P
er
Share
:
NSO
TOE
BVPS
EP
S=
Earn
ings P
er
Share
NI=
Net
Incom
eN
SO
=N
um
ber
of
Share
s
Outs
tan
din
gB
VP
S=
Book V
alu
e P
er
Share
TO
E=
Tota
l O
wners
’ E
quity
NS
O=
Num
ber
of
Share
s
Outs
tan
din
g
300
$
223
$74.0$
300
$
600
$2$
456
Em
plo
ym
ent
And
Manag
em
ent
Ratios
Payro
ll C
ost %
= TS
BP
Benefit
Cost
% =
TP
TB
Em
plo
yee
Turn
over
= TE
E1
Managem
ent
Weig
ht =
EM
Pro
ductivity p
er
em
plo
ye
e =
ETS
P=
Pa
yro
llB
=B
en
efits
TS
=T
ota
l S
ale
s
TB
=T
ota
l B
en
efits
TP
=T
ota
l P
ayro
ll
E1=
Em
plo
ye
es w
ho
left
in 1
ye
ar
TE
=T
ota
l E
mplo
ye
es
M=
Mana
gem
ent
E=
Em
plo
ye
es
TS
=T
ota
l S
ale
sE
=A
vera
ge
num
ber
of
Em
plo
ye
es
500
1
72
300
824
,$
$$
%.
300
$
72
$%
24
000
5
50
1,
%
000
5500
10
,%
000
5
500
130
,,$
$.
Mark
eting
R
atios
Impre
ssio
n C
ost
= MBI
Lead
Cost
= MB
SL
I =
Im
pre
ssio
ns
MB
= M
ark
eting
Budg
et
SL
= S
ale
s L
eads
MB
= M
ark
eting
Budg
et
150
000
320
$,$
150
500
110
$,$
457
Ris
k &
Re
turn
Eq
ua
tio
ns
Tab
le 1
– P
ossib
le S
tate
s –
On
e P
eri
od
in
to t
he F
utu
re
Sta
te1
23
4
Pro
ba
bili
ty(m
ust
= 1
00%
)20%
30%
30%
20%
Retu
rn o
nS
tock
A5%
10%
15%
20%
Retu
rn o
nS
tock
B50%
30%
10%
-10%
Nam
eE
quation
Info
rmation
Exam
ple
Expecte
dR
etu
rn
i
N i
iR
pR
E1
E(R
)=th
e E
xpecte
d
Retu
rn o
n the
Sto
ck
N =
the
num
ber
of
sta
tes
Pi =
the
pro
babili
ty o
f sta
te i
Ri =
the
Retu
rn o
n
the
Sto
ck in s
tate
i
Usin
g info
rmation
fro
m T
ab
le 1
, S
tock
A a
nd
Sto
ck
B
Sto
ck
A
%5.
12
%20
20.
%15
30.
%30
30.
%5
20.
AR
E
Sto
ck
B
%%
.%
.%
.%
.R
EB
20
10
20
10
30
30
30
50
20
458
Me
asu
re o
f R
isk –
Va
ria
nce
an
d S
tan
da
rd D
evia
tio
n
Vari
ance
2
1
2R
ER
pR
Var
i
N i
i
N =
the
num
ber
of
sta
tes
Pi =
the
pro
babili
ty o
f sta
te i
Ri =
the
Retu
rn o
n
the
Sto
ck in s
tate
i
E[R
] =
the
Expecte
d
Retu
rn o
n the
Sto
ck
Usin
g T
ab
le 1
and
the
giv
en
Exp
ecte
d R
etu
rn f
rom
the
pre
vio
us p
ag
e,
its
Vari
an
ce
can
no
w b
e c
alc
ula
ted
.S
tock
A
00263
.125
.20.
20.
125
.15.
30.
125
.10.
30.
125
.05.
20.
22
22
2 A
Sto
ck
B
04200
.20.
10.
20.
20.
10.
30.
20.
30.
30.
20.
05.
20.
22
22
2 B
Sta
ndard
Devia
tion
21
22
RSD
Sta
nd
ard
Devia
tion
is
calc
ula
ted
as the
positiv
e s
quare
root
of
the
Vari
ance
Usin
g the
Vari
an
ce
fro
m a
bove,
its S
tan
dard
Devia
tio
n c
an
no
w b
e c
alc
ula
ted
Sto
ck
A
%12.5
0512
.00263
.A
S
tock
B
%49.
20
2049
.04200
.B
Po
rtfo
lio R
isk a
nd
Re
turn
Port
folio
Expecte
dR
etu
rn
i
N i
ip
RE
wR
E1
A p
ort
folio
with
tw
o a
ssets
, S
tock
A a
nd
Sto
ck B
fro
m T
able
1,
the
equ
atio
n a
bove
can
be
expre
ssed
as
21
11
1R
Ew
RE
wR
Ep
E[R
p]
=th
e
Expecte
d R
etu
rn
on
the
Port
folio
N=
the
num
ber
of
Sto
cks in t
he
P
ort
folio
wi=
the
pro
port
ion
of
the
Port
folio
in
veste
d in S
tock i
E[R
i]=
the
Expecte
d
Retu
rn o
n S
tock i
Note
: %5.
12
AR
E a
nd
%20
BR
E
Po
rtfo
lio
co
nsis
tin
g o
f 50
% S
tock
A a
nd
50
% S
tock
B
%25.
16
%20
50.
1%5.
12
50.
pR
E
Po
rtfo
lio
co
nsis
tin
g o
f 75
% S
tock
A a
nd
25
% S
tock
B
%38.
14
%20
75.
1%5.
12
75.
pR
E
459
Po
rtfo
lio V
ari
an
ce
an
d S
tan
da
rd D
evia
tio
ns
Nam
eE
qu
atio
nIn
form
ation
Covariance
Equ
atio
n2
21
1
1
12
21,
RE
RR
ER
PR
RCOV
ii
N i
i
12
=th
e C
ovari
ance
betw
ee
n t
he
Retu
rns o
n S
tocks 1
and
2
N=
the
num
ber
of
sta
tes
Pi=
the
pro
ba
bili
ty o
f sta
te i
R1i=
the
Retu
rn o
n S
tock 1
in s
tate
iE
[R1]=
the
Expecte
d R
etu
rn o
n S
tock 1
R2i=
the
Retu
rn o
n S
tock 2
in s
tate
iE
[R2]=
the
Expecte
d R
etu
rn o
n S
tock 2
Corr
ela
tio
nC
oeff
icie
nt
Equ
atio
n2
1
21
21
12
12
21
,,
RSD
RSD
RR
Cov
RR
Corr
12
=th
e C
orr
ela
tion
betw
ee
n the
retu
rns o
n S
tocks 1
and
2
12
=th
e C
ovari
ance
betw
ee
n t
he
retu
rns o
n S
tocks 1
and
2
1=
the
Sta
ndard
Devia
tion
on
sto
ck 1
2=
the
Sta
nd
ard
Devia
tion
on
Sto
ck 2
Exam
ple
s
Exam
ple
of
Co
vari
an
ce
an
d C
orr
ela
tio
n C
oeff
icie
nt
betw
een
th
e R
etu
rns o
n S
tock
A a
nd
B in
Fig
ure
1
No
te:
%5.
12
AR
E
%
20
BR
E
%
12.5
A
%
49.
20
B
2.1.
125
.2.
2.2.
1.125
.15.2.
2.3.
125
.1.
3.2.
5.125
.05.2.
AB
0105
.AB
1
2049
.0512
.
0105
.AB
Either
the
Corr
ela
tion
Coeff
icie
nt
or
the
Covariance
can
be
used
to
calc
ula
te the
Vari
ance
on
a T
wo-A
sset
Port
folio
21
12
11
2 2
2
12 1
2
12
12
1w
ww
wp
12
11
2 2
2
12 1
2
11
21
ww
ww
460
Exam
ple
of
Vari
an
ce
an
d S
tan
dard
Devia
tio
n o
n P
ort
folio
of
Sto
cks
A a
nd
B in
Fig
ure
1
No
te:
%5.
12
AR
E
%20
BR
E
%12.5
A
%49.
20
B
1
AB
Po
rtfo
lio
co
nsis
tin
g o
f 50
% S
tock
A a
nd
50
% S
tock
B
%68.7
0768
.00591
.
00591
.2049
.0512
.1
5.1
5.2
2049
.5.
10512
.5.
22
22
2 pp
Po
rtfo
lio
co
nsis
tin
g o
f 75
% S
tock
A a
nd
25
% S
tock
B
%28.1
0128
.00016
.
00016
.2049
.0512
.1
75.
175.2
2049
.75.
10512
.75.
22
22
2 pp
461
WA
CC
& G
ord
on
Gro
wth
Mod
el
Nam
eE
qu
atio
nIn
form
ation
Exam
ple
Weig
hte
d
Avera
ge
C
ost
of
Capital
(WA
CC
)
WACC
ce
TF
e
tcd
TF
d
)(
)1)(
(
d=
Debt
TF
=T
ota
l F
inancin
g
(debt
+ e
quity)
cd
=C
ost
of
Debt
t=ta
xce
=C
ost
of
Equity
The M
ark
et
Valu
e o
f D
ebt
= $
30
0 m
illio
nT
he M
ark
et
Valu
e o
f E
quity =
$400
mill
ion
The C
ost
of
Debt
= 8
%T
he C
orp
ora
te T
ax r
ate
= 3
5%
The C
ost
of
Equity =
18%
%5.
12
)18
(.700400
)35.
1)(
08
(.700
300
Gord
on
Gro
wth
Model
GK
DP
P=
Pri
ce
D=
Div
idend
per
Share
1
year
from
now
K
=R
equir
ed
Rate
of
Retu
rn f
or
Equity
investo
rG
=G
row
th R
ate
in
div
iden
ds
Last
year's d
ivid
ed
= $
1.0
0,
Gro
wth
Rate
= 5
%,
Rate
of
Retu
rn =
10%
.
Fir
st figure
out
D
N
ext, u
se
the
form
ula
GD
D1
0
%5
%10
05.1$
P
)05.1(
00.1$
D
5
105
%5
05.1$
P
05.1$
D
00.
21
$P
462
Ris
k &
Re
turn
Eq
ua
tio
ns
Nam
eE
quation
Info
rmatio
nE
xam
ple
Arb
itra
ge
Pri
cin
gT
he
ory
(AP
T)
ii
br
E1
0
irE
Exp
ecte
d R
etu
rn
0=
the
pro
port
ion o
f th
e
Port
folio
consis
tin
g o
f th
e
Ris
k-f
ree
Securi
ty
1=
repre
se
nts
th
e R
isk
Pre
miu
m f
or
the
Macro
econ
om
ic F
acto
r
ib
=th
e s
ensitiv
ity o
f th
e
Retu
rn c
om
pare
d t
o t
he
M
ark
et
Retu
rn
ib1
=re
pre
se
nts
th
e
pro
port
ion o
f th
e R
isky
Asset
Com
pa
ny A
Facto
r F
ore
cast fo
r M
ark
et
Retu
rn2%
2.5
%
-1.5
%
0
.0%
Sta
nd
ard
ize
d E
xposure
s (
facto
r lo
adin
g o
r fa
cto
r be
tas)
Gro
wth
B
on
d
S
ize
RO
E
B
eta
-.
16
.7
4
1.4
7
-0.5
9
.84
AP
T5.3
3%
= (
-.16X
.02)
+ (
.74x.0
25)
+ (
1.4
7X
-.0
15)
+ (
-0.5
9X
0)
Capital A
sset
Pri
cin
g M
odel
(CA
PM
)
if
mf
iR
RE
RR
E
E[R
i]=
the E
xpecte
d R
etu
rn
on
Asset
iR
f=th
e R
isk-f
ree R
ate
E[R
m] =
the
Exp
ecte
d
Retu
rn o
n t
he
Mark
et
Port
folio
Bi =
th
e B
eta
on a
sset
iE
[Rm
]-R
f =
th
e m
ark
et ri
sk
pre
miu
m
Fin
din
g t
he
Exp
ecte
d R
etu
rn o
n S
tock w
here
th
e R
isk-f
ree R
ate
is 6
%,
the
E
xp
ecte
d R
etu
rn o
n t
he
Mark
et
Port
folio
is 1
2%
an
d t
he
Be
ta o
f th
e s
tock is
2.
iR
E=
6%
+ (
12%
-6
%)2
= 1
8%
The
Beta
for
a S
tock
m
imi
2
im=
the
Covari
ance
be
twee
n t
he
Retu
rns o
n
Asset
i a
nd
th
e M
ark
et
Port
folio
m2
=th
e V
ari
ance
of
the
Mark
et
Port
folio
Fin
din
g t
he
Beta
of
a S
tock w
hen
its
Expecte
d R
etu
rn is 1
6%
, th
e R
isk-f
ree
R
ate
is 4
%,
and
th
e E
xpecte
d R
etu
rn o
n th
e M
ark
et P
ort
folio
is 1
2%
.
16%
= 4
% +
(12%
- 4
%)
i
i
5.1
%8
%12
%4
%12
%4
%16
463
Du
Po
nt R
atio
Ana
lysis
fo
r E
valu
atin
g R
etu
rn o
n E
qu
ity (
RO
E)
Nam
eE
qu
atio
nIn
form
ation
Exam
ple
($ in m
illio
ns)
Net
Pro
fit
Marg
inRNI
NPM
Com
pon
ent
1
NP
M=
Net
Pro
fit
Marg
inN
I=N
et
Incom
eR
=R
evenu
e
Revenue
= $
30,0
00
N
et In
com
e =
$4,0
00
A
ssets
= $
30,0
00
Share
hold
ers
’ E
quity =
$14,0
00.
000
,30
$
000
,4$
1333
.0
Asset
Turn
over
ARAT
Com
pon
ent
2
AT
=A
sset
Turn
over
R=
Revenu
eA
=A
ssets
000
,30
$
000
,30
$00.1
Equity
Multip
lier
SEA
EM
Com
pon
ent
3
EM
=E
quity M
ultip
lier
A=
Assets
SE
=S
hare
hold
er
Equity
000
,14
$
000
,30
$1429
.2
Fin
ally
, m
ultip
ly the
thre
e c
om
po
ne
nts
to c
alc
ula
te t
he
Retu
rn o
n E
quity.
Retu
rn
on
E
quity
))(
)((
EM
AT
NPM
ROE
RO
E is o
ne
of
the
most
import
ant
indic
ato
rs o
f a c
om
pany’s
pro
fita
bili
ty
and
pote
ntial gro
wth
.
RO
E=
Retu
rn o
n E
quity
NP
M=
Net
Pro
fit
Marg
inA
T=
Asset
Turn
over
EM
=E
quity M
ultip
lier
%65.
28
2865
.0
)1429
.2(
)00.1(
)1333
.0(
xx
When lookin
g a
t th
e c
om
pone
nts
of
the
Retu
rn o
n E
quity o
ver
time,
the
analy
st
gain
s insig
ht
into
wh
at
were
the
causes f
or
impro
vem
ents
of
sim
ilar
com
panie
s,
even
wh
en
their
RO
E is e
qu
al.
464
Fa
ma
Fre
nch
Ris
k a
nd
Re
turn
Eq
ua
tio
ns
Nam
eE
qu
atio
nIn
form
ation
Exam
ple
Fam
aF
rench
T
hre
eF
acto
rM
odel
HML
SMB
RR
RR
Ef
mi
fi
32
E(R
i)=
Expecte
d
Retu
rn f
or
Asset
iR
m=
Expecte
d R
etu
rn
for
the
Mark
et
Rf=
the
Retu
rn f
or
a
Ris
k-f
ree A
sset
Rm
-Rf=
the
Mark
et
Ris
k P
rem
ium
SM
B=
Expecte
d
Retu
rn d
iffe
rence
of
Sm
all
and
Big
Sto
cks
(Sm
all
Min
us B
ig)
HM
L=
the
Expecte
d
Retu
rn d
iffe
rence
of
Sto
cks w
ith
Hig
h a
nd
Lo
w B
ook-t
o-M
ark
et
Equity R
atio
(H
igh
M
inus L
ow
)B
i=B
eta
of
Sto
ck i
B2=
perc
enta
ge
of
Sm
all
and
Big
Caps in
P
ort
folio
B3=
perc
en
tage
of
Sm
all
and
Larg
e C
ap
S
tock in P
ort
folio
Fin
din
g the
Expecte
d R
etu
rn o
n S
tock i w
here
the
Ris
k-
free R
ate
is 6
%,
the
Expecte
d R
etu
rn o
n the
Mark
et
Port
folio
is 1
2%
and
the
Beta
of
Sto
ck i =
2.
B2
has 5
0%
S
mall
Cap a
nd
50%
Larg
e C
aps in this
Port
folio
. B
3 a
lso
has 5
0%
Sm
all
Caps a
nd
50%
Larg
e C
aps in
this
P
ort
folio
. S
MB
= -
.1 a
nd
HM
L =
.1.
1.5.
1.5.
%6
%12
2%6
iR
E
1.5.
1.5.
06.
12.2
06.
iR
E
05.
05.
12.
06.
iR
E
%18
18.
iR
E
465
Info
rma
tio
n P
rod
uctivity A
sse
ssm
en
tN
am
eE
quation
Info
rmation
Exam
ple
Info
rmation
Pro
ductivity
Form
ula
CIM
EVA
IP
IP=
Info
rmation
Pro
ductivity
EV
A=
Econ
om
ic V
alu
e A
dde
dC
IM=
Cost
of
Info
rmation
Managem
ent
Com
pan
y A
%98.8
122
,128
,1$
300
,101
$IP
466
Tre
asu
ry M
an
ag
em
en
t E
qu
atio
ns
Nam
eE
quation
Info
rmation
Exam
ple
($ in m
illio
ns)
Gro
ss
Pro
fit
Marg
inRGP
GPM
GP
M=
Gro
ss P
rofit M
arg
inG
P=
Gro
ss P
rofit
R=
Revenue
Note
: S
ale
s –
Cost of G
ood S
old
= G
ross P
rofit
71
016
10
73
5,
$$%.
Opera
ting
Pro
fit
Marg
inR
EBITDA
OPM
OP
M=
Opera
ting P
rofit M
arg
inE
BIT
DA
=E
arn
ings b
efo
re Inte
rest,
Taxes, D
epre
cia
tion, and
A
mort
ization
R=
Revenues
71
015
30
31
,$$
%
Net
Pro
fit
Marg
inSNI
NPM
NP
M=
Net P
rofit M
arg
inN
I=N
et In
com
eS
=S
ale
s7
10
134
32
0,
$$%
Cash
Flo
w to
Tota
lD
ebt R
atio
TD
CF
CFTDR
CF
TD
R=
Cash F
low
to T
ota
l D
ebt
Ratio
CF
=C
ash F
low
TD
=Tota
l D
ebt
Note
: C
ash F
low
is N
et In
com
e p
lus D
epre
cia
tion
571
$420
$%
5.73
Work
ing
C
apital
CL
CA
WC
WC
=W
ork
ing C
apital
CA
=C
urr
ent A
ssets
CL=
Curr
ent Lia
bili
ties
770
150
1380
$,
$$
Cash
Convers
ion
Effic
iency
S
CFO
CCE
CC
E=
Cash C
onvers
ion E
ffic
iency
CF
O=
Cash F
low
fro
m O
pera
tions
S=
Sale
s
Note
: C
ash F
low
fro
m O
pera
tions =
EB
IT+
Depre
cia
tion-T
axes
71
014
70
52
7,
$%.
Taxable
Equiv
ale
nt
Yie
ld)
MTR
(
TY
TEY
1
TE
Y=
Taxable
Equiv
ale
nt Y
ield
TY
=Tax-e
xem
pt Y
ield
MT
R =
Marg
inal T
ax R
ate
)28
.1(
%5.
4%
25
.6
Hold
ing
P
eri
od
Yie
ldI
ICRM
HPY
)(
HP
Y=
Hold
ing P
eri
od Y
ield
CR
M=
Cash R
eceiv
ed a
t M
atu
rity
I=A
mount In
veste
d000
1
000
1200
120
,$
,$
,$
%
467
Annual
Yie
ld
DM
DY
HPY
AY
AY
=A
nnual Y
ield
HP
Y=
Hold
ing P
eri
od Y
ield
DY
=D
ays in Y
ear
DM
=D
ays to M
atu
rity
365
365
20.
%20
Purc
hase
Pri
ce
DD
PPP
PP
=P
urc
hase P
rice
P=
Par
Valu
eD
D=
Dolla
r D
iscount
10
$100
$90
$
Dolla
rD
iscount
360
360
360
DM
PDR
DD
DD
=D
olla
r D
iscount
DR
=D
iscount R
ate
P=
Par
Valu
eD
M=
Days to M
atu
rity
360
360
)100
)(10
(.10
$
Dis
count
Rate
360
DM
P
DD
DR
DR
=D
iscount R
ate
DD
=D
olla
r D
iscount
P=
Par
Valu
eD
M=
Days to M
atu
rity
360
360
100
$
10
$%
10
Money
Mark
et
Yie
ldDM
HPY
MMY
360
MM
Y=
Money M
ark
et Y
ield
HP
Y=
Hold
ing P
eri
od Y
ield
DM
=D
ays to M
atu
rity
360
360
20.
%20
Bond
E
quiv
ale
nt
Yie
ldDM
HPY
BEY
365
BE
Y=
Bond E
quiv
ale
nt Y
ield
HP
Y=
Hold
ing P
eri
od Y
ield
DM
=D
ays to M
atu
rity
360
365
20.
%3.
20