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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