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© Practising Law Institute

CORPORATE LAW AND PRACTICECourse Handbook Series

Number B-2157

How to ReadFinancial Statements

2015

ChairChad Rucker

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9

A Valuation Primer for Attorneys (PowerPoint slides)

Chad Rucker

Valuation Research Corporation

If you find this article helpful, you can learn more about the subject by going to www.pli.edu to view the on demand program or segment for which it was written.

305


306


A V

alu

ation P

rim

er

for

Attorn

eys

Co

nta

ct:

Ch

ad

Ru

cker

Ma

na

gin

g D

ire

cto

r

Valu

ati

on

Researc

h C

orp

ora

tio

n

500 F

ifth

Aven

ue

New

Yo

rk,

New

Yo

rk 1

0110

Mo

bile (

732)

855-9

241

Ph

on

e (

917)

338-5

613

Em

ail:

cru

cker@

valu

ati

on

researc

h.c

om

307


Pri

nc

ipa

l C

on

ce

pt

2

A d

ollar

tom

orr

ow

is w

ort

h l

ess t

han

a d

ollar

tod

ay.

To d

ete

rmin

e t

he v

alu

e o

f th

e d

olla

r th

at

you w

ill r

eceiv

e tom

orr

ow

in today’s

dolla

rs

you a

re c

oncern

ed w

ith t

wo p

rincip

al is

sues.

Ho

w m

uch

am

I s

up

po

se t

o r

eceiv

e t

om

orr

ow

?

Ho

w m

uch

ris

k i

s t

here

to

me i

n a

ctu

ally r

eceiv

ing

th

ose d

ollars

tom

orr

ow

?

308


Pri

nc

ipa

l C

on

ce

pt

3

R

isk in r

eceiv

ing

Tom

orr

ow

’s D

olla

rs

Today

Tom

orr

ow

Tom

orr

ow

’s D

olla

rs

Valu

e T

oday ?

?

0

1

$10

2

Tim

elin

e

309


Pri

nc

ipa

l C

on

ce

pt

4

When w

e r

efe

r to

the v

alu

e o

f a c

om

pany w

e a

re t

ypic

ally

refe

rrin

g t

o e

nte

rprise

valu

e.

Ente

rprise V

alu

e =

V

alu

e o

f E

quity

+

De

bt

-

Exce

ss C

ash

= E

nte

rpri

se

Valu

e

310


Ob

jecti

ves

The o

bje

ctives o

f to

day’s

pre

senta

tion a

re t

o e

xpla

in fundam

enta

l valu

ation c

oncepts

to

attorn

eys.

Our

goals

are

:

5

Go

al

#1

Expla

in d

iscounte

d c

ash flo

w a

naly

sis

;

Go

al

#2

Expla

in E

BIT

DA

Multip

le V

alu

ations

Go

al

#3

Expla

in the r

ela

tionship

betw

een D

CF

’s a

nd E

BIT

DA

multip

les

- A

n E

BIT

DA

mu

ltip

le is a

sh

ort

ha

nd

me

tho

d o

f D

CF

- C

an

be

use

d w

he

n y

ou

do

n’t h

ave

sp

ecific

ca

sh

flo

w p

roje

ctio

ns

- A

n E

BIT

DA

mu

ltip

le im

plic

itly

assu

me

s c

ert

ain

gro

wth

ra

tes th

at

m

ay b

e b

ase

d u

po

n a

n in

du

str

y o

f co

mp

ara

ble

co

mp

an

y a

pp

roa

ch

Our

overa

ll obje

ctive is to p

rovid

e y

ou w

ith a

basic

unders

tandin

g o

f valu

ation

concepts

so that

you w

ill b

e a

ble

to p

rovid

e t

he a

bsolu

te b

est

legal serv

ices p

ossib

le

to y

our

clie

nts

.

311


Dis

counte

d C

ash F

low

Analy

sis

“DC

F”

6

312


DC

F

A D

CF

analy

sis

dis

counts

futu

re f

ree c

ash f

low

s p

roje

ction t

o a

rriv

e a

t a p

resent

valu

e

(valu

e today in today’s

dolla

rs)

of

those c

ash flo

ws.

7

Fre

e C

ash

Flo

w

“F

CF

”

Fre

e c

ash

flo

w is e

xce

ss c

ash

th

at a

co

mp

an

y g

en

era

tes a

fte

r it p

ays its

exp

en

se

s, m

ake

s n

ece

ssa

ry c

ap

ita

l e

xp

en

ditu

res a

nd

ta

ke

s in

to a

cco

un

t

its w

ork

ing

ca

pita

l n

ee

ds.

Dis

co

un

tR

ate

Th

e in

tere

st ra

te th

at is

use

d to

dis

co

un

t th

e p

roje

cte

d c

ash

flo

ws. T

he

less r

isky t

he c

ash

flo

ws,

the l

ow

er

the d

isco

un

t ra

te.

Th

e

riskie

r th

e c

ash

flo

ws t

he h

igh

er

the d

isco

un

t ra

te.

Term

inal V

alu

e

Th

e v

alu

e o

f th

e c

om

pa

ny a

t th

e e

nd

of a

pro

jecte

d p

eri

od

. T

his

va

lue

rep

rese

nts

th

e v

alu

e o

f a

ll fu

ture

ca

sh

flo

ws o

f th

e c

om

pa

ny a

fte

r a

sp

ecifie

d p

eri

od

.

313


FC

F

8

Revenues

- C

ost of goods s

old

(E

xclu

din

g D

epre

cia

tion)

= G

ross p

rofi

ts

- S

elli

ng G

enera

l Adm

inis

trative E

xpenses

= E

arn

ing

s B

efo

re In

tere

st

Taxes a

nd

Dep

recia

tio

n (

“E

BIT

DA

”)

- D

epre

cia

tion a

nd A

mort

ization

= U

nle

vere

d P

reta

x In

co

me

- Taxe

s %

= U

nle

vere

d N

et

Inco

me

+ D

epre

cia

tion a

nd A

mort

ization

- In

cre

ase in W

ork

ing C

apital (+

Decre

ase in W

ork

ing c

apital)

- C

apital expenditure

s

= F

ree C

ash

Flo

w

Fo

rmu

la f

or

Calc

ula

tin

g F

ree C

ash

Flo

w

314


EB

ITD

A A

lte

rna

tiv

e M

eth

od

9

N

et

Incom

e

+ T

axe

s

+ Inte

rest

Expense (

net

of

inte

rest

incom

e)

+ D

epre

cia

tion a

nd A

mort

ization

= E

arn

ing

s B

efo

re In

tere

st

Taxes a

nd

Dep

recia

tio

n (

“E

BIT

DA

”)

- E

BIT

DA

Adju

stm

ents

(one-t

ime ite

ms)

= A

dju

ste

d E

BIT

DA

Alt

ern

ati

ve F

orm

ula

fo

r C

alc

ula

tin

g E

BIT

DA

an

d A

dju

ste

d E

BIT

DA

315


FC

F E

xam

ple

10

AB

C c

orp

ora

tion e

xpects

to d

evelo

p a

nd m

anufa

ctu

re a

new

table

t pc to c

om

pete

again

st th

e p

opula

r IP

AD

. A

BC

has a

n e

xecutive m

anagem

ent

team

that

earn

s

appro

xim

ate

ly $

20 m

illio

n a

nnually

. I

t anticip

ate

s o

n s

elli

ng 1

mill

ion table

t pcs a

t

$200 pie

ce. A

BC

anticip

ate

s o

n b

ein

g a

ble

to m

anufa

ctu

re t

he t

able

t pcs for

appro

xim

ate

ly $

75 e

ach.

In o

rder

to a

chie

ve these g

row

th t

arg

ets

, A

BC

will

have to incre

ase its

work

ing c

apital

levels

because o

f hig

her

invento

ry a

nd a

ccounts

receiv

able

s. W

ork

ing c

apital is

expecte

d to incre

ase fro

m $

30 m

illio

n to $

57 m

illio

n. A

BC

als

o e

xpects

to h

ave to

invest $10 m

illio

n in e

xpandin

g its

manufa

ctu

ring p

lant

and w

ill h

ave a

marg

inal ta

x

rate

of

30%

. T

he c

om

pany a

nticip

ate

s o

n incurr

ing d

epre

cia

tion e

xpense o

f $3 m

illio

n

this

year.

Com

pute

AB

C’s

FC

F o

n t

he f

ollo

win

g p

age.

316


FC

F E

xam

ple

11

Com

puting A

BC

’s F

CF

317


FC

F E

xam

ple

12

Revenues

- C

ost of goods s

old

(E

xclu

din

g D

epre

cia

tion)

200.0

- 75.0

= G

ross p

rofi

ts

- S

elli

ng G

enera

l Adm

inis

trative E

xpenses

125.0

- 20.0

= E

arn

ing

s B

efo

re In

tere

st

Taxes a

nd

Dep

recia

tio

n (

“E

BIT

DA

”)

- D

epre

cia

tion a

nd A

mort

ization

105.0

-

3.0

= U

nle

vere

d P

reta

x In

co

me

- Taxe

s %

102.0

0

- 30.6

0

= U

nle

vere

d N

et

Inco

me

71.4

+ D

epre

cia

tion a

nd A

mort

ization

- In

cre

ase in W

ork

ing C

apital

- C

apital expenditure

s

+

3.0

- 27.0

- 10.0

= F

ree C

ash

Flo

w

37.4

The A

nsw

er

318


Dete

rmin

ing D

iscount

Rate

13

319


Dis

co

un

t R

ate

s

Havin

g a

dolla

r to

day is w

ort

h m

ore

than h

avin

g a

dolla

r to

morr

ow

. I

n o

rder

to

dete

rmin

e t

he v

alu

e o

f a d

olla

r th

at

you w

ill r

eceiv

e tom

orr

ow

it m

ust

be d

iscounte

d to

dete

rmin

e w

hat

that

valu

e is t

oday.

The a

mount

that

you d

iscount th

at

by is c

alle

d the d

iscount ra

te.

To d

ete

rmin

e t

he D

iscount ra

te y

ou n

eed t

he f

ollo

win

g ite

ms

14

Eq

uit

y

• R

isk fre

e R

ate

• R

equired m

ark

et

retu

rn

• C

ost

of

equity

• B

eta

of

the c

om

pany

• P

erc

enta

ge o

f equity in c

apital str

uctu

re

Deb

t

• C

ost

of

Debt

• P

erc

enta

ge o

f D

ebt

in c

apital str

uctu

re

• T

ax r

ate

320


Co

st

of

Eq

uit

y

15

Ris

k F

ree R

ate

Curr

ent

yie

ld o

n 2

0 y

ear

U.S

. T

reasury

bond

Beta

C

orr

ela

tion o

f R

etu

rns w

ith that

of

the F

inancia

l

mark

ets

as a

whole

-

Beta

of

1.0

would

repre

sent

perf

ect

co

rre

latio

n t

o t

he

ma

rke

t

-

Beta

of

1.1

5 w

ould

repre

sent

retu

rns

that

are

1.1

5 t

imes t

he m

ark

et

-

Beta

is d

ete

rmin

ed b

y lookin

g a

t re

turn

s

of

sim

ilar

co

mp

an

ies

Req

uir

ed

mark

et

retu

rn

The d

iffe

rence b

etw

een t

he e

xpecte

d m

ark

et

retu

rn

and r

isk fre

e r

ate

of

retu

rn

321


Co

st

of

Eq

uit

y

16

The C

apital A

sset P

ricin

g M

odel is

used to c

alc

ula

te the c

ost

of

equity

Ris

k F

ree

Ra

te

+

[B

eta

x (

Re

qu

ire

d M

ark

et

Re

turn

– R

isk F

ree

Ra

te)]

C

ost o

f e

qu

ity

=

Co

st o

f E

qu

ity

322


Co

st

of

Eq

uit

y

17

Com

pute

the c

ost

of

equity for

the f

ollo

win

g.

A c

om

pany h

as a

beta

that

is e

qual to

2.0

. T

he c

urr

ent

20 y

ear

U.S

. T

reasury

is

yie

ldin

g 1

0%

and t

he r

equired m

ark

et

retu

rn is 1

5%

. W

hat

is the c

ost

of

equity.

_

__

__

__

+ _

____

x (

___

- ___ )

_____________________________

Cost of

equity

= _

______

______

+_____x_____

Cost of

equity

= _

______

323


Co

st

of

Eq

uit

y

18

C

ost

of

eq

uity

= 1

0%

+

2.0

x (

15%

- 1

0%

)

10%

+ 2

.0 (

5%

)

C

ost

of

eq

uity

=

20

%

324


Co

st

of

De

bt

19

Lik

e the c

ost

of

equity,

the c

ost

of

debt

is d

ete

rmin

ed b

y lookin

g a

t th

e c

ost

of

debt

of

com

para

ble

com

panie

s w

ith s

imila

r risk p

rofile

s.

The c

ost

of

debt

for

sim

ilar

com

panie

s c

an b

e d

ete

rmin

ed b

y lookin

g a

t

Blo

om

berg

or

oth

er

such

data

sourc

es.

Because d

ebt

inte

rest

is tax d

eductible

, th

e c

ost

of

debt

of

com

para

ble

com

panie

s m

ust

be m

ultip

lied b

y (

1 –

tax r

ate

).

325


Co

st

of

De

bt

20

Co

st

of

De

bt

(Yie

ld)

Com

pany A

15%

Com

pany B

10%

Com

pany C

5%

____________________________________

Hig

h

15%

Media

n

10%

Lo

w

5%

Sele

cte

d R

ate

326


Dis

co

un

t R

ate

21

Dis

count R

ate

= P

erc

enta

ge E

quity x

Cost

of

Equity

+ P

erc

en

tag

e D

eb

t x [

Co

st

of

De

bt

x (

1-T

ax r

ate

)]

______________________________________

= D

isco

un

t R

ate

327


Dis

co

un

t R

ate

22

For

our

exam

ple

, assum

e that

60%

of

the c

om

pany’s

capital str

uctu

re is e

quity that

has a

20%

cost, a

nd 4

0%

of

the c

om

pany’s

capital str

uctu

re is d

ebt

with a

10%

cost.

The c

om

pany’s

tax r

ate

is 3

0%

.

Dis

count R

ate

= P

erc

enta

ge E

quity x

Cost

of

Equity

+

Pe

rce

nta

ge

De

bt x [

Co

st

of

De

bt

x (

1-T

ax R

ate

)]

=

Dis

count R

ate

Dis

count R

ate

= .

60 x

.20

+ .

40

x .

10

(1

-.3

0)

Dis

count R

ate

= .

120

+ .

40

x .

10

(.7

0)

Dis

count R

ate

= .

120

+ .

02

8

= .

148 =

14.8

%

~

15%

Rounded

328


Net P

resent

Valu

e

23

329


Ne

t P

res

en

t V

alu

e

Y

ea

r

0

1

2

3

F

CF

$

37

.4

$

41

.4

$

45

.3

Pre

sent V

alu

e e

quals

the s

um

of

the p

resent

valu

es o

f cell

of

the s

ubsequent cash flo

ws

P

resent

Valu

e o

f Y

ear

1 F

CF

+ P

resent

Valu

e o

f Y

ear

2 F

CF

+ P

resent

Valu

e o

f Y

ear

3 F

CF

+ T

he P

resent

Valu

e o

f th

e Y

ear

3 T

erm

inal V

alu

e

= P

resen

t V

alu

e o

f cash

flo

w

24

330


Ne

t P

res

en

t V

alu

e

In o

rder

to d

ete

rmin

e t

he p

resent

valu

e o

f th

e Y

ear

1 F

CF

, th

e Y

ear

1 F

CF

must

be

dis

counte

d Y

ear

0 (

curr

ent

period).

T

he Y

ear

1 F

CF

is d

iscounte

d t

o t

he c

urr

ent

period

by d

ivid

ing that

num

ber

by (

1 +

dis

count

rate

).

Ye

ar

0

1

2

3

F

CF

$3

7.4

25

PV

of Y

ear

1 F

CF

= 3

7.4

(

1 +

dis

co

un

t ra

te)

Assum

e the d

iscount ra

te is 1

5%

PV

of Y

ear

1 F

CF

= 3

7.4

(

1.1

5)

=

32

.5

331


Ne

t P

res

en

t V

alu

e

Y

ea

r

0

1

2

3

F

CF

$

41

.4

26

Year

2 C

F taken b

ack o

ne y

ear

= 4

1.4

(

1 +

dis

co

un

t ra

te)

= 4

1.4

(

1 +

.1

5)

= 4

1.4

(

1.1

5)

=

36

.0

PV

of Y

ea

r 2

CF

ta

ke

n b

ack o

ne

ad

ditio

na

l ye

ar

= 3

6.0

(

1 +

dis

co

un

t ra

te)

= 3

6.0

(

1 +

.1

5)

= 3

6.0

(

1.1

5)

= 3

1.3

In o

rder

to d

ete

rmin

e t

he p

resent

valu

e o

f th

e Y

ear

2 F

CF,

the Y

ear

2 F

CF

must

be

firs

t dis

counte

d b

ack to Y

ear

1. T

hen t

hat

am

ount

must

be d

iscounte

d to t

he

curr

ent

period.

36

.0

332


Ne

t P

res

en

t V

alu

e

In o

rder

to d

ete

rmin

e t

he p

resent

valu

e o

f th

e Y

ear

3 F

CF,

the Y

ear

3 F

CF

must

be f

irst

dis

counte

d b

ack to Y

ear

2.

Then that

am

ount

must

be d

iscounte

d b

ack to Y

ear

1.

Then

that

am

ount

must

be d

iscounte

d b

ack to Y

ear

0.

3

4.3

39

.4

Y

ea

r

0

1

2

3

4

5.3

27

Year

3 C

F d

iscounte

d b

ack to y

ear

2

Ye

ar

3 C

F d

isco

un

ted

fro

m y

ea

r 2

to

ye

ar

1

= 4

5.3

(

1 +

dis

co

un

t ra

te)

= 4

5.3

(

1 +

.1

5)

= 4

5.3

(

1.1

5)

= 3

9.4

= 3

9.4

(

1 +

dis

co

un

t ra

te)

= 3

9.4

(

1 +

.1

5)

= 3

4.3

333


Ne

t P

res

en

t V

alu

e

28

Year

3 C

F d

iscounte

d f

rom

Year

1 t

o Y

ear

0

= 34.3

(

1 +

dis

co

un

t ra

te)

= 34.3

(

1 +

.15)

= 34.3

(

1.1

5)

= 2

9.8

334


Ne

t P

res

en

t V

alu

e

A s

hort

cut

for

doin

g a

calc

ula

tion for

each y

ear

is

F

CF

(

1 +

dis

count)

num

ber

of

years

For

exam

ple

a s

hort

cut

for

com

puting t

he P

V o

f Y

ear

3 F

CF

is

= _

_____Y

ear

3 F

CF

______

(

1 +

.15)

(1 +

.15)

(1 +

.15)

= Y

ear

3 F

CF

(

1 +

.1

5)3

or

Y

ear

3 F

CF

(

1 +

dis

co

un

t) n

um

be

r o

f ye

ars

= 4

5.3

(

1 +

.1

5)3

= 4

5.3

(

1.1

5)3

= 4

5.3

(

1.5

2)

= 2

9.8

29

335


Term

inal V

alu

e

30

336


Te

rmin

al V

alu

e

31

So far

we h

ave o

nly

dis

counte

d c

ash flo

ws fo

r th

ree y

ears

. H

ow

ever, the b

usin

ess

will

continue t

o o

pera

te longer

than t

hose t

hre

e y

ears

.

There

fore

we m

ust

account fo

r th

ose c

ash flo

ws that

occur

past th

e p

eriod in w

hic

h

we h

ave e

stim

ate

s.

We a

ccount

these a

dditio

nal cash flo

ws thro

ugh t

he t

erm

inal valu

e.

Term

inal V

alu

e r

epre

sents

the v

alu

e o

f all

expecte

d futu

re c

ash flo

ws a

fter

a p

art

icula

r

period.

Typic

ally

, an e

stim

ate

is m

ade o

f w

hat

the f

ree c

ash flo

w w

ill b

e f

or

one a

dditio

nal

period.

337


Te

rmin

al V

alu

e

32

Term

inal V

alu

e r

epre

sents

the v

alu

e o

f all

expecte

d futu

re c

ash flo

ws a

t a p

art

icula

r

period.

In o

ur

exam

ple

, w

e h

ave looked a

t 3 y

ears

of

Fre

e C

ash F

low

. H

ow

ever

the b

usin

ess

still

will

genera

te c

ash flo

w a

fter

that

period. T

he c

ash flo

ws d

o n

ot

sto

p a

fter

year

3.

Sin

ce w

e h

ave the c

ash flo

ws for

3 y

ears

, w

e e

stim

ate

the c

ash flo

ws for

one

additio

nal period,

year

4 a

nd d

iscount th

at

back t

o p

resent

valu

e.

The term

inal valu

e r

epre

sents

the v

alu

e in Y

ear

4 o

f all

of

those e

xpecte

d f

utu

re c

ash

flow

s.

One m

eth

od o

f doin

g that

is the G

ord

on G

row

th m

eth

od.

T

V =

Ye

ar

4 F

CF

(Dis

count R

ate

– E

xpecte

d G

row

th R

ate

)

338


Te

rmin

al V

alu

e

33

First, w

e m

ust

estim

ate

what

the Y

ear

4 c

ash f

low

will

be.

For

our

purp

oses,

assum

e t

hat

in Y

ear

4,

Fre

e C

ash F

low

s w

ill b

e $

50.

We w

ill a

lso a

ssum

e t

hat

the e

xpecte

d p

erp

etu

ity

gro

wth

rate

will

be 3

%.

50.0

T

V =

(.1

5-.

03

)

Y

ea

r

0

1

2

3

4

50

T

V

$4

16

.6

T

V =

.12

T

V =

4

16.6

Rem

em

ber

this

term

inal valu

e r

epre

sents

a v

alu

e in Y

ear

4.

As a

result,

the Y

ear

4 t

erm

inal valu

e m

ust

be d

iscounte

d b

ack t

o Y

ear

0.

Pre

se

nt

Valu

e o

f Term

ina

l V

alu

e

= 416.6

(

1 +

dis

count ra

te)4

= 416.6

(

1 +

.15)4

= 416.6

(

1.1

5)4

= 2

38

.1

Exponent r

epre

sents

dis

counting back for

3

pe

riods

339


Pre

se

nt

Va

lue

P

rese

nt

Va

lue

of

Ye

ar

1 F

CF

3

2.5

+ P

rese

nt

Va

lue

of

Ye

ar

2 F

CF

31

.3

+ P

rese

nt

Va

lue

of

Ye

ar

3 F

CF

2

9.8

+ T

he P

resent

Valu

e o

f th

e Y

ear

4 T

erm

inal V

alu

e

2

38

.1

= P

res

en

t V

alu

e

$3

01

.9

34

340


NOTES

341


NOTES

342

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