option valuation by aswath damodaran

8/2/2019 Option Valuation by Aswath Damodaran

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1

EquityInstrum

entsan

dMarkets:

PartIII

B40.3331

RealOptions

Acq

uisitionValuation

Va

lueEnhancement

AswathDamodaran


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2

Unde

rlyingTheme:Searching

foranElusive

Premium

Tra

ditionaldiscounted

cashflowmodelsu

nderestimatethev

alueof

inv

estments,wherethereareoptionsemb

eddedintheinvestmentsto

Delayordefermakingtheinvestment(de

lay)

Adjustoralterproductionschedulesaspricechanges(flexibility)

Expandintonewma

rketsorproductsatlaterstagesintheproc

ess,based

uponobservingfavo

rableoutcomesatthe

earlystages(expansion)

Stopproductionora

bandoninvestmentsiftheoutcomesareun

favorable

atearlystages(aban

donment)

Putanotherway,realoptionadvocatesbe

lievethatyoushou

ldbe

pay

ingapremiumondiscountedcashflow

valueestimates.


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3

ThreeBasicQuestions

Wh

enistherearealoptionembeddedinadecisionoranass

et?

Wh

endoesthatrealoptionhavesignifica

nteconomicvalue?

Canthatvaluebeestim

atedusinganoptionpricingmodel?


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4

Wh

enistherea

noptionembeddedinan

action?

An

optionprovidestheholderwiththerighttobuyorsella

specified

quantityofanunderlyingassetatafixed

price(calledastrik

epriceor

anexerciseprice)atorbeforetheexpirationdateoftheoption.

Therehastobeaclearlydefinedunderlyingassetwhosevalue

cha

ngesovertimeinu

npredictableways.

Thepayoffsonthisasset(realoption)havetobecontingent

onan

spe

cifiedeventoccurringwithinafinitep

eriod.


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5

PayoffD

iagramona

Call

Priceofunderlyingasset

Stri

ke

Price

NetPa

yoff

onCall


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6

PayoffDia

gramonPutOption

Priceof

underlyingasset

Strike

Price

NetPayoff

On

Put


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7

W

hendoestheoptionhavesignificant

eco

nomicvalue?

Foranoptiontohavesignificanteconomicvalue,therehastobea

restrictiononcompetitionintheeventof

thecontingency.In

a

per

fectlycompetitiveproductmarket,no

contingency,nomatterhow

positive,willgenerate

positivenetpresen

tvalue.

At

thelimit,realoptio

nsaremostvaluablewhenyouhaveexclusivity

-youandonlyyoucantakeadvantageof

thecontingency.T

hey

bec

omelessvaluableasthebarrierstoco

mpetitionbecomelesssteep.


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8

Determinantsofoptionvalue

VariablesRelatingtoUn

derlyingAsset

ValueofUnderlyingA

sset;asthisvalueincreases,therighttobuyatafixedprice

(calls)willbecomemo

revaluableandtherigh

ttosellatafixedprice(puts)will

becomelessvaluable.

Varianceinthatvalue;asthevarianceincreases,bothcallsandputsw

illbecome

morevaluablebecause

alloptionshavelimited

downsideanddependuponprice

volatilityforupside.

Expecteddividendson

theasset,whicharelikelytoreducethepriceappreciation

componentoftheasset,reducingthevalueofcallsandincreasingthevalueofputs.

VariablesRelatingtoOp

tion

StrikePriceofOptions;therighttobuy(sell)atafixedpricebecomes

more(less)

valuableatalowerprice.

LifeoftheOption;bot

hcallsandputsbenefitfromalongerlife.

Lev

elofInterestRates;asratesincrease,therighttobuy(sell)ata

fixedprice

inthefuturebecomesmore(less)valuable.


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9

Whe

ncanyouuseoptionpricingmodelsto

valuerealoptions?

Thenotionofareplicatingportfoliothatdrivesoptionpricin

gmodels

makesthemmostsuitedforvaluingrealo

ptionswhere

Theunderlyingassetistraded-thisyield

notonlyobservablepricesand

volatilityasinputstooptionpricingmodelsbutallowsforthepossibility

ofcreatingreplicatingportfolios

Anactivemarketpla

ceexistsfortheoptio

nitself.

Thecostofexercisingtheoptionisknownwithsomedegreeo

fcertainty.

Wh

enoptionpricingm

odelsareusedtov

aluerealassets,wehaveto

acc

eptthefactthat

Thevalueestimates

thatemergewillbefarmoreimprecise.

Thevaluecandeviatemuchmoredramaticallyfrommarketpr

icebecause

ofthedifficultyofarbitrage.


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10

Creatinga

replicatingportfolio

Theobjectiveincreatingareplicatingportfolioistouseaco

mbination

ofriskfreeborrowing/lendingandtheund

erlyingassettocre

atethe

sam

ecashflowsasthe

optionbeingvalue

d.

Call=Borrowing+

Buyingo

ftheUnderlyingStock

Put=SellingShortonUnderlyingAsse

t+Lending

Thenumberofsharesboughtorsoldiscalledtheoptiondelta

.

Theprinciplesofarbit

ragethenapply,andthevalueoftheo

ptionhas

tobeequaltothevalueofthereplicating

portfolio.


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11

TheBinomia

lOptionPric

ingModel

50

70

35

100

50

25

K=$40

t=2

r=11%

OptionDetails

Stock

Price

Call

60

10

0

50D-

1.1

1B=10

25D-

1.1

1B=0

D=0.4,B=9.01

Call=

0.4

*35-9.01=4.99

C

all=4.9

9

100D

-1.11B=60

50D-1.1

1B=10

D=1,

B=36.0

4

Call=

1*70-36.0

4=33.96

Call=33.9

6

70D-1.1

1B=33.9

6

35D-1.1

1B=4.9

9

D=0.8

278,B=21.61

Call=0.8278*50-21.61=19.42

Call=19.4

2


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12

TheLimit

ingDistributions.

As

thetimeintervalis

shortened,thelimitingdistribution,as

t->0,

can

takeoneoftwofo

rms.

Ifast->0,pricech

angesbecomesmaller,thelimitingdistributionisthe

normaldistributionandthepriceprocess

isacontinuousone.

Ifast->0,pricecha

ngesremainlarge,thelimitingdistributio

nisthe

poissondistribution,i.e.,adistributionthatallowsforpricejumps.

TheBlack-Scholesm

odelapplieswhenthelimitingdistrib

utionis

the

normaldistribution,andexplicitlyassumesthatthepriceprocess

isc

ontinuousandthat

therearenojumps

inassetprices.


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13

TheBlack-ScholesM

odel

TheversionofthemodelpresentedbyBlackandScholeswas

des

ignedtovalueEuropeanoptions,whic

hweredividend-protected.

Th

evalueofacallop

tionintheBlack-Scholesmodelcanbewritten

asafunctionofthefollowingvariables:

S=Currentvalueoftheunderlyingasset

K

=Strikepriceoftheoption

t=

Lifetoexpirationoftheoption

r=

Risklessinterestratecorrespondingtothelifeoftheoption

2=Varianceintheln(value)oftheunderly

ingasset


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14

TheBlackS

cholesModel

Va

lueofcall=SN(d1)-Ke-rtN(d2)

wher

e,

d2=d1-

t

ThereplicatingportfolioisembeddedintheBlack-Scholesm

odel.To

rep

licatethiscall,you

wouldneedto

BuyN(d1)sharesof

stock;N(d1)iscalledtheoptiondelta

BorrowKe-rtN

(d2)

d1=

lnSK

+(r+

2 2

)t

t


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15

TheNo

rmalDistribution

d

N(d)

d

N(d)

d

N(d)

-3.00

0.0013

-1.00

0.1587

1.05

0.8531

-2.95

0.0016

-0.95

0.1711

1.10

0.8643

-2.90

0.0019

-0.90

0.1841

1.15

0.8749

-2.85

0.0022

-0.85

0.1977

1.20

0.8849

-2.80

0.0026

-0.80

0.2119

1.25

0.8944

-2.75

0.0030

-0.75

0.2266

1.30

0.9032

-2.70

0.0035

-0.70

0.2420

1.35

0.9115

-2.65

0.0040

-0.65

0.2578

1.40

0.9192

-2.60

0.0047

-0.60

0.2743

1.45

0.9265

-2.55

0.0054

-0.55

0.2912

1.50

0.9332

-2.50

0.0062

-0.50

0.3085

1.55

0.9394

-2.45

0.0071

-0.45

0.3264

1.60

0.9452

-2.40

0.0082

-0.40

0.3446

1.65

0.9505

-2.35

0.0094

-0.35

0.3632

1.70

0.9554

-2.30

0.0107

-0.30

0.3821

1.75

0.9599

-2.25

0.0122

-0.25

0.4013

1.80

0.9641

-2.20

0.0139

-0.20

0.4207

1.85

0.9678

-2.15

0.0158

-0.15

0.4404

1.90

0.9713

-2.10

0.0179

-0.10

0.4602

1.95

0.9744

-2.05

0.0202

-0.05

0.4801

2.00

0.9772

-2.00

0.0228

0.00

0.5000

2.05

0.9798

-1.95

0.0256

0.05

0.5199

2.10

0.9821

-1.90

0.0287

0.10

0.5398

2.15

0.9842

-1.85

0.0322

0.15

0.5596

2.20

0.9861

-1.80

0.0359

0.20

0.5793

2.25

0.9878

-1.75

0.0401

0.25

0.5987

2.30

0.9893

-1.70

0.0446

0.30

0.6179

2.35

0.9906

-1.65

0.0495

0.35

0.6368

2.40

0.9918

-1.60

0.0548

0.40

0.6554

2.45

0.9929

-1.55

0.0606

0.45

0.6736

2.50

0.9938

-1.50

0.0668

0.50

0.6915

2.55

0.9946

-1.45

0.0735

0.55

0.7088

2.60

0.9953

-1.40

0.0808

0.60

0.7257

2.65

0.9960

-1.35

0.0885

0.65

0.7422

2.70

0.9965

-1.30

0.0968

0.70

0.7580

2.75

0.9970

-1.25

0.1056

0.75

0.7734

2.80

0.9974

-1.20

0.1151

0.80

0.7881

2.85

0.9978

-1.15

0.1251

0.85

0.8023

2.90

0.9981

-1.10

0.1357

0.90

0.8159

2.95

0.9984

-1.05

0.1469

0.95

0.8289

3.00

0.9987

-1.00

0.1587

1.00

0.8413

d1

N(d1)


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16

AdjustingforDivide

nds

Ifthedividendyield(y=dividends/Currentvalueoftheasset)ofthe

underlyingassetisexp

ectedtoremainun

changedduringthe

lifeofthe

option,theBlack-Scholesmodelcanbem

odifiedtotakediv

idends

intoaccount.

C=Se-ytN(d1)-Ke-rtN

(d2)

where,

d2=d1-

t

Thevalueofaputcan

alsobederived:

P=Ke-rt(

1-N(d

2))-Se-yt(1-N(d1))

d1=

lnSK

+(r-y+

2 2

)t

t


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17

ChoiceofO

ptionPricingModels

Mo

stpractitionerswhouseoptionpricing

modelstovaluere

aloptions

arg

ueforthebinomial

modelovertheBlack-Scholesandjus

tifythis

cho

icebynotingthat

Earlyexerciseisthe

ruleratherthanthee

xceptionwithrealop

tions

Underlyingassetvaluesaregenerallydiscontinous.

Ify

oucandevelopab

inomialtreewithoutcomesateachnode,it

loo

ksagreatdeallike

adecisiontreefrom

capitalbudgeting.The

questionthenbecomeswhenandwhythe

twoapproachesyi

eld

differentestimatesofvalue.


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18

TheDecis

ionTreeAlte

rnative

Traditionaldecisiontreeanalysistendsto

use

Onecostofcapitaltodiscountcashflows

ineachbranchtothepresent

Probabilitiestocom

puteanexpectedvalue

Thesevalueswillgenerallybediffere

ntfromoptionpricingmodel

values

Ifyoumodifieddecisiontreeanalysisto

Usedifferentdiscountratesateachnode

toreflectwhereyouareinthe

decisiontree(ThisistheCopelandsolution)

(or)

Usetheriskfreeratetodiscountcashflow

sineachbranch,estimatethe

probabilitiestoestimateanexpectedvalueandadjusttheexpe

ctedvalue

forthemarketriskintheinvestment

DecisionTreescouldyieldthesamevaluesasoptionpricin

gmodels


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19

KeyTestsforRealO

ptions

Ist

hereanoptionemb

eddedinthisasset/

decision?

Canyouidentifythe

underlyingasset?

Canyouspecifythe

contigencyunderwh

ichyouwillgetpayoff?

Ist

hereexclusivity?

Ifyes,thereisoptionvalue.

Ifno,thereisnone.

Ifinbetween,youhavetoscalevalue.

Canyouuseanoption

pricingmodeltov

aluetherealoption

?

Istheunderlyingassettraded?

Cantheoptionbeboughtandsold?

Isthecostofexercisingtheoptionknown

andclear?


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20

OptionPricingApplicationsin

Investmen

t/StrategicA

nalysis


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21

Optio

nsinProjects/Investmen

ts/Acquisitio

ns

Oneofthelimitations

oftraditionalinvestmentanalysisisth

atitis

staticanddoesnotdo

agoodjobofcaptu

ringtheoptionsem

beddedin

inv

estment.

Thefirstoftheseoptionsistheoptiontodelaytakingainvestm

ent,when

afirmhasexclusive

rightstoit,untilalaterdate.

Thesecondofthese

optionsistakingone

investmentmayallowustotake

advantageofothero

pportunities(investm

ents)inthefuture

Thelastoptionthatisembeddedinprojectsistheoptiontoabandona

investment,iftheca

shflowsdonotmeasureup.

Theseoptionsalladdvaluetoprojectsan

dmaymakeabad

inv

estment(fromtraditionalanalysis)intoagoodone.


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22

TheO

ptiontoDelay

Wh

enafirmhasexclu

siverightstoaprojectorproductforaspecific

per

iod,itcandelaytak

ingthisprojectorproductuntilalaterdate.

At

raditionalinvestme

ntanalysisjustanswersthequestiono

fwhether

the

projectisagood

oneiftakentoday.

Thus,thefactthataprojectdoesnotpass

mustertoday(beca

useits

NP

Visnegative,oritsIRRislessthanitshurdlerate)doesnotmean

thattherightstothisp

rojectarenotvalua

ble.


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23

V

aluingtheO

ptiontoDela

yaProject

PresentValueofExpected

CashFlowsonProduct

PVofCashFlows

fromProject

InitialInvestmentin

Project

Projecthasn

egative

NPVinthissection

Project'sNPVturns

positiveinthissection


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24

Insightsfor

InvestmentAnalyses

Havingtheexclusiverightstoaproducto

rprojectisvaluabl

e,evenif

the

productorprojectisnotviabletoday.

Thevalueoftheserightsincreaseswiththevolatilityoftheunderlying

business.

Thecostofacquiringtheserights(bybuy

ingthemorspendingmoney

on

development,forin

stance)hastobew

eighedoffagainstthese

ben

efits.


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Example1:Valuingproductpa

tentsasoptions

Ap

roductpatentprovidesthefirmwiththerighttodevelopthe

pro

ductandmarketit.

Itw

illdosoonlyifthepresentvalueoftheexpectedcashflowsfrom

the

productsalesexceedthecostofdevelopment.

Ifthisdoesnotoccur,

thefirmcanshelve

thepatentandnot

incurany

furthercosts.

IfI

isthepresentvalueofthecostsofdev

elopingtheproduc

t,andVis

the

presentvalueoftheexpectedcashflow

sfromdevelopme

nt,the

pay

offsfromowningaproductpatentcan

bewrittenas:

Payoff

fromowningapro

ductpatent

=V-I

ifV>I

=0

ifV

I


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26

Payoffo

nProductO

ption

PresentValueof

cashflowso

nproduct

NetPay

offto

introduction

Costofproduct

introduction


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27

O

btainingInputsforPaten

tValuation

Input

Estim

ationProcess

1.Valueof

theUnderlyingAsset

PresentValueofCas

hInflowsfromtakingproje

ct

now

Th

iswillbenoisy,butthataddsvalue.

2.Variance

invalueofunderlyingasset

Varianceincashflow

sofsimilarassetsorfirms

Varianceinpresentv

aluefromcapitalbudgeting

simulation.

3.Exercise

PriceonOption

Op

tionisexercisedw

heninvestmentismade.

Costofmakinginvestmentontheproject;assumed

tobeconstantinpre

sentvaluedollars.

4.Expiratio

noftheOption

Lifeofthepatent

5.Dividend

Yield

Costofdelay

Eachyearofdelaytr

anslatesintoonelessyearo

f

value-creatingcashflows

Annualcostofdelay=

1 n


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28

ValuingaProductPatent:Avonex

Bio

gen,abio-technolo

gyfirm,hasapatentonAvonex,adrugtotreat

mu

ltiplesclerosis,for

thenext17years,a

nditplanstoproduceand

sellthedrugbyitself.

Thekeyinputsonthedrugareasfollo

ws:

PV

ofCashFlowsfrom

IntroducingtheDrugNow=S=$3.422

billion

PV

ofCostofDevelopingDrugforCommercialUse=K=$2.87

5billion

Pa

tentLife=t=17yea

rs

RisklessRate=

r=6.7%(17-yearT.Bondrate)

VarianceinExpectedP

resentValues=2=0.224(Industryaveragefirm

varianceforbio-tech

firms)

ExpectedCostofDelay

=y=1/17=5.89%

d1

=1.1362

N(d1)=

0.8720

d2

=-0.8512

N(d2)=

0.2076

CallV

alue=3,422exp(-0.0589)(17)(

0.8720)-2,875(exp(-0.067)(17) (0

.2076)=$

907million


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TheOptim

alTimetoE

xercise

PatentvalueversusNetPresentvalue

0100

200

300

400

500

600

700

800

900

1000

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

Numberofyearsleftonpatent

Value

Valueofpatentasoption

Netpr

esentvalueofpatent

Exercisetheoptionhere:Convertpatenttocommercialproduct


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30

Valuingafirmwithpatents

Thevalueofafirmwithasubstantialnum

berofpatentscan

be

der

ivedusingtheoptionpricingmodel.

Value

ofFirm=Valueof

commercialproducts(usingDCFvalu

e

+Value

ofexistingpatents

(usingoptionpricing)

+(Valu

eofNewpatentsth

atwillbeobtained

inthe

future

Costofobtainingthesepatents)

Thelastinputmeasure

stheefficiencyofthefirminconvertingits

R&

Dintocommercialproducts.Ifweassumethatafirmearnsitscost

ofcapitalfromresearc

h,thistermwillbecomezero.

Ifw

eusethisapproach,weshouldbecarefulnottodoublec

ountand

allowforahighgrowthrateincashflows(intheDCFvaluation).


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31

ValueofBiogensexistingproducts

Bio

genhadtwocomm

ercialproducts(a

drugtotreatHepa

titisBand

Intron)atthetimeo

fthisvaluationthatithadlicensedtoother

pha

rmaceuticalfirms.

Thelicensefeesontheseproductswer

eexpectedtogenerate$50

millioninafter-taxcashflowseachyearforthenext12

years.To

valuethesecashflows,whichwereguaranteedcontractually,thepre-

tax

costofdebtofthe

guarantorswasuse

d:

Presen

tValueofLicense

Fees=$50million

(1(1.07)-12)/.07

=$397.13million


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32

ValueofB

iogensFutu

reR&D

Bio

gencontinuedtof

undresearchintonewproducts,spendingabout

$1

00milliononR&D

inthemostrecen

tyear.TheseR&D

expenses

wereexpectedtogro

w20%

ayearforthenext10years,and5%

thereafter.

Itw

asassumedthate

verydollarinveste

dinresearchwouldcreate$

1.2

5invalueinpatents(valuedusingtheoptionpricingmodel

des

cribedabove)forthenext10years,a

ndbreakevenafte

rthat(i.e.,

gen

erate$1inpatentvalueforevery$1

investedinR&D).

Therewasasignifican

tamountofriskassociatedwiththiscomponent

and

thecostofcapital

wasestimatedtobe15%.


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33

Value

ofFutureR&D

YrValueof

R&DCo

st

ExcessVa

lue

PresentVa

lue

Patents

(at15%)

1

$

150.00

$

120

.00

$

30.00

$

26.09

2

$

180.00

$

144

.00

$

36.00

$

27.22

3

$

216.00

$

172

.80

$

43.20

$

28.40

4

$

259.20

$

207

.36

$

51.84

$

29.64

5

$

311.04

$

248

.83

$

62.21

$

30.93

6

$

373.25

$

298

.60

$

74.65

$

32.27

7

$

447.90

$

358

.32

$

89.58

$

33.68

8

$

537.48

$

429

.98

$

107.50

$

35.14

9

$

644.97

$

515

.98

$

128.99

$

36.67

10$

773.97

$

619

.17

$

154.79

$

38.26

$

318.30


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34

ValueofBiogen

ThevalueofBiogena

safirmisthesum

ofallthreecomponentsthe

pre

sentvalueofcashflowsfrom

existingproducts,thevalueof

Avonex(asanoption)

andthevaluecreatedbynewresearch

:

Value

=Existingproducts+ExistingPatents

+Value:FutureR&D

=$

397.13million+$

907million+$31

8.30million

=$

1622.43million

Sin

ceBiogenhadno

debtoutstanding,thisvaluewasdividedbythe

numberofsharesoutstanding(35.50million)toarriveata

valueper

sha

re:Valuepershare=$1,622.43million/35.5=$45.70


35/223

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35

T

heRealOptionsTest:Patentsand

T

echnology

TheOptionTest:

UnderlyingAsset:Productthatwouldbegeneratedbythepatent

Contingency:

IfPVofCFsfromdeve

lopment>Costofdevelopment:PV-Cost

IfPVofCFsfromdeve

lopmentX

=0

ifV

X


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PayoffDiagramonNaturalResourceFirm

s

Valueofestimatedreserve

ofnaturalresourceN

etPay

offon

Extraction

CostofDev

eloping

Reserve


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Aswa

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38

Estima

tingInputsforNaturalResourceOptions

Input

EstimationProcess

1.ValueofAvailabl

eReservesoftheResource

Expertestimates(Geologistsforoil..);The

presentvalueoftheafter-taxcashflowsfrom

theresourcearet

henestimated.

2.CostofDevelopin

gReserve(StrikePrice)

Pastcostsandthe

specificsoftheinvestment

3.TimetoExpiratio

n

RelinqushmentPe

riod:ifassethastobe

relinquishedatapointintime.

Timetoexhaustinventory-basedupon

inventoryandcap

acityoutput.

4.Varianceinvalue

ofunderlyingasset

baseduponvariab

ilityofthepriceofthe

resourcesandvar

iabilityofavailablereserves.

5.NetProductionRevenue(DividendYield)

Netproductionre

venueeveryyearaspercent

ofmarketvalue.

6.DevelopmentLag

Calculatepresent

valueofreservebasedupo

n

thelag.


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39

ValuinganOilReserve

Co

nsideranoffshoreoilpropertywithanestimatedoilreserveof50

millionbarrelsofoil,wherethepresentvalueofthedevelopmentcost

is$

12perbarrelandthedevelopmentlag

istwoyears.

Thefirmhastherightstoexploitthisrese

rveforthenexttwentyyears

and

themarginalvalueperbarrelofoilis

$12perbarrelcurr

ently

(Priceperbarrel-marginalcostperbarre

l).

Oncedeveloped,then

etproductionreven

ueeachyearwillb

e5%of

the

valueofthereserves.

Therisklessrateis8%

andthevarianceinln(oilprices)is0.03.


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40

InputstoO

ptionPricingModel

CurrentValueofthea

sset=S=Valueof

thedevelopedrese

rve

discountedbackthele

ngthofthedevelopmentlagatthediv

idend

yield=$12*50/(1.05)2=

$544.22

(If

developmentisstartedtoday,theoilw

illnotbeavailable

forsale

untiltwoyearsfromnow.Theestimatedopportunitycostof

thisdelay

isthelostproductionrevenueoverthedelayperiod.Hence,the

discountingoftherese

rvebackatthedividendyield)

ExercisePrice=Prese

ntValueofdevelopmentcost=$12*

50=$600

million

Tim

etoexpirationon

theoption=20yea

rs

Varianceinthevalueoftheunderlyingasset=0.03

Ris

klessrate=8%

DividendYield=Net

productionrevenue

/Valueofreserve

=5%


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41

Valu

ingtheOptio

n

Basedupontheseinpu

ts,theBlack-Scholesmodelprovidesthe

followingvalueforthecall:

d1

=1.0359

N(d1)=

0.8498

d2

=0.2613

N(d2)=

0.6030

CallValue=544.22exp(-0.05)(20)(

0.8498)

-600(exp(-0.08)(20)(0

.6030)=$

97.08million

Thisoilreserve,thoug

hnotviableatcurrentprices,stillisa

valuable

pro

pertybecauseofitspotentialtocreate

valueifoilpricesgoup.


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Aswa

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42

Extendingtheoptionpricingap

proachtova

lue

natura

lresourcefirms

Sin

cetheassetsownedbyanaturalresou

rcefirmcanbeviewed

primarilyasoptions,thefirmitselfcanb

evaluedusingoption

pricingmodels.

Thepreferredapproachwouldbetoconsidereachoptionseparately,

valueitandcumulatethevaluesoftheop

tionstogetthefirm

value.

Sin

cethisinformation

islikelytobedifficulttoobtainforlarge

naturalresourcefirms,suchasoilcompanies,whichownhundredsof

suc

hassets,avarianti

stovaluetheentire

firmasoneoption

.

Ap

uristwouldprobab

lydisagree,arguingthatvaluinganoptionona

portfolioofassets(as

inthisapproach)

willprovidealow

ervalue

tha

nvaluingaportfo

lioofoptions(whichiswhatthenatural

resourcefirmreallyow

n).Nevertheless,thevalueobtainedf

romthe

mo

delstillprovidesan

interestingperspectiveonthedeterminantsof

the

valueofnaturalresourcefirms.


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43

InputstotheMod

el

Inputtomodel

Correspondinginputforvaluingfirm

Valueofunderlyingasset

Valueofcumulated

estimatedreservesofthe

resourceownedbythefirm,discountedbackatthe

dividendyieldforthedevelopmentlag.

ExercisePrice

Estimatedcumulate

dcostofdevelopingestimated

reserves

Timetoexpirationonoption

Averagerelinquishmentperiodacrossallreserves

ownedbyfirm(ifk

nown)orestimateof

when

reserveswillbeexh

austed,givencurrent

productionrates.

Riskles

srate

Risklessratecorrespondingtolifeofthe

option

Varianceinvalueofasset

Varianceinthepric

eofthenaturalresou

rce

Dividendyield

Estimatedannualnetproductionrevenue

as

percentageofvalue

ofthereserve.


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ValuingGulfOil

GulfOilwasthetargetofatakeoverinearly1984at$70pershare(It

had

165.30millionsharesoutstanding,an

dtotaldebtof$9.9

billion).

Ithadestimatedrese

rvesof3038million

barrelsofoilandthe

average

costofdevelopingthesereserveswasestimatedtobe$10aba

rrelin

presentvaluedollars(Thedevelopmentlagisapproximatelytw

oyears).

Theaveragerelinquishmentlifeofthereservesis12years.

Thepriceofoilwas

$22.38perbarrel,andtheproductioncost,taxesand

royaltieswereestimatedat$7perbarrel.

Thebondrateatthe

timeoftheanalysisw

as9.00%.

Gulfwasexpectedtohavenetproduction

revenueseachyearo

f

approximately5%o

fthevalueofthedev

elopedreserves.The

variancein

oilpricesis0.03.


45/223

Aswa

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45

ValuingUn

developedR

eserves

Inputsforvaluingundev

elopedreserves

Valueofunderlyingas

set=Valueofestimatedreservesdiscountedba

ckforperiod

ofdevelopmentlag=3038*($22.38-$7)/1.052=$42,380.44

Exerciseprice=Estim

ateddevelopmentcosto

freserves=3038*$10

=$30,380

million

Timetoexpiration=A

veragelengthofrelinquishmentoption=12years

Varianceinvalueofasset=Varianceinoilprices=0.03

Risklessinterestrate=

9%

Dividendyield=Netp

roductionrevenue/Valueofdevelopedreserves=5%

Basedupontheseinputs,theBlack-Scholesm

odelprovidesthefollowing

valueforthecall:

d1

=1.6548

N(d1)=0

.9510

d2

=1.0548

N(d2)=0

.8542

CallValue=42,380.44exp(-0.05)(12)(0.9510)-3

0,380(exp(-0.09)(12)(0

.8542)=$

13,306million


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46

ValuingGulfOil

Inaddition,GulfOilh

adfreecashflowstothefirmfromitsoilandgas

pro

ductionof$915millionfromalreadydevelopedreserves

andthese

cas

hflowsarelikelyto

continuefortenyears(theremaining

lifetimeof

dev

elopedreserves).

Thepresentvalueofthesedevelopedrese

rves,discountedat

the

weightedaveragecost

ofcapitalof12.5%

,yields:

Valueofalreadydevelopedreserves=91

5(1-1.125-10)/.125=

$5065.83

Addingthevalueofth

edevelopedandun

developedreserves

Valueofundevelopedreserves

=$13,306million

Valueofproduction

inplace

=$5,066million

Totalvalueoffirm

=$18,372million

LessOutstandingDebt

=$9,900million

ValueofEquity

=$8,472million

Valuepershare

=$8,472/165.3=

$51.25


47/223

Aswa

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47

Puttin

gNaturalResourceOptionstotheTest

TheOptionTest:

UnderlyingAsset:Oil

orgoldinreserve

Contingency:Ifvalue>Costofdevelopment:

Value-DevCost

IfvalueExpansionCost:PV

-ExpansionCost

If

PVofCFfromexpansionL:Excessdebtcapacitycanbeuse

dtocoverthedifferenceand

investinprojects

IfX

L:[(ROC-Costof

capital)/Costofcapital]Newinvestm

ents

IfX


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TheValueofFlexib

ility

A

ctual

R

einvestment

N

eeds

Expected

(Normal)

Reinvestment

Needsthatcan

befinanced

without

flexibility

Costo

fMaintainingFinancingF

lexibility

Usefinancin

gflexibility

totakeunan

ticipated

investments

(acquisitions)

Payoff:(S-K)*ExcessReturn/WACC

Excess

Return/WACC=PVofe

xcessreturnsinperpetutity


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67

DisneysOptimalDeb

tRatio

DebtR

atio

Costof

Equity

Costof

Debt

Costof

Capital

0.00%

13.00%

4.61%

13.00%

10.00%

13.43%

4.61%

12.55%

Current:18%13.8

5%

4.8

0%

12.2

2%

20.00%

13.96%

4.99%

12.17%

30.00%

14.65%

5.28%

11.84%

40.00%

15.5

6%

5.7

6%

11.6

4%

50.00%

16.85%

6.56%

11.70%

60.00%

18.77%

7.68%

12.11%

70.00%

21.97%

7.68%

11.97%

80.00%

28.95%

7.97%

12.17%

90.00%

52.14%

9.42%

13.69%


68/223

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68

InputstoOptionValuationModel

Onewaytothinkaboutfirmsthatpreservedebtcapacitybe

causethey

wantflexibilityistha

ttheyareforegoingusethisdebttoinvestin

existingprojectsatexistingexcessreturn

sbecausetheythin

kthatthey

mighthaveanincreaseineitherinvestme

ntneedsorexcessreturns.

To

valueflexibilityas

apercentoffirmv

alue(asanannualcost),these

wouldbetheinputsto

themodel:

S=ExpectedReinvestmentneedsasperc

entofFirmValue

K=ExpectedReinv

estmentneedsthatcanbefinancedwithoutfinancing

flexibility

t=1year

2=Varianceinln(NetCapitalExpenditures)

Oncethisoptionhas

beenvalued,estim

atethepresentvalueofthe

exc

essreturnsthatwillbegainedbytakingtheadditionalinvestments

by

multiplyingby(ROC-WACC)/WAC

C


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Aswa

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69

TheIn

putsforDisney

Expectedreinvestmentneedsasapercentoffirmvalue:

Overthelast5years,reinvestment(netcapex,acquisitionsandchanges

inworkingcapital)hasbeenapproximate

ly5.3%offirmvalue

Iamassumingthatthisistheexpectedreinvestmentneed;thevariancein

ln(reinvestment)overthelast5yearsis0.375

Re

investmentneedsthatcanbefinanced

withoutflexibility.

Welookedatinternalfunds,afterdebtpa

ymentsbutbeforereinvestment

needs,asapercento

ffirmvalueoverthe

last5years.(Internalfunds=

(NetIncome+Depr

eciation)/MarketValueoftheFirm)

Welookedatnetdebtfinancingeachperiod,asapercentoffirmvalue(as

ameasureofaccess

toexternalfinancing

eachyear).(NewDebt-Debt

Repaid)/MarketValueofFirm)

Reinvestmentneeds

thatcanbefinancedwithoutflexibility=(Net

Income+Depreciation+NetDebtIssued

)/MarketValueofFirm

Thisnumberhasaveraged4.8%,overthe

last5years


70/223


71/223

Aswa

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71

DeterminantsoftheValue

ofFlexibility

Capacitytoraisefundstomeetfinancing

needs:Thegreater

the

cap

acitytoraisefunds

,eitherinternallyo

rexternally,theles

sthevalue

offlexibility.

1.1:Firmswithsign

ificantinternalopera

tingcashflowsshouldvalue

flexibilitylessthanfirmswithsmallorne

gativeoperatingcash

flows.

1.2:Firmswitheasy

accesstofinancialm

arketsshouldhavea

lowervalue

forflexibilitythanfirmswithoutthataccess.

Unpredictabilityofreinvestmentneeds:T

hemoreunpredictablethe

reinvestmentneedsof

afirm,thegreaterthevalueofflexibility.

Capacitytoearnexces

sreturns:Thegreaterthecapacitytoe

arnexcess

returns,thegreaterthe

valueofflexibility

.

1.3:Firmsthatdonothavethecapacitytoearnorsustainexcessreturns

getnovaluefromflexibility.


72/223

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72

Op

tionPricingApplications

inValuation

EquityValueinDeeplyTrouble

dFirms

ValueofUndeveloped

ReservesforNaturalResourceFirm

Valu

eofPatent/License


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73

Option

PricingApp

licationsinE

quityValuation

Equityinatroubledfirm(i.e.afirmwith

highleverage,negative

earningsandasignific

antchanceofbank

ruptcy)canbeview

edasa

calloption,whichisth

eoptiontoliquidatethefirm.

Naturalresourcecomp

anies,wheretheundevelopedreservescanbe

viewedasoptionsonthenaturalresource

.

Sta

rt-upfirmsorhigh

growthfirmswhichderivethebulkof

their

valuefromtherightstoaproductoraser

vice(eg.apatent)


74/223

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ValuingE

quityasan

option

Theequityinafirmis

aresidualclaim,i.e.,equityholderslayclaim

toallcashflowsleftov

erafterotherfinan

cialclaim-holders(debt,

pre

ferredstocketc.)havebeensatisfied.

Ifa

firmisliquidated,

thesameprinciple

applies,withequity

investors

rec

eivingwhateveris

leftoverinthefirmafteralloutstandingdebts

and

otherfinancialcla

imsarepaidoff.

Theprincipleoflimit

edliability,howev

er,protectsequityinvestors

inpubliclytradedfirm

sifthevalueofthe

firmislessthanth

evalueof

the

outstandingdebt,a

ndtheycannotlosemorethantheirinvestment

inthefirm.


75/223

Aswa

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Equity

asacalloption

Thepayofftoequityinvestors,onliquida

tion,canthereforebewritten

as:

Payofftoequityonliquidation=V-D

ifV>D

=0

ifV

D

where,V=Valueofthefirm

D=FaceValueoftheoutstandingdebtandotherexternalclaims

Ac

alloption,withastrikepriceofK,on

anassetwithacurrentvalue

ofS,hasthefollowing

payoffs:

Payoffonexercise

=S-K

ifS>K

=0

ifS

K


76/223

Aswa

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PayoffDiagramforLiquida

tionOption

Va

lueoffirm

NetPayoff

onEquity

FaceValue

of

Debt


77/223

Aswa

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77

App

licationtova

luation:Asimpleexample

Assumethatyouhave

afirmwhoseassetsarecurrentlyvalu

edat$100

millionandthatthestandarddeviationin

thisassetvalueis4

0%.

Further,assumethatthefacevalueofdeb

tis$80million(It

iszero

cou

pondebtwith10y

earslefttomaturity

).

Iftheten-yeartreasury

bondrateis10%,

howmuchistheequ

ityworth?

Whatshouldtheinterestrateondebtbe?


78/223

Aswa

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78

Mod

elParameters

Valueoftheunderlyin

gasset=S=Valueofthefirm=$100million

Exerciseprice=K=F

aceValueofoutstandingdebt=$80million

Lifeoftheoption=t=

Lifeofzero-coupondebt=10years

Varianceinthevalueoftheunderlyingasset=2=Varianceinfirm

value=0.16

Ris

klessrate=r=Tre

asurybondratecor

respondingtooptio

nlife=

10%


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Aswa

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79

ValuingEq

uityasaCallOption

Basedupontheseinpu



d1=1.5994

N(d1)=0

.9451

d2=0.3345

N(d2)=0

.6310

Valueofthecall=100(0.9451)-80exp(-0.10)(10)(0.6310)=$

75.94

million

Valueoftheoutstandingdebt=$100-$7

5.94=$24.06million

Interestrateondebt=

($80/$24.06)1/10-1=12.77%


80/223

Aswa

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The

EffectofCa

tastrophicD

ropsinValue

Assumenowthatacatastrophewipesout

halfthevalueofth

isfirm

(thevaluedropsto$5

0million),whileth

efacevalueofthe

debt

rem

ainsat$80million.Whatwillhappentotheequityvalueofthis

firm

?

Itw

illdropinvalueto

$25.94million[$

50million-marketvalueof

deb

tfrompreviouspage]

Itw

illbeworthnothin

gsincedebtoutstanding>FirmValue

Itw

illbeworthmorethan$25.94million


81/223

Aswa

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81

I

llustration:V

alueofatro

ubledfirm

Assumenowthat,inthepreviousexample,thevalueofthefirmwere

red

ucedto$50millionwhilekeepingthe

facevalueofthed

ebtat$80

million.

Thisfirmcouldbeviewedastroubled,sinceitowes(atleastinface

valueterms)morethanitowns.

Theequityinthefirm

willstillhavevalue,however.


82/223

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82

ValuingEquityintheTroubledFirm

Valueoftheunderlyin

gasset=S=Valueofthefirm=$50

million

Exerciseprice=K=F


Lifeoftheoption=t=



value=0.16

Ris

klessrate=r=Tre

asurybondratecor

respondingtooptio

nlife=

10%


83/223

Aswa

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83

TheValueo

fEquityasa

nOption

Basedupontheseinpu



d1=1.0515

N(d1)=0

.8534

d2=-0.2135

N(d2)=0

.4155

Valueofthecall=50

(0.8534)-80exp(-0.10)(10)(0.4155)=$3

0.44

million

Valueofthebond=$5

0-$30.44=$19.56million

Theequityinthisfirm

dropsby,because

oftheoptioncharacteristics

ofequity.

Thismightexplainwh

ystockinfirms,whichareinChapter

11and

essentiallybankrupt,s

tillhasvalue.


84/223

Aswa

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84

Equity

valuepersis

ts..

ValueofEquityasFirm

Value

Changes

010

20

30

40

50

60

70

80

100

90

80

70

60

50

40

30

20

1

0

Value

ofFirm

($

80

Face

Valu

e

ofDebt)

ValueofEquity


85/223

Aswa

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85

OptionPricin

gTheory

andReal

Option

Applicat

ions

As

wathDamodaran


86/223

Aswa

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daran

86

Th

eConflictbetweenbond

holdersand

stockholders

Sto

ckholdersandbondholdershavedifferentobjectivefunctions,and

thiscanleadtoconflic

tsbetweenthetwo.

Forinstance,stockholdershaveanincentivetotakeriskierprojects

thanbondholdersdo,andtopaymoreoutindividendsthan

bondholderswouldlik

ethemto.

Thisconflictbetween

bondholdersandstockholderscanbei

llustrated

dra

maticallyusingthe

optionpricingmod

el.

Sinceequityisacalloptiononthevalueofthefirm,anincrea

seinthe

varianceinthefirm

value,otherthings

remainingequal,w

illleadto

anincreaseinthev

alueofequity.

Itisthereforeconceivablethatstockholde

rscantakeriskyprojectswith

negativenetpresen

tvalues,whichwhilemakingthembetter

off,may

makethebondholde

rsandthefirmlessvaluable.Thisisillustratedinthe

followingexample.


87/223

Aswa

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87

Illustration:Effe

ctonvalueoftheconflic

t

be

tweenstockholdersandbondholders

Consideragainthefirmdescribedintheearlierexample,withavalue

ofassetsof$100million,afacevalueofzero-couponten-ye

ardebtof

$80million,astandarddeviationinthevalueofthefirmof40%.The

equ

ityanddebtinthis

firmwerevalueda

sfollows:

ValueofEquity=$75.94million

ValueofDebt=$24

.06million

ValueofFirm==$1

00million

Nowassumethatthes

tockholdershavetheopportunitytotakea

pro

jectwithanegativenetpresentvalueof-$2million,butassume

thatthisprojectisave

ryriskyprojecttha

twillpushupthestandard

dev

iationinfirmvalueto50%.


88/223

Aswa

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88

ValuingEq

uityafterthe

Project

Valueoftheunderlyin

gasset=S=Valueofthefirm=$100million-

$2

million=$98million(Thevalueofth

efirmisloweredb

ecauseof

the

negativenetpresentvalueproject)

Exerciseprice=K=F


Lifeoftheoption=t=



value=0.25

Ris

klessrate=r=Tre

asurybondratecor

respondingtooptio

nlife=

10%


89/223

Aswa

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89

OptionValuation

OptionPricingResultsforEquityandDe

btValue

ValueofEquity=$77.71

ValueofDebt=$20

.29

ValueofFirm=$98

.00

Thevalueofequityrisesfrom$75.94millionto$77.71million,

eve

nthoughthefirmv

aluedeclinesby$2million.Theincre

asein

equ

ityvaluecomesat

theexpenseofbondholders,whofind

their

wealthdeclinefrom$24.06millionto$20.19million.


90/223

Aswa

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90

Effects

ofanAcquis

ition

Assumethatyouarethemanagerofafirmandthatyoubuy

another

firm

,withafairmarke

tvalueof$150million,forexactly$

150

million.Inanefficientmarket,thestockpriceofyourfirmw

ill

Inc

rease

Decrease

RemainUnchanged


91/223

Aswa

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91

II.Effectsonequityofaconglo

meratemerger

Youareprovidedinform

ationontwofirms,w

hichoperateinunrelated

bus

inessesandhopetom

erge.

FirmA

FirmB

Valueofthefirm

$100million

$150million

FaceValueofDebt

$80million

$50million(Zero-coupondebt)

Maturityofdebt

10years

10years

Std.Dev.invalue

40%

50%

Correlationbetweencashflows

0.4

Theten-yearbondrate

is10%.

Thevarianceinthevalueofthefirmafterthe

acquisitioncanbecalculatedas

follows:

Varianceincombinedfirm

value

=w1212+

w2

222+

2w1w212

12

=(0.4)2(

0.16)+(0.6)2(0.

25)+2(0.4)(0.6)(0.4)

(0.4)(0.5)

=0.154


92/223

Aswa

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92

ValuingtheCombinedFirm

Thevaluesofequityand

debtintheindividua

lfirmsandthecombinedfirm

can

thenbeestimatedusingtheoptionpricing

model:

FirmA

FirmB

Combinedfirm

Valueofequityinthefirm

$75.94

$134.47

$207.43

Valueofdebtinthefirm

$24.06

$15.53

$42.57

Valueofthefirm

$100.00

$150.00

$250.00

Thecombinedvalueoftheequitypriortothe

mergeris$210.41m

illionandit

dec

linesto$207.43millionafter.

Thewealthofthebondholdersincreasesbyanequalamount.

Thereisatransferofwealthfromstockhold

erstobondholders,

asa

con

sequenceofthemerg

er.Thus,conglomera

temergersthatarenotfollowed

byincreasesinleverage

arelikelytoseethisredistributionofwealthoccur

acrossclaimholdersinthefirm.


93/223

Aswa

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93

Obtainingoption

pricinginputs-Somereal

wo

rldproblems

Theexamplesthathav

ebeenusedtoillustratetheuseofoptionpricing

theorytovalueequity

havemadesomesi

mplifyingassumptions.

Am

ongthemarethefollowing:

(1)Therewereonlytwoclaimholdersinthe

firm-debtandequity.

(2)Thereisonlyoneissueofdebtoutstandinganditcanberetiredatface

value.

(3)Thedebthasazero

couponandnospecialfeatures(convertibility,put

clausesetc.)

(4)Thevalueofthefirmandthevariancein

thatvaluecanbeestimated.


94/223


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95

Valu

ingEquityasanoption-

Eurotunnelin

early1998

Eurotunnelhasbeena

financialdisastersinceitsopening

In1997,Eurotunnel

hadearningsbeforeinterestandtaxesof-56million

andnetincomeof-

685million

Attheendof1997,itsbookvalueofequitywas-117million

Ith

ad8,865millioninfacevalueofdeb

toutstanding

Theweightedaveragedurationofthisdebtwas10.93years

DebtType

FaceValue

Duration

Shortterm

935

0.50

10year

2435

6.7

20year

3555

12.6

Longer

1940

18.2

Total

8,865mil

10.93years


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TheBasicDCFValu

ation

Thevalueofthefirmestimatedusingpro

jectedcashflowsto

thefirm,

discountedattheweig

htedaveragecosto

fcapitalwas2,31

2million.

Thiswasbaseduponthefollowingassum

ptions

Revenueswillgrow

5%ayearinperpetuity.

TheCOGSwhichis

currently85%ofrev

enueswilldropto65

%of

revenuesinyr5and

stayatthatlevel.

Capitalspendinganddepreciationwillgrow5%ayearinperp

etuity.

Therearenoworkin

gcapitalrequirements.

Thedebtratio,whichiscurrently95.35%

,willdropto70%afteryear5.

Thecostofdebtis1

0%inhighgrowthperiodand8%aftertha

t.

Thebetaforthestoc

kwillbe1.10forthe

nextfiveyears,anddropto0.8

afterthenext5years.

Thelongtermbond

rateis6%.


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O

therInputs

Thestockhasbeentra

dedontheLondon

Exchange,andthe

ann

ualizedstddeviationbaseduponln(p

rices)is41%.

ThereareEurotunnelbonds,thathavebeentraded;theannualizedstd

dev

iationinln(price)forthebondsis17%

.

Thecorrelationbetw

eenstockpriceandb

ondpricechangesha

sbeen0.5.

Theproportionofdebtinthecapitalstruc

tureduringtheperiod(1992-

1996)was85%.

Annualizedvariance

infirmvalue

=(0.15)2(

0.41)2+

(0.85)2(0.17)2+2(0.15)

(0.85)(0.5)(0.41)(0.17)=0.0335

The15-yearbondrate

is6%.(Iusedabo

ndwithadurationofroughly

11

yearstomatchthelifeofmyoption)


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V

aluingEurotunnelEquityandDebt

InputstoModel

Valueoftheunderlyingasset=S=Valueofthefirm=2,312million

Exerciseprice=K=F

aceValueofoutstandingdebt=8,865million

Lifeoftheoption=t=

Weightedaveragedura

tionofdebt=10.93yea

rs

Varianceinthevalueo

ftheunderlyingasset=

2=Varianceinfirmv

alue=

0.0335

Risklessrate=r=Treasurybondratecorrespo

ndingtooptionlife=6%

Basedupontheseinputs,theBlack-Scholesm

odelprovidesthefollowing

valueforthecall:

d1

=-0.8337

N(d1)=0.2023

d2

=-1.4392

N(d2)=0.0751

Valueofthecall=2312

(0.2023)-8,865exp(-0.06)(10.93)(0.0751)=122

million

Appropriateinterestrate

ondebt=(8865/2190)(1/10.93)-1=13.65%


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99

In

Closing

Therearerealoptions

everywhere.

Mo

stofthemhaveno

significanteconom

icvaluebecauseth

ereisno

exc

lusivityassociated

withusingthem.

Wh

enoptionshavesig

nificanteconomic

value,theinputsne

ededto

valuetheminabinom

ialmodelcanbeus

edinmoretraditional

app

roaches(decisiontrees)toyieldequiv

alentvalue.

Therealvaluefromre

aloptionsliesin

Recognizingthatbuildinginflexibilityan

descapehatchesinto

large

decisionshasvalue

Insightswegetonunderstandinghowandwhycompaniesbeh

avetheway

theydoininvestmentanalysisandcapitalstructurechoices.


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101

AcquisitionValuation

Itisnotwhatyou

buybutwhatyou

payforit.


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IssuesinA

cquisitionValuation

Acquisitionvaluations

arecomplex,becausethevaluationoften

inv

olvedissueslikesy

nergyandcontrol,

whichgobeyondjustvaluing

ata

rgetfirm.Itisimportantontherights

equence,including

Whenshouldyouco

nsidersynergy?

Wheredoesthemethodofpaymententer

theprocess.

Cansynergybevalued

,andifso,how?

Wh

atisthevalueofcontrol?Howcanyo

uestimatethevalue?


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StepsinvolvedinanAcquisitionValuation

Step1:Establishamo

tivefortheacquisition

Step2:Chooseatarget

Step3:Valuethetargetwiththeacquisitionmotivebuiltin

.

Step4:Decideonthemodeofpayment-cashorstock,and

ifcash,

arrangeforfinancing-debtorequity.

Step5:Choosetheaccountingmethodforthemerger/acquisition-

purchaseorpooling.


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104

Step1:Motivesbehindac

quisitions

(1)Simp

lestrationaleisundervaluation,i.e.,thatfirmsthatareundervaluedbyfinancialmarkets,

relativetotruevalue,willbetargetedforacquisitionbythosewhorecognizethisanomaly.

(2)Amorecontroversialreasonis

diversification,withtheintentofstabilizingearning

sandreducing

risk.

(3)Synergyreferstothepotentiala

dditionalvaluefromcombiningtwofirms,eitherfrom

operationalor

financialsources.

OperatingSynergycancomefromhighergrowthorlowercosts

FinancialSynergycancomef

romtaxsavings,increaseddebtcapacityorcashslack.

(4)Poorlymanagedfirmsaretak

enoverandrestructured

bythenewowners,wholayclaimtothe

additionalvalue.

(5)Managerialself-interestandhu

brisaretheprimary,thoughunstated,reasonsformanytakeovers.


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105

Step2

:Chooseatargetfirmfor

theacquisition

Ifmotiveis

Targetfirm

Undervaluation

tradesat

apricebelowtheestimatedvalue

Diversification

isinabu

sinesswhichisdifferen

tfromtheacquiringfirm

s

business

OperatingSynergy

havethe

characteristicsthatcrea

tetheoperatingsynergy

CostSavings:insamebusinesstocreateeconomiesofscale.

Higherg

rowth:shouldhavepotentialforhighergrowth.

FinancialSynergy

TaxSavings:providesataxbene

fittoacquirer

DebtCapacity:isunabletoborrowmoneyorpayhighrates

Cashslack:hasgreatprojects/nofunds

Control

badlymanagedfirmwhosestock

hasunderperformedth

e

market.

Manage

rsInterests

hascharacteristicsthatbestmeetCEOsegoandpower

needs.


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107/223

Aswa

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107

TheValuationProc

ess

StatusQuo

Valuation

Control

Premium

Synergy

Valuethecompanyasis,withexistinginputs

forinvestme

nt,financinganddividendpolicy.

Valuethecompanyasifoptimallymanaged.This

willusuallym

eanthatinvestment,financingand

dividendpo

licywillbealtered:

InvestmentPolicy:Higherreturnsonprojectsand

divestingunproductiveprojects.

FinancingP

olicy:Movetoabetterfinancing

structure;eg.optimalcapitalstructure

DividendPo

licy:Returnunusedcash

Practically,

1.Lookatin

dustryaveragesforoptimal(iflazy)

2.Doafull-fledgedcorporatefinancialanalysis

Valuethecombinedfirm

withsynergybuiltin

.Thism

ayinclude

a.ahigherg

rowthrateinrevenues:

growthsynergy

b.highermargins,becauseof

economiesofscale

c.lowertaxes,becauseoftaxbenefits:taxsynergy

d.lowercostofdebt:financingsynergy

e.higherde

btratiobecauseoflowerrisk:

debtcapa

city

Subtractthe

valueofthetargetfirm(withcontrolpremium)+

valueofthe

biddingfirm(pre-acquisition).Thisisthevalueof

thesynergy

.

Component

ValuationGuidelines

Shouldyoupay?

Ifmotiveis

undervaluation,thisis

themaximumyou

shouldpay.

Ifmotiveiscontrolor

inastand-alone

valuation,thisisthe

maximiumyoushould

pay.

Whichfirmis

indispensableforthe

synergy?

Ifitisthetarget,you

shouldbewillingto

payuptothe

synergy.

Ifitisthebidder,you

shouldnot.

VALUINGANACQUISITION


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ValuingNCRforAT&

T:1991

StatusQuo

Valuation

Control

Premium

Synergy

Valuethecompanyasis,withexistinginputs

forinvestme

nt,financinganddividendpolicy.

Valuethecompanyasifoptimallymanaged.This

willusuallym

eanthatinvestment,financingand

dividendpo

licywillbealtered:

InvestmentPolicy:Higherreturnsonprojectsand

divestingunproductiveprojects.

FinancingP

olicy:Movetoabetterfinancing

structure;eg.optimalcapitalstructure

DividendPo

licy:Returnunusedcash

Practically,

1.Lookatin

dustryaveragesforoptimal(iflazy)

2.Doafull-fledgedcorporatefinancialanalysis

Valuethecombinedfirm

withsynergybuiltin

.Thism

ayinclude

a.ahigherg

rowthrateinrevenues:

growthsynergy

b.highermargins,becauseof

economiesofscale

c.lowertaxes,becauseoftaxbenefits:taxsynergy

d.lowercostofdebt:financingsynergy

e.higherde

btratiobecauseoflowerrisk:

debtcapa

city

Subtractthe

valueofthetargetfirm(withcontrolpremium)+

valueofthe

biddingfirm(pre-acquisition).Thisisthevalueof

thesynergy

.

Component

ValuationGuidelines

Value

$5,949million

$6,723million-

$5,949million

=$774million

$11,278million

-$6,723million

=$4,552million

VALUINGNCRforAT&T


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Step

4:Decideon

paymentmechanism:Cash

versusStock

Generallyspeaking,firmswhichbelievethattheirstockisunder

valuedwillnotusestocktodoacquisitions.

Conversely,firmswhi

chbelievethattheirstockisoverorcorrectly

valuedwillusestock

todoacquisitions.

Notsurprisingly,thep

remiumpaidislargerwhenanacquisitionis

financedwithstockratherthancash.

Theremightbeanacc

ountingrationale

forusingstockasopposedto

cas

h.Youareallowed

tousepoolinginsteadofpurchase.

Theremightalsobea

taxrationaleforusingstock.Cashacquisitions

createtaxliabilitiesto

thesellingfirmss

tockholders.


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Th

eExchangeRatioinaSto

ckforStock

Exchange

CorrectExchangeRatiotouseinaValuation=ValueperShareof

TargetFirm(withcontrolpremiumandtarget-controlledsyn

ergies)/

ValueperShareofBiddingFirm

Iftheexchangeratioissettoohigh,therewillbeatransfer

ofwealth

fro

mthebiddingfirm

sstockholdersto

thetargetfirms

stockholders.

Iftheexchangeratioissettoolow,there

willbetransferof

wealth

fro

mthetargetfirmtothebiddingfirmsstockholders.


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Step

5:Choosean

accountingmethodforthe

merger

PurchaseMethod:

Theacquiringfirmrecord

stheassetsandliabilities

oftheacquiredfirmatmarketvalue,with

goodwillcapturingthedif

ferencebetweenmarketvalueandthevalueoftheassetsacquired.

Thisgoodwillwillthenb

eamortized,thoughtheamortizationisgenerallynottaxdeductible

(thoughaportionthatcanbeattributedtoassetsca

nbededucted).Ifafirmp

ayscashonan

acquisition,ithastousethepurchasemethodtorecordthetransaction.

Poo

lingofInterests:

Thebookvaluesoftheassetsandliabilitiesofthem

ergingfirmsareaddedto

arriveatvalues

forthecombinedfirm.Sincethemarketvalueofthe

transactionisnotrecognized,nogoodwill

iscreatedoramortized.

Thisapproachisallowed

onlyiftheacquiringfirm

exchangesitscommonsto

ckforcommon

stockoftheacquiredfirm

.

Sinceearningsarenotaff

ectedbytheamortizationo

fgoodwill,thereportedearningspershare

underthisapproachwillbegreaterthantherepo

rtedearningspershareinthepurchase

approach.


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112

TheV

alueofControl

Thevalueofcontrols

houldbeinversely

proportionaltothe

perceivedqualityofthatmanagementan

ditscapacitytomaximize

firm

value.

Valueofcontrolwillbemuchgreater

forapoorlyman

agedfirm

thatoperatesatbelow

optimumcapacity

thanitisforawellmanaged

firm

.

ValueofControl=V

alueoffirm,withrestructuring-Valueoffirm,

withoutrestructuring

Negligibleorfirmsw

hichareoperating

atorclosetotheiroptimal

value


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113

Emp

iricalEviden

ceontheVa

lueofControl

TargetC

haracteristics-Hostile

vs.FriendlyTakeovers

-5.00

%

0.00

%

5.00

%

10.00%

15.00%

20.00%

TargetROE-

IndustryROE

Target5-yrstock

returns-Ma

rket

Returns

%ofStockheld

byinsid

ers

H

ostileTakeovers

FriendlyTakeovers


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114

Afterthe

hostiletake

over..

Ma

nyofthehostile

takeoverswerefollowedbyanin

creasein

leverage,whichresul

tedinadowngradingofthedebt.Th

eleverage

wasquicklyreduced,however,withproceedsfromsaleofassets.

Therewasnosign

ificantchangein

theamountofcapital

inv

estmentinthesefirms,butinvestmentwasmorefocusedoncore

business.

Almost60%

ofth

e

takeoverswere

followed

by

significant

div

estitures,wherehalformoreofthefirm

wasdivested.The

overwhelmingmajorityofthedivestitureswereofunitswhichwerein

businessareasunrela

tedtothecompany'scorebusiness

,i.e.,they

con

stitutedreversalof

earliercorporatediversification.

Thereweresignifican

tmanagementch

angesin17ofthe

19hostile

takeovers,withtheentirecorporatemana

gementteamreplacedin7of

the

takeovers.


115/223


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116

Digital:StatusQuoVa

luation

Year

FCF

F

Termin

alValue

PV

1

$133.26

$119.42

2

$141.25

$113.43

3

$149.73

$107.75

4

$158.71

$102.35

5

$168.24

$2,717.35

$1,6

67.47

TerminalYear

$156.25

FirmValue=$2,110.41

The

capitalexpendituresareassumedtobe110%o

frevenuesinstablegrowth;working

capitalremains15%;

Deb

tratioremainsat10%,

butafter-taxcostofdeb

tdropsto4%.Betadeclinesto1.


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Digital:ChangeinControl

Digitalwillraiseitsdebtratioto20%.Th

ebetawillincrease

,butthe

cos

tofcapitalwilldec

rease.

NewBeta=1.25(U

nleveredBeta=1.07;Debt/EquityRatio=

25%)

CostofEquity=6%

+1.25(5.5%)=12.88%

NewAfter-taxCost

ofDebt=5.25%

CostofCapital=12

.88%(0.8)+5.25%(

0.2)=11.35%

Digitalwillraiseitsre

turnoncapitalto11.35%,whichisits

costof

cap

ital.(Pre-taxOpera

tingmarginwillgo

upto4%)

Thereinvestmentrate

remainsunchanged

,buttheincreaseinthe

returnoncapitalwillincreasetheexpecte

dgrowthrateinthenext5

yea

rsto10%.

Afteryear5,thebetawilldropto1,andtheafter-taxcostof

debtwill

dec

lineto4%.


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118

D

igitalValuation:Change

inControl

Year

FCFF

TerminalValue

PV

1

$156.29

$140.36

2

$171.91

$138.65

3

$189.11

$136.97

4

$208.02

$135.31

5

$228.82

$6,584.62

$3,980.29

TerminalYear

$329.23

Value

oftheFirm:withC

ontrolChange

=$4,531million

Value

oftheFirm:Status

Quo

=$2,110million

Value

ofControl

=$2,421m

illion


119/223


120/223


121/223

Aswa

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121

Aprocedureforvaluingsynergy

(1)thefirmsinvolved

inthemergerare

valuedindependently,by

discountingexpectedcashflowstoeach

firmattheweightedaverage

cos

tofcapitalforthat

firm.

(2)thevalueofthecom

binedfirm,with

nosynergy,isobtainedby

add

ingthevaluesobta

inedforeachfirminthefirststep.

(3)Th

eeffectsofsyner

gyarebuiltinto

expectedgrowth

ratesand

cas

hflows,andthecombinedfirmisre-valuedwithsynergy.

Value

ofSynergy=Valu

eofthecombinedfirm,withsynergy-Valueof

thec

ombinedfirm,with

outsynergy


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122

SynergyEffe

ctsinValuationInputs

Ifsynergyis

ValuationInputsthatwillbeaffectedare

EconomiesofScaleOper

atingMarginofco

mbinedfirmwillbegreater

than

therevenue-weightedoperatingmargi

nof

indiv

idualfirms.

GrowthSynergy

Moreprojects:HigherReinvestmentRate(R

etention)

Betterprojects:HigherReturnonCapital(

ROE)

Long

erGrowthPeriod

Again,theseinputswill

beestimatedforthe

combinedfirm.


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ValuingSynergy:CompaqandDigital

In1997,CompaqacquiredDigitalfor$30pershare+0.94

5Compaq

sha

resforeveryDigitalshare.($53-60p

ershare)Theacquisitionwas

mo

tivatedbythebeliefthatthecombine

dfirmwouldbea

bletofind

inv

estmentopportun

ities

and

compe

te

better

than

the

firms

ind

ividuallycould.


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Bac

kgroundDat

a

Compaq

Digital:OptMgd

Curren

tEBIT

$2,9

87million$522m

illion

Curren

tRevenues

$25,484mil

$13,046mil

Capita

lExpenditures-De

preciation

$18

4million

$14

Expectedgrowthrate-next5years

10%

10%

Expectedgrowthrateafte

ryear5

5%

5%

Debt/(Debt+Equity)

10%

20%

After-taxcostofdebt

5%

5.25%

Betaforequity-next5years

1.25

1.25

Betaforequity-afteryea

r5

1.00

1.0

WorkingCapital/Revenues

15%

15%

Taxrateis36%forbothc

ompanies


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125

ValuingCompaq

Year

FCFF

Terminal

Value

PV

1

$1,518.19

$1,354.47

2

$1,670.01

$1,329.24

3

$1,837.01

$1,304.49

4

$2,020.71

$1,280.19

5

$2,222.78

$56,654.81

$33,278.53

TerminalYear$2,832.74

$38,546.91

ValueofCompaq=$

38,547million

Afteryear5,capitalexpenditureswillbe

110%ofdepreciati

on.


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126

CombinedFirmValu

ation

The

Combinedfirmwillhavesomeeconomiesofscale,allowingittoincre

aseits

currentafter-taxoperatingmarginslightly.Thedollarsavingswillbeappro

ximately$

100

million.

CurrentOperatingMargin

=(2987+522)/(25484+130

46)=9.11%

NewOperatingMargin=

(2987+522+100)/(25484+1

3046)=9.36%

The

combinedfirmwillalsohaveaslightlyhigher

growthrateof10.50%o

verthenext

5years,becauseofoperatin

gsynergies.

The

betaofthecombinedfirmiscomputedintwosteps:

DigitalsUnleveredBeta=1.07;CompaqsUnlevere

dBeta=1.17

DigitalsFirmValue=4.5;CompaqsFirmValue=38.6

UnleveredBeta=1.07*(4.5/43.1)+1.17(38.6/43.1)=1.16

CombinedFirmsDebt/EquityRatio=13.64%

NewLeveredBeta=1.16

(1+(1-0.36)(.1364))=1.26

CostofCapital=12.93%

(.88)+5%(.12)=11.98%


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127

CombinedFirmValu

ation

Year

FCFF

Terminal

Value

PV

1

$1,726.65

$1,541.95

2

$1,907.95

$1,521.59

3

$2,108.28

$1,501.50

4

$2,329.65

$1,481.68

5

$2,574.26

$66,907.52

$39,463.87

TerminalYear$3,345.38

Value

ofCombinedFirm

=$45,511


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TheV

alueofSyne

rgy

ValueofCombinedFirmwitSynergy

=$45,511

million

ValueofCompaq+V

alueofDigital

=38,54

7+4532

=$43,079million

TotalValueofSynerg

y

=$2,432

million


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Digital:

ValuationBlocks

Value

ofFirm-StatusQ

uo

=$2,110million

+Valu

eofControl

=$2,521million

Value

ofFirm-Change

ofControl

=$4,531million

+ValueofSynergy

=$2,432million

TotalValueofDigitalwithSynergy

=$6,963million


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130

Estim

atingOfferP

ricesandExchangeRatios

Thereare146.789millionDigitalsharesoutstanding,andDigitalhad

$1,006millionindebt

outstanding.Estim

atethatmaximumpriceyou

wouldbewillingtoofferonthisdeal.

AssumethatCompaqwantedtodoanexchangeoffer,whereitwould

exc

hangeitssharesforDigitalshares.AssumingthatCompa

qstockis

valuedat$27pershare,whatwouldbetheexchangeratio?


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131

Evaluatin

gCompaqs

Offer

Value

ofDigitalwithSyn

ergy

=

$

6,963mil

-Valu

eofCashpaidind

eal=$30*146.78

9milshrs=

$

4,403mil

-DigitialsOutstandingDebt(assumedbyCompaq)

$

1,006mil

Remai

ningValue

$

1,554mil

/numberofSharesoutstanding

1

46.789

=Rem

ainingValueperShare

$

10.59

Compaqsvaluepershare

attimeofExchangeOffer

$

27

AppropriateExchangeRa

tio=10.59/27=0.39Compaqsharesforevery

Digitalshare

ActualExchangeRatio=

0.945Compaqshares/DigitalShare


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132

Citicorp+Travelers

=?

Citicorp

Travelers

Citigroup

NetIncome

$

3,

591

$

3,1

04

$

6,695

BVofEq

uity

$

20,

722

$

20,7

36

$

41,458

ROE

17.33%

14.97%

16.15%

Dividend

s

$

1,

104

$

5

87

$

1,691

PayoutR

atio

30.74%

18.91%

25.27%

RetentionRatio

69.26%

81.09%

74.73%

Expectedgrowth

12.00%

12.14%

12.07%

GrowthP

eriod

5

5

5

Beta

1.25

1.40

1.33

RiskPremium

4.00%

4.00%

4.00%

MVofEquity(bil)

81

84

165.00

CostofEquity

11.00%

11.60%

11.31%

Beta-stable

1.00

1.00

1.00

Growth-stable

6.00%

6.00%

6.00%

Payout-s

table

65.38%

59.92%

62.85%

DDM

$70,743

$53,464

$124,009

DDM/share

155.84

46.38


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133

TheRightExchange

Ratio

Baseduponthesenum

bers,whatexchang

eratiowouldyouagreetoas

aC

iticorpstockholder?

Theactualexchangeratiowas2.5shares

ofTravelersforeveryshare

ofCiticorp.AsaCiticorpstockholder,do

youthinkthatthis

isa

reasonableexchangeratio?


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TheV

alueofSyne

rgy

Increase

in

ValueofEqu

ityasROE

Increase

0

5000

10000

15000

20000

25000

30000

Increaseby1%

Increase

by2%

Increaseby3%

Change

in

ROEo

fcombined

firm

IncreaseinEquity

Value


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135

Fina

ncialSynerg

y

SourcesofFinancialS

ynergy

Diversification:Acq

uiringanotherfirmasawayofreducingriskcannot

createwealthfortwopubliclytradedfirm

s,withdiversifiedstockholders,

butitcouldcreatew

ealthforprivatefirmsorcloselyheldpubl

iclytraded

firms.

CashSlack:Whena

firmwithsignificant

excesscashacquires

afirm,

withgreatprojectsb

utinsufficientcapital,thecombinationcancreate

value.

TaxBenefits:Thetaxpaidbytwofirmscombinedtogethermaybelower

thanthetaxespaidb

ythemasindividual

firms.

DebtCapacity:Byc

ombiningtwofirms,

eachofwhichhaslittleorno

capacitytocarrydebt,itispossibletocre

ateafirmthatmayhavethe

capacitytoborrowm

oneyandcreatevalu

e.


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136

I.

Diversification:NoValue

Creation?

Atakeover,motivatedonlybydiversificationconsideratio

ns,hasno

effectonthecombinedvalueofthetwofirmsinvolvedinthetakeover.

Thevalueofthecombinedfirmswillalw

aysbethesumof

thevalues

oftheindependentfirm

s.

Inthecaseofprivate

firmsorcloselyheldfirms,wheretheowners

maynotbediversified

personally,therem

ightbeapotential

valuegain

fromdiversification.


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II.

CashSlack

Ma

nagersmayrejectprofitableinvestmentopportunitiesifthey

hav

etoraisenewcapi

taltofinancethem.

Itm

aythereforemakesenseforacompanywithexcessca

shandno

inv

estmentopportun

itiestotakeover

acash-poorfirm

withgood

inv

estmentopportunities,orviceversa.

Theadditionalvalue

ofcombiningthese

twofirmsliesinthepresent

valueoftheproject

sthatwouldnothavebeentakeniftheyhad

stayedapart,butcann

owbetakenbecauseoftheavailabilityofcash.


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ValuingCashSla

ck

AssumethatNetscap

ehasasevereca

pitalrationingpro

blem,that

resultsin

approximately

$500

millio

n

ofinvestments,with

a

cum

ulativenetpresentvalueof$100million,beingrejected.

IBMhasfarmorecas

hthanpromisingp

rojects,andhasac

cumulated

$4

billionincashthat

itistryingtoinvest.Itisunderpressuretoreturn

the

cashtotheowners

.

IfI

BMtakesoverNetscapeInc,itcanbearguedthatthevalueofthe

com

binedfirmwillincreasebythesynergybenefitof$100million,

whichisthenetpresentvalueoftheprojectspossessedbythelatter

thatcannowbetaken

withtheexcesscas

hfromtheformer.


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III.

TaxBenefits

(1)Ifoneofthefirmsha

staxdeductionsth

atitcannotusebe

causeitis

losingmoney,while

theotherfirmha

sincomeonwhichitpays

significanttaxes,the

combiningofthe

twofirmscanleadtotax

ben

efitsthatcanbesh

aredbythetwofirms.Thevalueofth

issynergy

isthepresentvalueofthetaxsavings

thataccruebecau

seofthis

merger.

(2)Th

eassetsofthefirm

beingtakenovercanbewrittenup

toreflect

new

marketvalue,in

someformsofmergers,leadingto

highertax

sav

ingsfromdepreciationinfutureyears.


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ValuingTax

Benefits:Ta

xLosses

AssumethatyouareB

estBuys,theelectronicsretailer,andthatyou

wouldliketoenterthe

hardwarecomponentofthemarket.Y

ouhave

bee

napproachedbyin

vestmentbankersf

orZenith,whichwhilestilla

recognizedbrandname,isonitslastlegs

financially.Thefirmhasnet

operatinglossesof$2

billion.Ifyourtax

rateis36%,estimatethetax

ben

efitsfromthisacquisition.

IfB

estBuyshadonly

$500millionintax

ableincome,howw

ouldyou

com

putethetaxbenefits?

Ifthemarketvalueof

Zenithis$800million,wouldyoupay

thistax

ben

efitasapremiumonthemarketvalue

?


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V

aluingTaxB

enefits:AssetWriteUp

Oneoftheearliestlev

eragedbuyoutswa

sdoneonCongoleumInc.,a

div

ersifiedfirminshipbuilding,flooringandautomotivea

ccessories,

in1979bythefirm'so

wnmanagement.

Afterthetakeover,

estimatedtocost$400million,thefirm

wouldbe

allowedtowriteupitsassetstoreflecttheirnewmarketvalues,andclaim

depreciationonthenewvalues.

Theestimatedchangeindepreciationandthepresentvaluee

ffectofthis

depreciation,discou

ntedatthefirm'sco

stofcapitalof14.5%isshown

below:


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Congole

umsTaxBe

nefits

Year

Deprec'n

Deprec'n

Changein

TaxSavings

PV

before

after

Deprec'n

1980

$8.00

$35.51

$27.51

$13.20

$1

1.53

1981

$8.80

$36.26

$27.46

$13.18

$1

0.05

1982

$9.68

$37.07

$27.39

$13.15

$8

.76

1983

$10.65

$37.95

$27.30

$13.10

$7

.62

1984

$11.71

$21.23

$9.52

$4.57

$2

.32

1985

$12.65

$17.50

$4.85

$2.33

$1

.03

1986

$13.66

$16.00

$2.34

$1.12

$0

.43

1987

$14.75

$14.75

$0.00

$0.00

$0

.00

1988

$15.94

$15.94

$0.00

$0.00

$0

.00

1989

$17.21

$17.21

$0.00

$0.00

$0

.00

1980-89

$123.05

$249

.42

$126.37

$60.66

$4

1.76


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IV.DebtCapacity

Diversificationwilll

eadtoanincreaseindebtcapaci

tyandan

inc

reaseinthevalue

ofthefirm.

Hastobeweighedagainsttheimmediate

transferofwealththatoccurs

toexistingbondholdersinbothfirmsfrom

thestockholders.


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Aswa

thDam

option valuation by aswath damodaran

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