option valuation by aswath damodaran
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EquityInstrum
entsan
dMarkets:
PartIII
B40.3331
RealOptions
Acq
uisitionValuation
Va
lueEnhancement
AswathDamodaran
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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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ThreeBasicQuestions
Wh
enistherearealoptionembeddedinadecisionoranass
et?
Wh
endoesthatrealoptionhavesignifica
nteconomicvalue?
Canthatvaluebeestim
atedusinganoptionpricingmodel?
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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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PayoffD
iagramona
Call
Priceofunderlyingasset
Stri
ke
Price
NetPa
yoff
onCall
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PayoffDia
gramonPutOption
Priceof
underlyingasset
Strike
Price
NetPayoff
On
Put
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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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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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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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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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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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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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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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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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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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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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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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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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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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OptionPricingApplicationsin
Investmen
t/StrategicA
nalysis
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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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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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V
aluingtheO
ptiontoDela
yaProject
PresentValueofExpected
CashFlowsonProduct
PVofCashFlows
fromProject
InitialInvestmentin
Project
Projecthasn
egative
NPVinthissection
Project'sNPVturns
positiveinthissection
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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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Payoffo
nProductO
ption
PresentValueof
cashflowso
nproduct
NetPay
offto
introduction
Costofproduct
introduction
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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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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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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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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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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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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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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=$45.70
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T
heRealOptionsTest:Patentsand
T
echnology
TheOptionTest:
UnderlyingAsset:Productthatwouldbegeneratedbythepatent
Contingency:
IfPVofCFsfromdeve
lopment>Costofdevelopment:PV-Cost
IfPVofCFsfromdeve
lopmentX
=0
ifV
X
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PayoffDiagramonNaturalResourceFirm
s
Valueofestimatedreserve
ofnaturalresourceN
etPay
offon
Extraction
CostofDev
eloping
Reserve
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Estima
tingInputsforNaturalResourceOptions
Input
EstimationProcess
1.ValueofAvailabl
eReservesoftheResource
Expertestimates(Geologistsforoil..);The
presentvalueoftheafter-taxcashflowsfrom
theresourcearet
henestimated.
2.CostofDevelopin
gReserve(StrikePrice)
Pastcostsandthe
specificsoftheinvestment
3.TimetoExpiratio
n
RelinqushmentPe
riod:ifassethastobe
relinquishedatapointintime.
Timetoexhaustinventory-basedupon
inventoryandcap
acityoutput.
4.Varianceinvalue
ofunderlyingasset
baseduponvariab
ilityofthepriceofthe
resourcesandvar
iabilityofavailablereserves.
5.NetProductionRevenue(DividendYield)
Netproductionre
venueeveryyearaspercent
ofmarketvalue.
6.DevelopmentLag
Calculatepresent
valueofreservebasedupo
n
thelag.
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ValuinganOilReserve
Co
nsideranoffshoreoilpropertywithanestimatedoilreserveof50
millionbarrelsofoil,wherethepresentvalueofthedevelopmentcost
is$
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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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=$600
million
Tim
etoexpirationon
theoption=20yea
rs
Varianceinthevalueoftheunderlyingasset=0.03
Ris
klessrate=8%
DividendYield=Net
productionrevenue
/Valueofreserve
=5%
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Valu
ingtheOptio
n
Basedupontheseinpu
ts,theBlack-Scholesmodelprovidesthe
followingvalueforthecall:
d1
=1.0359
N(d1)=
0.8498
d2
=0.2613
N(d2)=
0.6030
CallValue=544.22exp(-0.05)(20)(
0.8498)
-600(exp(-0.08)(20)(0
.6030)=$
97.08million
Thisoilreserve,thoug
hnotviableatcurrentprices,stillisa
valuable
pro
pertybecauseofitspotentialtocreate
valueifoilpricesgoup.
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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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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.
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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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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
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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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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%
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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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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
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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.
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Op
tionPricingApplications
inValuation
EquityValueinDeeplyTrouble
dFirms
ValueofUndeveloped
ReservesforNaturalResourceFirm
Valu
eofPatent/License
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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)
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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.
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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
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PayoffDiagramforLiquida
tionOption
Va
lueoffirm
NetPayoff
onEquity
FaceValue
of
Debt
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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?
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Mod
elParameters
Valueoftheunderlyin
gasset=S=Valueofthefirm=$100million
Exerciseprice=K=F
aceValueofoutstandingdebt=$80million
Lifeoftheoption=t=
Lifeofzero-coupondebt=10years
Varianceinthevalueoftheunderlyingasset=2=Varianceinfirm
value=0.16
Ris
klessrate=r=Tre
asurybondratecor
respondingtooptio
nlife=
10%
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ValuingEq
uityasaCallOption
Basedupontheseinpu
ts,theBlack-Scholesmodelprovidesthe
followingvalueforthecall:
d1=1.5994
N(d1)=0
.9451
d2=0.3345
N(d2)=0
.6310
Valueofthecall=100(0.9451)-80exp(-0.10)(10)(0.6310)=$
75.94
million
Valueoftheoutstandingdebt=$100-$7
5.94=$24.06million
Interestrateondebt=
($80/$24.06)1/10-1=12.77%
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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
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I
llustration:V
alueofatro
ubledfirm
Assumenowthat,inthepreviousexample,thevalueofthefirmwere
red
ucedto$50millionwhilekeepingthe
facevalueofthed
ebtat$80
million.
Thisfirmcouldbeviewedastroubled,sinceitowes(atleastinface
valueterms)morethanitowns.
Theequityinthefirm
willstillhavevalue,however.
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ValuingEquityintheTroubledFirm
Valueoftheunderlyin
gasset=S=Valueofthefirm=$50
million
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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TheValueo
fEquityasa
nOption
Basedupontheseinpu
ts,theBlack-Scholesmodelprovidesthe
followingvalueforthecall:
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=$19.56million
Theequityinthisfirm
dropsby,because
oftheoptioncharacteristics
ofequity.
Thismightexplainwh
ystockinfirms,whichareinChapter
11and
essentiallybankrupt,s
tillhasvalue.
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Equity
valuepersis
ts..
ValueofEquityasFirm
Value
Changes
010
20
30
40
50
60
70
80
100
90
80
70
60
50
40
30
20
1
0
Value
ofFirm
($
80
Face
Valu
e
ofDebt)
ValueofEquity
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OptionPricin
gTheory
andReal
Option
Applicat
ions
As
wathDamodaran
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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.
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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%.
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ValuingEq
uityafterthe
Project
Valueoftheunderlyin
gasset=S=Valueofthefirm=$100million-
$2
million=$98million(Thevalueofth
efirmisloweredb
ecauseof
the
negativenetpresentvalueproject)
Exerciseprice=K=F
aceValueofoutstandingdebt=$80million
Lifeoftheoption=t=
Lifeofzero-coupondebt=10years
Varianceinthevalueoftheunderlyingasset=2=Varianceinfirm
value=0.25
Ris
klessrate=r=Tre
asurybondratecor
respondingtooptio
nlife=
10%
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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.
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Effects
ofanAcquis
ition
Assumethatyouarethemanagerofafirmandthatyoubuy
another
firm
,withafairmarke
tvalueof$150million,forexactly$
150
million.Inanefficientmarket,thestockpriceofyourfirmw
ill
Inc
rease
Decrease
RemainUnchanged
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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
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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.
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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.
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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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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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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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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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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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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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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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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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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.
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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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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
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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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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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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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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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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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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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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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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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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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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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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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