VALUATION:PACKET3REALOPTIONS,ACQUISITIONVALUATIONANDVALUEENHANCEMENTAswathDamodaranUpdated:January2017

Aswath Damodaran 1

REALOPTIONS:FACTANDFANTASY

AswathDamodaran

Aswath Damodaran 2

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UnderlyingTheme:SearchingforanElusivePremium

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¨ Traditionaldiscountedcashflow modelsunderestimatethevalueofinvestments,wherethereareoptionsembeddedintheinvestmentsto¤ Delayordefermakingtheinvestment(delay)¤ Adjustoralterproductionschedulesaspricechanges(flexibility)¤ Expandintonewmarketsorproductsatlaterstagesintheprocess,baseduponobservingfavorableoutcomesattheearlystages(expansion)

¤ Stopproductionorabandoninvestmentsiftheoutcomesareunfavorableatearlystages(abandonment)

¨ Putanotherway,realoptionadvocatesbelievethatyoushouldbepayingapremiumondiscountedcashflowvalueestimates.

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Abadinvestment…

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+100

-120

1/2

1/2

Today

Success

Failure

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Becomesagoodone…

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3/4

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+20

-20

+80

-100

2/3

1/3

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ThreeBasicQuestions

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¨ Whenistherearealoptionembeddedinadecisionoranasset?

¨ Whendoesthatrealoptionhavesignificanteconomicvalue?

¨ Canthatvaluebeestimatedusinganoptionpricingmodel?

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Whenisthereanoptionembeddedinanaction?

Aswath Damodaran

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¨ Anoptionprovidestheholderwiththerighttobuyorsellaspecifiedquantityofanunderlyingassetatafixedprice(calledastrikepriceoranexerciseprice)atorbeforetheexpirationdateoftheoption.

¨ Therehastobeaclearlydefinedunderlyingassetwhosevaluechangesovertimeinunpredictableways.

¨ Thepayoffsonthisasset(realoption)havetobecontingentonanspecifiedeventoccurringwithinafiniteperiod.

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PayoffDiagramonaCall

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Price of underlying asset

StrikePrice

Net Payoff on Call

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PayoffDiagramonPutOption

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Price of underlying asset

StrikePrice

Net PayoffOn Put

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Whendoestheoptionhavesignificanteconomicvalue?

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¨ Foranoptiontohavesignificanteconomicvalue,therehastobearestrictiononcompetitionintheeventofthecontingency.Inaperfectlycompetitiveproductmarket,nocontingency,nomatterhowpositive,willgeneratepositivenetpresentvalue.

¨ Atthelimit,realoptionsaremostvaluablewhenyouhaveexclusivity- youandonlyyoucantakeadvantageofthecontingency.Theybecomelessvaluableasthebarrierstocompetitionbecomelesssteep.

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Determinantsofoptionvalue

Aswath Damodaran

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¨ VariablesRelatingtoUnderlyingAsset¤ ValueofUnderlyingAsset;asthisvalueincreases,therighttobuyatafixedprice

(calls)willbecomemorevaluableandtherighttosellatafixedprice(puts)willbecomelessvaluable.

¤ Varianceinthatvalue;asthevarianceincreases,bothcallsandputswillbecomemorevaluablebecausealloptionshavelimiteddownsideanddependuponpricevolatilityforupside.

¤ Expecteddividendsontheasset,whicharelikelytoreducethepriceappreciationcomponentoftheasset,reducingthevalueofcallsandincreasingthevalueofputs.

¨ VariablesRelatingtoOption¤ StrikePriceofOptions;therighttobuy(sell)atafixedpricebecomesmore(less)

valuableatalowerprice.¤ LifeoftheOption;bothcallsandputsbenefitfromalongerlife.

¨ LevelofInterestRates;asratesincrease,therighttobuy(sell)atafixedpriceinthefuturebecomesmore(less)valuable.

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Whencanyouuseoptionpricingmodelstovaluerealoptions?

Aswath Damodaran

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¨ Thenotionofareplicatingportfoliothatdrivesoptionpricingmodelsmakesthemmostsuitedforvaluingrealoptionswhere¤ Theunderlyingassetistraded- thisyieldnotonlyobservableprices

andvolatilityasinputstooptionpricingmodelsbutallowsforthepossibilityofcreatingreplicatingportfolios

¤ Anactivemarketplaceexistsfortheoptionitself.¤ Thecostofexercisingtheoptionisknownwithsomedegreeof

certainty.¨ Whenoptionpricingmodelsareusedtovaluerealassets,we

havetoacceptthefactthat¤ Thevalueestimatesthatemergewillbefarmoreimprecise.¤ Thevaluecandeviatemuchmoredramaticallyfrommarketprice

becauseofthedifficultyofarbitrage.

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Creatingareplicatingportfolio

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¨ Theobjectiveincreatingareplicatingportfolioistouseacombinationofriskfreeborrowing/lendingandtheunderlyingassettocreatethesamecashflowsastheoptionbeingvalued.¤ Call=Borrowing+BuyingDoftheUnderlyingStock¤ Put=SellingShortDonUnderlyingAsset+Lending¤ Thenumberofsharesboughtorsoldiscalledtheoptiondelta.

¨ Theprinciplesofarbitragethenapply,andthevalueoftheoptionhastobeequaltothevalueofthereplicatingportfolio.

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TheBinomialOptionPricingModel

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50

70

35

100

50

25

K = $ 40t = 2r = 11%

Option Details

StockPrice Call

60

10

0

50 D - 1.11 B = 1025 D - 1.11 B = 0D = 0.4, B = 9.01Call = 0.4 * 35 - 9.01 = 4.99

Call = 4.99

100 D - 1.11 B = 6050 D - 1.11 B = 10D = 1, B = 36.04Call = 1 * 70 - 36.04 = 33.96

Call = 33.9670 D - 1.11 B = 33.9635 D - 1.11 B = 4.99D = 0.8278, B = 21.61Call = 0.8278 * 50 - 21.61 = 19.42

Call = 19.42

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TheLimitingDistributions….

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¨ Asthetimeintervalisshortened,thelimitingdistribution,ast->0,cantakeoneoftwoforms.¤ Ifast->0,pricechangesbecomesmaller,thelimitingdistributionisthenormaldistributionandthepriceprocessisacontinuousone.

¤ Ifast->0,pricechangesremainlarge,thelimitingdistributionisthepoisson distribution,i.e.,adistributionthatallowsforpricejumps.

¨ TheBlack-Scholesmodelapplieswhenthelimitingdistributionisthenormaldistribution,andexplicitlyassumesthatthepriceprocessiscontinuousandthattherearenojumpsinassetprices.

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BlackandScholes…

Aswath Damodaran

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¨ TheversionofthemodelpresentedbyBlackandScholeswasdesignedtovalueEuropeanoptions,whichweredividend-protected.

¨ ThevalueofacalloptionintheBlack-Scholesmodelcanbewrittenasafunctionofthefollowingvariables:¤ S=Currentvalueoftheunderlyingasset¤ K=Strikepriceoftheoption¤ t=Lifetoexpirationoftheoption¤ r=Risklessinterestratecorrespondingtothelifeoftheoption¤ s2 =Varianceintheln(value)oftheunderlyingasset

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TheBlackScholesModel

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Valueofcall=SN(d1)- Ke-rt N(d2)where

d2=d1-s √t

¨ ThereplicatingportfolioisembeddedintheBlack-Scholesmodel.Toreplicatethiscall,youwouldneedto¤ BuyN(d1)sharesofstock;N(d1)iscalledtheoptiondelta¤ BorrowKe-rt N(d2)

d1 = ln S

K! "

# $ + (r + σ

2

2) t

σ t

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TheNormalDistribution

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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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AdjustingforDividends

Aswath Damodaran

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¨ Ifthedividendyield(y=dividends/Currentvalueoftheasset)oftheunderlyingassetisexpectedtoremainunchangedduringthelifeoftheoption,theBlack-Scholesmodelcanbemodifiedtotakedividendsintoaccount.

¨ C=Se-yt N(d1)- Ke-rt N(d2)where,

d2=d1-s √t¨ Thevalueofaputcanalsobederived:¨ P=Ke-rt (1-N(d2))- Se-yt (1-N(d1))

d1 = ln S

K! "

# $ + (r - y + σ

2

2) t

σ t

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ChoiceofOptionPricingModels

Aswath Damodaran

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¨ MostpractitionerswhouseoptionpricingmodelstovaluerealoptionsargueforthebinomialmodelovertheBlack-Scholesandjustifythischoicebynotingthat¤ Earlyexerciseistheruleratherthantheexceptionwithrealoptions

¤ Underlyingassetvaluesaregenerallydiscontinous.¨ Ifyoucandevelopabinomialtreewithoutcomesateachnode,itlooksagreatdeallikeadecisiontreefromcapitalbudgeting.Thequestionthenbecomeswhenandwhythetwoapproachesyielddifferentestimatesofvalue.

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TheDecisionTreeAlternative

Aswath Damodaran

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¨ Traditionaldecisiontreeanalysistendstouse¤ Onecostofcapitaltodiscountcashflows ineachbranchtothepresent¤ Probabilitiestocomputeanexpectedvalue¤ Thesevalueswillgenerallybedifferentfromoptionpricingmodel

values¨ Ifyoumodifieddecisiontreeanalysisto

¤ Usedifferentdiscountratesateachnodetoreflectwhereyouareinthedecisiontree(ThisistheCopelandsolution) (or)

¤ Usetheriskfree ratetodiscountcashflows ineachbranch,estimatetheprobabilitiestoestimateanexpectedvalueandadjusttheexpectedvalueforthemarketriskintheinvestment

¨ DecisionTreescouldyieldthesamevaluesasoptionpricingmodels

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AdecisiontreevaluationofapharmaceuticalcompanywithonedrugintheFDApipeline…

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Test

Abandon

Succeed

70%

Fail

30%-$50

-$140.91

Types 1 & 2

Type 2

Type 1

Fail

10%

10%

30%

Develop

Abandon

Develop

Abandon

Develop

Abandon

Succeed

Succeed

Succeed

Fail

Fail

Fail

75%

25%

80%

20%

80%

20%-$328.74

-$328.74

-$328.74

$585.62

-$328.74

-$97.43-$366.30

-$366.30

$887.05

50%

$50.36

$93.37

$573.71

-$143.69

$402.75

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KeyTestsforRealOptions

Aswath Damodaran

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¨ Isthereanoptionembeddedinthisasset/decision?¤ Canyouidentifytheunderlyingasset?¤ Canyouspecifythecontingencyunderwhichyouwillgetpayoff?

¨ Isthereexclusivity?¤ Ifyes,thereisoptionvalue.¤ Ifno,thereisnone.¤ Ifinbetween,youhavetoscalevalue.

¨ Canyouuseanoptionpricingmodeltovaluetherealoption?¤ Istheunderlyingassettraded?¤ Cantheoptionbeboughtandsold?¤ Isthecostofexercisingtheoptionknownandclear?

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I.OptionsinProjects/Investments/Acquisitions

Aswath Damodaran

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¨ Oneofthelimitationsoftraditionalinvestmentanalysisisthatitisstaticanddoesnotdoagoodjobofcapturingtheoptionsembeddedininvestment.¤ Thefirstoftheseoptionsistheoptiontodelaytakingainvestment,whenafirmhasexclusiverightstoit,untilalaterdate.

¤ Thesecondoftheseoptionsistakingoneinvestmentmayallowustotakeadvantageofotheropportunities(investments)inthefuture

¤ Thelastoptionthatisembeddedinprojectsistheoptiontoabandonainvestment,ifthecashflowsdonotmeasureup.

¨ Theseoptionsalladdvaluetoprojectsandmaymakea“bad” investment(fromtraditionalanalysis)intoagoodone.

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A.TheOptiontoDelay

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¨ Whenafirmhasexclusiverightstoaprojectorproductforaspecificperiod,itcandelaytakingthisprojectorproductuntilalaterdate.

¨ Atraditionalinvestmentanalysisjustanswersthequestionofwhethertheprojectisa“good” oneiftakentoday.

¨ Thus,thefactthataprojectdoesnotpassmustertoday(becauseitsNPVisnegative,oritsIRRislessthanitshurdlerate)doesnotmeanthattherightstothisprojectarenotvaluable.

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ValuingtheOptiontoDelayaProject

Aswath Damodaran

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Present Value of Expected Cash Flows on Product

PV of Cash Flows from Project

Initial Investment in Project

Project has negativeNPV in this section

Project's NPV turns positive in this section

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Example1:Valuingproductpatentsasoptions

Aswath Damodaran

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¨ Aproductpatentprovidesthefirmwiththerighttodeveloptheproductandmarketit.

¨ Itwilldosoonlyifthepresentvalueoftheexpectedcashflowsfromtheproductsalesexceedthecostofdevelopment.

¨ Ifthisdoesnotoccur,thefirmcanshelvethepatentandnotincuranyfurthercosts.

¨ IfIisthepresentvalueofthecostsofdevelopingtheproduct,andVisthepresentvalueoftheexpectedcashflowsfromdevelopment,thepayoffsfromowningaproductpatentcanbewrittenas:

Payofffromowningaproductpatent =V- I ifV>I=0 ifV≤I

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PayoffonProductOption

Aswath Damodaran

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Present Value ofcashflows on product

Net Payoff tointroduction

Cost of product introduction

ObtainingInputsforPatentValuation

Input Estimation Process

1. Value of the Underlying Asset • Present Value of Cash Inflows from taking projectnow

• This will be noisy, but that adds value.2. Variance in value of underlying asset • Variance in cash flows of similar assets or firms

• Variance in present value from capital budgetingsimulation.

3. Exercise Price on Option • Option is exercised when investment is made.• Cost of making investment on the project ; assumed

to be constant in present value dollars.4. Expiration of the Option • Life of the patent

5. Dividend Yield • Cost of delay• Each year of delay translates into one less year of

value-creating cashflowsAnnual cost of delay = 1

n

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ValuingaProductPatent:Avonex

Aswath Damodaran

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¨ Biogen,abio-technologyfirm,hasapatentonAvonex,adrugtotreatmultiplesclerosis,forthenext17years,anditplanstoproduceandsellthedrugbyitself.

¨ Thekeyinputsonthedrugareasfollows:¤ PVofCashFlowsfromIntroducingtheDrugNow=S=$3.422billion¤ PVofCostofDevelopingDrugforCommercialUse=K=$2.875billion¤ PatentLife=t=17yearsRisklessRate=r=6.7%(17-yearT.Bond rate)¤ VarianceinExpectedPresentValues=s2 =0.224(Industryaveragefirmvariancefor

bio-techfirms)¤ ExpectedCostofDelay=y=1/17=5.89%

¨ Theoutputfromtheoptionpricingmodel¤ d1=1.1362 N(d1)=0.8720¤ d2=-0.8512 N(d2)=0.2076CallValue=3,422exp(-0.0589)(17)(0.8720)- 2,875exp(-0.067)(17) (0.2076)=$907million

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TheOptimalTimetoExercise

Aswath Damodaran

31 Patent value versus Net Present value

0

100

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 1Number of years left on patent

Val

ue

Value of patent as option Net present value of patent

Exercise the option here: Convert patent to commercial product

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Valuingafirmwithpatents

Aswath Damodaran

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¨ Thevalueofafirmwithasubstantialnumberofpatentscanbederivedusingtheoptionpricingmodel.

ValueofFirm=Valueofcommercialproducts(usingDCFvalue+Valueofexistingpatents(usingoptionpricing)+(ValueofNewpatentsthatwillbeobtainedinthe

future– Costofobtainingthesepatents)¨ Thelastinputmeasurestheefficiencyofthefirmin

convertingitsR&Dintocommercialproducts.Ifweassumethatafirmearnsitscostofcapitalfromresearch,thistermwillbecomezero.

¨ Ifweusethisapproach,weshouldbecarefulnottodoublecountandallowforahighgrowthrateincashflows(intheDCFvaluation).

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ValueofBiogen’sexistingproducts

Aswath Damodaran

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¨ Biogenhadtwocommercialproducts(adrugtotreatHepatitisBandIntron)atthetimeofthisvaluationthatithadlicensedtootherpharmaceuticalfirms.

¨ Thelicensefeesontheseproductswereexpectedtogenerate$50millioninafter-taxcashflowseachyearforthenext12years.

¨ Tovaluethesecashflows,whichwereguaranteedcontractually,the pre-taxcostofdebtoftheguarantorswasused:PresentValueofLicenseFees=$50million(1– (1.07)-12)/.07

=$397.13million

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ValueofBiogen’sFutureR&D

Aswath Damodaran

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¨ Biogencontinuedtofundresearchintonewproducts,spendingabout$100milliononR&Dinthemostrecentyear.TheseR&Dexpenseswereexpectedtogrow20%ayearforthenext10years,and5%thereafter.

¨ Itwasassumedthateverydollarinvestedinresearchwouldcreate$1.25invalueinpatents(valuedusingtheoptionpricingmodeldescribedabove)forthenext10years,andbreakevenafterthat(i.e.,generate$1inpatentvalueforevery$1investedinR&D).

¨ Therewasasignificantamountofriskassociatedwiththiscomponentandthecostofcapitalwasestimatedtobe15%.

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ValueofFutureR&D

Aswath Damodaran

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Yr ValueofPatents R&DCost ExcessValue PV(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

Aswath Damodaran

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¨ ThevalueofBiogenasafirmisthesumofallthreecomponents– thepresentvalueofcashflowsfromexistingproducts,thevalueofAvonex(asanoption)andthevaluecreatedbynewresearch:Value=Existingproducts+ExistingPatents+Value:FutureR&D

=$397.13million+$907million+$318.30million=$1622.43million

¨ SinceBiogenhadnodebtoutstanding,thisvaluewasdividedbythenumberofsharesoutstanding(35.50million)toarriveatavaluepershare:¤Valuepershare=$1,622.43million/35.5=$45.70

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TheRealOptionsTest:PatentsandTechnology

Aswath Damodaran

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¨ TheOptionTest:¤ UnderlyingAsset:Productthatwouldbegeneratedbythepatent¤ Contingency:

n IfPVofCFsfromdevelopment>Costofdevelopment:PV- Costn IfPVofCFsfromdevelopment<Costofdevelopment:0

¨ TheExclusivityTest:¤ Patentsrestrictcompetitorsfromdevelopingsimilarproducts¤ Patentsdonotrestrictcompetitorsfromdevelopingotherproductstotreatthesamedisease.

¨ ThePricingTest¤ UnderlyingAsset:Patentsarenottraded.Notonlydoyouthereforehavetoestimatethepresentvaluesand

volatilitiesyourself,youcannotconstructreplicatingpositionsordoarbitrage.¤ Option:Patentsareboughtandsold,thoughnotasfrequentlyasoilreservesormines.¤ CostofExercisingtheOption:Thisisthecostofconvertingthepatentforcommercialproduction.Here,

experiencedoeshelpanddrugfirmscanmakefairlypreciseestimatesofthecost.¨ Conclusion:Youcanestimatethevalueoftherealoptionbutthequalityofyourestimatewillbea

directfunctionofthequalityofyourcapitalbudgeting.Itworksbestifyouarevaluingapubliclytradedfirmthatgeneratesmostofitsvaluefromoneorafewpatents- youcanusethemarketvalueofthefirmandthevarianceinthatvaluetheninyouroptionpricingmodel.