BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationof
RealEstateVentures
by
KeithChin‐KeeLeung
BachelorofCommerce,SauderSchoolofBusiness
UniversityofBritishColumbia,2007
SubmittedtothePrograminRealEstateDevelopmentin
ConjunctionwiththeCenterforRealEstate
inPartialFulfillmentoftheRequirementsfortheDegreeof
MasterofScienceinRealEstateDevelopment
atthe
MASSACHUSETTSINSTITUTEOFTECHNOLOGY
February2014
©2014MassachusettsInstituteofTechnology.Allrightsreserved.
SignatureofAuthor__________________________________________________________________________________
MITCenterforRealEstate
January30,2014
Certifiedby___________________________________________________________________________________________
RicharddeNeufville,PhD
ProfessorofEngineeringSystemsandofCivilandEnvironmental
Engineering
ThesisCo‐Supervisor
Certifiedby___________________________________________________________________________________________
DavidGeltner,PhD
ProfessorofRealEstateFinanceandofEngineeringSystems
DirectorofResearch,CenterforRealEstate
ThesisCo‐Supervisor
Acceptedby___________________________________________________________________________________________
DavidGeltner,PhD
Chairman,InterdepartmentalDegreePrograminRealEstateDevelopment
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationof
RealEstateVentures
by
KeithChin‐KeeLeung
SubmittedtothePrograminRealEstateDevelopmentin
ConjunctionwiththeCenterforRealEstate
onJanuary30,2014inPartialFulfillmentofthe
RequirementsfortheDegreeofMasterofSciencein
RealEstateDevelopment
ABSTRACT
Thisthesisintroducesprobabilisticvaluationtechniquesandencouragestheirusageinthe
realestateindustry.Includinguncertaintyandrealoptionsintorealestatefinancialmodels
isworthwhile,especiallywhenthereisanelevatedlevelofunpredictabilitysurrounding
theinvestmentdecision.
Incorporatinguncertaintyintorealestateproformasnotonlyprovidesdifferentresults
overdeterministicmodels,itchangestheangleofattacktorealestatevaluationproblems.
Whenuncertaintyistakenintoaccount,thefocusshiftsfromsimplymaximizingfinancial
returns,tomodelingandmanaginguncertaintytomakebetterexantefinanceanddesign
decisions.Theabilitytoaddoptionalityinprobabilisticfinancialmodelingcanenhance
returnsbycurtailinglossesduringdownturnsandtakingadvantageofupsideconditions.
Astep‐by‐stepexampleiscarefullycraftedtodemonstratethesimplicitywithwhich
uncertainty,MonteCarloSimulationsandRealOptionsmaybeincludedintorealestatepro
formas.TheexampleisentirelyExcelbasedandisseparatedintothreepartswitheach
progressivelyincreasingincomplexity.SimpleCoTowerestablishesthefamiliar
DiscountedCashFlowproformaasastartingpoint.ModerateCoTowerdescribeshow
uncertaintyandMonteCarlosimulationscanbeincorporatedintoaproformawhile
illustratingtheeffectofnon‐linearityonfinancialmodels.ChallengeCoTowerrevealshow
realoptionscanaddvaluetoaninvestmentandhowitshouldnotbeoverlooked.
Thecasestudyillustrateshowthetechniquesoutlinedinthisthesiscanaddsignificant
valuetorealestatedecisionswithoutmuchaddedeffortorinvestmentinexpensive
software.Thecasestudyalsoshowshowtheuseofrealworlddatatomodeluncertainty
canbeputintopractice.
ThesisCo‐Supervisor:
RicharddeNeufville,PhD
Title: ProfessorofEngineeringSystemsandCivilandofEnvironmentalEngineering
ThesisCo‐Supervisor:
DavidGeltner,PhD
Title: ProfessorofRealEstateFinanceandofEngineeringSystems
DirectorofResearch,CenterforRealEstate
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
2 TableofContents
ABSTRACT ................................................................................................................................................... 2 TableofContents ...................................................................................................................................... 3 TableofFigures ......................................................................................................................................... 5 Acknowledgements .................................................................................................................................. 6 CHAPTER1:Introduction ........................................................................................................................ 7 1.1 ThesisPurpose ............................................................................................................................ 7 1.2 FormatofPresentation ............................................................................................................... 8 1.3 CurrentIndustryPractice:Excel,ArgusandDiscountedCashFlowAnalysis ........................ 9 1.4 ReluctancetoAdoptNewTechniquesandRelianceonIntuition ......................................... 10 1.5 TheRoleofModernPedagogyinthisThesis .......................................................................... 12 CHAPTER2:SimpleCoTower–ADeterministicExample .............................................................. 14 2.1 AssumptionsofaDeterministicModel .................................................................................... 14 2.2 ProjectingCashFlowsforSimpleCoTower ............................................................................ 14 2.3 ReturnMeasures:NPVandIRR ................................................................................................ 15 CHAPTER3:ModerateCoTower‐IncorporatingUncertaintyintoaFinancialModel .............. 16 3.1 UncertaintyintheRentGrowthRateofModerateCoTower ................................................. 16 3.2 MonteCarloSimulationsandExpectedNPV ........................................................................... 17 3.3 TheFlawofAveragesandJensen’sInequality ........................................................................ 18 3.4 ADifferentApproachtoRealEstateFinancialAnalysis:DistributionsandRiskProfiles ... 20 3.5 StaticInputVariablesversusRandomWalks ......................................................................... 22 CHAPTER4:ChallengeCoTower‐ManagingUncertaintyinRealEstateProjects ..................... 24 4.1 RealOptionAnalysisinChallengeCousingIFStatements ..................................................... 24 4.2 ChallengeCoTower’sResultwithaRealOption ..................................................................... 25 CHAPTER5:QuantifyingUncertaintyintheRealWorld ................................................................. 28 5.1 PredictabilityintheRealEstateMarket .................................................................................. 28 5.2 RealEstateEconomicsandtheStockFlowModelforOfficeProperties .............................. 30 5.3 SourcesofUncertaintyinRealEstate ...................................................................................... 31 CHAPTER6:ManagingUncertaintyintheRealWorld .................................................................... 37 6.1 TheBasicsofFinancialOptions ................................................................................................ 37 6.2 SourcesofValueforFinancialOptions .................................................................................... 38 6.3 TheValuationofFinancialOptions .......................................................................................... 40 BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
3 6.4 RealOptions ............................................................................................................................... 41 CHAPTER7:TwoWorldTradeCenterCaseStudy ............................................................................ 44 7.1 ScenarioBackground ................................................................................................................ 44 7.3 ProjectingRents,CapRates,ConstructionCostsandOperatingExpenses .......................... 46 7.4 ProFormas ................................................................................................................................. 51 7.5 RealOptionTriggers ................................................................................................................. 52 7.6 Results ........................................................................................................................................ 53 CHAPTER8:Conclusion ......................................................................................................................... 55 BIBLIOGRAPHY ........................................................................................................................................ 57 AppendixA IncorporatingUncertaintyintoaFinancialModel ........................................... 60 AppendixB PerformingMonteCarloSimulations .................................................................. 62 AppendixC CreatingCumulativeDistributionFunctions(CDFs)inExcel ......................... 64 AppendixD UsingIFStatementstoModelRealOptionsforRealEstateVentures .......... 66 BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
4 TableofFigures
Figure1:SimpleCoTowerSketch ............................................................................................................ 14 Figure2:SimpleCoTowerAssumptions ................................................................................................. 14 Figure3:SimpleCoTowerProForma ..................................................................................................... 15 Figure4:ModerateCoTowerSketch ....................................................................................................... 16 Figure5:NormalDistributionCurveUsedtoModelRentGrowth ....................................................... 17 Figure6:ResultsfromtheMonteCarloSimulationENPVversusDeterministicNPV ........................ 18 Figure7:Non‐linearityintheRentGrowthRate .................................................................................... 20 Figure8:ModerateCoTowerCumulativeDistributionFunction .......................................................... 21 Figure9:RandomWalkIllustration ........................................................................................................ 23 Figure10:ComparisonofReturnsbetweenModerateCoandSimpleCo .............................................. 23 Figure11:ThreeChallengeCoTowerOptions ........................................................................................ 25 Figure12:ChallengeCoTowerExpectedNPVs ....................................................................................... 26 Figure13:WorldTradeCenterSitePlan(PANYNJ,2013) .................................................................... 44 Figure14:2WTCRendering(PANYNNJ,2013) ...................................................................................... 45 Figure15:RealEstateCycleLength ......................................................................................................... 49 Figure16:TheRegularSineCurve........................................................................................................... 49 Figure17:2WTCSketchupofAlternatives ........................................................................................... 51 Figure18:2WTCFinancialModelResults .............................................................................................. 53 Figure19:2WTCDistributionFunction ................................................................................................. 54 BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
5 Acknowledgements
PraisesandthankstoGodfortheblessingsthroughoutmytimeatMIT.Mymotivationand
drivecomesfromasenseofpurposethatGodprovidesmewith.
IwouldliketothanktheMIT‐SUTDInternationalDesignCenterforfundingthisresearch.It
ismygreathopethatthisthesiscould,eveninthetiniestway,helpempowerpeopleto
undertaketheimpossibleanddesigntheunexpected.
IextendsincereappreciationtoProfessorGeltnerandProfessordeNeufvillefortheir
wisdomandpatienceindevelopingthisthesis.Iamgratefulandhonoredtohaveworked
with,notonlytworenownedintellectuals,buttwogreatteachers.I’llmissthelaughs
duringourweeklymeetingsinDr.Geltner’soffice.ThanksalsotoProfessorSomervilleat
UBCforgivingmemyfirstbreakinrealestate‐‐I’llneverforgetit.
TheMITCREfacultyandalumniarethebest.Thankyouforyourinspiration.Ilook
forwardtoournextbeerandinsightfulconversationaboutrealestateandpolitics.Thanks
totheCREclassof2013forhelpingmeinthetrenchesatMIT.Itwasabattle,butweall
madeit,together.Ican’timaginelifewithouttheRECIII.
IamappreciativeofmyfriendswhoalwaysliftmeupwhenI’mdown,especiallythoseat
CoL,APG,GCF,BSF,andVCBC.ThankstoAKwhomakesmyday,everyday.
Thankyoutoallofmysuperbformerworkcolleaguesformoldingmyprofessional
characterandstillprovidingencouragementevenaftermydepartureyearsago.
Lastbutnotleast,aspecialacknowledgementgoestomyfamilywhosupportmenomatter
what.Wearen’talwaysaperfectbunch,butwhenitcounts,wearethereforeachother.
Thanksagaintoallofyou.Mysuccessisyoursasmuchasitismine.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
6 CHAPTER1:Introduction
“Maytheoddsbeeverinyourfavor.”
‐SuzanneCollins,authorofTheHungerGames
Intheblockbustersciencefictionnovelandmovieseries,TheHungerGames,Collins
describesadystopiansocietyinwhichahandfulofteenagersareengagedinanultra‐
competitivebattletothedeath.Thiscompetitiveenvironmentcoulddrawcomparisonsto
thearenaofrealestateinvesting,wheredealsarewonorlostbyrazor‐thinmargins.While
Collins’quotesuggeststhatnothingcanbedoneaboutone’soddsintheworldofherbook,
thisisnotthecasewithrealestate.Withknowledgeofprobabilisticvaluationmethods,
realoptions,andeconomics,realestateprofessionalscaneffectivelyimprovetheoddsin
theirfavor.
1.1
ThesisPurpose
TheworldofcorporatefinancewasintroducedtoMonteCarlomethodsapproximately50
yearsago,significantlyalteringthevaluationapproachforderivatives.Incontrast,there
hasnotbeenwide‐spreadadoptionofstochasticvaluationtechniquesinrealestatefinance
despitethepositivetrackrecordofMonte
CarloSimulationsincorporatefinance
KeyTerms:StochasticvsDeterministic
(Marshall&Kennedy,1992).Thebenefitsof
Astochasticorprobabilisticmodel
reliesonprobabilitytoobtainitsvalues
forfuturestatesofthesystem.
probabilisticvaluationtechniquesforreal
estatehavebeenwidelydocumentedsince
theearly1990’s(Baroni,Barthélémy,&
Mokrane,2006;Farragher&Savage,2008;
Adeterministicmodelhasno
randomnessinvolvedingeneratingits
futureoutputvalues.
Louargand,1992).Yet,therealestate
industrystillreliesonsensitivityanalysesfortheirriskassessmentofrealestate
investments.FarragherandSavage’s2005surveyof32intuitionalinvestorsand156
developersshowedthatonly2%ofthesefirmsutilizeMonteCarloSimulationtechniques.
Themessagefromacademiaisnotgettingthroughtoindustry.Therejectionof
probabilistictechniquesbyrealestateprofessionalsisdue,inlargepart,totheinabilityof
academicstopresentacompellingargumentforprobabilisticfinancialmodeling.Academic
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
7 thesestendtobeexcellentatdefiningwhatconceptsare,buthavedifficultywithcoaching
theapplicationoftheoreticalconceptstotherealworld.Thefragmentationoftheresearch,
whichoccursbecauseofthemulti‐disciplinarynatureofthesubjectmatter,inhibits
acceptanceofstochastictechniquesbecausethetruebenefitsarenotrealizedtogetherina
sweepingoverallviewfromthestartoftheprocess,allthewaytotheend.Withrootsin
engineering,mathematics,economicsandfinance,theconceptspresentedinthisthesis
haveneverbeenpresentedtogetherbefore.
Thisthesisadvocatesfortheuseofprobabilistically‐basedvaluationintherealestate
industryby:

organizingresearchfrommultipledisciplines,

demonstratingthegreatnumericalandstrategicadvantagesofstochasticmodeling,

clarifyinghowlittleadditionaleffortisrequiredtoachievethoseadvantages,and

emphasizingtheapplicabilityofconceptsdescribedabovetorealworldproblems.
Thisthesisattemptstomendthedisconnectbetweenacademiaandindustrybyfocusing
ontheeffectivepresentationofideasandapplicationofmodernpedagogicaltheory.
1.2
FormatofPresentation
Thisthesisisstructuredtoappealtoawiderangeofrealestateprofessionals.Themajor,
bigpictureargumentsforimplementingprobabilisticstrategiesmaybeofgreater
importancetoexecutivesandmanagers,whileananalystmaywanttounderstandthefiner
pointsofmodelinguncertaintyandrealoptionsinExcel.Thechaptersinthisthesisvaryin
theirlevelofdetail.Chapters2,3,and4walkthroughasimplifiedexamplethat
incorporateselementsofprobabilisticvaluationatabroadleveltodemonstratethemain
pointsofthisthesis.Discussioninthesechapterswilltendtobemorequalitative.Forthose
lookingforagreaterdetail,theappendixdescribeshowtheideaspresentedcanbe
implementedintoExcel,stepbystep.Additionally,anExcelworkbookofeveryexampleis
availableforrealestatepractitionerstoexploreeverycell.Chapters5and6showhowthe
probabilisticconceptstranslatetotherealworld,withadetailedcasestudyof2World
TradeCentertobookendthethesisinchapter7.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
8 1.3
CurrentIndustryPractice:Excel,ArgusandDiscountedCashFlowAnalysis
ThetoolsofthetradeforanalyzingincomeproducingpropertiesareMicrosoftExceland
Argus.Overthelastdecade,theabilitytoworkwithExcelhasbecomeessentialinthe
businessworld,especiallyforgraduatesofbusinessschools.Despitetheprevalentusageof
Excelintheworkplace,generallyveryfewfeaturesoftheprogramareusedby
professionals.Excelusersarelargelyunawareofthecomputingpoweravailabletothem
andresorttousingahandfulofcommonfinancecalculatorfunctions.However,thisisnot
thefaultofprofessionals,astheuserexperience,beyondbasiccalculatorfunctions,
becomesunintuitiveandfrustratingtothosenotfamiliarwithcomputerprogramming.
Goodcoachingandconstantpracticeisrequiredtodevelopskillsbeyondbasiccalculator
functionsinExcelandthisthesisaddressesthisbyprovidingeasy‐to‐followexamples.
Argusissoftwaredesignedtosaverealestateprofessionalstimebyallowingtheinputof
informationthroughagraphicaluserinterface(GUI).AproformaisgeneratedbyArgus
oncealltheinformationisimputed.Argus,inparticular,isusefulfororganizinglease
informationandproducingrentrolls,ataskthatistediouswhentheanalysisisperformed
manuallyinExcel.Argusallowsrealestateanalyststoassessthefinancialfeasibilityofa
dealquicker,enablingafirmtoinspectagreatervolumeofdeals.Unfortunately,Argus
doeshaveafewdrawbacks.WhiletheproformaisexportabletoExcel,Argusdoesnot
exporttheformulaswhichitusestocalculateitsnumbers,essentiallymakingArgusa
“blackbox”;theinnerworkingsandlogicoftheprogramcannotbeinspected.Relianceon
theautomationwhichArgusprovidestorealestateanalystscoulderodehuman
performance,aspracticefromworkingwiththenutsandboltsofarealestateproformais
reduced.Asimilarargumentismadeoverautomationinaircraftcockpits,asreports,such
asSarter&Woods(1994),expressconcernsovertheabilityofpilotstoreacttonon‐
normalsituations.AnotherissueistheinflexibilityofArgustoadapttoawiderangeofreal
estateventures.Argusisgreatatmodeling“cookie‐cutter”projects,butitseffectivenessis
reducedwhenit’susedtomodelcomplexrealestateprojects.
ThemainmethodofvaluationforincomeproducingrealestateistheDiscountedCash
Flow(DCF)approach.Whilethedirectcapitalizationmethod(usingcaprates)isalso
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
9 widelyused,theabsoluterelianceononeyear’snetoperatingincomerelegatesthedirect
capitalizationmethodtoquickback‐of‐the‐napkinanalyses.TheDCFapproachinvolves
projectingfutureyearsofcashflowanddiscountingthemusingarisk‐adjusteddiscount
ratetoarriveattheNetPresentValueoftheproject.
DCFproformasaretaughtinintroductoryrealestateandcorporatefinancecoursesin
universitiesaroundtheworld.ThereareslightvariationsinthewaytheDCFapproachis
taughtfromschooltoschool;thisdoeslittletodeterthewidespreadusageofDCFpro
formas.
ThedeterministicDCFapproachdoespossesslimitations,however.First,theanalysisof
uncertaintyisverylimitedinDCFmodels.Thediscountratereflectsthelevelofriskina
project,butthismethodoversimplifiesriskbyrelyingonsinglediscountratewhenthere
aremultiplesourcesofuncertainty.Also,thediscountratedoesn’ttakeintoaccountthe
asymmetrybetweenupsideanddownsiderisk–generally,downsideeventsmattermore
toinvestorsthanupsideevents.Thirdly,itignorestheeffectofoptionsorpossiblechanges
whichmayoccurtotherealestateoverthelifeoftheinvestmentasownersandmanagers
haveflexibilitytorespondtochangesintheeconomybymakingdecisionsthataffectfuture
cashflows.Despiteitspitfalls,theDCFapproachiswellunderstoodatalllevelsof
experienceintherealestateindustrywhichmakesitagoodstartingpointtodiscuss
probabilisticvaluationtechniquesfrom.ThebasicDCFproformaishighlightedinChapter
2.
1.4
ReluctancetoAdoptNewTechniquesandRelianceonIntuition
Whyhastheadoptionofprobabilisticvaluationtechniques,suchasMonteCarlo
Simulations,notoccurredintherealestateindustry?Byrne(1996)suggeststhatboththe
smallteamsandtheentrepreneurialnatureoftherealestateindustrypreventsthefull
acceptanceofprobabilisticmethodsinfinancialmodeling.Butshouldn’tthe
entrepreneurialspiritoftheindustrytranslateintoaninsatiableappetitetofindanedgeto
getaheadofthecompetition?
Withoutadoubtrealestateteamsaresmall.Whethertheteamsarebasedinthelargest
investmentbanksorinthelargestmulti‐nationaldevelopers,onlyafewanalystsandeven
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
10 fewermanagersareinvolvedinthedecision‐makingprocessinanygivenrealestate
investment.Theheavyworkloadonopendealscouldcrowdouttimeavailabletospendon
improvingprocesses,thusperpetuatingthestatusquo.Thenotionthatrealestatefirmsare
notembracingstochasticvaluationtechniquesbecausetheyaresmallshouldberejected.
Realestatefirmsfocusonefficiencyandarelikelytoadoptnewmethods,processes,or
technologyifthecost‐benefitrationalemakessensetothem.Incorporatinguncertainty
intothefinancialanalysisofrealestateventuresisa“lowhangingfruit”andrepresentsa
majorimprovementinanalyticswithverylittleeffortorcost.
Realestatehasalwaysbeenperceivedaslesssophisticatedcomparedtootherassetclasses
suchasstocksorbonds.Thisperceptionwaslargelyduetoprivatenatureofrealestate
transactionsandthelackofdataavailableforeconomicanalysis.Whilethemarketfor
stockshasbeendevelopingsincethe1600’s,realestateequityasasecuritizedassetonly
begantradinginthe1960’s.Withoutreliabledatatoguidefinancedecisions,realestate
professionalsdependedontheirinstinctsandintuitiontoremainsolventduring
recessions.
Asanyexperiencedprofessionalknows,ourinstinctsdofailusfromtimetotime.Partof
thereasonwhyuncertaintyisoverlookedisbecauseitinvolvesseeingfinanciallossesasa
possibility.Negativitybiasisapsychologicalphenomenonthatmayexplainwhathappens
whenweseelossesorexperiencenegativemoments(Baumeister,Bratslavsky,Finkenauer,
&Vohs,2001).Acommonexampleofthiseffectistheanti‐anticipationandstressof
receivingalargerestaurantbill,whichisfurtherexacerbatediftheactualbillamountis
unknown.Humanstendtrytoavoidthesenegativeexperiencesthatshakeourconfidence
evenifgreatbenefitsarepossible.
Previouslypublishedresearchadvocatingfortheuseofprobabilisticvaluationtechniques
weremissingakeycomponent:datafromasufficientnumberofmarketcyclestodescribe
thebehaviorofmarketfactorsanduncertainty.Withover50yearsofdataavailable,the
timeisripeforrealestatetoexplorescientificapproaches.Appropriateusageofrealestate
datafromindicesarediscussedfurtherinchapters5and6.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
11 Thetechniquesdescribedinthisthesiswillnoteliminatetheneedforgoodinstinctsinreal
estate,butrather,theywillenhancedecision‐makingbyprovidingdifferentperspectives
onrealestateproblems.
1.5
TheRoleofModernPedagogyinthisThesis
Thestruggleofuniversityresearcherstoconnectwithlearnersiswelldocumented
(Seymour,2008).Theacademictenuresystemiscitedasamajorreasonwhyteachingand
communicationhavetakenabackseat,asprofessorsareencouragedtopushout
publicationsmorethandevelopingteachingskills.Ifprofessorshavedifficultykeeping
studentsintheirclassroomsengaged,whathopedotheyhaveintryingtoengagereaders
inaone‐waymedium?Indeed,scholarlyarticlesseemtobemoreeffectivein
communicatingideastootheracademics,butwhatabouttherestofsociety?
Themainintentofthisthesisispresentprobabilisticconceptstorealestateprofessionals
withahighlevelofclarity.Oftentimes,authorsofscholarlyarticlesenterintoauto‐pilot
modeanddelivertheirideasbasedontheirownexperienceaslearnersorcasual
observations.Forthisthesis,specialattentionispaidtopedagogytopreventaresearcher‐
centeredteachingapproachandmovetowardsalearner‐centeredapproach.
Asyoumightimagine,thereisnoscarcityofresearchonhowadultslearn.Describedbelow
aretwomajortheoriesinmodernpedagogywhichguidethemannerofpresentationfor
conceptsintroducedinthisthesis.Thefirsttheoryisofmentalmodels,orschemas.Child
psychologistJeanPiagetproposedaprocessinwhichchildrenusetheirinteractionswith
theworldtodevelopmodelsofobjectsandpatternsofaction(Lang,2008).Itturnsout
thatwhatweknowalreadyabouttheworldgreatlyinfluenceshowweencounternew
experiences;ourexistingmodelsareunderconstantrevision.Whenadultsaremetwith
newexperiencesorideas,theyworktofitthesenewelementsintopatternswhichthey
alreadyunderstand.Therearetwolearningprocesseswhichcanoccurwhenaperson
encountersanewexperience:assimilationandaccommodation.Assimilationoccurswhen
apersontakesinanewideabymakingtheideafittointotheirexistingmodels.Onthe
otherhand,accommodationoccurswhenthenewideadoesnotfitintoanypre‐existing
modelsandchangesaremadetoaperson’sexistingmodelstotakeinthenewinformation.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
12 Awarenessofboththeseprocessesiscrucialtoeffectivedeliveryoftheideaspresentedin
thisthesis.Insomescenarios,assimilationneedstooccurwhichrequiresthepresenterto
helptheaudienceconnecttopre‐existingknowledge.Anexampleofthisoccurringinthis
thesisistheuseofthefamiliarDiscountedCashFlowproformaasastartingpointformore
complexfeatureadditions.Forscenariosinwhichaccommodationislikelytooccur,clarity
isvitaltoceasetheperpetuationofcommonmisconceptionsandpitfalls.Clarityis
emphasizedwhenpresentingtheFlawofAveragesinChapter3.
Bloom’sTaxonomyisthesecondpedagogicaltheorythatisappliedinthisthesis.Bloom’s
TaxonomyisaframeworkdevelopedbyBenjaminBloomin1956tocategorizelearning
objectives.Theframeworkdivideseducationalobjectivesintothreedomains:cognitive,
affective,andpsychomotor(Krathwohl,2002).Skillsinthecognitivedomainincludethose
ofknowledgeandcriticalthinking.Theaffectivedomainincludeskillsrelatingtoemotion,
whilethepsychomotordomainfocusesonskillswithphysicaltools,suchashammers.The
cognitivedomainismostrelevantfortheconceptspresentedinthisthesis.Intherevised
Bloom’sTaxonomy,Krathwohlpresents6levelsofprocessesinthecognitivedomain.From
lowestcomplexitytohighest,theyare:remember,understand,apply,analyze,evaluateand
create.Ifthegoalistoteachprofessionalshowtocreatetheirownsimulations,the
correspondingdiscussionsandexamplesshouldmatchthatgoalindetailandcomplexity.
Sincechaptersinthisthesisvaryintheirobjectives(someprofessionalsmightonlywantto
goupto‘understand’level,whileotherwillwantto‘create’),carefulattentionispaidto
maintainconsistencyincognitivelevels.Mismatchedobjectivesanddiscussionsleadto
frustrationforreaders.Theappendicesandchapters5,6,and7catertoreaderswhowant
toreachthe‘create’level,whilenext3chaptersresideatthe‘understand’level.Webegin
gentlybywalkingthroughthedeterministicdiscountedcashflowproforma.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
13 CHAPTER2:SimpleCoTower–ADeterministicExample
Thefirstexample,SimpleCoTower,isa
simplifieddiscountedcashflowproformaof
thekindanalyststypicallyusetofinancially
modelcommercialrealestatetransactions.
SimpleCoTowerisa10storyofficetowerwith
afloorplateof17,000sf.Afinancialmodelis
createdtoevaluatethepurchaseofthe
Figure1:SimpleCoTowerSketch
Avisualrepresentationofthe10‐
storyofficetower,SimpleCoTower.
buildingforapriceof$17million.Thereare
threemajorsectionstoaproforma:the
assumptions,thecashflowprojections,andtheoutputs.
2.1
AssumptionsofaDeterministicModel
Theassumptionsareasetofparameterswith
SimpleCo Tower Assumptions
Purchase Price
$100 /gsf
Gross Floor Area
170,000 sf
Efficiency
90%
Office Rent
$30 /sf
Rent Growth Rate
3%
Expense Growth 3%
Stabilized Vacancy
5%
Expenses
$15 /sf
Capital Expenditures
10% of NOI
Terminal Cap Rate
11.00%
OCC/Discount Rate
12.50%
Figure2:SimpleCoTowerAssumptions
Thischartcanbeviewedinthe
SimpleCoExcelfileontheCD.
whichthefinancialmodelmostabideby.
Someassumptionsarephysical(suchasfloor
areaandefficiency),whileothersare
economic(suchasrentanddiscountrate.)
Estimatingtheassumptionsaccuratelyis
importantbecausetheydriveallnumbersin
theproforma.
2.2 ProjectingCashFlowsforSimpleCo
Tower
Thecashflowprojectionsectionofthepro
formaprojectsmanylineitemseveralyears
intothefuture.Variablesintheformulasareoftenlinkedorreferencedtotheassumptions
onthispage.Thecashflowprojectionorganizestherevenuesandcostsassociatedwitha
particularpropertyandcalculatesthenetcashinflows/outflowsforeachyearofproperty
ownership.InSimpleCoTower,thePropertybeforeTaxCashFlow(PBTCF)iscalculated
withouttheeffectsofincometaxorleverage.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
14 (in 000's)
Potential Gross Income
Vacancy
Effective Gross Income
Year
1
2
3
4
5
6
7
8
9
10
11
$4,590 $4,728 $4,870 $5,016 $5,166 $5,321 $5,481 $5,645 $5,814 $5,989 $6,169
$230
$236
$243
$251
$258
$266
$274
$282
$291
$299
$308
$4,361 $4,491 $4,626 $4,765 $4,908 $5,055 $5,207 $5,363 $5,524 $5,689 $5,860
Operating Expenses
$2,550 $2,627 $2,705 $2,786 $2,870 $2,956 $3,045 $3,136 $3,230 $3,327 $3,427
Net Operating Income
$1,811 $1,865 $1,921 $1,978 $2,038 $2,099 $2,162 $2,227 $2,293 $2,362 $2,433
Capital Expenditures
$181
CF From Operations
Reversion (Purchase and Sale)
PBTCF
$186
$192
$198
$204
$210
$216
$223
$229
$236
$1,629 $1,678 $1,729 $1,781 $1,834 $1,889 $1,946 $2,004 $2,064 $2,126
‐$17,000
$22,120
‐$17,000 $1,629 $1,678 $1,729 $1,781 $1,834 $1,889 $1,946 $2,004 $2,064 $24,246
Figure3:SimpleCoTowerProForma
ThecashflowprojectionsareshownforSimpleCoTower.Thischartcanbeviewedin
theSimpleCoExcelfileontheCD.
2.3
ReturnMeasures:NPVandIRR
TheoutputsectionofaDCFproformacalculatestheobjectivereturnmeasures.Inthe
worldoffinance,noreturnmeasureisasprevalentasNetPresentValue(NPV),orits
siblingtheInternalRateofReturn(IRR).
NetPresentValueandIRR
ForSimpleCoTower,ourNPVata12.5%
Thetimevalueofmoneyprincipleisthe
mostfundamentalinfinance.Cashflow
todayisworthmorethancashflowinthe
futurebecauseofinterestearning
potential.Futurecashflowsare
discountedtoarriveatanequivalent
valuetodaycalledthePresentValue(PV).
discountrateis‐$135,000andtheIRRis
NetPresentValueisthesumofthePVsof
allfuturecashinflowsandoutflowsofa
project.
case)isdeterminedbytheinput
TheInternalRateofReturn(IRR)isthe
discountratewhichmakesNPVequal0.
12.37%.
SimpleCoTowerisadeterministicmodel.
Foreachuniquesetofassumptionsthereis
onesoleoutcome.Theoutput(NPVinthis
assumptionstotheexactcent.Thereisno
uncertaintyinthemodelbecauseasetof
assumptionsalwaysleadtoasoleoutput
returnmeasure.Pressingthe“F9”key
recalculatesformulasinExcel,butdoingsowillneverchangetheNPVintheSimpleCo
Towerproforma.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
15 TheNPVcanchangeifanassumptionismanuallyaltered.TheeffectonNPVofachangein
anassumptioncanberecordedinasensitivityanalysis.UtilizingadatatableinExcel,the
changeinNPVcanbeseenwhenoneortwovariableschange(asensitivityanalysisis
performedontherentgrowthrateinsection3.3).Unfortunately,thisanalysisislimitedto
twovariablesandtherealworldusuallydoesn’t“holdallelseconstant”.Whatalternatives
areoutthereforfinancialmodeling?
CHAPTER3:ModerateCoTower‐IncorporatingUncertaintyintoaFinancialModel
Mostrealestateprofessionalsarefamiliar
withthetechniquesdescribedintheSimpleCo
Towerproformabecausethedeterministic
DCFmodelistaughtinmanyintroductory
financecoursesaroundtheworld.
ModerateCoTowerexpandsontheSimpleCo
Towerproformabyaddinguncertaintytoone
Figure4:ModerateCoTowerSketch
AvisualrepresentationofModerateCo
Tower,a10‐storyofficetowerthatis
physicallyidenticaltoSimpleCoTower.
oftheassumptions,therentgrowthrate.
EverythingelseaboutModerateCoisthesame
asSimpleCo. 3.1
UncertaintyintheRentGrowthRateofModerateCoTower
TheSimpleCoTowerexampleassumedthattherentgrowthratewas3%peryear.Based
ontheaveragingofhistoricrentgrowthrates,3%isacommonassumptionamongreal
estateprofessionals.Whentherentgrowthrateissubjecttouncertainty,itis
acknowledgedthatthetruerentgrowthrateisunknownandvarieswithinarange.Excel’s
randomnumberfunctionisusedtosimulateuncertainbehavior.AppendixAgoesthrough
step‐by‐stephowuncertaintywasbuiltintotheModerateCoTowerfinancialmodel.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
16 InModerateCo,the
uncertaintyiscreated
asasymmetrical
Normaldistribution
aroundamean.Using
3%asthemeanforthe
rentgrowthrate,there
shouldbeanequal
chanceforthegrowth
ratetoappearaboveor
Figure5:NormalDistributionCurveUsedtoModelRentGrowth
Alsoknownasa‘GaussianDistribution’,arandomvariableis
‘normalized’accordingtothisdistribution.TheRANDfunction
inExcelfetchesarandomnumberbetween0and1andis
centralizedtowardsthemean.Forexample,ifthenumber
comesouttobe.159,itwillbeplaced‐1standarddeviation
fromthemean.68%ofvalues(.159to.841)willfallwithin1
standarddeviationofthemean.
3.2
below3%.
MonteCarloSimulationsandExpectedNPV
Oncethefinancialmodelhasinput
assumptionsthatrandomlychange,the
correspondingoutputNPVscanbe
recordedmanytimesusingaDataTablein
Excel.Theprocessofrunningamodelfora
specifiednumberofiterationsissimply
calledaMonteCarloSimulation.TheNPV
willvaryfromsimulationtosimulation
becausetheinputvariablesarealways
changing.InthecaseofModerateCo,the
inputvariable,RentGrowthRate,changes.
MonteCarlo:What’sinaname?
AsafavoritehangoutofIanFleming’s
fictionalcharacterJamesBond,Monte
Carloisoftenassociatedwithluxurious,
mysteriousandexoticliving.Perhaps,
MonteCarloSimulationssoundmore
foreignthentheyactuallyare.
“MonteCarlo”Simulationjustreferstoa
simulationwherethenumberof
iterationsaresetbytheuser.For
example,werun5,000iterationsfor
ModerateCoTower,notonemorenorone
less.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
17 Theinputvariablecouldbe2%leadingtoacertainNPVvalue,andinthenextiteration,the
rentgrowthratecouldbe3.5%,leadingtoahigherNPVvalue.
Afterrunning5,000iterationsofthemodel,ModerateCoTowercalculatesthemeanofthe
5,000NPVstoyieldanExpectedNetPresentValue(ENPV).Inthiscase,themeanofthe
simulatedNPV(ModerateCo)willbeconsistentlygreaterthanthedeterministicNPV
(SimpleCo)eventhough3%wasusedasthemeaninModerateCo.Inotherwords,evenif
multiplesetsof5,000simulationswereran,thesimulatedENPVofModerateCowill
generallybesignificantlygreaterthantheNPVofSimpleCo.
Figure6:ResultsfromtheMonteCarloSimulationENPVversusDeterministicNPV
Interestingresult!ThesimulatedENPVisanexpectedNPVbecause
itisjustanaverageofalltheresultsinaMonteCarloSimulation.In
thiscase,ModerateCo’sNPVwasrecorded5,000timesand
averagedtogetanaverageof$375,575.ThedeterministicNPVis
takendirectlyfromtheSimpleCoproforma.Thisresultcanbe
viewedintheModerateCoExcelfile.
Howcouldthisdifferenceoccur?Shouldn’ttheSimpleCoNPVandModerateCoENPVbethe
sameifweranmanysimulationsofModerateCo?
IntuitionmaytrytoapplytheCentralLimitTheoremorLawofLargeNumbersinthiscase.
Asthenumberofiterationsofarandomindependentvariablebecomesverylarge,the
variableswillbenormallydistributedaroundtheexpectedvalue(ifusingtheNORM.INV
function).Infact,thereshouldbeclosetoanequalnumberofoccurrencesofrentgrowth
rateaboveandbelowthemeanrentgrowthrateinModerateCosinceweareusinga
symmetricalnormaldistributiontomodeltheuncertaintyintherentgrowthrate.While
theinputvariablebehavesthiswaywiththeexpectedvalueasitsmean,thisactuallydoes
notextendtotheoutputNPV.TheFlawofAveragesexplainswhy.
3.3
TheFlawofAveragesandJensen’sInequality
FirstcoinedbySavage,Danziger,&Markowitz(2009),theFlawofAveragesisamajor
errorthatoccurswhenusingaveragesindeterministicmodelsinsteadofproperstochastic
variables.DeNeufville&Scholtes(2011)describetheFlawofAveragesasthewidespread‐
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
18 but‐mistakenassumptionthatevaluatingaprojectaroundaverageconditionsgivea
correctresult.
ThesimplemathbehindtheFlawofAveragesconceptisbasedonJensen’sInequality.In
1906,DanishmathematicianJohanJensenprovedthat:
Jensen’sInequality
Theaverageofallthepossibleoutcomesassociatedwithuncertainparametersis
generallynotequaltothevalueobtainedfromusingtheaveragevalueofthe
parameters.
Basicallywhathappensisasymmetricallydistributedinputvariableleadstoan
asymmetricdistributionofoutputvalues.Whenthisoccurs,thesystemormodelis
describedasnon‐linear.TheSimpleComodelisaperfectexamplebecauseit’sproforma
usesa3%historicaverageforitsrentgrowth.Whenthedeterministic3%isreplacedwith
aninputrandomvariablesymmetricaldistributedaround3%,theoutputNPVvalueends
upsignificantlygreaterforModerateCooverSimpleCo!
Thesourceofnon‐linearityinthiscaseisannualcompounding.Thesameeffectthatmakes
compoundinterest(non‐linear)greaterthansimpleinterest(linear)atthesamerate
generatesthedifferenceinreturnsbetweenSimpleCoandModerateCo.
ForModerateCoTower,3%isthemeangrowthrate,soa2%growthrateanda4%growth
rateshouldoccurwithequalprobability.Becausethecurveisconvex(dueto
compounding),goingupto4%resultsinagreaterupwardNPVimprovement[|2440‐(‐
135)|=2,575]thantheNPVerosionofgoingdowntoa2%growthrate[|‐2,528‐(‐135)|
=2,393].Systemsbehaveasymmetricallywhenupsideanddownsideeffectsarenotequal.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
19 Figure7:Non‐linearityintheRentGrowthRate
Let’ssaythatwehavetwoiterationsofthemodel.Inoneiteration,therentgrowth
rateis2%,andtheotheris4%.LeadingtoaNPVresultsetof‐2,528and2,440.Ifwe
averagethesetwovalues,weget‐44whichishigherthantheresultwewouldgetat
3%of‐$135!Thedifferencebecomesgreaterandgreaterasvaluesfurtherfromthe
meanareused.Thissensitivityanalysisoftherentgrowthratecanbefoundunder
theSimpleCoproforma,intheSimpleCoExcelfile.
TheFlawofAveragehasasignificantimpactonNPVandcouldspellthedifferencebetween
winningabidandlosingabid,asexemplifiedbytheSimpleCoandModerateCo
comparison.
3.4 ADifferentApproachtoRealEstateFinancialAnalysis:DistributionsandRisk
Profiles
Incorporatinguncertaintyintorealestateproformasnotonlygivesadifferentresultover
deterministicmodels(aspertheFlawofAverages),itchangestheapproachtorealestate
valuationproblems.InthedeterministicSimpleCoTowercase,thestrategyistolockina
setofexanteassumptionsbasedontheanalyst’sbestforecast,findthesinglebestvalue
andhopeforthebest.Whenuncertaintyisfactoredintotheanalysis,thefocusshiftsto
modelingandmanagingtheuncertaintytomakebetterfinanceanddesigndecisionstoday.
ThesinglebestexpectedvalueofNPVisnolongerthesoleobjectiveinastochasticmodel:
rangeanddistributionofoutcomesbecomerelevant.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
20 Introducingarealisticlevelofrandomnessintofinancialmodelschangestheframingofthe
valuationproblem.Understandingthelikelihoodoflosingorprofitingbecomeimportant
onceweintroduceuncertaintyintotheanalysis.Thecumulativedistributionfunction
(CDF)ofModerateCoprovidesinformationontheprobabilityoflossorprofitscenarios.
ModerateCohasabouta50%probabilityofhavingnegativeNPVanda50%probabilityof
ahavingapositiveNPV.Thedownsideprobabilityismorelimitedthantheupside
probability,asillustratedbythelongtailtowardstheright(morepositiveNPVs).
Thisscenarioisatypicalobservationforrealestateprojects.Ideally,ananalystwillwantto
managetheuncertaintybyfindingwaystolimitthedownsidelossesandaccentuatethe
upsideprofits.
Figure8:ModerateCoTowerCumulativeDistributionFunction
OntheCDF,thelikelihoodofNPVoutcomesisdisplayedaswellastheNPVforthe
deterministicSimpleCoTowerandtheprobabilisticexpectedNPVforModerateCo
Tower.ThischartanditscorrespondingMonteCarloSimulationisincludedinthe
ModerateCoExcelfile,onthe‘ModerateCoDistribution”tab.
OtherusefulmeasuresthatcomeoutofthisanalysisofdistributionsincludeValueatRisk
andValueatGain.ValueatRiskdenoteshowmuchlosscouldoccurataspecified
probabilityoveratimeframe.IntheModerateCoexample,theValueatRisk(V10number)
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
21 NPVis‐$6million.Thatis,thereisa10%probabilitythatanegative$6millionNPVor
worsewillbeincurredoverthe10yearlifehorizonoftheinvestment.Ontheotherside,
the“V90NPV”is$7million.ThisValueatGain“V90”numbercanbereadas:Thereisa
10%chancethattheNPVfortheprojectoverthe10yearinvestmenthorizonwillbeover
$7million.
3.5
StaticInputVariablesversusRandomWalks
Therentgrowthrate’sbehaviorintheModerateComodeliscurrentlyastaticvariable.
Oncearentgrowthrateisrandomlygeneratedforascenario,itremainsthesameforthe
lifeoftheinvestment.Deterministicproformasfrequentlymodelinputassumptionsasa
staticvariablebecausethebasisfortheirassumptionsarefromhistoricaveragesoflong‐
termannualrates.Economicconditionschangeoverthelifeofalong‐livedinvestmentand
deterministicfinancialmodelsarepooratmodelingthisbehavior.SinceModerateCo’s
inputvariablesarerandomlygeneratedanddonotrelyonhistoricaverages,achangeover
timeovercanbemodeledintotheannualrentgrowthrate.
Growthratesgenerallydonotmoveindependentlyfromyear‐to‐yearwithabsolute
randomness;ratestendtovaryaroundtheresultsfromtheprecedingperiod.Pearson
(1905)describedthisbehaviorasa“RandomWalk”.
Arandomwalkmodeledintoaproformawillallowaninvestment’sprofitability
performancetodeclineandrecoverovertheinvestmenthorizon.Thisupanddown
behaviorisessentialtothemodelingofrealoptionsintheproceedingchapter.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
22 Random Walk Illustration for Rent Growth Rate Starting at 3%
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
6%
5%
up 2%
x
4%
x
up 1%
3%
x
dn 1%
x
2%
x
dn 2%
1%
dn 2%
0%
x
Figure9:RandomWalkIllustration
Avisualrepresentationofayear‐to‐yearrandomwalk
evolutionoftherentgrowthrate.Thisbehaviorcanbe
exhibitedbymanydifferentvariables.
TheadditionalvariabilitytranslatesintogreatervolatilityintheresultsoftheMonteCarlo
simulationandamplifieseffectoftheFlawofAverages.
ThestrongeffectoftheFlawofAveragesandRandomWalkvolatilityshouldbeenough
motivetostartmodelingrealestateusingprobabilistictechniques.Thethesiscontinuesto
makethecaseforstochasticvaluationofrealestateinChallengeCoTowerbyusingReal
Options.
Results
ModerateCo
ModerateCo w/ Random Walk
SimpleCo Deterministic NPV
ENPV
St. Dev.
$192,043 $4,920,803
$1,042,254 $9,240,832
($134,701)
Figure10:ComparisonofReturnsbetweenModerateCo
andSimpleCo
Random‐walkbehavioraddsgreatervolatilitytothe
modelwhichinflatestheeffectoftheFlawof
Averagesevenfurther.TheMonteCarloSimulations
andresultscanbeviewedintheModerateCoExcel
file.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
23 CHAPTER4:ChallengeCoTower‐ManagingUncertaintyinRealEstateProjects
Withdistributions,wegatherinformationthatwillaidusinfinancedecision‐making.This
chapterfocusesonhowtousethisinformationadvantageously.Realoptionanalysisis
utilizedtoexplaintheimpactofaddingflexibilityintothedesignorfinancialmodels.
ARealOptionisdescribedspecificallyasa“rightwithoutanobligation”.Chapter6
providesadetaileddiscussiononRealOptions,butfornow,abasicoptiontoaddmore
floorsinthefuturetotheon‐goingexampleofSimpleCoandModerateCotowerswillbe
described.
ChallengeCodoesnotstraymuchfromtheenduringexample.Thesubjectbuildingisstilla
10storyofficebuilding.However,ChallengeCoTowerisnowaninvestmentina10story
developmentprojectinsteadofapre‐existingstabilizedofficetower.Ratherthana
purchaseprice,weuseadevelopmentcosttobuildtheproject.Anoptiontobuild10
additionalfloorsinthefutureisexaminedfurtherintheChallengeCoTowerproforma
providedintheChallengeCoExcelfile.
AlmostallinputassumptionsaresubjecttouncertaintyusingthesameNORM.INVfunction
describedinModerateCo.Additionally,theinputassumptionswillexhibit“randomwalk”
behavior,withtheprecedingyear’svalueusedasthemeanfornextyear’svalue.Eachinput
assumptionswillgothroughtheirownrandomwalks,culminatingintoaspecificNPVfora
unique10yearuniquestateoftheworld.
4.1
RealOptionAnalysisinChallengeCousingIFStatements
UsingIFstatementsinExcel,realoptionscanbemodeledwithease.Twopiecesof
informationarerequiredtomodelrealoptions.Firstly,the“trigger”conditionsneedtobe
specified:Whatconditionsneedtooccurbeforetheoptionisexercised?Secondly,the
exercisecostsandotherconsequencesoftheoptionneedtobeidentified:Whatistheeffect
iftheoptionisactuallyexercised?Oncethesetwopiecesofinformationaredetailed,the
optioncanbemodeledintotheproforma.Theobjectivehereistomodeltheoptioninsuch
awaythattheconsequencesofanexercisedoptionareautomaticallydisplayedinthepro
formaifthepredeterminedconditionsoccur.Then,aMonteCarloSimulationexaminesthe
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
24 effectsoftheoptionontheNPVincomparisonwithanidenticaldevelopmentwithoutthe
option.AppendixD,discussestheuseof“ifstatements”tomodelrealoptionsingreater
detail. Figure11:ThreeChallengeCoTowerOptions
ThebuildingontheleftrepresentstheInflexibleChallengeCoprojectat10floors.It
isphysicallyidenticaltoModerateCoandSimpleCoTowers.Inthemiddleshowsa
flexibledesignwhereanadditional10floorscanbebuiltontopofthefirstphaseof
10floors.Ontherightistheinflexible20floorChallengeCoTower.
ForChallengeCo,threeseparateproformasarecreatedtoshowthedifferenceinexpected
NPVanddistributions.OneproformacalculatestheNPVforadevelopmentprojectwitha
flexibledesignoptionbuilt‐intothemodeltoconstructanadditional10floorsatalater
date.ThesecondproformacalculatestheNPVforastandard10storydevelopmentwithno
optionbuilt‐in.ThethirdproformacalculatestheNPVfora20storydevelopmentwithout
anoptionbuilt‐intothedesign.
4.2
ChallengeCoTower’sResultwithaRealOption
TheresultsfromtheMonteCarloSimulationsshowthatdesignflexibilitycanhavea
significantfinancialvalue.Whilethedevelopmentwithflexibilityneverdominatesthetwo
option‐lessalternatives(theflexiblealternativedistributionfunctionisalwaystotheleftof
eitherthe10storyor20storydistributionfunction),theresultsshowhowtheflexible
alternativecanbeadvantageous.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
25 Figure12:ChallengeCoTowerExpectedNPVs
TheCDFshowshowtheflexibledesign(inred)usestherealoptiontotake
advantageofupsideconditions.Atthelowend,theflexibledesigndoesnotexercise
itsoptiontoexpand,soitsCDFcurvecloselyfollowsthecurveofthe10floor
inflexibledesign.Ifeconomicconditionsaregood,theflexibledesignbeginsto
deviatefromthe10floorinflexibledesignbyexercisingitsoptiontoexpandand
followsclosertothe20floorinflexibledesigncurvetotakeadvantageofthegood
economy.TheMonteCarloSimulationsandCDFscanbefoundintheChallengeCo
TowerExcelfile.
Ifeconomicconditionsturnsourinthenext10years,theoptiontoexpandisnotexercised
andthedistributionfunctionoftheflexiblealternative“hugs”the10floorinflexibleoption.
Inpooreconomictimes,theflexibleoptionwillnotperformaswellasthe10floor
inflexibledevelopmentbecausesomeextraconstructioncostsare“sunk”intotheinitial
constructioncostoftheflexiblealternative(forexample,constructingstrongercolumnsto
taketheloadofapossible10flooraddition).Ontheotherhand,theflexiblealternative
performsmuchbetterthanthe20floorinflexibledevelopmentduringapooreconomy.
Wheneconomicconditionsaregood,theflexiblealternativetakesadvantageoftheupside
byexercisingitsoptiontobuildmorespace.Thisisillustratedwhenthe10floorinflexible
alternativeiscomparedwiththeflexibleoptionabovethe$5millionNPVmark.The
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
26 flexiblealternativewilldeviatefromthe10floorinflexiblealternativeandcapitalizeonthe
opportunityofgreatmarketconditions.
TheexpectedNPVoftheflexiblealternativeisthegreatestamongthethreealternativesfor
ChallengeCoTower.Forinvestorsseekingtolimittheirdownsideexposure,whiletaking
advantageoftheupsideasmuchaspossible,flexibilitycanbeamajorwin.Flexibilityin
designshouldnotbeoverlookedwhenmakinginvestmentdecisions.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
27 CHAPTER5:QuantifyingUncertaintyintheRealWorld
TheexamplepresentedinChapters2to4issimplifiedtounderlinetheimportanceof
includinguncertaintyandmanagingtheriskthatexistsinrealestateinvesting.Inthis
chapter,thefocusshiftstotheexecutionofthesetechniquesintherealworld.To
implementstochastictechniquesintoarealworldfinancialmodel,theinputsthatare
subjecttouncertaintymustbequantifiedwithadecentlevelofaccuracyortheoutputs
cannotbetrusted–thecomputerscienceaxiom,“GarbageIn,Garbageout”isappropriate
here.Accuracyisimportant,buthowpreciseordetailedshouldafinancialmodelbe?The
realestateindustryhasembracedtheDCFmethodwhich,asdemonstratedbytheFlawof
Averagesinchapter3,isgenerallylessaccurateandmuchlessdetailedthanthesimplest
stochasticmodels.Fromthiscasualobservation,perhapsprofessionalsputmorestockin
accuracy(gettingclosetotheactualnumber)ratherthandetail.Thereisapossibilityof
increasingthecomplexityofafinancialmodelsomuchthatthemajorfundamentalsofthe
proformaarewashedout;losingsightofthe“forestthroughthetrees”.Thus,itis
importantthatincreasingdetailisnotpursuedattheexpenseofaccuracy.Thediscussion
hereinissciencebased,buttheimplementationoftheseconceptsremainsan‘art’requiring
realestateintuition.
5.1
PredictabilityintheRealEstateMarket
Inthe1960’s,apowerfultheoryemergedcalledtheEfficientMarketHypothesis(EMH)
withcontributionsfromeconomistssuchasPaulSamuelsonandEugeneFama(Malkiel&
Fama,1970;Samuelson,1965).Theirworkexplainshowthestockmarketissoefficient
andquicktoadapttonewinformationthatitisimpossibletopredictwherethemarketis
going,sincefutureinformationisunpredictable.Byextension,thestockmarketshould
behaveasacompleterandomwalk(Fama,1995).Lookingathistorictrendsisfutile
becausefutureinformationoccursindependentlyfromwhathasalreadyhappened.
Exchangetradedfunds(ETFs),whicharefundswhichtrytoreplicatetheentiremarket,
werecreatedtomakeuseoftheEMHmantra,“activemanagementoffundswon’thelp”.In
fact,Fama&French(2010)showthat65%ofactivelymanagedhighfeemutualfundsdid
notbeatpassivelymanagedETFs.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
28 Inrecentyears,theEMHhasbeenchallengedbyresearchthatarguesforalevelof
predictabilityexistinginthemarkets.Lo&MacKinlay(1988)usednewdatatorejectthe
ideaofthemarketsbehavingasarandomwalk.Jegadeesh&Titman(1993)discovered
thatmomentuminthestockmarketcanleadtoabovemarketreturns;thatis,relyingon
theshorttermtendencyforastock’spricetogoupifitwasgoingupthelastperiod.Shiller
(1990)proposedthatamean‐revertingbehaviorexistsinthestockmarketduetoinvestor
irrationality.Alas,somelevelofpredictabilityexistswhichcanbeusedadvantageously
whichkeepfinancialanalystsliketheauthorofthisthesisemployed.
Whileweakenedfrommodernempiricsandthe2008financialcrisis,theEMHstillaffects
thewayinvestors’modelfuturereturnsbycautioningmarketparticipantsabouthow
difficultitistoearnabove‐marketreturns.Inaddition,theEMHhighlightstheimportant
rolewhichuncertaintyplaysinthemarket.
Dothesetheoriesprimarilyfocusedonthestockmarkettranslateovertorealestate?Yes
andno.Forvariablesintheofficespacemarketsuchasrentandvacancy,alevelof
predictabilitydoesexistduetopatternsinmomentumandcyclicalitywhicharediscussed
ingreaterdetaillaterinthischapter.Inrealestateassetmarkets,theEMHholdsless
weightcomparedtostockexchanges,becausethecashflowsofrealestateasset(whichare
dependentonthespacemarket)arefairlypredictable.IngeneraltheEMHsuffersfroma
lackofapplicabilitytorealestatebecauseoftheheterogeneityofrealestate,thelackof
publicsalesinformation,andtimelagsinthetransactionprocess.Ontheotherhand,Real
EstateInvestmentTrusts(REITS)canbehavesimilarlytotherestofthepubliccapital
markets.Generally,themoreefficientamarketisatintegratingnewinformationinasset
prices,thelesspredictableitis.Thepredictivenaturecouldevenbecomeendogenousto
thepriceofanassetinaveryefficientmarket.Forexample,whenanewtechniqueis
developedandproventobecapableofmakingabove‐marketriskadjustedreturns,
everybodywillimmediatelycopythetechniquewhichbecomesthenewstandard.The
maintakeawayfromthissectionisthatmostrealestatemarketsbehavewithboth
predictabilityandrandomnessatthesametimeandthisshouldbereflectedintheway
financialmodelsarecreated.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
29 5.2
RealEstateEconomicsandtheStockFlowModelforOfficeProperties
Themechanicsofhowrealestatepricesmoveovertimehasbeenstudiedextensivelyand
canbedescribedusingaStockFlowModel.AStockFlowmodelissimplyanymodelwhich
describestheprocessofhowadurablestockofgoods,suchasrealestate,increasesand
decreasesandinteractsovertimewiththeflowofusage(i.e.leasing)ofthatstockofgoods.
Tostartoff,theStockFlowModeldrawsonthefamiliarconceptofsupplyanddemand,
withafewquirks,tocorrectlydescribewhatoccursinrealestate.Employmentisthe
driverforrentofofficespaceonthedemandside.OntheSupplyside,thestockofoffice
spaceisthemaindeterminingfactor.Thestockofofficespaceiscompletelyinelasticinthe
short‐termbecauseofficebuildingstaketimetobuild,Whendemand(employment)
increases,therentmustincreasebecauseittakestimefornewstocktoarriveintheform
ofnewconstruction.Whenemploymentfall,rentswillfallbyagreaterpercentagebecause
ofthedurabilityofrealestatecapitalleadingtocompleteinelasticityinsupplyintheshort
run.Newrealestatestockisgraduallyintroducedintothemarkettomeetdemandand
becauseofthis,rentsandpricesreactquicklytochangesinthedemand,butstockdoesnot.
Whattriggersnewconstruction?Assetprices–whichareafunctionofrentsandcaprates.
DiPasquale&Wheaton(1996)illustratestheserelationshipsbetweenconstruction,asset
marketsandspacemarketsintheFourQuadrantmodel.
Astheeconomygoesthroughitsupsanddowns,realestatepricesandrentsgoupand
downbecausedemandchangeswithoutaquickresponsefromthesupplysideduetothe
durabilityofrealestateandlagtodelivernewspace.Eventually,increasesinrentsand
pricespromotenewconstructionwhichgraduallyalleviatespressureonrentsasthenew
spaceisdeliveredtomarket.Sincethereisatimelaginconstruction,itisrarethatthe
exactamountofcompletionscomesonlineandperfectlymeetsdemand;therewillbe
overbuildingandunderbuildingwhichleadstorealestateincurringitsowncycle.
Thevariablesrequiredtocreateastockflowmodelcanbeobtainedbyusinglinear
regressiontechniquesonalargeresultsetofreliablehistoricdata.Multiplelinear
regressionattemptstoquantifytherelationshipbetweenadependentvariableand
multipleindependentvariables.Forexample,aregressioncanberanbetweenthesquare
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
30 footageofoccupiedspaceandemployment,amajordriverofofficedemand.Ifthe
numericalrelationshipcanbepredicted,forecastingemployment(asourceofdemand)will
leadtoapredictionforoccupiedspace.
Intermsofcomplexity,uncertaintycanbeincorporatedatdifferentlevelsinafinancial
model.Someanalystswillprefertomodeluncertaintyintorentsdirectly,whileotherswill
prefertoadduncertaintytomoreprimalsourcessuchasemploymentgrowthandrun
thesenumbersthroughastockflowmodeltoarriveatrents.PleaserefertoParadkar's
(2013)thesisforamodelwhichincorporatesuncertaintyusingthestock‐flowmodel.
5.3
SourcesofUncertaintyinRealEstate
Thereareinfinitepossibilitieswhenitcomestoeventsorshocksthatmayinfluencereal
estateassetvaluesandrents.Uncertaintycanbedrivenbychangesinthemacro‐economy
andlocaleconomy.Technologicalinnovationsuchashydrologicfrackingcomeoutofthe
bluetoeffectofficemarketscateringtotheenergysector.Transportationinfrastructure
changesgiverisetowinnersandlosersinrealestate.Theendlesslistofpotentialshocks
needtobesimplifiedintoafewsourcesbeforetheycanbequantified!
Withthehelpofrecentinnovationsinrealestateindices,7importantformsofuncertainty
canbequantified:long‐runmarkettrend,long‐runmarketcycle,marketvolatility,short‐
runinertia,individualassetspecificvolatility,individualassetpricingnoise,and‘Black
Swans”.
Long‐runMarketTrend:Thisisthestraightlineappreciationtrendwhichprevailsoverthe
longtermintherealestateassetmarket.Researchintoresidentialrealestatetrendshave
foundthatoverthesuper‐longterm(overthecourseofacentury),pricesappreciateclose
totherateofinflation(Eichholtz,1997).Growthincommercialrealestateoverthelong
haulhasbeenfoundtobeslightlylessthaninflationbecauseofdepreciation(Fisher,
Geltner,&Webb,1994;Wheaton,Baranski,&Templeton,2009).Withthisknowledge,
professionalsmaybetemptedtoinput1%or2%becauseofthestabilitytheFederal
ReserveBankoffersforinflationintheUnitedStates,butkeepinmindthatinvestment
horizonsforcommercialrealestatetendtobeshorterthan20years.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
31 Long‐runMarketCycle:Thelong‐runmarketcycleistheoscillatingnatureofrealestate
pricesthatiseasilyobservableonatime‐seriesgraph.Thepeak‐to‐peakortrough‐to‐
troughtiminghasbeenbetween15and20yearsinlastfewcommercialrealestatecycles.
Wheaton(1999)explainshowtherearetwowaysinwhichtherealestatemarketcould
manifestitself.Oneviewisthatrealestatedevelopersarecompletelyrationalandforward‐
lookingwhiletheotherviewisthatdevelopersarebackward‐looking(or‘myopic’)when
forecastingfuturesupplyanddemand.Whenagentsarerationalandforwardlooking,they
haveagoodunderstandingofhowthemarketbehaveswithuncertainty,sopricesreflect
thepresentvalueoffuturecashflowsandtheuncertaintysurroundingthecashflows.A
practicewhichwouldclassifyas“myopic”behaviorincludeextrapolatingaveragehistoric
ratesforwardinfinancialmodels.InWheaton’ssimulations,hefindsthatbothcasesstill
(myopicorforward‐looking)generateendogenouslong‐runcycleswithinrealestateas
developersstruggletoforecasttheexactamountofspacetobuild.
MarketVolatility:ZoominginalittlebitfromtheLong‐runMarketCyclelevel,thereis
volatilitywhichexistsmonth‐to‐monthandyear‐to‐yearalongthecyclepreventinga
smoothoscillatingcurve.Eventsthatcaninfluencethistypeofuncertaintyincludenatural
disastersorannouncementsbycentralbanks.Anynewdiscoveryofinformationthat
providesashockthatthemarkettakestimetoadjusttoareuncertaintiesrelatedtomarket
volatility.
Short‐runinertia:Alsocalledmomentum,thisisthetendencyforpricesthatarerisingto
wanttokeeprising–orfallingpricestokeepfalling.Tomeasureinertia,auto‐regressive
techniquesareemployedwhichmeasuresthelevelofinfluenceapreviousperiod’sprice
movementhasonthecurrentperiod’spricechange.Iftherelationshipishighbetweenthe
pricesforthetwoperiods,itmeansthatpeopleareusingthecurrentperiod’spriceasa
basistoforecastfutureperiods.Itisinterestingtonotethatinertiaisveryweakindata
involvingREITsbecauseofhowefficientsecuritiesmarketsare.Thefrictionsinprivatereal
estatemarkets,however,allowmomentumtooccur.
IndividualAssetVolatility:Ifafinancialmodelfocusesinonaparticularproperty,themodel
willbesubjecttoidiosyncraticassetvolatility,thatis,riskwhichisspecifictoanindividual
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
32 assetthatdoesn’tapplytotherestofthemarket.Forexample,amunicipalitymight
announceanewrapidtransitstationtobeconstructednexttoanofficetowerwhich
createdanunexpectedboostintheofficeproperty’svalue.
IndividualAssetPricingNoise:Intheprivaterealestatemarket,everyprofessionalwillhave
differingopinionsonthevalueofaproperty.Ifpolled,theopinionsofvalueforthousands
ofrealestateexpertsmightbescatteredaroundthe‘mostlikely’value,withagreater
spreadformoreuniquepropertiesandlessofaspreadforpropertieswithmultiple
comparables.Noiseistheeffectthatthesedifferingopinionshaveonthepricingofreal
estate.Appraiserstakeintoaccountnoisewhentheyprovidearangeofpricesthatthey
believeaspecificpropertycansellfor.
BlackSwans:IndefiningwhatBlackSwanseventsare,Taleb(2007)states:“first,itis
anoutlier,asitliesoutsidetherealmofregularexpectations,becausenothinginthepast
canconvincinglypointtoitspossibility.Second,itcarriesanextremeimpact.Third,inspite
ofitsoutlierstatus,humannaturemakesusconcoctexplanationsforits
occurrenceafterthefact,makingitexplainableandpredictable.”Anyeventwithmajor
impactonrealestatevaluesencompassesthisrisk.Forexample,anewrenewableenergy
source(makingcombustionenginesobsolete)suddenlydiscoveredinalabatMITcould
havemajor“BlackSwan”typeramificationsforrealestate.
Eachtypeofuncertaintydescribedabovecanbequantifiedontheirown.ThenaMonte
CarloSimulationoutputstheeffectofuncertaintyasawholeonarealestateproject.
Modelingtheeffectof7typesofuncertaintytogetherwithoutaMonteCarloSimulation
wouldbepracticallyimpossible.
5.4
RealEstateIndices
RealEstateindicesprovidesomeofthedatafromwhichthe7formsofuncertaintycanbe
extracted.Therearemanychoiceswithregardstorealestateindices,witheachhaving
theirownadvantagesanddisadvantages.Therearethreemajortypesofrealestateindices
intheUnitedStates:appraisal‐based,transactions‐based,andstockmarketbased(Geltner,
2014).
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
33 Appraisal‐basedindicesuseindependentprofessionalappraisalsofpropertiestotrackreal
estatemarkets.Theyweretheearliestformsofindicesinrealestate,sotheytendtohave
longerhistories.Themajordrawbackwithappraisal‐basedindicesisthattheyare
susceptibletoaphenomenoncalledappraisalsmoothing.Appraiserstendtouseempirical
informationsuchassalescomparabletodeterminethecurrentvalueofpropertieswhich
developsalagintheirestimatedvalue.Thislagcontributestoasmoothingeffectonthe
indexwhichreducestheapparentsystematicriskintherealestatereturns.
Transactions‐basedindices(TBI)useactualsalesdataofcommercialrealestatetotrack
themarket.Toaccomplishthis,manyoftheseindicesmonitorpairsofsalesonproperties
toensurethatthechangesreportedarefromanapples‐to‐applescomparison.TBIsare
relativelynewwithdataonlystretchingbackto2000buttheyholdgreatpromisebecause
theunderlyingtransactionpricedatanotonlyquantifiesmarketvolatilityreflectedinthe
indicesthemselves,butalsoquantifyindividualassetidiosyncraticuncertaintyusingthe
residualsofthepriceregressions.
Stockmarket‐basedindicestrackthemovementofpubliclytradedrealestateinvestment
trusts.BecauseeachREITgenerallyspecializesinonepropertytypeoranother,theycanbe
agreatsourceofdatawhenlookingataparticulargeographicalareaorindustry.Keepin
mindthatREITvaluesdonotperformthesameasprivaterealestateallthetime.The
efficiencyofthestockmarketeliminatesmuchoftheinertiathatwouldexistintheprivate
market.Inaddition,thereisevidencethattheREITmarketslightlyleadstheprivatereal
estatemarket(Barkham&Geltner,1995).
5.4
TranslatingDataonUncertaintyintoaProForma
QuantifyinguncertaintycanbedoneinmanyofwaysonExcel,butanemphasisshouldbe
placedonclarityandtransparencyastherearemanymovingpartstoastochasticpro
forma.Chapter6runsthroughacasestudyinwhichtheresearchpresentedinthischapter
canbeimplementedinExcel.Therearemanymodificationsthatcanbemadetoproforma
forthecasestudyinChapter6andsomeofthesepossiblevariationsarediscussedbelow.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
34 IntheModerateCoexampleinChapter3,anormaldistributionisusedtodispersethe
randomnessaroundamean,butthereareothercommonmethodsfordistributing
uncertainty.
UniformDistributions:TheRANDfunctioninExcelfunctionsasauniformdistributiononits
own.Everynumberbetween0and1hasthesamechanceofappearing.Ifananalystwants
tomodelarandomchangeinpricenextyearbetween‐10%and+10%,witheveryvalue
havinganequalchanceofappearing,theycanusethefunction=(RAND()/5)‐0.1.The
divisorof5createsa0%to20%range,whilesubtracting10%shiftsthedistributiondown
tocreatea‐10%and+10%bound.
Normal(Gaussian)Distributions:IntheModerateCoandChallengeCoexamples,anormal
distributionwasusedtodisperserandomvariables.Normaldistributionsarefamiliarwith
mostprofessionalswithcollegedegreesbecausethesedistributionsarecommonplacein
introductorystatisticscourses.Normaldistributionsareoftenobservedandnatureand
playanimportantroleinscienceandbusiness.Inthestandardnormaldistribution,
sometimesreferredtoasa“bellcurve”,onlytwounknownsarerequiredtocreateacurve:
meanandstandarddeviation.Themeanistheaveragevalueofalltherandomnumbersin
thedistribution,andinasymmetricalnormaldistribution,themeanwillliedirectlyinthe
middleofthecurve.Thestandarddeviation(denotedbyσ)isameasureofthespreadof
thedistribution.Thelargerthestandarddeviation,thewidertherangeofnumberswillbe.
Inastandardnormaldistributionanempiricalruleexiststhatstates:68%ofvaluesfall
withinonestandarddeviationfromthemean,95%within2standarddeviations,and
99.7%within3standarddeviations.Thisrulecanalsobereferredtoasthe68‐85‐99rule
orthe3sigmarule.Whensettingupanormaldistributionofrandomvariables,keepingthe
3sigmaruleinmindwillhelp“fit”adistributiontoobservedvolatilityinanindex.Excel
hasnumerousfunctionwhichrelatetonormaldistributionsbutformodelinguncertainty,
NORM.INVisthemostused.Thishandyfunctionfetchesthenumberatacertain
cumulativeprobabilityofastandardnormalcurvewithameanandstandarddeviationthat
ausercanspecify.Forexample,ifthenormalcurvemeanwas3%withastandard
deviationof1,aprobabilityof50%intheNORM.INVfunctionwillfetcha3%.Inthe
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
35 probabilityturnedouttobe15.9%,theNORM.INVfunctionwillfetcha2(sincea
cumulativeprobabilityof15.9%endsupa‐1σ).
TriangularDistributions:Sometimestherangeandmostlikelynumberforarandom
variableisknown.Fortheseproblemswherethereisnotmuchinformationavailable,a
triangulardistributioncanbeused.Amajorbenefittotriangulardistributionsisthatthe
boundsarelimited,comparedtothetheoreticallyinfiniteboundsofnormaldistributions.
Triangulardistributionsarecommonlyusedinbusinessbecausenotmuchinformationis
required,yetallowsfora“bestguess”asthemostlikelynumber(orthemode).Themode
doesnotneedtobeatthemedianbetweenthetwobounds,butifisn’t,itbecomesmore
difficulttomodelinExcel.Forcaseswherethetriangulardistributionisnotsymmetrical,it
issuggestedtouseanExceladd‐in,suchas@RISKsoftware,tosimplifyformulasusing
theirframework.Asforsymmetricaltriangulardistribution,imputing=rand()+rand()‐1in
toexcelwillmodelatriangulardistributionbetween‐1and1,centeredaround0.Tomove
thecenterandmodeofthedistribution,addorsubtractvalues.Forexample,
=[rand()+rand()]+19willmodeladistributionbetween19and21,with20inthemiddle.
Toexpandthebounds,multiplytheRAND+RANDexpressionwithadesiredfactor.For
example,=4*[rand()+rand()]willyieldadistributionbetween0and8centeredaround4.
Otherdistributionsarealsopossible,butitissuggestedthataprogramsuchas@RISK
softwareisusedtokeepformulasfrombecominguntidy.Long,elaborateformulas
decreasetransparencyandincreasedifficultieswhentroubleshooting.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
36 CHAPTER6:ManagingUncertaintyintheRealWorld
Quantifyingtheuncertaintyintheinputsofafinancialmodelwasthefocusinchapter5.
Nowthefocuswillshifttoadiscussiononmethodsthatmanageuncertainty.Theword
“option”isfrequentlyusedtodescribeanalternativeorachoiceineverydayspeech.The
definitionforanoptionusedinthisthesisismorespecificallydefinedas“aright,butnot
theobligation,tobuy(orsell)anassetunderspecifiedterms”(Luenberger,1998).This
chaptershedslightonhowfinancialoptionsgeneratevalueanddiscussestheapplicability
offinancialoptionanalysistoimprovethefinancialperformanceofrealestateprojects.
6.1
TheBasicsofFinancialOptions
Optionsareaclassoffinancialinstrumentswidelyknownasderivatives.Derivativesare
aptlynamedbecausetheirvaluesarederivedfromotherassets.Optionscanbeconceived
forstocks,bonds,commodities,foreigncurrencyandotherassets.Inessence,optionsare
contractsacquiredatacostthatallowapartytherighttopurchaseorsellanasset,without
obligation,usuallyataspecifiedtimeandatapredeterminedprice.Justliketheassets
whichthese“contracts”aredependenton,optionscanbetradedinprivateoronpublic
derivativemarkets,suchastheChicagoBoardOptionsExchange.
Twomajortypesoffinancialoptionsexist:calloptionsandputoptions.Calloptionsoffera
partytherighttopurchaseanassetforapredeterminedprice.Putoptionsofferapartythe
righttosellanassetforapredeterminedprice.Thispredeterminedpriceiscalledthestrike
priceorexerciseprice.
Hereisascenariothatdemonstrateshowacalloptionworks:
ProsperoMiningCompany’sstockpriceis$100todayandisundergoinganimportant
geologicalstudyatoneoftheirprospectiveminingsitesinCanada.Portia,therichsavvy
investor,onlywantstoinvestinProsperoifthegeologicalstudyfindsgold;itwouldbe
disastrousforthecompany’sstockpriceifgoldisnotfound.However,Portiaisalsoafraid
thatshemightloseoutifgoldisfoundbecausethestockpriceoftheProsperoMining
Companyhasthepotentialtodoubleortriple!Portia’ssolutionistopurchaseacalloption
fortheProsperostockfor$5(knownastheoptionpremium)atanexercisepriceof$110.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
37 For$5,PortiagainsarighttobuyProsperoMiningCompany’sstockat$110sometimein
thefuture.IfProsperoMiningCompany’sgeologicalstudyturnsoutpositive,thestock
pricedoubles,butPortiamaintainstherighttobuythestockat$110.
Themechanismforputoptionsworksthesameascalloptions,exceptitisnowarightto
sellinsteadofbuy.Forexample:
Antonioisawheatfarmerandhe’sworriedthatthemarketpriceofwheatmayfallfromits
currentpriceof$10abushel.Ifthepricefallsbelow$8,Antoniowillnothaveenough
incometogetbythisyearandwouldneedtosellhisfarm.Antoniobuysputoptionsfrom
Claudiusforanoptionpremiumof$1perbushelwithastrikepriceof$9.Nomatterwhat
happenstothewheatprice,Antoniowillbeabletosurvivebecausehehashedgedhis
downsiderisk.Ifthepriceofwheatincreases,Antoniowillnotexercisetheoption.Ifthe
priceofwheatfallsdramatically,Antonioissafebecauseoftheputoption.
Tosimplifythescenarios,thedurationthatanoptionisvalidforwasnotdiscussedin
Portia’sorAntonio’sexampleabove.Inreality,optionsvaryintheirexercisetermsand
expirationdates.ThetwomostcommontypesofoptionsareAmericanandEuropean
options.IntypicalAmericanoptions,theholderoftheoptioncanexercisetheoptionatany
timebeforetheexpirationdate;ifanoptionisgoodforayear,theoptionholdercan
exerciseitanytimewithinayear.InEuropeanoptions,theoptionholdercanonlyexercise
theoptionattheexpirationdate.Thus,theoptionholderofaEuropeanoptionhasmuch
lessflexibilityinexercisingtheoption.Otherexoticoptiontypesexist,butthevastmajority
ofoptionsaresoldinanAmericanorEuropeanstyle.
6.2
SourcesofValueforFinancialOptions
Optionsprovideriskmitigationbyeffectivelyoperatingasinsuranceformorecostlyassets.
Inthesection6.1examples,PortiaandAntoniowereabletochangetheirexposuretorisk
bypurchasingoptions.Thefuturemayleadtopositiveornegativeoutcomes,butoptions
allowinvestorstohedgeagainsttheriskofnegativeoutcomes.Thereisnodoubtthat
optionscanbeveryvaluable,butwhatactuallygeneratesthisvalueinoptions?
Fundamentally,therearetwodriversofvalueforanoption:timeanduncertainty.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
38 InAmericanoptions,thevalueincreasesastheexpirationdateisfurtherintothefuture
becauseitprovidestheoptionbuyermoreflexibilityintheexercisetiming.Thelongerthe
durationoftheoption,thegreaterthechancesoftheoptionpresentina“inthemoney”
statewhichincreasesthevalueoftheoption.
ThevalueofaEuropeanoptiondependsonthemarketpredictionofwhattheenvironment
willbelikeattheexercisedate,sinceEuropeanoptionscanonlybeexercisedatone
forwarddateandnotbefore.Allelsebeingequal,thefurtherintothefutureanexercise
dateisforaEuropeanoption,thegreatertheuncertainty;leadingtoahigheroption
premium.
Optionsareonlyrelevantbecauseofuncertainty.Inaworldvoidofuncertainty,noone
wouldbuyorselloptionsbecausemarketparticipantswouldsimplychosetobuyornot
buytheunderlyingassetwithcompleteknowledgeofwhattheirinvestmentreturnwould
be.Anoption’sfunctionistoprotectaninvestorfromrisk,butwithnorisktohedge
against,thereisnoneedforoptions.Itisinterestingtonotethat,asthelevelofuncertainty
increases,thevalueofanoptionincreasesaswell.Here,theuncertaintycanbethoughtof
intwocomponents:thepossibilityofloss,andthemagnitudeofthepotentialloss.
Thehighertheprobabilityofanoptionbeingexercised,thehighertheoptionpremiumwill
bepricedatbyoptionwriters.Ifthereisnearcertaintythatanoptionwillbeexercised,
optionwriterswillpricetheiroptionveryclosetothestrikepricetoensurethatthereisa
fairdealforboththebuyerandsellerinacompetitivemarket.
Themagnitudeoflossrelatestothevolatilityofanunderlyingasset’svalue.Assetswith
largepriceswingswillnotonlyhaveahigherpossibilityofbeingexercised,butalsohave
thepotentialtoovershoottheexercisepricebyagreatermargincreatingalargerlossfor
theoptionsellerandalargergainfortheoptionbuyer.Whilethepurchasersofoptionsare
protectedwitharightbutnotanobligation,thewritersofoptionsareobligatedtodeliver
ontheircontracts,exposingthemselvestorisk.Inacompetitivemarket(seethediscussion
onefficientmarketsinsection5.1),thisriskwillbepricedexanteintoanoptionwith
availableinformation,leavinglittleroomforabove‐averageriskadjustedreturns.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
39 6.3
TheValuationofFinancialOptions
Likeotherassetstradedonapublicexchanges,optionsaresubjecttocompetitivemarket
dynamics,wherethemarketcollectivelydeterminestheprice.Howdomarketparticipants
valueoptions?Therearethreemajortechniquesusedtovalueoptions:Black‐Scholes
(mathematical)models,BinomialPricingModelModels,andMonteCarloSimulations.
BlackandScholes(1973)introducedthefamousBlack‐Scholesformulatocalculatethe
priceofEuropeanStyleOptionsusing5knownvariables:strikeprice,stockprice,time,
volatility,andriskfreerate.Themodelworksontheassumptionthatoptionswillbe
pricedcorrectlyinthemarket‐‐arbitrageopportunities(usingreplicatingportfolios)
quicklybringoptionpricesbackinline.Inessence,BlackandScholesusedthisassumption
toderiveanequationforvaluingEuropeanoptions.Unfortunately,theBlack‐Scholes
formulaistremendouslycumbersometoworkwithforAmericanOptionsbecauseofthe
possibilityofexercisebeforetheexpirationdateofanoption.
FirstproposedbyCox,Ross,&Rubinstein(1979),BinomialTreeModelsquicklybecamea
favoriteamonganalyststryingtomodelAmericanOptionsbecauseofthemodel’sintuitive
simplicity.TheBinomialTreemodeliscreatedbyformulatingdifferentscenarioswhich
couldoccurtoanunderlyingassetovertimeandrecordingthemintoalatticestructure.
Eachlevelofthetreerepresentsaperiodoftime,withtworoutes(upordownroutes)
availablefortheasset’spricetofollowateachnode(Veronesi,2010).Probabilitiesare
assignedtoeachpath,butnormally,analystsdefineeachbranchashavinga50%chanceof
realizationtosimplifythemodel.Anewassetpriceisassignedforeachbranchinthetree,
leavingavisualrepresentationofavaryingpriceofanunderlyingassetovertime.Basedon
theforecastedvalues(atdiscretetimeintervals),theoptionpremiumiscalculatedstarting
fromtheendvaluesandgraduallycomputingtheoptionvaluesallthewaybacktothe
present.
AmajorlimitationoftheBinomialTreePricingModelistheinabilitytoincorporate
multiplesourcesofuncertainty.Alluncertaintymustfactoredintothepriceand
probabilitieswhichthemodeloperatoremploysateachnode.Toovercomethese
restrictions,analystshavestartedtoharnessthepowerofcomputingtechnologyto
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
40 simulatethousandsofscenariosinamatterofseconds,dwarfingthelimitednumberof
possibilitieswhichcanbemodeledinaBinomialTree.UsingMonteCarloSimulationsto
modelthevalueofoptionsallowsforvastcustomizationofuncertainty.Tomodeloption
premiumsusingMonteCarlomethod,ananalystfirstsetsupamodelinwhichan
underlyingasset’spriceissubjecttouncertaintyovertime.IFstatements(seeAppendixD)
areusedtomimicthelogicinoptionexercisedecisionsmadebasedonthesimulatedasset
value.Oncethemodelisinplace,manyiterationsareperformed,withthefinaleffectofthe
optionineachscenariobeingrecordedandanalyzed.
AMonteCarloSimulationactsasa“black‐box”orashort‐cutwheredifficultpartial
differenceequationsisnormallyrequiredfindanoption’svalue.Likeastewcookingina
largepot,ananalystcancontinuethrowingdifferentfactorsofuncertainty,payoffs,
probabilitiesandothernuancesintothefinancialmodel.Thecomputerdoesalltheheavy
liftingwithMonteCarloSimulations!Itisnosecretthatthisthesisadvocatesfortheuseof
MonteCarloMethodsbecauseofallofitsadvantagesforverylittleeffort.
6.4
RealOptions
Liketheirfinancialcounterparts,arealoptionisdefinedsimplyasarightwithout
obligation.Whilefinancialoptionsaretiedtosecuritiessuchasstocksorbonds,real
optionspertaintobusinessdecisionsandareoften,butnotalways,associatedwith
tangibleassetssuchasrealestateormachinery.Incorporatingdesignflexibilityintoareal
estateprojectisanexampleofrealoption.Theabilitytoalterthedesignofastructureto
meetfutureconditionsisachoicewhichcanbemadeinthefuture.Yet,thereisno
obligationtoexercisetheoptionifconditionsdonotsupportachangetothestructure.
Manyprinciplesoffinancialoptionstranslateovertorealoptionanalysis,buttherearea
fewkeydifferences.Realoptionsaremorevaluablewhenthereisgreateruncertainty
loomingoverbusinessdecisionsandtheytendtoruninperpetuitywithAmericanstyle
optionexerciseterms.Realoptionsarenotsoldonpublicoptionsexchanges,soarbitrage
opportunitiestocorrectpricesofrealoptionsdonotexist.Furthermore,realoptionsmay
notbederivedfromanythingatall,makingeachrealoptionveryuniquetotheirsituation.
Withnoassettoserveasabasisforitsvalue,realoptionsarenotreallyderivatives;they
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
41 aremorelikebusinessdecisionswhichcanbemadeinthefuture.Withfinancialoptions,
theunderlyingasset’spriceeffectsthevalueoftheoption,butforrealoptions,thefactors
thatdeterminesvaluearenotalwaystradablecommodities.Thesefactorscouldbe
intangiblessuchasdemand‐basedmeasureslikerentorvacancy.
Inarealoption,thecosttoimplementflexibilityisoftenindependentofeconomic
conditions.Toputitinanotherway,financialoptionshavetheexpectationsofthefuture
pricedintoitbythemarket,makingitdifficulttomakeaprofit.Typically,thisisnotusually
thecasewithrealoptionsbecausenopricecorrectionmechanismexists.Forexample,let’s
sayasmall‐capdevelopmentfirm,LearDevelopments,isplanningtobuildathreestory
parkinggarageandwantstoembedtheflexibilitytoexpandthegarageatafuturedateby
buildinganotherthreestoriesontopoftheexistingstructure.Theoptionpremiuminthis
caseistheextraconstructioncosttoaddtheflexibilityandthecosttobuildthethree
additionalstories.CapuletConstructionbuildstheparkinggarageandsendsLearan
invoicebasedonthecurrentlaborandbuildingmaterialprices.CapuletConstructiondoes
notcareaboutwhatprofitLearwillearn;theyjustwanttobuildtheparkinggarage,collect
theirfee,andmoveontoanotherconstructionproject.Thereisagreatopportunityfor
LeartomakeapositiveNPVontheprojectbyexploitingthedisconnectbetweenthe
constructioncostandtheeconomy;therealoptionpremiumisnotrelatedtothepotential
payoff!
Financialoptionstendtohavesimpleterms,butrealoptionscaninvolvemanyinterrelated
qualities.Ratherthanasimpleexerciseprice,realoptionscouldhaveagrandcriteriathat
needstobesatisfiedbeforeitisexercised.Inthesesituations,theBlack‐ScholesModeland
BinomialTreemodelcannotquantifythevalueofarealoption.Thelevelofcomplexity
requiredbyrealoptionsanalysismakestheMonteCarloSimulationthetoolofchoicewhen
dealingwithrealoptions.
Financialoptionsarevaluedbydirectlyinputtingunknowns,suchasstrikepriceand
exerciseperiod,intoequationstoarriveattheoptionpremium.Realoptionsarenotas
straightforward.Becauseoftheirintricacy,itcanbenearimpossibletodirectlycompute
thevalueofarealoption.MonteCarlosimulationsofferawork‐a‐roundsolutionby
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
42 allowinganalyststofindtheNPVofaprojectwithoutanoptionandcomparingittothe
NPVofthesameprojectwithanoptioninplace.Conceptually,theoptionvaluewouldbe
thedifferencebetweenthetwoNPVs.
Theabilitytomodeldifferentrealoptionsintoarealestatefinancialmodelisanoptionin
itself!TheNPVvalueswhicharecalculatedfromarealoptionsanalysisareneverbinding.
Realoptionmodelingenjoysasymmetricoutcomes;alloftherealoptionsthatwerenot
worthwhilearenotundertaken,while“homerun”optionsarepursuedfurther.Thereis
nothingtolosewhenmodelingoptions,butpotentiallyalottogain.
Sometimes,realoptionsarealreadyfreetoimplement.Thefreedomtowalkawayfroma
propertywithan‘underwater’loanpreventsfurtherlosses,effectivelycappingdownside
outcomes.Inafinancialmodelwhichincorporatesuncertainty,thisrealoptionofwalking
awayfromanunderwaterloanimprovesexpectedNPV,yetcostsnothing.Therefore,
modelingthisrealoptionintoafinancialmodelcanprovidethatextraedgethatis
differencefromwinningandlosingacompetitivelandbid.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
43 CHAPTER7:TwoWorldTradeCenterCaseStudy
Wedevelopedashortcasestudytoconnectandapplytheconceptspresentedinthisthesisto
arealisticsituation.Thescenariocreatedforthisthesisisinspiredbyanactualcasestudy
doneontheWorldTradeCentersiteinNewYorkCity(Queenan,2013).Whilethestoryis
fictitious,theassumptionsaremadetobeasrealisticaspossiblewithbasisfromlegitimate
sources.
7.1
ScenarioBackground
WallStreethasseenbetterdays.5yearsafteroneofthedeepestrecessionsinUShistory,
theblamegameisinfullflight.Recoveryhasbeenexcruciatinglyslowandthepopular
thingforpoliticianstodoistopickapartWallStreet.Nooneseemssureaboutthefuture
stateofthefinancialsector.
AftermuchdifficultywithleasingOneWorldTradeCenterandThreeWorldTradeCenter
inthethickofthefinancial
crisis,GoldsteinProperties
andThePortCommissionare
hopingtounloadthe
developmentrightstothe2.3
millionsquarefeetofficepiece
ofTwoWorldTradeCenter.
ArdenForestPropertiesis
interestedindevelopingthe
bluechipofficetowerand
broughtinTimonCapitaltobe
themoneypartner.
Figure13:WorldTradeCenterSitePlan(PANYNJ,2013)
Notsurprisingly,Timonis
TwoWorldTradeCentersitsonthemostNorth
Easternparcelinthesite.OneWTC,3WTC,and4
WTCareallofficetowers.
veryconcernedaboutthe
futureoftheofficemarketin
Manhattan.Inanefforttoput
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
44 theirbusinesspartneratease,ArdenForestcreatesaproformatoseehowthe
developmentwouldperformwithuncertaintyinthemarketandaddressthedownside
possibilities.MichaelCassio,asenioranalystatArdenForest,wondersifthisisagood
opportunitytousehisinternshipexperiencelastsummerataderivativesdeskinChicago.
AlthoughMichaelhasonlyseenthevaluecreatedbyfinancialoptionforaninvestor,he
suggestsimplementinganoptioninthisdevelopmenttoseewhatwouldhappen.
TwoWorldTradeCenterispartofa
majormixed‐usedevelopmentconsisting
of5officeskyscrapersplusretail,
cultural,andtransportation
infrastructure.SittingattheNorthEast
cornerofthesite,TwoWorldTrade
Centerwillbethesecondtallestbuilding
oftheWorldTradeCentercomplex.As
withalltheotherWTCsites,ThePort
Commissionwilllookafterthe
constructionofthefoundationsbecause
oftheintricatenetworkoftunnelsbelow
connectingtonewWTCtransportation
hubsouthofthe2WTCsite.
Goldsteinhasalreadycommittedto
developingtheretailpodiumatthefoot
of2WTC,butnowtheygoingthrougha
bidprocessforthedevelopmentrights
totheofficeportionoftheproperty.
Figure14:2WTCRendering(PANYNNJ,2013)
Arenderingof2WTCasviewedfromthe
9/11Memorial.
MichaelCassioknowsthatthiswillbea
verycompetitivebidforarareworld‐
classproperty.Thedollarsatstakearemuchhigherwithalandmarkskyscraperinthe
world’smostprominentfinancialcenter.Theslightestmiscalculationontheproformacan
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
45 costArdenForestbillions.Michaelhopesthathissecretweapon,realoptionsanalysis,will
helpArdenForestwinthesitewithoutexposingthemtoriskwithoutcompensation.
7.2
CreatingaDetailedStochasticProFormafor2WorldTradeCenter
Michaelbeginswithabigpicturestrategyfortheproforma:quantifyuncertaintyinthe
officemarket,createarealoptionsmodel,andevaluatetheproformabyperforminga
MonteCarloSimulation.Michaelunderstandsthatofficeemploymentgrowthisthemain
driverofrealestatedemand,butthereissimplynotenoughtimetocompilethedatahe
needsforthebidthatneedstobesubmittedinjustafewdays.Plus,he’snotcomfortable
creatingarealestatestock‐flowmodelbecausehedidn’treadsection5.2ofthisthesisor
SarweshParadkar’sawardwinningMSREDthesis.Mr.Paradkarshowshowthestockflow
modelcanbeimplementedwithalittleextradataonemployment,vacancy,andrealestate
stock(Paradkar,2013).Asfarasuncertaintygoes,Michaeldecidestodirectlyforecast
officerents.
7.3
ProjectingRents,CapRates,ConstructionCostsandOperatingExpenses
InitialRent
Firstoff,Michaelneedstoknowwhattheaverageofficeleasewouldgoforin2WTCifit
wereleasingtoday.Luckily,therearemanyleasecomparableswithinthesamecomplex!
OneWorldTradeCenterand4WorldTradeCenterareaskingfor$75persquareforin
grossrentforspacedespiteanabundanceofvacantspaceintheDowntownsubmarket
(Levitt,2013).NotallislostastheentranceofOneWorldTradeCentertothemarkethas
graduallyincreasesofficerentsdowntowntoanaverageof$60persquarefoot(Kozel,
2013).Michaeldecidesthat$65persquarefootisareasonablerentfor2WTC,sinceitwill
beabrandnewClassAbuilding.Ontheotherhand,Michaeldoesn’twanttoputrentsnear
$75persquarefootbecause2WTCneedstoenticetenantsawayfromothercompeting
WTCofficetowers.
Leadingwith$65persquarefoot,wecanfollowalongwithMichael’sworkinthe
‘Projections’tabofthe2WorldTradeCenterproforma.Wewillgraduallyaddlayersof
uncertaintytoourrentforecasting.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
46 Long‐RunTrend
ThiswasaneasyoneforMichael.Thelong‐runtrendforofficepropertieshasbeenwell
researchedintermsofassetpriceandrents.Officepropertiesdon’tbeattherateof
inflationoverthelong‐run(Eichholtz,1997;Fisheretal.,1994;Wheatonetal.,2009).In
fact,realestatewilldoslightlyworsebecauseofdepreciationintheproperty.SincetheUS
FederalBankhasastatedgoaltokeepinflationsataround2%,Michaelchoosestouse2%
asthelong‐runprevailingtrendandvariesitusinganormaldistribution.Bysettingahalf‐
rangeof1%,Michaeluses1%dividedby3asthestandarddeviationintheNORM.INV
function,whichmakesita99.7%probabilitythatthelong‐runtrendwillliebetween1%
and3%.Theinitialratenowexhibitslong‐runtrendingbyaddingthepercentageincrease
yearafteryear.
MarketVolatility
Formarketvolatility,Michaelusesgrossrentdatatofindthehistoricvolatility.Inthe
assumptionsExcelfile,thereisasheetcalledvolatilitywhichdetailshowtofindthe
volatilityofrents.Inthiscase,wehavequarterlydataofrentsandwefirstcoverttherents
intoapercentagechangefromquartertoquarter.Next,thestandarddeviationisfoundon
thequarterlychangesusingtheST.DEVfunction.Lastly,wetranslatethequarterly
volatilitytoanannualizednumberbutmultiplyingthequarterlyvolatilitybythesquare
rootofthenumberofperiods.Inthiscase,wemultiplethequarterlystandarddeviationby
thesquarerootof4togetanannualizednumber.Ofcourse,thevolatilitycouldbepositive
ornegativeinanygivenyear,soMichaelusestheNORM.S.INVfunction.Thisfunctionuses
acumulativedistributionfunctionandtranslatesarandomvariabletogoeitherpositiveor
negativearoundanormaldistribution.Arandomnumberof.5willmakethefactor0,while
andcumulativeprobabilityof16%(roughlyat‐1standarddeviation)willendupwitha
factorof‐1andsoon.Calculatingthestandarddeviationontheprojectedvolatilities
shouldreturnanumberclosetothehistorical7%.
Inertia
Formomentum,weusethegrossrentdataandtakethefirstdifferenceofit,whichisthe
rateofchangefromyeartoyear.Alinearregressionwasperformedwithalagged
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
47 percentagechangeinrentstoarriveataninertiafactor.Pleaserefertothelinear
regressionperformedintheARtabofthe“2WTCassumptions”toseehowtherateof
33.5%forinertiawasretrieved.Ifthemarketvolatilitywasnegativelastterm,thecurrent
periodwillhavesomedownwardpressurefrommomentum.
MarketCyclicality
Peak‐to‐peak,realestatecycleshavelastedbetween15and20years(Geltner,2013).
Whilenotalwayssynced,therealestateandassetandspacemarketsappeartohave
similardurations.Tomodelthiscyclicaleffect,Michaelusesasinecurvetocreateafactor
forrentseachyear.Thecoefficientinfrontofasinecurveaffectstheamplitude,orthe
heightofthewaves,andthenumbersinsidethesinefunctionaffectthedurationand
positionofthecurve.TheSinecurveonitsownhasacycledurationof2πandamplitude
rangeof1to‐1.So,MichaeltranslatestheSinecurvetoworkinthespreadsheetbyusing
theformula:
2
sin
2
1
Where:
Maximumamplitudein%
Numberofyearssincestartyear,withstartyear=0
CycleStartingPosition(yearsafterupwardmid‐point)
Durationofonefullcyclesinyears
The+1attheendofthefunctionshiftstheentiresinecoveruptohaveamid‐pointof1
insteadof0.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
48 Foramplitude,
Michaeldoesaquick
analysisofNYCoffice
rentsbetween1988
and2011.First,he
convertsthenominal
rentstorealrents,
thenheobservesthe
differencebetween
lowestandhighest
valueswiththetotal
Figure15:RealEstateCycleLength
Thepeak‐to‐peakandtrough‐to‐troughdurationisbetween
15and20years(Geltner,2013).
changefrompeakto
troughobservedtobe
closeto40%.Lastly,
MichaellooksattheMoody’s/RCACPPITBItoseewheretherealestateenvironmentisin
thecycle.Itseemslikeitshouldbearoundhalfwayontothepeakin2013,butMichael
decidestoretardthecycleintheanalysisabitbecauseeconomicrecoveryhasbeenslower
thanusual.
Withallthe
parametersaccounted
for,theSinewaveis
convertedtoafactor
withthecurrentyear
asafactorof1.
Figure16:TheRegularSineCurve
Whennottransformed,thesinecurvehasacycledurationof
2πandanamplitudeof1.Thecycle’sy‐interceptis0.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
49 Noise
Noiseistakenintoaccountsymmetricallywitha10%rangenormaldistribution.10%isa
typicalrangeusedbyappraiserswhenprovidingtheiropinionofvalue.
BlackSwan
Blackswansarebydefinition,impossibletopredictbutwecanstillsimulatetheeffect.
Michaelgiveseachyeara5%chancetooccur,whichgivesabouta40%chanceofablack
swaneventoccurringevery10years.Themagnitudeofimpactissetat‐25%,morethan
halfofthecycleeffectoccurringoneyearseemsappropriateforameaningeventthatwill
affecttheinvestment.
Nowthatrentsaremodeled,Michaelturnstomodelingotheritemswhichneedtobe
projectedforward.
CapRate
Projectingfuturecapratesisimportantbecauseitgreatlyaffectsourterminalvalue
calculationandoptiontrigger.Again,lookingatRCAdata,thecaprateseemstofluctuate
between8.5%and5%,givingamidpointof6.75%.Since2WTCwillbeamodernbluechip
officetower,Michaeldecidestosetthemeancapratealittlelowerat6.5%withthesame
halfrangeof1.75%.Theassetmarketcycletendstoleadthespacemarketcyclebutthey
canbeoutofsyncattimes.Goingfortheruleratherthantheexception,Michaelsetsthe
positionofthecapratecycleoneyearinfrontofthespacemarketcycle.
OperatingExpensesandConstructionCosts
Michaelusesthesamemethodtoaccountforuncertaintyinexpensesandconstruction
costsastheModerateCoexampleinchapter3ofthisthesis.Operatingexpensesaresetto
growataroundthetargetedrateofinflationbytheUSFederalReserveBank,2%.
ForConstructionCosts,RSMeansdatasaysthatofficebuildingconstructioncostsinNew
Yorkhaverisenabout5%inthelastyear(Carrick,2013).Thehardcostquotedby
RSMeansis$223persquarefoot.Assumingthat2WTCwillbeahighquality,expensive
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
50 building,Michaeluses$300persquareforhardcosts.Addingaruleofthumb(30%ofhard
cost)forsoftcosts,bringsthetotalconstructioncostnumberto$390persquarefoot.
7.4
ProFormas
Nowwithourparametersprojectedin
tothefuture,Michaelisreadytoset
upproformastotestouthisreal
optionshypothesis.Hewillcreate3
separateproformasandcompare
theirfinancialperformanceunder
uncertainty.Thefirstproformawill
bea60floorinflexiblecase.Another
inflexiblecasewillbemodeled,butfor
30floorsinsteadof60floors.Thelast
onewillhavearealoptionimbedded
intothedesignbystartingwith30
Figure17:2WTCSketchupofAlternatives
Thebuildingontheleftisamodelofa30
floorinflexibledesign.Themiddlebuilding
representsaflexibledesignoptionwhilethe
buildingontherightistheinflexible60floor
officetowerdesign.
floorsandallowingfortheflexibility
tobuildanother30floorsontopin
thefuture.
Theconstructiontimeshouldbe
longerforthe60floortower,so
Michaelmakessurethatthe60floortowertakes4yearstobuildversusthe3thatthe30
floortowersneed.TheconstructioncostsarediscountedatanOCCof1.6%,with50basis
pointsfromtheriskpremiumofconstructioncashflowsand110basispointsfortherisk
freerate.Theriskpremiumforconstructioncashflowsreflectthelowsystematicrisk
involved.Constructioncostsareusuallylockedinwithacontactanddonotmovewith
capitalmarkets.
Theriskfreerateis1.1%,usingthe10yearTreasurybillrate,minus150basispointsto
accountfortheyieldcurveeffect(BloombergMarkets,2014).Thecashflowfromthetower
duringitsfullyleased,stabilizedphaseisdiscountedat5.1%,reflectingtheaveragerisk
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
51 premiumof4.5%forallNCREIFcommercialrealestatebetween1970and2010(Geltner,
2014).Michaelhaircuttheriskpremiumby50basispointsbecausethisofficetowerwill
beabluechippropertyinoneofthemostdesirablelocationsintheworld.Lastly,the
stabilizedNPVwillbediscountedinthedevelopmentphaseby7.1%toaccountfortherisk
involvedinleasingupaprimarilyspeculativedevelopment.Geltner(2014)statesthatthe
riskpremiumfordevelopmentphasecashflowstypicallyhavea50‐200basispoint
premiumoverequivalentpropertiesinthestabilizedphase.
Manydevelopersmaybetemptedtouseasinglediscountratefortheentireproject.
However,itisimportantthateachphasewithadifferentlevelofriskhaveadifferent
opportunitycostofcapital.Thesediscountratesshouldalsobejustifiablethroughmarket
evidencebecauseitisthecapitalmarketsthatdeterminetheserates.
Theproformamodels5and10yearleaseswithrentescalationsusingifstatements.Thisis
keytoouranalysisbecauseleaserateswillbelockedinbytheirleasetermswhilethe
marketcanmoveeitherwayduringthelease.SinceMichaeldoesn’tknowwhatlengththe
leaseswillbe,hehasusedtheRANDfunctiontodetermineiftheleaseswillbe5yearor10
yearleases,themostcommonleaselengthsincommercialrealestate.
Theinflexible30and60floorproformasdonotstraymuchfromastandardproforma.The
flexible30floorproformawillneedtomodeltherealoptionthough.
7.5
RealOptionTriggers
Tomodelarealoption,twothingsneedtobedefined.Firstoff,thetriggerconditionsneed
tobemodeled.Fortheflexiblecase,thetriggerispulledwhenevertheadditionbecomes
profitable.Tomeasureprofitability,MichaelusestheNPVinvestmentdecisionrule:
1.MaximizetheNPVacrossallmutuallyexclusivealternatives;
2.NeverchooseanalternativethathasNPV<0.
Theacquisitioncostofthelanddoesnotfactorintothisdecisionbecauseitiswhatiscalled
a“sunkcost”.Sunkcostsarecostsincurredinthepastthatcannotberecoveredregardless
offutureoutcomes.So,theyshouldnotbeconsideredwhenmakingfuturedecisions.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
52 TheNPVforeachyeariseasytocalculateusingprojectcapratesandconstructioncosts.
MichaelusesanIFstatementtoactasaswitchtosignifyifconstructionbeginsonthe
additionornot.Sincetheadditioncanonlytakeplaceonce,anotherIFstatementisusedto
ensurethatnoadditionhasstartedpreviouslybeforebeginningconstructioninthatyear.
Theotherpiecethatneedstobedefinedforarealoptionistheconsequence.Inthiscase,
whathappensisthatanextra1.3millionsquarefeetisaddedtwoyears(toaccountfor
construction)aftertheyearoftheconstructiontrigger.Newleaseshavetokickin,anda
10%constructioncostpremiumisaddedtotheconstructioncost.TheNPVisthen
calculatedthesamewayastheinflexibleproformas.
7.6
Results
Inflex 30
($191)
($251)
($300)
$371
in Millions
Expected NPV
Median
Mode
Std Deviation
Value
At
Risk
Median
Value
At
Gain
5%
10%
25%
50%
75%
90%
95%
($686)
($604)
($455)
($251)
$7
$295
$509
Flex 30
$14
($145)
($500)
$710
Percentiles
($792)
($708)
($543)
($145)
$400
$979
$1,383
Flex 40
Flex 50
$9
($137)
($500)
$714
$4
($128)
($300)
$719
Inflex 60
$14
($95)
($300)
$731
($847)
($742)
($535)
($137)
$397
$963
$1,372
($901)
($770)
($527)
($128)
$388
$948
$1,349
($962)
($808)
($502)
($95)
$414
$977
$1,380
Figure18:2WTCFinancialModelResults
Theflexible30floordesignandtheinflexible60floordesign
outperformtheotherbuildings.Notethattheflexible30floordesign
hasthelowestpotentiallosses,yetmaintainsgoodgainswhenthe
economyisgood.
Michael
comparesthe
returnswith
distributions
afterperforming
aMonteCarlo
Simulationand
theresultsare
intriguing.The
firstthingthat
popsoutishow
theinflexible30
floormodel’sfinancialperformanceisterrible.Alsounfortunate,therealoptiondidnot
haveasmuchofaneffectonexpectedNPVasMichaelhoped.TheFlexible30flooroption
hasthesameexpectedNPVasbuildingtheentire60floorsoutright.However,notallislost
becausetheflexibledesignisdoingitsjob,protectingArdenForestPropertieswhenthe
economyisdoingpoorly.Thecumulativedistributionshowshowtheflexibledesign
behaveslikethe30floorinflexibleprojectatthelowendofpossibilities,butthenstartsto
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
53 behavelikethe60floorinflexibleprojectatthehigherend.Theflexible30flooroptionis
definitelythemostpreferableoption.
Iftherewasno
constructioncost
premium,the
flexible30floor
optionactuallyout
performsevenat
thetopendinthe
sameenvironmental
conditionsasthe
inflexible60floor
option.Duringthese
conditions,thereal
optionisalmost
Figure19:2WTCDistributionFunction
Theflexible30floordesign’sCDFperformsliketheinflexible
60floordesign,exceptatthelowendofNPVswherethe
downsideisminimized.
alwaysexercised
rightawayinthefirstyearpossible,2017.Despitetakinganextrayeartoconstruct60
floors,theflexibleoptioncomesonoutabovetheinflexibleoptionbecauseofthelease
timings.Theeconomyreachesthepeakofthecyclein2019,rightwhentheleasesfromthe
newadditioncomeonline,whilealloftheleasesoftheinflexibleschemesarestuckat
lowerratessigned2yearspreviously.Thosepoorperformingleaseswillalsoberenewed
atanotherlowpointinthecycle10yearsafterwardsinthelowestpointoftherealestate
cycle.
Whiletheflexible30floormodeloutperformstheotherschemes,itdoessounderspecific
conditionsmodeledbytheAnalyst.Regardless,Michaelisconvincedthatrealoption
analysiswillhelpArdenForestwinthebid,armingthecompanywithknowledgeof
distributionswillhelpthecompanyfocusonmanaginguncertaintyratherthanrelyingon
guessworkandgutfeelingsindeterministicfinancialmodelingofRealEstate.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
54 CHAPTER8:Conclusion
“Themoreyouknow,themoreyouknowthatyoudonotknow”isacommonlyused
maximaboutSocraticIgnorance.Itseemsthatuncertaintypersistsmoretodaythanever
before.Perhapsthehumanraceisjustlearningmoreaboutuncertaintythroughhumbling
eventssuchasthemega‐recessionin2008.Onethingthatwecanbeassuredofisthat
uncertaintywillcontinuetoplayaroleinrealestateinvestingwhetherprofessionals
acknowledgeuncertaintyornot.
Thereislittledoubtthatrealestatefirmsandinvestorswouldliketoincorporatethe
techniquespresentedinthisthesis.Theunfamiliaritywithstochasticmethodsisthemain
stumblingblockandisunderstandablewhenmillionsofdollarsareonthelinewitheach
realestateproject.Atthesametime,itisthefactthatalotofdollarsareatstakewhich
makesthesetechniquesimportant.EngineersandscientistshavereliedonMonteCarlo
Simulationstobuildatomicbombs,flytothemoon,andsavelivesduringpandemicsfor
almostacenturynow.Surelystochasticmethodswilladdvalueinrealestateifused
properly.
Inthisthesis,itwasshownhowsimpleitcanbetoadduncertaintyintootherwise
deterministicproformaswhicheveryrealestateprofessionalisfamiliarwith.The
unpleasanteffectofJensen’sinequalityonreturnmeasuresindeterministicmodelsis
exposed.MonteCarloSimulationsweredemystifiedinunder5minutesusingafew
keystrokesinExcel.Thevalueofdistributionsoverpointestimatewasdisplayed,which
gaveanentirelynewperspectiveonfinancialreturns.RealOptionswasthetoolpresented
thatenablesarealestateventuretakeadvantageofuncertainty.
InChapters5and6,theseconceptswerefurtherdetailedwithsolidtheoryandempirical
evidence.Uncertaintyinrealestatewasbrokendownandexplained,usingnewdatatools
andindicestoquantifyvolatilityandrisk.Theacademicunderpinningofrealoptionswas
presentedwiththeoryborrowedfromfinancialoptions.Thenwerevealedthemechanics
ofrealoptionsinthecontextofrealestate.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
55 Tohelptranslatetheoryintopractice,amodernexampleof2WorldTradeCenterwas
presented.Forsimplicity,onlyoneoutofavarietyofoptionswasemployedintheanalysis,
butthepowerofrealoptionsinrealestatewasclearlyondisplay.Whileitisnota
guaranteethatrealoptionsinarealestateventurewillincreasevaluemonetarily,theactof
analyzingrealoptionsisavaluableoptioninitsownrightforrealestatewhereirreversible
investmentdecisionsaremadefrequently.
Perhapsthegreatestadvantageofunderstandingtheseconceptsisthechangeinmindset
whenitcomestoapproachingrealestateproblems.Anewgrandavenueisopenedup
whenuncertaintybecomespartoftheanalysis.Thereareendlesspossibilitieswithreal
optionanalysesandcreativeproblemsolverswillbethegreatestbenefactors.
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BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
59 APPENDIX AppendixA IncorporatingUncertaintyintoaFinancialModel
TheRANDfunctioninExcelrandomlygeneratesanumberbetween0and1.Eachtimea
recalculationoccurs,theRANDfunctiongeneratesanewnumber.Thisfunctionisthe
sourceofuncertaintyintheModerateComodel.EachnumberintheRANDfunctionhasthe
sameprobabilityofoccurrence.Forexample,0.1hasthesameprobabilityofoccurringas
0.9.
Totranslatethisrandomnumbertoaworkingrentgrowthrateanotherfunctionmustbe
usedinconjunctionwiththeRANDfunction.
Chapter5isdedicatedtomodelinguncertaintyintherealworld.Fornow,averysimplified
methodisusedtotranslatetherandomnumbersgeneratedusingtheRANDfunctioninto
rentgrowthrates.InsteadofeverynumberintheRANDfunctionoccurringwithequal
chance,extremenumbersoroutliersshouldoccurwithlessprobabilitythannumbersin
the“center”ornearalong‐runmean.
TheNORM.INVfunctiontakesinarandomprobabilityandtranslatesthenumberusinga
normaldistributionfunction.Recallthat68%ofvaluesoccurwithinonestandard
deviationfromthemean.95%and99%ofvalueoccurwithintwoandthreestandard
deviationsofthemeanrespectively.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
60 NestingaRANDfunctionastheprobabilityinputfortheNORM.INVfunctionallowsthe
outputvaluetobenormallydistributedinsteadofevenlydistributed.
TheprobabilityacceptedbytheNORM.INVfunctionistakeninasacumulativeprobability
ofanormaldistribution.Ifa0.5isgivenbytheRANDfunction,theNORM.INVfunctionwill
outputthemean.If0.023isgivenbytheRANDfunction,theNORM.INVfunctionwilloutput
anumbertwostandarddeviationsbelowthemean.Anyprobabilitybetween0.16and0.84
willreturnavaluewithinonestandarddeviationfromthemean.Themeanandstandard
deviationmustbespecifiedtomaketheNORM.INVfunctionwork.
ThedeterministicSimpleCoexampleuseda3%rentgrowthrate.Tomaintainconsistency,
3%isalsousedasthemeanintheModerateCorentgrowthrateformula.Asan
assumption,2%isusedwasthestandarddeviationforrentgrowthrate.Using2%asour
assumedstandarddeviationmeansthatgrowthrateshouldbewithin±2%ofthemean(or
between1%and5%inourexample)68%ofthetimeandshouldbewithin±4%ofthe
mean95%ofthetime.
(in 000's)
Potential Gross Revenue
Vacancy
Effective Gross Revenue
Year
1
$4,590
$230
$4,361
2
$4,783
$239
$4,544
3
$4,985
$249
$4,736
4
$5,195
$260
$4,935
5
$5,414
$271
$5,144
6
$5,642
$282
$5,360
7
$5,880
$294
$5,586
8
$6,128
$306
$5,822
9
$6,386
$319
$6,067
10
$6,656
$333
$6,323
11
$6,936
$347
$6,589
Operating Expenses
$2,550
$2,627
$2,705
$2,786
$2,870
$2,956
$3,045
$3,136
$3,230
$3,327
$3,427
Net Operating Income
$1,811
$1,918
$2,031
$2,149
$2,273
$2,404
$2,541
$2,686
$2,837
$2,996
$3,162
$181
$192
$203
$215
$227
$240
$254
$269
$284
$300
$1,629
$1,726
$1,828
$1,934
$2,046
$2,164
$2,287
$2,417
$2,553
$1,629
$1,726
$1,828
$1,934
$2,046
$2,164
$2,287
$2,417
$2,553
$2,696
$28,749
$31,445
Capital Expenditures
CF From Operations
Reversion (Purchase and Sale)
PBTCF
NPV
‐$17,000
‐$17,000
$3,019
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
61 AppendixB PerformingMonteCarloSimulations
OurprobabilisticModerateCoproformalooksexactlythesameasthedeterministic
SimpleCoproforma,exceptthatourNPVnowchangeswhenwerecalculateformulasby
hittingF9.Eachrecalculationrepresentsadifferentscenariounderuncertainty.Whileitis
interestingtoseetheNPVjumparound,itwouldbeusefuliftherewasawaytorecordthe
NPVvaluesformanyiteration/simulationruns.
ThisproformaisnowsetupforMonteCarlosimulations.Manyiterationsofthemodelare
ranandtheoutputvalues(inourcase,NPV)arerecordedintoatable.
Tosetupthe2columnsimulationtable,referencetheoutputvalue(NPV)inthetoprowof
therightcolumn.
ThenextstepistoselecttheentiretableandbringuptheDatatablewindowfromData‐>
WhatifAnalysis‐>DataTable.Forthecolumninputselect,justselectanyblankcellinthe
spreadsheetanditshouldpopulatetherestofthesimulations.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
62 Inthissimplisticexample,weran10simulations.Thenumberofsimulationswhichcanbe
ranisonlylimitedbytheprocessingpowerofcomputers.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
63 AppendixC CreatingCumulativeDistributionFunctions(CDFs)inExcel
CreatingacumulativedistributionfunctionoftheresultsfromtheMonteCarloSimulation
issimpletodoinExcel.TheCDFisthechiefoutputresultfromtheproformaandprovides
muchmoreinformationthanasingleNPVvalue.
Onceadatatableiscreatedtorecordtheresultsfromthesimulations,anewtablecanbe
created,sortingtheresultsfromsmallesttolargestusingtheSMALLfunction.
TheSMALLfunctionselectsanumberfromtheresultcorrespondingtotherankspecified
as“k”.Thus,rank1wouldrefertothesmallestnumberintheresultset,andrank2would
refertothesecondsmallestnumberintheresultset.ThesortedNPVvalueswillbethex‐
axisvaluesforthecumulativedistributionfunction.Forthey‐axisvalues,1/(numberof
iterations)isgiventoeachresult.Effectively,in5,000runsofthemodel,eachresult
accountsfora1/5000or(0.02%)sliceofthedistribution.Asacumulativedistribution
function,0.02%isaddedtoeachsuccessiveresult.Graphthetableasascatterplotand
formatasnecessary.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
64 AfewobservationscanbemadeabouttheCDFfunctionofModerateCoTower.Thegreater
theslopeofthegraph,thegreaterthelikelihoodofthecorrespondingNPVs.In
ModerateCo,thereisabouta50%chanceofpositiveNPVand50%chanceofnegativeNPV,
butthelossandreturnsarenotsymmetrical.Thelossattheworst10%ofscenarioswasat
least‐$6million,whichthegainatthebest10%ofscenarioswasatleast$7million.These
numbersarecalledtheValue‐at‐risk(@10%)andValue‐at‐gain(@90%)numbers.
Anotherobservationonecouldmakeisthatthereisabouta30%chancethatthefinalNPV
willbebetween‐$2,000and$2,000.
InChallengeCoTower,multipleCDFsareplottedonthesamegraphtocompareand
analyzetheprobabilisticoutcomesacrossmultiplealternatives.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
65 AppendixD UsingIFStatementstoModelRealOptionsforRealEstateVentures
Aspresentedinsection5.3,TheBinomialLatticemethodiscommonlyusedtovaluereal
options,butthefocusofthisappendixwillbetheMonteCarlomethodusedinconjunction
withIFstatementstomodelthebehaviorofRealOptionsbecauseofthesimulation
method’sabilitytomodelseveraldifferentsourcesofuncertainty,Inthehandsofacreative
analyst,aplethoraofdifferentsituationsandcircumstancescanbemodeledwiththe
flexibilitythattheMonteCarloSimulationmethodoffers.
TheIFstatementisanimportantlogicfunctioninExcelthatallowstheprogramtomake
decisionsautomaticallyforyou(becausemanuallymaking5,000switchesismadness).
Basically,theIFstatementcanbeusedasanautomaticswitch‐inthecontextofReal
Options,theIFstatementallowsthespreadsheettomakeitsowndecisiononwhetherto
exerciseanoptionornot.
ForChallengeCo,theoptiontobuild10morefloorssometimeinthefutureneedstobe
modeled.Whenwillconstructionbeginforthe10additionalfloors?Constructionwillonly
commenceiftheeconomydoeswell;fewdeveloperswouldwanttoexercisethisoption
whenrentsarelowandvacancyishigh!Thefirststepinmodelingrealoptionsistospecify
the‘trigger’conditions.
ChallengeCo Parameters
Total Development Cost
Efficiency
Gross Floor Area (Addition Incl)
Option Exercise Trigger: Rent
Flex Development Cost
Office Rent
Rent Growth Rate
Expenses
Expense Growth Rate
Vacancy
Capital Expenditures
Terminal Cap Rate
OCC/Discount Rate
Year 0
1
2
3
$100 /gsf
90%
170,000 sf
0.00
0.00
0.00
$35 /sf
$105 /gsf $ 108.15 $ 110.30 $ 111.37
$30 /sf $ 30.90 $ 31.51 $ 31.82
3%
1.99%
0.97%
0.79%
$15 /sf $ 15.45 $ 16.00 $ 16.59
3%
3.56%
3.70%
7.11%
10%
19.38%
15.20%
26.38%
10% of NOI
10.16%
10.84%
10.97%
11.00%
11.18%
11.84%
11.57%
12.50%
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
66 InChallengeCo,theinputassumptionsaregivenahealthydoseofrandomwalk,plustwo
newassumptionsappear:totaldevelopmentcostandflexdevelopmentcosts.Total
developmentcostwillbetheinitialhardandsoftcostsofconstructingtheofficebuilding.
Theflexdevelopmentcostrepresentsthecosttoconstructanaddition,inflatedbythe
samerateastherentgrowthrate.Theoptionexercisetriggercannotbemissedwithathick
redborder.
Thegoalhereistomodeltheconstructionofanadditional10floorssometimeinthefuture
whentheeconomyimproves.Inthiscase,therentisinitially$30persquarefoot,sothe
optionshouldbeexercisedwhentherentrisesup.Letusseewhathappensifwetrigger
constructionoftheadditional10floorswhentherentsreach$35persquarefoot.
ChallengeCo Parameters
Total Development Cost
Efficiency
Gross Floor Area (Addition Incl)
Option Exercise Trigger: Rent
Flex Development Cost
Office Rent
Rent Growth Rate
Expenses
Expense Growth Rate
Vacancy
Capital Expenditures
Terminal Cap Rate
OCC/Discount Rate
Year 0
1
2
3
4
5
6
$100 /gsf
90%
170,000 sf
0.00
0.00
0.00
0.00
0.00 170,000 sf
$35 /sf
$105 /gsf $ 108.15 $ 108.46 $ 110.78 $ 113.79 $ 116.91 $ 123.14
$30 /sf $ 30.90 $ 30.99 $ 31.65 $ 32.51 $ 33.40 $ 35.18
3%
0.29%
2.13%
2.73%
2.74%
5.33%
0.43%
$15 /sf $ 15.45 $ 16.05 $ 16.62 $ 17.12 $ 17.73 $ 18.59
3%
3.89%
3.55%
2.97%
3.61%
4.84%
0.86%
10%
4.79%
12.95%
10.16%
9.99%
4.88%
0.00%
10% of NOI
9.85%
9.76%
9.44%
10.04%
9.72%
9.51%
11.00%
10.83%
11.31%
11.08%
11.60%
11.92%
11.49%
12.50%
Inthe6thyearoftheproforma,therentclimbsabove$35persquareandimmediately,an
additional170,000squarefeet(10floors)isaddedthroughbyusingIFstatements.TheIF
statementisusedasaswitchbetweenadding170,000squarefeetandnotaddingmore
floorarea.
value if true
Atitscore,theIFStatementhasthreeparts.
logical test
1)Logicaltest
2)Valueiftrue
value if false
3)Valueiffalse
Organizedinthisformat:
=IF(logicaltest,valueiftrue,valueiffalse)
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
67 ThinkoftheIFstatementasa"forkintheroad"withthelogicaltestastheinput.Valueif
trueandvalueiffalseareoutputs.
Thelogicaltestisanequationthattellsthecomputerwhattodowhenitencountersthe
forkintheroad.Verbally,thelogicaltestwillread:“iftherentisgreaterthan$35…”In
excelitwouldbe:“E$8$>B5”withB8beingtherentinthecurrentyearandB5asthe
triggerrent.
‘Valueiftrue’istheoutcomewhichwilloccurwhenthelogicaltestistrue,withthe
oppositebeingtrueforthe“valueiffalse”.
Build 170k sf
If Rent > Trigger
IF(Rent>Trigger,170000,0)
Don’t build
Foreachyearthatthepossibilityexiststoconstructanother170,000sf,anIFstatementis
required.
NewProblem:Incurrentform,theIFstatementswecreatedwillautomaticallyconstruct
anadditional170,000sfwithoutmemoryofwhathappenedinthepreviousyears.Thus,
therecouldbe170,000sfofconstructioneveryyeareventhoughtherealoptionthatis
beingmodeledcanonlyoccuronetime.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
68 Tosolvethis,anIFstatementisnestedinsideanotheronetocreateaswitchwithmore
thantwooutcomes.Herearethecomponents:
1)Logicaltest
value if true
logical test #1
2)Valueiftrue
value if true #2
3)Valueiffalse...anotherIFstatement
3a)Valueiftrue
3b)Valueiffalse
logical test #2
(value if false)
value if false #2
InthenestedIFstatement,thefirstlogicaltestissetuptoseeif170,000squarefeetwas
constructedbeforehand.Iftherehasbeenanother170,000squarefeetbuiltbeforehand,
thennoconstructiontakesplace(effectively,ignoringanythingrentdoesinthatyear).If
theadditionhasnotbeenconstructedyet,thenproceedtothesecondIFStatementlevel.
Onthesecondlevel,thepreviouslogicaltestandoutcomesarethesame.
IF(SUM(previousyearssf)>0,0,IF(Rent>Trigger,170000,0))
Now,theRealOptionofbuildinganadditional10floorssometimeinthefutureismodeled
andisreadyfortheMonteCarloSimulation.
Has construction already begun?
Don’t build
Build 170k sf
Is Rent > Trigger?
Don’t build
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
69 Rarelydoesrentmakeupatriggeronitsownforrealestate,vacancyisimportantfactor
also.AddingvacancyasanothertriggerissimplewithathirdnestedIFstatement.Notice
thatthedecisionistoonlybuildifthevacancyratefallsbelowthetrigger.Thelogiccanbe
followedbythetreebelow:
Has construction already begun?
Don’t build
Don’t build
Is Vacancy > Trigger?
Build 170k sf
Is Rent > Trigger?
Don’t build
IF(SUM(previousyearssf)>0,0,IF(Vac>Trigger,0,IF(Rent>Trigger,170000,0))
IFstatementsbecomemessyveryquickly,butwithgoodorganizationandpatience,even
themostthecomplexdecisionrulesinRealOptionscanbemodeled.Oncethereis
confidencethattheadditional170,000squarefeetisconstructedwhenthedecisionrules
aresatisfied,theparameterscanbetiedintotherestoftheproformatoeventually
calculatedowntotheNPV.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
70 ChallengeCo Parameters
Total Development Cost
Efficiency
Gross Floor Area (Addition Incl)
Option Exercise Trigger: Rent
Option Exercise Trigger: Vacancy
Flex Development Cost
Office Rent
Rent Growth Rate
Expenses
Expense Growth Rate
Vacancy
Capital Expenditures
Terminal Cap Rate
OCC/Discount Rate
ChallengeCo Flexibility
(in 000's)
Potential Gross Income
Vacancy
Effective Gross Income
Year 0
1
2
3
4
$100 /gsf
90%
170,000 sf
0.00
0.00
0.00
0.00
$35 /sf
5.00%
$105 /gsf $ 108.15 $ 111.67 $ 117.06 $ 119.86
$30 /sf $ 30.90 $ 31.91 $ 33.45 $ 34.24
3%
3.26%
4.82%
2.39%
7.27%
$15 /sf $ 15.45 $ 15.71 $ 15.41 $ 15.29
3%
1.69%
‐1.92%
‐0.76%
‐3.59%
10%
1.61%
4.01%
4.74%
0.00%
10% of NOI
10.18%
10.23%
10.32%
10.40%
11.00%
10.96%
11.27%
11.85%
12.06%
12.50%
Year
5
6
170,000 sf
0.00
$ 128.57 $ 139.67
$ 36.73 $ 39.91
8.64%
6.85%
$ 14.74 $ 14.91
1.12%
0.74%
0.00%
1.13%
9.53%
8.20%
12.12%
11.56%
1
$4,728
$76
$4,652
2
$4,882
$196
$4,686
3
$5,117
$243
$4,874
4
$5,239
$
$5,239
5
$5,620
$
$5,620
6
$12,212
$138
$12,073
Operating Expenses
$2,364
$2,404
$2,358
$2,340
$2,256
$4,562
Net Operating Income
$2,288
$2,282
$2,517
$2,900
$3,364
$7,511 ApplyingthesameMonteCarloSimulationasinModerateCoTower,theimpactoftheReal
OptionisevidenttheCDFiscomparedtotheCDFsofmodelswithoutflexibilitybuiltin.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
71 Whencomparedtoanotherwiseidentical10floorofficertower,ChallengeCoTowerwitha
RealOptionofbuildinganadditional10floorsinthefutureisslightlyworseoffwhen
economicconditionsturnouttobepoor.Theflexibleofficetower’sCDFisslightlyshifted
totheleftofthe10floorofficetower’sCDFbecauseoftheslightlyhigherconstructioncosts
wemodeledinforflexibility($105/sfvs$100/sf).Ontheotherhand,ifeconomic
conditionsturnoutexcellent,theflexibleChallengeCoTowerdominatesthe10flooroffice
towerbecausetherealoptiontoexpandisexercisedandallowstheflexiblebuildingtotake
advantageoffavorableconditions.
NowcontrasttheflexibleChallengeCoTowerwiththe20floornon‐flexiblebuilding.The
20floorbuildingisexposedtomuchmoreriskastheupsideisgood,butthedownsideis
absolutelydisastrous.Thishighlevelofriskinthe20floorofficebuildingoccursbecause
ofthehighoperationleveragecreatedfromthelargeconstructioncost.
ThereisnostandardwayofmodelingRealOptionsintoyourfinancialmodel.Thelevelof
complexityisonlylimitedbythecreativityandpatienceoftheanalystcreatingthepro
forma.ArmedwithknowledgeofahandfuloffunctionsinExcel,anyrealestate
professionalcaneasilymodeluncertaintyandrealoptionsintoproformastoprovide
valuableinsightsfortheirmulti‐milliondollarprojects.
Asillustratedinthisexample,incorporatingdesignand/orfinancialflexibilityintoreal
estateinvestmentscanhaveasignificantimpactinnotonlyExpectedNetPresentValue,
butriskprofilesaswell.Understandingtheeffectsofundercertaintyonrealestate
venturescanleadatremendouscompetitiveadvantage.
BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures
72