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BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures

by

KeithChin‐KeeLeung

BachelorofCommerce,SauderSchoolofBusinessUniversityofBritishColumbia,2007

SubmittedtothePrograminRealEstateDevelopmentin

ConjunctionwiththeCenterforRealEstateinPartialFulfillmentoftheRequirementsfortheDegreeof

MasterofScienceinRealEstateDevelopment

atthe

MASSACHUSETTSINSTITUTEOFTECHNOLOGY

February2014©2014MassachusettsInstituteofTechnology.Allrightsreserved.

SignatureofAuthor__________________________________________________________________________________

MITCenterforRealEstateJanuary30,2014

Certifiedby___________________________________________________________________________________________

RicharddeNeufville,PhDProfessorofEngineeringSystemsandofCivilandEnvironmentalEngineeringThesisCo‐Supervisor

Certifiedby___________________________________________________________________________________________

DavidGeltner,PhDProfessorofRealEstateFinanceandofEngineeringSystemsDirectorofResearch,CenterforRealEstateThesisCo‐Supervisor

Acceptedby___________________________________________________________________________________________

DavidGeltner,PhDChairman,InterdepartmentalDegreePrograminRealEstateDevelopment

BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures 2

BeyondDCFAnalysisinRealEstateFinancialModeling:ProbabilisticEvaluationofRealEstateVentures

by

KeithChin‐KeeLeung

SubmittedtothePrograminRealEstateDevelopmentinConjunctionwiththeCenterforRealEstate

onJanuary30,2014inPartialFulfillmentoftheRequirementsfortheDegreeofMasterofSciencein

RealEstateDevelopment

ABSTRACTThisthesisintroducesprobabilisticvaluationtechniquesandencouragestheirusageintherealestateindustry.Includinguncertaintyandrealoptionsintorealestatefinancialmodelsisworthwhile,especiallywhenthereisanelevatedlevelofunpredictabilitysurroundingtheinvestmentdecision.

Incorporatinguncertaintyintorealestateproformasnotonlyprovidesdifferentresultsoverdeterministicmodels,itchangestheangleofattacktorealestatevaluationproblems.Whenuncertaintyistakenintoaccount,thefocusshiftsfromsimplymaximizingfinancialreturns,tomodelingandmanaginguncertaintytomakebetterexantefinanceanddesigndecisions.Theabilitytoaddoptionalityinprobabilisticfinancialmodelingcanenhancereturnsbycurtailinglossesduringdownturnsandtakingadvantageofupsideconditions.

Astep‐by‐stepexampleiscarefullycraftedtodemonstratethesimplicitywithwhichuncertainty,MonteCarloSimulationsandRealOptionsmaybeincludedintorealestateproformas.TheexampleisentirelyExcelbasedandisseparatedintothreepartswitheachprogressivelyincreasingincomplexity.SimpleCoTowerestablishesthefamiliarDiscountedCashFlowproformaasastartingpoint.ModerateCoTowerdescribeshowuncertaintyandMonteCarlosimulationscanbeincorporatedintoaproformawhileillustratingtheeffectofnon‐linearityonfinancialmodels.ChallengeCoTowerrevealshowrealoptionscanaddvaluetoaninvestmentandhowitshouldnotbeoverlooked.

Thecasestudyillustrateshowthetechniquesoutlinedinthisthesiscanaddsignificantvaluetorealestatedecisionswithoutmuchaddedeffortorinvestmentinexpensivesoftware.Thecasestudyalsoshowshowtheuseofrealworlddatatomodeluncertaintycanbeputintopractice.

ThesisCo‐Supervisor: RicharddeNeufville,PhDTitle: ProfessorofEngineeringSystemsandCivilandofEnvironmentalEngineeringThesisCo‐Supervisor: DavidGeltner,PhDTitle: ProfessorofRealEstateFinanceandofEngineeringSystems

DirectorofResearch,CenterforRealEstate


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


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


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


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.


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

(Marshall&Kennedy,1992).Thebenefitsof

probabilisticvaluationtechniquesforreal

estatehavebeenwidelydocumentedsince

theearly1990’s(Baroni,Barthélémy,&

Mokrane,2006;Farragher&Savage,2008;

Louargand,1992).Yet,therealestate

industrystillreliesonsensitivityanalysesfortheirriskassessmentofrealestate

investments.FarragherandSavage’s2005surveyof32intuitionalinvestorsand156

developersshowedthatonly2%ofthesefirmsutilizeMonteCarloSimulationtechniques.

Themessagefromacademiaisnotgettingthroughtoindustry.Therejectionof

probabilistictechniquesbyrealestateprofessionalsisdue,inlargepart,totheinabilityof

academicstopresentacompellingargumentforprobabilisticfinancialmodeling.Academic

KeyTerms:StochasticvsDeterministic

Astochasticorprobabilisticmodelreliesonprobabilitytoobtainitsvaluesforfuturestatesofthesystem.

Adeterministicmodelhasnorandomnessinvolvedingeneratingitsfutureoutputvalues.


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.


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


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


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.


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.


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.


CHAPTER2:SimpleCoTower–ADeterministicExample

Thefirstexample,SimpleCoTower,isa

simplifieddiscountedcashflowproformaof

thekindanalyststypicallyusetofinancially

modelcommercialrealestatetransactions.

SimpleCoTowerisa10storyofficetowerwith

afloorplateof17,000sf.Afinancialmodelis

createdtoevaluatethepurchaseofthe

buildingforapriceof$17million.Thereare

threemajorsectionstoaproforma:the

assumptions,thecashflowprojections,andtheoutputs.

2.1 AssumptionsofaDeterministicModel

Theassumptionsareasetofparameterswith

whichthefinancialmodelmostabideby.

Someassumptionsarephysical(suchasfloor

areaandefficiency),whileothersare

economic(suchasrentanddiscountrate.)

Estimatingtheassumptionsaccuratelyis

importantbecausetheydriveallnumbersin

theproforma.

2.2 ProjectingCashFlowsforSimpleCoTower

Thecashflowprojectionsectionofthepro

formaprojectsmanylineitemseveralyears

intothefuture.Variablesintheformulasareoftenlinkedorreferencedtotheassumptions

onthispage.Thecashflowprojectionorganizestherevenuesandcostsassociatedwitha

particularpropertyandcalculatesthenetcashinflows/outflowsforeachyearofproperty

ownership.InSimpleCoTower,thePropertybeforeTaxCashFlow(PBTCF)iscalculated

withouttheeffectsofincometaxorleverage.

Figure1:SimpleCoTowerSketchAvisualrepresentationofthe10‐storyofficetower,SimpleCoTower.

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%

SimpleCo Tower Assumptions

Figure2:SimpleCoTowerAssumptionsThischartcanbeviewedintheSimpleCoExcelfileontheCD.


2.3 ReturnMeasures:NPVandIRR

TheoutputsectionofaDCFproformacalculatestheobjectivereturnmeasures.Inthe

worldoffinance,noreturnmeasureisasprevalentasNetPresentValue(NPV),orits

siblingtheInternalRateofReturn(IRR).

ForSimpleCoTower,ourNPVata12.5%

discountrateis‐$135,000andtheIRRis

12.37%.

SimpleCoTowerisadeterministicmodel.

Foreachuniquesetofassumptionsthereis

onesoleoutcome.Theoutput(NPVinthis

case)isdeterminedbytheinput

assumptionstotheexactcent.Thereisno

uncertaintyinthemodelbecauseasetof

assumptionsalwaysleadtoasoleoutput

returnmeasure.Pressingthe“F9”key

recalculatesformulasinExcel,butdoingsowillneverchangetheNPVintheSimpleCo

Towerproforma.

(in 000's) Year 1 2 3 4 5 6 7 8 9 10 11

Potential Gross Income $4,590 $4,728 $4,870 $5,016 $5,166 $5,321 $5,481 $5,645 $5,814 $5,989 $6,169

Vacancy $230 $236 $243 $251 $258 $266 $274 $282 $291 $299 $308

Effective Gross Income $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 $186 $192 $198 $204 $210 $216 $223 $229 $236

CF From Operations $1,629 $1,678 $1,729 $1,781 $1,834 $1,889 $1,946 $2,004 $2,064 $2,126

Reversion (Purchase and Sale) ‐$17,000 $22,120

PBTCF ‐$17,000 $1,629 $1,678 $1,729 $1,781 $1,834 $1,889 $1,946 $2,004 $2,064 $24,246

Figure3:SimpleCoTowerProFormaThecashflowprojectionsareshownforSimpleCoTower.ThischartcanbeviewedintheSimpleCoExcelfileontheCD.

NetPresentValueandIRR

Thetimevalueofmoneyprincipleisthemostfundamentalinfinance.Cashflowtodayisworthmorethancashflowinthefuturebecauseofinterestearningpotential.FuturecashflowsarediscountedtoarriveatanequivalentvaluetodaycalledthePresentValue(PV).

NetPresentValueisthesumofthePVsofallfuturecashinflowsandoutflowsofaproject.

TheInternalRateofReturn(IRR)isthediscountratewhichmakesNPVequal0.


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

oftheassumptions,therentgrowthrate.

EverythingelseaboutModerateCoisthesame

asSimpleCo.

3.1 UncertaintyintheRentGrowthRateofModerateCoTower

TheSimpleCoTowerexampleassumedthattherentgrowthratewas3%peryear.Based

ontheaveragingofhistoricrentgrowthrates,3%isacommonassumptionamongreal

estateprofessionals.Whentherentgrowthrateissubjecttouncertainty,itis

acknowledgedthatthetruerentgrowthrateisunknownandvarieswithinarange.Excel’s

randomnumberfunctionisusedtosimulateuncertainbehavior.AppendixAgoesthrough

step‐by‐stephowuncertaintywasbuiltintotheModerateCoTowerfinancialmodel.

Figure4:ModerateCoTowerSketchAvisualrepresentationofModerateCoTower,a10‐storyofficetowerthatisphysicallyidenticaltoSimpleCoTower.


InModerateCo,the

uncertaintyiscreated

asasymmetrical

Normaldistribution

aroundamean.Using

3%asthemeanforthe

rentgrowthrate,there

shouldbeanequal

chanceforthegrowth

ratetoappearaboveor

below3%.

3.2 MonteCarloSimulationsandExpectedNPV

Oncethefinancialmodelhasinput

assumptionsthatrandomlychange,the

correspondingoutputNPVscanbe

recordedmanytimesusingaDataTablein

Excel.Theprocessofrunningamodelfora

specifiednumberofiterationsissimply

calledaMonteCarloSimulation.TheNPV

willvaryfromsimulationtosimulation

becausetheinputvariablesarealways

changing.InthecaseofModerateCo,the

inputvariable,RentGrowthRate,changes.

Alsoknownasa‘GaussianDistribution’,arandomvariableis‘normalized’accordingtothisdistribution.TheRANDfunctioninExcelfetchesarandomnumberbetween0and1andiscentralizedtowardsthemean.Forexample,ifthenumbercomesouttobe.159,itwillbeplaced‐1standarddeviationfromthemean.68%ofvalues(.159to.841)willfallwithin1standarddeviationofthemean.

Figure5:NormalDistributionCurveUsedtoModelRentGrowth

MonteCarlo:What’sinaname?

AsafavoritehangoutofIanFleming’sfictionalcharacterJamesBond,MonteCarloisoftenassociatedwithluxurious,mysteriousandexoticliving.Perhaps,MonteCarloSimulationssoundmoreforeignthentheyactuallyare.

“MonteCarlo”Simulationjustreferstoasimulationwherethenumberofiterationsaresetbytheuser.Forexample,werun5,000iterationsforModerateCoTower,notonemorenoroneless.


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.

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‐

Figure6:ResultsfromtheMonteCarloSimulationENPVversusDeterministicNPV

Interestingresult!ThesimulatedENPVisanexpectedNPVbecauseitisjustanaverageofalltheresultsinaMonteCarloSimulation.Inthiscase,ModerateCo’sNPVwasrecorded5,000timesandaveragedtogetanaverageof$375,575.ThedeterministicNPVistakendirectlyfromtheSimpleCoproforma.ThisresultcanbeviewedintheModerateCoExcelfile.


but‐mistakenassumptionthatevaluatingaprojectaroundaverageconditionsgivea

correctresult.

ThesimplemathbehindtheFlawofAveragesconceptisbasedonJensen’sInequality.In

1906,DanishmathematicianJohanJensenprovedthat:

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.

Jensen’sInequality

Theaverageofallthepossibleoutcomesassociatedwithuncertainparametersisgenerallynotequaltothevalueobtainedfromusingtheaveragevalueoftheparameters.


TheFlawofAveragehasasignificantimpactonNPVandcouldspellthedifferencebetween

winningabidandlosingabid,asexemplifiedbytheSimpleCoandModerateCo

comparison.

3.4 ADifferentApproachtoRealEstateFinancialAnalysis:DistributionsandRiskProfiles

Incorporatinguncertaintyintorealestateproformasnotonlygivesadifferentresultover

deterministicmodels(aspertheFlawofAverages),itchangestheapproachtorealestate

valuationproblems.InthedeterministicSimpleCoTowercase,thestrategyistolockina

setofexanteassumptionsbasedontheanalyst’sbestforecast,findthesinglebestvalue

andhopeforthebest.Whenuncertaintyisfactoredintotheanalysis,thefocusshiftsto

modelingandmanagingtheuncertaintytomakebetterfinanceanddesigndecisionstoday.

ThesinglebestexpectedvalueofNPVisnolongerthesoleobjectiveinastochasticmodel:

rangeanddistributionofoutcomesbecomerelevant.

Let’ssaythatwehavetwoiterationsofthemodel.Inoneiteration,therentgrowthrateis2%,andtheotheris4%.LeadingtoaNPVresultsetof‐2,528and2,440.Ifweaveragethesetwovalues,weget‐44whichishigherthantheresultwewouldgetat3%of‐$135!Thedifferencebecomesgreaterandgreaterasvaluesfurtherfromthemeanareused.ThissensitivityanalysisoftherentgrowthratecanbefoundundertheSimpleCoproforma,intheSimpleCoExcelfile.

Figure7:Non‐linearityintheRentGrowthRate


Introducingarealisticlevelofrandomnessintofinancialmodelschangestheframingofthe

valuationproblem.Understandingthelikelihoodoflosingorprofitingbecomeimportant

onceweintroduceuncertaintyintotheanalysis.Thecumulativedistributionfunction

(CDF)ofModerateCoprovidesinformationontheprobabilityoflossorprofitscenarios.

ModerateCohasabouta50%probabilityofhavingnegativeNPVanda50%probabilityof

ahavingapositiveNPV.Thedownsideprobabilityismorelimitedthantheupside

probability,asillustratedbythelongtailtowardstheright(morepositiveNPVs).

Thisscenarioisatypicalobservationforrealestateprojects.Ideally,ananalystwillwantto

managetheuncertaintybyfindingwaystolimitthedownsidelossesandaccentuatethe

upsideprofits.

OtherusefulmeasuresthatcomeoutofthisanalysisofdistributionsincludeValueatRisk

andValueatGain.ValueatRiskdenoteshowmuchlosscouldoccurataspecified

probabilityoveratimeframe.IntheModerateCoexample,theValueatRisk(V10number)

OntheCDF,thelikelihoodofNPVoutcomesisdisplayedaswellastheNPVforthedeterministicSimpleCoTowerandtheprobabilisticexpectedNPVforModerateCoTower.ThischartanditscorrespondingMonteCarloSimulationisincludedintheModerateCoExcelfile,onthe‘ModerateCoDistribution”tab.

Figure8:ModerateCoTowerCumulativeDistributionFunction


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.


TheadditionalvariabilitytranslatesintogreatervolatilityintheresultsoftheMonteCarlo

simulationandamplifieseffectoftheFlawofAverages.

ThestrongeffectoftheFlawofAveragesandRandomWalkvolatilityshouldbeenough

motivetostartmodelingrealestateusingprobabilistictechniques.Thethesiscontinuesto

makethecaseforstochasticvaluationofrealestateinChallengeCoTowerbyusingReal

Options.

Avisualrepresentationofayear‐to‐yearrandomwalkevolutionoftherentgrowthrate.Thisbehaviorcanbeexhibitedbymanydifferentvariables.

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

6%

5% up 2% x

4% x

3% x x

2% x dn 2%

1%

0% x

dn 1%

dn 2%

up 1%

Random Walk Illustration for Rent Growth Rate Starting at 3%

Figure9:RandomWalkIllustration

Results ENPV St. Dev.

ModerateCo $192,043 $4,920,803

ModerateCo w/ Random Walk $1,042,254 $9,240,832

SimpleCo Deterministic NPV ($134,701)

Figure10:ComparisonofReturnsbetweenModerateCoandSimpleCoRandom‐walkbehavioraddsgreatervolatilitytothemodelwhichinflatestheeffectoftheFlawofAveragesevenfurther.TheMonteCarloSimulationsandresultscanbeviewedintheModerateCoExcelfile.


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


effectsoftheoptionontheNPVincomparisonwithanidenticaldevelopmentwithoutthe

option.AppendixD,discussestheuseof“ifstatements”tomodelrealoptionsingreater

detail.

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.

Figure11:ThreeChallengeCoTowerOptions

ThebuildingontheleftrepresentstheInflexibleChallengeCoprojectat10floors.ItisphysicallyidenticaltoModerateCoandSimpleCoTowers.Inthemiddleshowsaflexibledesignwhereanadditional10floorscanbebuiltontopofthefirstphaseof10floors.Ontherightistheinflexible20floorChallengeCoTower.


Ifeconomicconditionsturnsourinthenext10years,theoptiontoexpandisnotexercised

andthedistributionfunctionoftheflexiblealternative“hugs”the10floorinflexibleoption.

Inpooreconomictimes,theflexibleoptionwillnotperformaswellasthe10floor

inflexibledevelopmentbecausesomeextraconstructioncostsare“sunk”intotheinitial

constructioncostoftheflexiblealternative(forexample,constructingstrongercolumnsto

taketheloadofapossible10flooraddition).Ontheotherhand,theflexiblealternative

performsmuchbetterthanthe20floorinflexibledevelopmentduringapooreconomy.

Wheneconomicconditionsaregood,theflexiblealternativetakesadvantageoftheupside

byexercisingitsoptiontobuildmorespace.Thisisillustratedwhenthe10floorinflexible

alternativeiscomparedwiththeflexibleoptionabovethe$5millionNPVmark.The

Figure12:ChallengeCoTowerExpectedNPVs

TheCDFshowshowtheflexibledesign(inred)usestherealoptiontotakeadvantageofupsideconditions.Atthelowend,theflexibledesigndoesnotexerciseitsoptiontoexpand,soitsCDFcurvecloselyfollowsthecurveofthe10floorinflexibledesign.Ifeconomicconditionsaregood,theflexibledesignbeginstodeviatefromthe10floorinflexibledesignbyexercisingitsoptiontoexpandandfollowsclosertothe20floorinflexibledesigncurvetotakeadvantageofthegoodeconomy.TheMonteCarloSimulationsandCDFscanbefoundintheChallengeCoTowerExcelfile.


flexiblealternativewilldeviatefromthe10floorinflexiblealternativeandcapitalizeonthe

opportunityofgreatmarketconditions.

TheexpectedNPVoftheflexiblealternativeisthegreatestamongthethreealternativesfor

ChallengeCoTower.Forinvestorsseekingtolimittheirdownsideexposure,whiletaking

advantageoftheupsideasmuchaspossible,flexibilitycanbeamajorwin.Flexibilityin

designshouldnotbeoverlookedwhenmakinginvestmentdecisions.


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.


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.


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


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.


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


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).


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.


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


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.


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.


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.


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.


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


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


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


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.


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.

Notsurprisingly,Timonis

veryconcernedaboutthe

futureoftheofficemarketin

Manhattan.Inanefforttoput

Figure13:WorldTradeCenterSitePlan(PANYNJ,2013)

TwoWorldTradeCentersitsonthemostNorthEasternparcelinthesite.OneWTC,3WTC,and4WTCareallofficetowers.


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.

MichaelCassioknowsthatthiswillbea

verycompetitivebidforarareworld‐

classproperty.Thedollarsatstakearemuchhigherwithalandmarkskyscraperinthe

world’smostprominentfinancialcenter.Theslightestmiscalculationontheproformacan

Arenderingof2WTCasviewedfromthe9/11Memorial.

Figure14:2WTCRendering(PANYNNJ,2013)


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.


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


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:

2sin

21

Where: Maximumamplitudein%

Numberofyearssincestartyear,withstartyear=0

CycleStartingPosition(yearsafterupwardmid‐point)

Durationofonefullcyclesinyears

The+1attheendofthefunctionshiftstheentiresinecoveruptohaveamid‐pointof1

insteadof0.


Foramplitude,

Michaeldoesaquick

analysisofNYCoffice

rentsbetween1988

and2011.First,he

convertsthenominal

rentstorealrents,

thenheobservesthe

differencebetween

lowestandhighest

valueswiththetotal

changefrompeakto

troughobservedtobe

closeto40%.Lastly,

MichaellooksattheMoody’s/RCACPPITBItoseewheretherealestateenvironmentisin

thecycle.Itseemslikeitshouldbearoundhalfwayontothepeakin2013,butMichael

decidestoretardthecycleintheanalysisabitbecauseeconomicrecoveryhasbeenslower

thanusual.

Withallthe

parametersaccounted

for,theSinewaveis

convertedtoafactor

withthecurrentyear

asafactorof1.

Thepeak‐to‐peakandtrough‐to‐troughdurationisbetween15and20years(Geltner,2013).

Figure15:RealEstateCycleLength

Figure16:TheRegularSineCurve

Whennottransformed,thesinecurvehasacycledurationof2πandanamplitudeof1.Thecycle’sy‐interceptis0.


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


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

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

Thebuildingontheleftisamodelofa30floorinflexibledesign.Themiddlebuildingrepresentsaflexibledesignoptionwhilethebuildingontherightistheinflexible60floorofficetowerdesign.

Figure17:2WTCSketchupofAlternatives


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.


TheNPVforeachyeariseasytocalculateusingprojectcapratesandconstructioncosts.

MichaelusesanIFstatementtoactasaswitchtosignifyifconstructionbeginsonthe

additionornot.Sincetheadditioncanonlytakeplaceonce,anotherIFstatementisusedto

ensurethatnoadditionhasstartedpreviouslybeforebeginningconstructioninthatyear.

Theotherpiecethatneedstobedefinedforarealoptionistheconsequence.Inthiscase,

whathappensisthatanextra1.3millionsquarefeetisaddedtwoyears(toaccountfor

construction)aftertheyearoftheconstructiontrigger.Newleaseshavetokickin,anda

10%constructioncostpremiumisaddedtotheconstructioncost.TheNPVisthen

calculatedthesamewayastheinflexibleproformas.

7.6 Results

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

Inflex 30 Flex 30 Flex 40 Flex 50 Inflex 60

($191) $14 $9 $4 $14

($251) ($145) ($137) ($128) ($95)

($300) ($500) ($500) ($300) ($300)

$371 $710 $714 $719 $731

Value 5% ($686) ($792) ($847) ($901) ($962)

At 10% ($604) ($708) ($742) ($770) ($808)

Risk 25% ($455) ($543) ($535) ($527) ($502)

Median 50% ($251) ($145) ($137) ($128) ($95)

Value 75% $7 $400 $397 $388 $414

At 90% $295 $979 $963 $948 $977

Gain 95% $509 $1,383 $1,372 $1,349 $1,380

Percentiles

in Millions

Expected NPV

Median

Mode

Std Deviation

Theflexible30floordesignandtheinflexible60floordesignoutperformtheotherbuildings.Notethattheflexible30floordesignhasthelowestpotentiallosses,yetmaintainsgoodgainswhentheeconomyisgood.

Figure18:2WTCFinancialModelResults


behavelikethe60floorinflexibleprojectatthehigherend.Theflexible30flooroptionis

definitelythemostpreferableoption.

Iftherewasno

constructioncost

premium,the

flexible30floor

optionactuallyout

performsevenat

thetopendinthe

sameenvironmental

conditionsasthe

inflexible60floor

option.Duringthese

conditions,thereal

optionisalmost

alwaysexercised

rightawayinthefirstyearpossible,2017.Despitetakinganextrayeartoconstruct60

floors,theflexibleoptioncomesonoutabovetheinflexibleoptionbecauseofthelease

timings.Theeconomyreachesthepeakofthecyclein2019,rightwhentheleasesfromthe

newadditioncomeonline,whilealloftheleasesoftheinflexibleschemesarestuckat

lowerratessigned2yearspreviously.Thosepoorperformingleaseswillalsoberenewed

atanotherlowpointinthecycle10yearsafterwardsinthelowestpointoftherealestate

cycle.

Whiletheflexible30floormodeloutperformstheotherschemes,itdoessounderspecific

conditionsmodeledbytheAnalyst.Regardless,Michaelisconvincedthatrealoption

analysiswillhelpArdenForestwinthebid,armingthecompanywithknowledgeof

distributionswillhelpthecompanyfocusonmanaginguncertaintyratherthanrelyingon

guessworkandgutfeelingsindeterministicfinancialmodelingofRealEstate.

Figure19:2WTCDistributionFunctionTheflexible30floordesign’sCDFperformsliketheinflexible60floordesign,exceptatthelowendofNPVswherethedownsideisminimized.


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.


Tohelptranslatetheoryintopractice,amodernexampleof2WorldTradeCenterwas

presented.Forsimplicity,onlyoneoutofavarietyofoptionswasemployedintheanalysis,

butthepowerofrealoptionsinrealestatewasclearlyondisplay.Whileitisnota

guaranteethatrealoptionsinarealestateventurewillincreasevaluemonetarily,theactof

analyzingrealoptionsisavaluableoptioninitsownrightforrealestatewhereirreversible

investmentdecisionsaremadefrequently.

Perhapsthegreatestadvantageofunderstandingtheseconceptsisthechangeinmindset

whenitcomestoapproachingrealestateproblems.Anewgrandavenueisopenedup

whenuncertaintybecomespartoftheanalysis.Thereareendlesspossibilitieswithreal

optionanalysesandcreativeproblemsolverswillbethegreatestbenefactors.


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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.


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) Year 1 2 3 4 5 6 7 8 9 10 11

Potential Gross Revenue $4,590 $4,783 $4,985 $5,195 $5,414 $5,642 $5,880 $6,128 $6,386 $6,656 $6,936

Vacancy $230 $239 $249 $260 $271 $282 $294 $306 $319 $333 $347

Effective Gross Revenue $4,361 $4,544 $4,736 $4,935 $5,144 $5,360 $5,586 $5,822 $6,067 $6,323 $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

Capital Expenditures $181 $192 $203 $215 $227 $240 $254 $269 $284 $300

CF From Operations $1,629 $1,726 $1,828 $1,934 $2,046 $2,164 $2,287 $2,417 $2,553 $2,696

Reversion (Purchase and Sale) ‐$17,000 $28,749

PBTCF ‐$17,000 $1,629 $1,726 $1,828 $1,934 $2,046 $2,164 $2,287 $2,417 $2,553 $31,445

NPV $3,019


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.


Inthissimplisticexample,weran10simulations.Thenumberofsimulationswhichcanbe

ranisonlylimitedbytheprocessingpowerofcomputers.


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.


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.


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 Year 0 1 2 3

Total Development Cost $100 /gsf

Efficiency 90%

Gross Floor Area (Addition Incl) 170,000 sf 0.00 0.00 0.00

Option Exercise Trigger: Rent $35 /sf

Flex Development Cost $105 /gsf 108.15$ 110.30$ 111.37$

Office Rent $30 /sf 30.90$ 31.51$ 31.82$

Rent Growth Rate 3% 1.99% 0.97% 0.79%

Expenses $15 /sf 15.45$ 16.00$ 16.59$

Expense Growth Rate 3% 3.56% 3.70% 7.11%

Vacancy 10% 19.38% 15.20% 26.38%

Capital Expenditures 10% of NOI 10.16% 10.84% 10.97%

Terminal Cap Rate 11.00% 11.18% 11.84% 11.57%



InChallengeCo,theinputassumptionsaregivenahealthydoseofrandomwalk,plustwo

newassumptionsappear:totaldevelopmentcostandflexdevelopmentcosts.Total

developmentcostwillbetheinitialhardandsoftcostsofconstructingtheofficebuilding.

Theflexdevelopmentcostrepresentsthecosttoconstructanaddition,inflatedbythe

samerateastherentgrowthrate.Theoptionexercisetriggercannotbemissedwithathick

redborder.

Thegoalhereistomodeltheconstructionofanadditional10floorssometimeinthefuture

whentheeconomyimproves.Inthiscase,therentisinitially$30persquarefoot,sothe

optionshouldbeexercisedwhentherentrisesup.Letusseewhathappensifwetrigger

constructionoftheadditional10floorswhentherentsreach$35persquarefoot.

Inthe6thyearoftheproforma,therentclimbsabove$35persquareandimmediately,an

additional170,000squarefeet(10floors)isaddedthroughbyusingIFstatements.TheIF

statementisusedasaswitchbetweenadding170,000squarefeetandnotaddingmore

floorarea.

Atitscore,theIFStatementhasthreeparts.

1)Logicaltest

2)Valueiftrue

3)Valueiffalse

Organizedinthisformat: =IF(logicaltest,valueiftrue,valueiffalse)

ChallengeCo Parameters Year 0 1 2 3 4 5 6


Efficiency 90%

Gross Floor Area (Addition Incl) 170,000 sf 0.00 0.00 0.00 0.00 0.00 170,000 sf


Flex Development Cost $105 /gsf 108.15$ 108.46$ 110.78$ 113.79$ 116.91$ 123.14$

Office Rent $30 /sf 30.90$ 30.99$ 31.65$ 32.51$ 33.40$ 35.18$

Rent Growth Rate 3% 0.29% 2.13% 2.73% 2.74% 5.33% 0.43%

Expenses $15 /sf 15.45$ 16.05$ 16.62$ 17.12$ 17.73$ 18.59$

Expense Growth Rate 3% 3.89% 3.55% 2.97% 3.61% 4.84% 0.86%

Vacancy 10% 4.79% 12.95% 10.16% 9.99% 4.88% 0.00%

Capital Expenditures 10% of NOI 9.85% 9.76% 9.44% 10.04% 9.72% 9.51%

Terminal Cap Rate 11.00% 10.83% 11.31% 11.08% 11.60% 11.92% 11.49%


value if true

logical test

value if false


ThinkoftheIFstatementasa"forkintheroad"withthelogicaltestastheinput.Valueif

trueandvalueiffalseareoutputs.

Thelogicaltestisanequationthattellsthecomputerwhattodowhenitencountersthe

forkintheroad.Verbally,thelogicaltestwillread:“iftherentisgreaterthan$35…”In

excelitwouldbe:“E$8$>B5”withB8beingtherentinthecurrentyearandB5asthe

triggerrent.

‘Valueiftrue’istheoutcomewhichwilloccurwhenthelogicaltestistrue,withthe

oppositebeingtrueforthe“valueiffalse”.

IF(Rent>Trigger,170000,0)

Foreachyearthatthepossibilityexiststoconstructanother170,000sf,anIFstatementis

required.

NewProblem:Incurrentform,theIFstatementswecreatedwillautomaticallyconstruct

anadditional170,000sfwithoutmemoryofwhathappenedinthepreviousyears.Thus,

therecouldbe170,000sfofconstructioneveryyeareventhoughtherealoptionthatis

beingmodeledcanonlyoccuronetime.

Build 170k sf

If Rent > Trigger

Don’t build


Tosolvethis,anIFstatementisnestedinsideanotheronetocreateaswitchwithmore

thantwooutcomes.Herearethecomponents:

1)Logicaltest

2)Valueiftrue

3)Valueiffalse...anotherIFstatement

3a)Valueiftrue

3b)Valueiffalse

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.

Don’t buildHas construction already begun?

Build 170k sf

Don’t build

Is Rent > Trigger?

logical test #1

value if true

value if true #2

value if false #2

logical test #2(value if false)


Rarelydoesrentmakeupatriggeronitsownforrealestate,vacancyisimportantfactor

also.AddingvacancyasanothertriggerissimplewithathirdnestedIFstatement.Notice

thatthedecisionistoonlybuildifthevacancyratefallsbelowthetrigger.Thelogiccanbe

followedbythetreebelow:

IF(SUM(previousyearssf)>0,0,IF(Vac>Trigger,0,IF(Rent>Trigger,170000,0))

IFstatementsbecomemessyveryquickly,butwithgoodorganizationandpatience,even

themostthecomplexdecisionrulesinRealOptionscanbemodeled.Oncethereis

confidencethattheadditional170,000squarefeetisconstructedwhenthedecisionrules

aresatisfied,theparameterscanbetiedintotherestoftheproformatoeventually

calculatedowntotheNPV.

Don’t buildHas construction already begun?

Build 170k sf

Don’t build

Is Vacancy > Trigger?

Don’t build

Is Rent > Trigger?


ApplyingthesameMonteCarloSimulationasinModerateCoTower,theimpactoftheReal

OptionisevidenttheCDFiscomparedtotheCDFsofmodelswithoutflexibilitybuiltin.

ChallengeCo Parameters Year 0 1 2 3 4 5 6


Efficiency 90%

Gross Floor Area (Addition Incl) 170,000 sf 0.00 0.00 0.00 0.00 170,000 sf 0.00


Option Exercise Trigger: Vacancy 5.00%

Flex Development Cost $105 /gsf 108.15$ 111.67$ 117.06$ 119.86$ 128.57$ 139.67$

Office Rent $30 /sf 30.90$ 31.91$ 33.45$ 34.24$ 36.73$ 39.91$

Rent Growth Rate 3% 3.26% 4.82% 2.39% 7.27% 8.64% 6.85%

Expenses $15 /sf 15.45$ 15.71$ 15.41$ 15.29$ 14.74$ 14.91$

Expense Growth Rate 3% 1.69% ‐1.92% ‐0.76% ‐3.59% 1.12% 0.74%

Vacancy 10% 1.61% 4.01% 4.74% 0.00% 0.00% 1.13%

Capital Expenditures 10% of NOI 10.18% 10.23% 10.32% 10.40% 9.53% 8.20%

Terminal Cap Rate 11.00% 10.96% 11.27% 11.85% 12.06% 12.12% 11.56%


ChallengeCo Flexibility

(in 000's) Year 1 2 3 4 5 6

Potential Gross Income $4,728 $4,882 $5,117 $5,239 $5,620 $12,212

Vacancy $76 $196 $243 $ $ $138

Effective Gross Income $4,652 $4,686 $4,874 $5,239 $5,620 $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


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.