未来能源研究所-清洁能源转型中的运营与资本支出风险（英）

OperationalversusCapital

ExpenditureRiskinaClean

EnergyTransition

BrianC.PrestandJordanWingenroth

Report24-04

March2024

AbouttheAuthors

BrianC.PrestisaneconomistandfellowatResourcesfortheFuture(RFF)

specializingintheeconomicsofclimatechange,energyeconomics,andoiland

gassupply.Prestuseseconomictheoryandeconometricstoimproveenergyand

environmentalpoliciesbyassessingtheirimpactsonsociety.Hisrecentworkincludesimprovingthescientificbasisofthesocialcostofcarbonandeconomicmodelingof

variouspoliciesaroundoilandgassupply.Hisresearchhasbeenpublishedinpeer-

reviewedjournalssuchasNature,theBrookingsPapersonEconomicActivity,the

JournaloftheAssociationofEnvironmentalandResourceEconomists,andtheJournalofEnvironmentalEconomicsandManagement.Hisworkhasalsobeenfeaturedin

popularpressoutletsincludingtheWashingtonPost,theWallStreetJournal,theNewYorkTimes,Reuters,theAssociatedPress,andBarron’s.

JordanWingenrothisaresearchassociateatRFFwithafocusontheSocialCost

ofCarbon(SCC).JordanleadsthecurrentefforttoaddSCCestimatespertainingtobiodiversitylosstotheRFF-BerkeleyGreenhouseGasImpactValueEstimator(GIVE)model,havingformerlycontributedtothedevelopmentofGIVEaswaspublished

inNaturein2022.PriortojoiningRFF,JordanstudiedecologyintheDepartmentofEnvironmentalScience,Policy,andManagementattheUniversityofCalifornia,Berkeley.

Acknowledgements

ThisworkwassupportedbytheNationalRenewableEnergyLaboratory,anational

laboratoryoftheU.S.DepartmentofEnergy,OfficeofEnergyEfficiencyandRenewableEnergy,operatedbytheAllianceforSustainableEnergyLLC.Theauthorswouldlike

tothankPaulDonohoo-Vallett,DanielSteinberg,RyanWiser,andJunShepardfortheirvaluablecommentsandfeedbackonthiswork.Theirinsightsandsuggestionshelpedimprovethequalityandclarityofthemanuscript.

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AboutRFF

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Washington,DC.Itsmissionistoimproveenvironmental,energy,andnaturalresourcedecisionsthroughimpartialeconomicresearchandpolicyengagement.RFFis

committedtobeingthemostwidelytrustedsourceofresearchinsightsandpolicysolutionsleadingtoahealthyenvironmentandathrivingeconomy.

TheviewsexpressedherearethoseoftheindividualauthorsandmaydifferfromthoseofotherRFFexperts,itsofficers,oritsdirectors.

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OperationalversusCapitalExpenditureRiskinaCleanEnergyTransitionii

ResourcesfortheFutureiii

Abstract

Thisreportanalyzesthedifferencesbetweenriskprofilesposedbyfossilassets,suchasnaturalgaspowergenerationandgas-poweredvehicles,andthoseof“green”

alternatives,suchaswindpowerandelectricvehicles.Fossilassetstendtobe

exposedprimarilytouncertaintyinoperationalexpenditures(OPEX)suchasfuel

prices,whereasgreenassetstendtobeexposedprimarilytouncertaintyincapital

expenditures(CAPEX).Thisreportbuildsaquantitativedynamiceconomicmodelofinvestmentunderuncertaintythataccountsforthesedifferentkindsofrisk.The

resultsshowtherelativevalueofsuchCAPEX-exposedgreenassetsoverOPEX-

exposedfossilassetsforreducingexposuretofuturecostuncertainty.Themodel’skeyconclusionsarethat(1)correlatedOPEXriskacrossassetsimpliesthatanall-

greenportfoliohasloweruncertaintythananall-fossiloneevenwhentheassets

themselveshavesimilartotalcostuncertainty,(2)addingagreenassetoptiontoanotherwiseall-fossilinvestmentstrategytypicallyreducescostuncertaintybymore

thanaddingafossiloptiontoanall-greenstrategydoes,and(3)actuallyowningsuchagreenassetalmostuniformlyreducescostuncertaintybyshieldingsociety

(investorsandconsumers)fromOPEXrisk.Theprimarymechanismsdrivingthese

resultsarethreefold:first,aninvestmentinCAPEX-exposedassetsimmediately

resolvessubstantialcostuncertainty,second,spikesinfuelpricesincreaseOPEXforallexistingfossilassetswhereasspikesingreenCAPEXcostsonlyaffectnew

investments,andthird,theavailabilityofmultipleoptionsforfutureassetreplacementdecisionsavoidslockinginexposuretoCAPEXrisk.

OperationalversusCapitalExpenditureRiskinaCleanEnergyTransitioniv

Contents

1.Introduction

1

2.Methods

3

2.1.ModelFormulation

3

2.2.ParameterizingtheModel

5

3.Results

8

3.1.Cost-HarmonizedScenario

8

3.2.VehicleChoiceExample:ICEVversusEV

13

3.3.PowerPlantChoiceExample:NaturalGasversusWind

16

4.Discussion

19

5.Conclusions

20

References

22

AppendixA.EVandICEVModelParameters

24

A.1.DriftandVolatilityParameters

24

A.2.OPEXandCAPEXValues

27

AppendixB.NaturalGasandWindModelParameters

27

B.1.DriftandVolatilityParameters

27

B.2.OPEXandCAPEXValues

29

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1.Introduction

Recentspikesinthepriceofcrudeoilhavehighlightedtheriskstowhichindividualsandtheeconomyareexposedwhenreliantonvehiclesthatrunonpetroleum.Intheelectricitysector,fossilfuel–basedpowerplantsaresimilarlyexposedtoprice

volatility,asdemonstratedbythespikesinrecentyearsinnaturalgasandcoalprices.ThegrowingconnectionofUSnaturalgaspricestoincreasinglyvolatileglobal

marketsmayalsoservetomagnifytheriskexposureofnaturalgaspowergeneration.Manyseecleanenergyinvestments,includingzero-carbonelectricity,batterystorage,andelectricvehicles(EVs),aswaystoreducesuchexposuretounpredictable

commodityprices.Ontheotherhand,acounterargumentisthatthosecleanenergyassetsaremadeusingmineralsthatcanalsoexhibitvolatileprices.Thisraisesthe

question,Willacleanenergytransitionsimplysubstituteonekindofcommoditypriceriskforanother?Weassessthisquestionusingastochasticdynamiceconomicmodeldrawingfromtheeconomicliteratureoninvestmentunderuncertainty(Dixitand

Pindyck1994),concludingthattheanswerisnobecauseclean-energytechnologiesareexposedtoqualitativelydifferentkindsofrisks.

Whilethisconcernaboutcleanenergyriskexposurehassomesurface-level

plausibility,itneglectstorecognizeakeydifferencebetweenthetwokindsofprice

uncertainty.Inparticular,fossilfuelpurchasessuchasnaturalgasforelectricity

generationorgasolineforinternalcombustionengines(ICEs)representoperational

expenses(OPEX).Onceonehasinvestedinsuchalong-livedasset,oneistypically

exposedtoOPEXriskfortheentiretyoftheasset’susefullife.Bycontrast,low-carbon“green”assetslikerenewableandnuclearpowerorEVstypicallyfeaturehighcapitalexpenditures(CAPEX)butminimalOPEX,resultinginlittletonoexposuretovariablefuelcostsovertime.

1

WhilethereremainsuncertaintyinthefutureCAPEX

replacementcostofsuchagreenassetattheendofitsusefullife,oncetheCAPEXissunktoconstructtheproject,itremainsinsulatedfromvariableOPEX.Moreover,theoptiontoswitchtoalternativetechnologiesattheendofanasset’susefullifefurthershieldsinvestorsandconsumersfromfutureuncertaintyinCAPEX.

Inthisreport,wedemonstratethispointquantitativelybydevelopingastochastic

dynamicprogrammingmodelthatrevealsdifferencesinthenatureofriskexposure

associatedwiththesetwotypesofcosts.Forexample,whengasolinepricesspike,theownerofanICEvehicle(ICEV)willimmediatelyseealargelyunavoidablesurgein

operatingcosts.Naturally,EVownersareinsulatedfromthisgasolinepricerisk,buttheyarealsomostlyinsulatedfrompotentialincreasesincriticalminerals.Themostobviousreasonforthisisthatthecostofthosemineralswaslockedinwhenthe

vehiclewasacquired.Themodeldevelopedinthisreportisgeneralenoughto

1Whileoperatingexpendituresentailmorethanjustfuelcosts,otheroperatingand

maintenancecoststendtobesmallerandlessuncertainthancapitalandfuelcosts.See,for

example,EIA(2022).Forthisreason,weconsiderOPEXuncertaintyaseffectivelyrepresentingfuelpriceuncertainty.

OperationalversusCapitalExpenditureRiskinaCleanEnergyTransition

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representchoicesbetweenassetswithOPEX-centricandthosewithCAPEX-centricriskprofiles,butwealsoapplyittotwospecificexamplesofinvestmentchoices,

consideringfirstthechoicebetweengasolineandelectricvehicles,andsecondthechoicebetweennaturalgas–firedandwindelectricity.

Throughoutthisreport,thekeymetricofinterestrepresentingexposuretocost

uncertaintyisthestandarddeviationofthepresentvalue(PV)oflong-rundiscountedexpenditurestobuildandoperatetheportfolioofassets.Wefocusonhowthree

factorsaffectthisstandarddeviation.

First,weconsidertheoverallcostuncertaintyacrossaportfolioofall-fossilorall-

greenassets,whereeachindividualfossilorgreenassetnonethelesshassimilartotalcostuncertainty.Wefindthatanall-fossilportfoliocreatespositivelycorrelatedOPEXrisksacrosstheportfoliobecausespikesinfuelpricesincreaseOPEXforallexistingfossilassetswhereasspikesingreenCAPEXcostsonlyaffectnewinvestments.

Second,weconsiderboththeeffectofaddingthegreeninvestmentoptiontoan

otherwiseall-fossilinvestmentstrategyandtheeffectofaddingthefossilinvestmentoptiontoanotherwiseall-greeninvestmentstrategy.Byintroducingtheoptionto

switchtoalower-costinvestmentwhenitspriceislower,addinganinvestmentoption(whetherfossilorgreen)istypicallyexpectedtoreducecostuncertainty,butthesizeofthiseffectcanvarybetweenthegreenandfossilassets.

Third,weconsidertheadditionaleffectofactuallyhavinganall-greenportfolioata

givenpointintime,ratherthananall-fossilone,conditionalonhavingbothassetsasoptions.Addingeitherassetasanoption,whetherfossilorgreen,generallyreducesuncertaintyinexpendituresforbothassettypes(sincetheoptionneednotbe

exercised),butactuallyhavingthegreenassetinhandfurtherreducesuncertainty

becauseitpurelyreducesexposuretoOPEXrisk,whereasfutureCAPEXriskis

managedbyinvestors’futureoptimizingbehavior.Forthesamereason,switching

fromagreen-dominatedportfoliotoafossil-dominatedonehasthereverseeffectandgenerallyincreasesuncertaintybecauseitpurelyincreasesexposuretoOPEXrisk,

withlittleimplicationforfutureCAPEXrisk.

Inprinciple,theseeffectsdependonthecurrentuncertainCAPEXandOPEXcosts

andtheprobabilitydistributionsoftheirfuturetrajectories.Forexample,ifthefossilasset’sOPEXcostsarecurrentlyhighandareexpectedtoremainhighintothefuture,havingthegreenasset(eithersimplyasanoptionoractuallyheldinone’sportfolio)willsubstantiallyreduceuncertainty,asitoffersawaytoreduceexposureto

persistentlyhighfuelcosts.Bycontrast,ifOPEXcostsarelowandexpectedtoremainlow,thenthegreenasset’saddedvalueissmaller.

Todemonstratethequalitativedifferencebetweenthesetwokindsofassets,westartbyshowingcostuncertaintyatCAPEXandOPEXvaluesthatharmonizethemeans

andstandarddeviationsofthefossilandgreenassets’costs,whilenonethelesslettingthosevaluesvaryovertime.ThisisolatestheconceptuallydistincteffectsofCAPEX

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versusOPEXuncertainty.Theresultsdemonstratethataddingthegreeninvestmentoptiontoanotherwiseall-fossilinvestmentstrategyreducestheuncertaintyinthe

presentvalueofexpenditures,andonaverage,itcausesagreaterreductionthandoesaddingafossiloptiontoanall-greenstrategy.Theresultsalsodemonstratethatthevalueofowningthegreenasset,ratherthansimplyhavingtheoptiontodoso,nearlyuniformlyreducescostuncertaintybyshieldinginvestorsandconsumersfromOPEXriskwithoutnecessarilylockingthemintofutureCAPEXrisk.

WethenuseCAPEXandOPEXcalibrationsbasedonmorerealisticdataabout

uncertainfuturepricesforfossilfuels(gasolineandnaturalgas)andgreen

technologies(EVsandonshorewind).Theprojectionsweusefeatureamodest

upwarddriftinfossilfuelpricesovertimewitharelativelyhighdegreeofvolatility,

whereaswindpowerandEVpricesareprojectedtograduallydeclineandexhibitmorestability(Larsenetal.2023).Thesedifferencesmagnifytheconceptualadvantage

foundforgreentechnologiesinthestylizedmodelwherethecentralcostvaluesare

assumedtobeharmonized.Deployingthemodelwithrecenthistoricaldataonfossilversusgreenenergycostsdemonstratesthecurrentrisk-reducingadvantagesof

greenassets.

Theseconclusionscomewithanumberofcaveats,however.Whilethedynamic

programmingmodelallowsforanuancedtreatmentofdecision-makingunder

uncertainty,itnonethelessrequiressimplifyingassumptionsthatdonotfullyreflectallthecomplexitiesoftherealworld.Forexample,wemodelonlytwotypesof

technologies,fossilandgreen,whentherealsetofassetsismuchricherandmorenuancedthanthat.InSection4,wenoteotherfactorsomittedfromthemodelforsimplicity,suchasnationalsecurityandpoliticalrisksandtheroleofhedging.

2.Methods

2.1.ModelFormulation

TodevelopasimplemodelthatcapturestheCAPEX/OPEXdynamicsdescribedin

Section1,weconsideraninvestormaintainingamixedportfoliowithsomecombinationoffossilandgreenassets,whereeachassetcanbethoughtofasapowerplantora

vehicle.Theinvestormanagesthisportfoliowiththegoalofminimizingtheexpected

presentvalueofoperatingcosts.Theinvestorcanbethoughtofeitherasacompanyorasasocialplannerminimizingthetotalsocialcostsofmaintainingaportfolioofassetsneededtomeetenergyservicedemands.Thusthemodelanditslessonsareapplicablenotonlytoinvestorsbutalsotoconsumersandsocietywritlarge.

EachassethasausefullifeofLyears,wherewefocusonthecaseofL=10years.TheseassetsarecharacterizedbyupfrontCAPEXcostsdenotedkfandkg,tand

annualOPEXcostscf,tandcg.Asindicatedbythesubscripttrepresentingtime,theonlydistinctionbetweenthesetwoassetsisthatforthefossilasset,OPEXcf,tis

OperationalversusCapitalExpenditureRiskinaCleanEnergyTransition

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uncertainandvariesovertime(owingtouncertaintyinoilornaturalgasprices),

whereasforthegreenasset,CAPEXkg,tistheuncertainvariable.Eachcost

parameterisassumedtofollowgeometricBrownianmotionwithdrift,meaningyear-on-yearchangesarenormallydistributedwithknownpercentagedriftparametersμgandμfandpercentagevolatilityparametersσgandσf.

TheinvestormaintainsandoperatesaportfolioofLassetsandthusreplacesone

retiringasseteachyear.

2

TheportfolioofL−1legacyassetsthatarenotretiringisdenotedbythevectorAt={a1,t,…,aL−1,t}withai,t∈{g,f}.Thefirstsubscriptoneachai,treflectseachasset’sremainingusefullife,meaningai,twillretireinperiodt+i.

Thestatespaceisthusdefinedbythegreenasset’scapitalcostkg,tandthefossil

asset’soperatingcostcf,t,aswellastheportfoliooflegacyassetsrepresentedbyAt.Thetimelinefortheinvestor’sdecisionandtheresolutionofuncertaintyisasfollows:inperiodt,theinvestorobservesthecurrentknownvaluesofCAPEXcostskg,t,

OPEXcostscf,t,andtheexistingportfoliooflegacyassetsAt,collectivelyreferredtoasthe“state.”Basedonthisstateandtheknownprobabilitydistributions,theinvestormakesadecisiontobuildeitherthefossilassetorthegreenonetoreplacethe

retiringasset.Oncetheinvestmentdecisionismade,theinvestorimmediatelypaysthecapitalcostkforkg,tforthechosenasset.Forsimplicity,thenewassetbeginsoperatingimmediatelyatannualcostsofcf,tandcgforthefossilandgreenassets,respectively.Wethenmovetoperiodt+1,wherethelegacyassetportfolioAt+1isupdatedbasedonthenewlychosenassetandtheretiringone,

3

andnewvaluesof

kg,t+1andcf,t+1arerealized.Inperiodt+1,theinvestorfacesananalogous

investmentbasedonthenewstate.Theinvestorisassumedtouseadiscountrateofr=10%peryear(DixitandPindyck1994).

WecanwritethisinvestmentproblemintermsoftherecursiveBellmanequation,

denotedV(kg,t,cf,t,At),whichrepresentsthecost-minimizingpresentvalueoftheflowofcurrentandfutureexpenditures:

V(kg,t,cf,t,At)=Nf,tcf,t+Ng,tcg

+min{,[[,,tt|}

2Forsimplicity,wesetthelifeoftheassetinyearsequaltotheportfoliosize,whichitselfis

staggeredinincrementsofoneyear.Thisimpliesthattheinvestorismakingasinglediscretedecisioneachyear:whethertoinvestinafossilorgreenassettoreplacetheretiringassetthatisattheendofitsusefullife.

3Thatis,thevaluesofai,teachshiftleftbyone,representingoneyearofaging,ai,t+1=ai+1,tfori∈{1,…,L−2},andthelastelementofAt,aL−1,t,isreplacedby{f}ifafossilassetischoseninperiodtandby{g}otherwise.

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5

whereNf,tisthenumberoflegacyfossilassetsintheportfolio(Nf,t=

Σi1[ai,t={f}]),andNg,tisthenumberoflegacygreenassets(Nf,t+Ng,t=L−1).Inthisrecursiveform,V(kg,t,cf,t,At)representsthecost-minimizingpresent

valueoftheinfiniteflowofcapitalandoperatingexpenditures.Thefirstrowofthe

Bellmanequationrepresentsthecostofoperatingthelegacyfossilandgreenassetsattoday’sfuelcosts;thisisdictatedbypastchoicesandisunaffectedbytoday’s

investmentdecision.Thetworowsinsidetheminimizationoperatorrepresentthe

costsofchoosingthefossilandgreenassets,respectively.ThefirsttwotermsofeachrowinsidetheminimizationoperatorcorrespondtotheimmediateCAPEXandOPEXexpenditures,whereasthefinaltermrepresentstheconsequencesofthisinvestmentchoicefordiscountedexpectedfutureexpenditures.Thisfinaltermreflectshow

uncertaintyinfutureOPEXdrivesimmediatedecisions.Forexample,evenifcurrentfossilfuelpricesarelowandhenceannualOPEXcf,tislow,uncertaintyintheirfuturevaluesovertheL-yearlifeoftheassetwillaffecttoday’sinvestmentdecisionthroughthisfinalterm.

Weuseatechniquecalled“valuefunctioniteration”(DixitandPindyck1994)tosolvethismodelfortheoptimalchoiceofwhethertoreplacetheretiringassetineach

periodwithanewfossilorgreenone,achoicethatdependsonthecurrentstate:

currentCAPEXandOPEXvalues,theirfutureprobabilitydistributions,andthecurrentportfoliooflegacyassets.Finally,weuseMonteCarlosimulationtocalculatethe

degreeofuncertaintyinfuturecosts,asmeasuredbythestandarddeviationofPV

totalexpenditures.Wesolvethemodelandcomputethisuncertaintymetricunder

threealternativeinvestmentapproaches:theoptimalstrategy,anall-fossilstrategy,andanall-greenstrategy.Thesecondandthirdstrategiesrepresentscenarioswhereonlyoneoptionisassumedtobeavailable;theseserveasbenchmarksagainstwhichwecomparethecost-minimizingstrategy.

2.2.ParameterizingtheModel

BecausethepresentvalueofexpendituresdependsonbothcurrentCAPEXand

OPEXcostvalues,webeginbyfocusingontheirvalueswhenthetwoassetsare

definedinastylizedbutsymmetricfashiontofeaturethesamecentralCAPEXand

OPEXparameters:thatis,kt,g=kfandcg=cf,tatinitialtimet.Theirprobability

distributionsarecalibratedsuchthatthepresentvaluesofcostsoverasinglecycleofL=10yearshavethesameexpectationsandstandarddeviations.

4

Thisharmonizestheoverallaverageandvarianceincostsacrosstheassets(Table1),meaningtheonly

4Specifically,wefirstsetμf=μg=0,meaningnodrift.Becausekg,t=kfandcg=cf,tintheinitialperiod,thiszero-driftassumptionalignsexpectedcosts.Wethenchooseσg=5%andnumericallysolveforthevalueofσfsuchthatitequalizesthevariancesinthepresent

valueoftotalexpendituresofasingleassetpurchasedLyearsintothefuture.Wecomputethepresentvalueofthecostsofafutureassetpurchasetoinduceuncertaintyinkg,t+L.NotethatbecausethefossilOPEXvolatilityparameterappliesonlytoOPEX,whichisasmallerportionoftotalcoststhanCAPEXinthisexample,σfmustbelargerthanσgtoequalizethevarianceintotalexpenditures.

OperationalversusCapitalExpenditureRiskinaCleanEnergyTransition

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differencebetweenthetwoassetsiswhatkindofcostuncertaintytheyareexposed

to—CAPEXorOPEX.Thisthereforeisolatesthedistincteffectsofeachkindofriskexposure.

Table1.ParameterCalibrations

Cost-harmonized

Vehicle

choiceexample

Powerplant

choiceexample

Variable

Fossil

Green

Fossil

Green

Fossil

Green

CAPEXvalue($,kf,kg,t)

$450M

$450M

$31.23k

$39.09k

$297.6M

$464.6M

OPEXvalue($/year,cf,t,cg)

$25M

$25M

$1,141

$746

$21.21M

$0

Drift(%,OPEXforfossil,

CAPEXforgreen,μf,μg)

0%

0%

0.67%

–1.16%

3.66%

–1.76%

Volatility(%,OPEXforfossil,CAPEXforgreen,σf,σg)

12.23%

5%

13.85%

4.80%

14.49%

5.80%

Note:Inallcases,thevaluesreportedforuncertainvariables(e.g.,greenCAPEX)correspondtothecentralinitialvalue.ThefossilOPEXvolatilityinthe“cost-harmonized”columnswascomputednumericallytoalignthemeanandvarianceoftotalexpenditures.

Wealsoconsidertwoexamplesbasedonhistoricaldataofcompetingcleanandfossil-fuelinvestments.ThefirstexamplemodelsachoicebetweenEVsandICEVs.The

secondisapowergenerationexamplewherethefossilassetisrepresentedbya

naturalgaspowerplantandthegreenassetbyonshorewind(Table1).Inbothcases,wecalibratedthemodelusingdatafromthe“RhodiumClimateOutlook”(Larsenetal.2023),whichpresentsestimatesoffuturefossilfuelprices,EVbatterycosts,and

renewableenergycapitalcosts.Theseestimatesareprobabilistic,akeyfeaturethatallowsustoestimatevolatilityparametersforourmodel.ScalingfromthevariablesincludedinthereporttorealisticOPEXandCAPEXrepresentationsalsorequiredtheuseofotherdomain-specificresources.

Fortheexampleofchoosingbetweentwovehicles,weestimatetheparametersofthekg,tandcf,tdistributionsusingprojectedEVbatterycostsin2050(in$/kWh)and

Brentcrudeoilpricesin2030(in$/barrel),aswellasstandarddeviationsthereofandcorrespondingcontemporaneousvalues,alltakenfromthe“RhodiumClimate

Outlook”(Larsenetal.2023;seeAppendixAfordetailsofthiscalculation).

5

Wealsoestimatecorresponding(constant)kfandcgvalues.ICEVprices(kf)andthe

5The“RhodiumClimateOutlook”projectscostsforrenewableenergysourcesin2050andcostsforfossil-fuelenergysourcesin2030.

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