財政學課件chap11講義整理

Chapter11–Cost-BenefitAnalysisPublicFinanceAaronS.Yelowitz-Copyright2003?McGraw-Hill.1Chapter11–Cost-BenefitAnalIntroductionCost-benefitanalysisisasetofpracticalproceduresforguidingpublicexpendituredecisions..2IntroductionCost-benefitanalyPresentValueProjectevaluationusuallyrequirescomparingcostsandbenefitsfromdifferenttimeperiodsDollarsacrosstimeperiodsarenotimmediatelycomparable,becauseofinflationandreturnsinthemarket..3PresentValueProjectevaluatioPresentValue:

PresentDollarsintotheFutureSupposeyouinvest$100todayinthebank...Attheendofyear1,itisworth(1+.05)x$100,or$105Attheendofyear2,itisworth(1+.05)x$105,or$110.25Theinterestcompoundsovertime,thatis,theinterestisalsoearninginterest..4PresentValue:

PresentDollarsPresentValue:

PresentDollarsintotheFutureDefineR=initialinvestmentamountr=rateofreturnoninvestmentT=yearsofinvestmentThefuturevalue(FV)oftheinvestmentis:.5PresentValue:

PresentDollarsPresentValue:

FutureDollarsintothePresentSupposesomeonepromisestopayyou$100oneyearfromnow.Whatisthemaximumamountyoushouldbewillingtopaytodayforsuchapromise?Youareforgoingtheinterestthatyoucouldearnonthemoneythatisbeingloaned..6PresentValue:

FutureDollarsPresentValue:

FutureDollarsintothePresentThepresentvalueofafutureamountofmoneyisthemaximumamountyouwouldbewillingtopaytodayfortherighttoreceivethemoneyinthefuture..7PresentValue:

FutureDollarsPresentValue:

PresentDollarsintotheFutureDefineR=amounttobereceivedinfuturer=rateofreturnoninvestmentT=yearsofinvestmentThepresentvalue(PV)oftheinvestmentis:.8PresentValue:

PresentDollarsPresentValue:

FutureDollarsintothePresentInpreviousequation,risoftenreferredtoasthediscountrate,and(1+r)-Tisthediscountfactor.Finally,considerapromisetopayastreamofmoney,$R0today,$R1oneyearfromnow,andsoon,forTyears..9PresentValue:

FutureDollarsPresentValue:

FutureDollarsintothePresentPresentvalueisanenormouslyimportantconceptA$1,000,000payment20yearsfromnowisonlyworthtoday:$376,889ifr=.05$148,644ifr=.10.10PresentValue:

FutureDollarsPresentValue:

InflationNominalamountsarevaluedaccordingtothelevelofpricesintheyearthereturnoccurs.Realamountsarevaluedaccordingtothelevelofpricesinoneparticularyear.Inflationaffectsboththepayoutstreamandthediscountfactor,andthesetwocanceleachotherout..11PresentValue:

InflationNominaPrivateSectorProjectEvaluationSupposetherearetwoprojects,XandY.Eachentailscertainbenefitsandcosts,denotedasBX,CX,BY,andCY.Needtoask:Istheprojectadmissible?Istheprojectpreferable?.12PrivateSectorProjectEvaluatPrivateSectorProjectEvaluationAdmissible:Arethebenefitsgreaterthanthecosts?Preferable:Arethenetbenefitsthehighest?Mostprojectsinvolveastreamofbenefitsandcostsovertime..13PrivateSectorProjectEvaluatPrivateSectorProjectEvaluationDefine:BenefitsfromprojectiattimetCostsfromprojectiattimetThenthepresentvalueofprojectiis:.14PrivateSectorProjectEvaluatPrivateSectorProjectEvaluationThepresentvaluecriteriaforprojectevaluationarethat:Aprojectisadmissibleonlyifitspresentvalueispositive.Whentwoprojectsaremutuallyexclusive,thepreferredprojectistheonewiththehighestpresentvalue..15PrivateSectorProjectEvaluatPrivateSectorProjectEvaluationTable11.2showstwodifferentprojects(R&DorAdvertising).Thediscountrateplaysakeyroleindecidingwhatprojecttochoose,becausethecashinflowsoccuratdifferenttimes.Thelowerthediscountrate,themorevaluabletheback-loadedproject..16PrivateSectorProjectEvaluatTable11.2.17Table11.2.17PrivateSectorProjectEvaluationSeveralothercriteriaareoftenusedforprojectevaluation,butcangivemisleadinganswersInternalrateofreturnBenefit-costratio.18PrivateSectorProjectEvaluatPrivateSectorProjectEvaluationTheinternalrateofreturn,ρ,isdefinedastheρthatsolvestheequation:TheIRRisthediscountratethatwouldmakethepresentvalueoftheprojectequaltozero.Admissibleifρ>r.Theflawedanalysiswouldchooseanadmissibleprojectwiththehigherinternalrateofreturn,ignoringscale..19PrivateSectorProjectEvaluatPrivateSectorProjectEvaluationThebenefit-costratiodividesthediscountedstreamofbenefitsbythediscountedstreamofcosts.Inthiscase: B=streamofbenefitsandC=streamofcosts:.20PrivateSectorProjectEvaluatPrivateSectorProjectEvaluationAdmissibilityusingthebenefit-costratiorequires:Thisratioisvirtuallyuselessforcomparingacrossadmissibleprojects,however.Ratiocanbemanipulatedbycountingbenefitsas“negativecosts”andvice-versa..21PrivateSectorProjectEvaluatDiscountRateforGovernmentProjectsGovernmentdecisionmakinginvolvespresentvaluecalculations.Costs,benefits,anddiscountratesaresomewhatdifferentfromprivatesector..22DiscountRateforGovernmentPDiscountRateforGovernmentProjectsLessconsensusonappropriatediscountrateinpublicsector.Onepossibilityareratesbasedonreturnsinprivatesector.Assumesallofthemoneythatisraisedwouldhavebeeninvestedinaprivatesectorproject.Inreality,fundingcomesfromavarietyofsources–investmentandconsumption.Fundingthatcomefromconsumptionshouldbediscountedattheafter-taxdiscountrate.Hardinrealitytodeterminewhatproportionsoffundingcomefromconsumptionorinvestment..23DiscountRateforGovernmentPDiscountRateforGovernmentProjectsAnotherpossibilityisthesocialrateofdiscount–whichmeasuresthevaluationsocietyplaceonconsumptionthatissacrificedinthepresent.Differsfrommarketreturnsbecauseit:AccountsforconcernaboutfuturegenerationsInvolvespaternalismMaysolvesomemarketinefficiencysuchaspositiveexternalities.24DiscountRateforGovernmentPDiscountRateforGovernmentProjectsInreality,federalagenciesarerequiredtousearealrateofreturnof7%,ontheassumptionthatthismeasuresthebefore-taxrateofreturnintheprivatesector.Someuse2%realreturninstead,thoughttomeasuretheafter-taxrateofreturn..25DiscountRateforGovernmentPDiscountRateforGovernmentProjectsWhenanewtaxorexpenditureisintroduced,itseffectsovera5-yearor10-yearperiodareanalyzedtoseewhetheritwillputthebudgetoutofbalance.Ignoresdiscounting.Costs(orbenefits)outsideofthewindowarenotcountedtowarddeficit(orsurplus)..26DiscountRateforGovernmentPValuingPublicBenefitsandCostsRecallthatthediscountrate,benefits,andcostsareneededtocomputethepresentvalueofaproject.Forprivatecompany:Benefits=revenuesreceivedCosts=firm’spaymentsforinputs.27ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsForpublicsector,marketpricesmaynotreflectsocialbenefitsandcosts.Externalities,forexampleSeveralwaysofmeasuringbenefitsandcostsMarketpricesAdjustedmarketpricesConsumersurplusInferencesfromeconomicbehaviorValuingintangibles.28ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsMarketpricesInaproperlyfunctioningcompetitiveeconomy,thepriceofagoodsimultaneouslyreflectsitsmarginalsocialcostofproductionanditsmarginalvaluetoconsumers.IgnoresmarketimperfectionsEasytogather.29ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsAdjustedmarketpricesIfmarketsareimperfect,pricesgenerallydonotreflecttruemarginalsocialcost.Shadowpriceofacommodityisitstrue,underlyingmarginalsocialcost,whichcansometimesbeestimated.Exampleswhereinsightscanbegleanedincludemonopolyprice,taxes,andunemployment..30ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsConsumersurplusPublicsectorprojectscanbelargeandchangemarketprices.Figure11.1measuresthechangeinconsumersurplusfromagovernmentirrigationprojectthatlowersthecostofagriculturalproduction..31ValuingPublicBenefitsandCoFigure11.1.32Figure11.1.32ValuingPublicBenefitsandCostsInthisfigure,thechangeinconsumersurplusisareabcgd.Providedthegovernmentplannercanaccuratelymeasurethedemandcurve,theproject’sbenefitcanbemeasuredwiththischange..33ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsInferencesfromEconomicBehaviorManytimesagoodinquestionisnotexplicitlytraded,sonomarketpriceexists.Examples:ValueoftimeValueoflife.34ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsValueoftimeIncost-benefitanalysis,needtoestimatethevalueoftimetotakeadvantageoftheoryofleisure-incomechoice.After-taxwageisoftenusedButhoursofworknotalwaysa“choice,”andnotallusesoftimeawayfromjobequivalent..35ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsResearchershaveexaminedvalueoftimebytravelcommutingchoices.Trainsaremoreexpensive,butlesstime-consuming,thanbuses.Thesameistrueaboutnon-stopairlineflightsversusthosewithalayover.Estimatesarethatvalueoftimeapproximatelyhalfofthebefore-taxwage..36ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsValueoflifeThemindsetthat“l(fā)ifeispriceless”presentsobviousdifficultiesforcost-benefitanalysis.Ifthebenefitsofasavedlifeareinfinite,anyprojectthatleadstoevenasinglelifesavedhasaninfinitelyhighpresentvalue..37ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsEconomistsusetwomethodstoassignfinitevaluestohumanlife:Lostearnings:Netpresentvalueofindividual’safter-taxearningsoverlifetime.Takenliterally,nolossforaged,infirm,orseverelyhandicappedProbabilityofdeath:Mostprojectsaffectprobabilityofdeath(e.g.,cancerresearch).Peoplearewillingtoacceptincreasesintheprobabilityofdeathforafiniteamountofmoney..38ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsExamples:Purchasingamoreexpensive,safercarwithalowerprobabilityofdeathversusalessexpensive,lesssafecar.Occupationalchoice:Riskierjobshavehigherwages,allelseequalWillingnesstopayforsafetydeviseslikesmokealarms..39ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsEstimatessuggestvalueofalifebetween$4,000,000-$9,000,000Cancontrastthisversusthecostperlifesaved:Emergencyfloorlightsonairplanescostabout$900,000perlifesavedAsbestosremovalrulescost$100,000,000perlifesaved.40ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsValuingintangiblesNationalprestige,othersCanbeusedtosubvertentirecost-benefitanalysisCouldusedifferencebetweencostsandbenefitstomakeanargumentonhowlargeintangibleswouldhavetobetomaketheprojectadmissible.41ValuingPublicBenefitsandCoCost-Benefit“Games”Chain-ReactiongameIncludesecondarybenefitstomakeaproposalappearmorefavorable,withoutalsoincludingthesecondarycostsLaborgameWagesareviewedasbenefitsratherthancostsoftheprojectDoublecountinggameBenefitsareerroneouslycountedtwice.42Cost-Benefit“Games”Chain-ReacDistributionalConsiderationsTheHicks-KaldorcriterionbasesprojectselectiononwhetherthereisapotentialParetoimprovementMayimposescostsonsomeifbenefitsonothersarelargerOthersviewsomegroupsinpopulationas“moredeserving”andarguethisshouldbetakenintoaccountinprojectselection.43DistributionalConsiderationsTUncertaintyTheresultsofmanyprojectsareuncertain(e.g.,AIDSvaccineresearchordefenseresearch).Inriskyprojects,benefitsorcostsmustbeconvertedintocertaintyequivalents–theamountofcertainincometheindividualwouldtradeforasetofuncertainoutcomesgeneratedbyproject..44UncertaintyTheresultsofmanyUncertaintyRequiresinformationondistributionofreturnsandriskaversion.Figure11.2showsariskyproject(E,E+y)andacertainproject(C)thatgivethesameexpectedutility..45UncertaintyRequiresinformatioFigure11.2.46Figure11.2.46UncertaintyRequiresinformationondistributionofreturnsandriskaversion.Figure11.2showsariskyproject(E,E+y)andacertainproject(C)thatgivethesameexpectedutility..47UncertaintyRequiresinformatioRecapofCost-BenefitAnalysisPresentvaluePrivatesectorprojectevaluationDiscountrateforgovernmentprojectsValuingpublicbenefitsandcostsCost-benefit“games”DistributionalconsiderationsUncertainty.48RecapofCost-BenefitAnalysisChapter11–Cost-BenefitAnalysisPublicFinanceAaronS.Yelowitz-Copyright2003?McGraw-Hill.49Chapter11–Cost-BenefitAnalIntroductionCost-benefitanalysisisasetofpracticalproceduresforguidingpublicexpendituredecisions..50IntroductionCost-benefitanalyPresentValueProjectevaluationusuallyrequirescomparingcostsandbenefitsfromdifferenttimeperiodsDollarsacrosstimeperiodsarenotimmediatelycomparable,becauseofinflationandreturnsinthemarket..51PresentValueProjectevaluatioPresentValue:

PresentDollarsintotheFutureSupposeyouinvest$100todayinthebank...Attheendofyear1,itisworth(1+.05)x$100,or$105Attheendofyear2,itisworth(1+.05)x$105,or$110.25Theinterestcompoundsovertime,thatis,theinterestisalsoearninginterest..52PresentValue:

PresentDollarsPresentValue:

PresentDollarsintotheFutureDefineR=initialinvestmentamountr=rateofreturnoninvestmentT=yearsofinvestmentThefuturevalue(FV)oftheinvestmentis:.53PresentValue:

PresentDollarsPresentValue:

FutureDollarsintothePresentSupposesomeonepromisestopayyou$100oneyearfromnow.Whatisthemaximumamountyoushouldbewillingtopaytodayforsuchapromise?Youareforgoingtheinterestthatyoucouldearnonthemoneythatisbeingloaned..54PresentValue:

FutureDollarsPresentValue:

FutureDollarsintothePresentThepresentvalueofafutureamountofmoneyisthemaximumamountyouwouldbewillingtopaytodayfortherighttoreceivethemoneyinthefuture..55PresentValue:

FutureDollarsPresentValue:

PresentDollarsintotheFutureDefineR=amounttobereceivedinfuturer=rateofreturnoninvestmentT=yearsofinvestmentThepresentvalue(PV)oftheinvestmentis:.56PresentValue:

PresentDollarsPresentValue:

FutureDollarsintothePresentInpreviousequation,risoftenreferredtoasthediscountrate,and(1+r)-Tisthediscountfactor.Finally,considerapromisetopayastreamofmoney,$R0today,$R1oneyearfromnow,andsoon,forTyears..57PresentValue:

FutureDollarsPresentValue:

FutureDollarsintothePresentPresentvalueisanenormouslyimportantconceptA$1,000,000payment20yearsfromnowisonlyworthtoday:$376,889ifr=.05$148,644ifr=.10.58PresentValue:

FutureDollarsPresentValue:

InflationNominalamountsarevaluedaccordingtothelevelofpricesintheyearthereturnoccurs.Realamountsarevaluedaccordingtothelevelofpricesinoneparticularyear.Inflationaffectsboththepayoutstreamandthediscountfactor,andthesetwocanceleachotherout..59PresentValue:

InflationNominaPrivateSectorProjectEvaluationSupposetherearetwoprojects,XandY.Eachentailscertainbenefitsandcosts,denotedasBX,CX,BY,andCY.Needtoask:Istheprojectadmissible?Istheprojectpreferable?.60PrivateSectorProjectEvaluatPrivateSectorProjectEvaluationAdmissible:Arethebenefitsgreaterthanthecosts?Preferable:Arethenetbenefitsthehighest?Mostprojectsinvolveastreamofbenefitsandcostsovertime..61PrivateSectorProjectEvaluatPrivateSectorProjectEvaluationDefine:BenefitsfromprojectiattimetCostsfromprojectiattimetThenthepresentvalueofprojectiis:.62PrivateSectorProjectEvaluatPrivateSectorProjectEvaluationThepresentvaluecriteriaforprojectevaluationarethat:Aprojectisadmissibleonlyifitspresentvalueispositive.Whentwoprojectsaremutuallyexclusive,thepreferredprojectistheonewiththehighestpresentvalue..63PrivateSectorProjectEvaluatPrivateSectorProjectEvaluationTable11.2showstwodifferentprojects(R&DorAdvertising).Thediscountrateplaysakeyroleindecidingwhatprojecttochoose,becausethecashinflowsoccuratdifferenttimes.Thelowerthediscountrate,themorevaluabletheback-loadedproject..64PrivateSectorProjectEvaluatTable11.2.65Table11.2.17PrivateSectorProjectEvaluationSeveralothercriteriaareoftenusedforprojectevaluation,butcangivemisleadinganswersInternalrateofreturnBenefit-costratio.66PrivateSectorProjectEvaluatPrivateSectorProjectEvaluationTheinternalrateofreturn,ρ,isdefinedastheρthatsolvestheequation:TheIRRisthediscountratethatwouldmakethepresentvalueoftheprojectequaltozero.Admissibleifρ>r.Theflawedanalysiswouldchooseanadmissibleprojectwiththehigherinternalrateofreturn,ignoringscale..67PrivateSectorProjectEvaluatPrivateSectorProjectEvaluationThebenefit-costratiodividesthediscountedstreamofbenefitsbythediscountedstreamofcosts.Inthiscase: B=streamofbenefitsandC=streamofcosts:.68PrivateSectorProjectEvaluatPrivateSectorProjectEvaluationAdmissibilityusingthebenefit-costratiorequires:Thisratioisvirtuallyuselessforcomparingacrossadmissibleprojects,however.Ratiocanbemanipulatedbycountingbenefitsas“negativecosts”andvice-versa..69PrivateSectorProjectEvaluatDiscountRateforGovernmentProjectsGovernmentdecisionmakinginvolvespresentvaluecalculations.Costs,benefits,anddiscountratesaresomewhatdifferentfromprivatesector..70DiscountRateforGovernmentPDiscountRateforGovernmentProjectsLessconsensusonappropriatediscountrateinpublicsector.Onepossibilityareratesbasedonreturnsinprivatesector.Assumesallofthemoneythatisraisedwouldhavebeeninvestedinaprivatesectorproject.Inreality,fundingcomesfromavarietyofsources–investmentandconsumption.Fundingthatcomefromconsumptionshouldbediscountedattheafter-taxdiscountrate.Hardinrealitytodeterminewhatproportionsoffundingcomefromconsumptionorinvestment..71DiscountRateforGovernmentPDiscountRateforGovernmentProjectsAnotherpossibilityisthesocialrateofdiscount–whichmeasuresthevaluationsocietyplaceonconsumptionthatissacrificedinthepresent.Differsfrommarketreturnsbecauseit:AccountsforconcernaboutfuturegenerationsInvolvespaternalismMaysolvesomemarketinefficiencysuchaspositiveexternalities.72DiscountRateforGovernmentPDiscountRateforGovernmentProjectsInreality,federalagenciesarerequiredtousearealrateofreturnof7%,ontheassumptionthatthismeasuresthebefore-taxrateofreturnintheprivatesector.Someuse2%realreturninstead,thoughttomeasuretheafter-taxrateofreturn..73DiscountRateforGovernmentPDiscountRateforGovernmentProjectsWhenanewtaxorexpenditureisintroduced,itseffectsovera5-yearor10-yearperiodareanalyzedtoseewhetheritwillputthebudgetoutofbalance.Ignoresdiscounting.Costs(orbenefits)outsideofthewindowarenotcountedtowarddeficit(orsurplus)..74DiscountRateforGovernmentPValuingPublicBenefitsandCostsRecallthatthediscountrate,benefits,andcostsareneededtocomputethepresentvalueofaproject.Forprivatecompany:Benefits=revenuesreceivedCosts=firm’spaymentsforinputs.75ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsForpublicsector,marketpricesmaynotreflectsocialbenefitsandcosts.Externalities,forexampleSeveralwaysofmeasuringbenefitsandcostsMarketpricesAdjustedmarketpricesConsumersurplusInferencesfromeconomicbehaviorValuingintangibles.76ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsMarketpricesInaproperlyfunctioningcompetitiveeconomy,thepriceofagoodsimultaneouslyreflectsitsmarginalsocialcostofproductionanditsmarginalvaluetoconsumers.IgnoresmarketimperfectionsEasytogather.77ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsAdjustedmarketpricesIfmarketsareimperfect,pricesgenerallydonotreflecttruemarginalsocialcost.Shadowpriceofacommodityisitstrue,underlyingmarginalsocialcost,whichcansometimesbeestimated.Exampleswhereinsightscanbegleanedincludemonopolyprice,taxes,andunemployment..78ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsConsumersurplusPublicsectorprojectscanbelargeandchangemarketprices.Figure11.1measuresthechangeinconsumersurplusfromagovernmentirrigationprojectthatlowersthecostofagriculturalproduction..79ValuingPublicBenefitsandCoFigure11.1.80Figure11.1.32ValuingPublicBenefitsandCostsInthisfigure,thechangeinconsumersurplusisareabcgd.Providedthegovernmentplannercanaccuratelymeasurethedemandcurve,theproject’sbenefitcanbemeasuredwiththischange..81ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsInferencesfromEconomicBehaviorManytimesagoodinquestionisnotexplicitlytraded,sonomarketpriceexists.Examples:ValueoftimeValueoflife.82ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsValueoftimeIncost-benefitanalysis,needtoestimatethevalueoftimetotakeadvantageoftheoryofleisure-incomechoice.After-taxwageisoftenusedButhoursofworknotalwaysa“choice,”andnotallusesoftimeawayfromjobequivalent..83ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsResearchershaveexaminedvalueoftimebytravelcommutingchoices.Trainsaremoreexpensive,butlesstime-consuming,thanbuses.Thesameistrueaboutnon-stopairlineflightsversusthosewithalayover.Estimatesarethatvalueoftimeapproximatelyhalfofthebefore-taxwage..84ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsValueoflifeThemindsetthat“l(fā)ifeispriceless”presentsobviousdifficultiesforcost-benefitanalysis.Ifthebenefitsofasavedlifeareinfinite,anyprojectthatleadstoevenasinglelifesavedhasaninfinitelyhighpresentvalue..85ValuingPublicBenefitsandCoValuingPublicBenefitsandCostsEconomistsusetwomethodstoassignfinitevaluestohumanlife:Lostearnings:Netpresentvalueofindividual’safter-taxearningsoverlifetime.Takenliterally,nolossforaged,infirm,orseverelyhandicappedProbabilityofdeath:Mostprojectsaffectprobabilityofdeath(e.g.,cancerresearch).Peoplearewillingtoacceptincreasesintheprobabilityofdeathforafiniteamountofmoney..86ValuingPublicBenefitsandCoValuingPublicBenefitsan