《金融学》（第二版） 课件 （英文） Chapter05 Household Saving and Investment Decisions

Chapter5:

HouseholdSavingand InvestmentDecisionsObjectiveFinancialdecisionsinanuncertainworld;Humancapital,permanentincomedecisionsoverlifecycle1Chapter5Contents5.1ALife-CycleModelofSavings5.2TakingAccountofSocialSecurity5.3DeferringTaxesthroughVoluntaryRetirementPlans5.4ShouldyouInvestinaProfessionalDegree?5.5ShouldyouBuyorRent?2ObjectivesHowmuchtosaveforretirementWhethertodefertaxesorpaythemnowWhethertogetaprofessionaldegreeWhethertobuyorrentanapartment35.1ALife-CycleModelofSavingAssumethatyouarecurrently35yearsold,expecttoretirein30yearsat65,andthenlivefor15moreyearsuntil80Yourreallaborincomeis$30,000/yearuntilage65Interestratesexceedinflationby3%/year4HowMuchShouldISaveandConsume?Considertwoapproaches:Targetreplacementrateofpre-retirementincomeMaintainthesamelevelofconsumptionspending5Targetreplacementrateofpre-retirementincomeFirstcomputetheretirementincome.Manyexpertsrecommendarateof75%ofthepre-retirementincome.$30,000*0.75=$22,500/yearusingyourcalculatorcomputethepresentvalueoftheretirementfundsasanregularannuityn=15,i=3,FV=0,PMT=-22,500->PV=268,6046Targetreplacementrateofpre-retirementincome(Cont.)NextcomputetheretirementincomeNextcomputehowmuchyouneedtosaveeachyearn=15,i=3,PV=0,FV=-268,604->PMT=5,646

Toobtainareal$22,500youneedtosave$5,646peryear7TargetreplacementrateConclusionYouwillhavenoticedthatyourpre-retirementconsumptionis$30,000-$5,646=24,354;buttherealretirementincomeisonly$22,500Thenextmethodequatesconsumption8MaintainthesamelevelofconsumptionspendingAssumethatyourlevelofrealconsumptionisCThepresentvalueofconsumptionoverthenext45yearsmustequalthepresentvalueofearningsoverthenext30yearsn=30,i=3,FV=0,PMT=3,000,CPTPV,n=45CPTPMTgives$23,982Thesavingsarethen$30,000-$23,982=$6,0189HumanCapitalandPermanentIncome

HumancapitalThepresentvalueofone’sfuturelaborincomePermanentincomeTheconstantlevelof(real)consumptionspendingthathasapresentvalueequaltoone’shumancapital101112TheInter-temporalBudgetConstrainti=realinterestrateR=numberofyearstoretirementT=numberofyearsofremaininglifeW0=initialwealthB=bequest13Omar’sLife-CycleSavingsPlan145.2TakingAccountofSocialSecurityInmanycountriesthegovernmentobligescitizenstoparticipateinamandatoryretirementincomesystemcalledsocialsecurityContributorspayataxduringtheirworkingyears,andinreturnqualifyforalifetimeannuityintheiroldage15SocialSecurityasInvestmentSubstituteIfsocialsecuritypaysareturnequalto3%inthelastexample,thenjustreducethesavingsbythesocialsecuritytaxTheanalysisbecomesprogressivelymorecomplexaswemaketheassumptionsmorerealistic.Whatifyoudon’tknowyourdateofdeath.,returnsarerisky,etcetera?165.3DeferringTaxesThroughVoluntaryRetirementPlans

Manycountriesencouragevoluntarysavingsforretirementthroughprovisionsofthetaxcode.IntheUSemployeesarepermittedtosetupIndividualRetirementAccounts(IRA)thatdeferpaymentoftaxesuntilretirementTherulesarealittlecomplex,butanIRAmaybeusedbyaninvestortosavemoneyforretirement.Paymentsintotheplanaretax-deductible,buttheflowsfromtheplanafterretirementaretaxedItisusualformarginaltaxratestobelowerafterretirement,butthisisnotthekeybenefit17IRABenefitsThemajorbenefitsaremoresubtle.Assume:Youcanreserve$2,000ofpre-taxedincomeforinvestment,startingnextyear,forthenext40-years.Thiswillgrowattherateofinflationof3%Thattheinvestmentwillreturn10%/yearThatyouplantoremainretiredfor20-years,andwillrequireincomethatisindexedtoinflationThetaxrateonalltaxableincomestreamsis30%,bothnowandafterretirement18TheAdvantageofTax-DeferredSaving19ShelteredandUnshelteredCases

ShelteredcaseThefull(real)$2,000enterstheplan.Accumulationsarenottaxed,dispersionsaretaxed.Result:1styearaftertaxretirementbenefits=$82,785($24,639inrealterms)UnshelteredcaseOnlya(real)$2,000(1-0.30),enterstheplan.Earningsandrealizedcapitalgainsaretaxable,dispersionsarenottaxed.Result:1styearaftertaxretirementbenefits$31,671($9,426inrealterms)20IRAConclusionNottakingintoaccounttheadvantagesofdifferentialtaxation,theinvestorwillbe2.61timesbetteroffusingtheshelteredplan215.4ShouldYouInvestinaProfessionalDegree?EducationmaybeviewedasaninvestmentinhumancapitalOnepurposeofadditionalschoolingistoincreaseone’searningpowerExample:GettingaGraduateDegree22TheData:You'vedecidedtoobtainpracticalexperiencefor10years,andthengetaPh.D.InthreeyearsYouwantthesamestandardofincomeoverthenext13yearsAssumethatallcashflowsoccuratyear-endYourstartingsalaryis$50,000.Becauseyouaresmart,thiswillincreaseby15%/year.Youhaveagreedtobepaidthisattheendofthefirstyear,andyearlythereafterPh.D.Feesarecurrently$15,000peryear,andincreaseby3%/yearwithgeneralinflation.Feesarepaidattheendofeachyear,sothefeesfortheperiodfrom10to11arepaidatyear1123PersonalPlanningApplicationData(continued)Taxesare30%,andareassumedtobeconstant.AssumethatlendingandborrowingrateshavebeenadjustedfortaxAfundwithacceptableriskyields10%/yearYoumayalsoborrowat10%Lendingrate=borrowingrate!Therealreasonforthisistosimplifythemath,butthefundcouldbemoderatelyaggressive,andthedebtbeconsumerloans24DataExtractionLettheexpenditurerequiredforyourstandardoflivingbeXattheendofyear0(beginningofyear1),X*1.03inyear2,X*1.032inyear3,etceteraThefeesstartat$15,000*1.0310(year11),andcontinuetogrowatarateof3%Yournetsalarystartsat$35,000inyear1,andgrowsat15%for10yearsEverythingisdiscountedat10%25Salarycashflow(rateissue)Theafter-taxnominalcashflowinthefirstyearis$35,000,growsatanominal15%for10yearsWetreatthe15%asthecombinedeffectofinflationandrealgrowthInflationistheinterestrateTherealrateis(0.10-0.15)/1.15=-4.35%26Salarycashflow($issue)

Now,remember,wehaveassumedthatthecashflowsoccurattheendofeachyearThefirstnetincomeoccursattime1,andsomustbediscountedtoyear0Therealsalaryisnot$35,000but$35,000/1.15=$30,434.7827SalaryCashFlowComputation

Usingyourfinancialcalculators10->n;4.3478261“+/-”->I;PV=?;$30,434.78261->PMT;0->FVResultPV=$391,816.3459(in)28Feecashflow($issues)Thefeesarealreadyexpressedinrealterms,butthefirstcashflowoccursinyear11,not10(theevaluationpoint)Theyear11realcashflowmustbeadjustedtoyear1015000/1.03=$14563.106829SolutionbyRealConversionTherealinterestrateis(0.10-0.03)/1.03=6.7961165%orabout6.80%30FeeCashFlowComputationThepresentvalueofthefeesatyear10maybeobtainedusingyourfinancialcalculator:3->n;6.7961165->I;PV=?;$14563.1068->PMT;0->FVResultPV10=-$38,361.0067810->n;6.7961165->I;PV=?;PMT->0;FV10=38,361.00678(=PV10)ResultPV0=$19,876.2931(out)31LivingExpenditureCF$issuesCashflowsareassumedtooccurattheendofeachyearLetuscomputetherealamounttoday.DenotethisnominalamountintermsoftheunknownamountXinyear1X/1.03=0.970873786x32LivingExpenditureCFRateIssuesThiscaseiseasy.Therealratehasbeencomputedtobe6.7961165%inthefeesection33LivingExpenditureCFComputationWedonotknowboththePVnorthePNT.Setthepaymentto$1fornow,andmultiplybyXlaterUsingyourfinancialcalculators13->n;6.7961165->I;PV=?;$0.970873786->PMT;0->FVResultPV=$8.208829899*X(out)34SolutionbyRealConversionWearealmostdone.Allthatremainsistoassembletheparts,andsolvetheresultingequation35ConclusionThisamountistheactualamountthatwillbeexpendedforthefirstyear,paidattheendofthatyearThisisasimple,butnotatrivial,example,butitisloadedwithtrapsofeventhemostexperienced.ItrequiresmultistagelogicTheuseoftwodistinctinterestrateswillbothersomeofyouSomethinkersbelievethatitisbettertoavoidquantitiesthatcannotbeobserveddirectly

Whilewecertainlyfeeltheinfluenceofrealcashflowsandrealrates,observationisthroughtheinflationrateWeliveintheworldofthenominal,andanotherapproachistorecognizethisinoursystemoffinancialanalysis36SolutionbyGrowingAnnuityNotationAisthestartingyearofacashflowBistheendingyearofacashflowRisthenominaldiscountratefrom0tobGisthegeometricgrowthrateinnominalcashflowsXaisthestartingcashflowinyeara37SolutionbyGrowingAnnuityEquation38SolutionmethodJusta