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1、Chapter5:HouseholdSavingandInvestmentDecisionsObjectiveFinancial decisions in an uncertain world;Human capital,permanent income decisions over life cycle 1Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallContents 5.1ALife-CycleModelofSavings5.1ALife-CycleModelofSavings 5.2TakingAccountofSoc
2、ialSecurity5.2TakingAccountofSocialSecurity 5.3DeferringTaxesthroughVoluntary5.3DeferringTaxesthroughVoluntaryRetirementPlansRetirementPlans 5.4ShouldyouInvestinaProfessional5.4ShouldyouInvestinaProfessionalDegree?Degree?5.5ShouldyouBuyorRent?5.5ShouldyouBuyorRent?2Copyright2009PearsonEducation,Inc.
3、PublishingasPrenticeHallObjectives HowmuchtosaveforretirementHowmuchtosaveforretirement WhethertodefertaxesorpaythemnowWhethertodefertaxesorpaythemnow WhethertogetaprofessionaldegreeWhethertogetaprofessionaldegree WhethertobuyorrentanapartmentWhethertobuyorrentanapartment3Copyright2009PearsonEducati
4、on,Inc.PublishingasPrenticeHall5.1ALife-CycleModelofSavingAssumethatyouarecurrently35yearsold,expecttoretirein30yearsat65,andthenlivefor15moreyearsuntil80Yourreallaborincomeis$30,000/yearuntilage65Interestratesexceedinflationby3%/year4Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallHow Muc
5、h Should I Save and Consume?Considertwoapproaches:Targetreplacementrateofpre-retirementTargetreplacementrateofpre-retirementincomeincome MaintainthesamelevelofconsumptionMaintainthesamelevelofconsumptionspendingspending5Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallTargetreplacementrateo
6、fpre-retirementincomeFirstcomputetheretirementincome.Manyexpertsrecommendarateof75%ofthepre-retirementincome.$30,000*0.75=$22,500/year$30,000*0.75=$22,500/year usingyourcalculatorcomputethepresentusingyourcalculatorcomputethepresentvalueoftheretirementfundsasanregularvalueoftheretirementfundsasanreg
7、ularannuityannuityn=15,i=3,FV=0,PMT=-22,500-PV=268,604n=15,i=3,FV=0,PMT=-22,500-PV=268,6046Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallTargetreplacementrateofpre-retirementincome(Cont.)Nextcomputehowmuchyouneedtosaveeachyearn=30,i=3,PV=0,FV=-268,604-PMT=5,646n=30,i=3,PV=0,FV=-268,604-P
8、MT=5,646 Toobtainareal$22,500afterretirementyouneedtosave$5,646peryearfromnow.7Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallTargetreplacementrateConclusionYouwouldhavenoticedthatyourpre-retirementconsumptionis$30,000-$5,646=24,354;buttherealretirementincomeisonly$22,500Thenextmethodequa
9、tesconsumption8Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallMaintainthesamelevelofconsumptionspending AssumethatyourlevelofrealconsumptionisCAssumethatyourlevelofrealconsumptionisC ThepresentvalueofconsumptionoverthenextThepresentvalueofconsumptionoverthenext45yearsmustequalthepresentva
10、lueofearnings45yearsmustequalthepresentvalueofearningsoverthenext30yearsoverthenext30years UsingannuityformulawegotC=$23,982UsingannuityformulawegotC=$23,982 Thesavingsarethen$30,000-$23,982=Thesavingsarethen$30,000-$23,982=$6,018$6,018 Amoregeneralformula:Amoregeneralformula:9Copyright2009PearsonEd
11、ucation,Inc.PublishingasPrenticeHallHumanCapitalandPermanentIncomeHumancapital ThepresentvalueofonesfuturelaborThepresentvalueofonesfuturelaborincomeincomePermanentincome Theconstantlevelof(real)consumptionTheconstantlevelof(real)consumptionspendingthathasapresentvalueequaltospendingthathasapresentv
12、alueequaltooneshumancapitaloneshumancapital10Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall11Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall12Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallTheInter-temporalBudgetConstraint C=consumptionspendinginyeartC=consumptionsp
13、endinginyeart i=realinterestratei=realinterestrate R=numberofyearstoretirementR=numberofyearstoretirement T=numberofyearsofremaininglifeT=numberofyearsofremaininglife WW0 0=initialwealth=initialwealth B=bequestB=bequest13Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallStory Dr.OmarBenHolim
14、hasjustgraduatedfrommedicalDr.OmarBenHolimhasjustgraduatedfrommedicalschoolatage30,andhasstartedtrainingtobeasurgeonschoolatage30,andhasstartedtrainingtobeasurgeonatMountHeavenHospital.atMountHeavenHospital.Omarsrealsalaryforthenextfiveyearswillbe$25,000Omarsrealsalaryforthenextfiveyearswillbe$25,00
15、0peryear.peryear.Aftercompletinghisresidency,OmarexpectstoearnAftercompletinghisresidency,Omarexpectstoearn$300,000peryearinrealtermsuntilheretiresatage65.$300,000peryearinrealtermsuntilheretiresatage65.HewantstomaintainthesamelevelofrealconsumptionHewantstomaintainthesamelevelofrealconsumptionspend
16、ingfortherestofhislifeandhislifeexpectancyisspendingfortherestofhislifeandhislifeexpectancyis85years,howmuchshouldheplantosavenowandin85years,howmuchshouldheplantosavenowandinthefuture?thefuture?Assumetherealinterestrateis3%peryear.Assumetherealinterestrateis3%peryear.14Copyright2009PearsonEducation
17、,Inc.PublishingasPrenticeHallOmarsLife-CycleSavingsPlan15Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallillustration Omarshumancapitalinitiallyis$5,186,747,andhisOmarshumancapitalinitiallyis$5,186,747,andhispermanentincomeis$193,720.permanentincomeis$193,720.Inordertospend$193,720peryeard
18、uringthefiveInordertospend$193,720peryearduringthefiveyearsofhisresidency,hewillhavetoborrowyearsofhisresidency,hewillhavetoborrow(“dissave”)$168,720eachyeartosupplementhis(“dissave”)$168,720eachyeartosupplementhis$25,000salary.$25,000salary.HistotalindebtednesswillgrowtomaximumofHistotalindebtednes
19、swillgrowtomaximumof$895,758atage35,andthendeclinethereafteras$895,758atage35,andthendeclinethereafterasaresultofhissaving$106,280everyyearfromagearesultofhissaving$106,280everyyearfromage36untilheretiresatage65.36untilheretiresatage65.NotethathewillnothavepaidoffhisdebtuntilNotethathewillnothavepai
20、doffhisdebtuntilage45!age45!16Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallExample1 Supposethatyouare30yearsold,planstoSupposethatyouare30yearsold,planstoretireatage65,andexpectstolivetoage85.retireatage65,andexpectstolivetoage85.Yoursalaryis$25,000peryear,andyouintendYoursalaryis$25,00
21、0peryear,andyouintendtomaintainaconstantlevelofrealtomaintainaconstantlevelofrealconsumptionspendingoverthenext55years.consumptionspendingoverthenext55years.Assumenotaxes,nogrowthinreallaborAssumenotaxes,nogrowthinreallaborincome,andarealinterestrateof3%peryear.income,andarealinterestrateof3%peryear
22、.Whatisthevalueofyourhumancapital?Whatisthevalueofyourhumancapital?Whatisyourpermanentincome?Whatisyourpermanentincome?Whateffectwoulda$1millioninheritancethatyouWhateffectwoulda$1millioninheritancethatyouexpecttoreceive30yearsfromnowhaveonyourexpecttoreceive30yearsfromnowhaveonyourpermanentincome?p
23、ermanentincome?17Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall5.2TakingAccountofSocialSecurityInmanycountriesthegovernmentobligescitizenstoparticipateinamandatoryretirementincomesystemcalledsocialsecurityContributorspayataxduringtheirworkingyears,andinreturnqualifyforalifetimeannuityint
24、heiroldage18Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallSocialSecurityasInvestmentSubstitute IfsocialsecuritypaysareturnIfsocialsecuritypaysareturnequalequalto3%inthelastto3%inthelastexample,thenjustreducethesavingsbythesocialexample,thenjustreducethesavingsbythesocialsecuritytaxsecuri
25、tytax For example,the previous example(Slide 17).If you pay For example,the previous example(Slide 17).If you pay$2000 per year in social security taxes for 35 years,how$2000 per year in social security taxes for 35 years,how much will you receive in benefits per year for 20 years much will you rece
26、ive in benefits per year for 20 years starting at age 65.What impact will social security have on starting at age 65.What impact will social security have on your savings?your savings?TheanalysisbecomesprogressivelymorecomplexasTheanalysisbecomesprogressivelymorecomplexaswemaketheassumptionsmorereal
27、istic.wemaketheassumptionsmorerealistic.Whatifyoudontknowyourdateofdeath.,returnsarerisky,Whatifyoudontknowyourdateofdeath.,returnsarerisky,etcetera?etcetera?19Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallRedistributionamongtherichandthepoor Inmanycountries,thesocialsecuritysystemInmany
28、countries,thesocialsecuritysystemoffersahigherrateofreturntopeopleintheoffersahigherrateofreturntopeopleinthelowerendoftheincomedistributionthantolowerendoftheincomedistributionthantothoseintheupperend.thoseintheupperend.ButthefactthatbenefitsarepaidintheformofButthefactthatbenefitsarepaidintheformo
29、falifetimeannuityimpliesthatnomatterhowalifetimeannuityimpliesthatnomatterhowrichorpooryouare,thelongeryoulive,therichorpooryouare,thelongeryoulive,thehigheryouractualrateofreturn.higheryouractualrateofreturn.So,considerabonusawaitingyouifyouliveSo,considerabonusawaitingyouifyoulivelongenough.longen
30、ough.20Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall5.3DeferringTaxesThroughVoluntaryRetirementPlans ManycountriesencourageManycountriesencouragevoluntarysavingsvoluntarysavingsforretirementforretirementthroughprovisionsofthetaxcode.throughprovisionsofthetaxcode.IntheUSemployeesarepermi
31、ttedtosetupIndividualIntheUSemployeesarepermittedtosetupIndividualRetirementAccounts(IRA)thatdeferpaymentoftaxesRetirementAccounts(IRA)thatdeferpaymentoftaxesuntilretirementuntilretirement Therulesarealittlecomplex,butanIRAmaybeusedbyTherulesarealittlecomplex,butanIRAmaybeusedbyaninvestortosavemoney
32、forretirement.Paymentsintoaninvestortosavemoneyforretirement.Paymentsintotheplanaretheplanaretax-deductibletax-deductible,buttheflowsfromtheplan,buttheflowsfromtheplanafterretirementaretaxed.Theinterestontheseafterretirementaretaxed.Theinterestonthesecontributionsisnottaxeduntilthemoneyiswithdrawn.c
33、ontributionsisnottaxeduntilthemoneyiswithdrawn.ItisusualformarginaltaxratestobelowerafterItisusualformarginaltaxratestobelowerafterretirement,butthisisnotthekeybenefitretirement,butthisisnotthekeybenefit21Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallIRABenefits Themajorbenefitsaremoresu
34、btle.Assume:Themajorbenefitsaremoresubtle.Assume:Youcancontribute$1,000ofpre-taxedYoucancontribute$1,000ofpre-taxedincometotheIRAplan,startingnextyear,forincometotheIRAplan,startingnextyear,forthenext30-years.Thiswillgrowattheratethenext30-years.Thiswillgrowattherateofinflationof2%ofinflationof2%Tha
35、ttheplanwillreturn10%/yearThattheplanwillreturn10%/year ThetaxrateonalltaxableincomestreamsisThetaxrateonalltaxableincomestreamsis20%,bothnowandafterretirement20%,bothnowandafterretirement22Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallAcomparison UsingIRA:UsingIRA:Totalpre-taxamountaccu
36、mulatedinIRAwouldbeTotalpre-taxamountaccumulatedinIRAwouldbe Paytaxesattherateof20%,soyouwouldhavethePaytaxesattherateof20%,soyouwouldhavethefollowingamountleftaftertaxfollowingamountleftaftertax Usingothersavingaccounts:Usingothersavingaccounts:Youhavetopay20%of$1,000astaximmediately,soYouhavetopay
37、20%of$1,000astaximmediately,so$800leftaftertaxeachyear;$800leftaftertaxeachyear;Theafter-taxinterestrateearnedis,therefore,Theafter-taxinterestrateearnedis,therefore,SotheamountaccumulatedatthesavingsplanwouldbeSotheamountaccumulatedatthesavingsplanwouldbe23Copyright2009PearsonEducation,Inc.Publishi
38、ngasPrenticeHallTheAdvantageofTax-DeferredSaving24Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall5.4ShouldYouInvestinaProfessionalDegree?Educationmaybeviewedasaninvestmentinhumancapital OnepurposeofadditionalschoolingistoOnepurposeofadditionalschoolingistoincreaseonesearningpowerincreaseo
39、nesearningpowerExample:GettingaGraduateDegree(likeallofyou)25Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallExample2 Youare30yearsoldandareconsideringfull-timeYouare30yearsoldandareconsideringfull-timestudyforanMBAdegree.TuitionandotherdirectstudyforanMBAdegree.Tuitionandotherdirectcostsw
40、illbe$15,000peryearfortwoyears.Incostswillbe$15,000peryearfortwoyears.Inadditionyouwillhavetogiveupajobwithasalaryadditionyouwillhavetogiveupajobwithasalaryof$30,000peryear.Assumetuitionispaidandsalaryof$30,000peryear.Assumetuitionispaidandsalaryreceivedattheendoftheyear.Howmuchdoesyourreceivedatthe
41、endoftheyear.Howmuchdoesyoursalaryhavetoincrease(inrealterms)asaresultofsalaryhavetoincrease(inrealterms)asaresultofgettingyourMBAdegreetojustifytheinvestment?gettingyourMBAdegreetojustifytheinvestment?Assumearealinterestrateof3%peryearandAssumearealinterestrateof3%peryearandignoretaxes.Alsoassumeth
42、atthesalaryincreaseisignoretaxes.Alsoassumethatthesalaryincreaseisaconstantrealamountthatstartsafteryoucompleteaconstantrealamountthatstartsafteryoucompleteyourdegree(attheendoftheyearfollowingyourdegree(attheendoftheyearfollowinggraduation)andlastsuntilretirementatage65.graduation)andlastsuntilreti
43、rementatage65.26Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall AmorecomplicatedexampleAmorecomplicatedexample Youvedecidedtoobtainpracticalexperiencefor10years,Youvedecidedtoobtainpracticalexperiencefor10years,andthengetaPh.D.InthreeyearsandthengetaPh.D.Inthreeyears Youwantthesamestandar
44、dofincomeoverthenext13Youwantthesamestandardofincomeoverthenext13yearsyears Assumethatallcashflowsoccuratyear-endAssumethatallcashflowsoccuratyear-end Yourstartingsalaryis$35,000.Becauseyouaresmart,Yourstartingsalaryis$35,000.Becauseyouaresmart,thiswillincreaseby15%/year.Youhaveagreedtobethiswillinc
45、reaseby15%/year.Youhaveagreedtobepaidthisattheendofthefirstyear,andyearlythereafterpaidthisattheendofthefirstyear,andyearlythereafter Ph.D.Feesarecurrently$15,000peryear,andincreasebyPh.D.Feesarecurrently$15,000peryear,andincreaseby3%/yearwithgeneralinflation.Feesarepaidattheend3%/yearwithgeneralinf
46、lation.Feesarepaidattheendofeachyear,sothefeesfortheperiodfrom10to11areofeachyear,sothefeesfortheperiodfrom10to11arepaidatyear11paidatyear1127Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallCon.Taxesare30%,andareassumedtobeTaxesare30%,andareassumedtobeconstant.Assumethatlendingandborrowing
47、constant.Assumethatlendingandborrowingrateshavebeenadjustedfortaxrateshavebeenadjustedfortax Afundwithacceptableriskyields10%/yearAfundwithacceptableriskyields10%/year Youmayalsoborrowat10%Youmayalsoborrowat10%Lendingrate=borrowingrate!TherealreasonLendingrate=borrowingrate!Therealreasonforthisistos
48、implifythemath,butthefundforthisistosimplifythemath,butthefundcouldbemoderatelyaggressive,andthedebtbecouldbemoderatelyaggressive,andthedebtbeconsumerloansconsumerloans Question:LivingExpenditure?Question:LivingExpenditure?28Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallDataExtraction Le
49、ttheexpenditurerequiredforyourLettheexpenditurerequiredforyourstandardoflivingbeXattheendofyear0standardoflivingbeXattheendofyear0(beginningofyear1),X*1.03inyear2,(beginningofyear1),X*1.03inyear2,X*1.03X*1.032 2inyear3,etceterainyear3,etcetera Thefeesstartat$15,000*1.03Thefeesstartat$15,000*1.031010
50、(year11),(year11),andcontinuetogrowatarateof3%andcontinuetogrowatarateof3%YourYournetnetsalarystartsat$35,000salarystartsat$35,000（after-after-taxtax）inyear1,andgrowsat15%for10inyear1,andgrowsat15%for10yearsyears Everythingisdiscountedat10%Everythingisdiscountedat10%29Copyright2009PearsonEducation,I