《金融学教学课件》bodie2e_cha

Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,1,Chapter5:HouseholdSavingandInvestmentDecisions,ObjectiveFinancialdecisionsinanuncertainworld;Humancapital,permanentincomedecisionsoverlifecycle,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,2,Contents,5.1ALife-CycleModelofSavings5.2TakingAccountofSocialSecurity5.3DeferringTaxesthroughVoluntaryRetirementPlans5.4ShouldyouInvestinaProfessionalDegree?5.5ShouldyouBuyorRent?,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,3,Objectives,HowmuchtosaveforretirementWhethertodefertaxesorpaythemnowWhethertogetaprofessionaldegreeWhethertobuyorrentanapartment,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,4,5.1ALife-CycleModelofSaving,Assumethatyouarecurrently35yearsold,expecttoretirein30yearsat65,andthenlivefor15moreyearsuntil80Yourreallaborincomeis$30,000/yearuntilage65Interestratesexceedinflationby3%/year,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,5,HowMuchShouldISaveandConsume?,Considertwoapproaches:Targetreplacementrateofpre-retirementincomeMaintainthesamelevelofconsumptionspending,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,6,Targetreplacementrateofpre-retirementincome,Firstcomputetheretirementincome.Manyexpertsrecommendarateof75%ofthepre-retirementincome.$30,000*0.75=$22,500/yearusingyourcalculatorcomputethepresentvalueoftheretirementfundsasanregularannuityn=15,i=3,FV=0,PMT=-22,500-PV=268,604,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,7,Targetreplacementrateofpre-retirementincome(Cont.),Nextcomputehowmuchyouneedtosaveeachyearn=30,i=3,PV=0,FV=-268,604-PMT=5,646Toobtainareal$22,500afterretirementyouneedtosave$5,646peryearfromnow.,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,8,TargetreplacementrateConclusion,Youwouldhavenoticedthatyourpre-retirementconsumptionis$30,000-$5,646=24,354;buttherealretirementincomeisonly$22,500Thenextmethodequatesconsumption,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,9,Maintainthesamelevelofconsumptionspending,AssumethatyourlevelofrealconsumptionisCThepresentvalueofconsumptionoverthenext45yearsmustequalthepresentvalueofearningsoverthenext30yearsUsingannuityformulawegotC=$23,982Thesavingsarethen$30,000-$23,982=$6,018Amoregeneralformula:,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,10,HumanCapitalandPermanentIncome,HumancapitalThepresentvalueofonesfuturelaborincomePermanentincomeTheconstantlevelof(real)consumptionspendingthathasapresentvalueequaltooneshumancapital,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,11,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,12,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,13,TheInter-temporalBudgetConstraint,C=consumptionspendinginyearti=realinterestrateR=numberofyearstoretirementT=numberofyearsofremaininglifeW0=initialwealthB=bequest,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,14,Story,Dr.OmarBenHolimhasjustgraduatedfrommedicalschoolatage30,andhasstartedtrainingtobeasurgeonatMountHeavenHospital.Omarsrealsalaryforthenextfiveyearswillbe$25,000peryear.Aftercompletinghisresidency,Omarexpectstoearn$300,000peryearinrealtermsuntilheretiresatage65.Hewantstomaintainthesamelevelofrealconsumptionspendingfortherestofhislifeandhislifeexpectancyis85years,howmuchshouldheplantosavenowandinthefuture?Assumetherealinterestrateis3%peryear.,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,15,OmarsLife-CycleSavingsPlan,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,16,illustration,Omarshumancapitalinitiallyis$5,186,747,andhispermanentincomeis$193,720.Inordertospend$193,720peryearduringthefiveyearsofhisresidency,hewillhavetoborrow(“dissave”)$168,720eachyeartosupplementhis$25,000salary.Histotalindebtednesswillgrowtomaximumof$895,758atage35,andthendeclinethereafterasaresultofhissaving$106,280everyyearfromage36untilheretiresatage65.Notethathewillnothavepaidoffhisdebtuntilage45!,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,17,Example1,Supposethatyouare30yearsold,planstoretireatage65,andexpectstolivetoage85.Yoursalaryis$25,000peryear,andyouintendtomaintainaconstantlevelofrealconsumptionspendingoverthenext55years.Assumenotaxes,nogrowthinreallaborincome,andarealinterestrateof3%peryear.Whatisthevalueofyourhumancapital?Whatisyourpermanentincome?Whateffectwoulda$1millioninheritancethatyouexpecttoreceive30yearsfromnowhaveonyourpermanentincome?,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,18,5.2TakingAccountofSocialSecurity,InmanycountriesthegovernmentobligescitizenstoparticipateinamandatoryretirementincomesystemcalledsocialsecurityContributorspayataxduringtheirworkingyears,andinreturnqualifyforalifetimeannuityintheiroldage,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,19,SocialSecurityasInvestmentSubstitute,Ifsocialsecuritypaysareturnequalto3%inthelastexample,thenjustreducethesavingsbythesocialsecuritytaxForexample,thepreviousexample(Slide17).Ifyoupay$2000peryearinsocialsecuritytaxesfor35years,howmuchwillyoureceiveinbenefitsperyearfor20yearsstartingatage65.Whatimpactwillsocialsecurityhaveonyoursavings?Theanalysisbecomesprogressivelymorecomplexaswemaketheassumptionsmorerealistic.Whatifyoudontknowyourdateofdeath.,returnsarerisky,etcetera?,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,20,Redistributionamongtherichandthepoor,Inmanycountries,thesocialsecuritysystemoffersahigherrateofreturntopeopleinthelowerendoftheincomedistributionthantothoseintheupperend.Butthefactthatbenefitsarepaidintheformofalifetimeannuityimpliesthatnomatterhowrichorpooryouare,thelongeryoulive,thehigheryouractualrateofreturn.So,considerabonusawaitingyouifyoulivelongenough.,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,21,5.3DeferringTaxesThroughVoluntaryRetirementPlans,Manycountriesencouragevoluntarysavingsforretirementthroughprovisionsofthetaxcode.IntheUSemployeesarepermittedtosetupIndividualRetirementAccounts(IRA)thatdeferpaymentoftaxesuntilretirementTherulesarealittlecomplex,butanIRAmaybeusedbyaninvestortosavemoneyforretirement.Paymentsintotheplanaretax-deductible,buttheflowsfromtheplanafterretirementaretaxed.Theinterestonthesecontributionsisnottaxeduntilthemoneyiswithdrawn.Itisusualformarginaltaxratestobelowerafterretirement,butthisisnotthekeybenefit,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,22,IRABenefits,Themajorbenefitsaremoresubtle.Assume:Youcancontribute$1,000ofpre-taxedincometotheIRAplan,startingnextyear,forthenext30-years.Thiswillgrowattherateofinflationof2%Thattheplanwillreturn10%/yearThetaxrateonalltaxableincomestreamsis20%,bothnowandafterretirement,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,23,Acomparison,UsingIRA:Totalpre-taxamountaccumulatedinIRAwouldbePaytaxesattherateof20%,soyouwouldhavethefollowingamountleftaftertaxUsingothersavingaccounts:Youhavetopay20%of$1,000astaximmediately,so$800leftaftertaxeachyear;Theafter-taxinterestrateearnedis,therefore,Sotheamountaccumulatedatthesavingsplanwouldbe,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,24,TheAdvantageofTax-DeferredSaving,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,25,5.4ShouldYouInvestinaProfessionalDegree?,EducationmaybeviewedasaninvestmentinhumancapitalOnepurposeofadditionalschoolingistoincreaseonesearningpowerExample:GettingaGraduateDegree(likeallofyou),Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,26,Example2,Youare30yearsoldandareconsideringfull-timestudyforanMBAdegree.Tuitionandotherdirectcostswillbe$15,000peryearfortwoyears.Inadditionyouwillhavetogiveupajobwithasalaryof$30,000peryear.Assumetuitionispaidandsalaryreceivedattheendoftheyear.Howmuchdoesyoursalaryhavetoincrease(inrealterms)asaresultofgettingyourMBAdegreetojustifytheinvestment?Assumearealinterestrateof3%peryearandignoretaxes.Alsoassumethatthesalaryincreaseisaconstantrealamountthatstartsafteryoucompleteyourdegree(attheendoftheyearfollowinggraduation)andlastsuntilretirementatage65.,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,27,AmorecomplicatedexampleYouvedecidedtoobtainpracticalexperiencefor10years,andthengetaPh.D.InthreeyearsYouwantthesamestandardofincomeoverthenext13yearsAssumethatallcashflowsoccuratyear-endYourstartingsalaryis$35,000.Becauseyouaresmart,thiswillincreaseby15%/year.Youhaveagreedtobepaidthisattheendofthefirstyear,andyearlythereafterPh.D.Feesarecurrently$15,000peryear,andincreaseby3%/yearwithgeneralinflation.Feesarepaidattheendofeachyear,sothefeesfortheperiodfrom10to11arepaidatyear11,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,28,Con.,Taxesare30%,andareassumedtobeconstant.AssumethatlendingandborrowingrateshavebeenadjustedfortaxAfundwithacceptableriskyields10%/yearYoumayalsoborrowat10%Lendingrate=borrowingrate!Therealreasonforthisistosimplifythemath,butthefundcouldbemoderatelyaggressive,andthedebtbeconsumerloansQuestion:LivingExpenditure?,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,29,DataExtraction,LettheexpenditurerequiredforyourstandardoflivingbeXattheendofyear0(beginningofyear1),X*1.03inyear2,X*1.032inyear3,etceteraThefeesstartat$15,000*1.0310(year11),andcontinuetogrowatarateof3%Yournetsalarystartsat$35,000（after-tax）inyear1,andgrowsat15%for10yearsEverythingisdiscountedat10%,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,30,Salarycashflow(rateissue),Theafter-taxnominalcashflowinthefirstyearis$35,000,growsatanominal15%for10yearsWetreatthe15%asthecombinedeffectofinflationandrealgrowthApply,and“Inflation”isthe15%hereTherealrateis(0.10-0.15)/1.15=-4.35%,whichisthegrowthrateofpurchasingpowerofyoursalary,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,31,Salarycashflow($issue),Now,remember,wehaveassumedthatthecashflowsoccurattheendofeachyearThefirstnetincomeoccursattime1,andsomustbediscountedtoyear0Therealsalaryisnot$35,000but$35,000/1.15=$30,434.78,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,32,SalaryCashFlowComputation,Usingyourfinancialcalculators10-n;4.35“+/-”-I;PV=?;$30,434.78261-PMT;0-FVResultPV=$391,816.3459(in),Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,33,Feecashflow($issues),Thefeesarealreadyexpressedinrealterms,butthefirstcashflowoccursinyear11,not10(theevaluationpoint)Theyear11realcashflowmustbeadjustedtoyear1015000/1.03=$14563.1068,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,34,SolutionbyRealConversion,Therealinterestrateis(0.10-0.03)/1.03=6.7961165%orabout6.80%,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,35,FeeCashFlowComputation,Thepresentvalueofthefeesatyear10maybeobtainedusingyourfinancialcalculator:3-n;6.80-I;PV=?;$14563.1068-PMT;0-FVResultPV10=-$38,361.0067810-n;6.80-I;PV=?;PMT-0;FV10=38,361.00678(=PV10)ResultPV0=$19,876.2931(out),Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,36,LivingExpenditureCF$issues,CashflowsareassumedtooccurattheendofeachyearLetuscomputetherealamounttoday.DenotethisnominalamountintermsoftheunknownamountXinyear1X/1.03=0.970873786x,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,37,LivingExpenditureCFRateIssues,Thiscaseiseasy.Therealratehasbeencomputedtobe6.7961165%inthefeesection,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,38,LivingExpenditureCFComputation,WedonotknowboththePVnorthePMT.Setthepaymentto$1fornow,andmultiplybyXlaterUsingyourfinancialcalculators13-n;6.7961165-I;PV=?;$0.970873786-PMT;0-FVResultPV=$8.208829899*X(out),Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,39,SolutionbyRealConversion,Wearealmostdone.Allthatremainsistoassembletheparts,andsolvetheresultingequation,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,40,Conclusion,Thisamountistheactualamountthatwillbeexpendedforthefirstyear,paidattheendofthatyearThisisasimple,butnotatrivial,example,butitisloadedwithtrapsofeventhemostexperienced.ItrequiresmultistagelogicTheuseoftwodistinctinterestrateswillbothersomeofyouSomethinkersbelievethatitisbettertoavoidquantitiesthatcannotbeobserveddirectlyWhilewecertainlyfeeltheinfluenceofrealcashflowsandrealrates,observationisthroughtheinflationrateWeliveintheworldofthenominal,andanotherapproachistorecognizethisinoursystemoffinancialanalysis,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,41,SolutionbyGrowingAnnuity,Notationristhenominaldiscountratefrom0tobgisthegeometricgrowthrateinnominalcashflowspmtisthestartingcashflowNistheperiod,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,42,SolutionbyGrowingAnnuity,EquationWithacomparisontotheregularannuityPVformula,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,43,Solutionmethod,JustapplytheequationthreetimesToavoiderror,youmaywishtosummarizethedatainatablebeforeusingit,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,44,Algebra,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,45,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,46,Interpretation,Theplanprojectsyourgoingintodebtintheearlyyears.Youareprobablycollaterallizingyourexistinghumancapital,orfutureearningspotential,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,47,ConcludingRemark,Thereal(=nominal)value,xo,isnotaflow.Itisjustabasefromwhichthenominalflowsmaybecomputed,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,48,5.5ShouldYouBuyorRent,Interestpaidonamortgageistax-deductible,andthisprovidesasubstantialtaxbreakifyouareinahighertaxbracketThismaymakebuyingahouseattractivetoyouwhencomparedtorentingRememberthatthistaxshielddecays,Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall,49,Example3,Supposeyoucurrentlyrentanapartmentfor$10,000peryear,andhaveanoptiontobuyitfor$200,000.Propertytaxesare$2,400peryearandaredeductibleforincometaxpurposes.Annualmaintenancecostsonthepropertyare$1,200peryearandarenottaxdeductible.Thesecostsareassumedtobe