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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 5.2TakingAccountofS
2、ocialSecurity5.2TakingAccountofSocialSecurity 5.3DeferringTaxesthroughVoluntary5.3DeferringTaxesthroughVoluntaryRetirementPlansRetirementPlans 5.4ShouldyouInvestinaProfessional5.4ShouldyouInvestinaProfessionalDegree?Degree? 5.5ShouldyouBuyorRent?5.5ShouldyouBuyorRent?2Copyright2009PearsonEducation,I
3、nc.PublishingasPrenticeHallObjectives HowmuchtosaveforretirementHowmuchtosaveforretirement WhethertodefertaxesorpaythemnowWhethertodefertaxesorpaythemnow WhethertogetaprofessionaldegreeWhethertogetaprofessionaldegree WhethertobuyorrentanapartmentWhethertobuyorrentanapartment3Copyright2009PearsonEduc
4、ation,Inc.PublishingasPrenticeHall5.1ALife-CycleModelofSavingAssumethatyouarecurrently35yearsold,expecttoretirein30yearsat65,andthenlivefor15moreyearsuntil80Yourreallaborincomeis$30,000/yearuntilage65Interestratesexceedinflationby3%/year4Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallHow
5、Much Should I Save and Consume?Considertwoapproaches: Targetreplacementrateofpre-retirementTargetreplacementrateofpre-retirementincomeincome MaintainthesamelevelofconsumptionMaintainthesamelevelofconsumptionspendingspending5Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallTargetreplacementr
6、ateofpre-retirementincomeFirstcomputetheretirementincome.Manyexpertsrecommendarateof75%ofthepre-retirementincome. $30,000*0.75=$22,500/year$30,000*0.75=$22,500/year usingyourcalculatorcomputethepresentusingyourcalculatorcomputethepresentvalueoftheretirementfundsasanregularvalueoftheretirementfundsas
7、anregularannuityannuityn=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,
8、604-PMT=5,646 Toobtainareal$22,500afterretirementyouneedtosave$5,646peryearfromnow.7Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallTargetreplacementrateConclusionYouwouldhavenoticedthatyourpre-retirementconsumptionis$30,000-$5,646=24,354;buttherealretirementincomeisonly$22,500Thenextmetho
9、dequatesconsumption8Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallMaintainthesamelevelofconsumptionspending AssumethatyourlevelofrealconsumptionisCAssumethatyourlevelofrealconsumptionisC ThepresentvalueofconsumptionoverthenextThepresentvalueofconsumptionoverthenext45yearsmustequalthepres
10、entvalueofearnings45yearsmustequalthepresentvalueofearningsoverthenext30yearsoverthenext30years UsingannuityformulawegotC=$23,982UsingannuityformulawegotC=$23,982 Thesavingsarethen$30,000-$23,982=Thesavingsarethen$30,000-$23,982=$6,018$6,018 Amoregeneralformula:Amoregeneralformula:9Copyright2009Pear
11、sonEducation,Inc.PublishingasPrenticeHallHumanCapitalandPermanentIncomeHumancapital ThepresentvalueofonesfuturelaborThepresentvalueofonesfuturelaborincomeincomePermanentincome Theconstantlevelof(real)consumptionTheconstantlevelof(real)consumptionspendingthathasapresentvalueequaltospendingthathasapre
12、sentvalueequaltooneshumancapitaloneshumancapital10Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall11Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall12Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallTheInter-temporalBudgetConstraint C=consumptionspendinginyeartC=consumpt
13、ionspendinginyeart i=realinterestratei=realinterestrate R=numberofyearstoretirementR=numberofyearstoretirement T=numberofyearsofremaininglifeT=numberofyearsofremaininglife WW0 0=initialwealth=initialwealth B=bequestB=bequest13Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallStory Dr.OmarBen
14、HolimhasjustgraduatedfrommedicalDr.OmarBenHolimhasjustgraduatedfrommedicalschoolatage30,andhasstartedtrainingtobeasurgeonschoolatage30,andhasstartedtrainingtobeasurgeonatMountHeavenHospital.atMountHeavenHospital. Omarsrealsalaryforthenextfiveyearswillbe$25,000Omarsrealsalaryforthenextfiveyearswillbe
15、$25,000peryear.peryear. Aftercompletinghisresidency,OmarexpectstoearnAftercompletinghisresidency,Omarexpectstoearn$300,000peryearinrealtermsuntilheretiresatage65.$300,000peryearinrealtermsuntilheretiresatage65. HewantstomaintainthesamelevelofrealconsumptionHewantstomaintainthesamelevelofrealconsumpt
16、ionspendingfortherestofhislifeandhislifeexpectancyisspendingfortherestofhislifeandhislifeexpectancyis85years,howmuchshouldheplantosavenowandin85years,howmuchshouldheplantosavenowandinthefuture?thefuture? Assumetherealinterestrateis3%peryear.Assumetherealinterestrateis3%peryear.14Copyright2009Pearson
17、Education,Inc.PublishingasPrenticeHallOmarsLife-CycleSavingsPlan15Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallillustration Omarshumancapitalinitiallyis$5,186,747,andhisOmarshumancapitalinitiallyis$5,186,747,andhispermanentincomeis$193,720.permanentincomeis$193,720. Inordertospend$193,7
18、20peryearduringthefiveInordertospend$193,720peryearduringthefiveyearsofhisresidency,hewillhavetoborrowyearsofhisresidency,hewillhavetoborrow(“dissave”)$168,720eachyeartosupplementhis(“dissave”)$168,720eachyeartosupplementhis$25,000salary.$25,000salary. HistotalindebtednesswillgrowtomaximumofHistotal
19、indebtednesswillgrowtomaximumof$895,758atage35,andthendeclinethereafteras$895,758atage35,andthendeclinethereafterasaresultofhissaving$106,280everyyearfromagearesultofhissaving$106,280everyyearfromage36untilheretiresatage65.36untilheretiresatage65. NotethathewillnothavepaidoffhisdebtuntilNotethathewi
20、llnothavepaidoffhisdebtuntilage45!age45!16Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallExample1 Supposethatyouare30yearsold,planstoSupposethatyouare30yearsold,planstoretireatage65,andexpectstolivetoage85.retireatage65,andexpectstolivetoage85.Yoursalaryis$25,000peryear,andyouintendYoursa
21、laryis$25,000peryear,andyouintendtomaintainaconstantlevelofrealtomaintainaconstantlevelofrealconsumptionspendingoverthenext55years.consumptionspendingoverthenext55years.Assumenotaxes,nogrowthinreallaborAssumenotaxes,nogrowthinreallaborincome,andarealinterestrateof3%peryear.income,andarealinterestrat
22、eof3%peryear. Whatisthevalueofyourhumancapital?Whatisthevalueofyourhumancapital? Whatisyourpermanentincome?Whatisyourpermanentincome? Whateffectwoulda$1millioninheritancethatyouWhateffectwoulda$1millioninheritancethatyouexpecttoreceive30yearsfromnowhaveonyourexpecttoreceive30yearsfromnowhaveonyourpe
23、rmanentincome?permanentincome?17Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall5.2TakingAccountofSocialSecurityInmanycountriesthegovernmentobligescitizenstoparticipateinamandatoryretirementincomesystemcalledsocialsecurityContributorspayataxduringtheirworkingyears,andinreturnqualifyforalif
24、etimeannuityintheiroldage18Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallSocialSecurityasInvestmentSubstitute IfsocialsecuritypaysareturnIfsocialsecuritypaysareturnequalequalto3%inthelastto3%inthelastexample,thenjustreducethesavingsbythesocialexample,thenjustreducethesavingsbythesocialse
25、curitytaxsecuritytax 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
26、 years much will you receive 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? TheanalysisbecomesprogressivelymorecomplexasTheanalysisbecomesprogressivelymorecomplexas
27、wemaketheassumptionsmorerealistic.wemaketheassumptionsmorerealistic. Whatifyoudontknowyourdateofdeath.,returnsarerisky,Whatifyoudontknowyourdateofdeath.,returnsarerisky,etcetera?etcetera?19Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallRedistributionamongtherichandthepoor Inmanycountries,
28、thesocialsecuritysystemInmanycountries,thesocialsecuritysystemoffersahigherrateofreturntopeopleintheoffersahigherrateofreturntopeopleinthelowerendoftheincomedistributionthantolowerendoftheincomedistributionthantothoseintheupperend.thoseintheupperend. ButthefactthatbenefitsarepaidintheformofButthefac
29、tthatbenefitsarepaidintheformofalifetimeannuityimpliesthatnomatterhowalifetimeannuityimpliesthatnomatterhowrichorpooryouare,thelongeryoulive,therichorpooryouare,thelongeryoulive,thehigheryouractualrateofreturn.higheryouractualrateofreturn. So,considerabonusawaitingyouifyouliveSo,considerabonusawaiti
30、ngyouifyoulivelongenough.longenough.20Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall5.3DeferringTaxesThroughVoluntaryRetirementPlans ManycountriesencourageManycountriesencouragevoluntarysavingsvoluntarysavingsforretirementforretirementthroughprovisionsofthetaxcode.throughprovisionsofthet
31、axcode. IntheUSemployeesarepermittedtosetupIndividualIntheUSemployeesarepermittedtosetupIndividualRetirementAccounts(IRA)thatdeferpaymentoftaxesRetirementAccounts(IRA)thatdeferpaymentoftaxesuntilretirementuntilretirement Therulesarealittlecomplex,butanIRAmaybeusedbyTherulesarealittlecomplex,butanIRA
32、maybeusedbyaninvestortosavemoneyforretirement.Paymentsintoaninvestortosavemoneyforretirement.Paymentsintotheplanaretheplanaretax-deductibletax-deductible,buttheflowsfromtheplan,buttheflowsfromtheplanafterretirementaretaxed.Theinterestontheseafterretirementaretaxed.Theinterestonthesecontributionsisno
33、ttaxeduntilthemoneyiswithdrawn.contributionsisnottaxeduntilthemoneyiswithdrawn. ItisusualformarginaltaxratestobelowerafterItisusualformarginaltaxratestobelowerafterretirement,butthisisnotthekeybenefitretirement,butthisisnotthekeybenefit21Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallIRAB
34、enefits Themajorbenefitsaremoresubtle.Assume:Themajorbenefitsaremoresubtle.Assume: Youcancontribute$1,000ofpre-taxedYoucancontribute$1,000ofpre-taxedincometotheIRAplan,startingnextyear,forincometotheIRAplan,startingnextyear,forthenext30-years.Thiswillgrowattheratethenext30-years.Thiswillgrowattherat
35、eofinflationof2%ofinflationof2% Thattheplanwillreturn10%/yearThattheplanwillreturn10%/year ThetaxrateonalltaxableincomestreamsisThetaxrateonalltaxableincomestreamsis20%,bothnowandafterretirement20%,bothnowandafterretirement22Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallAcomparison Using
36、IRA:UsingIRA: Totalpre-taxamountaccumulatedinIRAwouldbeTotalpre-taxamountaccumulatedinIRAwouldbe Paytaxesattherateof20%,soyouwouldhavethePaytaxesattherateof20%,soyouwouldhavethefollowingamountleftaftertaxfollowingamountleftaftertax Usingothersavingaccounts:Usingothersavingaccounts: Youhavetopay20%of
37、$1,000astaximmediately,soYouhavetopay20%of$1,000astaximmediately,so$800leftaftertaxeachyear;$800leftaftertaxeachyear; Theafter-taxinterestrateearnedis,therefore,Theafter-taxinterestrateearnedis,therefore, SotheamountaccumulatedatthesavingsplanwouldbeSotheamountaccumulatedatthesavingsplanwouldbe23Cop
38、yright2009PearsonEducation,Inc.PublishingasPrenticeHallTheAdvantageofTax-DeferredSaving24Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall5.4ShouldYouInvestinaProfessionalDegree?Educationmaybeviewedasaninvestmentinhumancapital OnepurposeofadditionalschoolingistoOnepurposeofadditionalschooli
39、ngistoincreaseonesearningpowerincreaseonesearningpowerExample:GettingaGraduateDegree(likeallofyou)25Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallExample2 Youare30yearsoldandareconsideringfull-timeYouare30yearsoldandareconsideringfull-timestudyforanMBAdegree.Tuitionandotherdirectstudyfor
40、anMBAdegree.Tuitionandotherdirectcostswillbe$15,000peryearfortwoyears.Incostswillbe$15,000peryearfortwoyears.Inadditionyouwillhavetogiveupajobwithasalaryadditionyouwillhavetogiveupajobwithasalaryof$30,000peryear.Assumetuitionispaidandsalaryof$30,000peryear.Assumetuitionispaidandsalaryreceivedattheen
41、doftheyear.Howmuchdoesyourreceivedattheendoftheyear.Howmuchdoesyoursalaryhavetoincrease(inrealterms)asaresultofsalaryhavetoincrease(inrealterms)asaresultofgettingyourMBAdegreetojustifytheinvestment?gettingyourMBAdegreetojustifytheinvestment?Assumearealinterestrateof3%peryearandAssumearealinterestrat
42、eof3%peryearandignoretaxes.Alsoassumethatthesalaryincreaseisignoretaxes.Alsoassumethatthesalaryincreaseisaconstantrealamountthatstartsafteryoucompleteaconstantrealamountthatstartsafteryoucompleteyourdegree(attheendoftheyearfollowingyourdegree(attheendoftheyearfollowinggraduation)andlastsuntilretirem
43、entatage65.graduation)andlastsuntilretirementatage65.26Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall AmorecomplicatedexampleAmorecomplicatedexample Youvedecidedtoobtainpracticalexperiencefor10years,Youvedecidedtoobtainpracticalexperiencefor10years,andthengetaPh.D.Inthreeyearsandthengeta
44、Ph.D.Inthreeyears Youwantthesamestandardofincomeoverthenext13Youwantthesamestandardofincomeoverthenext13yearsyears Assumethatallcashflowsoccuratyear-endAssumethatallcashflowsoccuratyear-end Yourstartingsalaryis$35,000.Becauseyouaresmart,Yourstartingsalaryis$35,000.Becauseyouaresmart,thiswillincrease
45、by15%/year.Youhaveagreedtobethiswillincreaseby15%/year.Youhaveagreedtobepaidthisattheendofthefirstyear,andyearlythereafterpaidthisattheendofthefirstyear,andyearlythereafter Ph.D.Feesarecurrently$15,000peryear,andincreasebyPh.D.Feesarecurrently$15,000peryear,andincreaseby3%/yearwithgeneralinflation.F
46、eesarepaidattheend3%/yearwithgeneralinflation.Feesarepaidattheendofeachyear,sothefeesfortheperiodfrom10to11areofeachyear,sothefeesfortheperiodfrom10to11arepaidatyear11paidatyear1127Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallCon. Taxesare30%,andareassumedtobeTaxesare30%,andareassumedto
47、beconstant.Assumethatlendingandborrowingconstant.Assumethatlendingandborrowingrateshavebeenadjustedfortaxrateshavebeenadjustedfortax Afundwithacceptableriskyields10%/yearAfundwithacceptableriskyields10%/year Youmayalsoborrowat10%Youmayalsoborrowat10% Lendingrate=borrowingrate!TherealreasonLendingrat
48、e=borrowingrate!Therealreasonforthisistosimplifythemath,butthefundforthisistosimplifythemath,butthefundcouldbemoderatelyaggressive,andthedebtbecouldbemoderatelyaggressive,andthedebtbeconsumerloansconsumerloans Question:LivingExpenditure?Question:LivingExpenditure?28Copyright2009PearsonEducation,Inc.
49、PublishingasPrenticeHallDataExtraction 2 2inyear3,etceterainyear3,etcetera 1010(year11),andcontinuetogrowatarate(year11),andcontinuetogrowatarateof3%of3% YourYournetnetsalarystartsat$35,000salarystartsat$35,000（after-after-taxtax）inyear1,andgrowsat15%for10inyear1,andgrowsat15%for10yearsyears Everyth
50、ingisdiscountedat10%Everythingisdiscountedat10%29Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallSalarycashflow(rateissue) Theafter-taxnominalcashflowinthefirstyearisTheafter-taxnominalcashflowinthefirstyearis$35,000,growsatanominal15%for10years$35,000,growsatanominal15%for10years Wetreatt
51、he15%asthecombinedeffectofinflationWetreatthe15%asthecombinedeffectofinflationandrealgrowthandrealgrowth Apply,and“Inflation”isthe15%hereApply,and“Inflation”isthe15%here Therealrateis(0.10-0.15)/1.15=-4.35%,whichisTherealrateis(0.10-0.15)/1.15=-4.35%,whichisthegrowthrateofpurchasingpowerofyoursalary
52、thegrowthrateofpurchasingpowerofyoursalary30Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallSalarycashflow($issue) Now,remember,wehaveassumedthattheNow,remember,wehaveassumedthatthecashflowsoccurattheendofeachyearcashflowsoccurattheendofeachyear Thefirstnetincomeoccursattime1,andsoThefirst
53、netincomeoccursattime1,andsomustbediscountedtoyear0mustbediscountedtoyear031Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallSalaryCashFlowComputation UsingyourfinancialcalculatorsUsingyourfinancialcalculators 10-n;4.35“+/-”-I;PV=?;10-n;4.35“+/-”-I;PV=?;$30,434.78261-PMT;0-FV$30,434.78261-P
54、MT;0-FV ResultPV=$391,816.3459(in)ResultPV=$391,816.3459(in)32Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallFeecashflow($issues) Thefeesarealreadyexpressedinrealterms,Thefeesarealreadyexpressedinrealterms,butthefirstcashflowoccursinyear11,notbutthefirstcashflowoccursinyear11,not10(theeva
55、luationpoint)Theyear11real10(theevaluationpoint)Theyear11realcashflowmustbeadjustedtoyear10cashflowmustbeadjustedtoyear1033Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallSolutionbyRealConversion Therealinterestrateis(0.10-0.03)/1.03=Therealinterestrateis(0.10-0.03)/1.03=6.7961165%orabout6
56、.80%6.7961165%orabout6.80%34Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallFeeCashFlowComputation Thepresentvalueofthefeesatyear10mayThepresentvalueofthefeesatyear10maybeobtainedusingyourfinancialcalculator:beobtainedusingyourfinancialcalculator: 3-n;6.80-I;PV=?;$14563.1068-3-n;6.80-I;PV=
57、?;$14563.1068-PMT;0-FVPMT;0-FV ResultPVResultPV1010 10-n;6.80-I;PV=?;PMT-0;FV10-n;6.80-I;PV=?;PMT-0;FV1010=38,361.00678(=PV38,361.00678(=PV1010) ) ResultPVResultPV0 0=$19,876.2931(out)=$19,876.2931(out)35Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallLivingExpenditureCF$issues Cashflowsar
58、eassumedtooccurattheendofCashflowsareassumedtooccurattheendofeachyeareachyear Letuscomputetherealamounttoday.Letuscomputetherealamounttoday.DenotethisnominalamountintermsoftheDenotethisnominalamountintermsoftheunknownamountXinyear1unknownamountXinyear1 X/1.03=0.970873786xX/1.03=0.970873786x36Copyrig
59、ht2009PearsonEducation,Inc.PublishingasPrenticeHallLivingExpenditureCFRateIssues Thiscaseiseasy.TherealratehasbeenThiscaseiseasy.Therealratehasbeencomputedtobe6.7961165%inthefeecomputedtobe6.7961165%inthefeesectionsection37Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallLivingExpenditureCF
60、Computation WedonotknowboththePVnorthePMT.WedonotknowboththePVnorthePMT.Setthepaymentto$1fornow,andmultiplySetthepaymentto$1fornow,andmultiplybyXlaterbyXlater UsingyourfinancialcalculatorsUsingyourfinancialcalculators 13-n;6.7961165-I;PV=?;13-n;6.7961165-I;PV=?;$0.970873786-PMT;0-FV$0.970873786-PMT;
61、0-FV ResultPV=$8.208829899*X(out)ResultPV=$8.208829899*X(out)38Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallSolutionbyRealConversionWearealmostdone.AllthatremainsistoassembleWearealmostdone.Allthatremainsistoassembletheparts,andsolvetheresultingequationtheparts,andsolvetheresultingequat
62、ion39Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallConclusion ThisamountistheThisamountistheactualactualamountthatwillbeexpendedamountthatwillbeexpendedforthefirstyear,paidattheendofthatyearforthefirstyear,paidattheendofthatyear Thisisasimple,butnotatrivial,example,butitisloadedThisisasi
63、mple,butnotatrivial,example,butitisloadedwithtrapsofeventhemostexperienced.Itrequireswithtrapsofeventhemostexperienced.Itrequiresmultistagelogicmultistagelogic TheuseoftwodistinctinterestrateswillbothersomeofTheuseoftwodistinctinterestrateswillbothersomeofyouyou Somethinkersbelievethatitisbettertoav
64、oidquantitiesSomethinkersbelievethatitisbettertoavoidquantitiesthatcannotbeobserveddirectlythatcannotbeobserveddirectly WhilewecertainlyfeeltheinfluenceofrealcashflowsWhilewecertainlyfeeltheinfluenceofrealcashflowsandrealrates,observationisthroughtheinflationrateandrealrates,observationisthroughthei
65、nflationrate Weliveintheworldofthenominal,andanotherWeliveintheworldofthenominal,andanotherapproachistorecognizethisinoursystemoffinancialapproachistorecognizethisinoursystemoffinancialanalysisanalysis40Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallSolutionbyGrowingAnnuityNotation risthe
66、nominaldiscountratefrom0tobristhenominaldiscountratefrom0tob gisthegeometricgrowthrateinnominalgisthegeometricgrowthrateinnominalcashflowscashflows pmtisthestartingcashflowpmtisthestartingcashflow NistheperiodNistheperiod41Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallSolutionbyGrowingAn
67、nuity EquationEquation WithacomparisontotheregularannuityPVWithacomparisontotheregularannuityPVformulaformula42Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallSolutionmethod JustapplytheequationthreetimesJustapplytheequationthreetimes Toavoiderror,youmaywishtosummarizeToavoiderror,youmaywi
68、shtosummarizethedatainatablebeforeusingitthedatainatablebeforeusingit43Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallAlgebra44Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall45Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallInterpretationTheplanprojectsyourgoingintode
69、btintheearlyyears.Youareprobablycollaterallizingyourexistinghumancapital,orfutureearningspotential46Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallConcludingRemarkThereal(=nominal)value,xo,isnotaflow.Itisjustabasefromwhichthenominalflowsmaybecomputed47Copyright2009PearsonEducation,Inc.Pub
70、lishingasPrenticeHall5.5ShouldYouBuyorRentInterestpaidonamortgageistax-deductible,andthisprovidesasubstantialtaxbreakifyouareinahighertaxbracketThismaymakebuyingahouseattractivetoyouwhencomparedtorentingRememberthatthistaxshielddecays48Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallExampl
71、e3 Suppose you currently rent an apartment for $10,000 per year, and Suppose you currently rent an apartment for $10,000 per year, and have an option to buy it for $200,000. have an option to buy it for $200,000. Property taxes are $2,400 per year and are deductible for income tax Property taxes are
72、 $2,400 per year and are deductible for income tax purposes. Annual maintenance costs on the property are $1,200 per purposes. Annual maintenance costs on the property are $1,200 per year and are year and are notnot tax deductible. These costs are assumed to be fixed tax deductible. These costs are
73、assumed to be fixed in real terms, and currently included in the rent. in real terms, and currently included in the rent. Your income tax rate is 30%, and you plan to keep the apartment Your income tax rate is 30%, and you plan to keep the apartment forever. forever. The (real) interest rate is fixe
74、d in 3%.The (real) interest rate is fixed in 3%. What is a better choice for you, buying or renting the apartment?What is a better choice for you, buying or renting the apartment? What is the “break-even” annual rent such that you would buy it if What is the “break-even” annual rent such that you wo
75、uld buy it if the rent exceeds this amount?the rent exceeds this amount? 49Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallAnalysis ThepresentvalueofcostequalsthediscountedThepresentvalueofcostequalsthediscountedvalueoftheafter-taxoutflowsdiscountedatvalueoftheafter-taxoutflowsdiscountedat
76、theafter-taxrateofinterest.Becausepropertytheafter-taxrateofinterest.Becausepropertytaxescanbedeductedfromincome,theafter-taxescanbedeductedfromincome,theafter-taxoutflowforpropertytaxeseachyearistaxoutflowforpropertytaxeseachyearis0.7*$2,400=$1,680.andthesubtotalcost0.7*$2,400=$1,680.andthesubtotal
77、costwouldbe$1,200+$1,680=$2,880eachyear.wouldbe$1,200+$1,680=$2,880eachyear. Youkeepyourapartmentforever,soweYoukeepyourapartmentforever,soweassumeaninfinitehorizon,whichmeanstheassumeaninfinitehorizon,whichmeansthecostabovewouldbelikeaperpetuity.costabovewouldbelikeaperpetuity.50Copyright2009Pearso
78、nEducation,Inc.PublishingasPrenticeHallAsimplecomparison Letibethebefore-taxdiscountrate.Letibethebefore-taxdiscountrate. ThepresentvaluecostofowningtheapartmentThepresentvaluecostofowningtheapartmentis is AndthepresentvaluecostofrentingitisAndthepresentvaluecostofrentingitis Soitisobviousthatbuying
79、theapartmentisaSoitisobviousthatbuyingtheapartmentisacost-efficientchoicethanrentingit.cost-efficientchoicethanrentingit.51Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallInterpretation Thebuy-or-rentdecisionisreallyaninvestmentThebuy-or-rentdecisionisreallyaninvestmentdecisionforahousehol
80、d.decisionforahousehold. Ineffectyouarelayingout$200,000todayinIneffectyouarelayingout$200,000todayinordertoreceivefuturecashbenefitsequaltoordertoreceivefuturecashbenefitsequaltotheafter-taxsavingsinrentalcosts.theafter-taxsavingsinrentalcosts. Inpresentvalueterms,yousave$139,047(i.e.Inpresentvalue
81、terms,yousave$139,047(i.e.$476,190-337,143).ThisistheNPVofthe$476,190-337,143).ThisistheNPVoftheinvestmentintheapartment.investmentintheapartment.52Copyright2009PearsonEducation,Inc.PublishingasPrenticeHallBreak-evenannualrent LetitbeX,thenLetitbeX,then SolvingforX:SolvingforX: WhichmeansthatiftherentislessthanWhichmeansthatiftherentislessthan$7,080peryear,youwouldprefertokeep$7,080peryear,youwouldprefertokeeponrentingratherthantobuy.onrentingratherthantobuy.53Copyright2009PearsonEducation,Inc.PublishingasPrenticeHall
