4,Time Value of Money

TimeValueofMoney2LearningGoals1.Discusstheroleoftimevalueinfinance,theuseofcomputationalaids,andthebasicpatternsofcashflow.2.Understandtheconceptoffuturevalueandpresentvalue,theircalculationforsingleamounts,andtherelationshipbetweenthem.3.Findthefuturevalueandthepresentvalueofbothanordinaryannuityandanannuitydue,andthepresentvalueofaperpetuity.3LearningGoals(cont.)4.Calculateboththefuturevalueandthepresentvalueofamixedstreamofcashflows.5.Understandtheeffectthatcompoundinginterestmorefrequentlythanannuallyhasonfuturevalueandtheeffectiveannualrateofinterest.6.Describetheproceduresinvolvedin(1)determiningdepositsneededtoaccumulatetoafuturesum,(2)loanamortization,(3)findinginterestorgrowthrates,and(4)findinganunknownnumberofperiods.4QuestionWoulditbebetterforacompanytoinvest$100,000inaproductthatwouldreturnatotalof$200,000afteroneyear,oronethatwouldreturn$220,000aftertwoyears?TheRoleofTimeValueinFinance•Mostfinancialdecisionsinvolvecosts&benefitsthatarespreadoutovertime.•Timevalueofmoneyallowscomparisonofcashflowsfromdifferentperiods.5AnswerItdependsontheinterestrate!TheRoleofTimeValueinFinance(cont.)•Mostfinancialdecisionsinvolvecosts&benefitsthatarespreadoutovertime.•Timevalueofmoneyallowscomparisonofcashflowsfromdifferentperiods.6BasicConcepts•FutureValue:compoundingorgrowthovertime•PresentValue:discountingtotoday’svalue•Singlecashflows&seriesofcashflowscanbeconsidered•Timelinesareusedtoillustratetheserelationships7ComputationalAids•UsetheEquations•UsetheFinancialTables8ComputationalAids(cont.)9ComputationalAids(cont.)10ComputationalAids(cont.)11BasicPatternsofCashFlow•Thecashinflowsandoutflowsofafirmcanbedescribedbyitsgeneralpattern.•Thethreebasicpatternsincludeasingleamount,anannuity,oramixedstream:12SimpleInterest•Withsimpleinterest,youdon’tearninterestoninterest.•Year1:5%of$100=$5+$100=$105•Year2:5%of$100=$5+$105=$110•Year3:5%of$100=$5+$110=$115•Year4:5%of$100=$5+$115=$120•Year5:5%of$100=$5+$120=$12513CompoundInterest•Withcompoundinterest,adepositorearnsinterestoninterest!•Year1:5%of$100.00=$5.00+$100.00=$105.00•Year2:5%of$105.00=$5.25+$105.00=$110.25•Year3:5%of$110.25=$5.51+$110.25=$115.76•Year4:5%of$115.76=$5.79+$115.76=$121.55•Year5:5%of$121.55=$6.08+$121.55=$127.6314TimeValueTerms•PV0=presentvalueorbeginningamount•i=interestrate•FVn=futurevalueatendof“n”periods•n=numberofcompoundingperiods•A=anannuity(seriesofequalpaymentsorreceipts)15FourBasicModels•FVn=PV0(1+i)n=PVx(FVIFi,n)•PV0=FVn[1/(1+i)n]=FVx(PVIFi,n)•FVAn=A(1+i)n-1=Ax(FVIFAi,n)i•PVA0=A1-[1/(1+i)n]=Ax(PVIFAi,n)i16FutureValueofaSingleAmount•FutureValuetechniquestypicallymeasurecashflowsattheendofaproject’slife.•Futurevalueiscashyouwillreceiveatagivenfuturedate.•Thefuturevaluetechniqueusescompoundingtofindthefuturevalueofeachcashflowattheendofaninvestment’slifeandthensumsthesevaluestofindtheinvestment’sfuturevalue.•Wespeakofcompoundinteresttoindicatethattheamountofinterestearnedonagivendeposithasbecomepartoftheprincipalattheendoftheperiod.17$100x(1.08)1=$100xFVIF8%,1$100x1.08=$108FutureValueofaSingleAmount:UsingFVIFTables•IfFredMorenoplaces$100inasavingsaccountpaying8%interestcompoundedannually,howmuchwillhehaveintheaccountattheendofoneyear?18FV5=$800X(1+0.06)5=$800X(1.338)=$1,070.40FutureValueofaSingleAmount:TheEquationforFutureValue•JaneFarberplaces$800inasavingsaccountpaying6%interestcompoundedannually.Shewantstoknowhowmuchmoneywillbeintheaccountattheendoffiveyears.19PresentValueofaSingleAmount•Presentvalueisthecurrentdollarvalueofafutureamountofmoney.•Itisbasedontheideathatadollartodayisworthmorethanadollartomorrow.•Itistheamounttodaythatmustbeinvestedatagivenratetoreachafutureamount.•Calculatingpresentvalueisalsoknownasdiscounting.•Thediscountrateisoftenalsoreferredtoastheopportunitycost,thediscountrate,therequiredreturn,orthecostofcapital.20$300x[1/(1.06)1]=$300xPVIF6%,1$300x0.9434=$283.02PresentValueofaSingleAmount:UsingPVIFTables•PaulShorterhasanopportunitytoreceive$300oneyearfromnow.Ifhecanearn6%onhisinvestments,whatisthemostheshouldpaynowforthisopportunity?21PV=$1,700/(1+0.08)8=$1,700/1.851=$918.42PresentValueofaSingleAmount:TheEquationforFutureValue•PamValentiwishestofindthepresentvalueof$1,700thatwillbereceived8yearsfromnow.Pam’sopportunitycostis8%.22PresentValueofaSingleAmount:AGraphicalViewofPresentValue23Annuities•Annuitiesareequally-spacedcashflowsofequalsize.•Annuitiescanbeeitherinflowsoroutflows.•Anordinary(deferred)annuityhascashflowsthatoccurattheendofeachperiod.•Anannuityduehascashflowsthatoccuratthebeginningofeachperiod.•Anannuityduewillalwaysbegreaterthananotherwiseequivalentordinaryannuitybecauseinterestwillcompoundforanadditionalperiod.24TypesofAnnuitiesNotethattheamountofbothannuitiestotal$5,000.•FranAbramsischoosingwhichoftwoannuitiestoreceive.Bothare5-year$1,000annuities;annuityAisanordinaryannuity,andannuityBisanannuitydue.FranhaslistedthecashflowsforbothannuitiesasshowninTable4.1onthefollowingslide.25FutureValueofanOrdinaryAnnuity26FutureValueofanOrdinaryAnnuity(cont.)•FranAbramswishestodeterminehowmuchmoneyshewillha