财务管理(英文第十三版)ch 3_sheena.pptx

财务管理(英文第十三版)ch 3_sheena.pptx

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Chapter3,TimeValueofMoney,TheInterestRateSimpleInterestCompoundInterestCompoundingMoreThanOnceperYearAmortizingaLoan,ChapterOutline,BasicDefinition,PresentValueValuetodayofafuturecashflow.,FutureValueAmounttowhichaninvestmentwillgrowafterearninginterest,BasicDefinition,DiscountRateInterestrateusedtocomputepresentvaluesoffuturecashflows.,DiscountFactorPresentvalueofa$1futurepayment.,Obviously,$10,000today.ThereasonisthatthereisTIMEVALUEOFMONEY!

Whichwouldyouprefer-$10,000todayor$10,000in5years?

TheInterestRate,TIMEallowsyoutheopportunitytopostponeconsumptionandearnINTEREST.,WhyisTIMEsuchanimportantelementinyourdecision?

WhyTIME?

CompoundInterestInterestpaid（earned）onanypreviousinterestearned,aswellasontheprincipalborrowed（lent）.InterestonInterest,TypesofInterest,SimpleInterestInterestpaid（earned）ononlytheoriginalamount,orprincipal,borrowed（lent）.,FormulaSI=P0（i）（n）SI:

SimpleInterestP0:

Deposittoday（t=0）i:

InterestRateperPeriodn:

NumberofTimePeriods,SimpleInterestFormula,SI=P0（i）（n）=$1,000（.07）

（2）=$140,Assumethatyoudeposit$1,000inanaccountearning7%simpleinterestfor2years.Whatistheaccumulatedinterestattheendofthe2ndyear?

SimpleInterestExample,FV=P0+SI=$1,000+$140=$1,140FutureValueisthevalueatsomefuturetimeofapresentamountofmoney,oraseriesofpayments,evaluatedatagiveninterestrate.,WhatistheFutureValue（FV）ofthedeposit?

SimpleInterest（FV）,ThePresentValueissimplythe$1,000youoriginallydeposited.Thatisthevaluetoday!

P0=FV-SIPresentValueisthecurrentvalueofafutureamountofmoney,oraseriesofpayments,evaluatedatagiveninterestrate.,WhatisthePresentValue（PV）ofthepreviousproblem?

SimpleInterest（PV）,WhyCompoundInterest?

FutureValue（U.S.Dollars）,Assumethatyoudeposit$1,000atacompoundinterestrateof7%for2years.,FutureValueSingleDeposit（Graphic）,012,$1,000,FV2,7%,FV1=P0（1+i）1=$1,000（1.07）=$1,070CompoundInterestYouearned$70interestonyour$1,000depositoverthefirstyear.Thisisthesameamountofinterestyouwouldearnundersimpleinterest.,FutureValueSingleDeposit（Formula）,FV1=P0（1+i）1FV2=P0（1+i）2GeneralFutureValueFormula:

FVn=P0（1+i）norFVn=P0（FVIFi,n）SeeTableI,GeneralFutureValueFormula,FVIFi,nisonTableIattheendofthebook,ValuationUsingTableI,JulieMillerwantstoknowhowlargeherdepositof$10,000todaywillbecomeatacompoundannualinterestrateof10%for5years.,Example,012345,$10,000,FV5,10%,CalculationbasedonTableI:

FV5=$10,000（FVIF10%,5）=$10,000（1.611）=$16,110DuetoRounding,StoryProblemSolution,Calculationbasedongeneralformula:

FVn=P0（1+i）nFV5=$10,000（1+0.10）5=$16,105.10,Wewillusethe“Rule-of-72”,Quick!

Howlongdoesittaketodouble$5,000atacompoundrateof12%peryear（approx.）?

DoubleYourMoney!

72/12%=6Yearsor72/6years=12%,Assumethatyouneed$1,000in2years.Letsexaminetheprocesstodeterminehowmuchyouneedtodeposittodayatadiscountrateof7%compoundedannually.,PresentValueSingleDeposit（Graphic）,012,$1,000,7%,PV1,PV0,GeneralFutureValueFormula:

FVn=PV0（1+i）nFVn=PV0（FVIFi,n）GeneralPresentValueFormula:

PV0=FVn/（1+i）norPV0=FVn（PVIFi,n）-SeeTable2,GeneralPresentValueFormula,PVIFi,nisonTableIIattheendofthebook,ValuationUsingTableII,JulieMillerwantstoknowhowlargeofadeposittomakesothatthemoneywillgrowto$10,000in5yearsatadiscountrateof10%.,StoryProblemExample,012345,$10,000,10%,Calculationbasedongeneralformula:

PV0=FVn/（1+i）nPV0=$10,000/（1+0.10）5=$6,209.21CalculationbasedonTable2:

PV0=$10,000（PVIF10%,5）=$10,000（.621）=$6,210.00DuetoRounding,StoryProblemSolution,Ifyouinvest$1,000today,youwillreceive$3,000inexactly8years.Whatisthecompoundinterestrateimplicitinthissituation?

FVn=PV0（FVIFi,n）（FVIFi,8）=FV8/PV0=3,000/1,000=3i=14.68%,UnknownInterestRate,Howlongwouldittakeforaninvestmentof$1,000togrowto$1,900ifweinvesteditatacompoundannualinterestrateof10percent?

FVn=PV0（FVIFi,n）（FVIF10%,n）=FVn/PV0=1,900/1,000=1.9n=6.72years,UnknownNumberofCompoundingPeriods,Whatisthefuturevalueof$1millioninvestedat10percentfor25years?

FVn=PV0（FVIFi,n）FV25=PV0（FVIF10%,25）=$1,000,000*10.835=$10,835,000,QuickQuiz,Youneed$30,000incashtobuyahouse4yearsfromtoday.Youexpecttoearn5percentonyoursavings.Howmuchdoyouneedtodeposittodayifthisistheonlymoneyyousaveforthispurpose?

PV0=FVn（PVIFi,n）PV0=FV4（PVIF5%,4）=$30,000*0.823=$246,900,Yourfirmhasbeentoldthatitneeds$74,300todaytofunda$120,000expense6yearsfromnow.Whatrateofinterestwasusedinthecomputation?

FVn=PV0（FVIFi,n）（FVIFi,6）=FV6/PV0=120,000/74,300=1.615i=8.3%,OrdinaryAnnuity:

Paymentsorreceiptsoccurattheendofeachperiod.AnnuityDue:

Paymentsorreceiptsoccuratthebeginningofeachperiod.,TypesofAnnuities,AnAnnuityrepresentsaseriesofequalpayments（orreceipts）occurringoveraspecifiednumberofequaldistantperiods.,StudentLoanPaymentsCarLoanPaymentsInsurancePremiumsMortgagePaymentsRetirementSavings,ExamplesofAnnuities,OrdinaryAnnuity,0123,$100$100$100,EndofPeriod1,EndofPeriod2,Today,EqualCashFlowsEach1PeriodApart,EndofPeriod3,AnnuityDue,0123,$100$100$100,BeginningofPeriod1,BeginningofPeriod2,Today,EqualCashFlowsEach1PeriodApart,BeginningofPeriod3,Itisanordinaryannuitywhosepaymentsorreceiptscontinueforever.PVA=R/ITheABSCo.wantstoofferpreferredstockforsaleatapriceof$60ashare.Ifthecompanywantstheirinvestorstoearnatleasta7.5percentrateofreturn,whatistheminimumannualdividendtheywillneedtopaypershare?

R=PVA*i=60*7.5%=$4.5,Perpetuity,FVAn=R（FVIFAi,n）PVAn=R（PVIFAi,n）FVADn=R（FVIFAi,n）（1+i）PVADn=（1+i）（R）（PVIFAi,n）Ristheperiodreceipt,FormulaaboutAnnuities,Whatisthefuturevalueofannualpaymentsof$6,500foreightyearsat12percent?

FVAn=R（FVIFAi,n）FVA8=$6,500*（FVIFA12%,8）=$6,500*12.30=$79,950,ExampleofAnnuit,1.Readproblemthoroughly2.Createatimeline3.Putcashflowsandarrowsontimeline4.DetermineifitisaPVorFVproblem5.DetermineifsolutioninvolvesasingleCF,annuitystream（s）,ormixedflow6.Solvetheproblem7.Checkwithfinancialcalculator（optional）,StepstoSolveTimeValueofMoneyProblems,JulieMillerwillreceivethesetofcashflowsbelow.WhatisthePresentValueatadiscountrateof10%.,MixedFlowsExample,012345,$600$600$400$400$100,PV0,10%,1.Solvea“piece-at-a-time”bydiscountingeachpiecebacktot=0.2.Solvea“group-at-a-time”byfirstbreakingproblemintogroupsofannuitystreamsandanysinglecashflowgroups.Thendiscounteachgroupbacktot=0.,HowtoSolve?

“Piece-At-A-Time”,012345,$600$600$400$400$100,10%,$545.45$495.87$300.53$273.21$62.09,$1677.15=PV0oftheMixedFlow,“Group-At-A-Time”（#1）,012345,$600$600$400$400$100,10%,$1,041.60$573.57$62.10,$1,677.27=PV0ofMixedFlowUsingTables,$600（PVIFA10%,2）=$600（1.736）=$1,041.60$400（PVIFA10%,2）（PVIF10%,2）=$400（1.736）（0.826）=$573.57$100（PVIF10%,5）=$100（0.621）=$62.10,“Group-At-A-Time”（#2）,01234,$400$400$400$400,PV0equals$1677.30.,012,$200$200,012345,$100,$1,268.00,$347.20,$62.10,Plus,Plus,JulieMillerwillreceivethesetofcashflowsbelow.WhatisthePresentValueatadiscountrateof7%.（PIECEATATIMEANDGROUPATATIME）,SOLVEPROBLEM,012345,$100$500$500$500$500,7%,44,NominalInterestRate,Thisistheannualratethatisquotedbylawthathasnotbeenadjustedforfrequencyofcompounding.Ifinterestiscompoundedmorethatonceayear,theeffectiveinterestratewillbehigherthatthenominalrate.,45,EffectiveAnnualRate（EAR）,Thisistheactualratepaid（orreceived）afteradjustingforcompoundingthatoccursduringtheyearIfyouwanttocomparetwoalternativeinvestmentswithdifferentcompoundingperiodsyouneedtocomputetheEARandusethatforcomparison.,46,CompoundingMorethanOnceaYear,FutureValueswithMonthlyCompoundingSupposeyoudeposit$50amonthintoanaccountthathasaninterestrateof12%,basedonmonthlycompounding.Howmuchwillyouhaveintheaccountin1years?

FVn=P0（1+i/m）mnPV0=FVn/（1+i/m）mnFV1=$50（1+12%/12）12*1=$50*1.127=$56.35,47,ContinuousCompounding,SometimesinvestmentsorloansarefiguredbasedoncontinuouscompoundingFVn=PV0（e）in,48,ThingstoRemember,YouALWAYSneedtomakesurethattheinterestrateandthetimeperiodmatch.Ifyouarelookingatannualperiods,youneedanannualrate.Ifyouarelookingatmonthlyperiods,youneedamonthlyrate.,49,EAR-Formula,Rememberthattheiisthequotedratemisthenumberofcompoundingperiodsperyear,Ifasavingsplanofferedanominalinterestrateof8%compoundedquarterlyonaone-yearinvestment,whatstheeffectiveannualinterestrate?

EAR=1+（8%/4）4-1=8.243%,Example,LoanTypesandLoanAmortization,PurediscountloansAborrowerreceivesmoneytodayandrepaysasinglelumpsumatsometimeinthefuture.Interest-onlyloansAborrowerpaysinteresteachperiodandrepaystheentireprincipleatsomepointinthefuture.AmortizedloansAlenderrequirestheborrowertorepaypartsoftheloanamountovertime.,2023/7/2,EssentialsofCorporateFinance,51,Theprocessofpayingoffaloanbymakingregularprinciplereductionsiscalledamortizingtheloan.Installment-typeLoanItisrepaidinequalperiodicpaymentsthatincludebothinterestandprinciple.Thesepaymentscanbemademonthly,quarterly,semiannually,orannually.Commonexamples:

mortgageloans,autoloans,consumerloans,andcertainbusinessloans.,AmortizingaLoan,1.Calculatethepaymentperperiod.2.DeterminetheinterestinPeriodt.（LoanBalanceatt-1）x（i%/m）3.ComputeprincipalpaymentinPeriodt.（Payment-InterestfromStep2）4.DetermineendingbalanceinPeriodt.（Balance-principalpaymentfromStep3）5.StartagainatSte