会计学人大出版英文版第23版Chap006.ppt

TimeValueofMoneyConcepts 6 Copyright 2011bytheMcGraw HillCompanies Inc Allrightsreserved McGraw Hill Irwin SimpleInterest Interestamount P i nAssumeyouinvest 1 000at6 simpleinterestfor3years Youwouldearn 180interest 1 000 06 3 180 or 60eachyearfor3years CompoundInterest Assumewedeposit 1 000inabankthatearns6 interestcompoundedannually Whatisthebalanceinouraccountattheendofthreeyears CompoundInterest FutureValueofaSingleAmount Thefuturevalueofasingleamountistheamountofmoneythatadollarwillgrowtoatsomepointinthefuture Assumewedeposit 1 000forthreeyearsthatearns6 interestcompoundedannually 1 000 00 1 06 1 060 00and 1 060 00 1 06 1 123 60and 1 123 60 1 06 1 191 02 FutureValueofaSingleAmount Writinginamoreefficientway wecansay 1 191 02 1 000 1 06 3 FV PV 1 i n FutureValue AmountInvestedattheBeginningofthePeriod InterestRate NumberofCompoundingPeriods UsingtheFutureValueof 1Table wefindthefactorfor6 and3periodsis1 19102 So wecansolveourproblemlikethis FV 1 000 1 19102FV 1 191 02 FutureValueofaSingleAmount PresentValueofaSingleAmount Insteadofaskingwhatisthefuturevalueofacurrentamount wemightwanttoknowwhatamountwemustinvesttodaytoaccumulateaknownfutureamount Thisisapresentvaluequestion Presentvalueofasingleamountistoday sequivalenttoaparticularamountinthefuture PresentValueofaSingleAmount Rememberourequation FV PV 1 i nWecansolveforPVandget PresentValueofaSingleAmount Assumeyouplantobuyanewcarin5yearsandyouthinkitwillcost 20 000atthattime Whatamountmustyouinvesttodayinordertoaccumulate 20 000in5years ifyoucanearn8 interestcompoundedannually PresentValueofaSingleAmount i 08 n 5PresentValueFactor 68058 20 000 68058 13 611 60 Ifyoudeposit 13 611 60now at8 annualinterest youwillhave 20 000attheendof5years PresentValueof 1Table FV PV 1 i n FutureValue PresentValue InterestRate NumberofCompoundingPeriods Therearefourvariablesneededwhendeterminingthetimevalueofmoney Ifyouknowanythreeofthese thefourthcanbedetermined SolvingforOtherValues DeterminingtheUnknownInterestRate Supposeafriendwantstoborrow 1 000todayandpromisestorepayyou 1 092twoyearsfromnow Whatistheannualinterestrateyouwouldbeagreeingto a 3 5 b 4 0 c 4 5 d 5 0 Somenotesdonotincludeastatedinterestrate Wecallthesenotesnoninterest bearingnotes Eventhoughtheagreementstatesitisanoninterest bearingnote thenotedoes infact includeinterest Weimputeanappropriateinterestratefornoninterest bearingnotes AccountingApplicationsofPresentValueTechniques SingleCashAmount StatementofFinancialAccountingConceptsNo 7 UsingCashFlowInformationandPresentValueinAccountingMeasurements Theobjectiveofvaluinganassetorliabilityusingpresentvalueistoapproximatethefairvalueofthatassetorliability ExpectedCashFlowApproach BasicAnnuities Anannuityisaseriesofequalperiodicpayments Period1 Period2 Period3 Period4 10 000 10 000 10 000 10 000 Anannuitywithpaymentsattheendoftheperiodisknownasanordinaryannuity OrdinaryAnnuity Endofyear1 10 000 10 000 10 000 10 000 Endofyear2 Endofyear3 Endofyear4 AnnuityDue Anannuitywithpaymentsatthebeginningoftheperiodisknownasanannuitydue Beginningofyear1 10 000 10 000 10 000 10 000 Beginningofyear2 Beginningofyear3 Beginningofyear4 FutureValueofanOrdinaryAnnuity Tofindthefuturevalueofanordinaryannuity multiplytheamountoftheannuitybythefuturevalueofanordinaryannuityfactor FutureValueofanOrdinaryAnnuity Weplantoinvest 2 500attheendofeachofthenext10years Wecanearn8 compoundedinterestannually onallinvestedfunds Whatwillbethefundbalanceattheendof10years FutureValueofanAnnuityDue Tofindthefuturevalueofanannuitydue multiplytheamountoftheannuitybythefuturevalueofanannuityduefactor FutureValueofanAnnuityDue Computethefuturevalueof 10 000investedatthebeginningofeachofthenextfouryearswithinterestat6 compoundedannually PresentValueofanOrdinaryAnnuity Youwishtowithdraw 10 000attheendofeachofthenext4yearsfromabankaccountthatpays10 interestcompoundedannually Howmuchdoyouneedtoinvesttodaytomeetthisgoal PV1PV2PV3PV4 10 000 10 000 10 000 10 000 PresentValueofanOrdinaryAnnuity PresentValueofanOrdinaryAnnuity Ifyouinvest 31 698 60todayyouwillbeabletowithdraw 10 000attheendofeachofthenextfouryears PresentValueofanOrdinaryAnnuity CanyoufindthisvalueinthePresentValueofOrdinaryAnnuityof 1table MoreEfficientComputation 10 000 3 16986 31 698 60 PresentValueofanAnnuityDue Computethepresentvalueof 10 000receivedatthebeginningofeachofthenextfouryearswithinterestat6 compoundedannually PresentValueofaDeferredAnnuity Inadeferredannuity thefirstcashflowisexpectedtooccurmorethanoneperiodafterthedateoftheagreement PresentValueofaDeferredAnnuity OnJanuary1 2011 youareconsideringaninvestmentthatwillpay 12 500ayearfor2yearsbeginningonDecember31 2013 Ifyourequirea12 returnonyourinvestments howmuchareyouwillingtopayforthisinvestment MoreEfficientComputationCalculatethePVoftheannuityasofthebeginningoftheannuityperiod Discountthesinglevalueamountcalculatedin 1 toitspresentvalueasoftoday PresentValueofaDeferredAnnuity OnJanuary1 2011 youareconsideringaninvestmentthatwillpay 12 500ayearfor2yearsbeginningonDecember31 2013 Ifyourequirea12 returnonyourinvestments howmuchareyouwillingtopayforthisinvestment PresentValueofaDeferredAnnuity OnJanuary1 2011 youareconsideringaninvestmentthatwillpay 12 500ayearfor2yearsbeginningonDecember31 2013 Ifyourequirea12 returnonyourinvestments howmuchareyouwillingtopayforthisinvestment SolvingforUnknownValuesinPresentValueSituations Inpresentvalueproblemsinvolvingannuities therearefourvariables PresentvalueofanordinaryannuityorPresentvalueofanannuitydue Theamountoftheannuitypayment Thenumberofperiods Theinterestrate Ifyouknowanythreeofthese thefourthcanbedetermined SolvingforUnknownValuesinPresentValueSituations Assumethatyouborrow 700fromafriendandintendtorepaytheamountinfourequalannualinstallmentsbeginningoneyearfromtoday Yourfriendwishestobereimbursedforthetimevalueofmoneyatan8 annualrate Whatistherequiredannualpaymentthatmustbemade theannuityamount torepaytheloaninfouryears SolvingforUnknownValuesinPresentValueSituations Assumethatyouborrow 700fromafriendandintendtorepaytheamountinfourequalannualinstallmentsbeginningoneyearfromtoday Yourfriendwishestobereimbursedforthetimevalueofmoneyatan8 annualrate Whatistherequiredannualpaymentthatmustbemade theannuityamount torepaytheloaninfouryears AccountingApplicationsofPresentValueTechniques Annuities Becausefinancialinstrumentstypicallyspecifyequalperiodicpayments theseapplicationsquiteofteninvolveannuitysituations Long termBonds Long termLeases PensionObligations ValuationofLong termBonds CalculatethePresentValueoftheLump sumMaturityPayment FaceValue CalculatethePresentValueoftheAnnuityPayments Interest OnJune30 2011 EbsenElectricissued10 statedratebondswithafacevalueof 1million Thebondsmaturein5years Themarketrateofinterestforsimilarissueswas12 InterestispaidsemiannuallybeginningonDecember31 2011 Whatwasthepriceofthebondissue ValuationofLong termLeases Certainlong termleasesrequiretherecordingofanassetandcorrespondingliabilityatthepresentvalueoffutureleasepayments ValuationofLong termLeases OnJanuary1 2011 ToddFurnitureCompanysigneda20 yearnon cancelableleaseforanewretailshowroom Theleaseagreementcallsforannualpaymentsof 25 000for20yearsbeginningonJanuary1 2011 Theappropriaterateofinterestforthislong termleaseis8 CalculatethevalueoftheassetacquiredandtheliabilityassumedbyTodd thepresentvalueofanannuitydueat8 for20years ValuationofPensionObligations Somepensionplanscreateobligationsduringemployees serviceperiodsthatmustbepaidduringtheirretirementperiods Theamountscontributedduringtheemploymentperiodaredeterminedusingpresentvaluecomputationsoftheestimateofthefutureamounttobepaidduringretirement ValuationofPensionOblig