FRM前导课课件-不公开TVMCalculator_0 5D

TimeValueofMoney,1,TimeValueofMoney,Theideathatmoneyavailableatthepresenttimeisworthmorethanthesameamountinthefutureduetoitspotentialearningcapacity.Thiscoreprincipleoffinanceholdsthat,providedmoneycanearninterest,anyamountofmoneyisworthmorethesooneritisreceived.Itconcernsequivalencerelationshipsbetweencashflowsoccurringondifferentdates.,InterestRate,InterpretationsofInterestRateRequiredrateofreturnMinimumrateofreturnaninvestormustreceiveinordertoaccepttheinvestment.DiscountedRateOpportunityCostThevaluethatinvestorsforgoforcurrentconsumption.,InterestRate,ComponentsofInterestRateRealrisk-freeinterestrateSingle-periodinterestrateforrisk-freesecuritywithoutinflationexpected.InflationpremiumCompensatinginvestorsforexpectedinflationrisk.DefaultriskpremiumCompensatinginvestorsforthepossibilitythattheborrowerwillfailtomakeapromisedpaymentatthecontractedtimeandinthecontractedamount.,InterestRate,LiquiditypremiumCompensatinginvestorsfortheriskoflossrelativetoaninvestmentsfairvalueiftheinvestmentneedstobeconvertedtocashquicklyMaturitypremiumCompensatinginvestorsfortheincreasedsensitivityofthemarketvalueofdebttoachangeinmarketinterestratesasmaturityisextended,InterestRate,InterestRate(NominalInterestRate)=Realrisk-freeinterestrate+Inflationpremium+Defaultriskpremium+Liquiditypremium+MaturitypremiumNominalRisk-FreeInterestRate=Realrisk-freeinterestrate+Inflationpremium,5%=3%+2%,PresentValue,FutureValue,Compounding,PresentValue(PV)ThevalueofaninitialinvestmentattimeT=0.FutureValue(FV)ThevalueofaninitialinvestmentwouldbeworthatT=t,t=thenumberofcompoundingperiodsCompoundingThephenomenonthatinterestearnedoninterest.TheFrequencyofCompoundingThenumberoftimescompoundinginayear,denotedm.e.g.,annually,quarterly,monthly,daily,continuous.,AnnualRateandFrequencyofCompounding,StatedAnnualRateAlsoknownasquotedinterestrate,denotedrs.EffectiveAnnualRateAninvestmentsannualrateofinterestwhencompoundingoccursmoreoftenthanonceayear.PeriodicRateEqualtostatedannualratedividedbythecompoundingfrequencyinayear,denotedrs/m.,AnnualRateandFrequencyofCompounding,AnnualRateandFrequencyofCompounding,ExampleStatedannualrate=8%.Computetheeffectiveannualrate,compoundedquarterly.EAR=(1+8%/4)41=1.08241=8.24%,AnnualRateandFrequencyofCompounding,ExampleSupposea$10,000investment,statedannualinterestrateof8%,computethefuturevalue,given:CompoundingmonthlyContinuouscompounding,FutureValueandPresentValueofaSingleCashFlow,Example:FutureValueofaSingleCashFlowWhatisthefuturevalueof$200investedtodayintwoyearswhentheinterestrateis10%?,Method1(usingfinancialcalculator)N=2;I/Y=10;PV=200;PMT=0;CPTFV=242.00Method2FV=200(1.1)(1.1)=200(1.12)=242,FutureValueandPresentValueofaSingleCashFlow,Example:PresentValueofaSingleCashFlowWhatisthepresentvalueof$200tobereceivedintwoyearswhentheinterestrateis10%?,Method1(usingfinancialcalculator)N=2;I/Y=10;FV=200;PMT=0;CPTPV=$165.29Method2PV=200/1.12=$165.29,OrdinaryAnnuity,AnnuityDueandPerpetuity,AnnuityAfinitesetofconstantsequentialcashflows.OrdinaryAnnuityAllconstantcashflowsoccurringattheendofeachperiod.AnnuityDueAllconstantcashflowsoccurringatthebeginningofeachperiod.PerpetuityAsetofconstantnever-endingsequentialcashflowsoccurringattheendofeachperiod.,FutureValueandPresentValueofanOrdinaryAnnuity,Example:FutureValueofanOrdinaryAnnuityWhatisthevaluein3yearstimeof$200tobereceivedattheendofeachyearforthreeyearswhentheinterestrateis10%?,Method1(usingfinancialcalculator)Input:N=3;I/Y=10;PMT=200;CPTFV=$662.00Method2FV=PMT(1+r)N-1/r=200(1+0.1)3-1/0.1=$662.00,FutureValueandPresentValueofanOrdinaryAnnuity,Example:PresentValueofanOrdinaryAnnuityWhatisthepresentvalueof$200tobereceivedattheendofeachyearforthreeyearswhentheinterestrateis10%?,Method1(usingfinancialcalculator)Input:N=3;I/Y=10;PMT=200;CPTPV=$497.37Method2PV=PMT1-(1+r)-N/r=2001-(1+0.1)-3/0.1=$497.37,FutureValueandPresentValueofanAnnuityDue,Example:FutureValueofanAnnuityDueWhatisthevaluein3yearstimeof$200tobereceivedatthebeginningofeachyearforthreeyearswhentheinterestrateis10%?,Method1(usingfinancialcalculator)Input:N=3;I/Y=10;PMT=-200;PV=0;CPTFV=$662.001.1=$728.20Method2FV2=PMT(1+r)N-1/r=200(1+0.1)3-1/0.1=$662.00FV3=FV2(1+0.1)=$728.20,FutureValueandPresentValueofanAnnuityDue,Example:PresentValueofanAnnuityDueWhatisthepresentvalueof$200tobereceivedatthestartofeachyearforthreeyearswhentheinterestrateis10%?,Method1(usingfinancialcalculator)Input:N=2;I/Y=10;PMT=200;FV=0;CPTPV=$347.11+$200=$547.11Method2PV-1=PMT1-(1+r)-N/r=2001-(1+0.1)-3/0.1=$497.37PV0=PV-1(1+0.1)=$547.11,PresentValueofPerpetuity,ExampleApreferredstockwillpay$8/yearforeverandtherateofreturnis10%.Whatisitsvalue?PV=8/0.1=$80,r,PMT,PV,=,FutureValueofaSeriesofUnequalCashFlow,Example:,Method1FV=300(1.1)2+600(1.1)+200=$1,223Method2N=2;I/Y=10;PV=300;CPTFV=$363N=1;I/Y=10;PV=600;CPTFV=$660$200FVtotal=$1,223,PresentValueofaSeriesofUnequalCashFlow,Example:,Method1PV=200/1.13+600/1.12+300/1.1=$918.86Method2N=1;I/Y=10;FV=300;CPTPV=$272.73N=2;I/Y=10;FV=600;CPTPV=$495.87N=3;I/Y=10;FV=200;CPTPV=$150.26PVtotal=$918.86,OtherProblemsRelatedtoTimeValueofMoney,Example:Mortgage1.Whatisthemonthlypaymentona$100K,30-yearhomeloanwithstatedrateof6%?N=3012=360;I/Y=6/12=0.5;PV=100,000;FV=0CPTPMT=599.552.Howmuchistheremainingprincipal(payoffamount)justafterthe85thpaymentismade?N=36085=275paymentsleftCPTPV=89,488,OtherProblemsRelatedtoTimeValueofMoney,Example:RetirementSavingsClienthas$75,000insavingsnow,willretire20yearsfromtoday,andneeds25paymentsof$62,000/yeartobeginthen.Accountexpectedtoearn7%/year.Whatannualdepositmustshemakeattheendofeachyearfor20yearstoreachhergoal?Step1:Step2:,Howmuchneededatt=20?,ENDmodeN=24,FV=0,PMT=62,000,I/Y=7,CPTPV=711,099+62,000=$773,099,FV=773,099,I/Y=7,N=20,PV=75,000CPTPMT=11,778.68,OtherProblemsRelatedtoTimeValueofMoney,Example:DiscountRateElmerhaswonhis$4millionstatelotteryandhasbeenoffered20annualpaymentsof$200,000eachbeginningtodayorasinglepaymentof$2,267,000.Whatistheannualdiscountrateusedtocalculatethelump-sumpay-outamount?,InBGNmode,N=20,FV=0,PMT=200,000,PV=2,267,000,CPTI/Y=7%,OtherProblemsRelatedtoTimeValueofMoney,Example:NumberofCompoundingPeriodsElmerhaswonhis$4millionstatelotteryandhasbeenoffered20annualpaymentsof$200,000eachbeginningtodayorasinglepaymentof$2,267,000.IfElmercanchoosetheamountofhisannualpay-out,basedona7%discountrate,howmanypaymentsof$232,631couldElmerreceiveifhisfirstpaymentweretoday?,InBGNmode,FV=0,PMT=232,631,PV=2,267,000,I/Y=7%,CPTN=15,Practice(1),If12annualpaymentsof$13,000startedatthebeginningof2000,whatisthefuturevalueattheendof2012?Assumeaninterestrateof4%A.$195,335B.$211,275C.$162,240,Answer:BThefuturevalueoftheregularannuityis:$13,000 x(1+0.04)121dividedby0.04x(1.04)2=$211,275.,Practice(2),Afinancialproductofferstopayasumof$2,500perannumforaninfiniteperiodinreturnforanupfrontinvestmentof$38,462.Whatistheinterestrateimplicitwithinthisproduct?A.6.5%B.7%C.7.5%,Answer:BThepresentvalueoftheperpetuityat6.5%is:$2,500/0.065=$38,462,IntroductiontoFinancialCalculator,28,Understandingthefunctionsofkeysofyourcalculator,Understandingthefunctionsofkeysofyourcalculator,Understandingthefunctionsofkeysofyourcalculator,Example1:Calculate(3.54/2.21)1/41StepDisplay3.543.5400002.21yx1.60181041/x0.250000-1=0.125001,Understandingthefunctionsofkeysofyourcalculator,Example2:CalculateStepsDisplay0.890.8900002.17x1.473092x0.6041717.3+/-x2=32.196292,ClearingtheMemory,ClearingTVMmemoryCE/C2ndFVClearingCFfunctionmemoryCF2ndCE/CClearingBONDfunctionmemory2nd92ndCE/CClearingdatainMEMfunction2nd02ndCE/CClearingallthedatastoredandallsettingsPress“RESET”onthebackofcalculator,SettingUpTheCalculator,SettingupthedecimalpointsSettingupthealgorithm(CHN/AOS)SettinguptheP/YSettinguptheBGN/ENDmodeP.S.AlltheexamplesintheseslidesarepresentedbyusingTIBAIIPlus,Settingupthedecimalpoints,Example:Settingupto6decimalpointsStepsDisplay2nd.DEC=2.006ENTERDEC=6.0000002ndCPT0.000000P.S.Werecommendcandidatestouseupto6decimalpointsasitwillmeetouraccuracyrequirements,Settingupthealgorithm(CHN/AOS),ChangingfromCHNtoAOSMoststudentsprefertousethecalculatorinAOSmodehoweverthecalculatordefaultisCHNStepsDisplay2nd.DEC=6.000000Chn2ndENTERAOSP.S.ShouldyouliketochangeitbackfromAOStoCHN,justneedtopress2ndENTERagain,Settingupthealgorithm(CHN/AOS),CHNModeThecalculatorwillworkoutthefigurebasedonthenumbersyoukeyinorderly.e.g.3+5x4=32AOSModeThecalculatorwillworkoutthefigureaccordingtomathematicalalgorithm.e.g.3+5x4=23,SettinguptheP/Y,ThedefaultsettingofthecalculatorisP/Y=1Example:Thereare12paymentsperyearortherewouldbe12compoundingperiodsperyear,settinguptheP/Yaccordingly(ThisprocedureisNOTRECOMMENDED)StepsDisplay2ndI/YP/Y=1.00000012ENTERP/Y=12.000000,SettinguptheBGN/ENDmode,ThedefaultsettingofthecalculatorisENDmodeExample:SettingthecalculatorfromENDmodetoBGNmodeStepsDisplay2ndPMTEND2ndENTERBGN,Settingupthedates,SettingupthedatesandworkoutthenumberofdaysbetweenthesetwodatesExample:Findoutthenumberofdaysbetween2014-06-02and2014-12-06StepsDisplay2nd1DT1=12-31-1990(U.S.)6.0214ENTERDT1=6-02-2014DT2=12-31-199012.0614ENTERDT2=12-06-2014DBD=0.000000CPTDBD=187.000000ACT(Itmeansthecalculatorissetin365-daymode),Conversionbetweennominalrateandeffectiverate,Toworkouttheeffectiverate,givennominalrateandcompoundingfrequencyperyearExample:Nominalrate=6%,quarterlycompoundingperyearEffectiverate=?StepsDisplay2nd2NOM=0.0000006ENTERNOM=6.000000C/Y=1.0000004ENTERC/Y=4.000000EFF=0.000000CPTEFF=6.136355(Effectiverate=6.14%),Conversionbetweennominalrateandeffectiverate,Toworkoutthenominalrate,giveneffectiverateandcompoundingfrequencyperyearExample:Effectiverate=8.3%,monthlycompoundingperyearNominalrate=?StepsDisplay2nd2NOM=0.000000EFF=0.0000008.3ENTEREFF=8.300000C/Y=1.00000012ENTERC/Y=12.000000NOM=0.000000CPTNOM=8.000046(Nominalrate=8%),TimeValueofMoney,KeystrokeswewoulduseinTVMproblems:N-NumberofcompoundingperiodsI/Y-PeriodicratePV-PresentValuePMT-PeriodicPayments(e.g.,annuities,anyconstantcashflows)FV-FutureValue,TimeValueofMoney,UnderstandingtheTimeLine,-PV,-PMT,-PMT,-PMT,+FV,I/Y,N,FVofSingleSum,Example:Whatisthevalueof$100intenyearswiththeannuallycompoundinginterestrateof5%?,PV=-$100,10,2,1,9,I/Y=5%,N=10,FV=?,FVofSingleSum,StepsDisplay100+/-PVPV=-100.00000010NN=10.0000005I/YI/Y=5.0000000PMTPMT=0.000000CPTFVFV=162.889463P.S.Inputisusuallyenteredwithanegativesignsoastomaketheoutputcomeoutwithapositivesign.,Theorderthatthedataentereddoesnotmatter,PVofSingleSum,Example:Howmuchmustbeinvestedtoday,at8%interest,toaccumulateenoughtoretirea$10,000debtduesevenyearsfromtoday?,1,2,3,5,4,7,6,T=0,PV=?,FV=$10,000,I/Y=5%,N=7,PVofSingleSum,StepsDisplay10000FVFV=10,000.0000007NN=7.0000008I/YI/Y=8.0000000PMTPMT=0.000000CPTPVPV=-5,834.903953,Theorderthatthedataentereddoesnotmatter,FVofOrdinaryAnnuity,Example:Aninvestorwillreceiveanannuityof$4000ayearfortenyears.Thefirstpaymentistobereceivedattheendofthefirstyear.Ataannualinterestrateof9%,whatisthisannuitysworthattheendoftenyears?,T=0,1,2,3,10,9,FV=?,PMT=4000,PMT=4000,PMT=4000,PMT=4000,PMT=4000,I/Y=9%,N=10,PV=0,FVofOrdinaryAnnuity,StepsDisplay4000+/-PMTPMT=-4,000.00000010NN=10.0000009I/YI/Y=9.0000000PVPV=0.000000CPTFVFV=60,771.71887,Theorderthatthedataentereddoesnotmatter,PVofOrdinaryAnnuity,Example:Aninvestorhasjustwonthelotteryandwillreceive$50000peryearattheendofthenext20years.Ata10%interestrate,whatisthepresentvalueofthiswinnings?,T=0,1,2,20,19,PMT=50000,PMT=50000,PMT=50000,PMT=50000,I/Y=10%,N=20,PV=?,FV=0,PVofOrdinaryAnnuity,StepsDisplay50000+/-PMTPMT=-50,000.00000020NN=20.00000010I/YI/Y=10.0000000FVFV=0.000000CPTPVPV=425,678.1860,Theorderthatthedataentereddoesnotmatter,FVofAnnuityDue,Example:If$1000isinvestedtodayand$1000isinvestedatthebeginningofeachofthenextthreeyearsat12%interest(compoundedannually),whatistheamountthataninvestorwillhaveattheendofthefourthyear?,T=0,1,2,4,3,FV=?,PMT=1000PV=0,PMT=1000,PMT=1000,PMT=1000,I/Y=12%,N=4,FVofAnnuityDue,1stMethod(ENDMode)StepsDisplay1000+/-PMTPMT=-1,000.0000004NN=4.00000012I/YI/Y=12.0000000PVPV=0.000000CPTFVFV=4,779.328000(atendofyear3)x1.12=5352.847360(FVatendofyear4),FVofAnnuityDue,2ndMethod(BGNMode)StepsDisplay1000+/-PMTPMT=-1,000.0000004NN=4.00000012I/YI/Y=12.0000000PVPV=0.000000CPTFVFV=5,352.847360(FVatendofyear4),PVofAnnuityDue,Example:If$1000isinvestedtodayand$1000isinvestedatthebeginningofeachofthenextthreeyearsat12%interest(compoundedannually),whatisthepresentvalueofthesefourinvestments?,T=0,1,2,4,3,FV=0,PMT=1000PV=?,PMT=1000,PMT=1000,PMT=1000,I/Y=12%,N=4,FVofAnnuityDue,1stMethod(ENDMode)StepsDisplay1000+/-PMTPMT=-1,000.0000004NN=4.00000012I/YI/Y=12.0000000FVFV=0.000000CPTPVPV=3,037.349347(T=-1)x1.12=3,401.831268(T=0),PVofAnnuityDue,2ndMethod(BGNMode)StepsDisplay1000+/-PMTPMT=-1,000.0000004NN=4.00000012I/YI/Y=12.0000000FVFV=0.000000CPTPVPV=3,401.831268(T=0),PVofUnequalCashFlows,Example:If$100,$300,$500and$600areinvestedattheendofeachofthenextfouryearsat12%interest(compoundedannually)fromnow,whatisthepresentvalueofthesefourinvestments?,T=0,1,2,4,3,FV=0,PV=?,PMT=100,PMT=300,PMT=500,I/Y=12%,N=4,PMT=600,PVofUnequalCashFlows,StepsDisplayCFCF0=0.0000002ndCE/CCF0=0.000000(Clearpreviousworks)100ENTERC01=100.000000300ENTERC02=300.000000500ENTERC03=500.000000600ENTERC04=600.000000NPV12ENTERI=12.000000CPTNPV=1065.644849ThusPV0=1065.644849,CalculatingI/Y(DiscountedRate),Example:Elmerhaswonhisstatelotteryandhasbeenoffered20annualpaymentsof$200,000eachyearbeginningtodayorasinglepaymentof$2,267,000.Whatistheannualdiscountrateusedtocalculatethelump-sumpayoutamount?,T=0,1,2,20,19,FV=0,PMT=200000PV=2267000,PMT=200000,PMT=200000,PMT=200000,I/Y=?,N=20,WehavetoswitchtoBGNModefirstlyStepsDisplay200000+/-PMTPMT=-200,000.00000020NN=20.0000002267000PVPV=2,267,000.0000000FVFV=0.000000CPTI/YI/Y=7.000768(7%),CalculatingI/Y(DiscountedRate),CalculatingN(TheNumberofCompoundingPeriods),Example:IfElmercanchoosetheamountofhisannualpayout,basedonthesamediscountrateusedabove,howmanypaymentsof$232,631couldElmerreceiveifhisfirstpaymentweretoday?,T=0,1,2,T=?,3,FV=0,PMT=232631PV=2267000,PMT=232631,PMT=232631,PMT=232631,I/Y=7%,N=?,WehavetoswitchtoBGNModefirstlyStepsDisplay232631+/-PMTPMT=-232,631.0000007I/YI/Y=7.0000002267000PVPV=2,267,000.0000000FVFV=0.000000CPTNN=14.998877(N=15),CalculatingN(TheNumberofCompoundingPeriods),Mean,Example:Overthelast3yearsCernyPlcsstockreturnshavebeenasfollows,calculatethemeanreturn,Maybeenteredasdecimalsorwholenumbers,Mean,StepsDisplay2nd7X01=0.0000002ndCE/CX01=0.000000(Clearpreviousworks)6ENTERX01=6.0000008ENTERX02=8.0000004ENTERX03=4.0000002nd8Lin2ndENTER-Repeatedly1-V(Onevariable)X=6,MeanwithProbabilities,Example:Overthelast3yearsCernyPlcsstockreturnshavebeenasfollows,calculatethemeanreturn,Maybeenteredasdecimalsorwholenumbers,Mustbeenteredaswholenumbers,StepsDisplay2nd7X01=0.0000002ndCE/CX01=0.000000(Clearpreviousworks)6ENTERX01=6.00000030ENTERY01=30.0000008ENTERX02=8.00000020ENTERY02=20.0000004ENTERX03=4.00000050ENTERY03=50.0000002nd8Lin2ndENTER-Repeatedly1-V(Onevariable)X=5.400000,MeanwithProbabilities,PopulationStandardDeviation&SampleStandardDeviation,Example:Overthelast3yearsCernyPlcsstockreturnshavebeenasfollows,calculatethestandarddeviation,Maybeenteredasdecimalsorwholenumbers,StepsDisplay2nd7X01=0.0000002ndCE/CX01=0.000000(Clearpreviousworks)6ENTERX01=6.0000008ENTERX02=8.0000004ENTERX03=4.0000002nd8Lin2ndENTER-Repeatedly1-V(Onevariable)Sx=2.000000(SampleStandardDeviation)x=1.632993(PopulationStandardDeviation),PopulationStandardDeviation&SampleStandardDeviation,Example:Overthelast3yearsCernyPlcsstockreturnshavebeenasfollows,calculatethemeanreturn,Maybeenteredasdecimalsorwholenumbers,Mustbeenteredaswholenumbers,PopulationStandardDeviation&SampleStandard