Chapter 6 Accounting and the Time Value of Money.docx
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Chapter 6 Accounting and the Time Value of Money.docx
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Chapter6AccountingandtheTimeValueofMoney
Chapter6:
AccountingandtheTimeValueofMoney
1)BasicTimeValueConcepts:
TimeValue(TV)ofMoney:
Adollarreceivedtodayisworthmorethanadollarpromisedatsometimeinthefuture.Thisrelationshipexistsbecauseoftheopportunitytoinvesttoday’sdollarandreceiveinterestontheinvestment.
aApplicationsofTimeValueConcepts:
i)UsedformakingdecisionsaboutNotes,Leases,PensionsandOtherPostretirementBenefits,Long-TermAssets,SinkingFunds,BusinessCombinations,Disclosures,andInstallmentContracts.
ii)Also,TVconceptsareveryimportantinpersonalfinanceandinvestmentdecisions.Forexample,TVofMoneyisusedwhenpurchasinghomeorcar,planningforretirement,anddecidingoninvestments.
bTheNatureofInterest:
i)Interest:
ii)AmountofInterestintransactionisfunctionofthreevariables:
(1)Principal:
(2)InterestRate:
(3)Time:
Thelargertheprincipalthelargerthedollaramountofinterest.
Thehighertheinterestratethelargerthedollaramountofinterest.
Thelongerthetimeperiodthelargerthedollaramountofinterest.
cSimpleInterest:
dCompoundInterest:
i)
ii)Example:
Simplevs.CompoundInterest(Illustration6-1,page255)
Deposit$10,000atbank.
Letsimpleinterest=9%.
Letcompoundinterest=9%compoundedannually.
Assumenowithdrawaluntil3years.
Illustration6-1onpage255:
Year
SimpleInterestCalculation
CompoundInterestCalculation
SimpleInterestCalculation
SimpleInterest
AccumulatedYear-endBalance
CompoundInterestCalculation
CompoundInterest
AccumulatedYear-endBalance
Yr1
$10,000x9%
$900
$10,900
$10,000x9%
$900
$10,900
Yr2
$10,000x9%
$900
$11,800
$10,900x9%
$981.00
$11,881.00
Yr3
$10,000x9%
$900
$12,700
$11,880.10x9%
$1069.29
$12,950.29
Total
$2700
$2950.29
NotethattheCompoundedInterestis$250.29higherthantheSimpleInterest($2950.29-$2,700=$250.29)
SimpleInterestCalculation:
∙Usestheinitialprincipalof$10,000tocomputeinterestinall3years.
CompoundInterestCalculation:
∙Usestheaccumulatedbalance(principalplusinteresttodate)atendofeachyeartocomputeinterestforthenextyear.(Thisexplainswhycompoundedinterestislarger.)
Compoundingassumesthatunpaidinterestbecomesapartoftheprincipal.Theaccumulatedbalanceattheendofeachyearbecomesthenewprincipal,whichisusedtocalculateinterestforthenextyear.
Simpleinterest
iii)CompoundInterestTables:
Fivedifferenttypesofcompoundinteresttablesarepresentedattheendofthechapter.
(1)FutureValueof$1Table(SingleSumTable):
Amount$1willequalifdepositednowataspecifiedrateandleftforaspecifiednumberofperiods.Example:
Canbeusedtoanswerthequestion:
(Table6-1;page302and303.)
(2)PresentValueof$1Table:
Amountthatmustbedepositednowataspecifiedrateofinteresttoequal$1attheendofaspecifiednumberofperiods.Example:
Canbeusedtoanswerthequestion:
(Table6-2;page304and305.)
(3)FutureValueofanOrdinaryAnnuityof$1Table:
Amounttowhichpaymentsof$1willaccumulateifpaymentsareinvestedatENDofeachperiodatspecifiedrateofinterestforspecifiednumberofperiods.Example:
Canbeusedtoanswerthequestion:
(Table6-3;page306and307.)
(4)PresentValueofanOrdinaryAnnuityof$1Table:
Amountthatmustbedepositednowataspecifiedrateofinteresttopermitwithdrawalsof$1attheENDofregularperiodicintervalsforspecifiednumberofperiods.Example:
Canbeusedtoanswerthequestion:
(Table6-4;page308and309.)
(5)PresentValueofanAnnuitydueof$1Table:
Amountsthatmustbedepositednowataspecifiedrateofinteresttopermitwithdrawalsof$1attheBEGINNINGofregularperiodicintervalsforthespecifiednumberofperiods.Example:
Canbeusedtoanswerthequestion:
(Table6-5;page310and311.)
(6)General:
(a)Compoundtablesarecomputedusingbasicformulas.
(b)
(i)TOCONVERTANNUALINTERESTRATETOCOMPOUNDINGPERIODICINTERESTRATE:
(ii)TODETERMINETHENUMBEROFPERIODS:
(c)FrequencyofCompounding:
(Illustration6-4page257)
Thisillustrationshowshowtodetermine:
(1)Interestratepercompoundingperiod.
(2)Numberofcompoundingperiodsinfourdifferentscenarios.
12%AnnualInterestRateover5yearsCompounded
InterestRateperCompoundingPeriod
NumberofCompoundingPeriods
Annually
(1)
0.12/1=0.12
5yrsx1periodperyr=5periods
Semiannually
(2)
0.12/2=0.06
5yrsx2periodperyr=10periods
Quarterly(4)
0.12/4=0.03
5yrsx4periodperyr=20periods
Monthly(12)
0.12/12=0.01
5yrsx12periodperyr=60periods
(d)Definitions:
Example:
Assume9%annualinterestcompoundedDAILYprovidesa9.42%yield,oradifferenceof0.42%.
Effectiverate:
The9.42%isreferredtoastheeffectiveyield.
Statedrate(ornominalrateorfacerate):
The9%isreferredtoasthestatedrate.
Relationshipbetweeneffectiveandstatedrate:
Whencompoundingfrequencyisgreaterthanonceayear,theeffectiveinterestratewillalwaysbegreaterthanthestatedrate.
eFundamentalVariables:
Thefollowingfourvariablesarefundamentaltoallcompoundinterestproblems:
i)InterestRate:
Unlessotherwisestated,therategivenistheannualratethatmustbeadjustedtoreflectlengthofcompoundingperiodiflessthanayear.
ii)NumberofTimePeriods:
Numberofcompoundingperiods(Anindividualperiodmaybeequaltoorlessthan1year.)
iii)FutureValue:
Valueatafuturedategivensum(s)investedassumingcompoundinterest.
iv)PresentValue:
Valuenow(presenttime)offuturesum(s)discountedassumingcompoundinterest.
Insomecases,allfourvariablesareknown.However,manytimesatleastonevariableisunknown.
2)Single-SumProblems:
Twocategoriesofsingle-sumproblems:
aFutureValueofaSingleSum:
i)Computeunknownfuturevalueofknownsinglesumofmoneyinvestednowforcertainnumberofperiods(n)atacertaininterestrate(i).
ii)
iii)Determinefuturevalueofsinglesum:
Multiplythefuturevaluefactor(FVF)byitspresentvalue(principal).
whereFV=futurevalue;PV=presentvalue;FVF=futurevaluefactorfornperiodsatiinterest.
iv)Example1:
(p260)
Whatisfuturevalueof$50,000investedfor5yearscompoundedannuallyat11%?
FV=PV(FVF)
FV=
FV=
(Togetthe___________FVF,lookatTable6-1onpage303.The___%columnand____-periodrowgivesthefuturevaluefactorof___________.)
v)Example2:
(p260)
Whatisthefuturevalueof$250millionifdepositedin2002for4yearsifinterestis10%,compoundedsemi-annually?
FV=PV(FVF)
FV=
FV=
(Togetthe________,lookatTable6-1whichistheFutureValueof$1table.Thisisthetableusedtofigureoutthefuturevalueof$1investedtoday.Togetthenumberofperiods,______________________________________________________.Thus,thereare______periods.Togetthecorrectsemi-annualinterestrate,____________________________________.Thisgivesusa______________________________________Weusen=___(numberofperiods)andi=____%(interestrate)tofindthecorrectFVF.)
bPresentValueofaSingleSum:
i)
ii)Computeunknownpresentvalueofknownsinglesumofmoneyinthefuturethatisdiscountedfornperiodsatiinterestrate.
iii)
iv)Determinepresentvalueofsinglesum:
wherePV=presentvalue;FV=futurevalue;PVF=presentvaluefactorfornperiodsatiinterest.
v)Example1:
(page261-262)
Whatisthepresentvalueof$84,253tobereceivedorpaidin5yearsdiscountedat11%compoundedannually?
PV=FV(PVF)
PV=
PV=
(Togetthe__________PVF,lookatTable6-2onpage305.The___%columnand____-periodrowgivesthepresentvaluefactorof_________.)
vi)Example2:
(page262)
Ifwewant$2,000threeyearsfromnowandthecompoundedinterestrateis8%,howmuchshouldweinvesttoday?
PV=FV(PVF)
PV=
PV=
(Togetthe__________PVF,lookatTable6-2,page305.The____%columnandthe___-periodrowgivethePVFof__________.)
cSolvingforOtherUnknownsinSingle-SumProblems:
Unliketheexamplesgivenabove,manytimesboththefuturevalueandpresentvalueareknown,butthenumberofperiodsortheinterestrateisunknown.Ifanythreeofthefourvalues(FV,PV,n,i)areknown,theremainingunknownvariablecanbederived.
i)Illustration–ComputationoftheNumberofPeriods:
Howmanyyearswillittakeforadepositof$47,811at10%compoundedannuallytoaccumulateto$70,000?
Solution1:
FVF=
FVF=
LookatTable6-1,FutureValueof$1.Lookat____%columnandfindthecalculatedFVFof_________.Wefindthisfactorintherown=____.Thus,itwilltake___________.
Solution2:
PVF=
PVF=
LookatTable6-2,PresentValueof$1.Lookat____%columnandfindthecalculatedPVFof_________.Wefindthisfactorintherown=___.Thus,itwilltake____________.
ii)Illustration–ComputationoftheInterestRate:
Whatistheinterestrateneededifweinvest$800,000nowandwanttohave$1,409,870fiveyearsfromnow?
Solution1:
FVF=
FVF=
LookatTable6-1p303,FutureValueof$1.Lookatrown=____andfindthecalculatedFVFof_______.Wefindthisfactorinthecolumni=___%.Thus,wewouldneedaninterestrateof___%.
Solution2:
PVF=
PVF=
LookatTable6-2p305,PresentValueof$1.Lookatrown=____andfindthecalculatedPVFof________.Wefindthisfactorinthecolumnfor____%.Thus,wewouldneedaninterestrateof_____%.
3)Annuities:
aGeneral:
i)Uptothispoint,wehaveonlyworkedwithdiscountingasinglesum.However,manytimesaseriesofdolla
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