ConclusionsandReviewofFinancialManagementTypesofFinanceBusinessFinanceMacroFinanceMicroFinancePersonalFinanceGovernmentFinanceFinancecorporatefinancefinancialmarketinternationalfinanceinvestmentfinancialengineeringFunctionsofFinanceFinancingInvestingFunctionsofFinanceFinancingWheretogetfundsWhentogetfundsHowmuchtoraiseHowmuchtopayforfundsInvestingWhattodowithfundsonceraisedFormsofBusinessOrganizationSoleProprietorshipPartnershipCorporationSoleProprietorshipAdvantagesEaseofformationSubjecttofewregulationsNocorporateincometaxesDisadvantages LimitedlifeDifficulttoraisecapitalUnlimitedliabilityPartnershipAdvantagesPossiblesynergySubjecttofewregulationsNocorporateincometaxesDisadvantages LimitedlifeDifficulttoraisecapitalPossibleconflictsCorporationAdvantagesUnlimitedlifeEaseoftransferringownershipLimitedliabilityDisadvantages DoubletaxationCostoforganizationCostofreportfilingTheRoleofFinancialManagementWhatisFinancialManagement?TheGoaloftheFirmOrganizationoftheFinancialManagementFunctionWhatisFinancialManagement?Concernstheacquisition,financing,andmanagementofassetswithsomeoverallgoal

inmind.InvestmentDecisionsWhatistheoptimalfirmsize?Whatspecificassetsshouldbeacquired?Whatassets(ifany)shouldbereducedoreliminated?Mostimportantofthethreedecisions.FinancingDecisionsWhatisthebesttypeoffinancing?Whatisthebestfinancingmix?Whatisthebestdividendpolicy?Howwillthefundsbephysicallyacquired?Determinehowtheassets(LHSofbalancesheet)willbefinanced(RHSofbalancesheet).AssetManagementDecisionsHowdowemanageexistingassetsefficiently?FinancialManagerhasvaryingdegreesofoperatingresponsibilityoverassets.Greateremphasisoncurrentassetmanagementthanfixedassetmanagement.WhatistheGoaloftheFirm?MaximizationofShareholderWealth!Valuecreationoccurswhenwemaximizethesharepriceforcurrentshareholders.ShortcomingsofAlternativePerspectivesCouldincreasecurrentprofitswhileharmingfirm(e.g.,defermaintenance,issuecommonstocktobuyT-bills,etc.).Ignoresrisk.ProfitMaximizationMaximizingafirm’searningsaftertaxes.

ProblemsShortcomingsofAlternativePerspectivesDoesnotspecifytimingordurationofexpectedreturns.Ignoresrisk.Callsforazeropayoutdividendpolicy.EarningsperShareMaximizationMaximizingearningsaftertaxesdividedbysharesoutstanding. ProblemsStrengthsofShareholderWealthMaximizationTakesaccountof:currentandfutureprofitsandEPS;thetiming,duration,andriskofprofitsandEPS;dividendpolicy;andallotherrelevantfactors.Thus,shareprice

servesasabarometerforbusinessperformance.TheModernCorporationThereexistsaSEPARATIONbetweenownersandmanagers.ModernCorporationShareholdersManagementRoleofManagementAnagentisanindividualauthorizedbyanotherperson,calledtheprincipal,toactinthelatter’sbehalf.Managementactsasanagent

fortheowners(shareholders)ofthefirm.AgencyTheoryAgencyTheory

isabranchofeconomicsrelatingtothebehaviorofprincipalsandtheiragents.JensenandMecklingdevelopedatheoryofthefirmbasedonagencytheory.AgencyTheoryIncentivesinclude,

stockoptions,

perquisites,

and

bonuses.Principalsmustprovideincentives

sothatmanagementactsintheprincipals’bestinterestsandthenmonitor

results.SocialResponsibilityWealthmaximizationdoesnotprecludethefirmfrombeingsociallyresponsible.Assumeweviewthefirmasproducingbothprivateandsocialgoods.Then

shareholder

wealth

maximization

remainstheappropriategoalingoverningthefirm.OrganizationoftheFinancialManagementFunctionBoardofDirectorsPresident(ChiefExecutiveOfficer)VicePresidentOperationsVicePresidentMarketingVPofFinanceTreasurerCapitalBudgetingCashManagementCreditManagementDividendDisbursementFinAnalysis/PlanningPensionManagementInsurance/RiskMngmtTaxAnalysis/PlanningOrganizationoftheFinancialManagementFunctionVPofFinanceControllerCostAccountingCostManagementDataProcessingGeneralLedgerGovernmentReportingInternalControlPreparingFinStmtsPreparingBudgetsPreparingForecastsChapter2TheBusiness,Tax,andFinancialEnvironmentsTheBusiness,Tax,andFinancialEnvironmentsTheBusinessEnvironmentTheTaxEnvironmentTheFinancialEnvironmentTheBusinessEnvironmentSoleProprietorshipsPartnerships(generalandlimited)CorporationsLimitedliabilitycompaniesTheU.S.hasfourbasicformsofbusinessorganization:TheBusinessEnvironmentOldestformofbusinessorganization.Businessincomeisaccountedforonyourpersonal

incometaxform.SoleProprietorship

--Abusinessformforwhichthereisoneowner.Thissingleownerhasunlimitedliabilityforalldebtsofthefirm.Summaryfor SoleProprietorshipAdvantagesSimplicityLowsetupcostQuicksetupSingletaxfilingonindividualformDisadvantagesUnlimitedliabilityHardtoraiseadditionalcapitalTransferofownershipdifficultiesTheBusinessEnvironmentBusinessincomeisaccountedforoneachpartner’spersonal

incometaxform.Partnership--Abusinessforminwhichtwoormoreindividualsactasowners.TypesofPartnershipsLimitedPartnership

--limitedpartnershaveliabilitylimitedtotheircapitalcontribution(investorsonly).Atleastonegeneralpartnerisrequiredandallgeneralpartnershaveunlimitedliability.GeneralPartnership

--allpartnershaveunlimitedliabilityandareliableforallobligationsofthepartnership.SummaryforPartnershipAdvantagesCanbesimpleLowsetupcost,higherthansoleproprietorshipRelativelyquicksetupLimitedliabilityforlimitedpartnersDisadvantagesUnlimitedliabilityforthegeneralpartnerDifficulttoraiseadditionalcapital,buteasierthansoleproprietorshipTransferofownershipdifficultiesTheBusinessEnvironmentAnartificialentitythatcanownassetsandincurliabilities.Businessincomeisaccountedforontheincometaxformofthecorporation.Corporation--Abusinessformlegallyseparatefromitsowners.SummaryforCorporationAdvantagesLimitedliabilityEasytransferofownershipUnlimitedlifeEasiertoraiselargequantitiesofcapitalDisadvantagesDoubletaxationMoredifficulttoestablishMoreexpensivetosetupandmaintainTheBusinessEnvironmentBusinessincomeisaccountedforoneachmember’sindividualincometaxform.LimitedLiabilityCompanies

--Abusinessformthatprovidesitsowners(calledmembers)withcorporate-stylelimitedpersonalliabilityandthefederal-taxtreatmentofapartnership.LimitedLiabilityCompany(LLC)LimitedliabilityCentralizedmanagementUnlimitedlifeTransferofownershipwithoutotherowners?priorconsentGenerally,anLLCwillpossessonlythefirsttwoofthefollowingfourstandardcorporationcharacteristicsSummaryforLLCAdvantagesLimitedliabilityEliminatesdoubletaxationNorestrictiononnumberortypeofownersEasiertoraiseadditionalcapitalDisadvantagesLimitedlife(generally)Transferofownershipdifficulties(generally)CorporateIncomeTaxesIncomeTaxExampleLisaMillerofBasketWonders(BW)iscalculatingthe

incometaxliability,marginaltaxrate,

and

averagetaxrateforthefiscalyearendingDecember31.BW‘scorporatetaxableincomeforthisfiscalyearwas$250,000.IncomeTaxExampleMarginaltaxrate

=39%Averagetaxrate

=$80,750

/$250,000 =32.3%Incometaxliability

=$22,250+.39x($250,000-$100,000)=$22,250+$58,500 =$80,750DepreciationGenerally,profitablefirmsprefertouseanacceleratedmethodfortaxreportingpurposes.Depreciationrepresentsthesystematicallocationofthecostofacapitalassetoveraperiodoftimeforfinancialreportingpurposes,taxpurposes,orboth.CommonTypesofDepreciation

Straight-line(SL)

AcceleratedTypesDoubleDecliningBalance(DDB)ModifiedAcceleratedCostRecoverySystem(MACRS)DepreciationExampleLisaMillerofBasketWonders(BW)iscalculatingthedepreciationonamachinewithadepreciablebasisof$100,000,

a6-yearusefullife,anda5-yearpropertyclasslife.ShecalculatestheannualdepreciationchargesusingMACRS.MACRSExampleAssetsaredepreciatedbasedononeofeightdifferentpropertyclasses.Generally,thehalf-yearconventionisused.DepreciationinanyparticularyearisthemaximumofDDBorstraight-line.AswitchindepreciationmethodsismadefromDDBtoSLduringthelifeoftheasset.MACRSExampleMACRSScheduleOtherTaxIssuesQuarterlyTaxPayments

requirecorporationstopay25%oftheirestimatedannualtaxliabilityonthe15thofApril,June,September,andDecember.AlternativeMinimumTax

isaspecialtaxwhichequals20%ofalternativeminimumtaxableincome(generallynotequaltotaxableincome).CorporationspaythemaximumofAMTorregulartaxliability.InterestDeductibilityInterestExpense

istheinterestpaidonoutstandingdebtandistaxdeductible.CashDividend

isthecashdistributionofearningstoshareholdersandisnotataxdeductibleexpense.Theafter-taxcostofdebtis: (InterestExpense)X(1-TaxRate)Thus,debtfinancinghasataxadvantage!HandlingCorporateLossesandGainsLossesaregenerallycarriedbackfirstandthenforwardstartingwiththeearliestyearwithoperatinggains.Corporationsthatsustainanetoperatinglosscancarrythatlossback(Carryback)3yearsandforward(Carryforward)15yearstooffsetoperatinggainsinthoseyears.CorporateLossesandGainsExampleLisaMillerisexaminingtheimpactofanoperatinglossatBasketWonders(BW)in19X7.Thefollowingtimelineshowsoperatingincomeandlosses.Whatimpactdoesthe19X7losshaveonBW?-$500,000

$100,000

$150,000$150,00019X719X619X519X4CorporateLossesandGainsExampleThelosscanoffsetthegainineachoftheyears19X4through19X6.Theremaining$100,000canbecarriedforwardto19X8orbeyond.-$500,000

$100,000

$150,000$150,00019X719X619X519X4-$150,000-$150,000-$100,000$400,000000-$100,000CorporateCapitalGains/LossesOftenhistorically,capitalgainsincomehasreceivedmorefavorableU.S.taxtreatmentthanoperatingincome.Generally,thesaleofacapitalasset(asdefinedbytheIRS)generatesacapitalgain(assetsellsformorethanoriginalcost)orcapitalloss(assetsellsforlessthanoriginalcost).CorporateCapitalGains/LossesCapitallossesaredeductibleonlyagainstcapitalgains.Currently,capitalgainsaretaxedatordinaryincometaxratesforcorporations,oramaximum35%.PersonalIncomeTaxesTheU.S.hasaprogressivetaxstructurewithfourtaxbracketsof15%,28%,31%,

and36%.A10%surtaxisappliedtocertainhighincomeindividualsraisingtheirmarginalrateto39.6%.Personalincometaxesaredeterminedbytaxableincome,filingstatus,andvariouscredits.FinancialEnvironmentBusinessesinteractcontinuallywiththefinancialmarkets.FinancialMarkets

arecomposedofallinstitutionsandproceduresforbringingbuyersandsellersoffinancialinstrumentstogether.Thepurposeoffinancialmarketsistoefficientlyallocatesavingstoultimateusers.FlowofFunds intheEconomyINVESTMENTSECTORFINANCIALINTERMEDIARIESSAVINGSSECTORFINANCIALBROKERSSECONDARYMARKETFlowofFunds intheEconomyFINANCIALINTERMEDIARIESSAVINGSSECTORFINANCIALBROKERSSECONDARYMARKETINVESTMENTSECTORBusinessesGovernmentHouseholdsINVESTMENTSECTORFlowofFunds intheEconomyFINANCIALINTERMEDIARIESSAVINGSSECTORFINANCIALBROKERSSECONDARYMARKETSAVINGSSECTORHouseholdsBusinessesGovernmentINVESTMENTSECTORFlowofFunds intheEconomyFINANCIALINTERMEDIARIESSAVINGSSECTORFINANCIALBROKERSSECONDARYMARKETFINANCIALBROKERSInvestmentBankersMortgageBankersINVESTMENTSECTORFlowofFunds intheEconomyFINANCIALINTERMEDIARIESSAVINGSSECTORFINANCIALBROKERSSECONDARYMARKETFINANCIALINTERMEDIARIESCommercialBanksSavingsInstitutionsInsuranceCos.PensionFundsFinanceCompaniesMutualFundsINVESTMENTSECTORFlowofFunds intheEconomyFINANCIALINTERMEDIARIESSAVINGSSECTORFINANCIALBROKERSSECONDARYMARKETSECONDARYMARKETSecurityExchangesOTCMarketINVESTMENTSECTORAllocationofFundsInarationalworld,thehighestexpectedreturnswillbeofferedonlybythoseeconomicunitswiththemostpromisinginvestmentopportunities.Result:Savingstendtobeallocatedtothemostefficientuses.Fundswillflowtoeconomicunitsthatarewillingtoprovidethegreatestexpectedreturn(holdingriskconstant).Risk-ExpectedReturnProfileRISKEXPECTEDRETURN(%)U.S.TreasuryBills(risk-freesecurities)Prime-gradeCommercialPaperLong-termGovernmentBondsInvestment-gradeCorporateBondsMedium-gradeCorporateBondsPreferredStocksConservativeCommonStocksSpeculativeCommonStocksWhatInfluencesSecurityExpectedReturns?Marketabilityistheabilitytosellasignificantvolumeofsecuritiesinashortperiodoftimeinthesecondarymarketwithoutsignificantpriceconcession.DefaultRisk

isthefailuretomeetthetermsofacontract.RatingsbyInvestmentAgenciesonDefaultRiskInvestmentgraderepresentsthetopfourcategories.Belowinvestmentgraderepresentsallothercategories.WhatInfluencesExpectedSecurityReturns?Taxabilityconsiderstheexpectedtaxconsequencesofthesecurity.Maturity

isconcernedwiththelifeofthesecurity;theamountoftimebeforetheprincipalamountofasecuritybecomesdue.TermStructureofInterestRatesAyieldcurveisagraphoftherelationshipbetweenyieldsandtermtomaturityforparticularsecurities.UpwardSlopingYieldCurveDownwardSlopingYieldCurve0246810YIELD(%)051015202530(Usual)(Unusual)YEARSTOMATURITYWhatInfluencesExpectedSecurityReturns?Inflation

isariseintheaveragelevelofpricesofgoodsandservices.Thegreaterinflationexpectations,thenthegreatertheexpectedreturn.EmbeddedOptions

providetheopportunitytochangespecificattributesofthesecurity.Chapter3TimeValueofMoneyTheTimeValueofMoney

TheInterestRateSimpleInterestCompoundInterestAmortizingALoanObviously,$10,000today.YoualreadyrecognizethatthereisTIMEVALUETOMONEY!!TheInterestRateWhichwouldyouprefer--$10,000todayor$10,000in5years?TIMEallowsyoutheopportunitytopostponeconsumptionandearnINTEREST.WhyTIME?WhyisTIMEsuchanimportantelementinyourdecision?TypesofInterestCompoundInterestInterestpaid(earned)onanypreviousinterestearned,aswellasontheprincipalborrowed(lent).SimpleInterestInterestpaid(earned)ononlytheoriginalamount,orprincipalborrowed(lent).SimpleInterestFormulaFormula

SI=P0(i)(n)

SI: SimpleInterest

P0: Deposittoday(t=0)

i: InterestRateperPeriod n: NumberofTimePeriodsSI =P0(i)(n)

=$1,000(.07)(2) =$140SimpleInterestExampleAssumethatyoudeposit$1,000inanaccountearning7%simpleinterestfor2years.Whatistheaccumulatedinterestattheendofthe2ndyear?

FV =P0+SI =$1,000

+$140 =

$1,140FutureValue

isthevalueatsomefuturetimeofapresentamountofmoney,oraseriesofpayments,evaluatedatagiveninterestrate.SimpleInterest(FV)WhatistheFutureValue(FV)ofthedeposit?

ThePresentValueissimplythe $1,000youoriginallydeposited. Thatisthevaluetoday!PresentValue

isthecurrentvalueofafutureamountofmoney,oraseriesofpayments,evaluatedatagiveninterestrate.SimpleInterest(PV)WhatisthePresentValue(PV)ofthepreviousproblem?WhyCompoundInterest?FutureValue(U.S.Dollars)

Assumethatyoudeposit$1,000atacompoundinterestrateof7%for2years.FutureValue SingleDeposit(Graphic)

0

1

2$1,000FV27%FV1 =P0(1+i)1 =$1,000

(1.07) =$1,070CompoundInterest Youearned$70interestonyour$1,000depositoverthefirstyear. Thisisthesameinterestyouwould earnundersimpleinterest.FutureValue SingleDeposit(Formula)FV1 =P0

(1+i)1 =$1,000(1.07) =$1,070FV2 =FV1(1+i)1 =P0(1+i)(1+i) =$1,000(1.07)(1.07) =P0

(1+i)2 =$1,000(1.07)2 =$1,144.90YouearnedanEXTRA

$4.90inYear2withcompoundoversimpleinterest.FutureValue SingleDeposit(Formula)

FV1 =P0(1+i)1

FV2 =P0(1+i)2GeneralFutureValueFormula:

FVn =P0(1+i)n

or FVn=P0(FVIFi,n)--SeeTableIGeneralFutureValueFormulaetc.FVIFi,n

isfoundonTableIatEndofBookorontheCardInsert.ValuationUsingTableI

FV2 =$1,000(FVIF7%,2) =$1,000(1.145) =$1,145

[DuetoRounding]UsingFutureValueTables

JulieMillerwantstoknowhowlargeher$10,000depositwillbecomeatacompoundinterestrateof10%for5years.StoryProblemExample

012345$10,000FV510%CalculationbasedonTableI:

FV5

=$10,000

(FVIF10%,5)

=$10,000

(1.611) =$16,110 [DuetoRounding]StoryProblemSolutionCalculationbasedongeneralformula:

FVn =P0(1+i)n

FV5

=$10,000(1+0.10)5 =$16,105.10WewillusetheRule-of-72.DoubleYourMoney!!!Quick!Howlongdoesittaketodouble$5,000atacompoundrateof12%peryear(approx.)?Approx.YearstoDouble=72

/i%72/12%=6Years[ActualTimeis6.12Years]TheRule-of-72Quick!Howlongdoesittaketodouble$5,000atacompoundrateof12%peryear(approx.)?Assumethatyouneed$1,000

in2years.Let’sexaminetheprocesstodeterminehowmuchyouneedtodeposittodayatadiscountrateof7%.

0

1

2$1,0007%PV1PV0PresentValue SingleDeposit(Graphic)

PV0=FV2/(1+i)2 =$1,000

/(1.07)2 =FV2/(1+i)2

=$873.44PresentValue SingleDeposit(Formula)

0

1

2$1,0007%PV0

PV0

=FV1/(1+i)1

PV0=FV2/(1+i)2GeneralPresentValueFormula:

PV0 =FVn/(1+i)n

or PV0=FVn(PVIFi,n)--SeeTableIIGeneralPresentValueFormulaetc.PVIFi,n

isfoundonTableIIatEndofBookorontheCardInsert.ValuationUsingTableII

PV2 =$1,000(PVIF7%,2) =$1,000(.873) =$873

[DuetoRounding]UsingPresentValueTables

JulieMillerwantstoknowhowlargeofadeposittomakesothatthemoneywillgrowto$10,000

in5yearsatadiscountrateof10%.StoryProblemExample

012345$10,000PV010%

Calculationbasedongeneralformula:

PV0 =FVn/(1+i)n

PV0

=$10,000

/(1+0.10)5 =$6,209.21

CalculationbasedonTableI:

PV0

=$10,000

(PVIF10%,5)

=$10,000

(.621) =$6,210.00

[DuetoRounding]StoryProblemSolutionTypesofAnnuitiesOrdinaryAnnuity:Paymentsorreceiptsoccurattheendofeachperiod.AnnuityDue:Paymentsorreceiptsoccuratthe beginningofeachperiod.AnAnnuityrepresentsaseriesofequalpayments(orreceipts)occurringoveraspecifiednumberofequidistantperiods.ExamplesofAnnuitiesStudentLoanPaymentsCarLoanPaymentsInsurancePremiumsMortgagePaymentsRetirementSavingsPartsofanAnnuity0123

$100$100$100(OrdinaryAnnuity)EndofYear1(AnnuityDue)BeginningofYear1TodayEqualCashFlowsEach1YearApart(AnnuityDue)EndofYear1FVAn=R(1+i)n-1+R(1+i)n-2+ ...+R(1+i)1

+R(1+i)0Overviewofan OrdinaryAnnuity--FVARRR012nn+1FVAnR:PeriodicCashFlowEndofYeari%... FVA3=$1,000(1.07)2+ $1,000(1.07)1+$1,000(1.07)0

=$1,145

+

$1,070

+

$1,000

=

$3,215Exampleofan OrdinaryAnnuity--FVA$1,000$1,000$1,00001234$3,215=FVA3EndofYear7%$1,070$1,145

FVAn =R(FVIFAi%,n) FVA3 =$1,000(FVIFA7%,3) =$1,000(3.215)=$3,215ValuationUsingTableIIIFVADn=R(1+i)n+R(1+i)n-1+ ...+R(1+i)2

+R(1+i)1 =FVAn(1+i)Overviewofan AnnuityDue--FVADRRR012nn+1FVADnR:PeriodicCashFlowBeginningofYeari%... FVAD3=$1,000(1.07)3+ $1,000(1.07)2+$1,000(1.07)1

=$1,225

+

$1,145

+

$1,070

=

$3,440Exampleofan AnnuityDue--FVAD$1,000$1,000$1,000$1,07001234FVAD3=$3,440BeginningofYear7%$1,225$1,145

FVADn =R(FVIFAi%,n)(1+i) FVAD3 =$1,000(FVIFA7%,3)(1.07) =$1,000(3.215)(1.07)=$3,440ValuationUsingTableIIIPVAn=R/(1+i)1+R/(1+i)2 +...+R/(1+i)nOverviewofan OrdinaryAnnuity--PVARRR012nn+1PVAnR:PeriodicCashFlowEndofYeari%...

PVA3= $1,000/(1.07)1+ $1,000/(1.07)2+ $1,000/(1.07)3

=$934.58+$873.44+$816.30 =

$2,624.32Exampleofan OrdinaryAnnuity--PVA$1,000$1,000$1,00001234$2,624.32=PVA3EndofYear7%$934.58$873.44$816.30

PVAn =R(PVIFAi%,n) PVA3 =$1,000(PVIFA7%,3) =$1,000(2.624)=$2,624ValuationUsingTableIVPVADn=R/(1+i)0+R/(1+i)1+...+R/(1+i)n-1

=PVAn(1+i)Overviewofan AnnuityDue--PVADRRR012nn+1PVADnR:PeriodicCashFlowBeginningofYeari%...PVADn=$1,000/(1.07)2+$1,000/(1.07)1+ $1,000/(1.07)0=$2,808.02Exampleofan AnnuityDue--PVAD$1,000.00$1,000$1,00001234PVADn=$2,808.02BeginningofYear7%$934.58$873.44

PVADn=R(PVIFAi%,n)(1+i) PVAD3 =$1,000(PVIFA7%,3)(1.07) =$1,000(2.624)(1.07)=$2,808ValuationUsingTableIV1.ReadProblemThoroughly2.DetermineifitisaPVorFVProblem3.CreateaTimeLine4.PutCashFlowsandArrowsonTimeLine5.DetermineifSolutioninvolvesaSingle CF,AnnuityStream(s),orMixedFlow6.SolvetheProblemStepstoSolveTimeValueofMoneyProblems

JulieMillerwillreceivethesetofcashflowsbelow.WhatisthePresentValueatadiscountrateof10%.MixedFlowsExample

012345

$600$600$400$400$100PV010%

1. Solveapiece-at-a-timeby discountingeachpiecebacktot=0. 2. Solveagroup-at-a-time

byfirst breakingproblemintoannuity

groupstreamsandsingle

cash

flow

groups.Thendiscount eachgroupbacktot=0.HowtoSolve?Piece-At-A-Time

012345

$600$600$400$400$10010%$545.45$495.87$300.53$273.21$62.09$1677.15=PV0

oftheMixedFlowGroup-At-A-Time?(#1)

012345

$600$600$400$400$10010%$1,041.60$573.57$62.10$1,677.27

=PV0

ofMixedFlow[UsingTables]$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)=$62.10Group-At-A-Time?(#2)

01234

$400$400$400$400PV0

equals$1677.30.

012

$200$200

012345

$100$1,268.00$347.20$62.10PlusPlusGeneralFormula:FVn =PV0(1+[i/m])mn

n: NumberofYears m: CompoundingPeriodsperYear i: AnnualInterestRate FVn,m:FVattheendofYearn

PV0: PVoftheCashFlowtodayFrequencyofCompoundingJulieMillerhas$1,000toinvestfor2Yearsatanannualinterestrateof12%.Annual FV2 =1,000(1+[.12/1])(1)(2) =1,254.40Semi FV2 =1,000(1+[.12/2])(2)(2) =1,262.48ImpactofFrequencyQrtly FV2 =1,000(1+[.12/4])(4)(2) =1,266.77MonthlyFV2

=1,000(1+[.12/12])(12)(2) =1,269.73Daily FV2

=1,000(1+[.12/365])(365)(2) =1,271.20ImpactofFrequencyEffectiveAnnualInterestRateTheactualrateofinterestearned(paid)afteradjustingthenominalrate

forfactorssuchasthenumberofcompoundingperiodsperyear.(1+[i

/m])m

-1EffectiveAnnual InterestRateBasketWonders(BW)hasa$1,000CDatthebank.Theinterestrateis6%

compoundedquarterlyfor1year.WhatistheEffectiveAnnualInterestRate(EAR)?

EAR =(1+6%/4)4-1 =1.0614-1=.0614or6.14%!BWsEffective AnnualInterestRate