Chapter1TheRoleofFinancialManagement

AfterstudyingChapter1,youshouldbeableto:Explainwhytheroleofthefinancialmanagertodayissoimportant.Describe"financialmanagement"intermsofthethreemajordecisionareasthatconfrontthefinancialmanager.Identifythegoalofthefirmandunderstandwhyshareholders'wealthmaximizationispreferredoverothergoals.Understandthepotentialproblemsarisingwhenmanagementofthecorporationandownershipareseparated(i.e.,agencyproblems).Demonstrateanunderstandingofcorporategovernance.Discusstheissuesunderlyingsocialresponsibilityofthefirm.Understandthebasicresponsibilitiesoffinancialmanagersandthedifferencesbetweena"treasurer"anda"controller."TheRoleof

FinancialManagementWhatisFinancialManagement?TheGoaloftheFirmCorporateGovernanceOrganizationoftheFinancialManagementFunctionWhatisFinancialManagement?Concernstheacquisition,financing,andmanagementofassetswithsomeoverallgoal

inmind.InvestmentDecisionsWhatistheoptimalfirmsize?Whatspecificassetsshouldbeacquired?Whatassets(ifany)shouldbereducedoreliminated?Mostimportantofthethreedecisions.FinancingDecisionsWhatisthebesttypeoffinancing?Whatisthebestfinancingmix?Whatisthebestdividendpolicy(e.g.,dividend-payoutratio)?Howwillthefundsbephysicallyacquired?Determinehowtheassets(LHSofbalancesheet)willbefinanced(RHSofbalancesheet).AssetManagementDecisionsHowdowemanageexistingassetsefficiently?FinancialManagerhasvaryingdegreesofoperatingresponsibilityoverassets.Greateremphasisoncurrentassetmanagementthanfixedassetmanagement.WhatistheGoaloftheFirm?MaximizationofShareholderWealth!Valuecreationoccurswhenwemaximizethesharepriceforcurrentshareholders.ShortcomingsofAlternativePerspectivesCouldincreasecurrentprofitswhileharmingfirm(e.g.,defermaintenance,issuecommonstocktobuyT-bills,etc.).Ignoreschangesintherisklevelofthefirm.ProfitMaximizationMaximizingafirm’searningsaftertaxes.ProblemsShortcomingsofAlternativePerspectivesDoesnotspecifytimingordurationofexpectedreturns.Ignoreschangesintherisklevelofthefirm.Callsforazeropayoutdividendpolicy.EarningsperShareMaximizationMaximizingearningsaftertaxesdividedbysharesoutstanding.ProblemsStrengthsofShareholderWealthMaximizationTakesaccountof:currentandfutureprofitsandEPS;thetiming,duration,andriskofprofitsandEPS;dividendpolicy;andallotherrelevantfactors.Thus,shareprice

servesasabarometerforbusinessperformance.Whatcompaniessayabouttheircorporategoal*CadburySchweppes:“governingobjectiveisgrowthinshareownervalue”CreditSuisseGroup:“achievehighcustomersatisfaction,maximizeshareholdervalueandbeanemployerofchoice”DowChemicalCompany:“maximizelong-termshareholdervalue”ExxonMobil:“l(fā)ong-term,sustainableshareholdervalue”*RefertotextforadditionaldetailsTheModernCorporationThereexistsaSEPARATIONbetweenownersandmanagers.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.CorporateGovernanceCorporategovernance:representsthesystembywhichcorporationsaremanagedandcontrolled.Includesshareholders,boardofdirectors,andseniormanagement.Then

shareholder

wealth

maximization

remainstheappropriategoalingoverningthefirm.BoardofDirectorsTypicalresponsibilities:Setcompany-widepolicy;AdvisetheCEOandotherseniorexecutives;Hire,fire,andsetthecompensationoftheCEO;Reviewandapprovestrategy,significantinvestments,andacquisitions;andOverseeoperatingplans,capitalbudgets,andfinancialreportstocommonshareholders.CEO/ChairmanrolescommonlysamepersoninUS,butseparateinBritain(USmovingthisdirection).Sarbanes-OxleyActof2002Sarbanes-OxleyActof2002(SOX):addressescorporategovernance,auditingandaccounting,executivecompensation,andenhancedandtimelydisclosureofcorporateinformationImposesnewpenaltiesforviolationsofsecuritieslawsEstablishedthePublicCompanyAccountingOversightBoard(PCAOB)toadoptauditing,qualitycontrol,ethics,disclosurestandardsforpubliccompaniesandtheirauditors,andpolicingauthorityGenerallyincreasingthestandardsforcorporategovernanceOrganizationoftheFinancialManagementFunctionBoardofDirectorsPresident(ChiefExecutiveOfficer)VicePresidentOperationsVicePresidentMarketingVPofFinanceTreasurerCapitalBudgetingCashManagementCreditManagementDividendDisbursementFinAnalysis/PlanningPensionManagementInsurance/RiskMngmtTaxAnalysis/PlanningOrganizationoftheFinancialManagementFunctionVPofFinanceControllerCostAccountingCostManagementDataProcessingGeneralLedgerGovernmentReportingInternalControlPreparingFinStmtsPreparingBudgetsPreparingForecastsTexasInstrumentsBAII+IntegratedthroughouttheChaptersAUsefulFinancialToolDoesNOTreplacefinancialunderstandingChangeDisplaySettingChangethedecimalplacesdisplayedfrom“2”to“Floating”Press:

2nd Format 9 ENTER 2nd QUITAfterstudyingChapter2,youshouldbeableto:DescribethefourbasicformsofbusinessorganizationintheUnitedStates--andtheadvantagesanddisadvantagesofeach.Understandhowtocalculateacorporation'staxableincomeandhowtodeterminethecorporatetaxrate-bothaverageandmarginal.Understandvariousmethodsofdepreciation.Understandwhyacquiringassetsthroughtheuseofdebtfinancingoffersataxadvantageoverbothcommonandpreferredstockfinancing.Describethepurposeandmakeupoffinancialmarkets.Demonstrateanunderstandingofhowletterratingsofthemajorratingagencieshelpyoutojudgeasecurity’sdefaultrisk.Understandwhatismeantbytheterm“termstructureofinterestrates”andrelateittoa“yieldcurve.”TheBusiness,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.SummaryforCorporationAdvantagesLimitedliabilityEasytransferofownershipUnlimitedlifeEasiertoraiselargequantitiesofcapitalDisadvantagesDoubletaxationMoredifficulttoestablishMoreexpensivetosetupandmaintainTheBusinessEnvironmentBusinessincomeisaccountedforoneach“member’s”individualincometaxform.LimitedLiabilityCompanies

--Abusinessformthatprovidesitsowners(called“members”)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.[Note–ignore“bonus”depreciationdiscussedin2-25]MACRSExampleAssetsaredepreciatedbasedononeofeightdifferentpropertyclasses.Generally,thehalf-yearconventionisused.DepreciationinanyparticularyearisthemaximumofDDBorstraight-line.AswitchindepreciationmethodsismadefromDDBtoSLduringthelifeoftheasset.MACRSExampleMACRSScheduleJobsandGrowthTaxReliefReconciliationActof2003Increase&ExtensionofBonusDepreciation

Increasesalimitedandadditionaltemporarydepreciationdeductionof50%inthefirstyear--subjecttostipulations.Designedtoenhancecapitalinvestmentbybusinesses.JobsandGrowthTaxReliefReconciliationActof2003Increase&ExtensionofBonusDepreciation

Example:$200,000machineunder5-yearMACRSpropertyclass.Bonus=50%of$200K=$100K.Remaining$100K($200K-$100Kbonus)at20%ratebasedonMACRSis$20K.Resultis$120K($100K+$20K)depreciationchargeinthefirstyear.Settoexpiresoon,sowillignoreinsubsequentproblems(note–ignoredinslide2-20)OtherTaxIssuesQuarterlyTaxPayments

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)2yearsandforward(Carryforward)20yearstooffsetoperatinggainsinthoseyears.CorporateLossesandGainsExampleLisaMillerisexaminingtheimpactofanoperatinglossatBasketWonders(BW)in2007.Thefollowingtimelineshowsoperatingincomeandlosses.Whatimpactdoesthe2007losshaveonBW?-$500,000

$100,000

$150,000$150,0002007200620052004CorporateLossesandGainsExampleThelosscanoffsetthegainineachoftheyears2005and2006.Theremaining$250,000canbecarriedforwardto2008orbeyond.Impact:Taxrefundforfederaltaxespaidin2005and2006.-$500,000

$100,000

$150,000$150,0002007200620052004-$150,000-$100,000$250,000$150,00000-$250,000CorporateCapitalGains/LossesOftenhistorically,capitalgainsincomehasreceivedmorefavorableU.S.taxtreatmentthanoperatingincome.Generally,thesaleofa“capitalasset”(asdefinedbytheIRS)generatesacapitalgain(assetsellsformorethanoriginalcost)orcapitalloss(assetsellsforlessthanoriginalcost).CorporateCapitalGains/LossesCapitallossesaredeductibleonlyagainstcapitalgains.Currently,capitalgainsaretaxedatordinaryincometaxratesforcorporations,oramaximum35%.PersonalIncomeTaxesTheU.S.hasaprogressivetaxstructurewithfourtaxbracketsof10%,15%,25%,28%,33%,

and35%.Personalincometaxesaredeterminedbytaxableincome,filingstatus,andvariouscredits.Resultisthatlowincomeindividualspaynofederaltaxandothersmayfluctuatebetweenthemarginalrates.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)YEARSTOMATURITYWhatisTimeValue?WesaythatmoneyhasatimevaluebecausethatmoneycanbeinvestedwiththeexpectationofearningapositiverateofreturnInotherwords,“adollarreceivedtodayisworthmorethanadollartobereceivedtomorrow”Thatisbecausetoday’sdollarcanbeinvestedsothatwehavemorethanonedollartomorrowTheTerminologyofTimeValuePresentValue-Anamountofmoneytoday,orthecurrentvalueofafuturecashflowFutureValue-AnamountofmoneyatsomefuturetimeperiodPeriod-Alengthoftime(oftenayear,butcanbeamonth,week,day,hour,etc.)InterestRate-Thecompensationpaidtoalender(orsaver)fortheuseoffundsexpressedasapercentageforaperiod(normallyexpressedasanannualrate)AbbreviationsPV-PresentvalueFV-FuturevaluePmt-PerperiodpaymentamountN-Eitherthetotalnumberofcashflowsor thenumberofaspecificperiodi-TheinterestrateperperiodTimelines012345PVFVTodayAtimelineisagraphicaldeviceusedtoclarifythetimingofthecashflowsforaninvestmentEachtickrepresentsonetimeperiodCalculatingtheFutureValueSupposethatyouhaveanextra$100todaythatyouwishtoinvestforoneyear.Ifyoucanearn10%peryearonyourinvestment,howmuchwillyouhaveinoneyear?012345-100?CalculatingtheFutureValue(cont.)Supposethatattheendofyear1youdecidetoextendtheinvestmentforasecondyear.Howmuchwillyouhaveaccumulatedattheendofyear2?012345-110?GeneralizingtheFutureValueRecognizingthepatternthatisdeveloping,wecangeneralizethefuturevaluecalculationsasfollows:Ifyouextendedtheinvestmentforathirdyear,youwouldhave:CompoundInterestNotefromtheexamplethatthefuturevalueisincreasingatanincreasingrateInotherwords,theamountofinterestearnedeachyearisincreasingYear1:$10Year2:$11Year3:$12.10ThereasonfortheincreaseisthateachyearyouareearninginterestontheinterestthatwasearnedinpreviousyearsinadditiontotheinterestontheoriginalprincipleamountCompoundInterestGraphicallyTheMagicofCompoundingOnNov.25,1626PeterMinuit,aDutchman,reportedlypurchasedManhattanfromtheIndiansfor$24worthofbeadsandothertrinkets.WasthisagooddealfortheIndians?Thishappenedabout371yearsago,soiftheycouldearn5%peryeartheywouldnow(in1997)have:Iftheycouldhaveearned10%peryear,theywouldnowhave:That’sabout54,563Trilliondollars!TheMagicofCompounding(cont.)TheWallStreetJournal(17Jan.92)saysthatallofNewYorkcityrealestateisworthabout$324billion.Ofthisamount,Manhattanisabout30%,whichis$97.2billionAt10%,thisis$54,562trillion!OurU.S.GNPisonlyaround$6trillionperyear.Sothisamountrepresentsabout9,094yearsworthofthetotaleconomicoutputoftheUSA!At5%itseemstheIndiansgotabaddeal,butiftheyearned10%peryear,itwastheDutchthatgottherawdealNotonlythat,butitturnsoutthattheIndiansreallyhadnoclaimonManhattan(thencalledManahatta).TheylivedonLongIsland!Asafinalinsult,theBritisharrivedinthe1660’sandunceremoniouslytossedouttheDutchsettlers.CalculatingthePresentValueSofar,wehaveseenhowtocalculatethefuturevalueofaninvestmentButwecanturnthisaroundtofindtheamountthatneedstobeinvestedtoachievesomedesiredfuturevalue:PresentValue:AnExampleSupposethatyourfive-yearolddaughterhasjustannouncedherdesiretoattendcollege.Aftersomeresearch,youdeterminethatyouwillneedabout$100,000onher18thbirthdaytopayforfouryearsofcollege.Ifyoucanearn8%peryearonyourinvestments,howmuchdoyouneedtoinvesttodaytoachieveyourgoal?AnnuitiesAnannuityisaseriesofnominallyequalpaymentsequallyspacedintimeAnnuitiesareverycommon:RentMortgagepaymentsCarpaymentPensionincomeThetimelineshowsanexampleofa5-year,$100annuity012345100100100100100ThePrincipleofValueAdditivityHowdowefindthevalue(PVorFV)ofanannuity?First,youmustunderstandtheprincipleofvalueadditivity:ThevalueofanystreamofcashflowsisequaltothesumofthevaluesofthecomponentsInotherwords,ifwecanmovethecashflowstothesametimeperiodwecansimplyaddthemalltogethertogetthetotalvaluePresentValueofanAnnuityWecanusetheprincipleofvalueadditivitytofindthepresentvalueofanannuity,bysimplysummingthepresentvaluesofeachofthecomponents:PresentValueofanAnnuity(cont.)Usingtheexample,andassumingadiscountrateof10%peryear,wefindthatthepresentvalueis:01234510010010010010062.0968.3075.1382.6490.91379.08PresentValueofanAnnuity(cont.)Actually,thereisnoneedtotakethepresentvalueofeachcashflowseparatelyWecanuseaclosed-formofthePVAequationinstead:PresentValueofanAnnuity(cont.)Wecanusethisequationtofindthepresentvalueofourexampleannuityasfollows:Thisequationworksforallregularannuities,regardlessofthenumberofpaymentsTheFutureValueofanAnnuityWecanalsousetheprincipleofvalueadditivitytofindthefuturevalueofanannuity,bysimplysummingthefuturevaluesofeachofthecomponents:TheFutureValueofanAnnuity(cont.)Usingtheexample,andassumingadiscountrateof10%peryear,wefindthatthefuturevalueis:100100100100100012345146.41133.10121.00110.00}=610.51atyear5TheFutureValueofanAnnuity(cont.)JustaswedidforthePVAequation,wecouldinsteaduseaclosed-formoftheFVAequation:Thisequationworksforallregularannuities,regardlessofthenumberofpaymentsTheFutureValueofanAnnuity(cont.)Wecanusethisequationtofindthefuturevalueoftheexampleannuity:AnnuitiesDueThusfar,theannuitiesthatwehavelookedatbegintheirpaymentsattheendofperiod1;thesearereferredtoasregularannuitiesAannuitydueisthesameasaregularannuity,exceptthatitscashflowsoccuratthebeginningoftheperiodratherthanattheend0123451001001001001001001001001001005-periodAnnuityDue5-periodRegularAnnuityPresentValueofanAnnuityDueWecanfindthepresentvalueofanannuitydueinthesamewayaswedidforaregularannuity,withoneexceptionNotefromthetimelinethat,ifweignorethefirstcashflow,theannuityduelooksjustlikeafour-periodregularannuityTherefore,wecanvalueanannuityduewith:PresentValueofanAnnuityDue(cont.)Therefore,thepresentvalueofourexampleannuitydueis:NotethatthisishigherthanthePVofthe,otherwiseequivalent,regularannuityFutureValueofanAnnuityDueTocalculatetheFVofanannuitydue,wecantreatitasregularannuity,andthentakeitonemoreperiodforward:012345PmtPmtPmtPmtPmtFutureValueofanAnnuityDue(cont.)Thefuturevalueofourexampleannuityis:Notethatthisishigherthanthefuturevalueofthe,otherwiseequivalent,regularannuityDeferredAnnuitiesAdeferredannuityisthesameasanyotherannuity,exceptthatitspaymentsdonotbeginuntilsomelaterperiodThetimelineshowsafive-perioddeferredannuity01234510010010010010067PVofaDeferredAnnuityWecanfindthepresentvalueofadeferredannuityinthesamewayasanyotherannuity,withanextrasteprequiredBeforewecandothishowever,thereisanimportantruletounderstand: WhenusingthePVAequation,theresultingPVisalwaysoneperiodbeforethefirstpaymentoccursPVofaDeferredAnnuity(cont.)TofindthePVofadeferredannuity,wefirstfindusethePVAequation,andthendiscountthatresultbacktoperiod0Hereweareusinga10%discountrate0123450010010010010010067PV2=379.08PV0=313.29PVofaDeferredAnnuity(cont.)Step1:Step2:FVofaDeferredAnnuityThefuturevalueofadeferredannuityiscalculatedinexactlythesamewayasanyotherannuityTherearenoextrastepsatallUnevenCashFlowsVeryoftenaninvestmentoffersastreamofcashflowswhicharenoteitheralumpsumoranannuityWecanfindthepresentorfuturevalueofsuchastreambyusingtheprincipleofvalueadditivityUnevenCashFlows:AnExample(1)Assumethataninvestmentoffersthefollowingcashflows.Ifyourrequiredreturnis7%,whatisthemaximumpricethatyouwouldpayforthisinvestment?012345100200300UnevenCashFlows:AnExample(2)Supposethatyouweretodepositthefollowingamountsinanaccountpaying5%peryear.Whatwouldthebalanceoftheaccountbeattheendofthethirdyear?012345300500700Non-annualCompoundingSofarwehaveassumedthatthetimeperiodisequaltoayearHowever,thereisnoreasonthatatimeperiodcan’tbeanyotherlengthoftimeWecouldassumethatinterestisearnedsemi-annually,quarterly,monthly,daily,oranyotherlengthoftimeTheonlychangethatmustbemadeistomakesurethattherateofinterestisadjustedtotheperiodlengthNon-