Introduction to Finance 財(cái)務(wù)管理講義x

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ModuleOne

Module01:IntroductiontoFinance

Topic1.1:WhatisFinancialManagement?

FinancialDecisions

Financialmanagementisconcernedwithdevelopinganalyticalskillstohelpmanagersmakebetterfinancialdecisions.Thesefinancialdecisionsare:

TheInvestmentDecision:Theevaluationofinvestmentprojects–whatprojectstoinvestin?Thisprocessissometimescalled“CapitalBudgeting”.

TheFinancingDecision:Wheretoobtainfundsfrom-Thetypeoffunds-Thecostoffunds-Whentoraisefunds-Howmuch?

TheDividendDecision:Increaseordecrease–howmuchtopayout-availabilityofcashtopayout–dividendsorcapitalgains.(TheDividendDecisionissometimesviewedaspartoftheFinancingDecisionandsometimesreferredtoasthePayoutDecision)

Theinvestment,financinganddividenddecisionsarelinkedbytheflowofcashthoughthefirm.Thesedecisionsareinterrelatedinthefollowingway:

CashInflows = CashOutflows

Themainsourcesoffundsarefromraisingnewcapitalbyborrowingorbytheissueofnewequity,andthenetcashflowsfromoperations.Sowedividethemintoexternalfundingandinternalfunding.Usesoffundsaredividedintoinvestmentsanddividends.

NewFunds + CashProfits = Investments + DividendF + X = I + D

ExternalFinancing[F]PlusInternalFinancing[X]=Investment[I]PlusDividend[D]

Where

F=externalfinancingviaeitherdebtorequity.

X=internalfinancingusingcashflowsgeneratedfrompreviousinvestments(retainedearnings).

I=cashoutlayforinvestmentsinassets,projects,etc.

D=cashdistributionstotheownersgenerallyintheformofdividends.

Bydefinition,cashinflowswillequalcashoutflowsforanytimeperiod.Wecannotchangeoneitemwithoutaffectingatleastoneotherintheequation.Thereforethedecisionsareinterrelatedandshouldbesolvedsimultaneously.

Considerthefollowingexample.Acompanyhasnetcashflowsfromoperationsof

$100m.Shareholderswereinformedthattheycouldexpectadividendtotalling$20minthisperiod.Thecurrentlevelofexternalfinancingiszerobutmanagementisnowinvestigatingaveryprofitableproject,whichneedsaninvestmentof$150m.

CashOutflowsare$150mininvestmentand$20mindividends.CashInflowsare$100mininternalfunding.

0+100m150m+20m

Thisisnotinbalance.Inflowstotal$100mandoutflowstotal$170m.Inordertomeetthecommitmentofacceptingtheprofitableinvestmentandpayingthedividendmanagementmustfindanextra$70minfunding.Theywillneedtoraisefundseitherbyborrowingorissuingnewequity.

TheFinanceFunction

SourceofFunds

Objectives

UseofFunds

Thefinancefunctioninvolvesthefinancialmanagerraisingfundsandusingthemtoaddvaluetothefirm.Sincemanagersendeavourtomakedecisionsthatincreasevaluetheyneedtoknowhowtomeasuretheimpactoftheirfinancialdecisionsonvalue.

Thecorrectdecisionscanonlybedeterminedinlightofthestatedobjectives.Toensuretheefficientandeffectivesourcingandutilisationoffunds,theobjectivesofthefirmmustbeconsidered.Inthisunitweadopttheobjectiveofmaximisingthemarketvalueofthefirm.Becarefulhere,maximisingaccountingprofitormaximisingreturnoninvestmentdoesnotalwaysmaximisevalue.Thispointwillbedemonstratedatvariouspointsthroughoutthecourse,especiallyinmodulefour.

Manyotherobjectivesofthefirmhavebeencanvassedintheliterature.Althoughthisisaninterestingissueitisnotonethatwewillpursueinthisunit.OneissuethatwillbecoveredbrieflyistheAgencyRelationship(seeSection1.5.8ofPBEHP.

TheConceptualFramework

ChapterTwoofyourtext,mostofwhichissetaslightreading,developsthetheoryofthefirmanddemonstrateshowwemightarriveatoptimalinvestment,financinganddividenddecisions.Thedecisionrulesderivedinthischapterareanessentialpartoftheconceptualframeworkoffinance.Soeventhoughwedonotstudythischapterindepthwerelyonitsconclusionsasastartingpointinourventureintotherealmoffinance.Themoreadventurousstudentsareinvitedtostudythischapterinmoredepth.

Insummary,thechapterconcludesthatundercertainrestrictiveconditions(perfectmarkets,perfectcertainty,notaxes,rationalinvestors,andnofrictions)thethreefinancialdecisionsareresolvedasfollows:

InvestmentDecisionSolution:

Takeallprojectsthataddvalue.StatedanotherwaythisgivesustheNetPresentValuerule,whichsaystakeallprojectsthathaveapositivenetpresentvalue(NPV)andrejectthosethathaveanegativenetpresentvalue.Analternateformistotakeallprojects,whichgiveareturngreaterthanthecostoffundsandrejectthosethatdonot.

FinancingDecisionSolution

Fundallprofitableprojects(allprojectsthataddvalue).Thesourceisirrelevant.Thatis,providedthatyouoptimisetheinvestmentdecisionbyfundingallprofitableinvestments,thequestionofwhereyoufinancefrom(debtvequity)makesnodifference.Ofcoursethisconclusionassumesthatweareoperatinginahighlycompetitivemarket.

DividendDecisionSolution

Providedthattheinvestmentandfinancingdecisionsareoptimisedthedividenddecision(dividendsvcapitalgains)isirrelevant.

ThesethreepoliciesarecoveredinChapter2ofthetext.

“Ifeverythingintherealworldoffinancewasthatsimplewecouldfinishourcourseinfinancehereandnow”Ihearyousay.

Myresponseis“yes,youareright”.

TheassumptionsusedinthemodeldevelopedinChapterTwoareveryrestrictiveanddonotreflecttherealworld.However,aswedevelopourconceptualframeworkwewillmovetomorecomplexmodels,whichprovidesolutionsthatareveryusefulandapplicabletotherealworldoffinance.Thereasonwestartwithasimplemodelissothatwecaneasilysee,whichvariablesorfactorsareimportant.Thiswillensurethatwearenotside-trackedintoaflawedanalysis.

Topic1.2The“FinancewayofThinking”andtheThreeLessonsofFinance

Thethemeofthisunitisthatbusinessesexisttocreatevalue.Ifafirmdoesnotcreatevaluecompetitionwillsoonforceitoutofbusiness.Weneedtoaddressquestionssuchas“Whatisvalueandhowisitcreated?".Inordertodothiswemustunderstandthethreebasicideasoffinancethatformtheconceptualframeworkandhelpusapplythe“FinancewayofThinking”

Thethreebasicideasare:

Timevalueofmoney

Arbitrage,and

Diversification

Throughoutourjourneyintothescience(orshouldIcallitthediscipline)offinancewewillregularlyreferbacktotheseideastohelpusresolveissuesandproblemsintheapplicationofourdiscipline.A“neat”explanationoftheseideascanbefoundonpage140ofRoss,Christensen,Drew,Thompson,WesterfieldandJordan,“FundamentalsofCorporateFinance”,2011,5thEdition,McGrawHill.

Thelogicissimple.Inanyvaluationprocesswewouldneedtoperformsomesortofcostbenefitanalysisinordertoseeifsomeactionaddsvalue.

Calculate/forecastthebenefits

Calculate/forecastthecosts

Comparethetwo

Ifbenefitsexceedthecoststheactionaddsvalue

Itiscontendedherethatbeforethecostsandbenefitscanbeevaluatedproperly,timevalueofmoney,arbitrageanddiversificationmustbeconsidered.

Beforemovingontothesethreebasicideas,herearesomedefinitionsandconcepts.

“FinanceHat”

Infinanceandeconomicsweuseadifferentmeasureofprofitfromthatusedinotherdisciplines.Thoseofyouwhohaveworkedorstudiedaccountingand/ortaxationwillneedtoadjustyourwayofthinkingbeforesolvingfinancialproblems.

Whendoingaccountingworkputonyour“AccountingHat”Whendoingtaxputonyour“TaxationHat”

Whensolvingfinanceproblemsputonyour“FinanceHat”Agoodexampleisdepreciation:

Infinancewedonotincludedepreciationasacostinourcost/benefitanalysisbecauseitisnotconsideredtobearelevantcashflowforvaluationpurposes.The

initialcostofourinvestment(asset)isconsideredasanupfrontcashflowratherthanacosttobeapportioned(depreciated)overthelifeoftheasset.

Inaccountingdepreciationisincludedasacosttobedeductedfromrevenuetogettheprofitfigure.

Fortaxationpurposes,depreciationiscommonlyanallowablededuction.However,theamountallowablemaydiffersignificantlyfromthatusedforaccountingpurposesandfromthedeclineineconomicvalueoftheasset.

Anotherexampleistherecognitionofcapitalgains.Foraccountingandtaxationpurposesacapitalgainisnotrecogniseduntilrealised(untiltheassetissold).Infinancewerecogniseacapitalgain(orloss)assoonasachangeinvalueoccurs.

Theunderstandingoffinancerequiresalittlebitof“l(fā)ateralthinking”onyourpart.Youwillcomeacrosstransactionsthatdonotappeartomakesensetothe“l(fā)ayperson”.Agoodexampleissellingsomethingthatyoudonothave–“goingshort”.Iwillleavetheexplanationofthistransactiontoalaterstageinthisunit.

Activity1.1

Lookupshortsellingandbepreparedtodiscussthesignificanceofthistransactioninclassnextweek.Try

.

Return

Infinanceweviewreturnsorprofitsasbeingmadeupoftwoparts:

Acashflowstream–normallyadividend,rentorinterestpayment,and

Acapitalgainorlossfromtheincreaseordecreaseinvalue.

Againdifferentapproachesareusedtomeasureprofitdependingonwhetherwearemeasuringeconomicreturns,accountingprofitortaxableincome.

Hereisanexampleofthecalculationofreturn.SupposewepurchasedashareinTelstraatthebeginningoftheyearfor$3.40.Weholdtheshareforoneyearanditspricerisesto$4.45attheendoftheyear.Duringtheyearwereceivedadividendof55cents.Wedonotselltheshare,asitisourintentiontoholditforafewyears.

Ourreturnismadeupof55centsindividendsand$1.05incapitalgain.Eventhoughwehavenotsoldtheshare,infinancewerecognisethecapitalgain.Contrastthiswiththeaccountingandtaxationpositions,whichdonotrecogniseacapitalgainuntilitisrealised(i.e.theshareissold).

Thetotaldollarreturnis$1.60.Tocalculatetheannualreturnasapercentagewedividethedollarreturnbythepriceatthebeginningoftheperiodinquestion.Inthiscasethepricewas$3.40.

Returnequals1.60/3.40giving47.06%pa.Thatwouldbenice,wouldn’tit?

Thisexamplemeasuresthehistoricoractualreturn.Wecanalsoconsiderreturninaforwardlookingsense.ForexampleifwebuyashareinBHPtodaywiththeintentionofholdingitforoneyear,whatreturncanweexpecttomakeovertheyear(expectedreturn)?OnewaywouldbetoprojectthepriceforBHPattheendoftheyearandmeasurethereturnasapercentageincrease.

Formulawithoutdividends

rC1C0

C0

Formulawithdividends

rC1D1C0

C0

Where:

r=return

C0=cashfloworvalueatthebeginningoftheperiodC1=cashfloworvalueatendofperiod

D1=dividendpaidatendofperiod

WealsomakethedistinctionbetweenNominalReturnsandRealReturns.SeeSection1.5.4ofPBEHP.

Activity1.2

Lookupthedefinitionsofnominalinterestratesandrealinterestratesandbepreparedtodiscusstheirrelationshiptoexpectedinflationinclass.

MarketValues

Anotherdifferenceisthatinfinanceweusemarketvalueswhereverpossibleinpreferencetobookvalues.

Thefollowingequalitywillbecommonlyreferredto:A = E + D

or

V = E + D

Themarketvalueofthefirm’sassetsisequaltothemarketvalueofthefirm’sequityplusthemarketvalueofthefirm’sdebt.

ThoseofyouthathavestudiedaccountingwillrecognisethisequationasbeingsimilartotheAccountingEquationusedinelementaryaccounting.Themajordifferenceisthatinfinanceweusecurrentmarketvalues,whereasaccountinguseshistoricorbookvalues(originalcost).

TimeValueofMoney

AssumethatyourfirmisinvestigatinganoilandgasprojectontheNorthWestShelfwiththefollowingsetofcashflows(inbillions$):

Year

0

1

2

3

…

25

CashFlow

(10)

1.0

1.0

1.0

1.0

1.0

Theprojectrequiresanoutlayof$10billionnow(time0)andpromisestogivecashflowreturnsof$1.0billionattheendofeachyearfor25years.Assumethatinvestorsinthemarketrequireareturnof10%paforthistypeofproject(thisrateissometimesreferredtoasthe“opportunitycostsoffunds”or“thecostofcapital”).

IfthenumbersarefamiliaritisbecausetheexampleisbasedonthesaleofgasfromtheNorthWestShelf(NWS)toChina,announcedinabout2002.Thenumbersarefictitious.

Shouldthefirmaccepttheproject?

Weaskthequestion,“Doestheprojectaddvaluetothefirm”?

Asimpleapproachwouldbetocomparethecostswiththebenefits.Costs: $10billion

Benefits: $25billion(25yearsat$1billion)Netbenefit: $25b–$10b=$15billionprofit

Thatshouldpaysomehandsomesalaries;buyafewFerraris,severalbeachfrontvillas,asuperyacht,aprivatejet,theoddtriptothemoonandrealestateonMars.

Unfortunately,ifyouannouncedthatyourfirmwastakingthisproject,thevalueofyourshareswouldfall.

Thereasonisthatyouhaveignoredthetimevalueofmoneyandtheopportunitycostoffunds.Animportantcosthasbeenomitted.Youarecomparing“appleswithoranges”.

NetPresentValue

InfinanceweevaluatesuchprojectsbycalculatingtheNPV(NetPresentValue)acost/benefitanalysis,whichatthesametimeadjustsforthetimevalueofmoney.

NPV=-InitialInvestment+thesumofthepresentvaluesofallfuturecashflows.

NPVInitialInvestment

CFt

t11it

Wedothecalculationusingtheformulaabove;moreaboutthislaterintheunit(Module04).

AtthisstageacceptmywordthattheNPVofourprojectis:

-$10b+$9.08b=-$0.92bThatis,thecostsequal$10b.

Thepresentvalueofthebenefitsis$9.08b.Afteradjustingforthetimevalueofmoneyattenpercent,$1bperyearfor25yearsisworth(equivalentto)only$9.08battimezero(now).

Overallthenetbenefitisnegative,andtheprojectwouldthereforecauseadropinvalueifitweretobeaccepted.

IfNPVmeasureschangeinvalue,thissuggestsarulefortheinvestmentdecision.ThefirmshouldtakeallprojectswithapositiveNPVandrejectallprojectswithanegativeNPV.Soundsfamiliar,thisiscalledtheNPVrule.

Arbitrage

Twoassetswiththesameriskandwhichproducethesamecashflowsshouldhavethesamevalue.Financialmarketsarehighlycompetitive.Therearemillions(perhapsbillions)ofinvestorsandplayersinthemarketlookingforprofitableopportunities.Iftwoassetswiththesamecashflowswerevalueddifferentlythenanopportunitytoprofitwithzeroriskwouldarise.Tradingonthistypeofopportunityisreferredtoasarbitrage.Arbitragewillquicklybringtheassetvaluesintobalance.

Takethisverysimpleexample.SupposethatatthesamepointintimeyounoticedthatsharesinBHPweresellingfor$A14inSydneyandat$A20inNewYork.Couldyouarbitragethis?

Yes!“Youbeauty,amoneymachine”!

YouwouldsimultaneouslybuyinSydneyat$14andsellinNewYorkfor$20,making$6profitpersharesoldlessthecostoftransacting.Ofcourseifthisimbalanceweretooccur,itwouldnotlastforlong,becauseeveryoneelseinthemarketwouldattempttoarbitrage.Thepriceswouldveryquicklycomebackintobalance.

Arbitrageisaverypowerfulideaandhasmanyapplicationsinvaluation.Giventhataddingvalueisthenameofthegame,weneedtounderstandhowcompetitivemarketsbehave.

Diversification

Wehaveallheardthehomily“donotputallyoureggsinonebasket,(lestthebasketfallandyoubreakallyoureggsatonce)”orsomethingtothateffect.Thisisgoodadviceintheworldoffinance.Giventhatmost,ifnotallinvestorsareriskaverse,itpaystodiversify.

Diversificationprovidesthepotentialtoreduceriskwithoutdecreasingreturns.Thefollowinggraphdemonstratesthis.Wemeasurethetotalriskofaninvestmentusingthestandarddeviationofexpectedreturns.Itturnsoutthatsomeofthistotalriskisdiversifiableandcanberemoved.Thiscomponentisreferredtoasdiversifiablerisk(orasnon-systematicrisk).

Noofassets

Keepingreturnconstant

systematicrisk

unsystematicrisk

TotalRisk

Diversification

TOTALRISK=SYSRISK+UNSYSRISK

Asweaddmoreandmoreassetstoourportfoliototalriskreduces(followtheblueline).But,notethatitdoesnotfullydisappear.Thereissomeresidualriskleft.Thisisreferredtoassystematicriskornon-diversifiablerisk.Giventhatthisriskcannot

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ModuleOne

bediversifiedaway,riskaverseinvestorswillwanttobecompensatedforsystematicrisk.

Thefactthat(intherealworld)investmentsarenotallperfectlycorrelatedwitheachother,allowsriskreductionviadiversification.Riskaverseinvestorsseektoavoidriskandiftheycannot,theywishtobecompensatedforit.

Thehigherthesystematicriskthehigherthereturnrequiredtocompensateforthatrisk.JustconsiderAustraliangovernmentbonds.Thesearefairlysafe(almostriskfree)andprovideareturn(yield)ofabout4%pa.Wouldyoutakeonariskyinvestmentthatproducedonly4%pa?

No!Youcanmake4%withnoriskbyputtingyourmoneyingovernmentbonds.

Activity1.3

Lookupthecurrentrate(yield)forten-yeargovernmentbondsinthenewspaperandbepreparedtodiscussthesignificanceofthisnumberinclass.

Topic1.3TimeValueofMoneyandtheMathematicsofFinance

Moneyhasatimevalue,andisgenerallyexpressedintermsofitsreceiptwithearlierreceiptsbeingbetterthanlaterones.Eveniftherewerezeroinflation,mostpeoplewouldprefertohave$1000intheirpocketnow,ratherthaninoneyear’stime.

Followingthislineofreasoning,itislogicalthatifapersonistoreceiveaseriesofcashflowsondifferentdates,thevalueofthosecashflowscannotbecalculatedsimplybyaddingthem.Thevalueof$1000receivedtoday,plus$1000tobereceivedattheendoftheyearplus$1000tobereceivedattheendoftwoyears,isnot

$3000,butisalesseramount.

Acashflowline

Thisexamplecanbedepictedusingthefollowingdiagramorsomevariationofit.Itisagoodideatodrawsomesortofdiagramtodepicttheproblemathand.Thishelpsthestudenttovisualisetheproblemandassistsinthesolution.Herewehaveusedacashflowline.

0 1 2 3

1000 1000 1000

Thisseriesofcashflowswhenaddedtogethergiveatotalof$3000,buttheyarenotworth$3000now.Whataretheyworth?

Thevalueisgivenbythefollowingformula:

PresentValue10001000

1000

(1r) (1r)2

Where“r”istheinterestrateexpressedasadecimal.Thevaluewillalwaysbelessthan$3000(iethesumofthecashflows).

Ifr=10%thenthepresentvalueis$2735.54.

PresentValue100010001000

(1.1) (1.1)2

Anotherfactorrelatingtotheutilityofmoneyisrisk.Anamountof$110,000inthefuturemayseemmoreusefulthananamountof$100,000today,butwhatisthelikelihoodofreceivingthatmoney?Othereventscouldtakeplacethatcouldmeanthatapersonreceivednothinginthefuture,butcouldhaveenjoyedthe$100,000today.Withmoney,thereisprobablynosuchthingascertainty.Therearedifferentratesofreturnanddifferentlevelsofrisksfordifferenttypesofinvestment,buta

commondenominatoristhatthegreaterthereturnoninvestment,thegreatertheriskingettingthatreturn-moreaboutthislaterintheunit.

Soweneedtoadjustfortimevalueofmoney.Howdowedothis?WeuseaseriesofcalculationsthatcomeundertheheadingofFinancialMathematics.Financialmathematicsincludesthewiderangeofcalculationsthatunderliethemulti-trilliondollarfinanceindustry.

Herearesomefundamentalconceptsunderpinningfinancialmathematics:

Cashflows–Payments(outflows)orreceipts(inflows)ofmoney(cash)–outflowsareshownasnegativeusingeitheraminussignorbrackets;

Rateofreturn–Therelationshipbetweenthecashinflowsandcashoutflows;

Marketyieldorrate–therateofreturnoryieldwhichequatesthefuturecashflowswiththepriceofthefinancialinstrumentinquestion(establishedbymarketforces);

Timingconvention(cashflowsareassumedtooccuratapointintime,witht=0representingnow,andt=1representingtheendofthefirsttimeperiod,t=2endofsecondtimeperiod,andsoon;

Couponrate–Thecontractedrateofpaymentondebtandotherfinancialinstruments;

Financialcontracts–whereamountstobereceivedandtobepaidareagreed.

Theseareadequatelycoveredinthetext.

Financialanalysisanddecisionmakingrequiresacompetentunderstandingandapplicationoffinancialmathematics.Studentsshouldrefertothetexttocompiletheirownlistofformulasusedinfinancialmathematicsasappliedinthisunit.Itshouldbenotedthatdifferenttextbooks(anddifferentlecturers)useslightlydifferentwaysofexpressingtheseformulas–thereisnostandardisation,andstudentsneedtodeveloptheirownexpressionsorbecomefamiliarwiththeformulasprovidedbytheteacherforexampurposes.

Studentsshouldbecarefulwhencompilingthislist,asfontsusedbydifferentcomputers,versionsofsoftware,andprinterdrivers,torepresenttheformulasina“wordprocessed”documentmaynotalwaysbereliablyreproduced.

Asummaryoftheformulasusedinthesenotesmaybefoundattheendofeachmodule.

Inthisunit,attentionisgiventothefollowingcalculations:

Return(coveredabove)

SimpleInterest

CompoundInterest

PresentValue

FutureValue

EffectiveInterestRates

PresentandFutureValuesofAnnuities

PresentValueofPerpetuities

PresentValueofGrowingPerpetuities

Thefirstfiveitemsarecoveredinthismodule.TheothersareintroducedhereandcoveredindepthinModuleTwo.

Thefollowingsymbolswillbeusedthroughoutthematerialthatfollows:NPV=netpresentvalue

V=valueofthefirm

D=valueofdebt

E=valueofequityr=requiredreturn

C0=cashfloworvalueattime0C1=cashfloworvalueattime1CFt=cashflowattimet

D1=dividendattime1

FV=futurevalueoraccumulatedamountPV=presentvalueorprincipal

i=interestrate(youmayfind“r”and“k”alsobeinguseddependingonthecontext)n=numberoftimeperiods

t=timeperiodrangingfromt=0tot=n

jm=nominalannualratecompounded“m”timesperyearEAR=effectiveannualrate

Inthesenotesformulaswillbeprovidedwithoutproofs.Thosewithamathematicalbentmayliketocheckthederivationofalloftheformulasandsolvetheequationsfordifferentsituations.Thiswillhelpyouunderstandwhatyouaredoing.Theminimumrequirementisthatyouareabletosolvetheseproblemsusingaformulaandacalculator.Thetextbookhastablesatthebacktoassistwithcalculations.Studentsneedtobecompetentintheoperationsofthefinancialcalculatorsufficientlywelltobeabletoquicklycalculatetheanswerinanexam.

Studentsareencouragedtolearntousetheirfinancialcalculatorsasquicklyaspossible,andarepermittedtobringthemintotheexam.YoushouldalsolearnhowtodothesecalculationsusingthefinancialfunctionsinExcel.AsaguideastotestwhetheryouhaveyouhavemasteredthistopicyoushouldbeabletodoallofthequestionsatthebackofChapterThreeofthetextbookwithoutlookingatthesolutions.

SimpleInterest:SeeSection3.3ofPBEHP

Simpleinterestiswhereinterestovertheentireperiodoftheagreementorloaniscalculatedontheoriginalamountofprincipal.Thisisinfrequentlyusednowadaysincommercialsituations,butoftenformsthebasisofprivatefamilyloansandlessformalagreements.

Theformulais:

FV=PV(1+in)

Example:

Polycorpborrows$1000todayandagreestorepayinalumpsumintwoyearstime.HowmuchwouldPolycorphavetorepayifinterestis10%pasimpleinterest?

Solution:

PV=$1000

n=2yearsi=10%pa

FV=tobecalculated

FV=PV(1+in)

FV=1000(1+.1x2)=1000(1.2)=1200

Fromnowonyouassumethatacompoundinterestcalculationisrequiredunlessspecificallyinstructedotherwise.

CompoundInterest:SeeSection3.4ofPBEHP

Interestoninterest.Compoundinterestiswhereinterestiscalculatedeachperiodontheprincipalamountandonanyaccruedinteresttothatpointintime.Thisiscommonlyusedforloansandinvestments.Itisimportanttoknowthefrequencyofcompoundingaswellasthestatedinterestrate,asthiscanhaveahugeimpactonbothperiodicrepaymentsorreceiptsandthetotalamountpaidovertheperiodoftheagreement.Note:Whenthereisonlyonecompoundingperiodthenbothsimpleinterestandcompoundinterestapproachesproducethesameresult.

Theformulais:

FV=PV(1+i)n

Example:

Polycorpborrows$1000todayandagreestorepayinalumpsumintwoyearstime.HowmuchwouldPolycorphavetorepayifinterestis10%pacompoundedannual?

Solution:

Compoundedannually,meansthatinterestisaddedtotheaccountattheendofeachyear.

PV=$1000

n=2yearsi=10%pa

FV=tobecalculated

FV=PV(1+i)n

FV=1000(1.1)2=1000x1.21=$1210

NominalversusEffectiveRates(nottobeconfusedwithNominalvReal)

Itisalsoimportanttounderstandthedifferencebetweennominalandeffectiveinterestrateswhencalculatingeitherrepaymentsorreceipts,astheeffectiveinterestrateistheonethattakesaccountofthefrequencyofthecompounding.Thetotalamountofinterestpaidorreceivedisgreaterasthenumberofcompoundingperiodsisincreased.Inpracticeitisusualtoquotethenominalinterestrate.Forexample,myhousingloanhasaninterestrateof6%pa.Butthebankchargesinterestonamonthlybasis(thatistheyaddinteresttomyaccounteverymonth).Theeffectiveannualrateforthisloanis6.17%.Accuratetoonebasispoint.

Thecalculationoftheeffectiveinterestrateshouldbeusedbeforecomparingdifferentloansorinvestmentproductswithdifferentnominalinterestratesanddifferentcompoundingperiods.HerewewillcallthisratetheEffectiveAnnualRate(EAR).[AER=AnnualEffectiveRateisalsocommonusage]

Theformulais:

jm

EAR1m1

m

Example:

Polybankoffersabankcardfacility(Polycard)toitscustomersandadvertisesarateof18%pabutwiththeinterestaddedtotheaccounteverymonth.WhateffectiveannualrateisPolybankchargingitscustomers?

Solution:

jm=.18(18%)

m=12(monthly)

.1812

12

EAR1 1

EAR=19.56%

(SeeSection