技術經(jīng)濟學英文版演示文稿C3課件

CHAPTER3

METHODSFORECONOMICANALYSIS3.1MethodsWithoutTimeValueofMoney3.2PresentValueAnalysis3.3AnnualValueAnalysis3.4RateofReturnAnalysis3.5GrowthRateofReturnAnalysis3.6ProfittoInvestmentRatio3.7MinimumRateofReturnCHAPTER3經(jīng)濟評價原理：利潤最大化原理

π=B–CB——Benefit,C——EconomicCostsC：投入各種要素的機會成本，包括企業(yè)家的正常利潤。

π——超額利潤。計算

π的公式如下：技術經(jīng)濟學英文版演示文稿C3課件項目不僅能達到正常利潤水平，且有超額利潤。項目僅能達到正常利潤水平。項目不能達到正常利潤水平（但并不意味著虧損）項目不僅能達到正常利潤水平，且有超額利潤。項目僅能達到正常利潤水平。項目不能達到正常利潤水平（但并不意味著虧損）項目不僅能達到正常利潤水平，且有超額利潤。項目僅能達到正常利潤水平。項目不能達到正常利潤水平（但并不意味著虧損）π=B/Cπ=B-Cπ=(B–C)/C項目不僅能達到正常利潤水平，且有超額利潤。項目不僅能達到正常公式類型單方案經(jīng)濟可行性方案比選結論一致可以結論一致不可以結論一致不可以π=B-Cπ=B/Cπ=(B–C)/C公式類型單方案方案結論一致可以結論一致不可以結論一致不可以π3.METHODSFORECONOMICANALYSISInthisChapter,wewilldiscussvariousmethodsusedforevaluatingeconomicfeasibilityofprojects.ThefoundationforthesemethodswaslaidinthepreviousChapterwhenwediscussedtheimportanceoftimevalueofmoneyanditsimpactonthecashflow.InthisChapter,wewillformalizethoseconceptsthroughvariousmethodsandillustratetheapplicationsofthesemethodsbynumerousexamples.3.METHODSFORECONOMICANALYInevaluatingprojectswewillrestrictourattentiontoprojectsinvolvingmutuallyexclusivealternatives（互斥方案）only.Insimpleterms,mutuallyexclusivealternativesareexclusiveofeachother.Byselectingonealternative,wewillautomaticallyeliminatetheotheralternatives.Asimpleexamplewouldbebuyingacomputerforpersonaluse.Ifoneisinterestedinbuyingonlyonecomputerforpersonaluse,selectionofanyonecomputerfromanarrayofalternativeswillautomaticallyeliminatealltheotheralternatives.Forexample,ifonedecidestouseanIBM-compatiblePC,thenanotheralternative,Applecomputer,wouldbeautomaticallyeliminated.InevaluatingprojectswewillInthepetroleumindustry,inseveralinstancesonewilldealwithprojectswhereonlyonealternativewillhavetobeselectedafterevaluatingseveralalternatives.Someexamplesare:*Selectionofacontractortoconduct3-Dseismicsurveyforanexplorationventure.*Selectionofadrillingcontractortodrillawell.*Selectionofaservicecompanytoconductlogsurveys.*Selectionofapumpingunittoimprovetheproduction.*Evaluationofanin-filldrillingoptiontoincreasetheproduction.*Selectionofacompressortoincreasethegasproduction.Inthepetroleumindustry,inInalltheaboveprojects,wecanselectonlyoneoftheseveralalternativesbeingconsidered.Onceaparticularalternativeisselected,alltheotheralternativesareautomaticallyeliminatedfromfurtherconsideration.Inalltheaboveprojects,weThroughoutthisChapter,wewilluseaminimumrateofreturn（最小收益率）(MROR)toevaluatetheattractivenessofvariousalternatives.ThechoiceofMRORisverycriticalinevaluatingthealternatives.Insimpleterms,theMRORistheminimumraterequiredbyacorporationoranindividualtomaketheprojectattractive.ThroughoutthisChapter,wewiForexample,ifoneborrowsthemoneyfromabankataninterestrateof10%peryeartoinvestinadrillingventure,theMRORis10%.Thisisbecause,iftheprojectdoesnotyieldatleast10%ofreturnontheinvestment,thepersonwillbeanetloser.Iftheprojectearns15%return,thenafterpaying10%interesttothebank,thepersoncanmakesomemoneyforhimselforherself.Iftheprojectonlyearns5%return,thepersonwillhavetopayfromhisorherownpockettocovertheinterestpaymenttothebank.Iftheprojectearns10%thenthereisnonetgainorloss.Therefore,10%becomestheminimumacceptablerate.Forexample,ifoneborrowsthMRORissometimesalsocalledasthecostofcapital.Thecomputationofthecostofcapitalforthecorporationismuchmorecomplexthantheaboveexamplebecauseofthevariedsourcesofcapital.WewilldelaythediscussiononthissubjectuntilalatersectionofthisChapter.Itissufficetostatethatanyalternativewhichdoesnotsatisfytheminimumrateofreturn(MROR)criteriawillbeautomaticallyrejected.Ideally,whenevaluatingmutuallyexclusivealternatives,wewouldliketohavetheeconomiccriteriontopossessthefollowingcharacteristics:MRORissometimesalsocalled*Itshouldbesuitableforrankingvariousalternatives.*Itshouldreflectthecostofthecapital.*Itshouldincorporateuncertaintiesinourassumptions.*Itshouldreflectgoalsandobjectivesofthecorporation.Inpractice,nosinglecriterionwouldbeabletosatisfythesecharacteristics.Especially,althoughtechniquesareavailabletoquantifytheuncertaintiesineconomicevaluation,forsimplicity,wewillassumethatalltheinformationregardinganygivenalternativeisknownwithcertainty.Regardingthelastidealcharacteristicofacriterion,wewillassumethatourgoalwillalwaysbeeithertominimizecostortomaximizeprofitorbenefit.Wewillnotconsiderotherobjectivesinouranalysis.*ItshouldbesuitableforraSeveraleconomiccriteriaareavailabletoevaluatemutuallyexclusivealternatives;eachcriterionhavingcertainadvantagesanddisadvantages.wewilldiscusstechniqueswhichdonotaccountfortimevalueofmoney.presentthepresentvalue(PV)analysis.theannualvalue(AV)analysis.rateofreturnmethod(ROR),growthrateofreturnmethod(GROR),theprofittoinvestmentratiomethod(PIR).(MROR)Inthelastsection,(MROR).Severaleconomiccriteriaare3.1MethodsWithoutTimeValueofMoneyThemethodsusedwithoutaccountingfortimevalueofmoneyaresimpletouse.Thesemethodsdonotrequiresignificantnumberofcalculations.Althoughusedextensivelyintheabsenceofcalculatorsandcomputers,evenbybigcorporations,atpresent,thesemethods,atbest,providearuleofthumbsolutiontoaproblem.Inthealternative,thesemethodsmaybeconsideredasprimaryscreeningtoolstoevaluatethealternatives.Inthefollowing,wediscusssomeofthesemethodsandexplaintherelativeadvantagesanddisadvantagesofthesemethods.3.1MethodsWithoutTimeVal3.1.1ReturnonInvestment(ROI)Thisisoneofthemostcommonlyusedmethodsintheoilindustry.Itisaratiooftotalincomeduringthelifeoftheprojectdividedbythetotalinvestmentduringthesameperiod.Inmathematicalform,wecanwrite,Asaruleofthumb,avalueofROIgreaterthan2isconsideredagoodinvestment.Sincethemethodignoresthetimevalueofmoney,itshouldonlybeusedinconjunctionwithothermethodswhichaccountforthetimevalueofmoney.3.1.1ReturnonInvestment(Example3.1Thefollowingcashflowprofileisgivenforanexplorationproject.Calculatethereturnoninvestment(ROI)fortheproject.Year012345678CashFlow-20-3030506040403020(1000’sofdollars)Solutiontotalcumulativeincome=30+50+60+40+40+30+20=270totalinvestment=-50UsingEq.3.l,

Usingruleofthumb,since5.4>2.0,itisagoodinvestment.

Example3.1ThefollowingcAnothermethod,whichisalsoused,iscalledprofittoinvestmentratioandisdefinedas,Inotherwords,bysimplysubtractingonefromtheROI,wecancalculatethePIR.Asaruleofthumb,itispreferredthatPIRbegreaterthan1.0.Eq.3.2isslightlydifferentthanthePIRmethodwediscussinSection3.6.InSection3.6,weexpandthisdefinitiontoincludetheeffectoftimevalueofmoney.Anothermethod,whichisalsoExample3.2Thefollowingtwoalternativeprojectsareconsideredforapotentialinvestment.UsingROIorPIRasacriterion,whichalternativewillbeselected?

Year012345678AlternativeI-100-50-201009080706060AlternativeII-170120100806050000SolutionAlternativeIcumulativeinvestment=100+50+20=170cumulativeincome=100+90+80+70+60+60=460UsingEq.3.l.

UsingEq.3.2,PIR=ROI-1=1.7

Example3.2ThefollowingtwoAlternativeIIcumulativeinvestment=170.cumulativeincome=120+100+80+60+50=410UsingEq.3.l,

UsingEq.3.2,PIR=ROI-l=l.4.Usingtheruleofthumbcriteria,boththealternativesarefeasible.Comparingthetwoalternatives,AlternativeIissuperiortoAlternativeIIbasedonbothcriteria.AlternativeII3.1.2PaybackPeriodPaybackperiodisoneofthesimplesttechniquesusedinevaluatingthefeasibilityofaproject.Itisdefinedasthetimerequiredtoreceivetheinitialinvestmentback.Inthealternative,itisthetimerequiredforthecumulativenetcashflowtobecomepositive.Itisaquantitativemeasureofturnaroundtimeafterwhichthecapitalcanbereinvestedinotherprojects.Itisausefultechniquewhentheprojectrequiresrelativelysmallinvestmentwithaquickpayback;e.g.,wellstimulationusingacidizing.Itisalsousefulwhentheinvestmentisatriskduetopoliticalinstability,orduetocontractualagreement(合同)requiringapull-outafteracertainperiod.3.1.2PaybackPeriodPaybackperiod,however,hascertaindrawbacks.Asexplainedbefore,itdoesnotaccountforthetimevalueofmoney.Italsodoesnotaccountfortheprofitgeneratedafterthepaybackperiod.Asaresult,thepaybackperiodmaynotbeavalidcriterionforprojectswhichrequiresignificantleadtimeandmaylastoverseveralyears.Itisnotacriterionindicatingeconomicefficiency;i.e.,howefficientlythemoneyisinvested.Paybackperiod,however,hascInstead,itisacriterionofeconomicexpediency;i.e.,howquicklythecapitalcanberecovered.Foracompanyinterestedinliquidityofcapital,paybackperiodprovidesausefultoolforknowinghowquicklytheinvestedcapitalisrecovered.However,itdoesnottellushowgoodtheinvestmentisintermsofmaximizingthebenefit.Thefollowingexamplesillustratetheusefulnessanddrawbacksofapaybackperiodtechnique.

Instead,itisacriterionofExample3.3Basedonevaluationofanoilwell,itwasdeterminedthatafteracidizingthewell,theproductionofthewellwillincreasefrom10bbl/dayto15bbl/day.Ifthepriceofoilis$20/bbl,andthecostofacidizingis$5,000,whatisthepaybackperiod?SolutionIncrementaloilproduction=15-10=5bbl/dayTherefore,$5,000wouldberecoveredinlessthantwomonths,$5,000/$3,000=1.67Thepaybackperiodwouldbe1.67months.Example3.3BasedonevaluatiExample3.5Aninitiationofawaterfloodprojectwillrequireaninitialinvestmentof$2million.Itisexpectedthattheprojectwillgenerateadditionalrevenuesof$700,000inthefirstyearfollowedbyadeclineof10%peryear.Calculatethepaybackperiod(i)withoutdiscountingforthetimevalueofmoney,and(ii)bydiscountingforthetimevalueofmoney.Assumethediscountratetobe8%.Example3.5AninitiationofSolutionThefollowingtableshowstheyearlycashflowsanddiscountedcashflowsforthisproblem.Thesamplecalculationsfollow.CashCumulativeDiscountedCumulativeYearFlowCashFlowCashFlowDiscountedCashFlow0-2,000,000-2,000,000-2,000,000-2,000,0001700,000-1,300,000648,148-1,351,8522630,000-670,000540,123-811,7283567,000-103,000450,103-361,6264510,300407,300375,08613,4605459,270866,570312,571326,032SolutionSampleCalculationsTocalculatecashflowinyear2,=700,000x0.9=$630,000Thecashflowinotheryearsaresimilarlycalculated.Forpart(i),thecumulativecashflowbecomespositiveafter3.2years.Therefore,thepaybackperiodis3.2years.Fordiscountedpaybackperiod,cashflowineachyearisdiscountedbyusinganinterestrateof8%.Forexample,SampleCalculationsinyear1,Foryear2.Usingthediscountedcashflowvalues,thecumulativecashflowbecomespositiveafterfouryears.Therefore,thediscountedpaybackperiodisfouryears.Obviously,thediscountedpaybackperiodisastrongfunctionoftheinterestrateatwhichthecashflowisdiscounted.Forthesameexample,ifweuseadiscountrateof15%,thediscountedpaybackperiodis5.2yearsinsteadoffouryears.inyear1,Forsituationswherethecashflowinvestmentsandbenefitsareoveralongterm,thediscountedpaybackperiodisamuchmorerealisticmeasureofinvestmentexpediencythanasimplepaybackperiodmethod.Tosummarize,themethodswhichdonotaccountfortimevalueofmoneyaresimpletouseandmayprovideaprimaryscreeningtooltoevaluatealternatives.However,thesemethodsshouldonlybeusedinconjunctionwithothermethodstoproperlyevaluatetheproject’sfeasibility.Forsituationswherethecash3.2PresentValueAnalysisPresentvalue(orworth)(PV)analysisevaluatesprojectsbasedonthefinancialpositionofvariousalternativesatthepresenttime.Thistechniqueaccountsforthetimevalueofmoneyandprovidesawayofcomparingvariousalternativesatthesameframeofreference.Iftheprojecthasafixedoutput,theobjectiveshouldbetominimizethepresentworthofcosts.3.2PresentValueAnalysisAsdiscussedinChapter1,iftheprojecthasafixedinput,theobjectiveshouldbetomaximizethepresentworthofbenefits,andiftheprojecthasneitherfixedinputoroutput,theobjectiveshouldbetomaximizethedifferencebetweenthepresentworthofbenefitsandpresentworthofcosts.Letusillustratethesethreealternativesthroughvariousexamples.Intheseillustrations,wewillassumethatthelivesofthevariousalternativesareequal.AsdiscussedinChapter1,if公式推導012345n-1n0123Example3.6Acompanyisconsideringtwoalternativestosatisfyitsphotocopyingrequirements.Thecostofeachmachineisshownbelow:(a)(b)InitialCost$10,000$8,000AnnualCost$1,000$1,400Theannualcostincludesthereplacementandmaintenancecosts.Ifbothmachineshavealifeoffiveyearsandtheminimumrateofreturn(MROR)is10%,whichprojectshouldbeselected?Example3.6AcompanyisconSolutionBothalternativeswillperformthesamefunctions,i.e.,theyofferthesameoutput.Therefore,ourobjectiveshouldbetominimizethecost.Foralternative(a),Foralternative(b),Comparingthepresentworthcostsofthetwoalternatives,alternative(b)shouldbeselected.SolutionExample3.7Aproposalcallsforaninvestmentof$100,000indrillinganewwell.Itisexpectedthattheproductionwillgeneratearevenueof$30,000peryearforsixyears.Attheendofsixyears,theproductionequipmentcanbesoldfor$10,000.Anotherproposalrequiresa$100,000investment.Itwillgenerate$50,000inthefirstyearfollowedby8%declineineachyear.Thelifeoftheprojectwillbesixyears.Thereisnosalvagevalueassociatedwiththeproposal.Iftheminimumrateofreturnis12%,whichprojectshouldbeselected?Example3.7AproposalcallsSolutionWehaveafixedamountofinvestment.Ourobjectiveshouldbetomaximizeouroutputortomaximizethepresentvalueofbenefitsreceivedafterthefixedinvestment.Forthefirstproposal,Forthesecondproposal,ComparingthePVbenefits,forboththeproposals,thesecondproposalshouldbeselected.SolutionExample3.8Acompanyisconsideringtwoalternativecomputermodelstosatisfyitscomputerneeds.Duetotheirdifferingpowers,thebenefitsreceivedbyboththecomputersaredifferent.Basedontheworkprojections,thecompanythinksthateitherofthecomputerscanbeusedtotheirfullestpotential.Iftheminimumrateofreturnis10%,whichcomputershouldthecompanyselect?AlternativeInitialCostAnnualbenefitLife,YearsSalvageValue(a)$4,500$1,5005$600(b)$3,200$1,0005$300Example3.8AcompanyisconsSolutionThesalvagevalueindicatesthepricereceivedifthecomputerissoldafterfiveyears.Sinceneitherthecosts,northebenefitsarefixed,weneedtoselectanalternative,whichmaximizesthedifferencebetweenthebenefitsandcosts.Wecandefinethedifferenceas,(3.3)whereNPVisthenetpresentvalueofthealternativeForalternative(a),Foralternative(b),Basedonthecomparisonofthetwoalternatives,(a)shouldbeselected.SolutionNPV的意義NPV〉0，項目不僅能達到基準收益率的水平,而且有超額利潤；NPV〉0，項目僅能達到基準收益率的水平；NPV〉0，項目不僅能達到基準收益率的水平加權平均值其中：1/(1+ic)t

權重，越靠近現(xiàn)在的年份，其NCF對NPV的貢獻越大，否則越小。NPV大小與基準點有關。0年和第一年相差(1+ic)1

優(yōu)缺點NPV的意義3.2.2BondEvaluation（債券評價）Anotherinterestingapplicationofpresentvalueanalysisistodeterminetheworthofbondsissuedbycorporationsorgovernments.Abondisatypeofloanwherethedebtor(債務人)promisestopayastated(一定的)interestatspecifiedintervals(時間間隔)foradefiniteperiodandthentorepaytheprincipalatthematuritydate

（到期日）ofthebonds.Bondsareissuedbycorporationsandgovernmentstoraisemoney.Individualbondsareissuedinevendenominationssuchas$1,000ormultiplesof$1,00BondEvaluation（債券評價）Thefacevalueofthebondatthetimeofissuanceiscalledtheparvalue(票面價值).Thebondsareissuedforafixedperiodoftime,i.e.,5years,10years,etc.Afterthatperiod,theprincipalwillhavetobepaidback.Duringthatperiod,thedebtorwillperiodicallypayaninterestonthebond.Theannualrateatwhichtheinterestispaidiscalledacouponrate.Althoughsemiannual(每半年的)paymentofinterestisthemostcommon,othertypesofpaymentsarealsoallowed.

ThefacevalueofthebondatThebonds,althoughissuedforafixedperiod,canbetradedinafinancialmarketatafacevalueotherthantheparvalue.Thisaffectsthepresentvalueofthebond.Forexample,abondpurchasedatacouponrateof10%canbesoldatahigherpricethantheparvalueinthefutureifinthefuture,theinterestpaidbynewbondsislessthan10%.Thisisbecause,ifsomeonewantsabondwhichpays10%interestrate,theywillhavetopayapremiumprice(溢價)toreflectthathigherinterestrate.Thereverseisturnifinthefuturethenewbondsarepayinghigherinterestratesthan10%.Undertheseconditions,thebondmayhavetobesoldatadiscountpricecomparedtotheparvalue.Thefollowingexamplesillustratetheevaluationofbondsmoreclearly.

Thebonds,althoughissuedforExample3.9Amajoroilcompanyissuednominal9%couponratebondsin$10,000denominationspayablein10years.Interestispaidonasemiannualbasis.a.Whatistheinterestearnedevery6months?b.If,after5years,theaveragebondisprovidingonly6%interestrate,whatpricecanyousellthatbondatsothatthebuyerwillreceive,effectivelya6%interestrate?c.Whatwillbeyoureffectivepresentvalueofthebondifyousellitatthatprice?Example3.9AmajoroilcompSolutiona.Theinterestispaidonasemiannualbasis.Therefore,thenominalinterestratepersixmonths,Therefore,theinterestpaidpersixmonths,

Solutionb.$450isthesemiannualpaymentyouwillbereceivingonthisbond.Thisisaperiodicpayment.Inaddition,attheendofitslife,youwillreceivetheprincipalback.Wecouldtreatitasasalvagevalue.Schematically,thecashflowprofileafter5yearsisshowninFig.3.2.12………10P=?$10,000$450Figure3.2:CashFlowProfileforExample3.9b.$450isthesemiannualpaWeneedtocalculatethepresentvalueofthiscashflowprofilesuchthatthesemiannualinterestrateof(6/2)3%isreceived.Thisisthepriceatwhichyoucansellthebondtothebuyer.Weneedtocalculatethepresec.Ifthebondissoldtothebuyerat$11,280,thesellerbuysthebondat$10,000,andthesalvagevalueofthebondtothesellerafter5yearsis$ll,280.Theeffectiveinterestthesellerhasearnedhastobecalculatedbytrialanderror.Wecanshowthecashprofilesas(Fig.3.3),Wecanwritethepresentvalueas,iftheinterestisi,Bytrialanderror,fori=5.5%,bothsidesareequal.Sincethisissemiannualinterestrate,thenominalratereceivedbytheselleris11%peryear.12………10$10,000$11,280$450Figure3.3:CashFlowProfileofaseller$450$450c.IfthebondissoldtotExample3.10Abondissuedbyacompanywithaparvalueof$l,000iscurrentlysoldinthemarketat$939.Thecoupononthebondis8.5%,interesttobepaidsemiannually.IfyoubuythebondonJanuaryl,1993andthematuritydateisOctober1,1997,whatistheinterestrateyouwillearnonthisbond？SolutionInterestpaidsemiannually,Thisistheperiodicpayment.ThecashflowprofilecanbeshownasinFig.3.4.$42.50$42.5012

Apr-93Oct-93……………Oct-97Jan-93$939$1,000$42.50Figure3.4:CashFlowProfileforExample3.10Example3.10AbondissuedbyThefirstpaymentwillbereceivedinApril,1993.Thetotalnumberofpaymentsreceivedis10.Therefore,wecanwrite,Throughtrialanderror,i=5.4%.Therefore,thenominalinterestratereceivedbyyouwillbe10.8%peryear.Notethatthelasttermintheequationrepresentsthefactthatonly3months(insteadofsix)areelapsedbeforethefirstpaymentisreceived.Threemonthsis0.5periodofthesemiannualperiod.Thefirstpaymentwillberece3.2.3AlternativewithUnequalLives不等生命周期Intheexamplesinthefirstsection,weconsideredalternativeswithequallives.Inthissection,wewillextendtheanalysisforcaseswherethealternativeshaveunequallives.Thesearethecasesonecommonlyencountersforservicecontractswheredifferentvendors(賣主)mayoffercontractsextendingoverdifferentperiods.Asanexample,asacorporationinterestedinleasingcomputers,twovendorsmayoffercontractsoverdifferentperiods.3.2.3AlternativewithUnequalOnemayextenditoverathreeyearperiod,whereas,theothermayextenditoverafiveyearperiod.Ifweassumethatthecorporationwillrequirethecomputersoveramuchlongerperiodthaneitherofthetwocontracts,thequestionsishowtocomparethetwocontracts.Thedifficultybeing,ifweselectathreeyearperiodcontract,weneedtoaccountfortheremainingtwoyearperiodwhichiscoveredbythealternatecontract.OnemayextenditoverathreeThetwomethodsnormallyusedforcomparingsuchservicecontractsare:l)eithertoadjustthesalvagevalueofalongerperiodalternativetoreflectashortenedlife,or2)assumethatallthealternativesarerepeatedacertainnumberoftimessuchthatthecumulativelivesoftherepeatedcyclesarethesameforallthealternatives.Wewilldiscussboththeoptionsbelow.ThetwomethodsnormallyusedAdjustingtheSalvageValueThesimplestwaytoaccommodatevaryingusefullivesfordifferentalternativesistoadjustthesalvagevalueofthealternatives.Ifthegoalistocomparevariousalternativesusingtheshortestusefullifeamongallthealternatives,theusefullivesofalltheotheralternativesarereducedtothatlevelandthesalvagevaluesareincreasedtoreflectthereductionintheusefullives.TheschematicrepresentationofthemethodisshowninFig.3.5.

LASA△LALABS’BSBS’B〉SBLA+△LA=LBLA=UsefullifeofalternativeALB=UsefullifeofalternativeBSA=SalvagevalueofalternativeSB=SalvagevalueofalternativeBFigure3.5:ComparingAlternativeswithUnequalLivesAdjustingtheSalvageValueLASLASA△LALABS’BSBS’B〉SBLA+△LA=LBLA=UsefullifeofalternativeALB=UsefullifeofalternativeBSA=SalvagevalueofalternativeASB=SalvagevalueofalternativeBFigure3.5:ComparingAlternativeswithUnequalLivesLASA△LALABS’BSBS’B〉SBLA+△LA=LBExample3.11Acompanyisconsideringtwopossiblealternativesforneededequipment.Thecostsinvolvedinbothalternativesaregivenbelow.Iftheminimumrateofreturnis8%,whichalternativeshouldbeselected?

(A) (B)InitialCost $10,000 $25,000AnnualBenefit $2,800 $7,000UsefulLife,Years5 7SalvageValue $1,000 $2,000Example3.11AcompanyisconSolutionIntheaboveexample,alternativesAandBhavedifferentusefullives.Beforewecanapplythenetpresentvalueanalysis,weneedtomaketheusefullivesequal.Inthismethod,wearegoingtoreducetheusefullifeofprojectBandadjustthesalvagevalueappropriately.IfweassumethatbyreducingtheusefullifeofprojectB,thesalvagevalueincreasesto$5,000,wecanapplytheNPVanalysistobothalternatives,BasedontheNPVanalysis,BisabetteralternativethanA.SolutionMethodofaCommonMultipleAnothermethodtocomparetwoalternativeshavingunequallivesistocomparethemusingacommondenominator.Thismethodisusefulifthecommondenominatorisrelativelysmall.Thefollowingexampleillustratesthismethod.Example3.13Thefollowingtwoalternativesareconsideredforaproject.IftheMRORis10%,selectthebestalternative.(A)(B)InitialCost$12,000$18,000AnnualBenefit$4,000$5,000UsefulLife,Years48SalvageValue$3,000$4,000MethodofaCommonMultiple(A)SolutionsAlternativeAhasausefullifeoffouryears,whereas,alternativeBhasausefullifeofeightyears.Insteadofarbitrarilyadjustingthesalvagevalueofeitherofthetwoalternatives,wecanassumethatalternativeA