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CenterforAccountingStudiesofXiamenUniversity2007Lecture2AdvancedFinancialManagementMakingInvestmentDecisionsWiththeNetPresentValueRuleProfessorYuanlueFuXiamenUniversity–AdvancedFinancialManagementFU-2Sub-topicsCovered•AReviewofTheBasics(NPV,IRR,PBP)•WhatToDiscount•IM&CProject•EquivalentAnnualCosts•ProjectInteraction•OptimalTiming•FluctuatingLoadFactors(chapter5-6)XiamenUniversity–AdvancedFinancialManagementFU-3NPVandCashTransfers•Everypossiblemethodforevaluatingprojectsimpactstheflowofcashaboutthecompanyasfollows.CashInvestmentopportunity(realasset)FirmShareholderInvestmentopportunities(financialassets)InvestAlternative:paydividendtoshareholdersShareholdersinvestforthemselvesXiamenUniversity–AdvancedFinancialManagementFU-4CFODecisionToolsProfitabilityIndex,12%Payback,57%IRR,76%NPV,75%Bookrateofreturn,20%0%10%20%30%40%50%60%70%80%90%100%SurveyDataonCFOUseofInvestmentEvaluationTechniquesSOURCE:GrahamandHarvey,“TheTheoryandPracticeofFinance:EvidencefromtheField,”JournalofFinancialEconomics61(2001),pp.187-243.XiamenUniversity–AdvancedFinancialManagementFU-5BookRateofReturnBookRateofReturn-Averageincomedividedbyaveragebookvalueoverprojectlife.Alsocalledaccountingrateofreturn.Managersrarelyusethismeasurementtomakedecisions.Thecomponentsreflecttaxandaccountingfigures,notmarketvaluesorcashflows.assetsbookincomebookreturnofrateBook=XiamenUniversity–AdvancedFinancialManagementFU-6Payback•Thepaybackperiodofaprojectisthenumberofyearsittakesbeforethecumulativeforecastedcashflowequalstheinitialoutlay.•Thepaybackrulesaysonlyacceptprojectsthat“payback”inthedesiredtimeframe.•Thismethodisflawed,primarilybecauseitignoreslateryearcashflowsandthethepresentvalueoffuturecashflows.XiamenUniversity–AdvancedFinancialManagementFU-7PaybackExampleExaminethethreeprojectsandnotethemistakewewouldmakeifweinsistedononlytakingprojectswithapaybackperiodof2yearsorless.0123PaybackProjectCCCCNPV@10%PeriodA-20005005005000B-200050018000C-200018005000XiamenUniversity–AdvancedFinancialManagementFU-8PaybackExampleExaminethethreeprojectsandnotethemistakewewouldmakeifweinsistedononlytakingprojectswithapaybackperiodof2yearsorless.502050018002000-C58-2018005002000-B2,624350005005002000-A10%@NPVPeriodPaybackCCCCProject3210++XiamenUniversity–AdvancedFinancialManagementFU-9InternalRateofReturnExampleYoucanpurchaseaturbopoweredmachinetoolgadgetfor$4,000.Theinvestmentwillgenerate$2,000and$4,000incashflowsfortwoyears,respectively.WhatistheIRRonthisinvestment?XiamenUniversity–AdvancedFinancialManagementFU-10InternalRateofReturnExampleYoucanpurchaseaturbopoweredmachinetoolgadgetfor$4,000.Theinvestmentwillgenerate$2,000and$4,000incashflowsfortwoyears,respectively.WhatistheIRRonthisinvestment?0)1(000,4)1(000,2000,421=++++−=IRRIRRNPV%08.28=IRRXiamenUniversity–AdvancedFinancialManagementFU-11InternalRateofReturn-2000-1500-1000-50005001000150020002500102030405060708090100Discountrate(%)NPV(,000s)IRR=28%XiamenUniversity–AdvancedFinancialManagementFU-12InternalRateofReturnPitfall1-LendingorBorrowing?•Withsomecashflows(asnotedbelow)theNPVoftheprojectincreasessthediscountrateincreases.•ThisiscontrarytothenormalrelationshipbetweenNPVanddiscountrates.364%50500,1000,1364%50500,1000,1%10@Project10−+−++++−BANPVIRRCCXiamenUniversity–AdvancedFinancialManagementFU-13InternalRateofReturnPitfall2-MultipleRatesofReturn•CertaincashflowscangenerateNPV=0attwodifferentdiscountrates.•ThefollowingcashflowgeneratesNPV=$A3.3million(@10%),andtherearetwoIRR%of(-44%)and+11.6%.15121260............10910−−CCCCCashFlows(millionsofAustraliandollars)XiamenUniversity–AdvancedFinancialManagementFU-14InternalRateofReturnPitfall2-MultipleRatesofReturn•CertaincashflowscangenerateNPV=0attwodifferentdiscountrates.•ThefollowingcashflowgeneratesNPV=0millionatbothIRR%of(-44%)and+11.6%.600NPV3000-30-600DiscountRateIRR=11.6%IRR=-44%XiamenUniversity–AdvancedFinancialManagementFU-15InternalRateofReturnPitfall2-MultipleRatesofReturn•ItispossibletohaveazeroIRRandapositiveNPV339500,2000,3000,1%10@Project210++++NoneCNPVIRRCCCXiamenUniversity–AdvancedFinancialManagementFU-16InternalRateofReturnPitfall3-MutuallyExclusiveProjects•IRRsometimesignoresthemagnitudeoftheproject.•Thefollowingtwoprojectsillustratethatproblem.818,11%75000,30000,20182,8%100000,20000,10%10@Project10+++−++−EDNPVIRRCCXiamenUniversity–AdvancedFinancialManagementFU-17InternalRateofReturnPitfall3-MutuallyExclusiveProjectsXiamenUniversity–AdvancedFinancialManagementFU-18InternalRateofReturnPitfall4-TermStructureAssumption•Weassumethatdiscountratesarestableduringthetermoftheproject.•ThisassumptionimpliesthatallfundsarereinvestedattheIRR.•Thisisafalseassumption.XiamenUniversity–AdvancedFinancialManagementFU-19InternalRateofReturnCalculatingtheIRRcanbealaborioustask.Fortunately,financialcalculatorscanperformthisfunctioneasily.*WecanuseEXCELtocalculateIRR.HP-10BEL-733ABAIIPlus-350,000CFj-350,000CFiCF16,000CFj16,000CFfi2nd{CLRWork}16,000CFj16,000CFi-350,000ENTER466,000CFj466,000CFi16,000ENTER{IRR/YR}IRR16,000ENTER466,000ENTERIRRCPTAllproduceIRR=12.96Xiamen