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finance
8.1PaybackPeriodandNetPresentValue.Ifaprojectwithconventionalcashflowshasapayback
periodlessthanitslife,canyoudefinitivelystatethealgebraicsignoftheNPV?
Whyorwhynot?
Answer:
Apaybackperiodlessthantheproject’slifemeansthattheNPVispositiveforazerodiscountrate,
butnothingmoredefinitivecanbesaid.Fordiscountratesgreaterthanzero,thepaybackperiod
willstillbelessthantheproject’slife,buttheNPVmaybepositive,zero,ornegative,depending
onwhetherthediscountrateislessthan,equalto,orgreaterthantheIRR.
8.2.NetPresentValue.SupposeaprojecthasconventionalcashflowsandapositiveNPV.Whatdo
youknowaboutitspayback?
Itsprofitabilityindex?
ItsIRR?
Explain.
Answer:
IfaprojecthasapositiveNPVforacertaindiscountrate,thenitwillalsohaveapositiveNPVfor
azerodiscountrate;thusthepaybackperiodmustbelessthantheprojectlife.IfNPVispositive,
thenthepresentvalueoffuturecashinflowsisgreaterthantheinitialinvestmentcost;thusPImust
begreaterthan1.IfNPVispositiveforacertaindiscountrateR,thenitwillbezeroforsome
largerdiscountrateR*;thustheIRRmustbegreaterthantherequiredreturn.
8.3PaybackPeriod.Concerningpayback:
a.Describehowthepaybackperiodiscalculatedanddescribetheinformationthismeasure
providesaboutasequenceofcashflows.Whatisthepaybackcriteriondecisionrule?
b.Whataretheproblemsassociatedwithusingthepaybackperiodasameansofevaluatingcash
flows?
c.Whataretheadvantagesofusingthepaybackperiodtoevaluatecashflows?
Arethereany
circumstanceunderwhichusingpaybackmightbeappropriate?
Explain.
Answer:
a.Paybackperiodissimplythebreak-evenpointofaseriesofcashflows.Toactuallycomputethe
paybackperiod,itisassumedthatanycashflowoccurringduringagivenperiodisrealized
《公司金融》校级精品课程(双语类)章后习题
CHAPTER8NETPRESENTVALUEANDOTHERINVESTMENTCRITERIA8-2continuouslythroughouttheperiod,andnotatasinglepointintime.Thepaybackisthenthe
pointintimefortheseriesofcashflowswhentheinitialcashoutlaysarefullyrecovered.Given
somepredeterminedcutoffforthepaybackperiod,thedecisionruleistoacceptprojectsthat
paybackbeforethiscutoff,andrejectprojectsthattakelongertopayback.
b.Theworstproblemassociatedwithpaybackperiodisthatitignoresthetimevalueofmoney.In
addition,theselectionofahurdlepointforpaybackperiodisanarbitraryexercisethatlacksany
steadfastruleormethod.Thepaybackperiodisbiasedtowardsshort-termprojects;itfully
ignoresanycashflowsthatoccurafterthecutoffpoint.
c.Despiteitsshortcomings,paybackisoftenusedbecause
(1)theanalysisisstraightforwardand
simpleand
(2)accountingnumbersandestimatesarereadilyavailable.Materiality
consider-actionsoftenwarrantapaybackanalysisassufficient;maintenanceprojectsareanother
examplewherethedetailedanalysisofothermethodsisoftennotneeded.Sincepaybackis
biasedtowardsliquidity,itmaybeausefulandappropriateanalysismethodforshort-term
projectswherecashmanagementismostimportant.
8.4AverageAccountingReturn.ConcerningAAR:
a.Describehowtheaverageaccountingreturnisusuallycalculatedanddescribetheinformation
thismeasureprovidesaboutasequenceofcashflows.WhatistheAARcriteriondecisionrule?
b.WhataretheproblemsassociatedwithusingtheAARasameansofevaluatingaproject'scash
flows?
WhatunderlyingfeatureofAARismosttroublingtoyoufromafinancialperspective?
DoestheAARhaveanyredeemingqualities?
Answer:
a.Theaverageaccountingreturnisinterpretedasanaveragemeasureoftheaccounting
performanceofaprojectovertime,computedassomeaverageprofitmeasureduetotheproject
dividedbysomeaveragebalancesheetvaluefortheproject.ThistextcomputesAARasaverage
netincomewithrespecttoaverage(total)bookvalue.GivensomepredeterminedcutoffforAAR,
thedecisionruleistoacceptprojectswithanAARinexcessofthetargetmeasure,andrejectall
otherprojects.
b.AARisnotameasureofcashflowsandmarketvalue,butameasureoffinancialstatement
accountsthatoftenbearlittlesemblancetotherelevantvalueofaproject.Inaddition,the
selectionofacutoffisarbitrary,andthetimevalueofmoneyisignored.Forafinancialmanager,
boththerelianceonaccountingnumbersratherthanrelevantmarketdataandtheexclusionof
timevalueofmoneyconsiderationsaretroubling.Despitetheseproblems,AARcontinuestobe
usedinpracticebecause
(1)theaccountinginformationisusuallyavailable,
(2)analystsoften
useaccountingratiostoanalyzefirmperformance,and(3)managerialcompensationisoftentied
totheattainmentofcertaintargetaccountingratiogoals.
《公司金融》校级精品课程(双语类)章后习题
CHAPTER8NETPRESENTVALUEANDOTHERINVESTMENTCRITERIA8-38.5NetPresentValue.ConcerningNPV:
a.DescribehowNPViscalculatedanddescribetheinformationthismeasureprovidesabouta
sequenceofcashflows.WhatistheNPVcriteriondecisionrule?
b.WhyisNPVconsideredtobeasuperiormethodofevaluationthecashflowsfromproject?
SupposetheNPVforaproject'scashflowsiscomputedtobe$2,500.Whatdoesthisnumber
representwithrespecttothefirm'sshareholders?
Answer:
a.NPVissimplythesumofthepresentvaluesofaproject’scashflows.NPVspecificallymeasures,
afterconsideringthetimevalueofmoney,thenetincreaseordecreaseinfirmwealthduetothe
project.ThedecisionruleistoacceptprojectsthathaveapositiveNPV,andrejectprojectswitha
negativeNPV.
b.NPVissuperiortotheothermethodsofanalysispresentedinthetextbecauseithasnoserious
flaws.Themethodunambiguouslyranksmutuallyexclusiveprojects,andcandifferentiate
betweenprojectsofdifferentscaleandtimehorizon.TheonlydrawbacktoNPVisthatitrelies
oncashflowanddiscountratevaluesthatareoftenestimatesandnotcertain,butthisisa
problemsharedbytheotherperformancecriteriaaswell.AprojectwithNPV=$2,500implies
thatthetotalshareholderwealthofthefirmwillincreaseby$2,500iftheprojectisaccepted.
8.6InternalRateofReturn.ConcerningIRR:
a.DescribehowNPViscalculatedanddescribetheinformationthismeasureprovidesabouta
sequenceofcashflows.WhatistheNPVcriteriondecisionrule?
b.WhatisrelationshipbetweenIRRandNPV?
Arethereanysituationinwhichyoumightprefer
onemethodovertheother?
Why?
c.Despiteitsshortcomingsinsomesituations,whydomostfinancialmanagersuseIRRalongwith
NPVwhenevaluatingprojects?
CanyouthinkofasituationinwhichIRRmightbeamore
appropriatemeasuretousethanNPV?
Explain.
Answer:
a.TheIRRisthediscountratethatcausestheNPVofaseriesofcashflowstobeequaltozero.
IRRcanthusbeinterpretedasafinancialbreak-evenrateofreturn;attheIRRdiscountrate,the
netvalueoftheprojectiszero.TheIRRdecisionruleistoacceptprojectswithIRRsgreaterthan
thediscountrate,andtorejectprojectswithIRRslessthanthediscountrate.
b.IRRistheinterestratethatcausesNPVforaseriesofcashflowstobezero.NPVispreferredin
allsituationstoIRR;IRRcanleadtoambiguousresultsiftherearenon-conventionalcashflows,
andalsoambiguouslyrankssomemutuallyexclusiveprojects.However,forstand-aloneprojects
withconventionalcashflows,IRRandNPVareinterchangeabletechniques.
c.IRRisfrequentlyusedbecauseitiseasierformanyfinancialmanagersandanalyststorate
performanceinrelativeterms,suchas“12%”,thaninabsoluteterms,suchas“$46,000.”IRR
《公司金融》校级精品课程(双语类)章后习题
CHAPTER8NETPRESENTVALUEANDOTHERINVESTMENTCRITERIA8-4maybeapreferredmethodtoNPVinsituationswhereanappropriatediscountrateisunknown
oruncertain;inthissituation,IRRwouldprovidemoreinformationabouttheprojectthanwould
NPV.
8.7ProfitabilityIndex.Concerningtheprofitabilityindex:
a.Describehowtheprofitabilityindexiscalculatedanddescribetheinformationthismeasure
providesaboutasequenceofcashflows.Whatistheprofitabilityindexdecisionrule?
b.WhatistherelationshipbetweentheprofitabilityindexandtheNPV?
Arethereanysituationsin
whichyoumightpreferonemethodovertheother?
Explain.
Answer:
a.Theprofitabilityindexisthepresentvalueofcashinflowsrelativetotheprojectcost.Assuch,it
isabenefit/costratio,providingameasureoftherelativeprofitabilityofaproject.The
profitabilityindexdecisionruleistoacceptprojectswithaPIgreaterthanone,andtoreject
projectswithaPIlessthanone.
b.PI=(NPV+cost)/cost=1+(NPV/cost).IfafirmhasabasketofpositiveNPVprojects
andissubjecttocapitalrationing,PImayprovideagoodrankingmeasureoftheprojects,
indicatingthe“bangforthebuck”ofeachparticularproject.
8.8PaybackandInternalRateofReturn.AprojecthasperpetualcashflowsofCperperiod,a
costofI,andarequiredreturnofR.Whatistherelationshipbetweentheproject'spaybackandits
IRR?
Whatimplicationsdoesyouranswerhaveforlong-livedprojectswithrelativelyconstantcash
flows?
Answer:
Foraprojectwithfuturecashflowsthatareanannuity:
Payback=I/C
AndtheIRRis:
0=–I+C/IRR
SolvingtheIRRequationforIRR,weget:
IRR=C/I
Noticethisisjustthereciprocalofthepayback.So:
IRR=1/Payback
Forlong-livedprojectswithrelativelyc