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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