02 discounted cash flow applications

TestID:7658688DiscountedCashFlowApplications

Question#1of72 QuestionID:412839

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Inordertocalculatethenetpresentvalue(NPV)ofaproject,ananalystwouldleastlikelyneedtoknowthe:

internalrateofreturn(IRR)oftheproject.

opportunitycostofcapitalfortheproject.

timingoftheexpectedcashflowsfromtheproject.

Explanation

TheNPViscalculatedusingtheopportunitycost,discountrate,expectedcashflows,andtimingoftheexpectedcashflowsfromtheproject.Theproject'sIRRisnotusedtocalculatetheNPV.

ATreasurybill(Tbill)withafacevalueof$10,000and219daysuntilmaturityissellingfor97.375%offacevalue.WhichofthefollowingisclosesttotheholdingperiodyieldontheTbillifhelduntilmaturity?

2.81%.

2.70%.

2.63%.

Explanation

Theformulaforholdingperiodyieldis:(P P +D )/(P ),whereD foraTbilliszero(itdoesnothaveacoupon).Therefore,theHPYis:($10,000$9,737.50)/($9,737.50)=0.0270=2.70%.

Alternatively(100/97.375)1=0.02696.

CalabashCrabHouseisconsideringaninvestmentinmutuallyexclusivekitchenupgradeprojectswiththefollowingcashflows:

ProjectA ProjectBInitialYear $10,000 $9,000

Year1 2,000 200Year2 5,000 2,000Year3 8,000 11,000Year4 8,000 15,000

AssumingCalabashhasa12.5%costofcapital,whichofthefollowinginvestmentdecisionsismostappropriate?

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AcceptProjectAbecauseitsinternalrateofreturnishigherthanthatofProjectB.

Acceptbothprojectsbecausetheybothhavepositivenetpresentvalues.

AcceptProjectBbecauseitsnetpresentvalueishigherthanthatofProjectA.

Explanation

Whennetpresentvalue(NPV)andinternalrateofreturn(IRR)giveconflictingprojectrankings,NPVisthemostappropriatemethodfordecidingbetweenmutuallyexclusiveprojects.Here,theNPVofprojectAis$6,341andtheNPVofProjectBis$6,688.BothNPVsarepositive,soCalabashshouldselecttheProjectBbecauseofitshigherNPV.

Assumeaninvestormakesthefollowinginvestments:

Today,shepurchasesashareofstockinRedwoodAlternativesfor$50.00.Afteroneyear,shepurchasesanadditionalsharefor$75.00.Afteronemoreyear,shesellsbothsharesfor$100.00each.

Therearenotransactioncostsortaxes.Theinvestor'srequiredreturnis35.0%.

Duringyearone,thestockpaida$5.00persharedividend.Inyeartwo,thestockpaida$7.50persharedividend.

Thetimeweightedreturnis:

51.7%.

51.4%.

23.2%.

Explanation

Tocalculatethetimeweightedreturn:

Step1:Separatethetimeperiodsintoholdingperiodsandcalculatethereturnoverthatperiod:

Holdingperiod1:P =$50.00

D =$5.00

P =$75.00(frominformationonsecondstockpurchase)

HPR =(7550+5)/50=0.60,or60%

Holdingperiod2:P =$75.00

D =$7.50

P =$100.00

HPR =(10075+7.50)/75=0.433,or43.3%.

Step2:Usethegeometricmeantocalculatethereturnoverbothperiods

Return=[(1+HPR )(1+HPR )] 1=[(1.60)(1.433)] 1=0.5142,or51.4%.

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ATreasurybillwithafacevalueof$1,000,000and45daysuntilmaturityissellingfor$987,000.TheTreasurybill'sbankdiscountyieldisclosestto:

7.90%.

10.40%.

10.54%.

Explanation

Theactualdiscountis1.3%,1.3%(360/45)=10.4%

Thebankdiscountyieldiscomputedbythefollowingformula,r=(dollardiscount/facevalue)(360/numberofdaysuntilmaturity)=[(1,000,000987,000)/(1,000,000)](360/45)=10.40%.

Ananalystmanagedaportfolioformanyyearsandthenliquidatedit.Computingtheinternalrateofreturnoftheinflowsandoutflowsofaportfoliowouldgivethe:

timeweightedreturn.

netpresentvalue.

moneyweightedreturn.

Explanation

Themoneyweightedreturnistheinternalrateofreturnonaportfoliothatequatesthepresentvalueofinflowsandoutflowsoveraperiodoftime.

Fisher,Inc.,isevaluatingthebenefitsofinvestinginanewindustrialprinter.Theprinterwillcost$28,000andincreaseaftertaxcashflowsby$8,000duringeachofthenextfiveyears.Whataretherespectiveinternalrateofreturn(IRR)andnetpresentvalue(NPV)oftheprinterprojectifFisher'srequiredrateofreturnis11%?

5.56%$3,180.

17.97%$5,844.

13.20%$1,567.

Explanation

IRRKeystrokes:CF =$28,000CF =$8,000F =5CPTIRR=13.2%.

NPVKeystrokes:CF =$28,000CF =$8,000F =5I=11CPTNPV=1,567.

Sincecashflowsarelevel,analternativeis:IRR:N=5PMT=8,000PV=28,000CPTI/Y=13.2%.

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NPV:I/Y=11CPTPV=29,567+28,000=1,567

Aninvestorexpectsastockcurrentlysellingfor$20persharetoincreaseto$25byyearend.Thedividendlastyearwas$1butheexpectsthisyear'sdividendtobe$1.25.Whatistheexpectedholdingperiodreturnonthisstock?

31.25%.

28.50%.

24.00%.

Explanation

Return=[dividend+(endbegin)]/beginningprice

R=[1.25+(2520)]/20=6.25/20=0.3125

ATreasurybillhas90daysuntilitsmaturityandaholdingperiodyieldof3.17%.Itseffectiveannualyieldisclosestto:

13.49%.

12.68%.

13.30%.

Explanation

Theeffectiveannualyield(EAY)isequaltotheannualizedholdingperiodyield(HPY)basedona365dayyear.EAY=(1+HPY) 1=(1.0317) 1=13.49%.

Aninvestormakesthefollowinginvestments:

Shepurchasesashareofstockfor$50.00.

Afteroneyear,shepurchasesanadditionalsharefor$75.00.

Afteronemoreyear,shesellsbothsharesfor$100.00each.

Therearenotransactioncostsortaxes.

Duringyearone,thestockpaida$5.00persharedividend.Inyear2,thestockpaida$7.50persharedividend.Theinvestor'srequired

returnis35%.Hermoneyweightedreturnisclosestto:

7.5%.

48.9%.

16.1%.

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Explanation

Todeterminethemoneyweightedrateofreturn,useyourcalculator'scashflowandIRRfunctions.Thecashflowsareasfollows:

CF0:initialcashoutflowforpurchase=$50

CF1:dividendinflowof$5cashoutflowforadditionalpurchaseof$75=netcashoutflowof$70

CF2:dividendinflow(2$7.50=$15)+cashinflowfromsale(2$100=$200)=netcashinflowof$215

EnterthecashflowsandcomputeIRR:

CF0=50CF1=70CF2=+215CPTIRR=48.8607

ATreasurybill,with45daysuntilmaturity,hasaneffectiveannualyieldof12.50%.Thebill'sholdingperiodyieldisclosestto:

1.57%.

1.46%.

1.54%.

Explanation

Theeffectiveannualyield(EAY)isequaltotheannualizedholdingperiodyield(HPY)basedona365dayyear.EAY=(1+HPY) 1.HPY=(EAY+1) 1=(1.125) 1=1.46%.

OnJanuary1,JonathanWoodinvests$50,000.AttheendofMarch,hisinvestmentisworth$51,000.OnApril1,Wooddeposits$10,000intohisaccount,andbytheendofJune,hisaccountisworth$60,000.Woodwithdraws$30,000onJuly1andmakesnoadditionaldepositsorwithdrawalstherestoftheyear.Bytheendoftheyear,hisaccountisworth$33,000.Thetimeweightedreturnfortheyearisclosestto:

10.4%.

7.0%.

5.5%.

Explanation

JanuaryMarchreturn=51,000/50,0001=2.00%AprilJunereturn=60,000/(51,000+10,000)1=1.64%JulyDecemberreturn=33,000/(60,00030,000)1=10.00%Timeweightedreturn=[(1+0.02)(10.0164)(1+0.10)]1=0.1036or10.36%

Aninvestorbuysoneshareofstockfor$100.Attheendofyearoneshebuysthreemoresharesat$89pershare.Attheendofyeartwoshesellsallfoursharesfor$98each.Thestockpaidadividendof$1.00pershareattheendofyearoneand

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yeartwo.Whatistheinvestor'stimeweightedrateofreturn?

6.35%.

11.24%.

0.06%.

Explanation

Theholdingperiodreturninyearoneis($89.00$100.00+$1.00)/$100.00=10.00%.

Theholdingperiodreturninyeartwois($98.00$89.00+$1.00)/$89=11.24%.

Thetimeweightedreturnis[{1+(0.1000)}{1+0.1124}] 1=0.06%.

Astockiscurrentlyworth$75.Ifthestockwaspurchasedoneyearagofor$60,andthestockpaida$1.50dividendoverthecourseoftheyear,whatistheholdingperiodreturn?

27.5%.

22.0%.

24.0%.

Explanation

(7560+1.50)/60=27.5%.

Whichofthefollowingisleastlikelyaproblemassociatedwiththeinternalrateofreturn(IRR)methodformakinginvestmentdecisions?

TheIRRmethoddeterminesthediscountratethatsetsthenetpresentvalueofaprojectequaltozero.

Aninvestmentprojectmayhavemorethanoneinternalrateofreturn.

IRRandNPVcriteriacangiveconflictingdecisionsformutuallyexclusiveprojects.

Explanation

TheIRRmethodequatesaninvestment'spresentvalueofinflowstoitspresentvalueofoutflows.TheIRRbydefinitionisthediscountratethatsetsthenetpresentvalueofaprojectequaltozero.Therefore,thedecisionruleforindependentprojectsisasfollows:iftheIRRisabovethefirm'scostofcapital,theprojectshouldbeaccepted,andiftheIRRisbelowthecostofcapital,theprojectshouldberejected.

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ATreasurybillhas40daystomaturity,aparvalueof$10,000,andwasjustpurchasedbyaninvestorfor$9,900.Itsholdingperiodyieldisclosestto:

1.00%.

1.01%.

9.00%.

Explanation

Theholdingperiodyieldisthereturnthattheinvestorwillearnifthebillishelduntilitmatures.Theholdingperiodyieldformulais(pricereceivedatmaturityinitialprice+interestpayments)/(initialprice)=(10,0009,900+0)/(9,900)=1.01%.RecallthatwhenbuyingaTbill,investorspaythefacevaluelessthediscountandreceivethefacevalueatmaturity.

Theeffectiveannualyield(EAY)foraTbillmaturingin150daysis5.04%.Whataretheholdingperiodyield(HPY)andmoneymarketyield(MMY)respectively?

2.04%4.90%.

2.80%5.41%.

5.25%2.04%.

Explanation

TheEAYtakestheholdingperiodyieldandannualizesitbasedona365dayyearaccountingforcompounding.TheHPY=(1+0.0504) =1.20411=2.04%.UsingtheHPYtocomputethemoneymarketyield=HPY(360/t)=0.0204(360/150)=0.04896=4.90%.

ThefinancialmanageratGenesisCompanyislookingintothepurchaseofanapartmentcomplexfor$550,000.Netaftertaxcashflowsareexpectedtobe$65,000foreachofthenextfiveyears,thendropto$50,000forfouryears.Genesis'requiredrateofreturnis9%onprojectsofthisnature.Afternineyears,GenesisCompanyexpectstosellthepropertyforaftertaxproceedsof$300,000.Whatistherespectiveinternalrateofreturn(IRR)andnetpresentvalue(NPV)onthisproject?

6.66%$64,170.

7.01%$53,765.

13.99%$166,177.

Explanation

IRRKeystrokes:CF =$550,000CF =$65,000F =5CF =$50,000F =3CF =$350,000F =1.

NPVKeystrokes:CF =$550,000CF =$65,000F =5CF =$50,000F =3CF =$350,000F =1.

ComputeNPV,I=9.

150/365

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Note:Althoughtherateofreturnispositive,theIRRislessthantherequiredrateof9%.Hence,theNPVisnegative.

Aninvestorbuysashareofstockfor$200.00attimet=0.Attimet=1,theinvestorbuysanadditionalsharefor$225.00.Attimet=2theinvestorsellsbothsharesfor$235.00.Duringbothyears,thestockpaidapersharedividendof$5.00.Whataretheapproximatetimeweightedandmoneyweightedreturnsrespectively?

10.8%9.4%.

7.7%7.7%.

9.0%15.0%.

Explanation

Timeweightedreturn=(225+5200)/200=15%(470+10450)/450=6.67%[(1.15)(1.0667)] 1=10.8%

Moneyweightedreturn:200+[225/(1+return)]=[5/(1+return)]+[480/(1+return) ]moneyreturn=approximately9.4%

Notethattheeasiestwaytosolveforthemoneyweightedreturnistosetuptheequationandplugintheanswerchoicestofindthediscountratethatmakesoutflowsequaltoinflows.

Usingthefinancialcalculatorstocalculatethemoneyweightedreturn:(Thefollowingkeystrokesassumethatthefinancialmemoryregistersareclearedofpriorwork.)

TIBusinessAnalystIIPlus

EnterCF :200,+/,Enter,downarrowEnterCF :220,+/,Enter,downarrow,downarrowEnterCF :480,Enter,downarrow,downarrow,ComputeIRR:IRR,CPTResult:9.39

HP12C

EnterCF :200,CHS,g,CFEnterCF :220,CHS,g,CFEnterCF :480,g,CF ComputeIRR:f,IRRResult:9.39

Whichofthefollowingstatementsaboutmoneyweightedandtimeweightedreturnsisleastaccurate?

Themoneyweightedreturnappliestheconceptofinternalrateofreturntoinvestmentportfolios.

Ifaclientaddsfundstoaninvestmentpriortoanunfavorablemarket,thetimeweightedreturnwillbedepressed.

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Iftheinvestmentperiodisgreaterthanoneyear,ananalystmustusethegeometricmeantocalculatetheannualtimeweightedreturn.

Explanation

Thetimeweightedmethodisnotaffectedbythetimingofcashflows.Theotherstatementsaretrue.

MirandaCromwell,CFA,buys2,000worthofSmith&JonesPLCsharesatthebeginningofeachyearforfouryearsatpricesof100,120,150and130respectively.AttheendofthefourthyearthepriceofSmith&JonesPLCis140.Thesharesdonotpayadividend.Cromwellcalculatesheraveragecostpershareas[(100+120+150+130)/4]=125.Cromwellthenusesthegeometricmeanofannualholdingperiodreturnstoconcludethathertimeweightedannualrateofreturnis8.8%.HasCromwellcorrectlydeterminedheraveragecostpershareandtimeweightedrateofreturn?

AveragecostTimeweightedreturn

Incorrect Correct

Correct Incorrect

Correct Correct

Explanation

BecauseCromwellpurchasesshareseachyearforthesameamountofmoney,sheshouldcalculatetheaveragecostpershareusingtheharmonicmean.Cromwelliscorrecttousethegeometricmeantocalculatethetimeweightedrateofreturn.Thecalculationisasfollows:

Year Beginningprice EndingpriceAnnualrateof

return

1 100 120 20%

2 120 150 25%

3 150 130 13.33%

4 130 140 7.69%

TWR=[(1.20)(1.25)(0.8667)(1.0769)] 1=8.78%.Or,moresimply,(140/100) 1=8.78%.

Theestimatedannualaftertaxcashflowsofaproposedinvestmentareshownbelow:

Year1:$10,000

Year2:$15,000

Year3:$18,000

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Aftertaxcashflowfromsaleofinvestmentattheendofyear3is$120,000

Theinitialcostoftheinvestmentis$100,000,andtherequiredrateofreturnis12%.Thenetpresentvalue(NPV)oftheprojectisclosestto:

$63,000.

$66,301.

$19,113.

Explanation

10,000/1.12=8,929

15,000/(1.12) =11,958

138,000/(1.12) =98,226

NPV=8,929+11,958+98,226100,000=$19,113

Alternatively:CFO=100,000CF1=10,000CF2=15,000CF3=138,000I=12CPTNPV=$19,112.

Abondthatpays$100ininteresteachyearwaspurchasedatthebeginningoftheyearfor$1,050andsoldattheendoftheyearfor$1,100.Aninvestor'sholdingperiodreturnis:

10.5%.

10.0%.

14.3%.

Explanation

Inputintoyourcalculator:N=1FV=1,100PMT=100PV=1,050CPTI/Y=14.29

Whyisthetimeweightedrateofreturnthepreferredmethodofperformancemeasurement?

Thereisnopreferencefortimeweightedversusmoneyweighted.

Timeweightedreturnsarenotinfluencedbythetimingofcashflows.

Timeweightedallowsforinterperiodmeasurementandthereforeismoreflexiblein

determiningexactlyhowaportfolioperformedduringaspecificintervaloftime.

Explanation

Moneyweightedreturnsaresensitivetothetimingorrecognitionofcashflowswhiletimeweightedratesofreturnarenot.

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Aninvestorstartedtheyearwitha$10,000portfolio.Hemadea$1,000contributionattheendofthefirstquarter,a$2,000withdrawalattheendofthethirdquarter,andendedtheyearwithaportfoliovalueof$10,553.Thequarterlyholdingperiodreturnsfortheinvestor'sportfolioareasfollows.

Q1 Q2 Q3 Q4

3% 5% 8% 10%

Theeffectiveannualmoneyweightedandtimeweightedreturnsareclosestto:

Moneyweighted

Timeweighted

15.13% 3.84%

3.59% 16.25%

15.13% 16.25%

Explanation

ThemoneyweightedreturnissimplytheIRR.TocalculatethequarterlyIRRfortheportfolio,usethecashflowfunctionsofthefinancialcalculator.Cashinflowsareinputasnegativenumbersandcashoutflowsarepositivenumbers.Thevalueoftheportfolioattheendoftheyearisconsideredacashoutflowbecausethatistheamountyoucouldpotentiallywithdrawifyouliquidatedtheportfolio.

CF0=10,000CF1=1,000CF2=2,000CF3=10,553CPTIRR=3.5856%.ThisistheperiodicIRR(quarterly).Theeffectiveannualreturnis(1+0.035856) 1=15.13%.

Thetimeweightedreturnisthegeometricallylinkedsubperiodreturns:(1.03)(0.95)(1.08)(1.10)1=16.25%.

Aninvestmentwithacostof$5,000isexpectedtohavecashinflowsof$3,000inyear1,and$4,000inyear2.Theinternalrateofreturn(IRR)forthisinvestmentisclosestto:

30%.

25%.

15%.

Explanation

TheIRRisthediscountratethatmakesthenetpresentvalueoftheinvestmentequalto0.

Thismeans$5,000+$3,000/(1+IRR)+$4,000/(1+IRR) =0

OnewaytocomputethisproblemistousetrialanderrorwiththeexistinganswerchoicesandchoosethediscountratethatmakesthePVofthecashflowsclosestto5,000.

$3,000/(1.25)+$4,000/(1.25) =4,960.

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Alternatively:CFO=5,000CF1=3,000CF2=4,000CPTIRR=24.3%.

ATbillwithafacevalueof$100,000and140daysuntilmaturityissellingfor$98,000.Whatisthemoneymarketyield?

5.25%.

2.04%.

5.41%.

Explanation

Themoneymarketyieldisequivalenttotheholdingperiodyieldannualizedbasedona360dayyear.=(2,000/98,000)(360/140)=0.0525,or5.25%.

Themoneyweightedreturnalsoisknownasthe:

measureofthecompoundrateofgrowthof$1overastatedmeasurementperiod.

internalrateofreturn(IRR)ofaportfolio.

returnoninvestedcapital.

Explanation

ItistheIRRofaportfolio,takingintoaccountallofthecashinflowsandoutflows.

WhenAnnetteFamiglettihearsthatabaseballlovingfriendiscomingtovisit,shepurchasestwopremiumseatingticketsfor$45perticketforaneveninggame.Asthedateofthegameapproaches,Famigletti'sfriendtelephonesandsaysthathistriphasbeencancelled.FortunatelyforFamigletti,theticketssheholdsareinhighdemandasthereischancethattheleadingMajorLeagueBaseballhitterwillbreakthehomerunrecordduringthegame.Seeinganopportunitytoearnahighreturn,Famiglettiputstheticketsupforsaleonaninternetsite.Theauctionclosesat$150perticket.Afterpayinga10%commissiontothesite(ontheamountofthesale)andpaying$8totalinshippingcosts,Familgletti'sholdingperiodreturnisapproximately:

182%.

202%.

191%.

Explanation

Theholdingperiodreturniscalculatedas:(endingpricebeginningprice+/anycashflows)/beginningprice.Here,thebeginningandendingpricesaregiven.Theothercashflowsconsistofthecommissionof$30(0.101502tickets)andthe


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shippingcostof$8(totalforbothtickets).Thus,herholdingperiodreturnis:(2150245308)/(245)=1.91,orapproximately191%.

WhatistheeffectiveannualyieldofaTbillthathasamoneymarketyieldof5.665%and255daystomaturity?

4.01%.

5.92%.

5.79%.

Explanation

HoldingPeriodYield=4.0127%=5.665%(255/360)

EffectiveAnnualYield=(1.040127) =1.05711=5.79%.

Whichofthefollowingstatementsregardingmakinginvestmentdecisionsusingnetpresentvalue(NPV)andinternalrateofreturn(IRR)isleastaccurate?

Iftwoprojectsaremutuallyexclusive,oneshouldalwayschoosetheprojectwiththehighestIRR.

ProjectswithapositiveNPVsincreaseshareholderwealth.

IfafirmundertakesazeroNPVproject,thefirmwillgetlarger,butshareholderwealthwillnotchange.

Explanation

Iftwoprojectsaremutuallyexclusive,thefirmshouldalwayschoosetheprojectwiththehighestNPVratherthanthehighestIRR.Iftwoprojectsaremutuallyexclusive,thefirmmayonlychooseone.ItispossibleforNPVandIRRtogiveconflictingdecisionsforprojectsofdifferentsizes.BecauseNPVisadirectmeasureofthechangeinshareholderwealth,NPVcriteriashouldbeusedwhenNPVandIRRdecisionsconflict.

WhenaprojecthasapositiveNPV,itwilladdtoshareholderwealthbecausetheprojectisearningmorethantheopportunitycostofcapitalneededtoundertaketheproject.IfafirmtakesonazeroNPVproject,thefirmwillearnexactlyenoughtocovertheopportunitycostofcapital.Thefirmwillincreaseinsizebytakingtheproject,butshareholderwealthwillnotchange.

Theinternalrateofreturn(IRR)methodandnetpresentvalue(NPV)methodofprojectselectionwillalwaysprovidethesameacceptorrejectdecisionwhen:

upfrontprojectcostsareunder$1.0million.

theprojectsaremutuallyexclusive.

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theprojectsareindependent.

Explanation

Ifaproject'sIRRexceedsthecostofcapital,theproject'sNPVwillbepositive.TheonlywayinwhichacceptingapositiveNPVprojectwouldreducefirmvalueisifitsselectionprecludesselectionofaprojectthatwouldhaveenhancedfirmvaluetoagreaterextent(i.e.,hadahigherNPV).IRRandNPVmethodaccuracydonotdependuponprojectdurationorcosts.

ATbillwithafacevalueof$100,000and140daysuntilmaturityissellingfor$98,000.Whatisitsholdingperiodyield?

2.04%.

5.14%.

5.25%.

Explanation

TheholdingperiodyieldisthereturntheinvestorwillearniftheTbillisheldtomaturity.HPY=(100,00098,000)/98,000=0.0204,or2.04%.

Timeweightedreturnsareusedbytheinvestmentmanagementindustrybecausethey:

takeallcashinflowsandoutflowsintoaccountusingtheinternalrateofreturn.

resultinhigherreturnsversusthemoneyweightedreturncalculation.

arenotaffectedbythetimingofcashflows.

Explanation

Timeweightedreturnsarenotaffectedbythetimingofcashflows.Moneyweightedreturns,bycontrast,willbehigherwhenfundsare

addedatafavorableinvestmentperiodorwillbelowerwhenfundsareaddedduringanunfavorableperiod.Thus,timeweightedreturns

offerabetterperformancemeasurebecausetheyarenotaffectedbythetimingofflowsintoandoutoftheaccount.

ATreasurybill(Tbill)with38daysuntilmaturityhasabankdiscountyieldof3.82%.WhichofthefollowingisclosesttothemoneymarketyieldontheTbill?

3.81%.

3.87%.

3.84%.

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Theformulaforthemoneymarketyieldis:[360bankdiscountyield]/[360(tbankdiscountyield)].Therefore,themoneymarketyieldis:[3600.0382]/[360(380.0382)]=(13.752)/(358.548)=0.0384,or3.84%.

Alternatively:Actualdiscount=3.82%(38/360)=0.4032%.

TBillprice=1000.4032=99.5968%.

HPR=(100/99.5968)1=0.4048%.

MMY=0.4048%(360/38)=3.835%.

ATbillwithafacevalueof$100,000and140daysuntilmaturityissellingfor$98,000.Whatistheeffectiveannualyield(EAY)?

2.04%.

5.41%.

5.14%.

Explanation

TheEAYtakestheholdingperiodyieldandannualizesitbasedona365dayyearaccountingforcompounding.HPY=(100,00098,000)/98,000=0.0204.EAY=(1+HPY) 1=(1.0204) 1=0.05406=5.41%.

Ifaninvestorboughtastockfor$32andsolditoneyearlaterfor$37.50afterreceiving$2individends,whatwastheholdingperiodreturnonthisinvestment?

6.25%.

23.44%.

17.19%.

Explanation

HPR=[D+EndPriceBegPrice]/BegPrice

HPR=[2+37.5032]/32=0.2344.

WilliamsWarehousingcurrentlyhasawarehouseleasethatcallsforfiveannualpaymentsof$120,000.Thewarehouseowner,whoneedscash,isofferingWilliamsadealwhereinWilliamswillpay$200,000thisyearandthenpayonly$80,000eachoftheremaining4years.(Assumethatallleasepaymentsaremadeatthebeginningoftheyear.)ShouldWilliamsWarehousingaccepttheofferifitsrequiredrateofreturnis9%,andwhy?

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Yes,thereisasavingsof$45,494inpresentvalueterms.

No,thereisanadditional$80,000paymentinthisyear.

Yes,thereisasavingsof$49,589inpresentvalueterms.

Explanation

Thepresentvalueofthecurrentleaseis$508,766.38,whilethepresentvalueoftheleasebeingofferedis$459,177.59asavingsof49,589.Alternatively,thepresentvalueoftheextra$40,000atthebeginningofeachofthenext4yearsis$129,589whichis$49,589morethantheextra$80,000addedtothepaymenttoday.

JackSmith,CFA,isanalyzingindependentinvestmentprojectsXandY.Smithhascalculatedthenetpresentvalue(NPV)andinternalrateofreturn(IRR)foreachproject:

ProjectX:NPV=$250IRR=15%

ProjectY:NPV=$5,000IRR=8%

Smithshouldmakewhichofthefollowingrecommendationsconcerningthetwoprojects?

AcceptProjectYonly.

AcceptProjectXonly.

Acceptbothprojects.

Explanation

Theprojectsareindependent,meaningthateitheroneorbothprojectsmaybechosen.BothprojectshavepositiveNPVs,thereforebothprojectsaddtoshareholderwealthandbothprojectsshouldbeaccepted.

AninvestorhasjustpurchasedaTreasurybillfor$99,400.Ifthesecuritymaturesin40daysandhasaholdingperiodyieldof0.604%,whatisitsmoneymarketyield?

5.650%.

5.436%.

5.512%.

Explanation

Themoneymarketyieldistheannualizedyieldonthebasisofa360dayyearanddoesnottakeintoaccounttheeffectofcompounding.Themoneymarketyield=(holdingperiodyield)(360/numberofdaysuntilmaturity)=(0.604%)(360/40)=5.436%.


A)

B)

C)


A)

B)

C)


A)

B)

C)

AninvestorisconsideringinvestinginTawariCompanyforoneyear.Heexpectstoreceive$2individendsovertheyearandfeelshecansellthestockfor$30attheendoftheyear.Torealizeareturnontheinvestmentovertheyearof14%,thepricetheinvestorwouldpayforthestocktodayisclosestto:

$29.

$28.

$32.

Explanation

HPR=[Dividend+(EndingpriceBeginningprice)]/Beginningprice

0.14=[2+(30P)]/P

1.14P=32soP=$28.07

ATreasurybill(Tbill)withafacevalueof$10,000and44daysuntilmaturityhasaholdingperiodyieldof1.1247%.WhichofthefollowingisclosesttotheeffectiveannualyieldontheTbill?

12.47%.

8.76%.

9.72%.

Explanation

Theformulafortheeffectiveannualyieldis:((1+HPY) )1.Therefore,theEAYis:((1.011247) )1=0.0972,or9.72%

ThecapitalbudgetingdirectorofGreenManufacturingisevaluatingalaserimagingprojectwiththefollowingcharacteristics:Cost:$150,000Expectedlife:3yearsAftertaxcashflows:$60,317peryearSalvagevalue:$0

IfGreenManufacturing'scostofcapitalis11.5%,whatistheproject'sinternalrateofreturn(IRR)?

13.6%.

10.0%.

$3,875.

Explanation

SinceweareseekingtheIRR,theanswerhastobeintermsofarateofreturn,thiseliminatestheoptionnotwrittenina

365/t (365/44)


A)

B)

C)


A)

B)

C)


A)

B)

C)

percentage.

Sincetheypayments(cashflows)areequals,wecancalculatetheIRRas:N=3PV=150,000PMT=60,317CPTI/Y=9.999

IftheholdingperiodyieldonaTreasurybill(Tbill)with197daysuntilmaturityis1.07%,whatistheeffectiveannualyield?

0.58%.

1.07%.

1.99%.

Explanation

TocalculatetheEAYfromtheHPY,theformulais:(1+HPY) 1.Therefore,theEAYis:(1.0107) 1=0.0199,or1.99%.

WhatistheeffectiveannualyieldforaTreasurybillpricedat$98,853withafacevalueof$100,000and90daysremaininguntilmaturity?

1.16%.

4.79%.

4.64%.

Explanation

HPY=(100,00098,853)/98,853=1.16%

EAY=(1+0.0116) 1=4.79%

Aninvestorbuysoneshareofstockfor$100.Attheendofyearoneshebuysthreemoresharesat$89pershare.Attheendofyeartwoshesellsallfoursharesfor$98each.Thestockpaidadividendof$1.00pershareattheendofyearoneandyeartwo.Whatistheinvestor'smoneyweightedrateofreturn?

5.29%.

0.06%.

6.35%.

Explanation

T=0:Purchaseoffirstshare=$100.00

(365/t) (365/197)

365/90


A)

B)

C)


A)

B)

C)

T=1:Dividendfromfirstshare=+$1.00

Purchaseof3moreshares=$267.00

T=2:Dividendfromfourshares=+4.00

Proceedsfromsellingshares=+$392.00

Themoneyweightedreturnistheratethatsolvestheequation:

$100.00=$266.00/(1+r)+396.00/(1+r) .

CFO=100CF1=266CF2=396CPTIRR=6.35%.

SarahKelley,CFA,isanalyzingtwomutuallyexclusiveinvestmentprojects.Kelleyhascalculatedthenetpresentvalue(NPV)andinternalrateofreturn(IRR)foreachproject:

Project1:NPV=$230IRR=15%

Project2:NPV=$4,000IRR=6%

Kelleyshouldmakewhichofthefollowingrecommendationsconcerningthetwoprojects?

AcceptProject2only.

AcceptProject1only.

Acceptbothprojects.

Explanation

Becausetheinvestmentprojectsaremutuallyexclusive,onlyoneprojectcanbechosen.TheNPVandIRRcriteriaaregivingconflictingprojectrankings.Whendecisioncriteriaconflict,alwaysusetheNPVcriteriabecauseNPVevaluatesprojectsusinganappropriatediscountrate,theweightedaveragecostofcapital.TheIRRmaynotbeamarketrate,thereforefuturecashflowsassociatedwiththeprojectmaynotbecapableofearningarateofreturnequaltotheIRR.

WhatistheyieldonadiscountbasisforaTreasurybillpricedat$97,965withafacevalueof$100,000thathas172daystomaturity?

3.95%.

2.04%.

4.26%.

Explanation

($2,035/$100,000)(360/172)=0.04259=4.26%=bankdiscountyield.

2


A)

B)

C)


A)

B)

C)

Financialmanagersshouldalwaysselecttheprojectthatprovidesthehighestnetpresentvalue(NPV)wheneverNPVandIRRmethodsconflict,becausemaximizing:

shareholderwealthisthegoaloffinancialmanagement.

theshareholders'rateofreturnisthegoaloffinancialmanagement.

revenuesisthegoaloffinancialmanagement.

Explanation

Focusingonthemaximizationofearningsdoesnotconsiderthedifferencesinriskacrossprojects,whilefocusingonrevenuesprecludesconcernfortheexpensesincurred.Earningahigherreturnonasmallprojectprovideslessofabenefitthanearningaslightlylowerrateofreturnonamuchlargerproject.

Aninvestorbuysfoursharesofstockfor$50pershare.Attheendofyearoneshesellstwosharesfor$50pershare.Attheendofyeartwoshesellsthetworemainingsharesfor$80each.Thestockpaidnodividendattheendofyearoneandadividendof$5.00pershareattheendofyeartwo.Whatisthedifferencebetweenthetimeweightedrateofreturnandthemoneyweightedrateofreturn?

14.48%.

20.52%.

9.86%.

Explanation

T=0:Purchaseoffourshares=$200.00

T=1:Dividendfromfourshares=+$0.00

Saleoftwoshares=+$100.00

T=2:Dividendfromtwoshares=+$10.00

Proceedsfromsellingshares=+$160.00

Themoneyweightedreturnistheratethatsolvestheequation:

$200.00=$100.00/(1+r)+$170.00/(1+r) .

Cfo=200,CF1=100,Cf2=170,CPTIRR=20.52%.

Theholdingperiodreturninyearoneis($50.00$50.00+$0.00)/$50.00=0.00%.

Theholdingperiodreturninyeartwois($80.00$50.00+$5.00)/$50=70.00%.

Thetimeweightedreturnis[(1+0.00)(1+0.70)] 1=30.38%.

Thedifferencebetweenthetwois30.38%20.52%=9.86%.

2

1/2


A)

B)

C)


A)

B)

C)


ATreasurybillhas40daystomaturity,aparvalueof$10,000,andiscurrentlysellingfor$9,900.Itseffectiveannualyieldisclosestto:

9.60%.

1.00%.

9.00%.

Explanation

Theeffectiveannualyield(EAY)isbasedona365dayyearandaccountsforcompoundinterest.EAY=(1+holdingperiodyield) 1.Theholdingperiodyieldformulais(pricereceivedatmaturityinitialprice+interestpayments)/(initialprice)=(10,0009,900+0)/(9,900)=1.01%.EAY=(1.0101) 1=9.60%.

ThefinancialmanageratIBFM,afarmimplementdistributor,iscontemplatingthefollowingthreemutuallyexclusiveprojects.IBFM'srequiredrateofreturnis9.5%.Basedontheinformationprovided,whichshouldthefinancialmanagerselectandwhy?

Project Investmentatt=0 CashFlowatt=1 IRR [email protected]%

A $10,000 $11,300 13.00 $320

B $25,000 $29,000 16.00 $1,484

C $35,000 $40,250 15.00 $1,758

Alloftheprojects,becausetheyallearnmorethan9.5%.

ProjectAwiththelowestinitialinvestment.

ProjectCwiththehighestnetpresentvalue.

Explanation

Whenprojectsaremutuallyexclusive,onlyonecanbechosen.Projectselectionshouldbedoneonthebasisofwhichprojectwillenhancefirmvaluethemost.Thatproject,ProjectCinthiscase,istheonewiththehighestNPV.

RobertMackenzie,CFA,buys100sharesofGWNBrewerieseachyearforfouryearsatpricesofC$10,C$12,C$15andC$13respectively.GWNpaysadividendofC$1.00attheendofeachyear.OneyearafterhislastpurchasehesellsallhisGWNsharesatC$14.Mackenziecalculateshisaveragecostpershareas[(C$10+C$12+C$15+C$13)/4]=C$12.50.Mackenziethenusestheinternalrateofreturntechniquetocalculatethathismoneyweightedannualrateofreturnis12.9%.HasMackenziecorrectlydeterminedhisaveragecostpershareandmoneyweightedrateofreturn?

Averagecost Moneyweightedreturn

365/t

365/40

A)

B)

C)


A)

B)

C)


A)

B)

C)

Correct Correct

Incorrect Correct

Correct Incorrect

Explanation

BecauseMackenziepurchasedthesamenumberofshareseachyear,thearithmeticmeanisappropriateforcalculatingtheaveragecostpershare.Ifhehadpurchasedsharesforthesameamountofmoneyeachyear,theharmonicmeanwouldbeappropriate.Mackenzieisalsocorrectinusingtheinternalrateofreturntechniquetocalculatethemoneyweightedrateofreturn.Thecalculationisasfollows:

Time Purchase/Sale Dividend Netcashflow

0 1,000 0 1,000

1 1,200 +100 1,100

2 1,500 +200 1,300

3 1,300 +300 1,000

4 40014=+5,600 +400 +6,000

CF0=1,000CF1=1,100CF2=1,300CF3=1,000CF4=6,000CPTIRR=12.9452.

ATreasurybill,with80daysuntilmaturity,hasaneffectiveannualyieldof8%.Itsholdingperiodyieldisclosestto:

1.75%.

1.70%.

1.72%.

Explanation

Theeffectiveannualyield(EAY)isequaltotheannualizedholdingperiodyield(HPY)basedona365dayyear.EAY=(1+HPY) 1.HPY=(EAY+1) 1=(1.08) 1=1.70%.

Theeffectiveannualyieldforaninvestmentis10%.Whatistheyieldforthisinvestmentonabondequivalentbasis?

9.76%.

4.88%.

10.00%.

Explanation

365/t t/365 80/365


A)

B)

C)


A)

B)

C)


A)

B)

C)

First,theannualyieldmustbeconvertedtoasemiannualyield.Theresultisthendoubledtoobtainthebondequivalentyield.

Semiannualyield=1.1 1=0.0488088.Thebondequivalentyield=20.0488088=0.097618.

ATreasurybill(Tbill)withafacevalueof$10,000and137daysuntilmaturityissellingfor98.125%offacevalue.WhichofthefollowingisclosesttothebankdiscountyieldontheTbill?

4.56%.

4.93%.

5.06%.

Explanation

Theformulaforbankdiscountyieldis:(D/F)(360/t).Actualdiscountis10.98125=0.01875.Annualizedis:0.01875(360/137)=0.04927

Ifthemoneymarketyieldis3.792%onaTbillwith79daystomaturity,whatistheholdingperiodyield?

0.89%.

0.77%.

0.83%.

Explanation

Theholdingperiodyieldcanbecalculatedfromthemoneymarketyieldas:(moneymarketyield)(360t).Therefore,theHPYis(0.03792)(79360)=0.0083=0.83%.

ThefinancialmanageratJohnson&Smithestimatesthatitsrequiredrateofreturnis11%.WhichofthefollowingindependentprojectsshouldJohnson&Smithaccept?

ProjectArequiresanupfrontexpenditureof$1,000,000andgeneratesanNPVof$4,600.

ProjectCrequiresanupfrontexpenditureof$600,000andgeneratesapositiveinternalrateofreturnof12.0%.

ProjectBrequiresanupfrontexpenditureof$800,000andgeneratesapositiveIRRof10.5%.

Explanation

0.5


A)

B)

C)


Whenprojectsareindependent,youcanuseeithertheNPVmethodorIRRmethodtomaketheacceptorrejectdecision.OnlyProjectChasanIRRinexcessof11%.AcceptanceofProjectAreducesthefirm'svalueby$4,600.

ThefinancialmanageratKyserJonesisconsideringtwomutuallyexclusiveprojectswiththefollowingprojectedcashflows:

ProjectedCashFlows

Year ProjectM ProjectZ

0 $60,000 $60,000

1 22,500 0

2 22,500 0

3 22,500 0

4 22,500 111,000

IfKyserJones'requiredrateofreturnis11%,whichprojectwouldbechosenandwhy?

ProjectZ,becauseithasthehighernetpresentvalue.

Bothprojectsbecausetheirnetpresentvaluesarepositive.

ProjectM,becauseithasthehigherinternalrateofreturn.

Explanation

Sincetheprojectsaremutuallyexclusive,onlyoneoftheprojectsmaybechosen.ProjectZhasthehigherNPV.Ontheexam,alwaysuseNPVforchoosingbetweenmutuallyexclusiveprojects.

CashFlowInputValues

ProjectM ProjectZ

CF 60,000 60,000

CF 22,500 0

F 4 3

CF 111,000

F 1

OutputValues

ProjectM ProjectZ

NPV $9,805 $13,119

IRR 18.45% 16.62%

TheholdingperiodyieldforaTBillmaturingin110daysis1.90%.Whataretheequivalentannualyield(EAY)andthemoney

0

1

1

2

2

A)

B)

C)


A)

B)

C)


A)

B)

C)


marketyield(MMY)respectively?

5.25%5.59%.

6.90%6.80%.

6.44%6.22%.

Explanation

TheEAYtakestheholdingperiodyieldandannualizesitbasedona365dayyearaccountingforcompounding.(1+0.0190) 1=1.064441=6.44%.UsingtheHPYtocomputethemoneymarketyield=HPY(360/t)=0.0190(360/110)=0.06218=6.22%.

A10%couponbondwaspurchasedfor$1,000.Oneyearlaterthebondwassoldfor$915toyield11%.Theinvestor'sholdingperiodyieldonthisbondisclosestto:

9.0%.

1.5%.

18.5%.

Explanation

HPY=[(interest+endingvalue)/beginningvalue]1=[(100+915)/1,000]1=1.0151=1.5%

Aninvestorbuysa$1,000parvalue,10.375%coupon,annualpaybondfor$1,033.44andsellsitoneyearlaterfor$1,014.06.Whatistheholdingperiodyield?

8.16%.

8.22%.

8.14%.

Explanation

Therateofreturnequalsthe[(endingcashprice)/price]100=

[(1014.06+103.751033.44)/1033.44]100=8.16%

Abondwaspurchasedexactlyoneyearagofor$910andwassoldtodayfor$1,020.Duringtheyear,thebondmadetwosemiannualcouponpaymentsof$30.Whatistheholdingperiodreturn?

365/110

A)

B)

C)


A)

B)

C)


A)

B)

C)


A)

6.0%.

18.7%.

12.1%.

Explanation

HPY=(1,020+30+30910)/910=0.1868or18.7%.

ATbillwithafacevalueof$100,000and140daysuntilmaturityissellingfor$98,000.Whatisthebankdiscountyield?

4.18%.

5.14%.

5.41%.

Explanation

Actualdiscountis2%,annualizeddiscountis:0.02(360/140)=5.14%

Aninvestorsolda30yearbondatapriceof$850afterhepurchaseditat$800ayearago.Hereceived$50ofinterestatthetimeofthesale.Theannualizedholdingperiodreturnis:

12.5%.

15.0%.

6.25%.

Explanation

Theholdingperiodreturn(HPR)iscalculatedasfollows:

HPR=(P P +D )/P

where:

P =pricepershareattheendoftimeperiodt

D =cashdistributionsreceivedduringtimeperiodt.

Here,HPR=(850800+50)/800=0.1250,or12.50%.

AbrokercallswithaproposaltobuyaTreasurybill(Tbill)with186daystomaturity.HesaystheeffectiveannualyieldontheTbillis4.217%.Whatistheholdingperiodyieldifyouholdthebilluntilmaturity?

2.13%.

t t1 t t

t

t

B)

C)


A)

B)

C)


A)

B)

C)


A)

B)

C)

8.44%.

2.02%.

Explanation

TocalculatetheHPYfromtheEAY,theformulais:(1+EAY) 1.Therefore,theHPYis:(1.04217) 1=0.0213,or2.13%.

WhichofthefollowingisNOTaproblemwiththeinternalrateofreturn(IRR)?

NonnormalcashflowpatternsmayresultinmultipleIRRs.

SometimestheIRRexceedsthecostofcapital.

AhigherIRRdoesnotnecessarilyindicateamoreprofitableproject.

Explanation

IftheIRRexceedsthecostofcapital,thatmerelyindicatesthattheprojectisacceptablethisisnotaproblemassociatedwithIRR.Nonnormalcashflowpatternssuchascashoutflowsduringtheproject'slifecanresultinmultipleIRRs,leavingopenthequestionastowhichoneisvalid.AhigherIRRwillonlyberealizediftheproject'scashflowscanbereinvestedattheIRR,andthetrueprofitabilityofaprojectalsodependsonprojectsize,notjustIRR.

TheholdingperiodyieldofaTbillthathasabankdiscountyieldof4.70%andamoneymarketyieldof4.86%andmaturesin240daysis

closestto:

3.2%.

2.8%.

4.9%.

Explanation

4.86(240/360)=3.24%.

Thebankdiscountofa$1,000,000Tbillwith135daysuntilmaturitythatiscurrentlysellingfor$979,000is:

6.1%.

5.6%.

5.8%.

Explanation

(t/365) (186/365)


A)

B)

C)


A)

B)

C)


A)

B)

($21,000/1,000,000)(360/135)=5.6%.

BancaHakalapurchasestwofrontrowconcertticketsovertheInternetfor$90perseat.Onemonthlater,therockgroupannouncesthatitisdissolvingduetopersonalityconflictsandtheconcertthatHakalahasticketsforwillbethe"farewell"concert.Hakalaseesachancetoraisesomequickcash,sosheputstheticketsupforsaleonthesameinternetsite.Theauctionclosesat$250perticket.Afterpayinga10%commissiontothesiteontheamountofthesaleandpaying$10inshippingcosts,Hakala'sonemonthholdingperiodreturnisapproximately:

139%.

144%.

44%.

Explanation

Theholdingperiodreturniscalculatedas:(endingpricebeginningprice+/anycashflows)/beginningprice.Here,thebeginningandendingpricesaregiven.Theothercashflowsconsistofthecommissionof0.10$2502tickets=$50andtheshippingcostof$10(totalforbothtickets).

Thus,heronemonthholdingperiodreturnis:[(2$250)(2$90)$50$10]/(2$90)=1.44,orapproximately144%.

Whichofthefollowingismostaccuratewithrespecttotherelationshipofthemoneyweightedreturntothetimeweightedreturn?Iffundsarecontributedtoaportfoliojustpriortoaperiodoffavorableperformance,the:

moneyweightedrateofreturnwilltendtobeelevated.

moneyweightedrateofreturnwilltendtobedepressed.

timeweightedrateofreturnwilltendtobeelevated.

Explanation

Thetimeweightedreturnsarewhattheyareandwillnotbeaffectedbycashinflowsoroutflows.Themoneyweightedreturnissusceptibletodistortionsresultingfromcashinflowsandoutflows.Themoneyweightedreturnwillbebiasedupwardifthefundsareinvestedjustpriortoaperiodoffavorableperformanceandwillbebiaseddownwardiffundsareinvestedjustpriortoaperiodofrelativelyunfavorableperformance.Theoppositewillbetrueforcashoutflows.

Whichofthefollowingstatementsregardingthemoneyweightedandtimeweightedratesofreturnisleastaccurate?

Themoneyweightedrateofreturnremovestheeffectsofthetimingofadditionsandwithdrawalstoaportfolio.

Thetimeweightedrateofreturnreflectsthecompoundrateofgrowthofoneunitofcurrencyoverastatedmeasurementperiod.

C) Thetimeweightedrateofreturnisthestandardintheinvestmentmanagementindustry.

Explanation

Themoneyweightedreturnisactuallyhighlysensitivetothetimingandamountofwithdrawalsandadditionstoaportfolio.Thetimeweightedreturnremovestheeffectsoftimingandamountofwithdrawalstoaportfolioandreflectsthecompoundrateofgrowthof$1overastatedmeasurementperiod.Becausethetimeweightedrateofreturnremovestheeffectsoftiming,itisthestandardintheinvestmentmanagementindustry.

02 discounted cash flow applications

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