2025年CFA一级真题解析试卷

2025年CFA一级真题解析试卷考试时间：______分钟总分：______分姓名：______Part1:Breadth1.Aninvestorisconsideringaddingastocktotheirportfolio.Thestockhasanexpectedreturnof12%andastandarddeviationof20%.Theportfoliocurrentlyconsistsofrisk-freeassetsandstockswithanexpectedreturnof8%andastandarddeviationof10%.Thecorrelationcoefficientbetweenthenewstockandtheexistingportfoliostocksis0.3.Whatistheexpectedreturnandstandarddeviationoftheportfolioiftheinvestoradds20%oftheirfundstothisnewstock?2.AcompanyreportsthefollowingfinancialdatafortheyearendedDecember31,2023:*Sales:$500,000*CostofGoodsSold:$300,000*GrossProfit:$200,000*OperatingExpenses:$100,000*InterestExpense:$20,000*IncomeTaxExpense:$30,000*PreferredDividends:$10,000Whatisthecompany'searningspershare(EPS)ifthenumberofoutstandingcommonsharesis100,000?3.WhichofthefollowingstatementsabouttheCapitalAssetPricingModel(CAPM)ismostaccurate?*a)Themodelassumesthatinvestorsarerisk-averseandpreferhigherexpectedreturnsforhigherlevelsofrisk.*b)Themodelsuggeststhattheexpectedreturnofanassetissolelydeterminedbyitsbeta.*c)Themodelimpliesthatallinvestorsholdthemarketportfolioinoptimalproportions.*d)Themodelisonlyapplicabletoindividualassetsandnottoportfolios.4.Abondwithafacevalueof$1,000paysasemi-annualcouponof5%.Thebondhasamaturityof5years.Ifthemarketyieldtomaturityis6%,whatistheapproximatepriceofthebond?5.Thefollowingistheprobabilitydistributionofreturnsforastock:*Returnof10%withaprobabilityof0.3*Returnof15%withaprobabilityof0.5*Returnof20%withaprobabilityof0.2Whatistheexpectedreturnandstandarddeviationofthestock?6.Whichofthefollowingisacharacteristicofefficientmarkets?*a)Pricesquicklyreflectallavailableinformation.*b)Itispossibletoconsistentlyachievereturnsabovethemarketaveragewithlittlerisk.*c)Marketparticipantsareallrationalandhaveaccesstothesameinformation.*d)Marketpricesaredrivenprimarilybyinvestorsentiment.7.Acompanyisconsideringtwomutuallyexclusiveprojects.ProjectAhasaninitialoutlayof$100,000andexpectedcashflowsof$40,000peryearfor4years.ProjectBhasaninitialoutlayof$150,000andexpectedcashflowsof$60,000peryearfor4years.Iftherequiredrateofreturnforbothprojectsis10%,whichprojectshouldbeselectedbasedontheNetPresentValue(NPV)criterion?8.Whichofthefollowingstatementsregardingtheweightedaveragecostofcapital(WACC)ismostaccurate?*a)TheWACCincreasesastheproportionofdebtinthecapitalstructureincreases,assumingthedebtcostremainsconstant.*b)TheWACCistypicallylowerthanthecostofequity.*c)TheWACCreflectsthecostofcapitalforallprojectsundertakenbythefirm.*d)TheWACCisunaffectedbychangesinthemarketriskpremium.9.Acompany'sinventoryturnoverratiois6timesperyear.Thecostofgoodssoldfortheyearis$300,000.Whatisthecompany'saverageinventory?10.WhichofthefollowingisalimitationoftheDividendDiscountModel(DDM)?*a)Itassumesthatdividendsareexpectedtogrowataconstantrateindefinitely.*b)Itisdifficulttoestimatetherequiredrateofreturn.*c)Itismostsuitableforvaluingcompaniesthatdonotpaydividends.*d)Itonlyconsiderspastdividendpaymentsandnotfutureprospects.Part2:Depth11.Astockhasthefollowinghistoricalreturnsoverthepast5years:*Year1:10%*Year2:-5%*Year3:15%*Year4:0%*Year5:20%Calculatethestock'sarithmeticmeanreturn,variance,andstandarddeviation.12.Acompanyisconsideringaprojectwithaninitialoutlayof$200,000.Theprojectisexpectedtogeneratecashinflowsof$80,000attheendofeachofthenext4years.Thecompany'srequiredrateofreturnis12%.Calculatetheproject'sNetPresentValue(NPV),InternalRateofReturn(IRR),andPaybackPeriod.13.Acompanyhasadebt-equityratioof0.5.Thecostofdebtis5%,andthecostofequityis15%.Thecompany'staxrateis30%.Calculatethecompany'sweightedaveragecostofcapital(WACC).14.Youaregiventhefollowinginformationaboutacompany:*Earningsbeforeinterestandtaxes(EBIT):$100,000*Interestexpense:$20,000*Taxrate:30%*Sharesoutstanding:50,000Calculatethecompany'searningspershare(EPS)usingtheDuPontanalysisframework.15.Acompanyisevaluatingthepurchaseofanewmachine.Themachinecosts$100,000andhasausefullifeof5yearswithnosalvagevalue.Themachineisexpectedtogenerateadditionalannualcashinflowsof$30,000.Thecompany'srequiredrateofreturnis10%.CalculatetheNetPresentValue(NPV)ofthemachineanddeterminewhetheritshouldbepurchasedbasedontheNPVcriterion.16.Youaregiventhefollowinginformationabouttwostocks:*StockA:Expectedreturn=12%,Standarddeviation=15%*StockB:Expectedreturn=10%,Standarddeviation=10%Thecorrelationcoefficientbetweenthetwostocksis0.2.Aninvestorholdsaportfolioconsistingof60%StockAand40%StockB.Calculatetheexpectedreturnandstandarddeviationoftheportfolio.17.Acompanyisexpectedtopayadividendof$2persharenextyear.Thedividendisexpectedtogrowataconstantrateof5%peryearindefinitely.Therequiredrateofreturnforthestockis12%.CalculatetheintrinsicvalueofthestockusingtheDividendDiscountModel(DDM).18.Acompany'sinventoryturnoverratiois8timesperyear,anditsaccountspayableturnoverratiois12timesperyear.Thecompany'scostofgoodssoldis$400,000.Whatisthecompany'sdayspayableoutstanding(DPO)?19.Acompanyisconsideringissuingnewequitytofinanceanewproject.Thecurrentstockpriceis$50pershare,andthecompanyplanstoissue1millionnewshares.Theunderwritingspreadis5%.Calculatethenetproceedsfromtheequityissuance.20.Aprojecthasaninitialoutlayof$100,000andexpectedcashflowsof$40,000attheendofeachofthenext3years.Theproject'sinternalrateofreturn(IRR)is12%.Ifthecompany'srequiredrateofreturnis10%,shouldtheprojectbeacceptedbasedontheIRRcriterion?Explainyourreasoning.Part3:EthicsandProfessionalStandards21.Ananalystatabrokeragefirmiscoveringacompanythatisaclientofthefirm.Theanalystreceivesnon-publicinformationindicatingthatthecompany'searningswillbesignificantlylowerthanpreviouslyexpected.Theanalyst'sbrotherworksasamanageratthecompanyandisnotawareoftheupcomingannouncement.Theanalystisconsideringsharingtheinformationwiththeirbrother.Whatisthemostappropriatecourseofactionfortheanalyst?22.Aportfoliomanagerismanagingaclient'sportfolio.Theclientrequeststhattheportfoliomanagerinvestaportionoftheportfolioinahedgefundthattheportfoliomanager'ssistermanages.Theportfoliomanagerisawarethatthehedgefundhasahighfeestructureandalimitedtrackrecord.Whatshouldtheportfoliomanagerdo?23.Twoportfoliomanagersarediscussingapotentialinvestmentopportunity.Oneportfoliomanagersuggeststhattheymanipulatethedataslightlytomaketheinvestmentappearmoreattractivetotheirclients.Whatistheethicalissuewiththissuggestion?24.ACFAcharterholderisattendingaconferencewhereaspeakerismakingcontroversialstatementsthatarelikelytomisleadinvestors.Whatshouldthecharterholderdo?25.ACFAcharterholderisofferedajobatacompanythatengagesinpracticesthatmaybeconsideredunethical.ThecharterholderisawarethatthesepracticesviolatetheCFAInstituteCodeandStandards.Whatshouldthecharterholderdo?试卷答案Part1:Breadth1.ExpectedReturn:0.12*0.20+0.88*0.08=0.024+0.0704=0.0944or9.44%StandardDeviation:sqrt[(0.20*0.10*0.3)^2+(0.88*0.10*0.3)^2+2*(0.20*0.10*0.3)*(0.88*0.10*0.3)]=sqrt[0.000144+0.0005776+0.00001296]=sqrt[0.00073456]≈0.0857or8.57%2.EBT(EarningsBeforeTax):$100,000-$20,000=$80,000NetIncome:$80,000-$30,000=$50,000EPS(EarningsPerShare):$50,000/100,000=$0.503.a)4.PVofCoupons:$1,000*5%*(1-(1+0.06/2)^-10)/(0.06/2)=$50*(1-0.55839)/0.03=$50*27.8567≈$1,392.84PVofFaceValue:$1,000/(1+0.06/2)^10=$1,000/1.8194≈$548.84ApproximatePrice:$1,392.84+$548.84=$1,941.68(Note:Actualpriceusingbondtablesorprecisecalculatorwouldbeslightlydifferent,butthisistheapproximatecalculationmethodrequested).5.ExpectedReturn:(0.3*10%)+(0.5*15%)+(0.2*20%)=3%+7.5%+4%=14.5%Variance:(0.3*(10%-14.5%)^2)+(0.5*(15%-14.5%)^2)+(0.2*(20%-14.5%)^2)=(0.3*(-4.5%)^2)+(0.5*0.5%^2)+(0.2*5.5%^2)=(0.3*0.2025%)+(0.5*0.0025%)+(0.2*0.3025%)=0.06075%+0.00125%+0.0605%=0.1225%StandardDeviation:sqrt(0.1225%)=sqrt(0.001225)≈0.035or3.5%6.a)7.ProjectANPV:$40,000/(1+0.10)^1+$40,000/(1+0.10)^2+$40,000/(1+0.10)^3+$40,000/(1+0.10)^4-$100,000=$40,000/1.10+$40,000/1.21+$40,000/1.331+$40,000/1.4641-$100,000=$36,363.64+$33,057.85+$30,052.59+$27,320.55-$100,000≈$24,794.63ProjectBNPV:$60,000/(1+0.10)^1+$60,000/(1+0.10)^2+$60,000/(1+0.10)^3+$60,000/(1+0.10)^4-$150,000=$60,000/1.10+$60,000/1.21+$60,000/1.331+$60,000/1.4641-$150,000=$54,545.45+$49,586.78+$45,078.90+$40,982.81-$150,000≈$39,194.94ProjectBshouldbeselectedasithasahigherNPV.8.c)9.AverageInventory:$300,000/6=$50,00010.b)Estimatingtherequiredrateofreturncanbechallengingandsubjective.Part2:Depth11.ArithmeticMeanReturn:(10%-5%+15%+0%+20%)/5=40%/5=8%Variance:[(10%-8%)^2+(-5%-8%)^2+(15%-8%)^2+(0%-8%)^2+(20%-8%)^2]/5=[0.04%+169%+49%+64%+144%]/5=416%/5=83.2%StandardDeviation:sqrt(83.2%)≈9.12%12.NPV:$80,000/1.12+$80,000/1.12^2+$80,000/1.12^3+$80,000/1.12^4-$200,000=$71,428.57+$63,775.51+$56,742.69+$50,663.16-$200,000≈$42,510.93IRR:Usingafinancialcalculatororspreadsheetfunction(e.g.,IRR),theIRRisapproximately18.03%.PaybackPeriod:$200,000/$80,000=2.5years13.WACC:(0.5/(0.5+1))*5%*(1-0.30)+(1/(0.5+1))*15%=(0.5/1.5)*0.05*0.70+(1/1.5)*0.15=(1/3)*0.035+(1/3)*0.15=0.01167+0.05=0.06167or6.17%14.NetIncome:$100,000-$20,000-(0.30*($100,000-$20,000))=$100,000-$20,000-$24,000=$56,000EPS(DuPont):($56,000/$100,000)*($100,000/50,000)=0.56*2=$1.1215.NPV:$30,000/1.10+$30,000/1.10^2+$30,000/1.10^3+$30,000/1.10^4+$30,000/1.10^5-$100,000=$27,272.73+$24,836.86+$22,539.44+$20,490.40+$18,627.64-$100,000=$113,777.07-$100,000=$13,777.07ThemachineshouldbepurchasedastheNPVispositive.16.ExpectedReturn(Portfolio):0.60*12%+0.40*10%=7.2%+4%=11.2%PortfolioVariance:0.60^2*0.15^2+0.40^2*0.10^2+2*0.60*0.40*0.15*0.10*0.2=0.36*0.0225+0.16*0.01+2*0.60*0.40*0.15*0.10*0.2=0.0081+0.0016+0.000288=0.009988StandardDeviation(Portfolio):sqrt(0.009988)≈0.0999or9.99%17.IntrinsicValue(DDM):$2/(0.12-0.05)=$2/0.07≈$28.5718.InventoryTurnover(Days):365/8=45.625daysDPOCalculation:AssumeAccountsPayable=COGS/AccountsPayableTurnoverAccountsPayable=$400,000/12≈$33,333.33DPO:$33,333.33/($400,000/365)=$33,333.33/1,092.59≈30.5days19.GrossProceeds:1,000,000*$50=$50,000,000UnderwritingSpread:$50,000,000*5%=$2,500,000NetProceeds:$50,000,000-$2,500,000=$47,500,00020.Accept:Yes,theprojectshouldbeacceptedbasedontheIRRcriterionbecausetheIRR(12%)isgreaterthantherequiredrateofreturn(10%).Part3:EthicsandProfessionalStandards21.ConfidentialityandFairDealing:Theanalysthasconfidentialinformationandadutytoclientstoactfairly.Sharingmaterialnon-publicinformationwiththebrotherwouldviolatetheseprinciplesandlikelytheMarketManipulationandAberrantTradingstandardifthebrotheractsonit.Themostappropriatecourseistonotsharetheinformationandreportthesituationtotheircompliancedepartmentifnecessary.22.ClientInterestandFairDealing:Theportfoliomanagermustprioritizetheclient'sbestinterests.Investinginasister'shedge