2025年CFA一級(jí)考試模擬卷及答案考試時(shí)間：______分鐘總分：______分姓名：______試卷內(nèi)容一、依據(jù)以下信息回答問題：StandardCorp.isexpectedtopayadividendof$2.00persharenextyear(D1).Thedividendisexpectedtogrowataconstantrateof6%peryearforever.TherequiredrateofreturnforStandardCorp.stockis12%.1.CalculatetheexpectedpriceofStandardCorp.stockoneyearfromnow(P1).2.CalculatethecurrentpriceofStandardCorp.stock(P0)usingtheconstantgrowthmodel.3.IfthecurrentmarketpriceofStandardCorp.stockis$35,whatistheimpliedrequiredrateofreturnbasedontheconstantgrowthmodel?二、XYZCompanyhasthefollowingfinancialdataforthemostrecentyear:Sales=$500,000CostofGoodsSold(COGS)=$300,000OperatingExpenses=$150,000InterestExpense=$20,000TaxRate=30%CalculateXYZCompany's:4.GrossProfit.5.OperatingIncome(EBIT).6.NetIncome.三、Considerabondwithafacevalueof$1,000,acouponrateof5%,andamaturityof10years.Thebondpayscouponsannually.7.Calculatethepriceofthebondifthemarketrequiredyieldtomaturity(YTM)is5%.8.CalculatethepriceofthebondifthemarketrequiredYTMis6%.9.Explaininonesentencewhythebondpriceinquestion8isdifferentfromthebondpriceinquestion7.四、Youaremanagingaportfoliowiththefollowinginvestments:Asset|ExpectedReturn|StandardDeviation|Weight----------------|-----------------|--------------------|-------StockA|10%|15%|40%StockB|14%|20%|35%Risk-FreeAsset|2%|0%|25%10.Calculatetheexpectedreturnoftheportfolio.11.AssumingthereturnsofStockA,StockB,andtheRisk-FreeAssetareuncorrelated,calculatethestandarddeviationoftheportfolio.五、WhichofthefollowingstatementsregardingtheCapitalAssetPricingModeliscorrect?12.Selectthebestanswer:a)TheCAPMassumesthatallinvestorshavethesamerisktolerance.b)AccordingtotheCAPM,theexpectedreturnofanassetisdeterminedbyitsbetaandthemarketriskpremium.c)Therisk-freeratecannotbeusedastherequiredrateofreturnforanyassetintheCAPMformula.d)Themarketportfoliomustincludeallrealandfinancialassetsintheworld.六、Definethefollowingtermsrelatedtofinancialstatements:13.Define"AccruedExpense".14.Define"DeferredRevenue".七、Acompanyisevaluatingtwomutuallyexclusiveprojects.ProjectAhasaninitialcostof$100,000andgeneratescashinflowsof$40,000peryearfor4years.ProjectBhasaninitialcostof$120,000andgeneratescashinflowsof$50,000peryearfor4years.Therequiredrateofreturnforbothprojectsis10%.15.CalculatetheNetPresentValue(NPV)ofProjectA.16.CalculatetheNetPresentValue(NPV)ofProjectB.17.BasedontheNPVcriterion,whichprojectshouldthecompanyselect?八、DiscusstheprimarypurposeoftheCFAInstituteCodeandStandardsinthecontextofinvestmentpractice.九、Explaintheconceptof"Duration"asitrelatestofixedincomesecurities.Whyisdurationimportanttobondinvestors?十、Youareanalyzingacompanyinthetechnologysector.Identifythreekeyfinancialratiosthatwouldbeparticularlyimportanttoanalyzeforthiscompanyandexplainwhyeachratioisrelevant.試卷答案一、1.P1=D1*(1+g)/(k-g)=$2.00*(1+0.06)/(0.12-0.06)=$2.12/0.06=$35.002.P0=D1/(k-g)=$2.00/(0.12-0.06)=$2.00/0.06=$33.333.Impliedk=D1/P0+g=$2.00/$35.00+0.06=0.0571+0.06=0.1171or11.71%解析思路：1.應(yīng)用常數(shù)增長模型公式計(jì)算未來一年價(jià)格(P1)。P1=D1*(1+g)/(k-g)。已知D1=$2,g=6%,k=12%。代入計(jì)算得到P1。2.應(yīng)用常數(shù)增長模型公式計(jì)算當(dāng)前價(jià)格(P0)。P0=D1/(k-g)。已知D1=$2,k=12%,g=6%。代入計(jì)算得到P0。3.反向應(yīng)用模型計(jì)算隱含必要回報(bào)率(k)。已知P0=$35,D1=$2,g=6%。使用P0=D1/(k-g)變形得到k=D1/P0+g。代入計(jì)算得到k。二、4.GrossProfit=Sales-COGS=$500,000-$300,000=$200,0005.OperatingIncome(EBIT)=GrossProfit-OperatingExpenses=$200,000-$150,000=$50,0006.NetIncome=EBIT-InterestExpense-(EBIT-InterestExpense)*TaxRate=EBIT*(1-1*TaxRate)-InterestExpense*TaxRate=$50,000*(1-0.30)-$20,000*0.30=$50,000*0.70-$6,000=$35,000-$6,000=$29,000*(Alternatively:NetIncome=OperatingIncome-InterestExpense-Taxes=$50,000-$20,000-($50,000-$20,000)*0.30=$30,000-$15,000=$29,000)解析思路：4.根據(jù)公式：毛利潤=銷售收入-銷貨成本。代入已知數(shù)值計(jì)算。5.根據(jù)公式：營業(yè)利潤(EBIT)=毛利潤-營業(yè)費(fèi)用。代入已計(jì)算的毛利潤和已知營業(yè)費(fèi)用計(jì)算。6.根據(jù)公式：凈利潤=營業(yè)利潤-利息費(fèi)用-(營業(yè)利潤-利息費(fèi)用)*稅率。或者使用簡化公式：凈利潤=營業(yè)利潤*(1-稅率)-利息費(fèi)用*稅率。代入已知數(shù)值計(jì)算。三、7.Price=[C*(1-(1+YTM)^-n)/YTM]+[F/(1+YTM)^n]Price=[$1,000*5%*(1-(1+0.05)^-10)/0.05]+[$1,000/(1+0.05)^10]Price=[$50*(1-0.61391)/0.05]+[$1,000/1.62889]Price=[$50*0.38609/0.05]+[$613.91]Price=[$50*7.7218]+[$613.91]=$386.09+$613.91=$1,000.008.Price=[$1,000*5%*(1-(1+0.06)^-10)/0.06]+[$1,000/(1+0.06)^10]Price=[$50*(1-0.55839)/0.06]+[$1,000/1.79085]Price=[$50*0.44161/0.06]+[$558.39]Price=[$50*7.36017]+[$558.39]=$368.01+$558.39=$926.409.Thebondpriceinquestion8islowerthanthebondpriceinquestion7becausewhenthemarketrequiredyieldtomaturity(YTM)increases,thepresentvalueofthebond'sfuturecashflows(bothcouponsandfacevalue)decreases,resultinginalowerbondprice.解析思路：7.應(yīng)用債券定價(jià)公式計(jì)算價(jià)格。公式為：價(jià)格=[C*(1-(1+YTM)^-n)/YTM]+[F/(1+YTM)^n]，其中C=票面利率*面值=$1,000*5%=$50,F=面值=$1,000,n=期數(shù)=10,YTM=5%。代入計(jì)算得到價(jià)格。8.使用相同的債券定價(jià)公式，但將YTM更改為6%。代入計(jì)算得到價(jià)格。9.解釋債券價(jià)格與市場必要回報(bào)率（YTM）的反向關(guān)系。當(dāng)YTM升高時(shí)，未來現(xiàn)金流折現(xiàn)到現(xiàn)在的價(jià)值降低，因此債券價(jià)格下跌。四、10.ExpectedReturn(Rp)=wA*Ra+wB*Rb+wRF*RRF=0.40*10%+0.35*14%+0.25*2%=4%+4.9%+0.5%=9.4%11.StandardDeviation(σp)=sqrt[wA^2*σA^2+wB^2*σB^2+wRF^2*σRF^2+2*wA*wB*Cov(A,B)+2*wA*wRF*Cov(A,RF)+2*wB*wRF*Cov(B,RF)]Sincereturnsareuncorrelated,Cov(A,B)=0,Cov(A,RF)=0,Cov(B,RF)=0.σp=sqrt[(0.40^2*0.15^2)+(0.35^2*0.20^2)+(0.25^2*0^2)]σp=sqrt[(0.16*0.0225)+(0.1225*0.04)+0]σp=sqrt[0.0036+0.0049+0]=sqrt[0.0085]=0.0922or9.22%解析思路：10.應(yīng)用投資組合預(yù)期回報(bào)率公式計(jì)算。Rp=wA*Ra+wB*Rb+wRF*RRF。代入各資產(chǎn)的權(quán)重和預(yù)期回報(bào)率計(jì)算。11.應(yīng)用投資組合標(biāo)準(zhǔn)差公式計(jì)算。由于題目說明資產(chǎn)間不相關(guān)，協(xié)方差和相關(guān)系數(shù)為0。公式簡化為σp=sqrt(wA2*σA2+wB2*σB2+wRF2*σRF2)。代入各資產(chǎn)的權(quán)重和標(biāo)準(zhǔn)差計(jì)算。五、12.b解析思路：CAPM模型的核心公式為E(Ri)=Rf+βi*[E(Rm)-Rf]，其中E(Ri)是資產(chǎn)的預(yù)期回報(bào)率，Rf是無風(fēng)險(xiǎn)回報(bào)率，βi是資產(chǎn)的風(fēng)險(xiǎn)系數(shù)，E(Rm)是市場組合的預(yù)期回報(bào)率，[E(Rm)-Rf]是市場風(fēng)險(xiǎn)溢價(jià)。選項(xiàng)(b)正確地描述了這一關(guān)系。選項(xiàng)(a)錯(cuò)誤，CAPM假設(shè)所有投資者具有相同的風(fēng)險(xiǎn)偏好（風(fēng)險(xiǎn)厭惡系數(shù)相同）而非風(fēng)險(xiǎn)容忍度。選項(xiàng)(c)錯(cuò)誤，無風(fēng)險(xiǎn)率Rf是CAPM公式中的關(guān)鍵輸入。選項(xiàng)(d)錯(cuò)誤，市場投資組合通常指包含所有風(fēng)險(xiǎn)資產(chǎn)，但具體定義可能有限制，不一定包含“所有”資產(chǎn)。六、13.AccruedExpense:Anexpensethathasbeenincurredbutnotyetpaid.Itrepresentsanobligationtopayforgoodsorservicesreceivedintheperiodbutforwhichpaymentwillbemadeinafutureperiod.Itisrecordedonthebalancesheetasaliabilityandontheincomestatementasanexpenseintheperioditisincurred,followingthematchingprinciple.14.DeferredRevenue:Alsoknownasunearnedrevenue,itrepresentscashreceivedbyacompanyinadvanceofprovidinggoodsorservices.Sincetherevenuerecognitionprinciplerequiresthatrevenueberecognizedonlywhenitisearned,deferredrevenueisrecordedasaliabilityonthebalancesheet.Itislaterrecognizedasrevenueontheincomestatementwhenthegoodsorservicesaredeliveredorperformed.解析思路：13.定義“應(yīng)計(jì)費(fèi)用”。強(qiáng)調(diào)費(fèi)用已經(jīng)發(fā)生（incurred），但尚未支付（notyetpaid），代表未來需要履行的支付義務(wù)（liability），并應(yīng)在發(fā)生期間確認(rèn)為費(fèi)用（expense），遵循配比原則（matchingprinciple）。14.定義“遞延收入”。強(qiáng)調(diào)是預(yù)先收到的現(xiàn)金（cashreceivedinadvance），但商品或服務(wù)尚未提供（goodsorservicesnotyetprovided），因此企業(yè)尚未賺取該收入（revenuenotyetearned），應(yīng)作為負(fù)債（liability）在資產(chǎn)負(fù)債表上記錄，待未來提供商品或服務(wù)時(shí)再確認(rèn)為收入（revenue）。七、15.NPV_A=-InitialCost+PV(CF1toCF4)NPV_A=-$100,000+[$40,000/(1+0.10)^1]+[$40,000/(1+0.10)^2]+[$40,000/(1+0.10)^3]+[$40,000/(1+0.10)^4]NPV_A=-$100,000+[$40,000/1.10]+[$40,000/1.21]+[$40,000/1.331]+[$40,000/1.4641]NPV_A=-$100,000+$36,363.64+$33,057.85+$30,052.59+$27,320.55=-$100,000+$126,794.63=$26,794.6316.NPV_B=-InitialCost+PV(CF1toCF4)NPV_B=-$120,000+[$50,000/(1+0.10)^1]+[$50,000/(1+0.10)^2]+[$50,000/(1+0.10)^3]+[$50,000/(1+0.10)^4]NPV_B=-$120,000+[$50,000/1.10]+[$50,000/1.21]+[$50,000/1.331]+[$50,000/1.4641]NPV_B=-$120,000+$45,454.55+$41,322.31+$37,565.74+$34,150.67=-$120,000+$158,593.27=$38,593.2717.BasedontheNPVcriterion,theprojectwiththehigherNPVshouldbeselected.SinceNPV_B($38,593.27)isgreaterthanNPV_A($26,794.63),ProjectBshouldbeselected.解析思路：15.應(yīng)用凈現(xiàn)值公式計(jì)算項(xiàng)目A的NPV。NPV=-初始投資+未來現(xiàn)金流的現(xiàn)值之和。計(jì)算每期現(xiàn)金流$40,000在10%貼現(xiàn)率下的現(xiàn)值，然后加總并減去初始投資$100,000。16.應(yīng)用相同的凈現(xiàn)值公式計(jì)算項(xiàng)目B的NPV。計(jì)算每期現(xiàn)金流$50,000在10%貼現(xiàn)率下的現(xiàn)值，然后加總并減去初始投資$120,000。17.根據(jù)凈現(xiàn)值決策規(guī)則，選擇NPV較高的項(xiàng)目。比較項(xiàng)目A和B的NPV，$38,593.27>$26,794.63，因此選擇項(xiàng)目B。八、TheprimarypurposeoftheCFAInstituteCodeandStandardsistoestablishandmaintainhighethicalandprofessionalstandardsforinvestmentpractitionersworldwide.Itprovidesaframeworkforconduct,ensuringthatinvestmentprofessionalsactwithintegrity,objectivity,professionalism,andsensitivitytodiverseopinions.TheCodesetsoutfundamentalprinciples,whiletheStandardsprovidespecificguidanceonhowtoapplytheseprinciplesinpractice.Ultimately,itaimstoprotectinvestors,maintainpublictrustinthefinancialmarkets,andpromotefairandefficientcapitalmarkets.解析思路：闡述CFA協(xié)會(huì)道德與專業(yè)標(biāo)準(zhǔn)的主要目的。強(qiáng)調(diào)其建立和維持全球投資從業(yè)者高標(biāo)準(zhǔn)的重要性。說明其提供了一個(gè)行為框架，要求從業(yè)者具備誠信、客觀、專業(yè)和尊重不同意見的素質(zhì)。指出代碼（Code）是原則性聲明，標(biāo)準(zhǔn)（Standards）是具體應(yīng)用指南。最終目標(biāo)是保護(hù)投資者利益，維護(hù)公眾對金融市場的信任，促進(jìn)市場公平高效。九、Durationisameasureofthesensitivityoftheprice(value)ofafixedincomesecuritytochangesininterestrates.Itrepresentstheweightedaveragetimeuntilthecashflowsfromabondarereceived,withtheweightsbeingthepresentvalueofeachcashflow.Therearedifferenttypesofduration,butMacaulaydurationismostcommonlyused.Durationisimportanttobondinvestorsbecauseitprovidesanestimateofhowmuchthebond'spricewillchangeinresponsetoachangeinmarketinterestrates.Abondwithahigherdurationwillexperiencealargerpricechangeforagivenchangeininterestratescomparedtoabondwithalowerduration.Thishelpsinvestorsmanageinterestrateriskintheirportfoliosbyselectingbondswithdurationsthatmatchtheirinvestmenthorizonorrisktolerance.解析思路：定義“久期”。說明它是衡量固定收益證券價(jià)格對利率變動(dòng)敏感性的指標(biāo)，代表了現(xiàn)金流加權(quán)平均收回時(shí)間。解釋久期的重要性在于為投資者提供了估計(jì)利率變動(dòng)對債券價(jià)格影響的依據(jù)。強(qiáng)調(diào)高久期債券對利率變動(dòng)更敏感，幫助投資者管理利率風(fēng)險(xiǎn)。十、Threekeyfinancialratiosimportantforanalyzingatechnologycompanyare:1.RevenueGrowthRate:Technologycompaniesareoftencharacterizedbyrapidinnovationandcompetition.Therevenuegrowthrate(e.g.,year-over-yearpercentageincreaseinrevenue)iscrucialasitindicatesthecompany'sabilitytoexpanditsmarketshare,introducesuccessfulproductsorservices,andmaintainacompetitiveedge.Ahighand