2025年CFA二級(jí)公司金融模擬測(cè)試卷考試時(shí)間：______分鐘總分：______分姓名：______Question1:CompanyAisexpectedtopayadividendof$3nextyear.Dividendsareexpectedtogrowataconstantrateof5%peryearindefinitely.IftherequiredrateofreturnonCompanyA'sstockis12%,whatisthevalueofCompanyA'sstocktodayusingtheGordonGrowthModel?Question2:CompanyBisconsideringaprojectthatrequiresaninitialinvestmentof$100,000.Theprojectisexpectedtogeneratecashinflowsof$40,000attheendofeachyearfor4years.Ifthecompany'srequiredrateofreturnis10%,whatistheNetPresentValue(NPV)oftheproject?Question3:CompanyChasadebt-to-equityratioof0.5.Thecostofdebtis6%andthecostofequityis12%.Ifthecorporatetaxrateis30%,whatisthecompany'sWeightedAverageCostofCapital(WACC)?Question4:CompanyDisvaluinganothercompany,CompanyE,usingtheComparableCompaniesApproach.CompanyEhasearningspershare(EPS)of$3.TheaverageP/Eratioofthreecomparablecompaniesis15.WhatistheestimatedvaluepershareofCompanyE?Question5:CompanyFisevaluatingaprojectwiththefollowingcashflows:InitialInvestment:-$50,000Year1:$20,000Year2:$30,000Year3:$40,000Ifthecompanyusesapaybackperiodmethodwithacutoffof2years,shouldtheprojectbeaccepted?Question6:Whatisthe1-dayVaRata95%confidencelevelforaportfoliowithamarketvalueof$10millionandastandarddeviationofdailyreturnsof1%?Question7:Aninvestorbuysacalloptionwithastrikepriceof$50forapremiumof$2.Thecurrentpriceoftheunderlyingstockis$55.Whatisthebreak-evenpricefortheinvestor?Question8:Whatisthedurationofabondwitha5-yearmaturity,an8%couponrate,ayieldtomaturityof6%,andafacevalueof$1,000?Question9:CompanyGisconsideringissuingbondstofinanceanewproject.Thebondshavea10-yearmaturity,afacevalueof$1,000,andacouponrateof7%.Ifthemarketinterestrateforsimilarbondsis8%,whatistheapproximatepriceofthebond?Question10:Aninvestorisconcernedabouttheinterestrateriskofabondportfolio.WhichofthefollowingstatementsisTRUE?a)Abondwithahighercouponratewillhavelowerduration.b)Abondwithalongermaturitywillhavelowerduration.c)Abondwithahigheryieldtomaturitywillhavelowerduration.d)Abondwithahigheryieldtomaturitywillhavehigherduration.Question11:Acompanyisconsideringacapitalbudgetingprojectwithaninitialinvestmentof$200,000andexpectedcashflowsof$60,000peryearfor5years.Theproject'sinternalrateofreturn(IRR)is12%.Ifthecompany'srequiredrateofreturnis10%,shouldtheprojectbeacceptedbasedontheIRRrule?Question12:Whatisthepriceofa1-yearEuropeanputoptionwithastrikepriceof$100onastockthatcurrentlytradesat$110?Therisk-freerateis5%andtheoptionhasnotimevalue(i.e.,itisat-the-money).Question13:CompanyHhasaportfolioconsistingoftwoassets,AandB.AssetAhasaweightof60%andastandarddeviationofreturnsof10%.AssetBhasaweightof40%andastandarddeviationofreturnsof15%.ThecorrelationcoefficientbetweenthereturnsofAssetAandAssetBis0.2.Whatisthestandarddeviationoftheportfolioreturns?Question14:Acompanyisconsideringtheuseofaforwardcontracttohedgeitsexposuretoforeigncurrencyrisk.Thecompanyneedstopay$1millionin6months.Thecurrentspotexchangerateis1USD=0.85EUR.The6-monthforwardexchangerateis1USD=0.83EUR.WhatisthecostinUSDforthecompanytolockintheexchangerateusingtheforwardcontract?Question15:WhichofthefollowingstatementsabouttheModigliani-MillertheoremwithtaxesisTRUE?a)Thevalueofaleveredfirmisalwaysgreaterthanthevalueofanunleveredfirm.b)Thevalueofaleveredfirmisequaltothevalueofanunleveredfirmplusthepresentvalueofthetaxshieldprovidedbydebt.c)Thecostofequityincreasesasthedegreeofleverageincreases.d)Theweightedaveragecostofcapital(WACC)increasesasthedegreeofleverageincreases.Question16:CompanyIisconsideringaprojectthathasaninitialinvestmentof$100,000.Theprojectisexpectedtogenerateannualcashflowsof$30,000for5years.Thecompanyusesadiscountrateof10%tocalculatetheNetPresentValue(NPV).Whatistheprofitabilityindex(PI)oftheproject?Question17:Acompanyhasacurrentratioof2.5andanacid-testratioof1.5.Thecompany'sinventoryturnoverratiois5.Whatisthecompany'saccountsreceivableturnoverratio,assumingthataccountsreceivablearetheonlycurrentassetbesidescashandinventory?Question18:CompanyJisconsideringissuingpreferredstocktofinanceitsoperations.Thepreferredstockhasaparvalueof$100andpaysadividendof$8peryear.Ifthemarketpriceofthepreferredstockis$90,whatisthecostofpreferredstock?Question19:Whatistheput-callparityrelationshipforEuropeanoptionsonanon-dividend-payingstock?a)CallPrice+PutPrice=StockPrice+PresentValueofStrikePriceb)CallPrice-PutPrice=StockPrice-PresentValueofStrikePricec)CallPrice+PutPrice=StockPrice-PresentValueofStrikePriced)CallPrice-PutPrice=StockPrice+PresentValueofStrikePriceQuestion20:Acompanyisanalyzingtwomutuallyexclusiveprojects,ProjectAandProjectB.ProjectAhasanNPVof$100,000andanIRRof12%.ProjectBhasanNPVof$80,000andanIRRof14%.Whichprojectshouldthecompanychooseifthecompany'srequiredrateofreturnis10%?試卷答案Question1:Value=D1/(r-g)=$3/(0.12-0.05)=$3/0.07=$42.86解析思路：該題考察的是戈登增長(zhǎng)模型（GordonGrowthModel），用于評(píng)估無(wú)限期恒定增長(zhǎng)型股票的價(jià)值。公式為：股票價(jià)值=下一年預(yù)期股利/(要求回報(bào)率-股利增長(zhǎng)率)。將題目中給出的數(shù)據(jù)代入公式即可計(jì)算得出股票價(jià)值。Question2:NPV=-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)^4NPV=-100,000+$36,363.64+$33,057.85+$30,052.59+$27,320.55NPV=$26,794.63解析思路：該題考察的是凈現(xiàn)值（NPV）的計(jì)算。NPV等于項(xiàng)目所有未來(lái)現(xiàn)金流的現(xiàn)值之和減去初始投資。使用年金現(xiàn)值公式或分別計(jì)算每期現(xiàn)金流現(xiàn)值后加總，再減去初始投資，即可得到NPV。結(jié)果為正，表示項(xiàng)目可行。Question3:WACC=(E/V*Re)+(D/V*Rd*(1-Tc))E/V=1/(1+D/E)=1/(1+0.5)=1/1.5=2/3D/V=1/(1+D/E)=1/1.5=1/3WACC=(2/3*12%)+(1/3*6%*(1-0.30))WACC=(2/3*0.12)+(1/3*0.06*0.70)WACC=0.08+(0.02*0.70)WACC=0.08+0.014WACC=0.094or9.4%解析思路：該題考察的是加權(quán)平均資本成本（WACC）的計(jì)算。WACC是公司所有資本來(lái)源的成本的加權(quán)平均值。公式為：WACC=(E/V*Re)+(D/V*Rd*(1-Tc))，其中E/V和D/V分別是股權(quán)和債務(wù)的市場(chǎng)價(jià)值比重，Re是股權(quán)成本，Rd是債務(wù)成本，Tc是公司所得稅率。根據(jù)題目給出的債務(wù)權(quán)益比計(jì)算E/V和D/V，代入公式計(jì)算即可。Question4:EstimatedValueperShare=CompanyE'sEPS*AverageP/ERatioEstimatedValueperShare=$3*15=$45解析思路：該題考察的是可比公司法（ComparableCompaniesApproach）在估值中的應(yīng)用。通過(guò)找到與目標(biāo)公司業(yè)務(wù)、規(guī)模、風(fēng)險(xiǎn)等方面相似的幾家可比公司，計(jì)算其估值指標(biāo)（如P/E比率、P/B比率等），然后使用可比公司的平均或中位數(shù)指標(biāo)乘以目標(biāo)公司的相應(yīng)財(cái)務(wù)指標(biāo)（如EPS、BookValueperShare等），從而得到目標(biāo)公司的估值。本題中，使用可比公司的平均P/E比率乘以目標(biāo)公司的EPS即可得到估值。Question5:PaybackPeriod=InitialInvestment/AnnualCashFlowPaybackPeriod=$50,000/$40,000=1.25yearsSincethepaybackperiod(1.25years)isgreaterthanthecutoffperiod(2years),theprojectshouldberejected.解析思路：該題考察的是回收期（PaybackPeriod）的決策規(guī)則?；厥掌谑侵疙?xiàng)目投資通過(guò)其產(chǎn)生的凈現(xiàn)金流收回初始投資所需的時(shí)間。計(jì)算方法為初始投資除以每年的凈現(xiàn)金流。決策規(guī)則是：如果計(jì)算出的回收期小于或等于公司設(shè)定的回收期標(biāo)準(zhǔn)，則接受項(xiàng)目；否則，拒絕項(xiàng)目。本題中，計(jì)算出的回收期為1.25年，小于2年的標(biāo)準(zhǔn)，因此應(yīng)接受項(xiàng)目。（注意：題目給出的現(xiàn)金流是Year1:$20,000,Year2:$30,000,Year3:$40,000，總現(xiàn)金流入為$90,000，不足以在2年內(nèi)收回$50,000的初始投資，因此根據(jù)題目信息，項(xiàng)目應(yīng)被拒絕。此處解析基于題目問(wèn)“是否應(yīng)該接受”，并假設(shè)考察的是常規(guī)的靜態(tài)回收期，如果題目意圖是動(dòng)態(tài)回收期或隱含項(xiàng)目總現(xiàn)金流足夠覆蓋初始投資，則結(jié)論可能不同。根據(jù)標(biāo)準(zhǔn)定義，若回收期>標(biāo)準(zhǔn)，則拒絕。）Question6:VaRat95%confidencelevel≈1.645*($10,000,000*0.01)=1.645*$100,000=$164,500(Note:1.645isthez-scorefor95%confidencelevelinanormaldistribution)解析思路：該題考察的是在險(xiǎn)價(jià)值（VaR）的計(jì)算。VaR衡量在給定的置信水平下，投資組合在特定持有期內(nèi)可能遭受的最大損失。對(duì)于正態(tài)分布的資產(chǎn)回報(bào)率，1天95%置信水平的VaR可以使用公式：VaR=Z*(PortfolioValue*StandardDeviationofReturns)，其中Z是置信水平對(duì)應(yīng)的Z分?jǐn)?shù)（95%置信水平約等于1.645），PortfolioValue是投資組合價(jià)值，StandardDeviationofReturns是投資組合回報(bào)率的標(biāo)準(zhǔn)差。將題目數(shù)據(jù)代入公式計(jì)算即可。Question7:Break-EvenPrice=StrikePrice+PremiumBreak-EvenPrice=$50+$2=$52解析思路：該題考察的是看漲期權(quán)（CallOption）的盈虧平衡點(diǎn)（Break-EvenPoint）計(jì)算。對(duì)于看漲期權(quán)，買(mǎi)方的盈虧平衡點(diǎn)價(jià)格等于期權(quán)行權(quán)價(jià)加上期權(quán)費(fèi)。當(dāng)股票價(jià)格等于盈虧平衡點(diǎn)價(jià)格時(shí)，買(mǎi)方的總成本（期權(quán)費(fèi)）正好被行權(quán)收入抵消，盈虧為零。因此，盈虧平衡點(diǎn)價(jià)格=行權(quán)價(jià)+期權(quán)費(fèi)。Question8:ApproximateDuration=[Σ(t*CFt/PV)]/PVofBondPVofBond=$796.56(calculatedusingPVofannuityformulaandPVoflumpsumformula)ApproximateDuration=[(1*$80/$796.56)+(2*$80/$796.56)+(3*$80/$796.56)+(4*$80/$796.56)+(5*($80+$1,000)/$796.56)]/$796.56ApproximateDuration=[($80/$796.56)*(1+2+3+4)+($1,080/$796.56)*5]/$796.56ApproximateDuration=[($80/$796.56)*10+($1,080/$796.56)*5]/$796.56ApproximateDuration≈0.1005+0.6789≈0.7794years(approximately8months)解析思路：該題考察的是債券久期（Duration）的計(jì)算。久期衡量債券價(jià)格對(duì)收益率變化的敏感度，表示支付給債券持有人的現(xiàn)金流的加權(quán)平均到期時(shí)間，權(quán)重為各期現(xiàn)金流現(xiàn)值占債券總現(xiàn)值的比例。常用的是麥考利久期（MacaulayDuration）或近似久期。此處使用近似久期公式：近似久期=Σ(t*CFt/PV)/PV，其中t是現(xiàn)金流發(fā)生的時(shí)間，CFt是t時(shí)期的現(xiàn)金流，PV是債券的現(xiàn)值。需要先計(jì)算債券的現(xiàn)值，然后計(jì)算加權(quán)平均時(shí)間，得到久期。（計(jì)算略繁瑣，需使用金融計(jì)算器或spreadsheet）Question9:ApproximateBondPrice=[Σ(C/(1+Rd)^t)]+[F/(1+Rd)^n]ApproximateBondPrice=[$70/(1+0.08)^1+$70/(1+0.08)^2+...+$70/(1+0.08)^10]+[$1,000/(1+0.08)^10]ApproximateBondPrice≈$499.45+$463.19=$962.64解析思路：該題考察的是債券價(jià)格的近似計(jì)算。債券價(jià)格是未來(lái)所有預(yù)期現(xiàn)金流（利息和本金）的現(xiàn)值之和。使用年金現(xiàn)值公式計(jì)算利息現(xiàn)金流的現(xiàn)值，使用復(fù)利現(xiàn)值公式計(jì)算到期本金的現(xiàn)值，然后將兩者相加得到債券的近似價(jià)格。公式為：債券價(jià)格≈(C*[1-(1+Rd)^-n])/Rd+F/(1+Rd)^n，其中C是年couponpayment，Rd是市場(chǎng)利率（yieldtomaturity），n是債券剩余期限。將題目數(shù)據(jù)代入公式計(jì)算即可。（此處使用分步計(jì)算說(shuō)明思路，實(shí)際應(yīng)用中可直接用年金現(xiàn)值系數(shù)和單期現(xiàn)值系數(shù)）Question10:c)Abondwithahigheryieldtomaturitywillhavelowerduration.解析思路：該題考察的是久期與債券特征的關(guān)系。久期與債券的到期時(shí)間、票面利率和到期收益率相關(guān)。一般來(lái)說(shuō)，債券的到期時(shí)間越長(zhǎng)，久期越長(zhǎng)；票面利率越低，久期越長(zhǎng)；到期收益率越高，久期越短。因此，選項(xiàng)c)是正確的。Question11:Yes,theprojectshouldbeaccepted.SincetheIRR(12%)isgreaterthantherequiredrateofreturn(10%),theprojectisexpectedtogeneratereturnsthatexceedthecostofcapital.解析思路：該題考察的是基于內(nèi)部收益率（IRR）的資本預(yù)算決策規(guī)則。IRR是使項(xiàng)目NPV等于零的貼現(xiàn)率。如果IRR高于公司的要求回報(bào)率（或資本成本），則項(xiàng)目創(chuàng)造的價(jià)值大于其成本，應(yīng)接受該項(xiàng)目；反之，則拒絕。本題中，項(xiàng)目的IRR(12%)高于要求的回報(bào)率(10%)，因此應(yīng)接受項(xiàng)目。Question12:PutPrice≈StockPrice+PV(StrikePrice)-CallPricePutPrice≈$110+$100/(1+0.05)^1-$10PutPrice≈$110+$95.24-$10PutPrice≈$195.24-$10PutPrice≈$185.24解析思路：該題考察的是歐式看跌期權(quán)（PutOption）的近似定價(jià)，基于看跌期權(quán)一看漲期權(quán)平價(jià)定理（Put-CallParityforEuropeanoptionsonnon-dividend-payingstocks）：看跌期權(quán)價(jià)格+股票價(jià)格=行權(quán)價(jià)現(xiàn)值+看漲期權(quán)價(jià)格。題目中給出看漲期權(quán)價(jià)格和股票價(jià)格，可以計(jì)算出看跌期權(quán)價(jià)格的近似值。公式為：PutPrice≈StockPrice+PV(StrikePrice)-CallPrice。將題目數(shù)據(jù)代入公式計(jì)算即可。（注意：此為近似計(jì)算，未考慮期權(quán)的時(shí)間價(jià)值）Question13:σp=[wA2*σA2+wB2*σB2+2*wA*wB*σA*σB*ρAB]^0.5σp=[(0.6)^2*(0.10)^2+(0.4)^2*(0.15)^2+2*0.6*0.4*0.10*0.15*0.2]^0.5σp=[0.36*0.01+0.16*0.0225+2*0.6*0.4*0.10*0.15*0.2]^0.5σp=[0.0036+0.0036+0.000288]^0.5σp=[0.007488]^0.5σp≈0.0865or8.65%解析思路：該題考察的是投資組合標(biāo)準(zhǔn)差（PortfolioStandardDeviation）的計(jì)算。投資組合的標(biāo)準(zhǔn)差衡量組合整體的風(fēng)險(xiǎn)，考慮了資產(chǎn)間的相關(guān)性。公式為：σp=[wA^2*σA^2+wB^2*σB^2+2*wA*wB*σA*σB*ρAB]^0.5，其中wA和wB是資產(chǎn)A和B的權(quán)重，σA和σB是資產(chǎn)A和B的標(biāo)準(zhǔn)差，ρAB是資產(chǎn)A和B回報(bào)率的相關(guān)系數(shù)。將題目數(shù)據(jù)代入公式計(jì)算即可。Question14:CostinUSD=$1,000,000/ForwardRateCostinUSD=$1,000,000/0.83CostinUSD≈$1,204,819.27解析思路：該題考察的是使用遠(yuǎn)期合約（ForwardContract）進(jìn)行套期保值的成本計(jì)算。遠(yuǎn)期合約允許以約定的未來(lái)價(jià)格買(mǎi)入或賣出某種資產(chǎn)。本題中，公司需要支付歐元，因此可以買(mǎi)入歐元遠(yuǎn)期合約。遠(yuǎn)期合約的成本等于需要買(mǎi)入的歐元數(shù)量乘以遠(yuǎn)期匯率。題目中公司需要支付$1,000,000，遠(yuǎn)期匯率為1USD=0.83EUR，即買(mǎi)入1美元需要支付0.83歐元，因此買(mǎi)入$1,000,000需要支付1,000,000/0.83≈1,204,819.27美元。Question15:b)Thevalueofaleveredfirmisequaltothevalueofanunleveredfirmplusthepresentvalueofthetaxshieldprovidedbydebt.解析思路：該題考察的是考慮稅收的莫迪利安尼-米勒定理（MM定理）。該定理指出，在有公司所得稅的情況下，杠桿公司的價(jià)值（V_L）等于無(wú)杠桿公司的價(jià)值（V_U）加上債務(wù)利息的稅盾現(xiàn)值（Tc*D）。稅盾是指利息支出帶來(lái)的稅負(fù)減少，對(duì)公司價(jià)值有正面影響。因此，選項(xiàng)b)是正確的。Question16:PI=(NPV+InitialInvestment)/InitialInvestmentPI=($26,794.63+$100,000)/$100,000PI=$126,794.63/$100,000PI=1.268解析思路：該題考察的是盈利指數(shù)（ProfitabilityIndex,PI）的計(jì)算。PI是項(xiàng)目未來(lái)現(xiàn)金流的現(xiàn)值與初始投資的比率，表示每單位初始投資能帶來(lái)的凈現(xiàn)值。公式為：PI=(NPV+InitialInvestment)/InitialInvestment。將之前計(jì)算的NPV和初始投資代入公式計(jì)算即可。PI大于1表示項(xiàng)目可行。Question17:Acid-TestRatio=(CurrentAssets-Inventory)/CurrentLiabilities$1.5=(CurrentAssets-Inventory)/CurrentLiabilitiesCurrentAssets=$1.5*CurrentLiabilities+InventoryCurrentRatio=CurrentAssets/CurrentLiabilities$2.5=($1.5*CurrentLiabilities+Inventory)/CurrentLiabilities$2.5=1.5+Inventory/CurrentLiabilitiesInventory/CurrentLiabilities=$2.5-$1.5=$1.0Inventory=$1.0*CurrentLiabilitiesAccountsReceivable=CurrentAssets-Cash-InventoryAccountsReceivable=($1.5*CurrentLiabilities+Inventory)-Cash-InventoryAccountsReceivable=$1.5*CurrentLiabilities-CashAccountsReceivableTurnover=Sales/AverageAccountsReceivableAccountsReceivableTurnover=Sales/[($1.5*CurrentLiabilities-Cash)/2]AssumingCashispartofCurrentAssetsbutnotInventory,andwithoutSalesdata,wecannotcalculateanumericalanswer.However,therelationshipshowsAccountsReceivableTurnoverdependsonSalesandthespecificvaluesofCurrentLiabilitiesandCash.IfweassumeCashisnegligibleorpartofInventorycalculationimplicitly,wemightestimate,butadefinitivenumericalanswerrequiresmoreinfo.解析思路：該題考察的是流動(dòng)比率、速動(dòng)比率和應(yīng)收賬款周轉(zhuǎn)率的關(guān)系。流動(dòng)比率（CurrentRatio）是衡量公司短期償債能力的一個(gè)指標(biāo)，速動(dòng)比率（Acid-TestRatio）是流動(dòng)比率的一個(gè)改進(jìn)版本，它排除了變現(xiàn)能力較差的存貨。題目給出了這兩個(gè)比率，并給出了存貨周轉(zhuǎn)率（Inventory