CFA课后习题：数量.docx

PRACTICEPROBLEMS1Thetablebelowgivescurrentinformationontheinterestratesfortwotwo-yearandtwoeight-yearmaturityinvestments.Ihetablealsogivesthematurity,liquidity,anddefaultriskcharacteristicsofanewinvestmentpossibility(Investment3).Allinvestmentspromiseonlyasinglepayment(apaymentatmaturity).Assumethatpremiumsrelatingtoinflation,liquidity,anddefaultriskareconstantacrossalltimehorizons.InvestmentMaturity(inYears)LiquidityDefaultRiskInterestRate()12HighLow2022LowLow2.537LowLowt348HighLow4.058LowHigh6.5Basedontheinformationintheabovetable,addressthefollowing:AExplainthedifferencebetweentheinterestratesonInvestment1andInvestment2.BEstimatethedefaultriskpremium.CCalculateupperandlowerlimitsfortheinterestrateonInvestment3,¾.2Acoupleplanstosetaside$20,000peryearinaconservativeportfolioprojectedtoearn7percentayear.Iftheymaketheirfirstsavingscontributiononeyearfromnow,howmuchwilltheyhaveattheendof20years?3Twoyearsfromnow,aclientwillreceivethefirstofthreeannualpaymentsofS20,(X)0fromasmallbusinessproject.Ifshecanearn9percentannuallyonherinvestmentsandplanstoretireinsixyears,howmuchwillthethreebusinessprojectpaymentsbeworthatthetimeofherretirement?ITocoverthefirstyearstotalcollegetuitionpaymentsforhistwochildren,afatherwillmakea$75,000paymentfiveyearsfromnow.Howmuchwillheneedtoinvesttodaytomeethisfirsttuitiongoaliftheinvestmentearns6percentannually?5Aclientcanchoosebetweenreceiving10annualSlOOfOOOretirementpayments,startingoneyearfromtoday,orreceivingalumpsumtoday.Knowingthathecaninvestatarateof5percentannually,hehasdecidedtotakethelumpsum.Whatlumpsumtodaywillbeequivalenttothefutureannualpayments?6Youareconsideringinvestingintwodifferentinstruments.Thefirstinstrumentwillpaynothingforthreeyears,butthenitwillpayS20,0(X)peryearforfouryears.Thesecondinstrumentwillpay$20,000forthreeyearsand$30,000inthefourthyear.Allpaymentsaremadeatyear-end.Ifyourrequiredrateofreturnontheseinvestmentsis8percentannually,whatshouldyoubewillingtopayfor:AThefirstinstrument?BThesecondinstrument(usetheformulaforafour-yearannuity)?©2016CFAInstitute.AUrightsreserved.7Supposeyouplantosendyourdaughtertocollegeinthreeyears.Youexpecthertoearntwo-thirdsofhertuitionpaymentinscholarshipmoney,soyouestimatethatyourpaymentswillbe$10,000ayear£brfouryears.Tbestimatewhetheryouhavesetasideenoughmoney,youignorepossibleinflationintuitionpaymentsandassumethatyoucanearn8percentannuallyonyourinvestments.Howmuchshouldyousetasidenowtocoverthesepayments?8Aclientplanstosendachildtocollegeforfouryearsstarting18yearsfromnow.Havingsetasidemoneyfortuition,shedecidestoplanforroomandboardalso.Sheestimatesthesecostsat$20,000peryear,payableatthebeginningofeachyear,bythetimeherchildgoestocollege.Ifshestartsnextyearandmakes17paymentsintoasavingsaccountpaying5percentannually,whatannualpaymentsmustshemake?9Acoupleplanstopaytheirchild'scollegetuitionfor4yearsstarting18yearsfromnow.ThecurrentannualcostofcollegeisC$7,000,andtheyexpectthiscosttoriseatanannualrateof5percent.Intheirplanning,theyassumethattheycanearn6percentannually.Howmuchmusttheyputasideeachyear,startingnextyear,iftheyplantomake17equalpayments?10Thenominalrisk-freerateisbestdescribedasthesumoftherealrisk-freerateandapremiumfor:Amaturity.Bliquidity.Iexpectedinflation.11WhiChofthefollowingriskpremiumsismostrelevantinexplainingthedifferenceinyieldsbetween30-yearbondsissuedbytheUSTreasuryand30-yearbondsissuedbyasmallprivateissuer?AInflationBMaturityCLiquidity12Abankquotesastatedannualinterestrateof4.00%.Ifthatrateisequaltoaneffectiveannualrateof4.08%,thenthebankiscompoundinginterest:Adaily.Bquarterly.Csemiannually.13ThevalueinsixyearsofS75,000investedtodayatastatedannualinterestrateof7%compoundedquarterlyisclosestto:A$11*555.B$113,330.C$113,733.14Aclientrequires£100,000oneyearfromnow.Ifthestatedannualrateis2.50%compoundedweekly,thedepositneededtodayisclosestto:A£97,500.B£97,532.C£97,561.15Foralumpsuminvestmentof¥250,000investedatastatedannualrateOf3%compoundeddaily,thenumberofmonthsneededtogrowthesumtoYlf0,000isclosestto：A555.R563.C576.16Givena1,000,000investmentforfouryearswithastatedannualrateof3%compoundedcontinuously,thedifferenceinitsinterestearningscomparedwiththesameinvestmentcompoundeddailyisclosestto:A1.B6.c455.17Aninvestmentpays300annuallyforfiveyears,withthefirstpaymentoccurringtoday.Thepresentvalue(PV)oftheinvestmentdiscountedata4%annualrateisclosestto:A1,336.B1,389.c1,625.18Aperpetualpreferredstockmakesitsfirstquarterlydividendpaymentof$2.00infivequarters.Iftherequiredannualrateofreturnis6%compoundedquarterly,thestockspresentvalueisclosestto:A$31.B$126.C$133.19Asaverdepositsthefollowingamountsinanaccountpayingastatedannualrateof4%,compoundedsemiannually：YearEndofYearDeposits($)14,00028,00037.0410,0AttheendofYear4,thevalueoftheaccountisclosestto：A$30,432B$30,447c$31,67720Aninvestmentof500,0(X)todayt