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1、PRACTICEPROBLEMS1Thetablebelowgivescurrentinformationontheinterestratesfortwotwo-yearandtwoeight-yearmaturityinvestments.Ihetablealsogivesthematurity,liquidity,anddefaultriskcharacteristicsofanewinvestmentpossibility(Investment3).Allinvestmentspromiseonlyasinglepayment(apaymentatmaturity).Assumethat
2、premiumsrelatingtoinflation,liquidity,anddefaultriskareconstantacrossalltimehorizons.InvestmentMaturity(inYears)LiquidityDefaultRiskInterestRate()12HighLow2022LowLow2.537LowLowt348HighLow4.058LowHigh6.5Basedontheinformationintheabovetable,addressthefollowing:AExplainthedifferencebetweentheinterestra
3、tesonInvestment1andInvestment2.BEstimatethedefaultriskpremium.CCalculateupperandlowerlimitsfortheinterestrateonInvestment3,.2Acoupleplanstosetaside$20,000peryearinaconservativeportfolioprojectedtoearn7percentayear.Iftheymaketheirfirstsavingscontributiononeyearfromnow,howmuchwilltheyhaveattheendof20y
4、ears?3Twoyearsfromnow,aclientwillreceivethefirstofthreeannualpaymentsofS20,(X)0fromasmallbusinessproject.Ifshecanearn9percentannuallyonherinvestmentsandplanstoretireinsixyears,howmuchwillthethreebusinessprojectpaymentsbeworthatthetimeofherretirement?ITocoverthefirstyearstotalcollegetuitionpaymentsfo
5、rhistwochildren,afatherwillmakea$75,000paymentfiveyearsfromnow.Howmuchwillheneedtoinvesttodaytomeethisfirsttuitiongoaliftheinvestmentearns6percentannually?5Aclientcanchoosebetweenreceiving10annualSlOOfOOOretirementpayments,startingoneyearfromtoday,orreceivingalumpsumtoday.Knowingthathecaninvestatara
6、teof5percentannually,hehasdecidedtotakethelumpsum.Whatlumpsumtodaywillbeequivalenttothefutureannualpayments?6Youareconsideringinvestingintwodifferentinstruments.Thefirstinstrumentwillpaynothingforthreeyears,butthenitwillpayS20,0(X)peryearforfouryears.Thesecondinstrumentwillpay$20,000forthreeyearsand
7、$30,000inthefourthyear.Allpaymentsaremadeatyear-end.Ifyourrequiredrateofreturnontheseinvestmentsis8percentannually,whatshouldyoubewillingtopayfor:AThefirstinstrument?BThesecondinstrument(usetheformulaforafour-yearannuity)?2016CFAInstitute.AUrightsreserved.7Supposeyouplantosendyourdaughtertocollegein
8、threeyears.Youexpecthertoearntwo-thirdsofhertuitionpaymentinscholarshipmoney,soyouestimatethatyourpaymentswillbe$10,000ayearbrfouryears.Tbestimatewhetheryouhavesetasideenoughmoney,youignorepossibleinflationintuitionpaymentsandassumethatyoucanearn8percentannuallyonyourinvestments.Howmuchshouldyouseta
9、sidenowtocoverthesepayments?8Aclientplanstosendachildtocollegeforfouryearsstarting18yearsfromnow.Havingsetasidemoneyfortuition,shedecidestoplanforroomandboardalso.Sheestimatesthesecostsat$20,000peryear,payableatthebeginningofeachyear,bythetimeherchildgoestocollege.Ifshestartsnextyearandmakes17paymen
10、tsintoasavingsaccountpaying5percentannually,whatannualpaymentsmustshemake?9Acoupleplanstopaytheirchildscollegetuitionfor4yearsstarting18yearsfromnow.ThecurrentannualcostofcollegeisC$7,000,andtheyexpectthiscosttoriseatanannualrateof5percent.Intheirplanning,theyassumethattheycanearn6percentannually.Ho
11、wmuchmusttheyputasideeachyear,startingnextyear,iftheyplantomake17equalpayments?10Thenominalrisk-freerateisbestdescribedasthesumoftherealrisk-freerateandapremiumfor:Amaturity.Bliquidity.Iexpectedinflation.11WhiChofthefollowingriskpremiumsismostrelevantinexplainingthedifferenceinyieldsbetween30-yearbo
12、ndsissuedbytheUSTreasuryand30-yearbondsissuedbyasmallprivateissuer?AInflationBMaturityCLiquidity12Abankquotesastatedannualinterestrateof4.00%.Ifthatrateisequaltoaneffectiveannualrateof4.08%,thenthebankiscompoundinginterest:Adaily.Bquarterly.Csemiannually.13ThevalueinsixyearsofS75,000investedtodayata
13、statedannualinterestrateof7%compoundedquarterlyisclosestto:A$11*555.B$113,330.C$113,733.14Aclientrequires100,000oneyearfromnow.Ifthestatedannualrateis2.50%compoundedweekly,thedepositneededtodayisclosestto:A97,500.B97,532.C97,561.15Foralumpsuminvestmentof250,000investedatastatedannualrateOf3%compound
14、eddaily,thenumberofmonthsneededtogrowthesumtoYlf0,000isclosestto：A555.R563.C576.16Givena1,000,000investmentforfouryearswithastatedannualrateof3%compoundedcontinuously,thedifferenceinitsinterestearningscomparedwiththesameinvestmentcompoundeddailyisclosestto:A1.B6.c455.17Aninvestmentpays300annuallyfor
15、fiveyears,withthefirstpaymentoccurringtoday.Thepresentvalue(PV)oftheinvestmentdiscountedata4%annualrateisclosestto:A1,336.B1,389.c1,625.18Aperpetualpreferredstockmakesitsfirstquarterlydividendpaymentof$2.00infivequarters.Iftherequiredannualrateofreturnis6%compoundedquarterly,thestockspresentvalueisc
16、losestto:A$31.B$126.C$133.19Asaverdepositsthefollowingamountsinanaccountpayingastatedannualrateof4%,compoundedsemiannually：YearEndofYearDeposits($)14,00028,00037.0410,0AttheendofYear4,thevalueoftheaccountisclosestto：A$30,432B$30,447c$31,67720Aninvestmentof500,0(X)todaythatgrowsto800,(XX)aftersixyear
17、shasastatedannualinterestrateclosestto:A7.5%compoundedcontinuously.B7.7%compoundeddaily.(8.0%compoundedsemiannually.21Asweepstakeswinnermayselecteitheraperpetuityof2,000amonthbeginningwiththefirstpaymentinonemonthoranimmediatelumpsumpaymentof350,000.Iftheannualdiscountrateis6%compoundedmonthly,thepr
18、esentvalueofthePerPetUityis:Alessthanthelumpsum.Bequaltothelumpsum.(greaterthanthelumpsum.22Ata5%interestrateperyearcompoundedannually,thepresentvalue(PV)ofa10-yearordinaryannuitywithannualpaymentsof$2,000is$15,443.47,IhePVofa10-yearannuityduewiththesameinterestrateandpaymentsisclosestto:A$14,708.B$
19、16,216.C$17,443.23Grandparentsarefundinganewbornsfutureuniversitytuitioncosts,estimatedat$50,(X)0/yearforfouryears,withthefirstpaymentdueasalumpsumin18years.Assuminga6%effectiveannualrate,therequireddeposittodayisclosestto:A$60,699.B$64,341.C$68,201.24Thepresentvalue(PV)Ofaninvestmentwiththefollowin
20、gyear-endcashflows(CF)anda12%requiredannualrateofreturnisclosestto:YearCashFlow)1100,02150,(XX)5-10,000A201,747.B203,191.c227,573.25Asportscar,purchasedfor200,000,isfinancedforfiveyearsatanannualrateof6%compoundedmonthly.Ifthefirstpaymentisdueinonemonth,themonthlypaymentisClOSeSltD：AS47.B3,867.C3,95
21、7.26Givenastatedannualinterestrateof6%compoundedquarterly,thelevelamountthat,depositedquarterly,willgrowto25,000attheendof10yearsisclosestto：A461.B474.C836.27Giventhefollowingtimelineandadiscountrateof4%ayearcompoundedannually,thepresentvalue(PV),asoftheendofYear5(PV5),ofthecashflowreceivedattheendo
22、fYear20isclosestto:012345.20IlllII1PV5$5(X000A$22,819.B$27,763.c$28,873.28Aclientinvests20,000inafour-yearcertificateofdeposit(CD)thatannuallypaysinterestof3.5%.TheannualCDinterestpaymentsareautomaticallyreinvestedinaseparatesavingsaccountatastatedannualinterestrateof2%compoundedmonthly.Atmaturity,t
23、hevalueofthecombinedassetisclosestto:A21,670.b22,890.c22,950.$2QooO $2Q(XX)$2QOOO S2Q000SOLUTIONS1Ainvestment2isidenticaltoInvestment1exceptthatInvestment2haslowliquidity.ThedifferencebetweentheinterestrateonInvestment2andInvestment1is0.5percentagepoint.ThiSamountrepresentstheliquiditypremium,whichr
24、epresentscompensationfortheriskoflossrelativetoaninvestmenfsfairvalueiftheinvestmentneedstobeconvertedtocashquickly.BToestimatethedefaultriskpremium,findthetwoinvestmentsthathavethesamematuritybutdifferentlevelsofdefaultrisk.BothInvestments4and5haveamaturityofeightyears.Investment5,however,haslowliq
25、uidityandthusbearsaliquiditypremium.ThedifferencebetweentheinterestratesofInvestments5and4is2.5percentagepoints.Theliquiditypremiumis0.5percentagepoint(fromPartA).Thisleaves2.5-0.5=2.0percentagepointsthatmustrepresentadefaultriskpremiumreflectingInvestment5,shighdefaultrisk.CInvestment3hasliquidityr
26、iskanddefaultriskcomparabletoInvestment2,butwithitslongertimetomaturity,Investment3shouldhaveahighermaturitypremium.IheinterestrateonInvestment3,巧,shouldthusbeabove2.5percent(theinterestrateonInvestment2).IftheliquidityofInvestment3werehigh,Investment3wouldmatchInvestment4exceptforInvestment3sshorte
27、rmaturity.WewouldthenconcludethatInvestment3,sinterestrateshouldbelessthantheinterestrateonInvestment4,whichis4percent.IncontrasttoInvestment4,however,Investment3haslowliquidity.ItispossiblethattheinterestrateonInvestment3exceedsthatofInvestment4despite3sshortermaturity,dependingontherelativesizeOft
28、heliquidityandmaturitypremiums.However,weexpectr3tobelessthan4.5percent,theexpectedinterestrateonInvestment4ifithadlowliquidity.Thus2.5percentr32584O4XEquation7=$7Q919Insummary,yourclientwillhavetosave$2,744.50eachyearifshestartsnextyearandmakes17paymentsintoasavingsaccountpaying5percentannually.iDr
29、awatimeline.0121718192021O218C$7,000Year1Year2Year3Year4payBentpaymentpaynentpaymentEquntinfi2C$1&846AC$17,689C$1&573C$1&502ivLfeingtheformulaforthepresentvalueofalumpsum(r=6%),equatethefourcollegepaymentstosinglepaymentsasoft=17andaddthemtogether.C$16,846(1.06)7+c$17,689(1.06)-2+C$18,573(1.06)3+CS1
30、9,502(1.06)-4=C$62,677vEquatethesumofC$62,677att=17tothe17paymentsofX,usingtheformulaforthefuturevalueofanannuity(Equation7).ThensolveforX.toe)11-1C$62,677=X=28,21288XoX=C$222L58NotationUsedNumericalValueonMostCalculatorsforThisProblem%iPVFVPMTcompute176n/a(=0)C$62,6772821288XEquation7=C$62677Insummary,thecouplewillneedtoputasideC$2,221.58eachyeariftheystartnextyearandmake17equalpayments.10Ciscorrect.Thesumoftherealrisk-freeinterestrateandtheinflationpremiumisthenominalrisk-freerate.11Ciscorrect.USTreasuryrbondsarehighlyliquid,whereasthebondsofsmallissue
