公司理财第5章

ConceptQuestions◆Definepurediscountbonds,level-couponbonds,andconsols.Apurediscountbondisonethatmakesnointerveninginterestpayments.Onereceivesasinglelumpsumpaymentatmaturity.Alevel-couponbondisacombinationofanannuityandalumpsumatmaturity.Aconsolisabondthatmakesinterestpaymentsforever.◆Contrastthestateinterestrateandtheeffectiveannualinterestrateforbondspayingsemi-annualinterest.Effectiveannualinterestrateonabondtakesintoaccounttwoperiodsofcompoundingperyearreceivedonthecouponpayments.Thestateratedoesnottakethisintoaccount.◆Whatistherelationshipbetweeninterestratesandbondprices?Thereisaninverserelationship.Whenonegoesup,theothergoesdown.◆Howdoesonecalculatetheyieldtomaturityonabond?Onefindsthediscountratethatequatesthepromisedfuturecashflowswiththepriceofthebond.◆Whatarethethreefactorsdeterminingafirm'sP/Eratio?Today'sexpectationsoffuturegrowthopportunities.Thediscountrate.Theaccountingmethod.◆WhatistheclosingpriceofGeneralData?TheclosingpriceofGeneralDatais63/16.◆WhatisthePEofGeneralHouse?ThePEofGeneralHouseis29.◆WhatistheannualdividendofGeneralHost?TheannualdividendofGeneralHostiszero.ConceptQuestions-AppendixToChapter5◆Whatisthedifferencebetweenaspotinterestrateandtheyieldtomaturity?Theyieldtomaturityisthegeometricaverageofthespotratesduringthelifeofthebond.◆Definetheforwardrate.Givenaone-yearbondandatwo-yearbond,oneknowsthespotratesforboth.Theforwardrateistherateofreturnimplicitonaone-yearbondpurchasedinthesecondyearthatwouldequatetheterminalwealthofpurchasingtheone-yearbondtodayandanotherinoneyearwiththatofthetwo-yearbond.◆Whatistherelationshipbetweentheone-yearspotrate,thetwo-yearspotrateandtheforwardrateoverthesecondyear?Theforwardratef2=[(1+r2)2/(1+r1)]-1◆Whatistheexpectationhypothesis?Investorssetinterestratessuchthattheforwardrateoveragivenperiodequalsthespotrateforthatperiod.◆Whatistheliquidity-preferencehypothesis?Thishypothesismaintainsthatinvestorsrequireariskpremiumforholdinglonger-termbonds(i.e.theyprefertobeliquidorshort-terminvestors).Thisimpliesthatthemarketsetstheforwardrateforagivenperiodabovetheexpectedspotrateforthatperiod.QuestionsAndProblemsHowtoValueBonds5.1Whatisthepresentvalueofa10-year,purediscountbondthatpays$1,000atmaturityandispricedtoyieldthefollowingrates?a.5percentb.10percentc.15percentSolutionsa.$1,000/1.0510=$613.91b.$1,000/1.1010=$385.54c.$1,000/1.1510=$247.185.2Microhardhasissuedabondwiththefollowingcharacteristics:Principal:$1,000Termtomaturity:20yearsCouponrate:8percentSemiannualpaymentsCalculatethepriceoftheMicrohardbondifthestatedannualinterestrateis:a.8percentb.10percentc.6percentSolutionsTheamountofthesemi-annualinterestpaymentis$40(=$1,0000.08/2).Thereareatotalof40periods;i.e.,twohalfyearsineachofthetwentyyearsinthetermtomaturity.Theannuityfactortablescanbeusedtopricethesebonds.Theappropriatediscountratetouseisthesemi-annualrate.Thatrateissimplytheannualratedividedbytwo.Thus,forpartbtheratetobeusedis5%andforpartcisit3%.a.$40(19.7928)+$1,000/1.0440=$1,000Noticethatwheneverthecouponrateandthemarketratearethesame,thebondispricedatpar.b.$40(17.1591)+$1,000/1.0540=$828.41Noticethatwheneverthecouponrateisbelowthemarketrate,thebondispricedbelowpar.c.$40(23.1148)+$1,000/1.0340=$1,231.15Noticethatwheneverthecouponrateisabovethemarketrate,thebondispricedabovepar.5.3Considerabondwithafacevalueof$1,000.Thecouponispaidsemiannuallyandthemarketinterestrate(effectiveannualinterestrate)is12percent.Howmuchwouldyoupayforthebondifa.thecouponrateis8percentandtheremainingtimetomaturityis20years?b.thecouponrateis10percentandtheremainingtimetomaturityis15years?SolutionsSemi-annualdiscountfactor=(1.12)1/2-1=0.05830=5.83%a.Price=$40400583.0+$1,000/1.058340=$614.98+$103.67=$718.65b.Price=$50300583.0+$1,000/1.058330=$700.94+$182.70=$883.645.4PettitTruckinghasissuedan8-percent,20-yearbondthatpaysinterestsemiannually.Ifthemarketpricesthebondtoyieldaneffectiveannualrateof10percent,whatisthepriceofthebond?SolutionsEffectiveannualrateof10%:Semi-annualdiscountfactor=(1.1)0.5-1=0.04881=4.881%Price=$404004881.0+$1,000/1.0488140=$846.335.5Abondissoldat$923.14(belowitsparvalueof$1,000).Thebondhas15yearstomaturityandinvestorsrequirea10-percentyieldonthebond.Whatisthecouponrateforthebondifthecouponispaidsemiannually?Solutions$923.14=C3005.0+$1,000/1.0530=(15.37245)C+$231.38C=$45Theannualcouponrate=$452/$1,000=0.09=9%5.6Youhavejustpurchasedanewlyissued$1,000five-yearVanguardCompanybondatpar.Thisfive-yearbondpays$60ininterestsemiannually.YouarealsoconsideringthepurchaseofanotherVanguardCompanybondthatreturns$30insemiannualinterestpaymentsandhassixyearsremainingbeforeitmatures.Thisbondhasafacevalueof$1,000.a.Whatiseffectiveannualreturnonthefive-yearbond?b.Assumethattherateyoucalculatedinpart(a)isthecorrectrateforthebondwithsixyearsremainingbeforeitmatures.Whatshouldyoubewillingtopayforthatbond?c.Howwillyouranswertopart(b)changeifthefive-yearbondpays$40insemiannualinterest?Solutionsa.Thesemi-annualinterestrateis$60/$1,000=0.06.Thus,theeffectiveannualrateis1.062-1=0.1236=12.36%.b.Price=$301206.0+$1,0