17金融学概论讲义(北大光华管理学院)lecture02

1PrinciplesofFinanceLecture02BondandShareValuation2ObjectivesToapplytheideasofdiscountingandpresentvalue:BondfeaturesandpricesBondyieldsSharevaluationusingdividenddiscountingmodelsReturn,yield,growth,andprice/earningsratios3ValuingMultiperiodCashFlows460,1£FV,100,4£,200,2£321FVFVandannum.per%5.9r?PV58.654001.111244.341913.2009095.1460,1£095.1100,4£095.1200,2£32PV4ValuingMultiperiodCashFlows0123£2,200£4,100£1,460£2,009.13£3,419.44£1112.01£6,540.58+5ValuingMultiperiodCashFlows(1)(1)(1)1nnnnFVPViFViPVFViPVFViPV6ValuingMultiperiodCashFlowsIfyouinvest$15,000for10years,youreceive$30,000.Whatisyourannualrateofreturn?110101013000012121150000.0717734637.18%nFViPV7ValuingMultiperiodCashFlowsiPVFViPVFVniniPVFViPVFViPVFVnnn1lnlnln1lnln1ln*)1(lnln)1()1(*8PerpetuityAstreamofcashflowsthatlastsforeverValuingalevelperpetuity32111rCrCrCPV2111rCrCCPVrCPVrrCPV9PerpetuityValuingagrowingperpetuity32211111rgCrgCrCPV322111111rgCrgCrgPVrCPV1grCPV10AnnuityAstreamofcashflowsthatlastsforafixednumberofyearsValuingan(ordinary)annuity012tt+1AnnuityPerpetuityStartingatt+1PerpetuityStartingat111AssumptionsofOrdinaryAnnuity1.Thefirstcashflowoccursexactlyoneperiodfromnow2.Allsubsequentcashflowsareseparatedbyexactlyoneperiod3.Allperiodsareofequallength4.Allcashflowshavethesamenominalvalue5.Thetermstructureofinterestrateisflat12PresentValueofAnnuityPVofAnnuityPVofPerpetuityStartingattime1PerpetuityStartingattimet+1ttrrCrrCrCPV111113PresentValueofAnnuity1111tnCPVrrPVrCr14PresentValueofAnnuity11(1)1ln(1)ln1ln1ln(1)tnCPVrrPVrrCPVrnrCPVrCnr15ExampleofAnnuityChoice1:Leaseacarfor4yearsat£300permonthChoice2:Buythecarat£18,000andyoucansellitattheendof4yearsat£6,000Ifthecostofcapitalis0.5%permonthwithmonthlycompounding,whichoneisthebetterdeal?Answer:774,12£005.11005.0300Leaseof48PV277,13£005.1000,6000,18£Buyof48PV16PureDiscountBondsApurediscount(zero-coupon)bondisasecuritythatpromisestopayaspecifiedsinglecashpayment(facevalueorparvalue)atitsmaturitydateWecanalwaysdisaggregateanyfixedincomesecurityintosumofpurediscountbondsExampleofpurediscountbond:Aone-yearpurediscountbondwithparvalueof£1,000istradingat£950,atitsmaturitytheinvestorreceives£1,00017CouponBondsAcouponbondobligatestheissuertomakeperiodicpaymentsofinterest(calledcouponpayments)tothebondholderuntilthebondmaturesatwhichtimethefacevalue(parvalue)isalsorepaidtothebondholderCouponrateistheinterestrateappliedtothefacevalueinordertocomputecouponpaymentCurrentyieldisthecouponpaymentdividedbybondpriceAcouponbondcanbeviewedasaportfolioofpurediscountbonds18CouponBondsExampleofacouponbondA30-yearbondwithparvalueof£1,000,thecouponrateis8%withsemi-annualpayment£40couponpaymenteverysix-month19Par,PremiumandDiscountBondsAcouponbondwithitscurrentpricetoitsparvalueisaparbondIfitistradingbelowparitisadiscountbondIfitistradingaboveparitisapremiumbondPurediscountbondsarealwayspurchasedatadiscountfromtheirfacevalueorparvalue20BondMarketsTreasurybonds:Thegovernmentissuesbondstofundnationalexpenditure.Treasurybondsvaryinmaturity,someupto30yearsCorporatebonds:CompaniesborrowmoneybyissuingbondsConvertiblebonds:givesthebondholdertheoptiontoconverteachbondforaspecifiednumberofsharesCallablebonds:givestheissuertheoptiontoredeemthebondbeforematurity21ValuingBondsThefairpriceofabondisgivenbythediscountedpresentvalueofitscouponpaymentsandpaymentofparvalue,usingthemarket-determineddiscountrate:TTTTrFrcrcrcp1111221Wherep:thefairpricec:annualcouponrateF:parvalue(facevalue)r:spotdiscountrateT:thetermtomaturity(weareassumingcouponsarepaidannually!)22ExampleofBondPricingTreasurybond8%,redeemablein3years(assumingannualcouponpayments)Termstructureofinterestrateisflatat6%perannum3206.01100806.01806.018p105.3523ExampleofBondPricingAbondmaturesin3years,withannualcouponpaymentof$100andfacevalueof$1000.Youwanttoestimateitsmarketvalue,butyoufinditdifficulttoestimatetheappropriateinterestrates.However,youhavenoticedthat3purediscountbonds,eachwith$1000parvalue,aretradedat$960,$890,and$810respectively.Sincecouponbondsareportfoliosofpurediscountbonds,wecanestimateitspriceusingthemarketpriceofpurediscountbonds.24ExampleofBondPricing9608908101001001000100100010001000$1076.00PP25ExampleofBondPricingAlternatively,wecanestimatetheinterestrateusingthepriceofpurediscountbond.91.075,1$0728.110010000600.11000417.1100%28.71810000,1%00.61890000,1%17.41960000,132313,0212,0111,0PPiii26InterestRatesandBondPricesBondpricesfallwheninterestratesriseBondpricesrisewheninterestratesfallInterestratescouldbeviewedasameasureoftheopportunitycostsofinvestinginbond27BondYieldtoMaturity(YTM)Theyield-to-maturityisameasureoftheaveragerateofreturnthatwillbeearnedonabondifitisboughtnowandhelduntilmaturityTheyield-to-maturityisthediscountratethatmakest