财务管理(英文第十三版)Ch 4-sheena

Chapter4

TheValuationofLong-TermSecurities1LearningObjectivesDistinguishamongthevarioustermsusedtoexpressvalue,includingliquidationvalue,going-concernvalue,bookvalue,marketvalue,andintrinsicvalue.Valuebonds,preferredstocks,andcommonstocks.Calculatetheratesofreturn(oryields)ofdifferenttypesoflong-termsecurities.Listandexplainanumberofobservationsregardingthebehaviorofbondprices.2ConceptsofValueGoing-concernvalue

representstheamountafirmcouldbesoldforasacontinuingoperatingbusiness.Liquidationvalue

representstheamountofmoneythatcouldberealizedifanassetorgroupofassetsissoldseparatelyfromitsoperatingorganization.3ConceptsofValue(2)afirm:totalassetsminusliabilitiesandpreferredstockaslistedonthebalancesheet.Bookvalue

representseither(1)anasset:theaccountingvalueofanasset--theasset’scostminusitsaccumulateddepreciation;4ConceptsofValueIntrinsicvalue

representsthepriceasecurity“oughttohave”basedonallfactorsbearingonvaluation.Marketvalue

representsthemarketpriceatwhichanassettrades.5SecurityValuationIngeneral,theintrinsicvalueofanasset=thepresentvalueofthestreamofexpectedcashflowsdiscountedatanappropriaterequiredrateofreturn.6BondValuationImportantTermsTypesofBondsValuationofBondsHandlingSemiannualCompounding7Definition:Abondisalong-termdebtinstrumentissuedbyacorporationorgovernment.Debtors CreditorsImportantBondTerms8TheFacevalueofabond:isthestatedvalue.InthecaseofaU.S.bond,thefacevalueisusually$1,000.TheMaturity

ofabond:isthetimewhenthecompanyisobligatedtopaythebondholderthefacevalueofthebond.

ImportantBondTerms9Thecoupons

(couponpayments)arethestatedinterestpaymentmadeonbond.Thebond’scouponrate

isthestatedrateofinterest;theannualinterestpaymentdividedbythebond’sfacevalue.ImportantBondTerms10ImportantBondTermsThediscountrate

(requiredrateofreturn)isdependentontheriskofthebondandiscomposedoftherisk-freerateplusapremiumforrisk.11QuickQuizTheprincipalamountofabondthatisrepaidattheendoftermiscalled:discountamount.

facevalue.

back-endamount.

coupon.

couponrate.12Aperpetualbondisabondthatnevermatures.Ithasaninfinitelife.CashFlow:OnlythefixedannualinterestpaymentofIforever.

TypesofBonds13Aperpetualbondisabondthatnevermatures.Ithasaninfinitelife.(1+

kd)1(1+kd)2(1+kd)¥V=++...+III=S¥t=1(1+kd)tIorI(PVIFAkd,¥

)V=I/kd [ReducedForm]PerpetualBond14BondPhasa$1,000facevalueandprovidesan8%couponrate.Theappropriatediscountrateis10%.Whatisthevalueoftheperpetualbond?

I =$1,000(8%) =$80.

kd

=10%.

V =I/kd [ReducedForm] =$80/10%=$800.PerpetualBondExample15Anon-zerocoupon-payingbondisabondhasafinitematurityandthebondholderreceiveinterestpaymentandfacevalueatmaturityCashFlow:notonlythefixedannualinterestpayment,butalsothefacevalueatmaturity.TypesofBonds16Anon-zerocoupon-payingbondisabondhasafinitematurityandthebondholderreceiveinterestpaymentandfacevalueatmaturity(1+

kd)1(1+kd)2(1+kd)nV=++...+II+MVI=Snt=1(1+kd)tIV=I(PVIFAkd,n)+MV(PVIFkd,n)(1+kd)n+MVCouponBond17BondChasa$1,000facevalueandprovidesan8%annualcouponfor30years.Theappropriatediscountrateis10%.Whatisthevalueofthe

couponbond?V =$80(PVIFA10%,30)+$1,000(PVIF10%,30) =

$80

(9.427)+$1,000(.057)

[TableIV]

[TableII] =$754.16+$57 =$811.16.CouponBondExample18BondChasa$1,000facevalueandprovidesan10%annualcouponfor30years.Theappropriatediscountrateis10%.Whatisthevalueofthe

couponbond?V =$100(PVIFA10%,30)+$1,000(PVIF10%,30) =

$100

(9.427)+$1,000(.057)

[TableIV]

[TableII] =$942.7+$57 =$1000CouponBondExample19BondChasa$1,000facevalueandprovidesan12%annualcouponfor30years.Theappropriatediscountrateis10%.Whatisthevalueofthe

couponbond?V =$120(PVIFA10%,30)+$1,000(PVIF10%,30) =

$120

(9.427)+$1,000(.057)

[TableIV]

[TableII] =$1131.24+$57 =$1188.24CouponBondExample20BondPrices:RelationshipBetweenCouponandYieldYTM=kdIfYTM=couponrate,thenparvalue=bondpriceIfYTM>couponrate,thenparvalue>bondpricePricebelowparvalue,calledadiscountbondIfYTM<couponrate,thenparvalue<bondpricePriceaboveparvalue,calledapremiumbond21Azero-couponbondisabondthatpaysnointerestbutsellsatadeepdiscountfromitsfacevalue;itprovidescompensationtoinvestorsintheformofpriceappreciation.CashFlow:onlythefacevaluereceivedatmaturity.TypesofBonds22Azero-couponbondisabondthatpaysnointerestbutsellsatadeepdiscountfromitsfacevalue;itprovidescompensationtoinvestorsintheformofpriceappreciation.(1+

kd)nV=MV=MV(PVIFkd,n)Zero-CouponBond23

V =$1,000(PVIF10%,30) =

$1,000(.057) =$57.00BondZhasa$1,000facevalueanda30-yearlife.Theappropriatediscountrateis10%.Whatisthevalueofthe

zero-couponbond?Zero-CouponBondExample24Whatistheintrinsicvalueofa$1,000facevalue,zero-couponbondthatmaturesin20yearsifaninvestor'srequiredrateofreturnforthebondis8%?(Assumeannualdiscounting.)V =$1,000(PVIF8%,20) =

$1,000(.215) =$215Exercise25

(1)Dividekdby2 (2)Multiplynby2 (3)DivideIby2MostbondsintheU.S.payinteresttwiceayear(1/2oftheannualcoupon).Adjustmentsneeded:SemiannualCompounding26(1+kd/2)2*n(1+

kd/2)1Anon-zerocouponbondadjustedforsemiannualcompounding.V=++...+I/

2I/

2

+MV=S2*nt=1(1+kd

/2)tI/

2=I/2

(PVIFAkd

/2,2*n)+MV(PVIFkd

/2,2*n)(1+kd

/2)2*n+MVI/

2(1+

kd/2)2SemiannualCompounding27V =$40(PVIFA5%,30)+$1,000(PVIF5%,30)

=

$40

(15.373)+$1,000(.231)

[TableIV]

[TableII] =$614.92+$231.00 =$845.92BondChasa$1,000facevalueandprovidesan8%semiannualcouponfor15years.Theappropriatediscountrateis10%(annualrate).Whatisthevalueofthe

couponbond?SemiannualCouponBondExample28GovernmentBondTreasurySecuritiesFederalgovernmentdebtT-bills–purediscountbondswithoriginalmaturityofoneyearorlessT-notes–coupondebtwithoriginalmaturitybetweenoneandtenyearsT-bonds:Thelong-termbondsissuedbytheUnitedStatesgovernment29GovernmentBondMunicipalSecuritiesDebtofstateandlocalgovernmentsVaryingdegreesofdefaultrisk,ratedsimilartocorporatedebt,alwayscallable.Interestreceivedistax-exemptatthefederallevel30TreasuryQuotationsHighlightedquote8Nov21

132:23

132:24

-12 5.14Whatisthecouponrateonthebond?Whendoesthebondmature?Whatisthebidprice?Whatdoesthismean?Whatistheaskprice?Whatdoesthismean?Howmuchdidthepricechangefromthepreviousday?Whatistheyieldbasedontheaskprice?31Couponrate=8%MaturesinNovember2021Bidpriceis132and23/32percentofparvalue.Ifyouwanttosell$100,000parvalueT-bonds,thedealeriswillingtopay1.3271875(100,000)=$132,718.75Askpriceis132and24/32percentofparvalue.Ifyouwanttobuy$100,000parvalueT-bonds,thedealeriswillingtosellthemfor1.3275(100,000)=$132,750.00Thedifferencebetweenthebidandaskpricesiscalledthebid-askspreadanditishowthedealermakesmoney.Thepricechangedby-12/32percentor$375fora$100,000worthofT-bondsTheyieldis5.14%32Section233PreferredStockisatypeofstockthathasnostatedmaturitydate,promisesa(usually)fixeddividend,butatthediscretionoftheboardofdirectors.PreferredStockhaspreferenceovercommonstockinthepaymentofdividendsandclaimsonassets.PreferredStockValuation34CashFlow:futurefixeddividendpaymentinalongtime.PreferredStockValuation35Thisreducestoaperpetuity!(1+

kP)1(1+kP)2(1+kP)¥V=++...+DPDPDP=S¥t=1(1+kP)tDPorDP(PVIFAkP,¥

)V=DP/kPPreferredStockValuation36

DP=$100(8%)=$8.00.

kP

=10%. V=DivP/kP=$8.00/10% =$80StockPShasan8%,$100parvalueissueoutstanding.Theappropriatediscountrateis10%.Whatisthevalueofthepreferredstock?PreferredStockExample37

(1)Futuredividends (2)Futuresaleofthecommon stocksharesWhatcashflowswillashareholderreceivewhenowningsharesofcommonstock?CommonStockValuation38BasicdividendvaluationmodelaccountsforthePVofallfuturedividends.(1+

ke)1(1+ke)2(1+ke)¥V=++...+D1D¥D2=S¥t=1(1+ke)tDtDt: Cashdividend attimetke: Equityinvestor’s requiredreturnDividendValuationModels39Thebasicdividendvaluationmodeladjustedforthefuturestocksale.(1+

ke)1(1+ke)2(1+ke)nV=++...+D1Dn

+PricenD2n: Theyearinwhichthefirm’s sharesareexpectedtobesold.Pricen: Theexpectedsharepriceinyearn.

AdjustedDividendValuationModel40Weplantoownthestockforonlytwoyears,thedividendvaluationmodelbecomes(1+

ke)1(1+ke)2(1+ke)2V=++D1Price2D2AdjustedDividendValuationModel41Thedividendvaluationmodelrequirestheforecastofallfuturedividends.Thefollowingdividendgrowthrateassumptionssimplifythevaluationprocess.ConstantGrowthNoGrowthGrowthPhasesDividendGrowthPatternAssumptions42Theconstantgrowthmodelassumesthatdividendswillgrowforeverattherateg,alsoassumethatke>g(1+

ke)1(1+ke)2(1+ke)¥V=++...+D0(1+g)D0(1+g)¥=(ke

-g)D1D1: Dividendpaidattime1.g

: Theconstantgrowthrate.ke: Investor’srequiredreturn.D0(1+g)2ConstantGrowthModel43StockCGhasanexpectedgrowthrateof8%.Eachshareofstockjustreceivedanannual$3.24dividendpershare.Theappropriatediscountrateis15%.Whatisthevalueofthecommonstock?D1 =$3.24(1+.08)=$3.50VCG =D1/(ke

-g)=$3.50/(.15-.08) =$50ConstantGrowthModelExample44Thezerogrowthmodelassumesthatdividendswillgrowforeverattherateg=0.(1+

ke)1(1+ke)2(1+ke)¥VZG=++...+D1D¥=keD1D1: Dividendpaidattime1.ke: Investor’srequiredreturn.D2NoGrowthModel45StockZGhasanexpectedgrowthrateof0%.Eachshareofstockjustreceivedanannual$3.24dividendpershare.Theappropriatediscountrateis15%.Whatisthevalueofthecommonstock?D1 =$3.24(1+0)=$3.24VZG =D1/(ke

-0)=$3.24/(.15-0) =$21.60NoGrowthModelExample46D0(1+g1)tDn(1+g2)tThegrowthphasesmodelassumesthatdividendsforeachsharewillgrowattwoormoredifferentgrowthrates.(1+

ke)t(1+ke)tV=St=1nSt=n+1¥+GrowthPhasesModel47D0(1+g1)tDn+1Notethatthesecondphaseofthegrowthphasesmodelassumesthatdividendswillgrowataconstantrateg2.Wecanrewritetheformulaas:(1+

ke)t(ke

-g2)V=St=1n+1(1+

ke)nGrowthPhasesModel48StockGPhasanexpectedgrowthrateof16%forthefirst3yearsand8%thereafter.Eachshareofstockjustreceivedanannual$3.24dividendpershare.Theappropriatediscountrateis15%.Whatisthevalueofthecommonstockunderthisscenario?GrowthPhasesModelExample49StockGPhastwophasesofgrowth.Thefirst,16%,startsattimet=0for3yearsandisfollowedby8%

thereafterstartingattimet=3.Weshouldviewthetimelineastwoseparatetimelinesinthevaluation.0123456

D1

D2

D3

D4

D5

D6Growthof16%for3yearsGrowthof8%toinfinity!GrowthPhasesModelExample50NotethatwecanvaluePhase#2usingtheConstantGrowthModel0123

D1

D2

D3

D4

D5

D60123456GrowthPhase#1plustheinfinitelylongPhase#2GrowthPhasesModelExample51NotethatwecannowreplacealldividendsfromYear4toinfinitywiththevalueattimet=3,V3!Simpler!!

V3=

D4

D5

D60123456

D4k-gWecanusethismodelbecausedividendsgrowataconstant8%ratebeginningattheendofYear3.GrowthPhasesModelExample52Nowweonlyneedtofindthefirstfourdividendstocalculatethenecessarycashflows.0123

D1

D2

D3

V30123NewTimeLine

D4k-g

WhereV3=GrowthPhasesModelExample53Determinetheannualdividends.

D0=$3.24(thishasbeenpaidalready)

D1=D0(1+g1)1=$3.24(1.16)1=$3.76D2=D0(1+g1)2=$3.24(1.16)2=$4.36D3=D0(1+g1)3=$3.24(1.16)3=$5.06D4=D3(1+g2)1=$5.06(1.08)1=$5.46GrowthPhasesModelExample54Nowweneedtofindthepresentvalueofthecashflows.0123

3.76

4.36

5.06

780123ActualValues

5.46.15-.08

Where$78

=GrowthPhasesModelExample55WedeterminethePVofcashflows.PV(D1)=D1(PVIF15%,1)=$3.76(.870)=$3.27PV(D2)=D2(PVIF15%,2)=$4.36(.756)=$3.30PV(D3)=D3(PVIF15%,3)=$5.06(.658)=$3.33P3=$5.46/(.15-.08)=$78[CGModel]PV(P3)=P3(PVIF15%,3)=$78(.658)=$51.32GrowthPhasesModelExample56D0(1+.16)tD4Finally,wecalculatetheintrinsicvaluebysummingallthecashflowpresentvalues.(1+

.15)t(.15-.08)V=St=13+1(1+.15)nV=$3.27+$3.30+$3.33+$51.32V=$61.22GrowthPhasesModelExample57JamesConsolCompanycurrentlypaysadividendof$1.60pershareonitscommonstock.Thecompanyexpectstoincreasethedividendata20%annualrateforthefirstfouryearsandata13%forthenextfouryears,andthengrowthedividendata7%

thereafter.Yourequirea16%returntoinvestinthisstock,whatvalueshouldyouplaceonashareofthisstock?

Exercise581.Determinetheexpectedcashflows.2.Replacetheintrinsicvalue(V)withthemarketprice(P0).3.Solveforthemarketrequiredrateofreturnthatequatesthediscountedcashflowstothemarketprice.Stepstocalculatetherateofreturn(oryield).CalculatingRatesofReturn(MarketYields)59

Themarketrequiredrateofreturnonabondiscommonlyreferredtoasthebond’syieldtomaturity.Yieldtomaturity(YTM):istheexpectedrateofreturnonabondifboughtatitscurrentmarketpriceandheldtomaturity.

DeterminingBondYTM60DeterminetheYield-to-Maturity(YTM)forthecoupon-payingbondwithafinitelife.P0=Snt=1(1+kd

)tI=I(PVIFAkd

,n)+MV(PVIFkd

,n)(1+kd

)n+MVkd

=YTMDeterminingBondYTM61JulieMillerwanttodeterminetheYTMforanissueofoutstandingbondsatIBMCorporation.IBMhasanissueof10%annualcouponbondswith15yearslefttomaturity.Thebondshaveacurrentmarketvalueof$1,250.WhatistheYTM?DeterminingYTMExample62$1,250 = $100(PVIFA9%,15)+ $1,000(PVIF9%,15)$1,250 = $100(8.061)+ $1,000(.275)$1,250 = $806.10+$275.00 = $1,081.10 [Rateistoohigh!]YTMSolution(Try9%)63$1,250 = $100(PVIFA7%,15)+ $1,000(PVIF7%,15)$1,250 = $100(9.108)+ $1,000(.362)$1,250 = $910.80+$362.00 = $1,272.80 [Rateistoolow!]YTMSolution(Try7%)64

.07 $1,273

.02

YTM $1,250 $192 .09 $1,081 X $23 .02 $192$23X=YTMSolution(Interpolate)65

.07 $1273 .02 YTM $1250 $192 .09 $1081 ($23)(0.02) $192

$23XX=X=.0024YTM=.07+.0024=.0724or7.24%YTMSolution(Interpolate)66P0=S2nt=1(1+kd

/2)tI/2=(I/2)(PVIFAkd/2,2n)+MV(PVIFkd/2

,2n)+MV[1+(kd

/2)]2-1=(effectiveannual)YTMDeterminetheYield-to-Maturity(YTM)forthesemiannualcoupon-payingbondwithafinitelife.(1+kd

/2)2nDeterminingSemiannualCouponBondYTM67JulieMillerwanttodeterminetheYTMforanotherissueofoutstandingbonds.Thefirmhasanissueof8%semiannualcouponbondswith20yearslefttomaturity.Thebondshaveacurrentmarketvalueof$950.WhatistheYTM?DeterminingSemiannualCouponBondYTMExample

68P0=(I/2)(PVIFAkd/2,2n)+MV(PVIFkd/2

,2n)$950=($80/2)(PVIFAkd/2,

40)+$1000(PVIFkd/2,40)Kd/2=4.2626%Kd=8.5252%DeterminingSemiannualCouponBondYTMExample

69[1+(kd

/2)]2-1=(effectiveannual)YTMDeterminetheYield-to-Maturity(YTM)forthesemiannualcoupon-payingbondwithafinitelife.[1+(.042626)]2-1=.0871

or8.71%DeterminingSemiannualCouponBondYTMExample

70(1)DiscountBond

--Themarketrequiredrateofreturnexceedsthecouponrate(Par>P0).Thepriceofthebondwillbelessthanitsfacevalue.(2)PremiumBond

--Thecouponrateexceedsthemarketrequiredrateofreturn(P0>Par).Thepriceofthebondwillbemorethanitsfacevalue.(3)Par

Bond

--Thecouponrateequalsthemarketrequiredrateofreturn(P0=Par).Thepriceofthebondwillequalitsfacevalue

BondPrice-YieldRelationship71

CouponRateMARKETREQUIREDRATEOFRETURN(%)BONDPRICE($)1000Par160014001200600002468101214161815YearBondPrice-YieldRelationship72BondPrice-YieldRelationshipInterest-rateRisk/YieldRiskThevariationinthemarketpriceofasecuritycausedbychangesininterestratesisinterest-raterisk.Long-termbondshavemorepriceriskthanshort-termbondsLowcouponratebondshavemorepriceriskthanhighcouponratebonds7374Determinetheyieldforpreferredstockwithaninfinitelife.P0

=DP/kP

SolvingforkP

suchthatkP=DP/P0DeterminingYieldonPreferredStock75kP=$10/$100.kP=10%.Assumethattheannualdividendoneachshareofpreferredstockis$10.Eachshareofpreferredstockiscurrentlytradingat$100.Whatistheyieldonpreferredstock?PreferredStockYieldExample76Assumetheconstantgrowthmodelisappropriate.Determinetheyieldonthecommonstock.P0

=D1/(ke-g)Solvingforke

suchthatke=(D1/P0)+g

Fromthisequation,itclearlyshowsthatyieldcomesfromtwosources:dividendyield,D1/P0andexpectedcapitalgainyield,g.DeterminingtheYieldonCommonStock77ke=($3/$30)+5%ke=15%Assumethattheexpecteddividend(D1)oneachshareofcommonstockis$3.Eachshareofcommonstockiscurrentlytradingat$30andhasanexpectedgrowthrateof5%.Whatistheyieldoncommonstock?CommonStockYieldExample78EndofChapter479QuickQuiz1.Whichofthefollowingbestdescribesintrinsicvalue?Thepriceasecurity"oughttohave"basedonallfactorsbearingonvaluation.B.Theamountafirmcouldbesoldforasacontinuingoperatingbusiness.Theamountofmoneythatcouldberealizedifanassetoragroupofassetsissoldseparatelyfromitsoperatingorganization.D.Themarketpriceatwhichanassettrades.80Exercises2.Whatisthemarketvalueofa$1,000face-valuebondwitha10%couponratewhenthemarket’srateofreturnis9%?MorethanitsfacevalueLessthanitsfacevalue$1,000813.BetaBudgetBroomswillpayabig$2dividendnextyearonitscommonstock,whichiscurrentlysellingat$50pershare.Whatisthem