【財(cái)務(wù)管理英文課件】TheValuationofLongTermSecurities

Chapter4TheValuationofLong-TermSecuritiesChapter4TheValuationofLongTheValuationof Long-TermSecuritiesDistinctionsAmongValuationConceptsBondValuationPreferredStockValuationCommonStockValuationRatesofReturn(orYields)TheValuationof Long-TermSWhatisValue?Going-concernvalue

representstheamountafirmcouldbesoldforasacontinuingoperatingbusiness.Liquidationvalue

representstheamountofmoneythatcouldberealizedifanassetorgroupofassetsissoldseparatelyfromitsoperatingorganization.WhatisValue?Going-concernvaWhatisValue?(2)afirm:totalassetsminusliabilitiesandpreferredstockaslistedonthebalancesheet.Bookvalue

representseither(1)anasset:theaccountingvalueofanasset--theasset‘scostminusitsaccumulateddepreciation;WhatisValue?(2)afirm:totaWhatisValue?Intrinsicvalue

representsthepriceasecurityoughttohave?basedonallfactorsbearingonvaluation.Marketvalue

representsthemarketpriceatwhichanassettrades.WhatisValue?IntrinsicvalueBondValuationImportantTermsTypesofBondsValuationofBondsHandlingSemiannualCompoundingBondValuationImportantTermsImportantBondTermsThematurityvalue

(MV)[orfacevalue]ofabondisthestatedvalue.InthecaseofaU.S.bond,thefacevalueisusually$1,000.Abondisalong-termdebtinstrumentissuedbyacorporationorgovernment.ImportantBondTermsThematuriImportantBondTermsThediscountrate

(capitalizationrate)isdependentontheriskofthebondandiscomposedoftherisk-freerateplusapremiumforrisk.Thebond’scouponrate

isthestatedrateofinterest;theannualinterestpaymentdividedbythebond’sfacevalue.ImportantBondTermsThediscouDifferentTypesofBondsAperpetualbondisabondthatnevermatures.Ithasaninfinitelife.(1+

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

)=I/kd [ReducedForm]DifferentTypesofBondsAperpPerpetualBondExampleBondPhasa$1,000facevalueandprovidesan8%coupon.Theappropriatediscountrateis10%.Whatisthevalueoftheperpetualbond?

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

kd

=10%.

V =I/kd [ReducedForm] =$80/10%=$800.PerpetualBondExampleBondPhDifferentTypesofBondsAnon-zerocouponbondisacouponpayingbondwithafinitelife.(1+

kd)1(1+kd)2(1+kd)nV=++...+II+MVI=nt=1(1+kd)tI=I(PVIFAkd,n)+MV(PVIFkd,n)(1+kd)n+MVDifferentTypesofBondsAnon-BondChasa$1,000facevalueandprovidesan8%annualcouponfor30years.Theappropriatediscountrateis10%.Whatisthevalueofthe

couponbond?

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

$80

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

[TableIV]

[TableII] =$754.16+$57.00 =$811.16.CouponBondExampleBondChasa$1,000facevalueDifferentTypesofBondsAzerocouponbondisabondthatpaysnointerestbutsellsatadeepdiscountfromitsfacevalue;itprovidescompensationtoinvestorsintheformofpriceappreciation.(1+

kd)nV=MV=MV(PVIFkd,n)DifferentTypesofBondsAzero

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

$1,000(.057) =$57.00Zero-CouponBondExampleBondZhasa$1,000facevalueanda30yearlife.Theappropriatediscountrateis10%.Whatisthevalueofthe

zero-couponbond? V =$1,000(PVIF10%,30) =SemiannualCompounding (1)Dividekdby2 (2)Multiplynby2 (3)DivideIby2MostbondsintheU.S.payinteresttwiceayear(1/2oftheannualcoupon).Adjustmentsneeded:SemiannualCompounding (1)D(1+kd/2)2*n(1+

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

2I/

2

+MV=2*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)2(1+kd/2)2*n(1+kd/2)1SemV =$40(PVIFA5%,30)+$1,000(PVIF5%,30) =

$40

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

[TableIV]

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

couponbond?V =$40(PVIFA5%,30)+$1,000PreferredStockisatypeofstockthatpromisesa(usually)fixeddividend,butatthediscretionoftheboardofdirectors.PreferredStockhaspreferenceovercommonstockinthepaymentofdividendsandclaimsonassets.PreferredStockValuationPreferredStockisatypeofsPreferredStockValuationThisreducestoaperpetuity!(1+

kP)1(1+kP)2(1+kP)V=++...+DivPDivPDivP=t=1(1+kP)tDivPorDivP(PVIFAkP,

)V=DivP/kPPreferredStockValuationThisPreferredStockExample

DivP=$100(8%)=$8.00. kP

=10%. V =DivP/kP=$8.00/10% =$80StockPShasan8%,$100parvalueissueoutstanding.Theappropriatediscountrateis10%.Whatisthevalueofthepreferredstock?PreferredStockExample DivPCommonStockValuationProratashareoffutureearnings afterallotherobligationsofthe firm(ifanyremain).Dividendsmaybepaidoutof theproratashareofearnings.Commonstockrepresentsaresidualownershippositioninthecorporation.CommonStockValuationProrataCommonStockValuation (1)Futuredividends (2)Futuresaleofthecommon stocksharesWhatcashflowswillashareholderreceivewhenowningsharesofcommonstock?CommonStockValuation (1)DividendValuationModelBasicdividendvaluationmodelaccountsforthePVofallfuturedividends.(1+

ke)1(1+ke)2(1+ke)V=++...+Div1DivDiv2=t=1(1+ke)tDivtDivt: CashDividend attimetke: Equityinvestor’s requiredreturnDividendValuationModelBasicAdjustedDividendValuationModelThebasicdividendvaluationmodeladjustedforthefuturestocksale.(1+

ke)1(1+ke)2(1+ke)nV=++...+Div1Divn

+PricenDiv2n: Theyearinwhichthefirm’s sharesareexpectedtobesold.Pricen: Theexpectedsharepricein yearn.AdjustedDividendValuationMoDividendGrowthPatternAssumptionsThedividendvaluationmodelrequirestheforecastofallfuturedividends.Thefollowingdividendgrowthrateassumptionssimplifythevaluationprocess.ConstantGrowthNoGrowthGrowthPhasesDividendGrowthPatternAssumpConstantGrowthModelTheconstantgrowthmodelassumesthatdividendswillgrowforeverattherateg.(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)2ConstantGrowthModelTheconstConstantGrowthModelExampleStockCGhasanexpectedgrowthrateof8%.Eachshareofstockjustreceivedanannual$3.24dividendpershare.Theappropriatediscountrateis15%.Whatisthevalueofthecommonstock?D1 =$3.24(1+.08)=$3.50VCG =D1/(ke

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

ke)1(1+ke)2(1+ke)V=++...+D1D=keD1D1: Dividendpaidattime1.ke: Investor’srequiredreturn.D2ZeroGrowthModelThezerogrowZeroGrowth ModelExampleStockZGhasanexpectedgrowthrateof0%.Eachshareofstockjustreceivedanannual$3.24dividendpershare.Theappropriatediscountrateis15%.Whatisthevalueofthecommonstock?D1 =$3.24(1+0)=$3.24VZG =D1/(ke

-0)=$3.24/(.15-0) =$21.60ZeroGrowth ModelExampleStD0(1+g1)tDn(1+g2)tGrowthPhasesModelThegrowthphasesmodelassumesthatdividendsforeachsharewillgrowattwoormoredifferentgrowthrates.(1+

ke)t(1+ke)tV=t=1nt=n+1+D0(1+g1)tDn(1+g2)tGrowthPhaseD0(1+g1)tDn+1GrowthPhasesModelNotethatthesecondphaseofthegrowthphasesmodelassumesthatdividendswillgrowataconstantrateg2.Wecanrewritetheformulaas:(1+

ke)t(ke

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

ke)nD0(1+g1)tDn+1GrowthPhasesModGrowthPhasesModelExampleStockGPhasanexpectedgrowthrateof16%forthefirst3yearsand8%thereafter.Eachshareofstockjustreceivedanannual$3.24dividendpershare.Theappropriatediscountrateis15%.Whatisthevalueofthecommonstockunderthisscenario?GrowthPhasesModelExampleStoGrowthPhasesModelExampleFirst,determinetheannualdividend.

D0=$3.24

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=$5.46GrowthPhasesModelExampleFirGrowthPhasesModelExampleSecond,determinethePVofcashflows.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)=$51.32GrowthPhasesModelExampleSecD0(1+.16)tD4GrowthPhases ModelExampleThird,calculatetheintrinsicvaluebysummingallofcashflowpresentvalues.(1+

.15)t(.15-.08)V=t=13+1(1+.15)nV=$3.27+$3.30+$3.33+$51.32V=$61.22D0(1+.16)tD4GrowthPhases MoCalculatingRatesofReturn(orYields)1.Determinetheexpectedcashflows.2.Replacetheintrinsicvalue(V)withthemarketprice(P0).3.Solveforthemarketrequiredrateofreturnthatequatesthediscountedcashflowstothemarketprice.Stepstocalculatetherateofreturn(orYield).CalculatingRatesofReturn(oDeterminingBondYTMDeterminetheYield-to-Maturity(YTM)forthecouponpayingbondwithafinitelife.P0=nt=1(1+kd

)tI=I(PVIFAkd

,n)+MV(PVIFkd

,n)(1+kd

)n+MVkd

=YTMDeterminingBondYTMDetermineDeterminingtheYTMJulieMillerwanttodeterminetheYTMforanissueofoutstandingbondsatBasketWonders(BW).BWhasanissueof10%annualcouponbondswith15yearslefttomaturity.Thebondshaveacurrentmarketvalueof$1,250.WhatistheYTM?DeterminingtheYTMJulieMilleYTMSolution(Try9%)$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%)$1,250 =YTMSolution(Try7%)$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%)$1,250 = .07 $1,273

.02

IRR

$1,250

$192 .09 $1,081 X

$23

.02

$192YTMSolution(Interpolate)$23X= .07 $1,273YTMSolution(In

.07 $1,273

.02

IRR

$1,250

$192

.09 $1,081

X

$23

.02

$192YTMSolution(Interpolate)$23X= .07 $1,273YTMSolution(In .07 $1273 .02 YTM $1250 $192 .09 $1081 ($23)(0.02) $192

YTMSolution(Interpolate)$23XX=X=.0024YTM=.07+.0024=.0724or7.24% .07 $1273YTMSolution(IntDeterminingSemiannualCouponBondYTMP0=2nt=1(1+kd

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

,2n)+MV[1+(kd

/2)2]-1=YTMDeterminetheYield-to-Maturity(YTM)forthesemiannualcouponpayingbondwithafinitelife.(1+kd

/2)2nDeterminingSemiannualCouponBondPrice-YieldRelationshipDiscountBond

--Themarketrequiredrateofreturnexceedsthecouponrate(Par>P0).PremiumBond

--Thecouponrateexceedsthemarketrequiredrateofreturn(P0>Par).ParBond

--Thecouponrateequalsthemarketrequiredrateofreturn(P0=Par).BondPrice-YieldRelationshiBondPrice-YieldRelationshipCouponRateMARKETREQUIREDRATEOFRETURN(%)BONDPRICE($)1000Par16001400120060000246810121416185Year15YearBondPrice-YieldRelationshiBondPrice-YieldRelationshipAssumethattherequiredrateofreturnona15year,10%couponpayingbondrisesfrom10%to12%.Whathappenstothebondprice?Wheninterestratesrise,thenthemarketrequiredratesofreturnriseandbondpriceswillfall.BondPrice-YieldRelationshipABondPrice-YieldRelationshipCouponRateMARKETREQUIREDRATEOFRETURN(%)BONDPRICE($)1000Par160014001200600002468101214161815Year5YearBondPrice-YieldRelationshiBondPrice-YieldRelationship(RisingRates)Therefore,thebondpricehasfallenfrom$1,000to$864.10.Therequiredrateofreturnona15year,10%couponpayingbondhasrisenfrom10%to12%.BondPrice-YieldRelationshipBondPrice-YieldRelationshipAssumethattherequiredrateofreturnona15year,10%couponpayingbondfallsfrom10%to8%.Whathappenstothebondprice?Wheninterestratesfall,thenthemarketrequiredratesofreturnfallandbondpriceswillrise.BondPrice-YieldRelationshipABondPrice-YieldRelationshipCouponRateMARKETREQUIREDRATEOFRETURN(%)BONDPRICE($)1000Par160014001200600002468101214161815Year5YearBondPrice-YieldRelationshiBondPrice-YieldRelationship(DecliningRates)Therefore,thebondpricehasrisen

from$1000to$1171.Therequiredrateofreturnona15year,10%couponpayingbondhasfallenfrom10%to8%.BondPrice-YieldRelationshipTheRoleofBondMaturityAssumethattherequiredrateofreturnonboththe5and15year,10%couponpayingbondsfallfrom10%to8%.Whathappenstothechangesinbondprices?Thelongerthebondmaturity,thegreaterthechangeinbondpriceforagivenchangeinthemarketrequiredrateofreturn.TheRoleofBondMaturityAssumBondPrice-YieldRelationshipCouponRateMARKETREQUIREDRATEOFRETURN(%)BONDPRICE($)1000Par160014001200600002468101214161815Year5YearBondPrice-YieldRelationshiTheRoleofBondMaturityThe5yearbondpricehasrisenfrom$1,000to$1,080.30forthe5yearbond(+8.0%).The15yearbondpricehasrisen

from$1,000to$1,171(+17.1%).Twiceasfast!Therequiredrateofreturnonboththe5and15year,10%couponpayingbondshasfallenfrom10%to8%.TheRoleofBondMaturityThe5TheRoleoftheCouponRateForagivenchangeinthemarketrequiredrateofreturn,thepriceofabondwillchangebyproportionallymore,the

lowerthecouponrate.TheRoleoftheCouponRateForExampleoftheRoleoftheCouponRateAssumethatthemarketrequiredrateofreturnontwoequallyrisky15yearbondsis10%.ThecouponrateforBondHis10%andBond

Lis8%.Whatistherateofchangeineachofthebondpricesifmarketrequiredratesfallto8%?ExampleoftheRoleoftheCouExampleoftheRoleoftheCouponRateThepriceforBondHwillrisefrom$1,000to$1,171(+17.1%).ThepriceforBondLwillrisefrom$847.88to$1,000(+17.9%).FasterRise!ThepriceonBondHandLpriortothechangeinthemarketrequiredrateofreturnis$1,000and$847.88respectively.ExampleoftheRoleoftheCouDeterminingtheYieldonPreferredStockDeterminetheyieldforpreferredstockwithaninfinitelife.P0

=DivP/kP

SolvingforkP

suchthatkP=DivP/P0DeterminingtheYieldonPrefePreferredStockYieldExamplekP=$10/$100.kP=10%.Assumethattheannualdividendoneachshareofpreferredstockis$10.Eachshareofpreferredstockiscurrentlytradingat$100.Whatistheyieldonpreferredstock?PreferredStockYieldExamplekDeterminingtheYieldonCommonStockAssumetheconstantgrowthmodelisappropriate.Determinetheyieldonthecommonstock.P0

=D1/(ke-g)Solvingforke

suchthatke=(D1/P0)+g

DeterminingtheYieldonCommoCommonStockYieldExampleke=($3/$30)+5%ke=15%Assumethattheexpecteddividend(D1)oneachshareofcommonstockis$3.Eachshareofcommonstockiscurrentlytradingat$30andhasanexpectedgrowthrateof5%.Whatistheyieldoncommonstock?CommonStockYieldExampleke=Chapter4TheValuationofLong-TermSecuritiesChapter4TheValuationofLongTheValuationof Long-TermSecuritiesDistinctionsAmongValuationConceptsBondValuationPreferredStockValuationCommonStockValuationRatesofReturn(orYields)TheValuationof Long-TermSWhatisValue?Going-concernvalue

representstheamountafirmcouldbesoldforasacontinuingoperatingbusiness.Liquidationvalue

representstheamountofmoneythatcouldberealizedifanassetorgroupofassetsissoldseparatelyfromitsoperatingorganization.WhatisValue?Going-concernvaWhatisValue?(2)afirm:totalassetsminusliabilitiesandpreferredstockaslistedonthebalancesheet.Bookvalue

representseither(1)anasset:theaccountingvalueofanasset--theasset‘scostminusitsaccumulateddepreciation;WhatisValue?(2)afirm:totaWhatisValue?Intrinsicvalue

representsthepriceasecurityoughttohave?basedonallfactorsbearingonvaluation.Marketvalue

representsthemarketpriceatwhichanassettrades.WhatisValue?IntrinsicvalueBondValuationImportantTermsTypesofBondsValuationofBondsHandlingSemiannualCompoundingBondValuationImportantTermsImportantBondTermsThematurityvalue

(MV)[orfacevalue]ofabondisthestatedvalue.InthecaseofaU.S.bond,thefacevalueisusually$1,000.Abondisalong-termdebtinstrumentissuedbyacorporationorgovernment.ImportantBondTermsThematuriImportantBondTermsThediscountrate

(capitalizationrate)isdependentontheriskofthebondandiscomposedoftherisk-freerateplusapremiumforrisk.Thebond’scouponrate

isthestatedrateofinterest;theannualinterestpaymentdividedbythebond’sfacevalue.ImportantBondTermsThediscouDifferentTypesofBondsAperpetualbondisabondthatnevermatures.Ithasaninfinitelife.(1+

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

)=I/kd [ReducedForm]DifferentTypesofBondsAperpPerpetualBondExampleBondPhasa$1,000facevalueandprovidesan8%coupon.Theappropriatediscountrateis10%.Whatisthevalueoftheperpetualbond?

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

kd

=10%.

V =I/kd [ReducedForm] =$80/10%=$800.PerpetualBondExampleBondPhDifferentTypesofBondsAnon-zerocouponbondisacouponpayingbondwithafinitelife.(1+

kd)1(1+kd)2(1+kd)nV=++...+II+MVI=nt=1(1+kd)tI=I(PVIFAkd,n)+MV(PVIFkd,n)(1+kd)n+MVDifferentTypesofBondsAnon-BondChasa$1,000facevalueandprovidesan8%annualcouponfor30years.Theappropriatediscountrateis10%.Whatisthevalueofthe

couponbond?

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

$80

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

[TableIV]

[TableII] =$754.16+$57.00 =$811.16.CouponBondExampleBondChasa$1,000facevalueDifferentTypesofBondsAzerocouponbondisabondthatpaysnointerestbutsellsatadeepdiscountfromitsfacevalue;itprovidescompensationtoinvestorsintheformofpriceappreciation.(1+

kd)nV=MV=MV(PVIFkd,n)DifferentTypesofBondsAzero

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

$1,000(.057) =$57.00Zero-CouponBondExampleBondZhasa$1,000facevalueanda30yearlife.Theappropriatediscountrateis10%.Whatisthevalueofthe

zero-couponbond? V =$1,000(PVIF10%,30) =SemiannualCompounding (1)Dividekdby2 (2)Multiplynby2 (3)DivideIby2MostbondsintheU.S.payinteresttwiceayear(1/2oftheannualcoupon).Adjustmentsneeded:SemiannualCompounding (1)D(1+kd/2)2*n(1+

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

2I/

2

+MV=2*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)2(1+kd/2)2*n(1+kd/2)1SemV =$40(PVIFA5%,30)+$1,000(PVIF5%,30) =

$40

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

[TableIV]

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

couponbond?V =$40(PVIFA5%,30)+$1,000PreferredStockisatypeofstockthatpromisesa(usually)fixeddividend,butatthediscretionoftheboardofdirectors.PreferredStockhaspreferenceovercommonstockinthepaymentofdividendsandclaimsonassets.PreferredStockValuationPreferredStockisatypeofsPreferredStockValuationThisreducestoaperpetuity!(1+

kP)1(1+kP)2(1+kP)V=++...+DivPDivPDivP=t=1(1+kP)tDivPorDivP(PVIFAkP,

)V=DivP/kPPreferredStockValuationThisPreferredStockExample

DivP=$100(8%)=$8.00. kP

=10%. V =DivP/kP=$8.00/10% =$80StockPShasan8%,$100parvalueissueoutstanding.Theappropriatediscountrateis10%.Whatisthevalueofthepreferredstock?PreferredStockExample DivPCommonStockValuationProratashareoffutureearnings afterallotherobligationsofthe firm(ifanyremain).Dividendsmaybepaidoutof theproratashareofearnings.Commonstockrepresentsaresidualownershippositioninthecorporation.CommonStockValuationProrataCommonStockValuation (1)Futuredividends (2)Futuresaleofthecommon stocksharesWhatcashflowswillashareholderreceivewhenowningsharesofcommonstock?CommonStockValuation (1)DividendValuationModelBasicdividendvaluationmodelaccountsforthePVofallfuturedividends.(1+

ke)1(1+ke)2(1+ke)V=++...+Div1DivDiv2=t=1(1+ke)tDivtDivt: CashDividend attimetke: Equityinvestor’s requiredreturnDividendValuationModelBasicAdjustedDividendValuationModelThebasicdividendvaluationmodeladjustedforthefuturestocksale.(1+

ke)1(1+ke)2(1+ke)nV=++...+Div1Divn

+PricenDiv2n: Theyearinwhichthefirm’s sharesareexpectedtobesold.Pricen: Theexpectedsharepricein yearn.AdjustedDividendValuationMoDividendGrowthPatternAssumptionsThedividendvaluationmodelrequirestheforecastofallfuturedividends.Thefollowingdividendgrowthrateassumptionssimplifythevaluationprocess.ConstantGrowthNoGrowthGrowthPhasesDividendGrowthPatternAssumpConstantGrowthModelTheconstantgrowthmodelassumesthatdividendswillgrowforeverattherateg.(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)2ConstantGrowthModelTheconstConstantGrowthModelExampleStockCGhasanexpectedgrowthrateof8%.Eachshareofstockjustreceivedanannual$3.24dividendpershare.Theappropriatediscountrateis15%.Whatisthevalueofthecommonstock?D1 =$3.24(1+.08)=$3.50VCG =D1/(ke

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

ke)1(1+ke)2(1+ke)V=++...+D1D=keD1D1: Dividendpaidattime1.ke: Investor’srequiredreturn.D2ZeroGrowthModelThezerogrowZeroGrowth ModelExampleStockZGhasanexpectedgrowthrateof0%.Eachshareofstockjustreceivedanannual$3.24dividendpershare.Theappropriatediscountrateis15%.Whatisthevalueofthecommonstock?D1 =$3.24(1+0)=$3.24VZG =D1/(ke

-0)=$3.24/(.15-0) =$21.60ZeroGrowth ModelExampleStD0(1+g1)tDn(1+g2)tGrowthPhasesModelThegrowthphasesmodelassumesthatdividendsforeachsharewillgrowattwoormoredifferentgrowthrates.(1+

ke)t(1+ke)tV=t=1nt=n+1+D0(1+g1)tDn(1+g2)tGrowthPhaseD0(1+g1)tDn+1GrowthPhasesModelNotethatthesecondphaseofthegrowthphasesmodelassumesthatdividendswillgrowataconstantrateg2.Wecanrewritetheformulaas:(1+

ke)t(ke

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

ke)nD0(1+g1)tDn+1GrowthPhasesModGrowthPhasesModelExampleStockGPhasanexpectedgrowthrateof16%forthefirst3yearsand8%thereafter.Eachshareofstockjustreceivedanannual$3.24dividendpershare.Theappropriatediscountrateis15%.Whatisthevalueofthecommonstockunderthisscenario?GrowthPhasesModelExampleStoGrowthPhasesModelExampleFirst,determinetheannualdividend.

D0=$3.24

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)