1984-A-Simplified-Common-Stock--Valuation-Model

CFAInstituteASimplifiedCommonStockValuationModelAuthor(s):RussellJ.FullerandChi-ChengHsiaSource:FinancialAnalystsJournal,Vol.40,No.5(Sep.-Oct.,1984),pp.49-56Publishedby:CFAInstituteStableURL::19/10/201021:09YouruseoftheJSTORarchiveindicatesyouracceptanceofJSTOR'sTermsandConditionsofUse,availableat://=cfa.EachcopyofanypartofaJSTORtransmissionmustcontainthesamecopyrightnoticethatappearsonthescreenorprintedpageofsuchtransmission.JSTORisanot-for-profitservicethathelpsscholars,researchers,andstudentsdiscover,use,andbuilduponawiderangeofcontentinatrusteddigitalarchive.Weuseinformationtechnologyandtoolstoincreaseproductivityandfacilitatenewformsofscholarship.FormoreinformationaboutJSTOR,[e-mail]ingwithJSTORtodigitize,preserveandextendaccesstoFinancialAnalystsJournal.(orincreases)inalinearfashionfromanabove-normal(orbelow-normal)ratetoanormal,long-termrate.Givenestimatesofthesetwogrowthrates,thelengthoftheperiodofabove-normalgrowth,andthediscountrate,ananalystmayusetheH-modeltosolveforcurrentstockprice.Likethepopularthree-phasemodel,theH-modelallowsforchangingdividendgrowthratesovertime.TheH-modelthusyieldsresultssimilartothoseofthethree-phasemodel.ButtheH-modelismucheasiertouse,requiringonlysimplearithmetic.Furthermore,itallowsfordirectsolutionofthediscountrate,orcostofequity,whereasmorecomplicatedmodelscangivenumericalsolutionsonlythroughtrialanderror.SECURITYANALYSTSNEEDcommonstockvaluationmodelstoestimatecor-rectpricesforsharesofcommonstockandtodeterminethestock'sexpectedreturn,givenitscurrentprice.Ideally,practitioners-andacademics-wouldlikeamodelthat(1)isconceptuallysound,(2)requiresrelativelyfewestimates,(3)allowssomeflexibilityindescrib-ingdividendgrowthratepatterns,and(4)al-lowsstraightforwardcalculationofeithertheprice(giventhediscountrate)orthediscountrate(giventheprice).Noneofthecommonvaluationmodelscurrentlyinusesatisfiesmorethanthreeoftheseobjectives.TheH-model,describedbelow,satisfiesallfour.CurrentModelsThegeneraldividenddiscountmodelstatesthatcurrentstockpriceequalsthepresentvalueofallexpecteddividends.Thisisstatedmathemat-icallyas:P0=t=I(I+r)twherePo=thecurrentstockprice,D,=expecteddividendinperiodt,andr=theappropriatediscountrate.Althoughtheoreticallysound,thedividenddis-countmodelisnotpracticalbecauseitrequirestheestimatesofaninfinite,oratleastaverylong,dividendstream.Inaddition,itdoesnotallowfordirectsolutionofthediscountrate.Themorepracticalconstantgrowthdividenddiscountmodelgreatlysimplifiestheproblemofestimatingfuturedividends.Itassumesthatdividendsgrowataconstantrateforever,sothatthepriceofashareofcommonstockmaybecalculatedasfollows:pDO(1+g)(2)r-gwhereDo=thedividendpaidinthemostrecent12monthsandRussellFullerisVicePresidentofConnersInvestorServ-icesandChi-ChengHsiaisProfessorofFinanceatWash-ingtonStateUniversity.FINANCIALANALYSTSJOURNAL/SEPTEMBER-OCTOBER1984O49FigureAConstantGrowthModel9tg:tg=theconstant,perpetualdividendgrowthrate.FigureAillustratesthepatternofdividendgrowthratesovertime(ge)accordingtotheconstantgrowthmodel.Inadditiontosimplicity,oneoftheadvan-tagesoftheconstantgrowthmodelisthatitallowsfordirectsolutionofthediscountrate,giventhecurrentstockpriceandanestimateofg.OnemerelyhastorearrangethetermsofEquation(2)toget:Do(I+g)+g(3)P0Theproblemwiththeconstantgrowthmod-el,however,isthatdividendgrowthratesarenotconstant.Thegrowthratesofmanystocksfluctuatesomuchthattheconstantgrowthmodelcannotevenprovideagoodfirstapproxi-mation.Securityanalystshavedevelopedalternativevaluationmodelsthattendtobemorecompli-catedthantheconstantgrowthmodelbutnotascomplexasthegeneraldividenddiscountmod-el.Thethree-phasedividenddiscountmodel,forexample,isbasedonadividendgrowthratepatternsimilartothatillustratedinFigureB.1InPhase1,dividendsareexpectedtogrowataconstantrate(denotedgj)foraperiodofAyears.DuringPhase2(atransitionphaselastingforB-Ayears),thedividendgrowthratedeclinesinalinearfashiontoaconstantgrowthrate(gn),whichisassumedtopersistfromtheyearBonward.2Thusgnmaybethoughtofasalong-run,steady-state,ornormalgrowthrateforthefirm.Inpractice,thethree-phasemodelallowsforcalculationofallfuturedividends,givenesti-matesofthegrowthratedu