北京大学-公司金融5

Lecture3(2)ValuingStocksThetwomajorsourcesofraisingfundsforcorporationsaredebtandequity.Debtholders’claimsmustbepaidinfullbeforetheclaimsoftheequityholderscanbepaid.Stockholdersreceivedividend,whichistheresidualclaimonthevalueofthefirm.Howcanwedeterminethepriceofastock?1DividendDiscountModel(股利贴现模型)Astockprovidestwokindsofcashflows.First,moststockspaydividendsonaregularbasis.Second,thestockholderreceivesthesalepricewhenshesellsthestock.Onetimeperiodcase:isthedividendpaidatdate1andisthesalepriceattheendofdate1.isthePVofthecommonstockinvestment.isthediscountrateofthestock.rPrDivP+++=111101Div1P0PrStockReturn=DividendYield+CapitalGain(股利收益率)(资本利得收益率)Thissaysthatthereturnonstock(i.e.,thestock’sdiscountrate)equalsthesumofthedividendyieldplustherateofcapitalgain.00101PPPPDivr−+=Butwheredoescomefrom?Thusthevalueofafirm’scommonstocktotheinvestorisequaltothepresentvalueofalltheexpectedfuturedividends.1PrPrDivP+++=11221222210)1()1(1rPrDivrDivP+++++=∑∞=+=++++++=1332210)1(...)1()1(1tttrDivrDivrDivrDivP(1)ZeroGrowthThedividendpaymentisconstantforever.Thevalueofastockwithaconstantdividendis:DivDivDivDiv====...321rDivrDivrDivrDivP1332210...)1()1(1=++++++=(2)ConstantGrowth(DividendGrowthModel)Dividendsgrowatrateg.Thevalueofacommonstockwithdividendsgrowingataconstantrategis:grDivrgDivrgDivrDivP−=++++++++=13212110...)1()1()1()1(1(3)DifferentialGrowthThedividendisexperiencingdifferentgrowthrate.Example1:Supposeastockwhichisexpectedtopayadividendof$2nextyear.Thedividendisprojectedtogrowat5%peryearindefinitely.Ifthediscountrateis15%,whatisthecurrentstockprice?StockpricesensitivitytorequiredreturnStockpricesensitivitytogrowthrate2NPVGOModel2.1GrowthrateandDiscountrate.First,wheredoesgrowthratecomefrom?earningsinincreaseyearthisearningsyearnextearnings+=earningsretainedonreturnyearthisearningsretainedyearthisearningsyearnextearnings×+=ratiopayoutratioplowbackratioretention=−)(1earningsretainedonreturnratioretentiong×=Example2:PagemasterEnterprisesjustreportedearningsof$2million.Itplanstoretain40percentofitsearnings.Thehistoricalreturnonequityhasbeen0.16,afigurethatisexpectedtocontinueintothefuture.Howmuchwillearningsgrowoverthecomingyear?Second,wheredoesthediscountratecomefrom?Thus,thediscountratecanbebrokenintotwoparts.placesthedividendreturnonapercentagebasis,itiscalleddividendyield.Thesecondtermgisthegrowthrateofdividends.gPDivr+=0101PDivExample3:Supposeafirmjustpaidadividendof$1pershareforitsstocks.Itisexpectedtoincreasethedividendby20%inoneyearandby15%intwoyears.Afterthat,dividendswillincreaseataconstantrateof5%peryearindefinitely.Thestockisexpectedtosellat$9.66aftertwoyears.Whataretheexpectedreturnsinyear1andyear2respectively?2.2TheNPVGOModelCase1CashCow(现金牛)Imagineacompanywithalevelstreamofearningspershareinperpetuity.Thecompanypaysalloftheseearningsouttostockholdersasdividends.ThenThevalueofashareofstockwhenfirmactsasacashcowisDivEPS=rDivrEPS=Case2:ThefirmwithgrowthopportunitiesThenetpresentvalueoftheprojectasofdate0isNPVGO,whichstandsforthenetpresentvalueofthegrowthopportunity.Becausethepersharevalueoftheprojectisaddedtotheoriginalstockprice,thestockpriceafterfirmcommitstonewprojectisNPVGOrEPS+Dividingby,wehaveThelefthandsideisprice-earningratio.(P/Eratio,市盈率).Theequationshowsthattheratioisrelatedtothenetpresentvalueofgrowthopportunities.EPSEPSNPVGOrEPSshareperice+=1PrExample4:SarroShipping,Inc.,expectstoearn$1millionperyearinperpetuityifitundertakesnonewinvestmentopportunities.Thereare100,000sharesofstockoutstanding,soearningspershareequal$10.Thefirmwillhaveanopportunityatdate1tospend$1,000,000inanewmarketingcampaign.Thenewcampaignwillincreaseearningsineverysubsequentperiodby$210,000.Thefirm’sdiscountrateis10percent.Whatisthevaluepersharebeforeandafterdecidingtoacceptthemarketingcampaign?3TherelationbetweendividenddiscountmodelandtheNPVGOmodelExample5:CumberlandBookPublishershasEPSof$10attheendofthefirstyear,adividendpayoutratioof40percent,adiscountrateof16percent,andareturnonitsretainedearningsof20percent.Becausethefirmretainssomeofitsearningseachyear,itisselectinggrowthopportunitieseachyear.WewishtocalculatethepricepershareusingboththedividenddiscountmodelandtheNPVGOmodel.RealWorldExample1:1)Itis2001andyouareattemptingtovalueAT&Tequity.Thelongdistancemarketismatureandnewcompetitionmakesgrowthdifficult.Infact,AT&Thasexperiencedlittlegrowthoverthelastfewyears,whichyoubelievewillcontinue.DividendsNogrowthformula:Year1996199719981999DPS0.880.880.880.8860.17$05.088.0%,5)25.17$(57.12$07.088.0%,7=======pricerIfpriceacturalpricerIf2)By2003,AT&T’ssituationhadchanged.Demandforlongdistanceandbroadlandisexpanding.AT&Tdecidestoreinvesthalfitsearnings,equalto$1.50persharein2002.AnalystsforecastthatAT&TwouldearnanROEof15%onitsinvestments.Ifinvestorsrequireda10%rateofreturn,whatisthevalueofAT&T’sstockattheendof2002?Whatinformationdoweneed?GrowthopportunitiesincreaseAT&T’sstockpricefrom$15.00to$32.24,or215%.75.0%5.750.1%50%1520022002==⇒===DivgEPSratioplowbackROE806.0075.175.02003=×=Div24.32$075.010.0806.0$=−=priceAT&TNogrowthGrowthEPS