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CHAPTER6STOCKVALUATIONAnswerstoConceptsReviewandCriticalThinkingQuestions1.Thevalueofanyinvestmentdependsonitscashflows;i.e.,whatinvestorswillactuallyreceive.Thecashflowsfromashareofstockarethedividends.2.Investorsbelievethecompanywilleventuallystartpayingdividends(orbesoldtoanothercompany).3.Ingeneral,companiesthatneedthecashwilloftenforgodividendssincedividendsareacashexpense.Young,growingcompanieswithprofitableinvestmentopportunitiesareoneexample;anotherexampleisacompanyinfinancialdistress.Thisquestionisexaminedindepthinalaterchapter.4.Thegeneralmethodforvaluingashareofstockistofindthepresentvalueofallexpectedfuturedividends.Thedividendgrowthmodelpresentedinthetextisonlyvalid(i)ifdividendsareexpectedtooccurforever;thatis,thestockprovidesdividendsinperpetuity,and(ii)ifaconstantgrowthrateofdividendsoccursforever.Aviolationofthefirstassumptionmightbeacompanythatisexpectedtoceaseoperationsanddissolveitselfsomefinitenumberofyearsfromnow.Thestockofsuchacompanywouldbevaluedbyapplyingthegeneralmethodofvaluationexplainedinthischapter.Aviolationofthesecondassumptionmightbeastart-upfirmthatisn’tcurrentlypayinganydividends,butisexpectedtoeventuallystartmakingdividendpaymentssomenumberofyearsfromnow.Thisstockwouldalsobevaluedbythegeneraldividendvaluationmethodexplainedinthischapter.5.Thecommonstockprobablyhasahigherpricebecausethedividendcangrow,whereasitisfixedonthepreferred.However,thepreferredislessriskybecauseofthedividendandliquidationpreference,soitispossiblethepreferredcouldbeworthmore,dependingonthecircumstances.6.Thetwocomponentsarethedividendyieldandthecapitalgainsyield.Formostcompanies,thecapitalgainsyieldislarger.Thisiseasytoseeforcompaniesthatpaynodividends.Forcompaniesthatdopaydividends,thedividendyieldsarerarelyoverfivepercentandareoftenmuchless.7.Yes.Ifthedividendgrowsatasteadyrate,sodoesthestockprice.Inotherwords,thedividendgrowthrateandthecapitalgainsyieldarethesame.8.Thethreefactorsare:1)Thecompany’sfuturegrowthopportunities.2)Thecompany’slevelofrisk,whichdeterminestheinterestrateusedtodiscountcashflows.3)Theaccountingmethodused.9.Inacorporateelection,youcanbuyvotes(bybuyingshares),somoneycanbeusedtoinfluenceorevendeterminetheoutcome.Manywouldarguethesameistrueinpoliticalelections,but,inprincipleatleast,noonehasmorethanonevote.10.Itwouldn’tseemtobe.Investorswhodon’tlikethevotingfeaturesofaparticularclassofstockareundernoobligationtobuyit.11.Investorsbuysuchstockbecausetheywantit,recognizingthattheshareshavenovotingpower.Presumably,investorspayalittlelessforsuchsharesthantheywouldotherwise.12.Presumably,thecurrentstockvaluereflectstherisk,timingandmagnitudeofallfuturecashflows,bothshort-termandlong-term.Ifthisiscorrect,thenthestatementisfalse.SolutionstoQuestionsandProblemsNOTE:Allend-of-chapterproblemsweresolvedusingaspreadsheet.Manyproblemsrequiremultiplesteps.Duetospaceandreadabilityconstraints,whentheseintermediatestepsareincludedinthissolutionsmanual,roundingmayappeartohaveoccurred.However,thefinalanswerforeachproblemisfoundwithoutroundingduringanystepintheproblem.Basic1.Theconstantdividendgrowthmodelis:Pt=Dt×(1+g)/(R–g)So,thepriceofthestocktodayis:P0=D0(1+g)/(R–g)=€1.40(1.06)/(.12–.06)=€24.73Thedividendatyear4isthedividendtodaytimestheFVIFforthegrowthrateindividendsandfouryears,so:P3=D3(1+g)/(R–g)=D0(1+g)4/(R–g)=€1.40(1.06)4/(.12–.06)=€29.46WecandothesamethingtofindthedividendinYear16,whichgivesusthepriceinYear15,so:P15=D15(1+g)/(R–g)=D0(1+g)16/(R–g)=€1.40(1.06)16/(.12–.06)=€59.27Thereisanotherfeatureoftheconstantdividendgrowthmodel:Thestockpricegrowsatthedividendgrowthrate.So,ifweknowthestockpricetoday,wecanfindthefuturevalueforanytimeinthefuturewewanttocalculatethestockprice.Inthisproblem,wewanttoknowthestockpriceinthreeyears,andwehavealreadycalculatedthestockpricetoday.Thestockpriceinthreeyearswillbe:P3=P0(1+g)3=€24.73(1+.06)3=€29.46Andthestockpricein20yearswillbe:P15=P0(1+g)20=€24.73(1+.06)20=€79.312.Weneedtofindtherequiredreturnofthestock.Usingtheconstantgrowthmodel,wecansolvetheequationforR.Doingso,wefind:R=(D1/P0)+g=($3.10/$50.00)+.05=11.20%3.Thedividendyieldisthedividendnextyeardividedbythecurrentprice,sothedividendyieldis:Dividendyield=D1/P0=$3.10/$50.00=6.20%Thecapitalgainsyield,orpercentageincreaseinthestockprice,isthesameasthedividendgrowthrate,so:Capitalgainsyield=5%4.Usingtheconstantgrowthmodel,wefindthepriceofthestocktodayis:P0=D1/(R–g)=£3.60/(.13–.062)=£52.945.Therequiredreturnofastockismadeupoftwoparts:Thedividendyieldandthecapitalgainsyield.So,therequiredreturnofthisstockis:R=Dividendyield+Capitalgainsyield=.039+.09=9.90%6.Weknowthestockhasarequiredreturnof14percent,andthedividendandcapitalgainsyieldareequal,so:Dividendyield=1/2(.14)=.07=CapitalgainsyieldNowweknowboththedividendyieldandcapitalgainsyield.Thedividendissimplythestockpricetimesthedividendyield,so:D1=.07(元70)=元4.90Thisisthedividendnextyear.Thequestionasksforthedividendthisyear.Usingtherelationshipbetweenthedividendthisyearandthedividendnextyear:D1=D0(1+g)Wecansolveforthedividendthatwasjustpaid:元4.90=D0(1+.07)D0=元4