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CorporateFinanceRoss Westerfield Jaffe SixthEdition ChapterOutline 5 1DefinitionandExampleofaBond5 2HowtoValueBonds5 3Bondconcepts5 4ThePresentValueofCommonStocks5 5EstimatesofParametersintheDividend DiscountModel5 6GrowthOpportunities5 7TheDividendGrowthModelandtheNPVGOModel Advanced 5 8PriceEarningsRatio5 9StockMarketReporting5 10SummaryandConclusions ValuationofBondsandStock FirstPrinciples Valueoffinancialsecurities PVofexpectedfuturecashflowsTovaluebondsandstocksweneedto Estimatefuturecashflows Size howmuch andTiming when Discountfuturecashflowsatanappropriaterate Therateshouldbeappropriatetotheriskpresentedbythesecurity 5 1DefinitionandExampleofaBond Abondisalegallybindingagreementbetweenaborrowerandalender Specifiestheprincipalamountoftheloan Specifiesthesizeandtimingofthecashflows Indollarterms fixed rateborrowing Asaformula adjustable rateborrowing 5 1DefinitionandExampleofaBond ConsideraU S governmentbondlistedas63 8ofDecember2009 TheParValueofthebondis 1 000 Couponpaymentsaremadesemi annually June30andDecember31forthisparticularbond Sincethecouponrateis63 8thepaymentis 31 875 OnJanuary1 2002thesizeandtimingofcashflowsare 5 2HowtoValueBonds Identifythesizeandtimingofcashflows Discountatthecorrectdiscountrate PureDiscountBonds Informationneededforvaluingpurediscountbonds Timetomaturity T Maturitydate today sdateFacevalue F Discountrate r Presentvalueofapurediscountbondattime0 PureDiscountBonds Example Findthevalueofa30 yearzero couponbondwitha 1 000parvalueandadiscountrateof6 Level CouponBonds Informationneededtovaluelevel couponbonds Couponpaymentdatesandtimetomaturity T Couponpayment C perperiodandFacevalue F Discountrate ValueofaLevel couponbond PVofcouponpaymentannuity PVoffacevalue Level CouponBonds Example Findthepresentvalue asofJanuary1 2002 ofa6 3 8couponT bondwithsemi annualpayments andamaturitydateofDecember2009ifthediscountrateis5 percent OnJanuary1 2002thesizeandtimingofcashflowsare 5 3BondConcepts Bondpricesandmarketinterestratesmoveinoppositedirections 2 Whencouponrate YTM yieldtomaturity price parvalue Whencouponrate YTM price parvalue premiumbond Whencouponrate YTM price parvalue discountbond Abondwithlongermaturityhashigherrelative pricechangethanonewithshortermaturitywheninterestrate YTM changes Allotherfeaturesareidentical 4 AlowercouponbondhasahigherrelativepricechangethanahighercouponbondwhenYTMchanges Allotherfeaturesareidentical YTMandBondValue 800 1000 1100 1200 1300 1400 0 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 0 1 DiscountRate BondValue WhentheYTM coupon thebondtradesatapremium WhentheYTM coupon thebondtradesatpar WhentheYTM coupon thebondtradesatadiscount MaturityandBondPriceVolatility Considertwootherwiseidenticalbonds Thelong maturitybondwillhavemuchmorevolatilitywithrespecttochangesinthediscountrate CouponRateandBondPriceVolatility Considertwootherwiseidenticalbonds Thelow couponbondwillhavemuchmorevolatilitywithrespecttochangesinthediscountrate 5 4ThePresentValueofCommonStocks DividendsversusCapitalGainsValuationofDifferentTypesofStocksZeroGrowthConstantGrowthDifferentialGrowth Case1 ZeroGrowth Assumethatdividendswillremainatthesamelevelforever Sincefuturecashflowsareconstant thevalueofazerogrowthstockisthepresentvalueofaperpetuity Case2 ConstantGrowth Sincefuturecashflowsgrowataconstantrateforever thevalueofaconstantgrowthstockisthepresentvalueofagrowingperpetuity Assumethatdividendswillgrowataconstantrate g forever i e Case3 DifferentialGrowth Assumethatdividendswillgrowatdifferentratesintheforeseeablefutureandthenwillgrowataconstantratethereafter TovalueaDifferentialGrowthStock weneedto Estimatefuturedividendsintheforeseeablefuture EstimatethefuturestockpricewhenthestockbecomesaConstantGrowthStock case2 Computethetotalpresentvalueoftheestimatedfuturedividendsandfuturestockpriceattheappropriatediscountrate Case3 DifferentialGrowth Assumethatdividendswillgrowatrateg1forNyearsandgrowatrateg2thereafter Case3 DifferentialGrowth Dividendswillgrowatrateg1forNyearsandgrowatrateg2thereafter 012 NN 1 Case3 DifferentialGrowth Wecanvaluethisasthesumof anN yearannuitygrowingatrateg1 plusthediscountedvalueofaperpetuitygrowingatrateg2thatstartsinyearN 1 Case3 DifferentialGrowth TovalueaDifferentialGrowthStock wecanuse ADifferentialGrowthExample Acommonstockjustpaidadividendof 2 Thedividendisexpectedtogrowat8 for3years thenitwillgrowat4 inperpetuity Whatisthestockworth WiththeFormula ADifferentialGrowthExample continued 01234 0123 Theconstantgrowthphasebeginninginyear4canbevaluedasagrowingperpetuityattime3 5 5EstimatesofParametersintheDividend DiscountModel Thevalueofafirmdependsuponitsgrowthrate g anditsdiscountrate r Wheredoesgcomefrom Wheredoesrcomefrom FormulaforFirm sGrowthRate g Retentionratio Returnonretainedearnings Wheredoesrcomefrom Thediscountratecanbebrokenintotwoparts ThedividendyieldThegrowthrate individends Inpractice thereisagreatdealofestimationerrorinvolvedinestimatingr 5 6GrowthOpportunities GrowthopportunitiesareopportunitiestoinvestinpositiveNPVprojects Thevalueofafirmcanbeconceptualizedasthesumofthevalueofafirmthatpaysout100 percentofitsearningsasdividendsandthenetpresentvalueofthegrowthopportunities 5 7TheDividendGrowthModelandtheNPVGOModel Advanced Wehavetwowaystovalueastock Thedividenddiscountmodel Thepriceofashareofstockcanbecalculatedasthesumofitspriceasacashcowplustheper sharevalueofitsgrowthopportunities TheDividendGrowthModelandtheNPVGOModel ConsiderafirmthathasEPSof 5attheendofthefirstyear adividend payoutratioof30 adiscountrateof16 percent andareturnonretainedearningsof20 percent Thedividendatyearonewillbe 5 30 1 50pershare Theretentionratiois 70 1 30 implyingagrowthrateindividendsof14 70 20 Fromthedividendgrowthmodel thepriceofashareis TheNPVGOModel First wemustcalculatethevalueofthefirmasacashcow Second wemustcalculatethevalueofthegrowthopportunities Finally 5 8PriceEarningsRatio Manyanalystsfrequentlyrelateearningspersharetoprice Thepriceearningsratioisa k athemultipleCalculatedascurrentstockpricedividedbyannualEPSTheWallStreetJournaluseslast4quarter searningsFirmswhosesharesare infashion sellathighmultiples Growthstocksforexample Firmswhosesharesareoutoffavorsellatlowmultiples Valuestocksforexample OtherPriceRatioAnalysis Manyanalystsfrequentlyrelateearningspersharetovariablesotherthanprice e g Price CashFlowRatiocashflow netincome depreciation cashflowfromoperationsoroperatingcashflowPrice SalescurrentstockpricedividedbyannualsalespersharePrice Book a k aMarkettoBookRatio pricedividedbybookvalueofequity whichismeasuredasassets liabilities 5 9StockMarketReporting Gapendedtradingat 19 25 down 1 75fromyesterday sclose 5 9StockMarketReporting GapIncorporatedishavingatoughyear tradingneartheir52 weeklow Imaginehowyouwouldfeelifwithinthepastyearyouhadpaid 52 75forashareofGapandnowhadashareworth 19 25 That9 centdividendwouldn tgoveryfarinmakingamends Yesterday Gaphadanotherroughdayinaroughyear Gap openedthedaydown beginningtradingat 20 50 whichwasdownfromthepreviouscloseof 21 00 19 25 1 75Lookslikecargopantsaren ttheonlythingsonsaleatGap 5 10SummaryandConclusions Int
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