Valuing Bonds and Stocks

Transcription

1 Leaig Objecives 5- Valuig Bods ad Socks 5 Copoae Fiacial Maageme e Emey Fiey Sowe 5- Udesad ypical feaues of bods & socks. Lea how o obai ifomaio abou bods ad socks. Ideify he mai facos ha affec he value of hese secuiies. Lea how o value hese secuiies. Udesad how chages i he udelyig facos affec he value of hese secuiies. Chape Oulie Focus o iciples 5-5. Bods 5. Bod Valuaio 5. Bod Riskiess 5.4 Sock Valuaio 5.5 Applyig he ivided Valuaio Model 5.6 Obaiig Commo Sock Ifomaio 5.7 The ice-eaigs Raio 5-4 Icemeal Beefis The icemeal beefis fom owig a fiacial secuiy ae is expeced fuue cash flows. Time Value of Moey The value of a fiacial secuiy is he pese value of is expeced fuue cash flows. Risk-Reu Tade-Off Value ad equied eu eflec he secuiy s isk Focus o iciples 5. Bods 5-5 Two-Sided Tasacios Use he fai pice of a fiacial secuiy o compue is expeced eu, because he fai pice does o favo eihe side i a asacio. Efficie Capial Makes Esimae he equied eu fo a fiacial secuiy wih is expeced eu. Opios Recogize a call povisio s value o he issue. 5-6 Bods epese loas exeded by ivesos o copoaios ad/o he goveme. Bods ae issued by he boowe, ad puchased by he lede. The legal coac udelyig he loa is called a bod ideue.

2 Key Feaues of Bods The pa (o face o mauiy) value is he amou epaid (excludig iees) by he boowe o he lede (bodholde) a he ed of he bod s life. The pa value fo U.S. copoae bods is $. The coupo ae deemies he iees paymes. Toal aual amou coupo ae x pa value. U.S. copoae bods pay semiaually. A bod s mauiy is is emaiig life, which deceases ove ime. Oigial mauiy is is mauiy whe i s issued. The fim pomises o epay he pa value a he ed of he bod s life (also called mauiy) Key Feaues of Bods A sikig fud equies piciple epaymes (buyig bods) pio o he issue s mauiy. Coveible bods ca be coveed io a pespecified umbe of shaes of sock. Typically, hese ae shaes of he issue s commo sock. The call povisio allows he issue o buy he bods (epay he loa) pio o mauiy fo he call pice. Callig may o be allowed i he fis few yeas Bod Valuaio The bod s fai value is he pese value of he pomised fuue coupo ad picipal paymes. A issue, he coupo ae is se such ha he fai value of he bods is vey close o is pa value. Lae, as make codiios chage, he fai value may deviae fom he pa value. 5- Example of Bod Valuaio Fid he fai value of a bod wih a $, pa value, a emaiig life of yeas, ad a coupo ae of 9% pe yea paid semi-aually. The equied eu o bods like his oe is cuely 6% AR. Semi-aual coupo payme [coupo ae / ] x pa value [.9 / ] x $, $45 Numbe of paymes x 4 Semiaual equied ae of eu % Example of Bod Valuaio Calculao Equaio Review Bod Value: B V(coupo paymes) V(pa value) V 4 (.) 45 4 (.)(.), (.) 4 4 (.) $45 (.) (.) $, (.) B 4 4 N4 i MT45 FV, V -,54. $,

3 Bod Values ad Requied Reus Yield To Mauiy (YTM) 5- Coupo ae 9% pe yea. Requied Reu 6. % 9. %. % Bod Value $, 54. $,. $ 8.74 pemium bod pa bod discou bod N4 i MT45 FV, V -,54. N4 i4.5 MT45 FV, V -,. N4 i6 MT45 FV, V The Yield o Mauiy is he AR (Aual eceage Rae) ha equaes he bod s make pice o he pese value of is pomised fuue cash flows. This assumes ha pomised paymes will be made i full ad exacly o ime. Calculaig a YTM Fid he Yield o Mauiy (YTM) of a bod wih a $, pa value, a emaiig life of yeas, ad a coupo ae of 9% pe yea paid semi-aually. The bod is cuely sellig fo $,76.. N4 V -,76. MT45 FV, Calculaig a YTM 4 ( YTM/), (YTM/)( YTM/), ( YTM/) N4 V -,76. MT45 FV, i 4. YTM/ 4% pe 6-mohs YTM i 8% pe yea Cue Yield A Compaiso of Bod Reus 5-7 Aual Coupo Iees Cue Yield Cue Bod ice Assume he 9% coupo bod i he pevious example is sellig fo $,76.. Is cue yield is he $9/$, % The cue yield igoes gai (o loss) esulig fom he diffeece bewee he puchase pice ad he pa value. 5-8 Bod Tems: a Value $,; Remaiig life yeas Coupo ae 9% / yea paid semi-aually. Bod ice Cue Yield YTM AY $,54. $,. $ % 9. %.9 % 6. % 9. %. % 6.9 % 9. %.6 %

4 Time ah of a Bod s Value Time ah of a Bod s Value $, $, % Bod Value $, $, $, $9 $8 $7 $6 6% 9% % Bod value $, $, $, $9 $8 $7 $6 % % % 9% 8% 7% 6% 5% 4% Make Rae Yeas o Mauiy 5- Yeas To Mauiy Bod Riskiess The YTM is he bod s pomised eu. Bu wha if he bod issue defauls? Aohe souce of isk lies wih chagig iees aes. As he iees ae ises, he pice of a fixed-coupo bod falls. Iees Rae Risk How does he value of a bod chage as iees aes ise? Bod values ae ivesely elaed o iees aes. Chages i bod values as iees aes chage is kow as iees ae isk. How much iees ae isk does a bod have? I depeds o he mauiy of he bod Bod Value 5- Iees Rae Risk of a Bod $,5 $,4 $, $, $, $, $9 $8 $7 $6 5 yea, 9% coupo bod yea, 9% coupo bod 6% 7% 7% 8% 8% 9% 9% Make Iees Rae % % % % % % 5-4 Bod Values ad Call ovisios Call ovisio allows he issue o pay off he bods pio o mauiy. Whe bods ae called by he issue, hey ae puchased fom he holde a he call pice. he bods ae he eied. The Yield-o-Call (YTC) is he bod s expeced eu up o he call dae. 4

5 Yield o Call of a Bod Coside ou 9% coupo, -yea bod, sellig fo $,54., wih a 6% YTM. Suppose he bod ca be called i 5 yeas fo $,9. Assumig i is called a ha ime, wha ae would you ea? Yield o Call Calculaio ( YTC/), (YTC/)( YTC/),9 ( YTC/) N V -,54. MT45 FV,9 i.46 So YTC (.46) 4.8% YTC < YTM Zeo-Coupo Bods A zeo-coupo bod does o pay ay coupo (peiodic) iees. The pa value is paid o he bodholde a mauiy. Zeo-coupo bods ae also kow as puediscou bods. Valuig Zeo-Coupo Bods The equied eu o a yea zeo-coupo bod wih a pa value of $, is 9% AY. Wha is he bod s value oday? (.9) V (.9)(.9), (.9) N i9 MT FV, V Sock Valuaio Thee ae wo basic ypes of sock: commo ad pefeed. Commo sock epeses he esidual oweship iees i a fim. Commo sockholdes ge whaeve is lef ove i he eve of a bakupcy. They ae las i lie o ge paid. efeed Sock Claims of pefeed sockholdes ae juio o claims of debholdes, bu seio o hose of commo sockholdes. Limied voig ighs compaed o commo sock. efeed sock has a pa value ad a divided ae. Failue o pay he divided does o foce he issuig fim io bakupcy. 5-5

6 5- efeed Sock Valuaio Coside a $ pa value shae of pefeed sock wih a 8% divided ae (paid quaely), ad a 5-yea life. The equied eu is % AR. Fid he shae s fai value oday. Value V(divideds) V(pa value) efeed Sock Valuaio N 5(4) 6 i /4 MT ivided (.8)/4 FV 6 (.) V 6 (.)(.) (.) N6 i MT FV V efeed Sock Valuaio Wha if he sock had bee pepeual? The he value of he sock would be: $66.67 /. N, i MT FV V Commo Sock Repeses esidual oweship of he fim. Commo sockholdes have impoa voig ighs. The issue may pay divideds o commo sockholdes. Howeve, i is o equied o do so. Moeove, hee is o pe-se divided ae. Fuue divideds ae uceai. We eed a way o foecas fuue divideds. The ivided iscou Model The fai value depeds oly o he sock s expeced fuue cash flows, which ae divideds ad a fuue sale pice. So wha is he value of a sock ha absoluely ca eve pay a divided? Each subseque fuue sellig pice depeds o he expeced subseque divideds. Theefoe, a sock s fai value ca be expessed i ems of oly he sock s expeced fuue divideds Applyig he ivided Valuaio Model Ivesos look a a fim as a souce of gowig wealh. Theefoe, hey ae ieesed i he udelyig gowh of a fim ad he implicaios of ha gowh ae fo he sock s value. 6

7 The ivided iscou Model The value of a shae of sock is he pese value of he expeced divideds ove he holdig peiod plus he expeced sale pice a he ed of he holdig peiod. ( ) ( ) ( ) ( ) ( ) The ivided iscou Model ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Cosa Gowh Assume divideds ae gowig a a cosa peceage ae of g pe yea. 4 ( g ) ( g ) ( g )( g ) ( g ) ( g ) ( g ) 5-4 Cosa Gowh ( ) ( g ) ( g ) ( ) Moe geeally, fom ay peiod wih cosa gowh foeve afe ime : ( g ) Commo Sock ivideds Fuue ivideds deped o: he fim s eaigs divided policy ayou Raio ivideds / Eaigs Commo Sock Valuaio The pe shae aual divided o a commo sock is expeced o be $. oe yea fom oday. Sockholdes equie a % ae of eu. Fid he fai value of he sock fo each of he followig cases:. Zeo Gowh: divideds ae cosa evey yea.. Five-ece Gowh: divideds ae gowig a a cosa ae of 5% pe yea foeve.. Supe-Nomal Gowh: divideds will gow a 5% fo yeas ad he a 5% pe yea foeve. 7

8 . Zeo Gowh. Five-ece Gowh Wih g, he divideds of $. pe shae fom a pepeuiy. Recall ha $.; %; ad g 5% $.. $5. $. (..5 ) $4.86 N, i MT FV V -5. N, i7 MT FV V ese Value of ivideds $8 $7 $6 $5 $4 $ V of ivideds ivideds Impoa Feaues of he Cosa Gowh Model The gowh ae i divideds (g) is always less ha he equied ae of eu (). Ohewise, he fim s gowh would exceed he ecoomy s gowh foeve, which is o possible. Also, he fai value would be egaive o ifiiy, which makes o sese. $ $ $ Time The gowh ae i divideds is also he capial gais yield o he sock. The capial gais yield is he ae of pice 5-46 appeciaio Impoa Feaues of he Cosa Gowh Model The sock s oal eu is divided yield ( ) plus capial gais yield ( g) g / % Supe-Nomal Gowh (.5) (.5) (.5) 5.86 (.5) $. $.75 $4.69 $5.86 $ Apply he cosa-gowh fomula o fid he value of he sock a - 4 $5.86 g..5 $8.7 Now add he hypoheical sale pice of $8.7 o he $4.69 divided o ge a cash flow a yea of $88.4. Fially, value he sock as he V of cash flows. 8

9 . Supe-Nomal Gowh Now add he hypoheical sale pice o he divided o ge a cash flow a yea : CF $88.4 The calculae he V of cash flows:. Supe-Nomal Gowh Model N i FV88.4 MT V-6.9 N i FV.75 MT V-.99 N i FV. MT V $. $.75 $88.4 $. $.75 $88.4. (.) (.) $ Souce of ivided Gowh If he ayou Raio (OR) is cosa, gowh i divideds depeds o he gowh i eaigs. The gowh i eaigs depeds o: he amou of eaigs eaied ( - OR), ad he eu eaed o ha moey, i. g ( - OR) i 5-5 Example of ivided Gowh Suppose K-Tel s ES was $5. his yea, i pays ou 6% of is eaigs i divideds, ad all is ivesmes ea a.5% eu. Wha is ex yea s expeced divided, ad wha is he divided gowh ae? This yea s divided ( ) is ES (OR) $5.(.6) $. The fim eivess 4% (-OR) of is ES Amou eivesed $5.(.4) $. 5-5 Example of ivided Gowh The fim will ea.5% o he eivesed $. ex yea, i addiio o he $5. of eaigs fom asses aleady i place ($4 woh of asses eaig.5%). ES $5. $.(.5%) $5.5 $5.5(.6) $.5 Noe ha boh divideds ad ES gow by 5%. g ( - OR) i ( -.6) (.5%) 5% Obaiig Commo Sock Ifomaio Souces of ifomaio iclude o-lie souces, such as Yahoo! Fiace ad Google Fiace (go o moe ad he eve moe ). Tadiioal souces iclude ewspapes, such as The Wall See Joual ad sock ad bod guides, such as Sadad & oo s. 9

10 The ice-eaigs Raio Like paicipas i covesaios abou fooball ad he weahe, may ivesos will joi io a discussio coceig he ivesme poeial of a sock ad feel good abou hei coibuio, egadless of ay kowledge hey migh have abou he sock. These ypes always big up he -E aio The ice-eaigs Raio ice pe Shae /E Eaigs pe Shae Coveioal wisdom holds ha a high /E is good ad a low /E is bad. Wha is he logic behid his saeme? The Logic of he /E Recall ha, g so ha g Also oe ha (OR)(ES ) ad g ( - OR)i The Logic of he /E ES ( OR ) ( OR )i The backeed amou is he E/ aio. Holdig ad OR cosa, he smalle he E/ aio, he lage i mus be. A smalle E/ aio is a lage /E. Theefoe, highe /E implies highe expeced eu o he eaigs eivesed by he fim Some Waigs abou he /E The logic of he /E depeds o expecaios, bu he /E is usually based o hisoical umbes. Cuely epoed accouig eaigs do o eflec he acual imig of he eaigs. The /E may be high because ece eaigs ae low! 5-6 Measuig he NV of Fuue Ivesmes The fai value of a sock ca be hough of as beig made up of wo compoes: he value due o asses aleady i place. he NV of fuue ivesmes expeced o be made by he fim.

11 5-6 Measuig he NV of Fuue Ivesmes divided yield capial gais yield ES (OR) ( OR) i Suppose he equied eu () equals he eu expeced fom eivesed icome (i). Solve his fo ES (OR) ( OR) ES 5-6 Measuig he NV of Fuue Ivesmes If we view he fim s eaigs as a pepeuiy, ES is he pese value of he equiy owed poio of he fim s ivesmes Measuig he NV of Fuue Ivesmes Bu suppose i does o equal? Now is highe o lowe ha he pese value of he fim s cue opeaios by he amou ha he fim is expeced o gai o lose o fuue ivesmes. ca be expessed as he value of he fim s cue opeaios plus NVGO, he pese value of he fim s gowh oppouiies. Measuig he NV of Fuue Ivesmes Suppose i > he fim makes posiive NV ivesmes. will be geae ha he pese value of he fim s cue opeaios ( ). Suppose i < he fim makes egaive NV ivesmes. will be less ha he pese value of he fim s cue opeaios ( ). 5-6 ES NVGO Measuig he NV of Fuue Ivesmes A fim is expeced o ea $4. pe shae ex yea. This amou epeses a good esimae of he fim s log-u pospecs. Shaeholdes equie a 5% ae of eu, ad he sock is cuely sellig fo $.5. Wha is he expeced NV (pe shae) of he fim s fuue ivesmes? ES NVGO 5-66 Measuig he NV of Fuue Ivesmes ES $.5 NVGO $4. $.5 NVGO $8. NVGO.5 NVGO $.5 Sice he sock is woh $.5, he NV of fuue ivesmes is posiive ad equals $.5 pe shae. The fim is expeced o icease value by makig good(i.e. posiive NV) ivesmes.

12 Some Fial Commes o Secuiy Valuaio Mahemaical models of secuiy valuaio ely o esimaes of vaious paamees. The esimaed value is oly as good as he qualiy of he ipu paamees. I a efficie make, he make pice is a good esimae of he secuiy s value. Summay This chape descibes he ypical feaues of bods ad socks ad peses valuaio models fo boh