Equity Valuation Using Multiples. Jing Liu. Anderson Graduate School of Management. University of California at Los Angeles (310)

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1 Equiy Valuaion Uing Muliple Jing Liu Anderon Graduae School of Managemen Univeriy of California a Lo Angele (310) Doron Niim Columbia Univeriy Graduae School of Buine (212) and Jacob Thoma Columbia Univeriy Graduae School of Buine (212) March, 2001 We received helpful commen from David Aboody, Sanjay Bhaga, Ted Chrienen, Glen Hanen, Jack Hughe, Jim Ohlon, Sephen Penman, Phil Shane, Michael William, and eminar paricipan a he AAA Annual Meeing a Philadelphia, Univeriy of Colorado, Columbia Univeriy, Copenhagen Buine School, Ohio Sae Univeriy, and UCLA.

2 Equiy Valuaion Uing Muliple Abrac We examine he valuaion performance of a comprehenive li of value driver and find ha muliple derived from forward earning explain ock price remarkably well for mo firm: pricing error are wihin 15 percen of ock price for abou half of our ample. In erm of relaive performance, he following general ranking are oberved conienly each year: forward earning meaure are followed by hiorical earning meaure, cah flow meaure and book value of equiy are ied for hird, and ale perform he wor. Conrary o he popular view ha differen indurie have differen be muliple, we find ha hee overall ranking are oberved conienly for almo all indurie examined. Adjuing he raio formulaion ypically followed in pracice o allow for an inercep offer ome improvemen, epecially for muliple ha perform poorly. No improvemen i oberved, however, when we conider more complex meaure of inrinic value baed on hor-cu reidual income model (where forward earning are combined wih book value, eimaed dicoun rae, and generic erminal value eimae). Since we require analy earning and growh foreca and poiive value for all meaure, our reul may no be repreenaive of he many firm-year excluded from our ample.

3 Equiy Valuaion Uing Muliple 1. Inroducion In hi udy we examine he proximiy o ock price of valuaion generaed by muliplying a value driver (uch a earning) by he correponding muliple, where he mul iple i obained from he raio of ock price o ha value driver for a group of comparable firm. While muliple are ued exenively in pracice, here i lile publihed reearch in he academic lieraure documening he abolue and relaive performance of differen muliple. 1 We eek o inveigae he performance of a comprehenive li of muliple, and alo examine a variey of relaed iue, uch a he variaion in performance acro indurie and over ime and he performance improvemen obained by uing alernaive approache o compue muliple. Alhough he acual valuaion proce ued by marke paricipan i unobervable, we aume ha ock price can be replicaed by comprehenive valuaion ha conver all available informaion ino deailed projecion of fuure flow. Given hi efficien marke framework for raded ock, wha role do muliple play? Even in iuaion where marke valuaion are aben, eiher becaue he equiy i privaely-held or becaue he propoed publicly raded eniy ha no ye been creaed (e.g., merger and pinoff), i here a role for muliple vi-à-vi comprehenive valuaion? While he muliple approach bypae explici projecion and preen value calculaion, i relie on he ame principle underlying he more comprehenive approach: value i an increaing funcion of fuure payoff and a decreaing funcion of rik. Therefore, muliple are ued ofen a a ubiue for comprehenive valuaion, becaue hey 1 Sudie offering decripive evidence include Boaman and Bakin [1981], LeClair [1990], and Alford [1992]. Recenly, a number of udie have examined he role of muliple for firm valuaion in pecific conex, uch a ax and bankrupcy cour cae and iniial public offering (e.g., Beay, Riffe, and Thompon [1999], Gilon, Huchki and Ruback [2000], Kim and Rier [1999], and Taker [1998]). 1

4 communicae efficienly he eence of hoe valuaion. Muliple are alo ued o complemen comprehenive valuaion, ypically o calibrae hoe valuaion and o obain erminal value. 2 In effec, our udy documen he exen o which differen value driver erve a a ummary aiic for he ream of expeced payoff, and comparable firm reemble he arge firm along imporan value aribue, uch a growh and rik. We fir evaluae value driver uing he convenional raio repreenaion (i.e., price double when he value driver double). To idenify he imporance of incorporaing he average effec of omied variable, we exend he raio repreenaion o allow for an inercep in he price/value driver relaion. To udy he impac of elecing comparable firm from he ame indury, we conra our reul obained by uing indury comparable (he middle caegory from he Secor/Indury/Group claificaion provided by IBES) wih reul obained when all firm available each year are ued a comparable. A in prior reearch, we evaluae performance by examining he diribuion of percen pricing error (acual price le prediced price, caled by acual price). The value driver we conider include meaure of hiorical cah flow, uch a cah flow from operaion and EBITDA (earning before inere, axe, depreciaion, and amorizaion), and hiorical accrual-baed meaure, uch a ale, earning, and book value of equiy. We alo conider forwardlooking meaure derived from analy foreca of EPS (earning per hare) and long-erm growh in EPS, uch a 2-year ou conenu EPS foreca and PEG (price-earning-growh) raio (e.g., Bradhaw [1999a; 1999b]). Since ale and EBITDA hould properly be aociaed wih enerprie value (deb plu equiy), raher han equiy alone, for hoe wo value driver we alo conider muliple baed on enerprie value (marke value of equiy plu book value of deb). Finally, we conider hor-cu inrinic value meaure baed on he reidual income model ha have been ued recenly in he academic lieraure (e.g., Frankel and Lee [1998], and Gebhard, Lee, and Swaminahan [2001]). 2 Anoher very differen role for muliple ha ha been examined in he lieraure i he idenificaion of mipriced ock. We do no inveigae ha role becaue we aume marke efficiency. Two uch marke inefficiency udie are Bau [1977] and Saman [1980]), where porfolio derived from earning and book value muliple are hown o earn abnormal reurn. 2

5 The following i an overview of he relaive performance of differen value driver: (1) forward earning perform he be, and performance improve if he foreca horizon lenghen (1-year o 2-year o 3-year ou EPS foreca) and if earning forecaed over differen horizon are aggregaed; (2) he inrinic value meaure, baed on hor-cu reidual income model, perform coniderably wore han forward earning 3 ; (3) among driver derived from hiorical daa, ale perform he wor, earning perform beer han book value; and IBES earning (which exclude many one-ime iem) ouperform COMPUSTAT earning; (4) cah flow meaure, defined in variou form, perform poorly; and (5) uing enerprie value, raher han equiy value, for ale and EBITDA furher reduce performance. Turning from relaive performance o abolue performance, forward earning meaure decribe acual ock price reaonably well for a majoriy of firm. For example, for 2-year ou forecaed earning, approximaely half he firm have abolue pricing error le han 16 percen. The diperion of pricing error increae ubanially for muliple baed on hiorical driver, uch a earning and cah flow, and i epecially large for ale muliple. Some oher imporan finding are a follow: (1) performance improve when muliple are compued uing he harmonic mean, rela ive o he mean or median raio of price o value driver for comparable firm, (2) performance decline ubanially when all firm in he cro-ecion each year are ued a comparable firm, (3) allowing for an inercep improve performance mainly for poorlyperforming muliple, (4) relaive performance i relaively unchanged over ime and acro indurie. Our finding have a number of implicaion for valuaion reearch. Fir, we confirm he validiy of wo precep underlying he valuaion role of accouning number: (1) accrual improve he valuaion properie of cah flow, and (2) depie he imporance of op-line revenue, i value relevance i limied unil i i mached wih expene. Second, we confirm ha forward earning conain coniderably more value-relevan informaion han hiorical daa, and hey hould be ued a long a earning foreca are 3 Bradhaw [1999a and 1999b] oberve reul ha are relaed o our. He find ha valuaion baed on PEG raio explain more variaion in analy arge price and recommendaion han more complex inrinic value model. 3

6 available. Third, conrary o general percepion, differen indurie are no aociaed wih differen be muliple. Finally, our inveigaion of he ignal/noie radeoff aociaed wih he more complex inrinic value driver baed on he reidual income model ugge ha even hough hee meaure uilize more informaion han ha conained in forward earning and impoe a rucure derived from valuaion heory on ha informaion, meauremen error aociaed wih he addiional variable required, epecially erminal value eimae, negaively impac performance. 4 Thee finding are aociaed wih cerain cavea. Since we exclude firm no covered by IBES, ypically firm wih low and medium marke capializaion, we are uncerain abou he exen o which our reul exend o hoe firm. Even firm wih IBES daa are no fully repreened in our ample, ince we exclude firm-year wih negaive value for any value driver. In paricular, our reul may no be decripive of ar-up firm reporing loe and high growh firm wih negaive operaing cah flow. 2. Prior Reearch While exbook on valuaion (e.g., Copeland, Koller, and Murrin [1994], Damodaran [1996] and Palepu, Healy, and Bernard [2000]) devoe coniderable pace o dicuing muliple, mo publihed paper ha udy muliple examine a limied e of firm-year and conider only a ube of muliple, uch a earning and EBITDA. Alo, comparion acro differen udie are hindered by mehodological difference. Among commonly ued value driver, hiorical earning and cah flow have received mo of he aenion. Boaman and Bakin [1981] compare he valuaion accuracy of P/E muliple baed on wo e of comparable firm from he ame indury. They find ha valuaion error are maller when comparable firm are choen baed on imilar hiorical earning growh, relaive o when hey are choen randomly. Alford [1992] inveigae he effec of chooing comparable baed on indury, ize (rik), and earning growh on he preciion of valuaion uing P/E muliple. He find ha pricing error decline 4 Given our efficien marke framework, we do no inveigae here wheher he relaively poor performance of he inrinic value meaure i due o an inefficien marke ha value ock uing 4

7 when he indury definiion ued o elec comparable firm i narrowed from a broad, ingle digi SIC code o claificaion baed on wo and hree digi, bu here i no addiional improvemen when he four-digi claificaion i conidered. He alo find ha conrolling for ize and earning growh, over and above indury conrol, doe no reduce valuaion error. Kaplan and Ruback [1995] examine he valuaion properie of he dicouned cah flow (DCF) approach for highly leveraged ranacion. While hey conclude ha DCF valuaion approximae ranaced value reaonably well, hey find ha imple EBITDA muliple reul in imilar valuaion accuracy. Beay, Riffe, and Thompon [1999] examine differen linear combinaion of value driver derived from earning, book value, dividend, and oal ae. They derive and documen he benefi of uing he harmonic mean, and inroduce he price-caled regreion we ue. They find he be performance i achieved by uing (1) weigh derived from harmonic mean book and earning muliple and (2) coefficien from price-caled regreion on earning and book value. In a recen udy, Baker and Ruback [1999] examine economeric problem aociaed wih differen way of compuing indury muliple, and compare he relaive performance of muliple baed on EBITDA, EBIT (or earning before inere and axe), and ale. They provide heoreical and empirical evidence ha abolue valuaion error are proporional o value. They alo how ha indury muliple eimaed uing he harmonic mean are cloe o minimum-variance eimae baed on Mone Carlo imulaion. Uing he minimum-variance eimaor a a benchmark, hey find ha he harmonic mean dominae alernaive imple eimaor uch a he imple mean, median, and value-weighed mean. Finally, hey ue he harmonic mean eimaor o calculae muliple baed on EBITDA, EBIT, and ale, and find ha indury-adjued EBITDA perform beer han EBIT and ale. Inead of focuing only on hiorical accouning number, Kim and Rier [1999], in heir inveigaion of how iniial public offering price are e uing muliple, add forecaed earning o a convenional li of value driver, which include book value, earning, cah flow, and ale. Conien muliple of forward earning. We find evidence inconien wih ha explanaion in a eparae paper (Liu, Niim, and Thoma [2001]). 5

8 wih our reul, hey find ha forward P/E muliple (baed on forecaed earning) dominae all oher muliple in valuaion accuracy, and ha he EPS foreca for nex year dominae he curren year EPS foreca. Uing large daa e could diminih he performance of muliple, ince he reearcher elec comparable firm in a mechanical way. In conra, marke paricipan may elec comparable firm more carefully and ake ino accoun iuaion-pecific facor no conidered by reearcher. Taker [1998] examine acro-indury paern in he elecion of comparable firm by invemen banker and analy in acquiiion ranacion. She find he yemaic ue of indury-pecific muliple, which i conien wih differen muliple being more appropriae in differen indurie Mehodology In hi ecion we decribe he differen value driver conidered, and he mehodology ued in he wo age of our analye: eimaing he price/value driver relaion wihou and wih an inercep. 3.1 Value Driver The following i a li of value driver examined in hi paper. We have grouped hem baed on wheher hey refer o cah flow or accrual, wheher hey relae o ock or flow, and wheher hey are baed on hiorical or forward-looking informaion. 6 We provide a brief decripion here for ome variable ha reader may no be familiar wih (deail for all variable are provided in Appendix A) and hen decribe he link drawn in he prior lieraure beween differen value driver and equiy value. (1) Accrual flow: ale, acual earning from COMPUSTAT (CACT) and acual earning from IBES (IACT). (2) Accrual ock: book value of equiy (BV). (3) Cah flow: cah flow from operaion (CFO), free cah flow o deb and equiy holder (FCF), mainenance cah flow (MCF), equal o free cah flow for he cae when capial expendiure equal depreciaion expene, and earning before inere, axe, 5 6 Since i i no clear wheher he objecive of invemen banker/analy i o achieve he mo accurae valuaion in erm of malle diperion in percen pricing error, our reul may no be direcly comparable wih hoe in Taker [1998]. Some value driver are no eaily claified. For example, Sale, which i caegorized a an accrual flow, could conain fewer accrual han EBITDA, which i caegorized a a cah flow meaure. 6

9 depreciaion and amorizaion (EBITDA). (4) Forward looking informaion: conenu (mean) one year and wo year ou earning foreca (EPS1, and EPS2), and wo forecaed earning-growh combinaion (EG1=EPS2*(1+g) and EG2=EPS2*g) which are derived from EPS2 and g (he mean long-erm EPS growh foreca provided by analy). (5) Inrinic value meaure (P1*, P2*, and P3*): Thee meaure are baed on he reidual income (or abnormal earning) valuaion approach, where equiy value equal he book value oday plu he preen value of fuure abnormal earning. Abnormal earning for year +1 o +5, projeced from explici or implied earning foreca for hoe year, are he ame for he fir wo meaure. Afer year +5, abnormal earning are aumed o remain conan for P1* and equal zero for P2*. For P3*, he level of profiabiliy (meaured by ROE) i aumed o rend linearly from he level implied by earning forecaed for year +3 o he indury median by year +12, and abnormal earning are aumed o remain conan hereafer. (6) Sum of forward earning (ES1 and ES2): Thee meaure aggregae he eparae forward earning foreca. ES1 i he um of he EPS foreca for year +1 o +5, and ES2 i he um of he preen value of hoe foreca. 7 A explained laer, hee wo meaure are deigned o provide evidence on he poor performance of he inrinic value meaure. Value driver baed on accrual, which diinguih accouning number from heir cah flow counerpar, have been ued exenively in muliple valuaion. Book value and earning, which are ofen aumed o repreen fundamenal, have been linked formally o firm value (e.g,, Ohlon [1995] and Felham and Ohlon [1995]). Alhough he ue of ale a a value driver ha le heoreical bai, relaive o earning and cah flow, we conider i becaue of i wide ue in cerain emerging indurie where earning and cah flow are perceived o be uninformaive. A an inuiive level, accouning earning could be more value-relevan han repored cah flow becaue ome cah flow do no reflec value creaion (e.g., ae purchae/ale), and accrual allow manager o reflec heir judgmen abou fuure propec. The COMPUSTAT EPS meaure we conider i repored primary EPS excluding exraordinary iem and diconinued operaion and he IBES EPS 7 We hank Jim Ohlon for uggeing ES1. 7

10 meaure i derived from repored EPS by deleing ome one-ime iem, uch a wrie-off and rerucuring charge. To he exen ha he IBES meaure i a beer proxy for permanen or core earning expeced o peri in he fuure, i hould exhibi uperior performance. The ue of cah flow muliple in pracice appear o be moivaed by he implici aumpion ha repored cah flow i he be available proxy for he fuure cah flow ha underlie ock price, and by he feeling ha hey are le ucepible o manipulaion by managemen. The four cah flow meaure we conider remove he impac of accrual o differen exen. EBITDA adju pre-ax earning o deb and equiy holder for he effec of depreciaion and amorizaion only. CFO deduc inere and axe from EBITDA and alo deduc he ne invemen in working capial. FCF deduc from CFO ne invemen in all long-erm ae, wherea MCF only deduc from CFO an invemen equal o he depreciaion expene for ha year. The poenial for analy EPS foreca o reflec value-relevan daa no capured by hiorical earning ha long been recognized in he lieraure. For example, Liu and Thoma [2000] find ha reviion in analy earning foreca along wih change in inere rae explain a ubanially larger porion of conemporaneou ock reurn han do earning urprie baed on repored earning. Conenu eimae are ofen available for forecaed earning for he curren year (EPS1) and he following year (EPS2). Conenu eimae are alo frequenly available for he long-erm growh foreca (g) for earning over he nex buine cycle (commonly inerpreed o repreen he nex 5 year). The meaure EG1 (=EPS2*(1+g)), which i an eimae of hree-year ou earning, hould reflec value beer han EPS2, if hree-year ou earning reflec long-erm profiabiliy beer han wo-year ou earning. While he econd earning-growh meaure EG2 (=EPS2*g) alo combine he informaion conained in EPS2 and g, i impoe a differen rucure. Recenly, analy have juified valuaion uing he following rule of humb: forward P/E raio (curren price divided by EPS2) hould equal g. If, for example, EPS i expeced o grow a 30 percen over he nex buine cycle, hen forward P/E hould equal 30. Saed differenly, he raio of forward P/E o g (referred o a he PEG raio) hould equal 1. For 8

11 cerain ecor, uch a echnology, analy have uggeed ha even higher PEG raio are appropriae. Uing EG2 a a value driver i equivalen o uing a PEG raio obained from he PEG raio of comparable firm. Several recen udie provide evidence ha he inrinic value derived uing he reidual income model explain ock price (e.g., Abarbanell and Bernard [2000], Clau and Thoma [2000]) and reurn (e.g., Liu and Thoma [2000], Liu [1999]). The hree generic paern we ue o projec abnormal earning pa a horizon dae have been conidered in Frankel and Lee [1998] (P1*), Palepu, Healy, and Bernard [2000] (P2*), and Gebhard, Lee, and Swaminahan [2001] (P3*). Alhough hee generic approache do no allow for firm-pecific growh paern for abnormal earning pa a erminal dae, hey offer a convenien alernaive o comprehenive valuaion a long a oberved long-erm growh paern end o converge o he generic paern aumed by hee meaure. While he wo final earning um meaure we conider (ES1 and ES2) have no been dicued in he lieraure, we examine hem o underand beer he poor performance oberved for he inrinic value meaure. ES1 imply um he earning forecaed for year +1 o +5, and ES2 aemp o conrol heuriically for he iming and rik of he differen earning number by dicouning hoe forecaed earning before umming hem. If boh ES1 and ES2 perform poorly, relaive o imple forward earning muliple (e.g., EPS2) he earning projeced for year +3 o +5 probably conain coniderable error. If ES1 perform well, bu ES2 doe no, eimaion error in he firm-pecific dicoun rae ued o dicoun flow a differen horizon are reponible for he poor performance of he inrinic value meaure. If boh ES1 and ES2 perform well, he poor performance of inrinic value meaure i probably becaue he aumed erminal value in each cae diverge ubanially from he marke eimae of erminal value. We alo conider he impac of uing enerprie value (TP), raher han equiy value, for ale and EBITDA muliple, ince boh value driver reflec an invemen bae ha include deb and equiy. We meaure TP a he marke value of equiy plu he book value of deb. To obain prediced hare price, 9

12 we eimae he relaion beween TP and he value driver for comparable firm, generae prediced TP for arge firm, and hen ubrac he book value of heir deb. 3.2 Tradiional Muliple Valuaion In he fir age of our analyi, we follow he radiional raio repreenaion and require ha he price of firm i (from he comparable group) in year (p i ) i direcly proporional o he value driver: p i = β x + ε (1) i i where x i i he value driver for firm i in year, pricing error. To improve efficiency, we divide equaion (1) by price: x ε β i he muliple on he value driver and i i 1 = β +. (2) pi pi ε i he Baker and Ruback [1999] and Beay, Riffe, and Thompon [1999] demonrae ha eimaing he lope uing equaion (2) raher han equaion (1) i likely o produce more precie eimae becaue he valuaion error (he reidual in equaion (1)) i approximaely proporional o price. When eimaing β, we eleced o impoe he rericion ha expeced percen pricing error (E[ε/p]) be zero, even hough an unrericed eimae for β from equaion (2) offer a lower value of mean quared percen pricing error. Empirically, we find ha our approach generae lower pricing error for mo firm, relaive o an unrericed eimae, bu i generae ubanially higher error in he ail of he diribuion. 8 By rericing ourelve o unbiaed percen pricing error, we are in effec aigning lower weigh o exreme pricing error, relaive o he unrericed approach. We are alo mainaining coniency wih he radiion in economeric ha rongly prefer unbiaedne over reduced diperion. 8 We eimaed equaion (2) for comparable firm from he cro-ecion wihou impoing he unbiaedne rericion. (When uing comparable firm from he ame indury, he eimaed muliple for hi unrericed cae generaed ubanial pricing error.) We find ha he percen pricing error diribuion for all muliple are hifed o he righ ubanially, relaive o he diribuion for he rericed cae repored in he paper (our diribuion end o peak around zero pricing error). Thi hif o he righ indicae ha he muliple and prediced valuaion for he unrericed cae are on average lower han our. We find ha he bia creaed by hi hif caue greaer pricing error for he bulk of he firm no in he ail of he diribuion, relaive o our rericed cae. 10

13 β i he only parameer o be eimaed in equaion (2), and i i deermined by he rericion we i impoe ha percen pricing error be zero on average, i.e., E ε = 0. Rearranging erm in equaion pi (2) and applying he expeced value operaor, we obain he harmonic mean of p / x a an eimae for β : ε E p i i βx i = 1 E = 0 pi 1 β = (3) xi E pi We muliply hi harmonic mean eimae for β by he arge firm value driver o obain a predicion for he arge firm equiy value, and calculae he percen pricing error a follow: 9 i i ε p β p i i i i =. (4) p i ^ x To evaluae he performance of muliple, we examine meaure of diperion, uch a he inerquarile range, for he pooled diribuion of ε / p. i i 3.3 Inercep Adjued Muliple For he econd age of our analyi, we relax he direc proporionaliy requiremen and allow for an inercep: p i = α + β x + ε. (5) i i Many facor, beide he value driver under inveigaion, affec price, and he average effec of uch omied facor i unlikely o be zero. 10 Since he inercep in equaion (5) capure he average effec of omied facor, allowing for an inercep hould improve he preciion of ou of ample predic ion. A wih he imple muliple approach, we divide equaion (5) by price o improve eimaion efficiency: 9 While ome udie meaure pricing error a prediced value minu price (e.g., Alford [1992]) we meaure pricing error a price minu prediced value. 11

14 1 x ε i i 1 = α + β +, (6) pi pi pi Eimaing equaion (6) wih no rericion minimize he quare of percen pricing error, bu he expeced value of hoe error i non-zero. 11 For he reaon menioned in ecion 3.2, we again impoe he rericion ha percen pricing error be unbiaed. 12 Tha i, we eek o eimae he parameer α and β ha minimize he variance of ε i / pi, ubjec o he rericion ha he expeced value of εi / pi i zero: min var( ε / p 1 xi ) = var[( pi α β xi) / pi] = var[1 ( α + β )] (7a) p p i i α, β i i ε i.. E = 0. pi I can be hown ha he eimae for α and β ha aify (7a) and (7b) are a follow x 1 1 x 1 E var cov, E β p p p p p = (8) x + x 1 1 x 1 x E var E var 2E E cov, p p p p p p p p (7b) x 1 β E p α = (9) 1 E p where he differen E [.], var(.), and cov(.) repreen he mean, variance, and covariance of hoe expreion for he populaion, and are eimaed uing he correponding ample momen for he If he relaion beween price and he value driver i non-linear, he omied facor include higher power of he value driver. In general, hi bia could be removed by allowing for an inercep. Tha avenue i no available, however, when he dependen variable i a conan (=1), ince he inercep capure all he variaion in he dependen variable, hereby making he independen variable redundan. A wih equaion (2), percen pricing error from he unrericed approach for equaion (6) are higher for mo firm (in he middle of he diribuion) bu here are fewer firm in he ail of he diribuion. (See foonoe 8.) 12

15 comparable group. We compue predicion error, defined by equaion (10), and examine heir diribuion o deermine performance. 4. Sample and Daa ε p i i ^ pi α β xi =. (10) p i ^ To conruc our ample, we merge daa from hree ource: accouning number from COMPUSTAT; price, analy foreca, and acual earning per hare from IBES; and ock reurn from CRSP. A of April of each year (labeled year +1), we elec firm-year ha aify he following crieria: (1) COMPUSTAT daa iem 4, 5, 12, 13, 25, 27, 58, and 60 are non-miing for he previou fical year (year ); (2) a lea 30 monhly reurn are available on CRSP from he prior 60 monh period; (3) price, acual EPS, forecaed EPS for year +1 and +2, and he long erm growh foreca are available in he IBES ummary file; and (4) all price o value-driver raio for he imple muliple (excluding he hree P* and wo ES meaure) lie wihin he 1 and 99 h percenile of he pooled diribuion. The reuling ample, which include 26,613 obervaion beween 1982 and 1999, i ued for he decripive aiic repored in Table 1. For he reul repored afer Table 1, we impoe hree addiional requiremen: (1) hare price on he day IBES publihe ummary foreca in April i greaer han or equal o $2; (2) all muliple are poiive; and (3) each indury-year combinaion ha a lea five obervaion. The fir condiion avoid large pricing error in he econd age analyi (where an inercep i allowed) due o firm wih low hare price. The econd condiion avoid negaive prediced price, and he hird condiion enure ha he comparable group i no unreaonably mall. Regarding he econd condiion, we dicovered ha many firm-year were eliminaed becaue of negaive value for wo cah flow meaure: free cah flow and mainenance cah flow. More imporan, preliminary analyi indicaed ha boh meaure exhibied larger pricing error han he oher meaure. A a reul, we fel ha hee wo meaure were unuiable for large ample muliple analye and dropped hem from he remainder of our udy. The final ample ha 19,879 firm-year. 13

16 Our ample repreen a mall fracion of he NYSE+AMAX+NASDAQ populaion ha i i drawn from: he fracion included varie beween 11 percen earlier in he ample period o 18 percen laer in our ample period. The fracion of marke value of he populaion repreened, however, i coniderably larger becaue he firm deleed for lack of analy daa are on average much maller han our ample firm. Alo, firm-year excluded becaue hey have negaive value driver are poenially differen from our ample, becaue hey are more likely o be young firm and/or echnology firm. For hee reaon, our reul may no be decripive of he general populaion. We adju all per hare number for ock pli and ock dividend uing IBES adjumen facor. If IBES indicae ha he conenu foreca for ha firm-year i on a fully dilued bai, we ue IBES diluion facor o conver hoe number o a primary bai. We ue a dicoun rae (k ) equal o he rik-free rae plu bea ime he equiy rik premium. The rik-free rae i he 10-year Treaury bond yield on April 1 of year +1 and we aume he equiy premium i 5 percen. We eimae bea uing monhly ock reurn and value-weighed CRSP reurn over he 60 monh period ending in March of year +1, and meaure bea a he median bea of all firm in he ame bea decile. 13 For a ubgroup of firm-year (le han 5 percen), we were able o obain mean IBES foreca for all year in he five-year horizon. For all oher firm, wih le han complee foreca available beween year 3 and 5, we generae foreca by applying he mean long-erm growh foreca (g) o he mean foreca for he prior year in he horizon; i.e., ep ep *(1 ) + = g. We obain book value for fuure year by auming he ex-ane clean urplu relaion (ending book value in each fuure period equal beginning book value plu forecae d earning le forecaed dividend). Since analy foreca of fuure dividend are no available on IBES, we aume ha he curren dividend payou raio will be mainained in he fuure. We meaure he curren dividend payou a he raio of he indicaed annual cah dividend o he earning foreca for year +1 (boh obained from 13 We ue decile median bea, ince firm-pecific bea are eimaed wih coniderable error. 14

17 he IBES ummary file). 14 To minimize biae ha could be induced by exreme dividend payou raio (caued by foreca +1 earning ha are cloe o zero), we Winorize payou raio o lie beween 10% and 50% Reul The following i an overview of hi ecion. Decripive univariae aiic for he differen value driver and bivariae correlaion among hem are provided in Secion 5.1 The diribuion of pricing error for he radiional no-inercep relaion beween price and value driver i provided in Secion 5.2, and he reul obained when an inercep i included are provided in Secion 5.3. In boh ubecion, he reul are repored eparaely for wo e of comparable firm wih daa available ha year: all firm from he ame indury and all firm in he cro-ecion. In eiher cae, our analyi i alway conduced ou of ample; i.e., he arge firm i removed from he group of comparable firm. Since he radiional approach involve he no-inercep relaion and he elecion of comparable firm from he ame indury, much of our dicuion focue on ha combinaion, and mo of our ancillary inveigaion relae only o hi combinaion. To conduc he analyi uing comparable firm from he ame indury, we conidered alernaive indury claificaion. Becaue of he evidence ha SIC code frequenly miclaify firm (Kim and Rier [1999]), we ue he indury claificaion provided by IBES, which i indicaed o be baed looely on SIC code, bu i alo ubjec o deailed adjumen. 16 The IBES indury claificaion ha hree level (in increaing finene): ecor, indury, and group. We ue he inermediae (indury) claificaion level becaue viual examinaion of firm included in he ame ecor uggeed i wa oo broad a claificaion o allow he elecion of homogeneou firm, and abulaion of he number of firm Indicaed annual dividend are four ime he mo recen quarer declared dividend. We ue EPS1 a he deflaor becaue i varie le han curren year' earning and i le likely o be cloe o zero or negaive. The impac of alering he dividend payou aumpion on he reul i negligible, becaue i ha a very mall impac on fuure book value and an even maller impac on he compued abnormal earning. The IBES claificaion reemble he indury grouping uggeed by Morgan Sanley. 15

18 in differen group uggeed i wa oo narrow o allow he incluion of ufficien comparable firm (given he lo of obervaion due o our daa requiremen). Becaue of he volume of reul generaed, we repor only ome repreenaive reul and decribe briefly ome inereing exenion. In paricular, we do no repor on e of aiical ignificance we conduced o compare difference in performance acro value driver. Our aiical ignificance e focu on he inerquarile range a he primary meaure of diperion ha i relevan o u, and we conduc a boorap-ype analyi for each pair of value driver for all e of reul repored in Table 2 and 3. We generae ample of 19,879 firm-year by drawing obervaion randomly from our ample, wih replacemen. For each rial we compue he iner-quarile range for each muliple, and hen compue he difference beween all pair of iner-quarile range. Thi proce i repeaed 100 ime and a diribuion i obained for each pairwie difference. 17 A -aiic i compued a he mean divided by he andard deviaion for each of hee diribuion. Thoe -aiic (available from he auhor) indicae ha almo every pairwie difference for he differen inerquarile range repored in our able i aiically ignifican (-aiic greaer han 2). In eence, reader can afely aume ha if difference in performance acro value driver are economically ignifican, hey are alo aiically ignifican. In Secion 5.4, we provide a ummary of our reul on variaion in performance of differen value driver acro differen indurie and year in our ample. Appendix B conain more deail of he acro-indury variaion in performance. 5.1 Decripive Saiic Table 1 repor he pooled diribuion of differen value driver, caled by price. While mo diribuion conain very few negaive value, he incidence of negaive value i higher for cah flow meaure. In paricular, free cah flow and mainenance cah flow are ofen negaive (approximaely 30% and 20% of he ample, repecively). Moreover, he mean of FCF/P i negaive, and he mean of MCF/P i cloe o zero, depie he deleion of obervaion wih exreme value (op and boom 1%). Including 17 Increaing he number of rial beyond 100 had lile impac on he -aiic generaed. 16

19 hee wo value driver would reul in a draic reducion in ample ize. Since we dicovered ha hey perform coniderably wore han oher value driver, we decided o remove hem from he e of value driver conidered here. Examinaion of correlaion for differen pair of value driver, caled by price, indicae ha mo value driver are poiively correlaed wih each oher, which ugge ha hey hare coniderable common informaion. (Thee reul, which are available from he auhor, how ha Pearon correlaion are very imilar o Spearman correlaion.) The correlaion among differen forward earning and earning-growh meaure are epecially high, generally around 90%. Inereingly, he correlaion beween he differen forward earning meaure and he hree inrinic value meaure (P1*, P2*, and P3*) are much lower (only abou 50 percen). 5.2 No-inercep relaion beween price and value driver The reul of he fir age analyi, baed on he raio repreenaion (no inercep), are repored in Table 2. Our primary reul are hoe repored in Panel A, where comparable firm are eleced from he ame indury. The reul repored in Panel B are baed on comparable firm including all firm in he cro-ecion. We repor he following aiic ha decribe he diribuion of he percen pricing error: wo meaure of cenral endency (mean and median) and four meaure of diperion (he andard deviaion and hree non-parameric diperion meaure: inerquarile range, 90 h percenile le 10 h percenile, and 95 h percenile le 5 h percenile). Our reul are eparaed ino four caegorie: hiorical value driver, forward earning meaure, inrinic value and earning um meaure, and muliple baed on enerprie value. To offer a viual picure of he relaive and abolue performance of differen caegorie of muliple, we provide in Figure 1, Panel A, he hiogram for percen pricing error for he following eleced muliple: EPS2, P1*, IACT, EBITDA, BV and Sale. The hiogram repor he fracion of he ample ha lie wihin range of pricing error ha are of widh equal o 10% of price (e.g. 0.1 o 0, 0 o 0.1, and o on). To reduce cluer, we draw a mooh line hrough he middle of he op of each hiogram column, raher han provide he hiogram for each of he muliple. A muliple i conidered beer if i 17

20 ha a more peaked diribuion. The difference in performance acro he differen value driver are clearly viible in Figure 1. The figure alo offer a beer view of he hape of he differen diribuion and enable reader o find he fracion of firm wihin differen pricing error range for each diribuion. In general, he valuaion error we repor are kewed o he lef, indicaed by median ha are greaer han mean. 18 While he kewne i le noiceable for muliple baed on forward earning, i i quie prominen for muliple baed on ale and cah flow. Since prediced value are bounded from below a zero, while hey are no bounded above, he righ ide of he pricing error diribuion canno exceed +1, wherea he lef ide i unbounded. One way o make he error diribuion more ymmerical i o ake he log of he raio of prediced price o oberved price (Kaplan and Ruback [1995]). Alhough we find ha he diribuion are indeed more ymmeric for he log pricing error meric, we eleced o repor he reul uing he percen pricing error meric becaue i i eaier o inerpre abolue performance uing ha meric. We did, however, recalculae he diperion meric repored here uing he log pricing error meric o confirm ha all our inference regarding relaive performance remain unchanged. Examinaion of he andard deviaion and he hree non-parameric diperion meaure in Panel A ugge he following ranking of muliple. Forecaed earning, a a group, exhibi he lowe diperion of percen pricing error. Thi reul i inuiively appealing becaue earning foreca reflec fuure profiabiliy beer han hiorical meaure. Conien wih hi reaoning, performance increae wih foreca horizon. The diperion meaure for wo-year ou forward earning (EPS2) are lower han hoe for one-year ou earning (EPS1), and hey are lower ill for hree-year ou forward earning (EG1). The muliple derived from PEG raio (EG2) doe no perform a well, however, uggeing ha he pecific relaion beween forward earning and growh implied by he PEG raio i no uppored for our ample of firm-year. 18 Mean are cloe o zero becaue we require pricing error o be unbiaed, on average. Of coure, he oberved mean would deviae lighly from zero by chance, ince he valuaion are done ou of ample. 18

21 Muliple generaed from he hree inrinic value meaure (P1*, P2*, and P3*) alo do no perform a well a he imple forward earning muliple. Thi reul i conien wih meauremen error in he eimaed dicoun rae, forecaed forward abnormal earning, or aumed erminal value for hee hree meaure. The larger percen pricing error aociaed wih P2* relaive o P1* ugge ha he erminal value aumpion of zero abnormal earning pa year +5 (for P2*) i le appropriae han he aumpion of zero growh in abnormal earning pa year +5 (for P1*). The very high pricing error aociaed wih P3* ugge ha he more complex rucure of profiabiliy rend impoed for hi meaure and/or he aumpion ha abnorma l earning remain conan pa year +12 a he level deermined by curren indury profiabiliy are inappropriae. The harp improvemen in performance oberved for ES1 and ES2 uppor he view ha he poor performance of he inrinic value meaure i caued by he generic erminal value aumpion. Recall ha ES1 imply aggregae he ame five year earning foreca ha are ued for P1* and P2*, and ES2 dicoun hoe foreca uing firm-pecific dicoun rae (k ) before umming hem. The fac ha he performance of ES2 i only lighly wore han ha of ES1 ugge ha he eimaed value of k in he denominaor of he inrinic value erm (ued o dicoun fuure abnormal earning) are unlikely o be reponible for he poor performance of hoe meaure. The improvemen in performance oberved for ES1 over he one, wo and hree-year earning foreca ugge ha depie he high correlaion oberved among hee foreca for differen horizon, hey conain independen value relevan informaion. Comparing book value and earning, he wo popular accouning value driver, we find ha earning meaure clearly ouperform book value. Percen pricing error for book value (BV) exhibi greaer diperion han hoe for COMPUSTAT earning (CACT). The performance of hiorical earning i furher enhanced by he removal of one-ime raniory componen. Conien wih he reul in Liu and Thoma [2000], pricing error for IBES earning (IACT) exhibi lower diperion han hoe for CACT. The ale muliple perform quie poorly, uggeing ha ale do no reflec profiabiliy unil expene have been conidered. 19

22 Conrary o he belief ha Cah i King in valuaion, our reul how cah flow perform ignificanly wore han accouning earning. Beween he wo cah flow meaure, CFO fare coniderably wore han EBITDA; in fac i i conienly he wor performer in all our analye. The la wo row in Panel A of Table 2 relae o valuaion for ale and EBITDA muliple baed on enerprie value. Even hough enerprie value i more appropriae for hee wo value driver, he performance for boh muliple i even wore han ha repored for he ame muliple baed on equiy value. For example, he inerquarile range of pricing error for ale increae from o when he bae i changed from equiy value (P) o enerprie value (TP). We find hi reul urpriing and are unable o provide any raionale for why uch a reul migh be oberved. (Similar reul are repored in Alford [1992].) A frequen reaon for uing ale a a value driver i becaue earning and cah flow are negaive. Since we reric our ample o firm wih poiive earning and cah flow, our ample i le likely o conain firm for which he ale muliple i more likely o be ued in pracice. In paricular, our ample i unlikely o conain emerging echnology firm uch a Inerne ock. While ome early reearch, uch a Hand [1999] and Trueman, Wong, and Zhang [2000], ugge ha radiional value driver are inappropriae for uch ock, Hand [2000] find ha economic fundamenal, epecially forward earning foreca, explain valuaion for uch firm. To provide ome evidence on he impac of deleing firm wih negaive value for earning and cah flow meaure, we examined he pricing error for ale and forward earning muliple for a larger ample of 44,563 firm-year wih poiive value for ale, EPS1, and EPS2. Alhough hi ample i obained by applying he ame condiion ued o generae our primary ample i i more han wice a large becaue we do no require poiive value for all he oher value driver. We find ha even hough he relaive performance difference repored in Table 2, Panel A, are oberved again in hi larger ample, he diperion of pricing error increae for all hree muliple. For example, he inerquarile range for ale, EPS1, and EPS2 increae o 0.805, 0.448, and 0.396, repecively, from 0.738, 0.348, 20

23 and in Table 2, Panel A. Thee reul emphaize our earlier cauion ha he reul repored for our main ample may no be decripive of oher ample. In addiion o ranking he relaive performance of differen muliple, he reul in Table 2, Panel A, and he hiogram in Figure 1 can alo be ued o infer abolue performance. Our main finding i ha indury muliple baed on imple forward EPS foreca provide reaonably accurae valuaion for a large fracion of firm. Conider, for example, he percenage of he ample covered by he wo inerval on eiher ide of zero for EPS2 in Figure 1. The um of hoe four percenage (13 percen beween 0.2 and 0.1, 18 percen beween 0.1 and 0, 16.5 percen beween 0 and 0.1, and 12 percen beween 0.1 and 0.2) ugge ha muliple baed on indury harmonic mean for EPS2 generae valuaion wihin 20 percen of oberved price for almo 60 percen of firm year. Alernaively, halving he inerquarile range of for EPS2 in Panel A ugge ha abolue pricing error below 17.4 percen are oberved for approximaely 50 percen of he ample. 19 The lower inerquarile range for oher value driver, uch a for EG1 and for ES1, indicae he poenial for furher improvemen wih oher value driver derived from forward earning. The pricing error diribuion in panel B of Table 2, when he comparable group include all firm in he cro-ecion, are yemaically more dipered for all muliple, relaive o hoe repored in Panel A. The uperior performance oberved when he comparable group i eleced from he ame indury, i conien wih he join hypohei ha (1) increaed homogeneiy in he value-relevan facor omied from he muliple reul in beer valuaion, and (2) he IBES indury claificaion idenifie relaively homogeneou group of firm. 20 Overall, we find ha he frequency of mall Thi aemen aume he diribuion i ymmeric around zero. Since ha aumpion i only approximaely rue, and only for beer-performing muliple (e.g. forward earning), hi decripion i inended primarily for illuraive purpoe. Even if hee condiion are aified, i i no clear ha here hould be an improvemen. Moving from he cro-ecion o each indury reul in a ubanial decreae in ample ize, and conequenly he eimaion i le precie. Thi fac i alo refleced in he increae in he deviaion of he ample mean of he valuaion error from zero. 21

24 (medium) pricing error increae (decreae), when comparable firm are eleced from he ame indury. (The frequency of large valuaion error remain relaively unchanged.) The muliple ued in calculaing he percen pricing error in Panel A and B are eimaed uing he harmonic mean. To allow comparion wih reul in previou udie (e.g., Alford [1992]), we repea he Panel A analyi uing he median inead of he harmonic mean. Thoe reul are repored in Panel C. Conien wih he evidence in Baker and Ruback [1999] and Beay, Riffe and Thompon [1999], we find ha he abolue performance of median muliple i wore han ha for harmonic mean muliple. To be ure, he mean pricing error i no longer cloe o zero, wherea he median pricing error i now cloe o zero. Noe ha he improvemen oberved for harmonic mean, relaive o median muliple, i inverely relaed o he abolue performance of ha muliple, and he improvemen for forward earning muliple i quie mall. Imporanly, he relaive performance of he differen muliple remain unchanged. We alo examined he impac of uing he indury mean of price-o-value driver raio a he muliple, raher han he harmonic mean (reul available from auhor). We find ha he pricing error diribuion for differen value driver exhibi much greaer diperion, and mean value ha are ubanially negaive. Similar o he reul repored for median, he decline in performance i greaer for muliple ha perform poorly in Table 2, Panel A. While i i inappropriae o include he arge firm in he group of comparable firm, we inveigaed he bia caued by doing o. The bia (in erm of he impac on he diribuion of pricing error for muliple compued in ample veru ou of ample) i negligible when we he group of comparable firm include all firm in he cro-ecion (correponding o Panel B reul), ince he addiion of one firm ha almo no effec on he muliple. When firm are eleced from he ame indury, however, here i a decreae in he diperion of pricing error when we ue in-ample harmonic mean (e.g. he inerquarile range for EPS2 decline from in Table 2, Panel A, o 0.301). The decline in diperion i even larger for in-ample median muliple (e.g., inerquarile range for EPS2 decline from in Table 2, Panel C, o 0.290). 22

25 We conidered wo oher exenion o he muliple approach (reul available upon reque). Fir, we combined wo or more value driver (e.g., Cheng and McNamara [1996]). Our reul, baed on a regreion approach ha i relaed o he inercep adjued muliple approach dicued in ecion 3.3 (e.g., Beay, Riffe, and Thompon [1999]) indicae only mall improvemen in performance over ha obained for forward earning. Second, we inveigaed condiional earning and book value muliple. Tha i, raher han ue he harmonic mean P/E and P/B value of comparable firm, we ue a P/E (P/B) ha i appropriae given he foreca earning growh (foreca book profiabiliy) for ha firm. We fir eimae he relaion beween forward P/E raio and foreca earning growh (P/B raio and foreca reurn on common equiy) for each indury-year, and hen read off from ha relaion he P/E (P/B) correponding o he earning growh foreca (foreca ROCE) for he firm being valued. Depie he inuiive appeal of condiioning he muliple on relevan informaion, lile or no improvemen in performance wa oberved over he uncondiional P/E and P/B muliple. 5.3 Inercep allowed in price-value driver relaion. In hi ubecion, we repor reul baed on he econd age analyi, where we allow for an inercep in he relaion beween price and value driver. Again, he analyi i conduced fir for comparable firm from he ame indury (Table 3, Panel A) and hen for comparable firm from he enire cro-ecion (Panel B). A prediced, relaxing he no-inercep rericion improve he performance of all muliple. The be performance i achieved when we allow for an inercep and elec comparable firm from he ame indury (Table 3, Panel A). Comparion of hee reul wih hoe in Table 2, Panel B, provide he join improvemen creaed by limiing comparable firm o be from he ame indury and allowing for an inercep. Generally, he improvemen generaed by elecing comparable firm from he ame indury (Panel B o Panel A in each Table) i relaively uniform acro value driver. In conra, he improvemen generaed by allowing an inercep (Table 2 o Table 3 for each Panel) i inverely relaed o ha value driver performance in Table 2. Value driver ha perform poorly in Table 2 improve more han hoe ha do well in ha Table. Conra, for example, he improvemen oberved for Sale 23

26 (inerquarile range of in Table 2, Panel A, o in Table 3, Panel A) wih he improvemen oberved for EG1 (inerquarile range of in Table 2, Panel A, o in Table 3, Panel A). Alhough he improvemen in abolue performance of he value driver i no uniform, he rank order of differen value driver remain unchanged from Table 2 o Table Variaion in performance acro indurie and year Given our focu on underanding he underlying informaion conen of he differen muliple, our reul o far relae o pooled daa. We conider nex variaion in he performance of differen value driver acro year and indurie o deermine if he overall reul are oberved conienly in differen year and indurie. Argumen have been made before for differen value driver o perform beer in cerain indurie han in oher. For example, Taker [1998] repor ha invemen banker and analy appear o ue differen preferred muliple in differen indurie. Alhough we recognize ha our earch i unlikely o offer concluive reul, ince we do no pick comparable firm wih he ame kill and aenion a i done in oher conex, we offer ome preliminary finding. Since invemen profeional ue imple muliple (no inercep) and elec comparable firm from he ame indury, we conduc he analyi only for ha combinaion (correponding o Table 2, Panel A). We pool he valuaion reul for each indury acro year, and rank muliple baed on he inerquarile range of pricing error wihin each indury. The reul for he 81 indurie we analyze are repored in Appendix B. The ranking range beween 1 (be) and 17 (wor). We alo repor ummary aiic of he ranking a he boom of he able. The ranking repored in our pooled reul are oberved wih remarkable coniency acro all indurie. To illurae graphically he eence of hee ranking, we focu only on he ix repreenaive value driver conidered in Figure 1, Panel A, compue ranking again for each indury, and abulae he number of ime each value driver wa ranked fir, econd, and o on in an indury. The reul of ha abulaion are repored in Figure 1, Panel B, and he coniency of he ranking acro indurie i clearly eviden. EPS2 i ranked fir in 66 of 81 indurie, ranked econd in 11 indurie and ranked hird and fourh in wo indurie each. I i never ranked fifh or ixh. The modal rank for P1* i econd, 24

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