Preliminary. Comments welcome. Equity Valuation Using Multiples

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1 Preliminary. Commens welcome. Equy Valuaion Using Muliples Jing Liu Anderson Graduae School of Managemen Universy of California a Los Angeles (310) Doron Nissim Columbia Universy Graduae School of Business (212) and Jacob Thomas Columbia Universy Graduae School of Business (212) January, 2000 We received helpful commens from David Aboody, Jack Hughes, Jim Ohlson, Sephen Penman, Michael Williams, and seminar paricipans a Columbia, Copenhagen Business School, Ohio Sae, and UCLA.

2 Equy Valuaion Using Muliples Absrac In his sudy we examine he valuaion performance of a comprehensive lis of commonly used price muliples. Our analysis indicaes he following ranking: forward earnings muliples perform he bes, followed by hisorical earnings measures, cash flow measures and book value of equy are ied for hird, and sales performs he wors. Conrary o he popular view ha differen indusries have differen bes muliples, we find ha hese overall rankings are observed consisenly for all indusries examined. Performance is improved by allowing for an inercep in he linear relaion beween price and value drivers, relaive o he raio formulaion ypically assumed in pracice. Performance is no improved, however, by he use of more complex value drivers, such as he shor cu value measures based on generic paerns for residual income growh pas he forecas horizon.

3 1. Inroducion Equy Valuaion Using Muliples In his sudy we examine he valuaion performance of a comprehensive lis of price muliples. The muliples we consider include hree measures of accrual flows (sales, COMPUSTAT earnings and IBES earnings), one accrual sock measure (book value), four measures of cash flows (cash flow from operaions, free cash flow, mainenance cash flow, and earnings before ineres, axes, depreciaion, and amorizaion (EBITDA)), and hree measures of forward earnings (EPS1, EPS2, and EPS3: 1, 2, and 3-year ou consensus analyss earnings forecass). We also consider more complex ways o incorporae value-relevan informaion, including varians of he popular shor cu value measures based on he residual income model. The muliple approach assumes firm value is direcly proporional o some value driver, such as earnings or book value. The approach is ypically applied as follows: firs, idenify a se of comparable firms; nex, generae a muliple equal o he mean (or median) raio of marke price o he value driver for ha se; and finally, generae firm value by applying ha muliple o he firm s value driver. Comprehensive equy valuaions, which require deailed pro forma analyses and presen value calculaions, should in heory perform beer han simple muliples. In addion o bringing less informaion o bear on he valuaion process, he muliple approach resuls in relaive no absolue valuaion, since firm value is esimaed relaive o he pricing of comparable firms. 1 There are, however, some concerns associaed wh implemening comprehensive valuaions. Firs, he quesion of how bes o conrol for risk remains largely unresolved. Alhough riskadjused discoun raes are used heurisically in pracice, here are concerns ha errors in 1 There is an elemen of relaive pricing even in he case of comprehensive valuaion, since socks are valued relaive o risk-free bonds. If here are concerns abou he risk-free rae (he so-called risk-free rae puzzle), hose concerns remain in sock valuaions based on discoun raes derived from risk-free raes. 1

4 assumed raes disor valuaions. Second, comprehensive valuaions require projecions o infiny. Raher han make specific projecions for all fuure years, simplifying assumpions (such as consan growh in free cash flows or a muliple of erminal earnings) are normally adoped o capure a erminal value, represening value beyond a horizon dae. Since a large fracion of oal value ypically resides in he erminal value, esimaes of firm value hinge subsanially on he simplifying assumpions. Given hese concerns abou comprehensive valuaions, muliples are used ofen in day-oday valuaion, eher as a subsue for or as a complemen o comprehensive valuaions. Analys repors, regulaory filings, valuaions for esae and gif ax purposes, and he financial press frequenly use muliples o value firms. When complemening comprehensive valuaions, muliples are ypically used o obain erminal values and o calibrae he comprehensive valuaion. The advanages of muliples, relaive o comprehensive valuaions, include exraordinary simplicy and he use of conemporaneous marke informaion. While his simplicy reduces informaion conen, also reduces poenial noise. I is no obvious a priori wheher he benefs of reduced noise exceed he coss of reduced informaion conen. Alhough he muliple approach bypasses explic projecions and presen value calculaions, relies on he same principles underlying he more comprehensive approach: value is an increasing funcion of fuure payoffs and a decreasing funcion of risk. Therefore, he muliple approach should perform reasonably well if he value driver reflecs fuure firm profabily, and he comparable group is similar o he firm being valued along various value aribues, such as growh and risk. To sudy he impac of selecing comparable firms from he same indusry, we conras our resuls obained by using indusry (as defined by IBES) comparables wh resuls obained when all firms in he cross-secion are used as comparables. 2

5 Regardless of he role of muliples vis-a-vis comprehensive valuaions, here is limed descripive evidence on he absolue and relaive performance of differen muliples, and he variaion across indusries in ha performance (e.g., Boasman and Baskin [1981], LeClair [1990], and Alford [1992]). Recenly, a number of sudies have examined he role of muliples for firm valuaion in specific conexs, such as ax and bankrupcy cour cases and inial public offerings (e.g., Beay, Riffe, and Thompson [1999], Gilson, Huchkiss and Ruback [2000], Kim and Rer [1999], and Tasker [1998]). Our sudy coninues in he same vein, bu is more comprehensive. As in mos prior research, we evaluae muliples by examining he disribuion of percen pricing errors: acual price less price prediced by he muliple, scaled by acual price. To eliminae in-sample bias and conrol for differences in he degrees of freedom across ess, we evaluae all muliples based on ou of sample predicion. Tha is, when calculaing muliples we always exclude he firm being valued. Our analysis consiss of wo sages. In he firs sage, we use he convenional raio represenaion (i.e., price doubles when he value driver doubles). In he second sage, we relax he requiremen ha value is direcly proporional o value drivers, while reaining he assumpion ha he relaion is linear. In essence, he second sage analysis allows for an inercep, whereas he firs sage does no. In he firs sage, muliples are calculaed using he harmonic mean of he raio of price o value driver (he reciprocal of he mean of he value driver-o-price raio) for comparable firms. Alhough his esimaor is rarely used (see Beay, Riffe, and Thompson [1999]), offers he desirable propery ha he percen pricing error is zero, on average. I is also recommended by Baker and Ruback [1999], based on deailed economeric analyses of alernaive esimaors. While he harmonic mean esimaor resuls in lower pricing errors han he simple mean or 3

6 median, our ranking of he relaive performance of differen muliples remains unchanged when he mean or median is used insead of he harmonic mean. The following is an overview of he relaive performance of differen muliples: forecased earnings perform he bes, even beer han more complex shor cu valuaions based on generic residual income growh paerns pas he erminal dae; among drivers derived from hisorical daa, earnings perform beer han book value; and IBES earnings (which exclude some one-ime ems) perform beer han COMPUSTAT earnings; cash flow measures, defined in various forms, perform poorly; and sales performs he wors. When comparable firms are resriced o be from he same indusry, performance improves for all muliples. We also find ha he relaive performance of he muliples we consider does no vary much across indusries. Tha is, conrary o general percepion, we do no find ha differen indusries are associaed wh differen bes muliples. This finding suggess ha our resul is driven by he inrinsic informaion conen of he differen value drivers, raher han heir abily o capure indusry-specific value-relevan facors. Turning from relaive performance o absolue performance, he forward earnings muliples describe acual sock prices reasonably well. For example, for 3 year ou forecased earnings or EPS3, he sandard deviaion of pricing error is abou 29%, and approximaely half he firms have absolue pricing errors less han 15%. While here are some firms wh very large pricing errors, sock prices for a subsanial majory of he firms are explained relaively well by simple muliples based on wo or hree year ou forecased earnings. The dispersion of pricing errors increases subsanially for muliples based on hisorical drivers, such as earnings and cash 4

7 flows, and is especially large for sales muliples. For example, approximaely half he firms have absolue pricing errors less han 21%, 25%, and 36% for IBES acual earnings, EBITDA, and sales, respecively. For he second sage, we esimae he inercep and slope of he price/value driver relaion by minimizing he sample variance of percen valuaion errors, subjec o he consrain ha he valuaion is on average unbiased. The procedure we follow is relaed o ha proposed by Beay, Riffe, and Thompson [1999]. As migh be expeced, allowing for an inercep reduces he dispersion of valuaion errors for all muliples, and he improvemen observed is inversely relaed o he performance of ha muliple in he firs sage (no inercep). 2 As in he firs sage, we find ha moving from a cross-secional comparison group o using comparable firms whin each indusry furher reduces pricing errors. These resuls sugges ha he radional raio formulaion should be replaced by a relaion ha allows for an inercep, especially for muliples ha perform poorly in he radional raio formulaion. We recognize, however, ha if simplicy is he primary moivaion o use muliples, he reducion in pricing errors may no be sufficien o compensae for he addional complexy inroduced by adding an inercep. To conras muliples wh comprehensive valuaions, we consruc inrinsic value measures based on he residual income model, assuming generic paerns for residual income pas he forecas horizon. Surprisingly, hese more complex value measures perform worse han simple muliples based on forecased earnings. We examine hree alernaive paerns for poshorizon residual income: (1) consan abnormal earnings pas year 5, (2) zero abnormal earnings pas year 5, and (3) ROE rending oward an indusry median (beween year 3 and year 12). 2 For example, for muliples based on IBES acual earnings, EBITDA, and Sales, approximaely half he firms have pricing errors less han 19%, 22%, and 29%, relaive o 21%, 25%, and 36%, respecively, in he raio formulaion. The improvemen is much smaller for muliples ha perform well in he firs sage; e.g. for EPS3, approximaely half he firms have pricing errors less han 14.6%, relaive o 15% in he raio formulaion. 5

8 These inrinsic value measures uilize informaion abou forward earnings a differen horizons, equy book values, firm-specific discoun raes, and indusry profabily. Furher, a srucure derived from valuaion heory is imposed o aggregae ha informaion. Despe hese advanages of inrinsic value measures over simple forward earnings muliples, hey do no perform beer han simple muliples based on forward earnings. 3 Preliminary invesigaions designed o uncover possible causes for his resul sugges ha errors in erminal value proxies and esimaed discoun raes are parially responsible. We find ha simply aggregaing earnings forecass for years 1 o 5 produces he lowes valuaion errors of all muliples. We also considered wo oher exensions o he muliple approach (resuls no repored in his version). 4 Firs, we combined wo or more value drivers (e.g., Cheng and McNamara [1996]). Our resuls, based on a regression approach (e.g., Beay, Riffe, and Thompson [1999]) indicae only small improvemens in performance over ha obained for forward earnings. Second, we invesigaed condional earnings and book value muliples. Tha is, raher han use he harmonic mean P/E and P/B values of comparable firms, we use a P/E (P/B) ha is appropriae given he forecas earnings growh (forecas book profabily) for ha firm. We firs esimae he relaion beween forward P/E raios and forecas earnings growh (P/B raios and forecas reurn on common equy) for each indusry-year, and hen read off from ha relaion he P/E (P/B) corresponding o he earnings growh forecas (forecas ROCE) for he firm being valued. Despe he inuive appeal of condioning he muliple on relevan informaion, we were unable o documen any improvemen in performance. Bradshaw [1999a and 1999b] is able 3 4 Bradshaw [1999a and 1999b] observes resuls ha are relaed o ours. He finds ha PEG, a consruc based on forward P/E raios and forecas long-erm earnings growh raes (g), explains more variaion in arge prices and recommendaions han more rigorous valuaion models. Deails of hose resuls are available from he auhors upon reques. 6

9 o find, however, ha a more resricive form of condioning (P/E equals forecas growh) improves performance for his sample of firms. Our findings have a number of implicaions for valuaion research. Firs, we confirm he validy of wo preceps underlying he valuaion role of accouning numbers: a) accruals improve he valuaion properies of cash flows, and b) despe he imporance of op-line revenues, s value relevance is limed unil is mached wh expenses. Second, we confirm ha forward-looking daa (specifically, near-erm forecased earnings) conain considerably more value-relevan informaion han hisorical daa. Third, we provide evidence on he signal/noise radeoff associaed wh developing more complex valuaion drivers. Finally, our resuls sugges ha forward earnings muliples should be used as long as earnings forecass are available, since hey ouperform he oher muliples in all 68 indusries we examine. The res of he paper is organized as follows: secion 2 conains a leraure review; secion 3 describes he mehodology; secion 4 describes our sample selecion process; secion 5 repors resuls and discusses implicaions; and secion 6 concludes he paper. 2. Leraure Review While mos of he popular exbooks on valuaion (e.g., Copeland, Koller, and Murrin [1994], Damodaran [1996]) devoe considerable space o discussing muliples, here is lle empirical research published on he valuaion properies of muliples. Mos exising papers ha sudy muliples use a limed daa se and consider only a subse of muliples, such as earnings and EBITDA. The mehodology used also varies from one sudy o anoher, making difficul o compare resuls from differen sudies. Among commonly used value drivers, earnings and cash flows have received mos of he aenion. Boaman and Baskin [1981] compare he valuaion accuracy of P/E muliples based on 7

10 wo ses of comparable firms from he same indusry. They find ha valuaion errors are smaller when comparable firms are chosen based on similar hisorical earnings growh, relaive o when hey are chosen randomly. Alford [1992] invesigaes he effecs of choosing comparables based on indusry, size (risk), and earnings growh on he precision of valuaion using P/E muliples. He finds ha valuaion errors decline when he indusry definion used o selec comparable firms is narrowed from a broad, single dig SIC code o classificaions based on wo and hree digs, bu here is no addional improvemen when he four-dig classificaion is considered. He also finds ha conrolling for size and earnings growh, over and above indusry conrols, does no reduce valuaion errors. Kaplan and Ruback [1995] examine he valuaion properies of he discouned cash flow (DCF) approach in he conex of highly leveraged ransacions. While hey conclude ha DCF performs well in valuaion, hey find ha simple EBITDA muliples resul in similar valuaion accuracy. Beay, Riffe, and Thompson [1999] examine differen linear combinaions of value drivers derived from earnings, book value, dividends, and oal asses. They derive and documen he benefs of using he harmonic mean, and inroduce he price-scaled regressions we use. They find he bes performance is achieved by using a) weighs derived from harmonic mean book and earnings muliples and b) coefficiens from price-scaled regressions on earnings and book value. In a recen sudy, Baker and Ruback [1999] examine economeric problems in idenifying indusry muliples, and compare he relaive performance of muliples based on EBITDA, EBIT and revenue. They provide heoreical and empirical evidence ha absolue valuaion errors are proporional o value. They furher show ha indusry muliples esimaed using he harmonic mean are close o minimum-variance esimaes based on Mone Carlo simulaions. Using he minimum-variance esimaor as a benchmark, hey find ha he harmonic mean dominaes 8

11 alernaive simple esimaors such as he simple mean, median, and value-weighed mean. Finally, hey use he harmonic mean esimaor o calculae muliples based on EBITDA, EBIT and revenue, and find ha indusry-adjused EBITDA performs beer han EBIT and revenue. Insead of focusing only on hisorical accouning numbers, Kim and Rer [1999] add forecased earnings o he convenional lis of value drivers, which includes book value, earnings, cash flows, and sales. They invesigae how inial public offering prices are se using muliples. Consisen wh our resuls, hey find ha forward P/E muliples (based on forecased earnings) dominae all oher muliples in valuaion accuracy, and ha he nex year EPS forecas (EPS2) dominaes he curren year EPS forecas (EPS1). I has been recognized ha he use of large daa ses could diminish he performance of muliples, since he researcher selecs comparable firms in a mechanical way. In conras, marke paricipans may selec comparable firms more carefully and ake ino accoun suaion-specific facors no considered by researchers. Tasker [1998] examines paerns in he selecion of comparable firms across indusries in acquision ransacions by invesmen bankers and analyss. She finds he sysemaic use of indusry-specific muliples, which is consisen wh differen muliples being more appropriae in differen indusries Mehodology In his secion we describe he differen value drivers considered, and he mehodology used in he wo sages of our analyses: esimaing he price/value driver relaion whou and wh an inercep. 5 Since is no clear wheher he objecive of invesmen bankers/analyss is o achieve he mos accurae valuaion in erms of smalles dispersion in percen pricing errors, our resuls may no be direcly comparable wh hose in Tasker [1998]. 9

12 3.1 Value Drivers The following is a lis of value drivers examined in his paper (deails of all variables are provided in he appendix): 6 Accrual sock: curren book value (BV). Accrual flows: sales, COMPUSTAT earnings (CACT) and IBES earnings (IACT). Cash flows: cash flow from operaions (CFO), free cash flow o deb and equy holders (FCF), mainenance cash flow (MCF, equal o free cash flows for he case when capal expendures equal depreciaion expense), and earnings before ineres, axes, depreciaion and amorizaion (EBITDA). Forward looking informaion: consensus one year ou, wo year ou and hree year ou earnings forecass (EPS1, EPS2 and EPS3), where eps *(1 ) 3 = eps2 + g, and g is he long erm eps growh forecas provided by analyss. Inrinsic pricing measure (P1*): This measure, which is based on he residual income (or abnormal earnings) valuaion approach, is considered since appears in a number of recen papers and s pricing properies are relaively beer undersood. 7 In essence, inrinsic value equals he book value plus he presen value of fuure abnormal earnings. For fuure years (beyond year +5) wh no available earnings forecass, abnormal earnings are esimaed by assuming ha hey do no grow. Deails of he implemenaion of P1* are discussed in he nex secion. All he variables lised above have been linked o value before. Accouning book value and earnings are used exensively for valuaion purposes. Ohlson [1995] and Felham and Ohlson 6 Some value drivers are no easily classified. For example, Sales, which is caegorized as an accrual flow, could conain less accruals han EBITDA, which is caegorized as a cash flow measure. 10

13 [1995] build valuaion models in which earnings and book value play insrumenal roles. In some marke inefficiency sudies (e.g., Basu [1977] and Saman [1980]), earnings and book value are assumed o represen fundamenals, and are even shown o conain value relevan informaion no refleced in marke prices. Accruals disinguish accouning numbers from cash flows. Accouning earnings could be more value-relevan han curren cash flows for a leas wo reasons: a) cash flows do no reflec value creaion in some cases (e.g., asse purchases), and b) accruals allow managers o reflec heir judgmen abou fuure prospecs. However, he flexibily allowed whin GAAP creaes he poenial for accouning numbers o be disored, hereby reducing heir value relevance. This poenial for earnings managemen, in combinaion wh he ruism ha price reflecs he presen value of fuure cash flows, has caused some o prefer cash flow muliples over muliples based on accouning numbers. To provide some empirical evidence on his debae, we consider four cash flow measures, and conras heir value-relevance wh wo muliples based on accouning earnings. The four cash flow measures considered are he mos popular ones used in pracice. Each measure removes he impac of accruals o a differen exen. EBITDA adjuss pre-ax earnings o deb and equy holders for he effecs of depreciaion and amorizaion only. CFO deducs ineres and ax expense from EBITDA and also deducs he ne invesmen in working capal. FCF deducs from CFO ne invesmens in all long-erm asses, whereas MCF only deducs from CFO an invesmen equal o he depreciaion expense for ha year. For earnings-based muliples, we consider repored earnings excluding exraordinary ems and disconinued operaion from COMPUSTAT, and acual earnings as defined by IBES. 7 Exising leraure gauges valuaion properies by comparing R 2 from cross-secional regressions. We use a differen meric, which we believe correcs some biases in he popular mehod. 11

14 The second measure is derived from he firs earnings measure by deleing some one-ime ems, such as wre-offs and resrucuring charges. To he exen ha he IBES measure is a beer proxy for permanen or core earnings (earnings ha are expeced o persis in he fuure), will be linked more direcly o price. Alhough he use of sales as a value driver has less heoreical basis, relaive o earnings and cash flows, we consider because of s wide use in cerain emerging indusries where earnings and cash flow are perceived o be uninformaive. The poenial mismach beween hisorical daa, such as repored earnings and cash flows, and he forward-looking informaion capured by prices has long been recognized in he leraure. Analyss forecass of fuure period earnings offer a possible soluion o his mismach. Liu and Thomas [1999] find ha revisions in analyss earnings forecass and changes in ineres raes explain a large porion of conemporaneous sock reurns. We include EPS1 and EPS2 because hese wo forecass are usually available for mos firms. To incorporae he informaion conained in he long-erm EPS growh forecas, we consruc EPS3 by adding he amoun implied by ha growh rae o EPS2. The discouned residual income model has been widely used as a way o calculae inrinsic values. Several recen sudies provide evidence ha he model explains sock prices (e.g., Frankel and Lee [1998], Abarbanell and Bernard [1997], Claus and Thomas [1999]) and reurns (e.g., Liu and Thomas [1999], Liu [1999]). Consisen wh many prior sudies, we assume zero growh in abnormal earnings pas a horizon dae. Alhough incorporaes more informaion han any of he simple muliples, his approach is no as deailed as a comprehensive valuaion based on pro forma projecions ha allow for firm-specific growh in abnormal earnings beyond he horizon dae. 12

15 3.2 Tradional Muliple Valuaion In he firs sage of our analysis, we follow he radional raio represenaion and require ha he price of firm i in year (p ) is direcly proporional o he value driver: p = b x + e (1) where x is he value driver of firm i in year, bis he muliple on he value driver and eis he pricing error. Since our focus is on percen pricing errors (ε /p ), no pricing errors, we divide equaion (1) by price, o obain he following. x e = +. (2) 1 b p p Baker and Ruback [1999] and Beay, Riffe, and Thompson [1999] discuss he problems associaed wh esimaing he slope using equaion (1), because he residual in ha equaion is approximaely proporional o price. When esimaing β, we eleced o impose he resricion ha expeced percen pricing errors (ε/p) be zero, even hough an unresriced OLS esimae for β from equaion (2) offers a lower value of mean squared percen pricing error. 8 Empirically, we find ha our approach generaes lower pricing errors for mos firms, relaive o an unresriced esimae, bu generaes subsanially higher errors in he ails of he disribuion. By resricing ourselves o unbiased pricing errors, we are in effec assigning lower weigh o exreme pricing errors, relaive o he 8 To invesigae he radeoff beween bias and dispersion of pricing errors associaed wh our choice of a resriced regression, we invesigaed he disribuion of pricing errors for he unresriced case. We esimaed equaion (2) for comparable firms from he cross-secion. (When using comparable firms from he same indusry, he esimaed muliples generaed subsanial pricing errors.) We find ha he disribuions of percen pricing errors for all muliples are shifed o he righ subsanially, relaive o he disribuions for he resriced case repored in he paper (our disribuions end o peak around zero pricing error). This shif o he righ indicaes ha he muliples and prediced valuaions for he unresriced case are on average lower han ours. We find ha he bias creaed by his shif causes greaer pricing errors for he bulk of he firms no in he ails of he disribuion, relaive o our resriced case. 13

16 unresriced approach. We are also mainaining consisency wh he radion in economerics ha appears o exhib a lexicographic preference for reduced bias over reduced dispersion. Our approach is o minimize mean squared percen pricing errors when esimaing æe ö equaion (2), subjec o he consrain ha hose errors be zero on average, i.e., E ç = 0. çè ø Since β is he only parameer o be esimaed in equaion (2), he unbiasedness resricion alone is sufficien o deermine ha parameer. Applying he expecaion operaor o equaion (2) and using he resricion, he esimae for b is he harmonic mean of he price-value driver raio. p 1 b = æ x ö E ç p çè ø (3) To eliminae in-sample bias, we esimae b for each firm using all relevan comparable firms excluding he firm ha is being valued. We predic he value of he firm by muliplying he b esimae by he firm s value driver, and hen calculae he percen pricing error as follows: 9 e p p -bˆ x =. (4) p The performance of muliples is evaluaed by examining he dispersion of he pooled disribuion of e / (lower dispersion indicaes beer performance). p 3.3 Inercep Adjused Muliples For he second sage of our analysis, we relax he direc proporionaly requiremen and allow for an inercep: p = a + b x + e. (5) 9 Noe ha some sudies measure he pricing error as he difference beween he prediced value and price (e.g, Alford [1992]) while we measure he pricing error as he difference beween price and he prediced value. 14

17 There are many facors, besides he value driver under invesigaion, ha affec price. The average effec on price of such omed facors is no likely o be zero. The inercep in equaion (5) capures he average effec of omed facors and misspecificaions and hus s inclusion may improve he precision of ou of sample predicions. pricing errors. As wh he simple muliple approach, we divide equaion (5) by price o focus on percen 1 x e = a + b +, (6) p p p 1 OLS esimaion of equaion (6), wh no resricions, minimizes he sum of he squares of percen pricing errors, bu he expeced value of hose errors is non-zero. 10 For he reasons menioned in secion 3.2, and o mainain consisency wh our esimaes from he no-inercep approach, we impose he resricion ha percen pricing errors be unbiased. 11 Tha is, we seek o esimae he parameers α and β ha minimize he mean squared error ( e / he expeced value of e / p is zero: p ), subjec o he resricion ha min var( ε / p ) = var[( p α β x ) / p ] = var[1 ( α α, β p æe ö s.. E ç = 0. p çè ø 1 p + β x )] (7a) (7b) To obain esimaes for α and β, we resae resricion (7b) as follows ε 1 E( ) = E 1 α β p p F HG x p I = KJ 0 (8) In general, his bias could be removed by allowing for an inercep. Tha avenue is no available, however, when he dependen variable is a consan (=1), since he inercep capures all he variaion in he dependen variable, hereby making he independen variables redundan. As wh equaion (2), pricing errors from he unresriced approach for equaion (6) were higher for mos firms (in he middle of he disribuion) bu were smaller in he ails. 15

18 Solve (8) for α, and subsue ino (7a) o resae he minimizaion problem in erms of he following regression wh no inercep: F HG 1 I L M F H G I O KJ P KJ = N HG KJ Q E 1 1 J x x p β F 1 M I (9) p E p ( ) p E p p P where he differen E (.) represen he mean values of hose expressions based on he comparable group. The esimae for β is hen subsued ino equaion (8) o obain an esimae for α. Those esimaes are hen used along wh he value driver for he firm being valued o generae a valuaion. 4. Sample and Daa To consruc he sample, we merge daa from hree sources: accouning numbers from COMPUSTAT; price, analys forecass, and acual earnings per share from IBES; and sock reurns from CRSP. As of April of each year, we selec a cross-secion of firms based on he following creria: (1) all COMPUSTAT value drivers for he previous year are available; (2) he fiscal year ends in December; (3) price, acual EPS, forecased EPS for years +1 and +2, and a long erm growh forecas are available in he IBES summary file; and (4) none of he price raios is an oulier (defined as lying ouside he 1% o 99% of he pooled disribuion). The resuling sample includes 17,505 observaions beween 1981 and This sample is used for he descripive saisics repored in Table 1. For he resuls repored afer Table 1, we impose four addional requiremens: (5) share price on he day IBES publishes summary forecass in April is greaer han or equal o $2; 12 (6) monhly sock reurns are available in he CRSP files 12 Since our valuaion model has an inercep, valuaion error would be abnormally large for socks wh very low share prices. 16

19 for a leas 30 of he 60 monhs prior o April; (7) all muliples are posive; and (8) each indusry-year se has a leas five observaions (indusry as defined by IBES). These requiremens reduce he sample o 9,658 observaions. We adjus all per share numbers for sock spls and sock dividends using IBES adjusmen facors. If IBES indicaes ha he majory of forecass for ha firm-year are on a fully dilued basis, we use IBES diluion facors o conver hose numbers o a primary basis. We summarize all variable definions in he appendix. The P1* variable is calculaed using he discouned residual income model, assuming zero growh in abnormal earnings afer year five: P1 å æe ( eps -kbv ) ö E ( eps -kbv ) (8) 5 * + s +- s = bv+ + s 5 ç s= 1 (1 k) è + ø k(1 + k) where bv = book value per share a ime (he end of year ), eps = earnings per share in year, k = he discoun rae for equy a ime. The discoun rae (k ) is calculaed as he risk-free rae plus bea imes he equy risk premium. We use he 10-year Treasury bond yield on April 1 of year +1 as he risk-free rae and assume a consan 5% equy risk premium. We measure bea as he median bea of all firms in he same bea decile in year. We esimae beas using monhly sock reurns and valueweighed CRSP reurns for he five years ha end in March of year +1 (a leas 30 observaions are required). 13 For a subgroup of firm-years (less han 5 percen), we were able o obain mean IBES forecass for all years in he five-year horizon. For all oher firms, wh less han complee 17

20 forecass available beween years 3 and 5, we generaed forecass by applying he mean longerm growh forecas (g) o he mean forecas for he prior year in he horizon; i.e., eps + s = eps+ s 1 *(1 + g). The book values for fuure years, corresponding o he earnings forecass, are deermined by assuming he ex-ane clean surplus relaion (ending book value in each fuure period equals beginning book value plus forecased earnings less forecased dividends). Since analys forecass of fuure dividends are no available on IBES, we assume ha he curren dividend payou raio will be mainained in he fuure. We measure he curren dividend payou as he raio of he indicaed annual cash dividends o he earnings forecas for year +1 (boh obained from he IBES summary file). 14 To minimize biases ha could be induced by exreme dividend payou raios (caused by forecas +1 earnings ha are close o zero), we Winsorize payou raios a 10% and 50%. 15 We also calculae four varians of P1* (P2* hrough P5*) ha we use o invesigae he informaion/noise radeoff among he componens of P1*. Definions for hese addional variables are provided in he appendix and he resuls are discussed in Secion Resuls 5.1 Descripive Saisics Table 1 repors he pooled disribuion of raios of value drivers o price. The able indicaes ha cash flow muliples are likely o perform poorly. Free cash flow and mainenance cash flow are ofen negaive (approximaely 30% and 20% of he sample, respecively) We use decile median beas, since firm-specific beas are esimaed wh considerable error. Indicaed annual dividends are four imes he mos recen quarer s declared dividends. We use EPS1 as he deflaor because varies less han curren year's earnings and is less likely o be close o zero or negaive. The impac of alering he dividend payou assumpions on he resuls is negligible, because has a very small impac on fuure book value and an even smaller impac on he compued abnormal earnings. 18

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