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Accounting Research Center, Booth School of Business, University of Chicago

Who Is My Peer? A Valuation-Based Approach to the Selection of Comparable FirmsAuthor(s): Sanjeev Bhojraj and Charles M. C. LeeSource: Journal of Accounting Research, Vol. 40, No. 2, Studies on Accounting,Entrepreneurship and E-Commerce (May, 2002), pp. 407-439Published by: Blackwell Publishing on behalf of Accounting Research Center, Booth School of Business,University of ChicagoStable URL: http://www.jstor.org/stable/3542390 .

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JournalofAccountingResearchVol.40No. 2 May2002Printedn U.S.A.

Who Is My Peer? A Valuation-BasedApproach to the Selection ofComparable FirmsSANJEEV BHOJRAJ AND CHARLES M. C. LEE*

Received4January2001;accepted4 September2001

ABSTRACTThis study presents a general approach for selecting comparable firms inmarket-based research and equity valuation. Guided by valuation theory, wedevelop a "warrantedmultiple" for each firm, and identify peer firms as thosehaving the closest warranted multiple. We test this approach by examiningthe efficacy of the selected comparable firms in predicting future (one- tothree-year-ahead) enterprise-value-to-salesand price-to-book ratios. Our tests

encompass the general universe of stocks as well as a sub-population of so-called "new economy" stocks. We conclude that comparable firms selected inthis manner offer sharp improvements over comparable firms selected on thebasis of other techniques.1. Introduction

Accounting-based market multiples are easily the most common tech-nique in equity valuation. These multiples are ubiquitous in the reportsand recommendations of sell-side financial analysts, and are widely used in

*Johnson Graduate School of Management, Cornell University. We thank BhaskaranSwaminathan, as well as workshop participants at the Australian Graduate School of Man-agement, Cornell University,Indiana University,the 2001 JournalofAccountingResearch onfer-ence, the 2001 HKUST Summer Symposium, Syracuse University,and an anonymous referee,for helpful comments. The data on analyst earnings forecasts are provided by I/B/E/S Inter-national Inc.407

Copyright , Universityf Chicagoon behalfof the Institute f ProfessionalAccounting, 002

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408 S. BHOJRAJNDC. M. C. LEEinvestment bankers' fairnessopinions (e.g., DeAngelo [1990]). They also ap-pear in valuations associated with initial public offerings (IPOs), leveragedbuyout transactions, seasoned equity offerings (SEOs), and other mergerand acquisition (M&A) activities.' Even advocates of projected discountedcash flow (DCF) valuation methods frequently resort to using market mul-tiples when estimating terminal values.Despite their widespread usage, little theory is available to guide the appli-cation of these multiples. With a few exceptions, the accounting and financeliterature contains little evidence on how or why certain individual multi-ples, or certain comparable firms, should be selected in specific contexts.Some practitioners even suggest that the selection of comparable firms isessentially "anart form" that should be left to professionals.2Yet the degreeof subjectivity nvolved in their application is discomforting from a scientificperspective. Moreover, the aura of mystique that surrounds this techniquelimits its coverage in financial analysis courses, and ultimately threatens itscredibility as a serious alternative in equity valuation.In this study, we re-examine the theoretical underpinnings for the useof market multiples in equity valuation, and develop a systematic approachfor the selection of comparable firms. Our premise is that the popularityof market-based valuation multiples stems from their function as a classic"satisficing"device (Simon [1997]). In using multiples to value firms, an-alystsforfeit some of the benefits of a more complete, but more complex,pro forma analysis.In exchange, they obtain a convenient valuation heuris-tic that produces satisfactory results without incurring extensive time andeffort costs. In fact, we believe it is possible to compensate for much of theinformation these multiples fail to capture through the judicious selectionof comparable firms. Our aim is to develop a more systematic technique fordoing so, through an appeal to valuation theory.Specifically, we argue that the choice of comparable firms should be afunction of the variables that drive cross-sectional variation in a given val-uation multiple. For example, in the case of the enterprise-value-to-salesmultiple, comparable firms should be selected on the basis of variables thatdrive cross-sectional differences in this ratio, including expected profitabil-ity, growth, and the cost-of-capital.3In this spirit, we use variables nomi-nated by valuation theory and recent advances in estimating the impliedcost-of-capital (i.e., Gebhardt, Lee, and Swaminathan [2001]) to develop a

1For example, Kim and Ritter [1999] discuss the use of multiples in valuing IPOs. Kaplanand Ruback [1995] examine alternative valuation approaches, including multiples, in highlylevered transactions.2For example, Golz [1986], Woodcock (1992), and McCarthy(1999).We use the enterprise-value-to-sales ratio (EVS) rather than the price-to-sales (PS) ratiobecause the former is conceptually superior when firms are differentially levered (we thank thereferee for pointing this out). We also report results for the price-to-book (PB) ratio. We focuson these two ratios because of their applicability to loss firm, which are particularlyimportant

among the so-called "neweconomy" (tech, biotech, and telecommunication) stocks. However,our approach is general, and can be applied to any of the widely used valuation multiples.

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WHO IS MYPEER? 409"warrantedmultiple" for each firm based on large sample estimations. Wethen identify a firm's "peers"as those firms having the closest warrantedvaluation multiple.

Our procedures result in two end products. First,we produce warrantedmultiples for each firmn-that is, a warranted enterprise-value-to-sales(WEVS)and a warranted price-to-book (WPB)ratio. These warranted mul-tiples are based on systematicvariations in the observed multiples in cross-section over large samples. The warranted multiples themselves are usefulfor valuation purposes, because they incorporate the effect of cross-sectionalvariations in firm growth, profitability,and cost-of-capital.Second, by rank-ing firms according to their warranted multiples, we generate a list of peerfirms for each target firm. For investors and analysts who prefer to con-duct equity valuation using market multiples, this approach suggests a moreobjective method for identifying comparable firms.For researchers, our approach suggests a new technique for selecting con-trol firms,and for isolating a variable of particularinterest. Recent methodol-ogy studies have demonstrated that characteristic-matched control samplesprovide more reliable inferences in market-basedresearch (e.g., BarberandLyon [1997], Lyon et al. [1999]). Our study extends this line of research bypresenting a more precise technique for matching sample firms based oncharacteristics identified by valuation theory. Our approach is designed toaccommodate both profitable and loss firms, which have become pervasivein the so called "neweconomy." In short, the methodology developed in thispaper can be useful whenever the choice of control firms playsa prominentrole in the research design of a market-related study.We test our approach byexamining the efficacyof the selected comparablefirms in predicting future (one- to three-year-ahead)EVSandPB ratios.4Ourtests encompass the general universe of stocks as well as a sub-populationof "new economy" stocks from the tech, biotech, and telecommunicationsectors. Our results show that comparable firms selected in this manneroffer sharp improvements over comparable firms selected on the basis ofother techniques, including industry and size matches. The improvementis most pronounced among the so-called new economy stocks.The main message from this study is that the choice of comparable firmscan be made more systematicand less subjective through the application ofvaluation theory. In the case of the EVSmultiple, our approach almost triplesthe adjusted r-squaresobtained from using simply industry or industry-sizematched selections. The PB multiple is more difficult to predict in general,but our approach still more than doubles the adjusted r-square relative toindustryor industry-sizematched selections. Interestingly,we find that usingthe actual multiples from the best comparable firms is generally better thanusing the warranted multiple itself. Moreover, the choice of comparable

4Weforecast future multiples because we do not regard the current stock price as necessarilythe best benchmark for assessing valuation accuracy. As discussed later, forecasting futuremultiples is not equivalent to forecasting future prices or returns.

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410 s. BHOJRAJAND C. M. C. LEEfirms is, to some extent, dependent on the market multiple underconsideration-the best firms for the EVSratio are not necessarily the bestfirms for the PB ratio. While we illustrate our approach using these two ra-tios, this technique can be generalized to other common market multiples,including: EBITDA/TEV, E/P, CF/P, and others.In the next section, we further motivate our study and discuss its relationto the existing literature. In section 3, we develop the theory that underpinsour analysis. In section 4, we discuss sample selection, research design andestimation procedures. Section 5 reports our empirical results,and section 6concludes with a discussion of the implications of our findings.2. Motivationand Relationto PriorLiterature

There are at least three situations in which comparable firms are useful.First, in conducting fundamental analysis,we often need to make forecastsof sales growth rates, profit margins, and asset efficiency ratios. In thesesettings, we typically appeal to comparable firms from the same industryas a source of reference. Second, in multiples-based valuation, the marketmultiples of comparable firms are used to infer the market value of the targetfirm. Third, in empirical research, academics seek out comparable firms asa research design device for isolating a variable of particular interest. Ourpaper is focused primarily on the second and third needs for comparablefirms.5

Given their widespread popularity among practitioners, market multiplesbased valuation has been the subject of surprisingly few academic studies.Three recent studies that provide some insights on this topic are Kim andRitter (KR; [1999]), Liu, Nissim, and Thomas (LNT; [1999]), and Baker andRuback (BR; [1999]). All three examine the relative accuracyof alternativemultiples in different settings. KR uses alternative multiples to value initialpublic offers (IPOs), while LNTand BRinvestigate the more general contextof valuation accuracyrelative to current stock prices. KR and LNT both findthat forward earnings perform much better than historical earnings. LNTshows that in terms of accuracy relative to current prices, the performanceof forwardearnings is followed by that of historical earnings measures, cashflow measures, book value, and finally,sales. In addition, Baker and Ruback[1999] discuss the advantages of using harmonic means-that is, the inverseof the average of inversed ratios-when aggregating common market multi-ples. None of these studies address the choice of comparable firms beyondnoting the usefulness of industry groupings.

5 Our technique is not directly relevant to the first situation, because it does not match firmson the basis of a single attribute (such as sales growth, or profit margin). Instead, our approachmatches firms on the basis of a set of variables suggested by valuation theory. Our paper alsodoes not address the trivial case whereby a firm is its own comparable. As we point out later, inmultiples-based valuation of public firms, a firm's own lagged multiple is often the most usefulempirical proxy for its current multiple.

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WHO IS MYPEER? 411Closer to this studyare three prior studies that either investigate the effectof comparable firm selection on multiple-based valuation, or examine thedeterminants cross-sectional variations in certain multiples. Boatsman and

Baskin [1981] compare the accuracy of value estimated based on earnings-to-price (EP) multiples of firms from the same industry. They find that,relative to randomly chosen firms,valuation errors are smaller when compa-rable firms are matched on the basis of historical earnings growth. Similarly,Zarowin [1990] examines the cross-sectional determinants of EPratios. Heshows forecasted growth in long-term earnings is a dominant source of vari-ation in these ratios. Other factors, such as risk, historical earnings growth,forecasted short-term growth, and differences in accounting methods, seemto be less important.Finally,Alford [1992] examines the relative valuation accuracyof EPmul-tiples when comparable firms are selected on the basis of industry, size,leverage, and earnings growth. He finds that valuation errors decline whenthe industry definition used to select comparable firms is narrowed to two-or three-digit SIC codes, but that there is no further improvement when afour-digit classification is used. He also finds that after controlling for in-dustry membership, further controls for firm size, leverage, and earningsgrowth do not reduce valuation errors.Several stylized facts emerge from these studies. First,the choice of whichmultiple to use affects accuracy results. In terms of accuracy relative to cur-rent prices, forecasted earnings perform relativelywell (KR,LNT); the price-to-sales and price-to-book ratios perform relatively poorly (LNT). Second,industry membership is important in selecting comparable firms (Alford[1992], LNT, KR). The relation between historical growth rates and EP ra-tios is unclear, with studies reporting conflicting results (Zarowin [1999],Alford [1992], Boatsman and Baskin [1981]), but forecasted growth ratesare important (Zarowin [1999]). Other measures, including risk-based met-rics (leverage and size) do not seem to provide much additional explanatorypower for E/P ratios.Our study is distinct from these prior studies in several respects. First,ourapproach is more general, and relies more heavilyon valuation theory. Thistheory guides us in developing a regression model that estimates a "war-ranted multiple" for each firm. We then define a firm's peers as those firmswith the closest warranted market multiple to the target firm, as identifiedby our model. The advantage of a regression-based approach is that it allowsus to simultaneously control for the effect of various explanatory variables.For example, some firms might have higher current profitability,but lowerfuture growth prospects, and higher cost-of-capital.This approach allows usto consider the simultaneous effect of all these variables, and to place ap-propriate weights on each variable based on empirical relations establishedin large samples.Our empirical results illustrate the advantage of this approach. Contraryto the mixed results in prior studies, we find that factors related to profitabil-ity, growth, and risk, are strongly and consistently correlated with the EVS

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412 S. BHOJRAJNDC.M.C.LEEand PB ratios. Collectively, factors that relate to profitability, growth, andrisk,play an important role in explaining cross-sectional variations of thesemultiples. In fact, we find that variables related to firm-specificprofitability,forecasted growth and risk are more important than industry membershipand firm size in explaining a firm's future EVSand PB ratios.Second, we employ recent advances in the empirical estimation of cost-of-capital (i.e., Gebhardt et al. [2001]) to help identify potential explanatoryvariables for estimating our model of warranted market multiples. The riskmetrics examined in prior studies are relativelysimple, and the results aremixed. We follow the technique in Gebhardt et al. [2001] to secure addi-tional explanatory variables that are associated with cross-sectional determi-nants of a firm's implied cost-of-capital.Several of these factors turn out tobe important in explaining EVSand PB ratios.Third, we do not assume that the current stock price of a firm is thebest estimate of firm value. Prior studies compare the valuation derived bythe multiples to a stock's current price to determine the valuation error. Ineffect, these studies assume that the current stock price is the appropriatenormative benchmark by which to judge a multiple's performance. Underthis assumption, it is impossible to derive an independent valuation usingmultiples that is useful for identifying over- or under-valued stocks.Our less stringent assumption of market efficiency is that a firm's currentprice is a noisy proxy for the true, but unobservable intrinsic value, definedas the present value of expected dividends. Moreover, due to arbitrage,price converges to value over time. As a result, price and various alternativeestimates of value based on accounting fundamentals will be co-integratedover time.6 Under this assumption, we estimate a "warrantedmultiple" thatdiffers from the actual multiple implicit in the current price. Consistentwith this philosophy, we test the efficacy of alternative estimated multiplesby comparing their predictive power for a firm's future multiples (e.g., itsone-, two-, or three-year-aheadEVSand PB ratios).'Finally,our approach can be broadly applied to loss firms,including many"new economy" stocks. Prior studies that examine comparable firms (e.g.,Alford [1992], Boatsman and Baskin [1981], and Zarowin [1999]) focussolely on the EP ratio. A limitation of these studies is that they do not per-tain to loss firms. This limitation has become more acute in recent years,as many technology, biotechnology, and telecommunication firms have re-ported negative earnings.

6 For a more formal statistical model of this co-integrated relationship between price andalternative estimates of fundamental value, see, Lee, Myers,and Swaminathan [1999].7 Note that forecasting future multiples is different from forecasting future prices or returns.In the current context, forecasting future price involves two steps:forecasting future multiples,and forecasting future fundamentals (e.g., sales or book value per share). Our main interestis in the stability of the multiples relation, and not in forecasting fundamentals. An example

of fundamental analysis that focuses on forecasting future fundamentals is Ou and Penman[1989].

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WHO IS MY PEER? 413Appendix A provides an indication of the magnitude of the problem.This appendix reports descriptive statisticsfor a sample of 3,515 firms fromNYSE/AMEX/NASDAQ as of 5/29/2000. To be included, a firm must beU.S. domiciled (i.e., not an ADR), have a market capitalization of over$100 million, and fundamental data for the trailing 12 months (i.e., nota recent IPO). Based on aggregate net income from the most recent fourquarters, we divide the sample into profitable firms (78% of sample) andloss firms (22% of sample).Panel A reports the percentage of these firms that have positive EBIT,Op-erating Income, EBITDA, Gross Margin, Sales, One-year-ahead forecastedearnings (FY1), and book value. This panel shows that only 40% of the loss

firms have positive operating income, only 47% have positive EBITDA,andonly 34% have positive FY1 orecasts. In fact, only 87% of the loss firms havepositive gross margins. The only reliably positive accounting measures aresales (100%) and book value (94%). Clearly,these loss firms are difficult tovalue.However, they are also difficult to ignore. Panel B reports the distribu-tion of realized returns in the past six months (11/31/99 to 5/29/00) sep-arately for the profit firms and loss firms. The returns for the loss firms

have higher mean (19.6% versus 7.8%), higher standard deviation (111.3%versus 42.3%), and "fatter tails." As a group, the loss firms appear to be ahigh-stake game that constitutes a substantial proportion of the universe oftraded stocks in the United States.Our study uses the two most reliablypositive multiples (EVSand PB). Liu,Nissim, and Thomas [1999] show that these two ratios are relatively poorperformers in terms of their valuation accuracy. We demonstrate that bychoosing an appropriate set of comparable firms, the accuracyof these ratioscan be improved sharply. In particular, we demonstrate the incrementalusefulness of the technique for a sub-population of "new economy" stocksfrom the technology, telecom, and biotechnology sectors.

3. Development f theTheoryThe valuation literature discusses two broad approaches to estimatingshareholder value. The first is "direct valuation," in which firm value is es-timated directly from its expected cash flows without appeal to the current

price of other firms. Most direct valuations are based on projected dividendsand/or earnings, and involve a present value computation of future cashflow forecasts. Common examples are the dividend discount model (DDM),the discounted cash flow (DCF) model, the residual income model (RIM),or some other variant.8 The second is a "relativevaluation" approach in

We do not discuss liquidation valuation, in which a firm is valued at the "breakup value"of its assets. Commonly used in valuing real estate and distressed firms, this approach is notappropriate for most going concerns.

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414 s. BHOJRAJAND C. M. C. LEEwhich firm value estimates are obtained by examining the pricing of com-parableassets. This approach involves applying an accounting-based mar-ket multiple (e.g., price-to-earnings, price-to-book, or price-to-sales ratios)from the comparable firm(s) to our accounting number to secure a valueestimate.9In relativevaluation, an analystapplies the market multiple from a "com-parable firm" to a target firm's corresponding accounting number: Ourestimated price = (Their market multiple) X (Our accounting number).In so doing, the analyst treats the accounting number in question as a sum-marystatisticfor the value of the firm. Assuming our firm in its current state"deserves" he same market multiple as the comparable firm, this procedureallows us to estimate what the market would pay for our firm.Which firm(s) "deserve"the same multiple as our target firm? Valuationtheory helps to resolve this question. In fact, explicit expressions for most ofthe most commonly used valuation multiples can be derived using little morethan the dividend discount model and a few additional assumptions. Forexample, the residual income formula allows us to re-expressthe discounteddividend model in terms of the price-to-book ratio:10

PB, Et[(ROEt+i - re)Bt+i-l] (1)Bt i=1 (1 + re)i Btwhere Pt* is the present value of expected dividends at time t, B, = bookvalue at time t;Et [.] = expectation based on information available at time t;re = cost of equity capital;and ROEt+i = the after-taxreturn on book equityfor period t + i. This equation shows that a firm's price-to-book ratio is afunction of itsexpected ROEs,its cost-of-capital,and its future growth rate inbook value. Firms that have similar price-to-book ratios should have presentvalues of future residual income (the infinite sum in the right-hand-side ofequation (1)) that are close to each other.In the same spirit, it is not difficult to derive the enterprise-value-to-salesratio in terms of subsequent profit margins, growth rates, and the cost ofcapital. In the case ofa stable growth firm, the enterprise-value-to-salesratiocan be expressed as:"

EV7 _ Et(PMxkx(1 + g))St (r- g)where EVZis total enterprise value (equity plus debt) at time t, St = to-tal sales at time t; Et[.] = expectation based on information available at

9 A third approach, not discussed here, is contingent claim valuation based on option pricingtheory. Designed for pricing traded assetswith finite lives, this approach encounters significantmeasurement problems when applied to equity securities. See Schwartz and Moon [2000]and Kellogg and Charnes [2000] for examples of how this approach can be applied to "neweconomy" stocks.10See Feltham and Ohlson [1995] or Lee [1999] and the references therein for a discussionof this model.'" See Damodaran [1994; page 245] for a similar expression.

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WHO IS MYPEER? 415time t; PM is operating profit margin (earnings before interest); k is a con-stant payout ratio (dividends and debt servicing costs as a percentage ofearnings; alternatively,it is sometimes called one minus the plow-backrate);r = weighted average cost of capital; and g is a constant earnings growthrate.

In the more general case, we can model the firm's growth in terms ofan initial period (say n years) of high growth, followed by a period of morestable growth in perpetuity.Under this assumption, a firm'senterprise-value-to-sales ratio can be expressed as:EVt EtPMxkx (1+ gl)(1- ((1 + gg)n/(l

+ r)n))St rL- r(1 + gi) n(l + g2) 1? (1+g1)n(1+ g2) ]ii (3)(1+ nir- g '

where EV7 is the total enterprise value (debt plus equity) at time t, St =total sales at time t; Et[.] = expectation based on information availableat time t; PM is operating profit margin; k is a constant payout ratio; r =cost of capital; gi is the initial earnings growth rate, which is applied forn years; and g2 is the constant growth rate applicable from period n+ 1onwards.Equation (3) shows that a firm's warranted enterprise-value-to-salesratiois a function of its expected operating profit margin (PM), payout ratio (k),expected growth rates (gi and g2), and cost of capital (re). If the marketvalueof equity and debt approximates the present value of expected cash flows,these variables should explain a significant portion of the cross-sectionalvariation in the EVSratio. In the tests that follow, we employ a multipleregression model to estimate the warranted EVSand PBratios for each firm.

The explanatory variableswe use in the model are empirical proxies for thekey elements in the right-hand side of equations (1) and (3).4. Research Design

In this section, we estimate annual regressions that attempt to explain thecross-sectional variation in the EVSandPBratios. Our goal is to develop a rea-sonably parsimonious model that produces a "warrantedmultiple" (WEVSor WPB)for each firm. These warranted multiples reflect the large samplerelation between a firm's EVS (or PB) ratio and variables that should ex-plain cross-sectional variations in the ratio. The estimated WEVS or WPB)becomes the basis of our comparable firm analysis.4.1 ESTIMATINGTHE WARRANTEDRATIOS

Weuse all firms in the intersection of (a) the merged COMPUSTAT ndus-trial and research files, and (b) the I/B/E/S historical database of analystearnings forecasts, excluding ADRs and REITs.We conduct our analysisas of June 30th of each year for the period 1982-1998. To be included

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416 s. BHOJRAJNDC.M.C. LEEin the analysis a firm must have at least one consensus forecast of long-term growth available during the 12 months endedJune 30th. In the eventthat more than one consensus forecast was made in any year, the mostrecent forecast is used. We use accounting information for each firm asof the most recent fiscal year end date, and stock prices as of the end ofJune.To facilitate estimation of a robust model, we drop firms with prices below$3 per share and sales below $100 million. We eliminate firms with negativebook value (defined as common equity), and anyfirms with missing price oraccounting data needed for the estimation regression.12We require that allfirms belong in an industry (based on two-digitSICcodes) with at least fivemember firms. In addition we eliminate firms in the top and bottom onepercent of all firms ranked by EVS,PB, Rnoa, Lev,Adjpm,and Adjgroeachyear (these variables are defined below). The number of remaining firms inthe sample range from 741 (in 1982) to 1,498 (in 1998).For each firm, we secure nine explanatory variables. We are guided inthe choice of these variables by the valuation equations discussed earlier,and several practical implementation principles. First,we wish to constructa model that can be applied to private as well as public firms, we thereforeavoid using the market value of the target firm in any of the explanatoryvariables. Second, in the spirit of the contextual fundamental analysis (e.g.,see Beneish, Lee, and Tarpley [2000]), we anchor our estimation procedureon specific industries. In other words, we use the mean industry marketmultiples as a startingpoint, and adjustfor key firm-specificcharacteristics.'3Finally, to the extent possible, we try to use similar variables for estimatingEVS and PB. Our goal is to generate relatively simple models that capturethe key theoretical constructs of growth, risk, and profitability. Specifically,our model includes the following variables,which are also summarized anddescribed in more detail in Appendix B:

Indevs--The harmonic mean of the enterprise-value-to-salesmultiple forall the firms with the same two-digit SIC code. For example, for the 1982regression, this variable is the harmonic mean industry EVS as of June 1,1982. Enterprise value is defined as total market capitalization of equity,plus book value of long-term debt. This variable controls for industry-wide factors, such as profit margins and growth rates, and we expectit to be positively correlated with current year firm-specific EVSand PBratios.Indpb-The harmonic mean of the price-to-book ratio for all firms in thesame industry. This variable controls for industry-wide factors that affectthe PBratio. In addition, Gebhardt et al. [2001] show firms with higher PB12 The two exceptions are research and development expense and long-term debt. Missingdata in these two fields are assigned a value of zero.1 More specifically, we use the harmonic means of industry EVSand PB ratios, that is, the

inverse of the average of inversed ratios (see Baker and Ruback [1999]).

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WHO IS MYPEER? 417ratios have lower implied costs of capital. To the extent that industries withlower implied costs-of-capitalhave higher market multiples, we expect thisvariable to be positively correlated with EVSand PB ratios.Adjpm--The industry-adjusted profit margin. We compute this variableas the difference between the firm's profit margin and the median industryprofit margin. In each case, the profit margin is defined as a firm'soperatingprofit divided by its sales. Theory suggests this variable should be positivelycorrelated with current year EVSratios.Losspm---Thisvariable is computed asAdjpm*Dum,where Dumis 1 if Adjpmis less than or equal to zero, and 0 otherwise. Used in conjunction withAdjpm, his variable captures the differential effect of profit margin on theP/S ratio for loss firms. Prior studies (e.g., Hayn [1995]) show that prices(and returns) are less responsive to losses than to profits. In univariate tests,this variable should be positively correlated with EVSand PB. However, con-trolling for Adjpm, his variable should be negatively correlated with EVSandPB ratios.

Adjgro--Industry-adjustedgrowth forecasts. This variable is computed asthe difference between a firm's consensus earnings growth forecast (fromIBES) and the industry median of the same. Higher growth firms merithigher EVSand PB ratios.Lev---Bookleverage. This variable is computed as the total long-term debtscaled by the book value of common equity. In univariate tests, Gebhardtet al. [2001] shows that firms with higher leverage have higher implied costs-of-capital. However, controlling for market leverage, they find that bookleverage is not significant in explaining implied cost-of-capital.We includethis variable for completeness, in case it captures elements of cross-sectionalrisk not captured by the other variables.Rnoa-Return on net operating asset. This variable is a firm's operatingprofit scaled by its net operating assets. Penman [2000] recommends thisvariable as a measure of a firm's core operation profitability.In our context,having already controlled for profit margins, this variable also serves as acontrol for a firm's asset turnover. We expect it to be positively correlatedwith the EVSand PB ratios.

Roe--Return on equity. This variable is net income before extraordinaryitems scaled bythe end of period common equity. Conceptually, thisvariableshould provide a better profitability proxy in the case of the PB ratio. Weuse this variable in place of Rnoa as an alternative measure of profitabilitywhen conducting the PB regression.Rd-Total research and development expenditures divided bysales. Firmswith higher R&Dexpenditures tend to have understated current profitabil-ity relative to future profitability. To the extent that this variable capturesprofitability growth beyond the consensus earnings forecast growth rate, weexpect it to be positively correlated with the EVSand PB ratios.

In addition to these nine explanatory variables, we also tested threeother variables-a dividend payout measure (actual dividends scaled by

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418 S. BHOJRAJ ND C. M. C. LEEtotal assets), an asset turnover measure, and a measure of the standarddeviation of the forecasted growth rate. The first two variables add lit-tle to the explanatory power of the model. The standard deviation mea-sure (suggested by Gebhardt et al. [2001] as a determinant of the cost-of-capital) contributed marginally, but was missing for a significant numberof observations. Moreover, this measure would be unavailable for privatefirms. For these reasons, we excluded all three variables from our finalmodel.

To recap, our research design involves estimating a series of annualcross-sectional regressions of either the EVSor PBratio on eight explanatoryvariables. The estimated coefficients from last year's regressions are used,in conjunction with each firm's current year information, to generate aprediction of the firm's current and future ratio. We refer to this predictionas a firm's "warrantedmultiple" (WEVSor WPB).This warranted multiplebecomes the basis for our identification of comparable firms in subsequenttests.4.2 DESCRIPTIVE TATISTICS

Table 1 presents annual summary statistics on the two dependent andnine explanatory variables. The overall average EVS of 1.20 (median of0.94) and average PB of 2.26 (median of 1.84) are comparable to priorstudies (e.g., LNT,BB), although our sample size is considerably larger dueto the inclusion of loss firms. This table also reveals some trends in thekey variables over time. Consistent with prior studies (e.g., Frankel andLee [1999]) we observe an increase over time in the accounting-basedmultiples (EVS,PB, Indps, and Indpb) and total R&D expenditures (Rd).This non-stationarity in the estimated coefficients could be attributableto systematic changes in the composition of firms over time. For exam-ple, the increased importance of the R&D variable could reflect the ris-ing prominence of technology firms in the sample. The accounting-basedrates of return (Rnoaand Roe)and book leverage (Lev) are relativelystableover time. As expected, the industry-adjustedvariables (Adjpm,Losspm,andAdjgro)have mean and median measures close to zero. Overall, this ta-ble indicates that the key input variables for our analysis make economicalsense.

Table 2 presents the average annual pairwise correlation coefficients be-tween these variables.The upper triangle reports Spearman rankcorrelationcoefficients; the lower triangle reports Pearson correlation coefficients. Asexpected, EVS s positively correlated with the industry enterprise-value-to-sales ratio (Indevs)and price-to-book ratio (Indpb). It is also positively cor-related with industry-adjustedmeasures of a firm's profit margin (Adjpm)and expected growth rate (Adjgro).It is negatively correlated with bookleverage (Lev), and positively correlated with accounting rates of return(Rnoa and Roe), as well as R&D expense (Rd). To a lesser degree, EVSis also positively correlated with profit margin among loss firms (Losspm).The results are similar for the PB ratio. All the correlation coefficients

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WHO IS MYPEER? 419TABLE 1

SummaryStatisticsofEstimationVariablesThis table provides information on the mean and median of the variables used in the annualestimation regressions. All accounting variables are from the most recent fiscalyearend publiclyavailable byJune 30th. Market values are as of June 30th. EVS s the enterprise value to salesratio, computed as the market value common equity plus long-term debt, divided by sales. PBis the price to book ratio. Indevs s the industry harmonic mean of EVSbased on two-digit SICcodes. Indpb s the industry harmonic mean of PB. Adjpm s the difference between the firm'sprofit margin and the industryprofit margin, where profit margin is defined as operating profitdivided by sales. Losspms Adjpm* indicator variable, where the indicator variable is 1 if profitmargin < 0 and 0 otherwise. Adjgros the difference between the analystsconsensus forecast ofthe firm's long-term growth and the industry average. Levis the total long-term debt scaled bybook value of stockholders equity. Rnoa is operating profit scaled by net operating assets. Rdisthe firm's R&Dexpressed as a percentage of net sales.year EVS PB Indevs Indpb Adjpm Losspm Adjgro Lev Rnoa Roe Rd1982 mean 0.63 1.11 0.50 0.92 0.006 0.000 0.50 0.45 20.85 14.39 1.23median 0.50 0.93 0.50 0.92 0.000 0.000 0.00 0.36 19.62 14.77 0.141983 mean 0.98 1.82 0.76 1.57 0.002 -0.003 0.21 0.49 17.18 11.88 1.33

median 0.77 1.48 0.77 1.59 0.000 0.000 -0.05 0.38 16.18 12.82 0.091984 mean 0.84 1.46 0.69 1.34 0.001 -0.004 0.44 0.43 17.85 12.04 1.51

median 0.69 1.26 0.72 1.30 0.000 0.000 -0.01 0.33 16.93 13.00 0.081985 mean 0.88 1.72 0.70 1.45 0.004 -0.002 0.66 0.44 19.96 13.49 1.66median 0.73 1.46 0.72 1.30 0.000 0.000 0.00 0.32 18.82 14.32 0.051986 mean 1.07 2.14 0.85 1.87 0.001 -0.004 0.30 0.50 17.58 11.45 1.75

median 0.88 1.82 0.86 1.69 0.000 0.000 -0.04 0.34 16.41 12.92 0.001987 mean 1.22 2.31 0.95 1.95 -0.002 -0.007 0.18 0.54 17.27 10.63 1.94median 1.00 1.92 0.95 1.82 0.000 0.000 -0.10 0.40 16.00 12.22 0.001988 mean 1.09 1.97 0.85 1.69 0.002 -0.004 0.29 0.56 19.05 12.61 1.83

median 0.90 1.70 0.80 1.61 0.000 0.000 0.00 0.43 17.68 12.93 0.001989 mean 1.07 2.02 0.84 1.79 0.003 -0.003 0.69 0.57 19.90 13.90 1.94median 0.89 1.70 0.76 1.63 0.000 0.000 0.00 0.41 18.54 14.71 0.001990 mean 1.09 1.99 0.83 1.69 0.002 -0.004 0.58 0.61 19.77 13.29 1.86

median 0.89 1.64 0.79 1.49 0.000 0.000 -0.08 0.44 17.97 13.51 0.001991 mean 1.10 1.93 0.80 1.65 0.003 -0.002 0.45 0.59 19.00 11.91 1.96median 0.87 1.54 0.69 1.39 0.000 0.000 -0.12 0.45 16.93 12.55 0.001992 mean 1.15 2.13 0.87 1.71 0.005 -0.004 0.23 0.59 17.86 10.31 2.03median 0.94 1.76 0.78 1.52 0.000 0.000 -0.19 0.42 15.97 11.29 0.001993 mean 1.22 2.48 0.90 1.91 0.002 -0.002 0.55 0.58 19.80 11.87 1.99median 1.02 2.04 0.86 1.76 0.000 0.000 -0.09 0.39 17.22 12.39 0.001994 mean 1.20 2.31 0.89 2.02 0.006 -0.002 0.49 0.58 20.08 11.57 1.90median 1.00 1.98 0.86 1.91 0.000 0.000 -0.15 0.36 17.47 12.37 0.001995 mean 1.36 2.49 0.95 2.06 0.007 -0.001 0.73 0.56 21.66 13.48 1.77

median 1.07 2.08 0.93 2.02 0.000 0.000 0.00 0.38 18.72 13.18 0.001996 mean 1.49 2.75 1.01 2.18 0.009 -0.002 0.40 0.58 22.19 12.57 2.01

median 1.13 2.24 0.98 1.99 0.000 0.000 -0.13 0.37 18.93 13.08 0.001997 mean 1.51 2.87 1.02 2.12 0.005 -0.003 0.36 0.61 21.56 12.46 2.01median 1.20 2.41 1.07 2.01 0.000 0.000 -0.17 0.36 18.97 12.89 0.001998 mean 1.59 3.06 1.09 2.20 0.004 -0.004 0.43 0.63 22.84 12.31 2.25median 1.24 2.55 1.08 2.05 0.000 0.000 0.00 0.38 20.24 12.76 0.00

Pooled mean 1.20 2.26 0.88 1.83 0.004 -0.003 0.44 0.56 20.00 12.35 1.86median 0.94 1.84 0.81 1.72 0.000 0.000 -0.05 0.38 17.96 13.01 0.00

are in the expected direction. Except for the correlation between Rnoaand Roe (which do not appear in the same estimation regression), noneof the average pairwise correlation coefficients exceed 0.60. These resultssuggest that the explanatory variables are not likely to be redundant.

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420 S. BHOJRAJAND C. M. C. LEETABLE 2Correlation etween stimationVariables

This table provides the correlation between the variables. The upper triangle reflects theSpearman correlation estimates; the lower triangle reflects the Pearson correlation coefficients.All accounting variables are based on the most recent fiscal year end information publiclyavailable byJune 30th. Market values are as of June 30th. EVS s the enterprise value to salesratio, computed as the market value common equity plus long-term debt, divided by sales. PBis the price to book ratio. Indevs s the industry harmonic mean of EVSbased on two-digit SICcodes. Indpb s the industry harmonic mean of PB. Adjpm s the difference between the firm'sprofit margin and the industryprofit margin, where profit margin is defined as operating profitdivided by sales. Losspms Adjpm* ndicator variable, where the indicator variable is 1 if profitmargin < 0 and 0 otherwise. Adjgros the difference between the analystsconsensus forecast ofthe firm's long-term growth and the industry average. Lev is the total long-term debt scaled bybook value of stockholders equity. Rnoa is operating profit scaled by net operating assets. Rd isthe firm's R&Dexpressed as a percentage of net sales.

Average Correlation (Pearson/Spearman)EVS PB Indevs Indpb Adjpm Losspm Adjgro Lev Rnoa Roe RdEVS 0.52 0.51 0.16 0.54 0.08 0.21 -0.07 0.21 0.28 0.17PB 0.47 0.09 0.33 0.38 0.14 0.29 -0.20 0.60 0.59 0.08Indevs 0.50 0.04 0.35 -0.07 0.04 -0.01 0.06 -0.01 0.05 0.19

Indpb 0.15 0.28 0.35 -0.03 0.06 -0.04 -0.14 0.26 0.15 0.11Adjpm 0.59 0.33 -0.06 -0.02 0.26 0.06 -0.17 0.54 0.55 0.03Losspm 0.06 0.09 0.02 0.04 0.32 0.06 -0.03 0.28 0.26 -0.05Adjgro 0.22 0.29 -0.01 -0.05 0.04 0.04 -0.01 0.10 0.09 -0.02Lev -0.03 -0.07 0.08 -0.09 -0.12 -0.02 0.02 -0.35 -0.16 -0.27Rnoa 0.22 0.54 -0.02 0.25 0.51 0.32 0.07 -0.24 0.75 0.03Roe 0.23 0.48 0.03 0.14 0.50 0.38 0.07 -0.12 0.66 -0.03Rd 0.24 0.09 0.10 0.06 0.06 -0.10 0.09 -0.23 -0.03 -0.06

5. EmpiricalResults5.1 MODEL ESTIMATION

Table 3 presents the results of annual cross-sectional regressions for eachyear from 1982 to 1998. The dependent variable is the enterprise-value-to-sales ratio (EVS). The eight independent variables are as described in theprevious section. Table values represent estimated coefficients, with accom-panying p-values presented in parentheses. Reported in the right columnsare adjusted r-squaresand the number of observations per year.The last tworowsreport the average coefficient for each variable,as well as a Newey-Westautocorrelation adjusted t-statisticon the mean of the time series of annualestimated coefficients.

The results from this table indicate that a consistently high proportionof the cross-sectional variation in the EVS ratio is captured by the eightexplanatory variables. The annual adjusted r-squares average 72.2%, andrange from a low of 66.1% to a high of 76.5%. The strongest six explana-toryvariables (Indevs,Adjpm,Losspm,Adjgro,Rnoa,and R&D) have the samedirectional sign in each of 17 annual regressions, and are individually sig-nificant at less than 1%. Indpb s positively correlated with EVS in 11 outof 17 years, and is significant at the 5% level. Controlling for Indpb,book

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WHO IS MYPEER? 421TABLE 3

Annual EstimationRegressionsor Warranted nterprise-Value-to-SalesThis table reports the results from the following annual estimation regression:

8EVSi,t= at + jtCj,i,t + Li,tj=1

where the dependent variable, EVS, s the enterprise value to sales ratio as ofJune 30th of eachyear. The eight explanatory variables are as follows: Indevsis the industry harmonic mean ofEVSbased on two-digit SIC codes; Indpb s the industry harmonic mean of the price-to-bookratio; Adjpms the difference between the firm's profit margin and the industry profit margin,where profit margin is defined as operating profit divided by sales; Losspms Adjpm indicatorvariable, where the indicator variable is 1 if profit margin < 0 and 0 otherwise; Adjgro s thedifference between the analystsconsensus forecast of the firm's long-term growth rate and theindustry average; Lev is long-term debt scaled by book equity; Rnoa is operating profit as apercent of net operating assets;and Rd is R&D expense as a percentage of sales. P-values areprovided in parentheses. The last rowrepresents the time-series average coefficients along withNewey-Westautocorrelation corrected t-statistics.The adjusted r-square (r-sq) and number offirms (# obs) are also reported.Year Intercept Indevs Indpb Adjpm Losspm Adjgro Lev Rnoa Rd R-sq # Obs1982 -0.0623 1.2643 0.1648 6.3052 -2.8510 0.0117 0.0665 -0.0091 0.0194 74.40 741

(0.135) (0.00) (0.00) (0.00) (0.119) (0.00) (0.007) (0.00) (0.00)1983 -0.0883 1.3531 -0.0301 8.1343 -5.3800 0.0392 0.1414 -0.0049 0.0463 70.80 748(0.121) (0.00) (0.342) (0.00) (0.00) (0.00) (0.00) (0.004) (0.00)1984 0.0192 1.2778 -0.0015 6.9266 -4.2894 0.0209 0.0707 -0.0088 0.0197 73.45 771(0.699) (0.00) (0.964) (0.00) (0.00) (0.00) (0.012) (0.00) (0.00)1985 0.1337 1.2231 -0.0152 7.9394 -4.0951 0.0177 0.0238 -0.0089 0.0153 74.66 797(0.002) (0.00) (0.604) (0.00) (0.00) (0.00) (0.351) (0.00) (0.00)1986 0.0225 1.3202 0.0047 9.4308 -6.2424 0.0316 -0.0246 -0.0080 0.0118 71.11 799(0.706) (0.00) (0.856) (0.00) (0.00) (0.00) (0.325) (0.00) (0.01)1987 0.1899 1.0908 -0.0324 9.8090 -6.8296 0.0363 0.0608 -0.0041 0.0319 66.84 856(0.007) (0.00) (0.339) (0.00) (0.00) (0.00) (0.035) (0.014) (0.00)1988 0.1774 1.0759 -0.0097 8.6458 -6.9959 0.0267 0.0228 -0.0054 0.0281 75.44 787(0.00) (0.00) (0.63) (0.00) (0.00) (0.00) (0.27) (0.00) (0.00)

1989 -0.0455 1.1264 0.0828 8.4475 -5.3691 0.0225 0.0143 -0.0032 0.0127 74.58 813(0.347) (0.00) (0.00) (0.00) (0.00) (0.00) (0.409) (0.01) (0.00)1990 0.1083 1.1263 0.0322 9.3485 -6.0607 0.0346 -0.0381 -0.0037 0.0191 73.54 829(0.027) (0.00) (0.019) (0.00) (0.00) (0.00) (0.065) (0.005) (0.00)1991 0.2321 1.0740 0.0256 10.4789 -6.9779 0.0316 -0.0430 -0.0053 0.0134 76.45 855(0.00) (0.00) (0.079) (0.00) (0.00) (0.00) (0.06) (0.00) (0.00)1992 0.2064 0.8277 0.1150 10.2810 -7.9414 0.0329 -0.0567 -0.0037 0.0157 71.63 902(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.004) (0.008) (0.00)1993 0.1811 1.0169 0.0579 11.4266 -6.4058 0.0333 -0.0129 -0.0045 0.0253 71.31 978(0.004) (0.00) (0.097) (0.00) (0.00) (0.00) (0.515) (0.00) (0.00)1994 0.2698 1.0027 0.0027 10.6165 -7.1717 0.0312 0.0219 -0.0060 0.0254 73.19 1102(0.00) (0.00) (0.913) (0.00) (0.00) (0.00) (0.202) (0.00) (0.00)1995 0.3148 1.0355 -0.0211 11.9432 -9.2245 0.0419 0.0100 -0.0069 0.0680 75.37 1190(0.00) (0.00) (0.512) (0.00) (0.00) (0.00) (0.618) (0.00) (0.00)1996 0.0713 1.1690 0.0430 11.3311-10.6464 0.0623 0.0001 -0.0023 0.0244 66.05 1341(0.249) (0.00) (0.141) (0.00) (0.00) (0.00) (0.996) (0.121) (0.00)1997 0.1192 1.1714 0.0366 12.5771 -7.5521 0.0452 0.0201 -0.0032 0.0313 71.75 1440(0.048) (0.00) (0.264) (0.00) (0.00) (0.00) (0.278) (0.011) (0.00)1998 -0.0269 1.0157 0.1561 13.0309-10.1430 0.0421 0.0362 -0.0006 0.0229 66.65 1498(0.683) (0.00) (0.00) (0.00) (0.00) (0.00) (0.069) (0.637) (0.00)All 0.1072 1.1277 0.0360 9.8043 -6.7162 0.0330 0.0184 -0.0052 0.0253 72.19 16447(0.007) (0.00) (0.031) (0.00) (0.00) (0.00) (0.235) (0.00) (0.00)

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422 s. BHOJRAJ ND C. M. C. LEEleverage (Lev) is not significantly correlated with EVS.Collectively, theseresults show that growth, profitability,and risk factors are incrementally im-portant in explaining EVSratios, even after controlling for industry means.Note that the estimated coefficients on severalof the keyexplanatory vari-ables change systematicallyover time. For example, the estimated coefficienton the industry adjusted profit margin (Adjpm)and forecasted growth rate(Adjgro)both trend upwardsover time, while the coefficient on the industryenterprise-value-to-salesratio (Indevs)shows some decline in recent years.These patterns imply that, in forecasting future EVSratios, the estimated co-efficients from the most recent year is likely to perform better than a rollingaverage of past years. In subsequent analyses, we use the estimated coeffi-cients from the prior year's regression to forecast current year's warrantedmultiple.Table 4 reports the results of annual cross-sectional regressions for the PBratio. The explanatory variables are the same as for the EVSregression intable 3, except for the replacement of Rnoa with Roe.Table 4 shows that allthe variables except Levcontribute significantly to the explanation of PB.The coefficient on Indps is reliably negative. Otherwise, the variables arecorrelated with PB in the same direction as expected. Overall, the modelis less successful at explaining PB than at explaining EVS.Nevertheless, theaverage adjusted r-square is still 51.2%, ranging from a low of 32.8% to ahigh of 61.0%.5.2 FORECASTING UTURE RATIOS

Recall that our goal is to identify comparable firms that will help us toforecast a target firm's future price-to-sales multiples. In this section, we ex-amine the efficacy of the warranted multiple approach in achieving thisgoal. Specifically, we examine the relation between a firm's future EVSand PB ratios, and a number of ex ante measures based on alternativedefinitions of comparable firms. The keyvariablesin this analysisare definedbelow.

EVSn and PBn, where n = 0, 1, 2, and 3-The current, one-, two-, andthree-year-aheadEVSand PB ratios. These are our dependent variables.IEVS and IPB--The harmonic mean of the industry EVS and PB ra-tios, respectively. Industry membership is defined in terms of two-digit SICcodes.ISEVSand ISPB--The harmonic mean of the actual EVSand PB ratios forthe four firms from the same industrywith the closest market capitalization.WEVS nd WPB--The warranted EVSand PB ratios. These variables arecomputed using the estimated coefficients from the prior year's regression(tables 3 and 4), and accounting or market-basedvariablesfrom the currentyear.COMP--Actual EVS(or PB) ratio for the closest comparable firms. Thisvariable is the harmonic mean of the actual EVS (or PB) ratio of the fourclosest firms based on their warranted multiple. To construct thisvariable,

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WHO IS MY PEER? 423

TABLE 4Annual EstimationRegressionsor Warranted rice-to-Book

This table reports the results from the following annual estimation regression:8

PBi,t = at + E j,tCj,i,t + ti,tj=1where the dependent variable, PB, is the price-to-book ratio as ofJune 30th of each year. Theeight explanatory variables are as follows: Indevs s the industry harmonic mean of EVSbasedon two-digit SIC codes; Indpb s the industry harmonic mean of the price-to-book ratio; Adjpmis the difference between the firm's profit margin and the industry profit margin, where profitmargin is defined as operating profit divided by sales; Losspms AdjpmeDum,where Dumis 1if profit margin < 0 and 0 otherwise; Adjgro s the difference between the analysts consensusforecast of the firm's long-term growth rate and the industry average; Lev is long-term debtscaled by book equity; Roe is net income before extraordinary items as a percent of bookequity; and Rd is R&Dexpense as a percentage of sales. The p-valuesare provided below eachof the coefficients in parentheses. The last row represents the time-series average coefficientsalong with Newey-Westautocorrelation corrected t- statistics. The adjusted r-square (r-sq) andnumber of firms (# obs) are also reported.Year Intercept Indevs Indpb Adjpm Losspm Adjgro Lev Roe Rd R-sq # Obs1982 -0.2990 -0.6056 1.1601 2.0331 -6.2544 0.0371 -0.2245 0.0402 0.0418 55.78 832

(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)1983 -0.3434 -0.5129 1.1696 3.2891-11.9301 0.1147 -0.1545 0.0541 0.0627 60.99 852(0.00) (0.001) (0.00) (0.00) (0.00) (0.00) (0.01) (0.00) (0.00)1984 -0.1065 -0.1806 0.9401 2.0887 -5.9880 0.0527 -0.2302 0.0397 0.0314 57.83 319

(0.143) (0.099) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)1985 -0.3518 -0.2882 1.0448 3.0154 -8.6571 0.0568 -0.2694 0.0585 0.0013 59.15 956(0.00) (0.009) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.845)1986 0.0998 -0.3548 0.9866 3.6912 -6.4419 0.0883 -0.3075 0.0542 0.0053 56.55 954(0.319) (0.005) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.528)1987 0.0632 -0.6468 1.0956 6.0189 -9.8553 0.0881 0.0583 0.0459 0.0323 52.97 1019(0.584) (0.00) (0.00) (0.00) (0.00) (0.00) (0.221) (0.00) (0.001)1988 0.0568 -0.5150 0.8393 2.0184 -9.9218 0.0694 -0.0675 0.0666 0.0266 54.15 940(0.566) (0.00) (0.00) (0.00) (0.00) (0.00) (0.083) (0.00) (0.001)1989 -0.3306 -0.5790 1.1269 2.6023-15.3872 0.0576 -0.0474 0.0574 0.0111 52.19 999(0.001) (0.00) (0.00) (0.00) (0.00) (0.00) (0.176) (0.00) (0.122)1990 -0.4592 -0.9002 1.3508 1.9280-10.8096 0.0815 -0.0663 0.0644 0.0144 53.16 1023(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.073) (0.00) (0.08)1991 0.0459 -0.9010 1.0963 3.0820-10.7620 0.0744 -0.1227 0.0683 -0.0052 54.88 1041(0.613) (0.00) (0.00) (0.00) (0.00) (0.00) (0.001) (0.00) (0.477)1992 0.1797 -0.6645 1.0051 3.5272-12.3146 0.0781 0.0018 0.0593 0.0203 48.51 1089(0.098) (0.00) (0.00) (0.00) (0.00) (0.00) (0.969) (0.00) (0.007)1993 0.2426 -0.5925 0.7907 1.6280-13.7791 0.0939 0.1131 0.0828 0.0468 46.82 1188(0.111) (0.00) (0.00) (0.005) (0.00) (0.00) (0.02) (0.00) (0.00)1994 -0.0187 -0.4753 1.0234 3.1253 -9.8989 0.0834 0.1650 0.0521 0.0436 44.96 1349(0.881) (0.00) (0.00) (0.00oo) 0.00) (0.00) (0.00) (0.00) (0.00)1995 -0.3095 -0.2491 0.9481 4.3329 -9,7318 0.0908 0.0409 0.0735 0.0742 53.52 1447(0.008) (0.00) (0.00) (0.00) (0.00) (0.00) (0.284) (0.00) (0.00)1996 -0.0713 -0.3475 1.0319 4.0730-13.0282 0.1221 0.1303 0.0649 0.0147 42.76 1628(0.569) (0.00) (0.00) (0.00) (0.00) (0.00) (0.006) (0.00) (0.133)1997 0.1104 -0.3565 0.8816 3.8790-13.5652 0.0948 0.1596 0.0837 0.0248 43.00 1723(0.402) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.006)1998 0.0247 -0.3666 1.0553 3.7902 -7.1481 0.0852 0.2276 0.0674 0.0341 32.82 1828(0.87) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)All -0.0863 -0.5021 1.0321 3.1837-10.3220 0.0805 -0.0349 0.0608 0.0282 51.18 19187(0.169) (0.00) (0.00) (0.00) (0.00) (0.00) (0.511) (0.00) (0.00)

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424 s. BHOJRAJAND C. M. C. LEEwe rank all the firms each year on the basis of their WEVS or WPB),andcompute the harmonic mean of the actual EVS(or PB) for these firms.ICOMP--Actual EVS(or PB) ratio for the closest comparable firms withinthe industry.This variable is the harmonic mean of the actual EVS(or PB)ratio of the four firms within the industrywith the closest warrantedmultiple.Essentially, this is the COMP variable with the firms constrained to comefrom the same industry.

In short, we compute five different EVS(or PB) measures for each firmbased on alternative methods of selecting comparable firms. IEVS andISEVS(or, IPB and ISPB) correspond to prior studies that control for in-dustry membership and firm size. The other measures incorporate risk,profitability,and growth characteristics beyond industry and size controls.We then examine their relative power in forecasting future EVS and PBratios.As an illustration, Appendix C presents selection details for Guidant Cor-poration (GDT), a manufacturer of medical devices. This appendix illus-trates the set of firms in the same two-digit SIC code, which are identifiedas peers of Guidant based on data as of April 30, 2001. Panel A reports thesix closest firms based on WEVS,Panel B reports the closest firms based

on WPB.We reviewed this list with a professional analyst who covers thissector. She agreed with most of the selections but questioned the absenceof St.Jude Medical Devices (STJ), which she regarded as a natural peer.She agreed with our choices, however, after we discussed the profitability,growth, and risk characteristics of STJin comparison to those of the firmslisted.Table 5 reports the results for a series of forecasting regressions. Inpanel A, the dependent variable is EVSn,and in panel B, the dependent

variable is PBn;where n = 0, 1, 2, 3, indicates the number of years into thefuture. In each case, we regress the future market multiple on various exante measures based on alternative definitions of comparable firms.14 Thetable values represent the estimated coefficient for each variable averagedacross 14 (n= 3) to 17 (n= 0) annual cross-sectional regressions. The bot-tom row reports the average adjusted r-squareof the annual regressions foreach model.These results show that the harmonic mean of the industry-matchedfirms

explains 17.5% (three-year-ahead) to 22.9% (current year) of the cross-sectional variation in future EVSratios. Including the mean EVS ratio fromthe closest four firms matched on size increases the adjusted r-squaresonlymarginally, so that collectively IEVSand ISEVS xplain 18% to 23% of thevariation in future EVSratios. These results confirm prior evidence on theusefulness of industry-based comparable firms.However,they also show that

14Even for the current year (n= 0), the warranted multiples are based on estimated coeffi-cients from the prior year'sregression. Therefore, the models that involve warrantedmultiplesare all forecasting regressions.

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TABLE 5PredictionRegressions

This table provides average estimated coefficients from the following prediction regressions:EVSi,t+k = at +

j,s tCji,t + I-i,t PBi, +k= at + ES

j=' j=1where k=0, 1, 2, 3. In Panel A, the dependent variable is the enterprise-value-to-sales ratio (EVS).ratio (PB). The expanatory variables are: IEVS, he harmonic mean of the industry EVSbased on cuthe harmonic mean of the actual EVS for the four closest firms matched on size after controlling fousing the coefficients derived from last year's estimation regressions and current year accounting anthe actual EVS for the four closest firms matched on WEVS; nd ICOMP,the harmonic mean of theafter controlling for industry. The variables for Panel B are defined analogously, replacing EVS withcoefficients from annual cross-sectional regressions. The bottom row reports the average adjusted r-sPanel A:Enterprise-value-to-salesCurrentyearEVS One yearahead EVS TwoyearaInter 0.24 0.22 0.06 0.00 0.00 0.24 0.23 0.07 0.01 0.01 0.27 0.25 0.IEVS 1.19 1.02 0.08 -0.27 -0.26 1.19 1.05 0.16 -0.17 -0.16 1.18 1.06 0.ISEVS 0.16 0.14 0.16 0.13 0.14 0.12 0.14 0.12 0.13 0.COMP 0.89 0.16 0.83 0.13 0.WEVS 0.98 0.83 0.93 0.80ICOMP 0.33 0.27r-sq 22.94 23.46 54.71 61.68 62.99 20.75 21.24 46.14 51.97 53.23 18.37 18.79 40.Panel B: Book-value-to-salesCurrentyearPB One yearahead PB TwoyearInter 0.40 0.35 0.07 -0.06 -0.07 0.46 0.40 0.15 0.04 0.05 0.57 0.50 0.IPB 1.19 1.04 0.26 -0.09 -0.07 1.17 1.00 0.38 0.12 0.12 1.16 0.96 0.ISPB 0.16 0.11 0.10 0.07 0.18 0.14 0.13 0.10 0.21 0.COMP 0.81 0.35 0.65 0.29 0.WPB 0.77 0.71 0.59 0.51ICOMP 0.44 0.40r-sq 11.80 12.34 35.21 41.94 43.20 7.62 8.02 19.91 22.94 23.38 5.01 5.47 12

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426 S. BHOJRAJAND C. M. C. LEEthe valuation accuracy of industry-based EVSratios leaves much to be de-sired. In fact, industry-sizebased comparable firms explain less than 20%ofthe variation in two-year-aheadEVSratios.

The predictive power of the model increases sharplywith the inclusion ofvariables based on the warranted EVSratio(WEVS).On average,a model thatincludes IEVS,ISEVS,and COMPexplains over 40% of the cross-sectionalvariation in two-year-aheadEVSratios. Including WEVSn the model in-creases the average adjusted r-square on the two-year-aheadregressions to45.5%. Moreover, even after controlling for WEVS,he actual WEVS atioof the closest comparable firms (COMPor ICOMP)is incrementally usefulin predicting future EVS ratios. It appears that comparable firms selectedon the basis of their WEVS dds to the prediction of future EVSratios evenafter controlling for WEVStself. COMPand ICOMPyield similar results. Amodel that includes IEVS, SEVS,WEVS,nd ICOMPexplainsbetween 63.0%(current year) and 43.1% (three-year-ahead) of the variation in future EVSratios.'5

Panel B reports forecasting regressions for PB.Compared to EVS,a muchsmaller proportion of the variation in PB is captured by these models. Inthe current year, the combination of IPBand ISPBexplains only 12.3% ofthe variation in PB.The inclusion of WPBand ICOMPincreasesthe adjustedr-square to 43.2%. In future years, the explanatory power of all the modelsdeclines sharply.However, over all forecast horizons, models based on war-ranted multiples explain more than twice the variation in future PB ratiosas compared to the industry-sizematched model.The rapid decay in the explanatory power of the PB model is a possibleconcern with these results. Either PB ratios are difficult to forecast, or ourmodel is missing some key forecasting variables. To shed light on this issue,we report below the serial correlation in annual EVSand PBratios. Table val-ues in the chart below are average Pearson correlation coefficients betweenthe current year's ratio, and the same ratio one, two, or three years later.Average Correlation Coefficient

EVS1 EVS2 EVS3 PB1 PB2 PB3EVSO 0.87 0.79 0.73 - - -PBO - - - 0.72 0.56 0.44These results show that with a one-year lag, EVS s seriallycorrelated at 0.87,suggesting an r-squareof around 76%.With a three-yearlag, EVS s seriallycorrelated at 0.73, suggesting an r-squareof 53%. Similarly,with a one-yearlag, PB is serially correlated at 0.72, suggesting an r-square of 52%. With

5 We also conducted year-by-year nalysisto examine the stabilityof these results over time.We find that a model that includes IEVS, SEVS,WEVS, nd ICOMP s extremely consistent inpredicting future EVSratios.All four variablesare incrementally important in predicting futureEVSratios in each forecasting period.

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WHO IS MY PEER? 427a three-year lag, PB is serially correlated at 0.44, suggesting an r-square ofonly 19.4%.These results show that PB is in fact inherently more difficult toforecast than EVS.Even when we know a firm's current PBratio,we can onlyexplain a relatively small proportion of the variation in future PB ratios.'16Two results from table 5 deserve emphasis. First, this table shows that thecommon practice of using industry and/or industry-sizebased comparablefirmsperforms relatively poorly in predicting a firm's EVSand PB ratios.Onlyaround 18% (4.5%) of the cross-sectional variation in three-year-aheadEVS(PB) ratios is captured by this approach. These results re-enforce the find-ing in LNT, in which the price-to-sales and price-to-book ratios of industry-matched firms generates relatively high valuation errors when comparedto the target firms' current market price. Later, we provide a more directcomparison based on the distribution of valuation errors.Second, these tables show that firms identified on the basis of a warrantedEVSorwarrantedPB (i.e., firms matched on the basis ofa weighted averageofeight variables including profit margin, growth, and determinants of cost-of-capital) offer a much better benchmark for comparison. With the inclusionof the warranted multiple (either WEVSorWPB)and the actual multiples ofcomparable firms (either COMPorICOMP),the adjusted r-squareincreasessharply.In fact, 43% (11.3%) of the variation in three-year-aheadEVS(PB)ratio can be predicted. This result suggests that by systematically matchingfirms on the basis of their warranted multiples, we can identify superiorcomparable firms.Prior studies generally computed a distribution of valuation errors forvarious prediction measures, expressed as a proportion of the actual price-per-share.To facilitate comparison, table 6 reports these valuation errors forour firms. Panel A reports the results for EVS,and Panel B reports the resultsfor PB. In each case, we provide separate results for n= 0 through 3. We alsocompare the errors for an industry-size matched model (ISEVSor ISPB)to a model using warranted multiples (WEVSor WPB)and a model usingindustry constrained comparables selected on the basis of their warrantedmultiples (ICOMP).We report the Absolute Error (the absolute differencebetween actual and implied price, scaled by the actual price), as well as theBias (the actual price minus the implied price, scaled by the actual price)."17Panel A shows that the median absolute error for the industry-sizematched firms in the current year is 0.55. This is slightly higher than theabsolute error reported by LNT. However, the difference is not surprising,

16As expected, the lagged multiple has strong predictive power for the current multiple.This result suggests that, for public firms, investors should use a firm's own lagged multipleas a predictor of its future multiples. However, this approach cannot be used to value privatefirms, nor can it be used to identify control firms for research purposes.17In each case, the implied price for the warranted multiples is based on the coefficientsestimated in year n= -1, applied to the accounting and market-related variables obtained inthe future (n= O0, , 2, or 3).

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428 S. BHOJRAJAND C. M. C. LEETABLE 6

Distribution f ValuationErrorsThis table presents the distribution of valuation errors for various prediction measures, ex-pressed as a proportion of actual price-per-share.EVSks the k year ahead enterprise-value-to-sales ratio. PBn is the k year ahead price-to-book ratio. The expanatory variables are: ISEVS,the harmonic mean of the actual EVS or the four closest firms matched on size after control-ling for industry, measured as of the current year (k= 0); WEVS,he firm's warranted EVS, sdetermined using the coefficients derived from lastyear'sestimation regressions (k = -1) andcurrent year accounting and market-based values (k= 0); and ICOMP, he harmonic mean ofthe actual EVS or the four closest firms matched on WEVS fter controlling for industry.Thevariables for Panel B are defined analogously, replacing EVS with PB. Absolute Error is theabsolute difference between actual and implied price, scaled by actual price. Bias is the actualprice minus the implied price, scaled by the actual price. Table values represent the mean,median, inter-quartile range (IQRange), 90th-percentile minus 10th-percentile (90%-10%),and 95th-percentile minus 5th-percentile (95%-5%).

Absolute Error BiasIQ 90%- 95%- IQ 90%- 95%-Mean Median Range 10% 5% Mean Median Range 10% 5%

Panel A: Enterprise-Value-to-SalesEVSO ISEVS 0.86 0.55 0.58 1.62 2.75 -0.27 0.13 1.09 2.44 3.67WEVS 0.61 0.35 0.51 1.24 1.91 -0.22 -0.04 0.75 1.68 2.53ICOMP 0.57 0.36 0.45 1.01 1.68 -0.12 0.08 0.70 1.55 2.36EVS1 ISEVS 0.89 0.56 0.72 1.69 2.73 -0.22 0.12 1.11 2.57 3.91WEVS 0.67 0.41 0.60 1.32 1.99 -0.18 -0.05 0.83 1.88 2.80ICOMP 0.63 0.40 0.55 1.18 1.79 -0.08 0.07 0.79 1.73 2.62EVS2 ISEVS 0.89 0.58 0.76 1.74 2.66 -0.15 0.12 1.12 2.57 3.87WEVS 0.70 0.43 0.65 1.40 2.08 -0.13 -0.03 0.88 1.99 2.98ICOMP 0.66 0.43 0.60 1.27 1.85 -0.02 0.08 0.84 1.83 2.76EVS3 ISEVS 0.91 0.59 0.80 1.78 2.64 -0.08 0.15 1.13 2.58 3.93WEVS 0.71 0.45 0.66 1.42 2.13 -0.09 -0.03 0.91 2.03 3.02ICOMP 0.69 0.44 0.63 1.34 2.00 0.03 0.08 0.88 1.93 2.85Panel B: Price-to-BookPBO ISPB 0.55 0.38 0.46 0.91 1.54 -0.12 0.09 0.74 1.61 2.30WPB 0.48 0.30 0.41 0.93 1.44 -0.14 -0.02 0.62 1.35 1.99ICOMP 0.44 0.29 0.38 0.74 1.19 -0.08 0.08 0.56 1.25 1.84PB1 ISPB 0.60 0.41 0.54 1.13 1.66 -0.07 0.08 0.79 1.73 2.54WPB 0.54 0.36 0.50 1.06 1.56 -0.10 -0.02 0.72 1.55 2.27ICOMP 0.51 0.35 0.47 0.96 1.41 -0.03 0.08 0.68 1.48 2.15PB2 ISPB 0.62 0.43 0.58 1.19 1.73 0.00 0.11 0.82 1.80 2.62WPB 0.57 0.39 0.55 1.15 1.63 -0.04 0.00 0.78 1.67 2.42

ICOMP 0.56 0.39 0.53 1.09 1.53 0.03 0.10 0.75 1.60 2.34PB3 ISPB 0.65 0.44 0.61 1.27 1.82 0.06 0.13 0.84 1.83 2.69WPB 0.60 0.40 0.57 1.19 1.76 0.02 0.01 0.81 1.74 2.52ICOMP 0.59 0.40 0.57 1.16 1.66 0.09 0.11 0.79 1.68 2.43

as LNT requires all accounting variables (including earnings and forecastedearnings) to be positive while we do not. In fact, our sample size is approx-imately twice as large as theirs. More important is the comparison betweenISEVS nd the warranted multiple models (WEVS nd ICOMP).The median

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WHO IS MYPEER? 429absolute error for the implied price based on WEVS ICOMP) is sharplylower at 0.35 (0.36). The advantage of the warranted multiples approach issustained in years n= 1, 2, and 3. The bias is also lower for WEVSnd ICOMPacross all forecasting horizons. In short, the implied prices computed basedon warranted multiples produce valuation errorswith lower means, a tighterinter-quartilerange, and less "fat-tailed"distributions. The results in panel Bshow similar findings for the PB ratio. Collectively these results support theearlier findings based on adjusted r-squares.5.3 NEW ECONOMYSTOCKS

In this section, we estimate warranted enterprise-value-to-salesand price-to-book ratios for firms in so-called "neweconomy" sectors. We define theseas firms within the following two-digit SIC code categories: biotechnology(2833-2836 and 8731-8734), computers (3570-3577 and 7371-7379), elec-tronics (3600-3674) and telecommunication (4810-4841). This technology-dominated sample is characterized by a higher proportion of growth firmsand firms that are not currently earning a profit. We are particularly inter-ested in the robustness of our method in valuing the firmsin this subsample.Table 7 reports the year-by-yearEVSestimation results for these technologyfirms. This table shows that the same eight explanatory variables explaina consistently large proportion of the variation in EVS ratios across thesefirms. The average adjusted r-square for this population is 70.1%, which isonly marginally lower than the average adjusted r-squareof 72.2% for theoverall population. Annually, the explanatory power of the model rangesfrom 63.1% to 84.9%, suggesting a good fit everyyear.Across the eight variables, the estimated coefficients for the technologyfirms are strikingly different from those for the overall population. Threevariables-the industry PB ratio (Indpb), leverage (Lev), and return on netoperating asset (Rnoa)-have much lower estimated coefficients in thissample. In fact, these variables are not individually significant at the 5%level. On the other hand, the profit margin variable (Adjpm), he profit mar-gin on loss firms (Losspm), he expected growth variable (Adjgro),and R&Dexpenditures (R&D), all playa much more important role for these firms.'8Table 8 reports the PB regression for technology firms. The average ad-justed r-squarefor these firmsof 52.6%compares favorablywiththe adjustedr-square for the full sample of 51.2% (see table 4). The best year had anadjusted r-square of 71.2% and the worst year had an adjusted r-square of35.3%. Lev,Adjgro,Adjpm,Losspm,and Rd all play more important roles inthis sample than in the full sample. Taken together, these results suggestthat the eight explanatory variables are effective in explaining variations inthe PB ratios even among "neweconomy" stocks.

8 To be consistent with the overall sample, we report resultsusing industries defined in termsof two-digit SIC codes. The results using three-digit SIC codes (not reported) are marginallystronger.

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430 s. BHOJRAJAND C. M. C. LEETABLE 7

Annual Estimationof Warranted nterprise-Value-to-Salesor TechnologyirmsThis table year-by-year stimation regression results for the following regression:

8EVSi,t = at + L y,tCj,i,t + it,tj=1

Only firms in the technology, biotechnology, and telecommunication sectors are included inthe sample. The independent variable, EVS, s the enterprise-value-to-salesratio as ofJune 30thof each year.The eight explanatoryvariables are as follows:Indevsisthe industryharmonic meanof EVSbased on two-digitSICcodes; Indpb s the industry harmonic mean of the price-to-bookratio; Adjpms the difference between the firm's profit margin and the industry profit margin,where profit margin is defined as operating profit divided by sales; Losspms adjpm indicatorvariable, where the indicator variable is 1 if profit margin < 0 and 0 otherwise; Adjgros thedifference between the analystsconsensus forecast of the firm's long-term growth rate and theindustry average; Lev is long-term debt scaled by book equity; Rnoa is operating profit as apercent of net operating assets; and Rd is R&D expense as a percentage of sales. P-values areprovided in parentheses. The last rowsrepresents the time series averagecoefficients along withNewey-West autocorrelation corrected t-statistics.The adjusted r-square (r-sq) and number offirms (# obs) are also reported.Year Intercept Indeos Indpb Adjpm Losspm Adjgro Lev Rnoa Rd R-sq # Obs1982 0.0746 2.5147 -0.7345 8.6017 - 0.0365 0.1998 -0.0104 0.0379 78.70 84(0.694) (0.00) (0.054) (0.00) (0.00) (0.11) (0.077) (0.001)1983 1.8275 1.3958 -0.6604 13.6505 - 0.0984 -0.3145 -0.0226 0.0705 78.13 88(0.00) (0.00) (0.03) (0.00) (0.00) (0.226) (0.006) (0.00)1984 0.3207 1.3194 -0.0248 10.4726 -2.1075 0.0537 -0.0420 -0.0259 0.0286 73.74 98(0.191) (0.00) (0.90) (0.00) (0.36) (0.00) (0.794) (0.00) (0.27)1985 -0.4148 0.9490 0.2765 8.6284 -6.2307 0.0419 0.1008 -0.0017 0.0494 84.92 118

(0.00) (0.00) (0.002) (0.00) (0.013) (0.00) (0.088) (0.575) (0.00)1986 -0.6893 0.9863 0.2137 6.8203 -6.1216 0.0354 0.2603 0.0021 0.0619 70.17 125(0.00) (0.00) (0.35) (0.00) (0.00) (0.00) (0.007) (0.698) (0.00)1987 -0.2585 0.6142 0.3837 10.7332 -6.9660 0.0878 0.2573 -0.0024 0.0449 64.98 143(0.248) (0.15) (0.03) (0.00) (0.002) (0.00) (0.081) (0.778) (0.004)1988 0.3333 0.8095 0.1195 9.2366 -5.5708 0.0752 -0.0649 -0.0088 0.0435 69.48 134(0.071) (0.00) (0.039) (0.00) (0.001) (0.00) (0.508) (0.107) (0.00)1989 -0.4446 1.8429 -0.1766 8.8866 -8.2629 0.0418 0.1172 0.0003 0.0268 75.64 131(0.077) (0.00) (0.11) (0.00) (0.00) (0.00) (0.148) (0.951) (0.008)1990 0.0290 2.5311 -0.7448 10.5869 -5.3715 0.0483 0.0934 -0.0107 0.0515 71.38 130(0.901) (0.00) (0.045) (0.00) (0.006) (0.00) (0.193) (0.07) (0.00)1991 0.3252 1.4312 -0.0199 12.5785 -5.5412 0.0402 -0.1464 -0.0226 0.0179 72.15 152(0.068) (0.00) (0.845) (0.00) (0.005) (0.00) (0.207) (0.00) (0.081)1992 0.2295 0.4087 0.4255 10.1490 -6.3325 0.0689 0.0977 -0.0112 0.0031 68.15 168(0.116) (0.058) (0.011) (0.00) (0.00) (0.00) (0.199) (0.113) (0.733)1993 0.1469 0.8104 0.0694 13.0156 -6.3610 0.0908 -0.0130 -0.0007 0.0550 64.55 173(0.484) (0.003) (0.581) (0.00) (0.019) (0.00) (0.879) (0.906) (0.00)

1994 0.4518 0.6072 0.0902 12.2570 -8.5298 0.0340 -0.0012 -0.0034 0.0249 70.39 185(0.004) (0.00) (0.261) (0.00) (0.00) (0.00) (0.99) (0.42) (0.002)1995 1.3244 0.6868 -0.1303 15.4918 -8.6079 0.1054 0.1448 -0.0108 0.0663 65.21 213(0.00) (0.003) (0.447) (0.00) (0.004) (0.00) (0.38) (0.114) (0.00)1996 -0.0339 0.5914 0.2069 10.1740 -9.6489 0.1174 0.1133 0.0140 0.0521 63.07 261(0.911) (0.007) (0.249) (0.00) (0.00) (0.00) (0.387) (0.008) (0.00)1997 -0.1878 0.7185 0.3130 12.9300-10.9113 0.0870 0.1287 0.0064 0.0355 62.83 286(0.583) (0.00) (0.056) (0.00) (0.00) (0.00) (0.053) (0.216) (0.001)1998 -0.4906 0.3496 0.5722 13.3263-13.8360 0.1340 0.1851 0.0092 0.0393 58.85 290(0.103) (0.142) (0.001) (0.00) (0.00) (0.00) (0.168) (0.182) (0.001)

All 0.1496 1.0922 0.0105 11.0317 -7.3600 0.0704 0.0657 -0.0061 0.0417 70.14 2779(0.385) (0.00) (0.928) (0.00) (0.00) (0.00) (0.086) (0.09) (0.00)

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WHO IS MY PEER? 431TABLE 8

Annual Estimationof Warranted rice-to-Bookor TechnologyirmsThis table provides yearwise coefficients from the following regression:

8PBi, = at + Sj, tCj,i,t -+Li,tj=1

Only firms in the technology, biotechnology, and telecommunication sectors are included inthe sample. The independent variable,PBis the price-to-book ratio as ofJune 30th of each year.The eight explanatory variables are as follows: Indevs is the industry harmonic mean of EVSbased on two-digit SIC codes; Indpb s the industry harmonic mean of the price-to-book ratio;Adjpms the difference between the firm's profit margin and the industry profit margin, whereprofit margin is defined as operating profit divided bysales;Losspms adjpm indicator variable,where the indicator variable is 1 if profit margin _0 and 0 otherwise; Adjgros the differencebetween the analysts consensus forecast of the firm's long-term growth rate and the industryaverage; Lev is long-term debt scaled by book equity; Roe is net income before extraordinaryitems scaled by common equity; and Rdis R&Dexpense as a percentage of sales. P-values areprovided in parentheses. The last rowsrepresents the time series averagecoefficients along withNewey-Westautocorrelation corrected t-statistics.The adjusted r-square (r-sq) and number offirms (# obs) are also repoted.Year Intercept Indevs Indpb Adjpm Losspm Adjgro Lev Roe Rd R-sq # Obs1982 -0.3719 0.2384 0.3554 2.4541 - 0.0725 0.1017 0.0727 0.0936 71.24 84

(0.521) (0.845) (0.68) (0.168) (0.00) (0.64) (0.00) (0.00)1983 1.0815 -1.4809 0.2848 1.9356 - 0.1713 0.6545 0.1242 0.1876 57.22 87(0.195) (0.051) (0.564) (0.604) (0.00) (0.178) (0.00) (0.00)1984 0.8739 0.8572 0.0138 6.4148 0.8036 0.0915 -0.1966 0.0277 0.0265 59.03 102

(0.064) (0.074) (0.972) (0.00) (0.91) (0.00) (0.36) (0.066) (0.177)1985 -0.6571 -0.1940 0.8856 5.1695 -9.7264 0.0597 0.2904 0.0683 0.0375 62.75 121(0.05) (0.668) (0.01) (0.00) (0.016) (0.00) (0.113) (0.00) (0.012)1986 -0.5377 -1.0501 1.5479 4.6753 -6.5886 0.0375 0.2447 0.0362 0.0439 47.50 124(0.221) (0.165) (0.003) (0.03) (0.017) (0.039) (0.415) (0.023) (0.039)1987 0.1112 -0.4919 0.8625 4.5022-15.3127 0.1294 0.4758 0.0966 0.0280 53.02 141(0.796) (0.531) (0.077) (0.077) (0.001) (0.00) (0.01) (0.00) (0.277)1988 0.3808 -0.3979 0.7731 2.8966 -9.1768 0.1100 -0.3173 0.0776 0.0269 58.17 138(0.388) (0.546) (0.128) (0.14) (0.001) (0.00) (0.017) (0.00) (0.0142)1989 -0.7627 -1.0294 1.5381 6.2005-25.9330 0.0809 0.0533 0.0681 0.0054 60.01 138(0.204) (0.312) (0.036) (0.001) (0.00) (0.00) (0.728) (0.00) (0.736)1990 -1.5790 -0.4220 1.6713 3.7374-17.0171 0.0894 0.1774 0.0848 0.0256 60.99 138(0.002) (0.48) (0.00) (0.048) (0.00) (0.00) (0.354) (0.00) (0.173)1991 -0.3213 0.5554 0.8374 6.7005 -9.1000 0.0467 0.1309 0.0445 0.0211 54.38 158(0.365) (0.197) (0.013) (0.00) (0.005) (0.001) (0.454) (0.00) (0.231)1992 -0.4658 -1.3092 1.8016 6.2668-10.3212 0.1516 1.3935 0.0355 -0.0036 52.53 169(0.195) (0.008) (0.00) (0.019) (0.023) (0.00) (0.00) (0.002) (0.881)1993 0.9354 -0.2871 0.7052 6.0891-18.4597 0.1503 0.1518 0.0640 0.0169 42.93 177(0.123) (0.691) (0.172) (0.011) (0.002) (0.00) (0.583) (0.00) (0.43)

1994 0.2271 -0.4288 1.0209 8.0718 -7.2491 0.0769 0.7869 0.0180 0.0530 42.59 196(0.74) (0.403) (0.047) (0.00) (0.018) (0.00) (0.001) (0.033) (0.001)1995 0.9133 -0.6040 0.6983 8.1740-17.0127 0.1720 0.5063 0.0735 0.0885 44.25 220(0.415) (0.198) (0.201) (0.00) (0.019) (0.00) (0.071) (0.00) (0.00)1996 0.0096 -0.3468 1.0941 6.3722 -5.7468 0.1487 0.6142 0.0580 0.0411 35.31 164(0.988) (0.299) (0.00) (0.002) (0.218) (0.00) (0.039) (0.00) (0.068)1997 -1.1275 -0.4317 1.5256 4.9177-10.6854 0.1473 0.6558 0.1190 0.0092 44.02 294(0.115) (0.354) (0.00) (0.022) (0.001) (0.00) (0.007) (0.00) (0.633)1998 -0.9291 -0.8094 1.8563 6.3907 -8.3244 0.2128 1.0429 0.0676 -0.0268 47.93 301(0.076) (0.037) (0.00) (0.006) (0.019) (0.00) (0.00) (0.00) (0.163)

All -0.1306 -0.4490 1.0278 5.3511-11.3234 0.1146 0.3980 0.0668 0.0397 52.58 2752(0.554) (0.001) (0.00) (0.00) (0.00) (0.00) (0.001) (0.00) (0.009)

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432 S. BHOJRAJNDC. M.C. LEETable 9 reports the forecasting regression results for technology firms.Panel A shows that using the industry harmonic mean alone (JEVS)resultsin 13.4% to 16.4% in adjusted r-squares. Adding size-matched compara-

ble firms improves the results marginally, to between 14.5% and 16.8%.However, the predictive power of the model does not increase substantiallyuntil we include comparable firms selected on the basis of warranted multi-ples. Adding the four nearest comparable firms matched on WEVSCOMP)almost triples the r-square in the current year, and more than doubles ther-squarefor all the other years. Adding WEVSincreases he adjusted r-squareby a further 5 to 10%. Panel B shows that the adjusted r-squaresare againlower for the PB ratio. However, the incremental contribution of WPBandeither COMPor ICOMPremains sharp. Evidently the warranted multiplesapproach is effective in controlling for differences in profitability,growth,and risk that affect the EVSand PBratios of new economy stocks. In fact, theincremental usefulness of this approach seems to be even more pronouncedin the sub-sample of "neweconomy" firms than in the full-sample.6. Summary

Our goal in this paper is to develop a more systematic technique for select-ing comparable firms. Our approach selects comparable firms on the basisof profitability, growth, and risk characteristics that theory suggests shouldbe cross-sectional drivers of a particularvaluation multiple. Specifically,weuse regression analysisand large sample estimation techniques to generatea "warrantedmultiple" for each firm. The comparable firms are those firmswhose warranted multiple is closest to that of the target firm.Wetest our approach byexamining the efficacyof the selected comparablefirms in predicting future (one- to three-year-ahead) enterprise-value-to-sales and price-to-book ratios. Our tests encompass the general universe ofstocks as well as a sub-population of "new economy" stocks from the tech,biotech, and telecommunication sectors. Our results show that comparablefirms selected in this manner offer sharp improvements over comparablefirms selected on the basis of other techniques, including industry and sizematches. The improvement is most pronounced among the so-called neweconomy stocks.These findings suggest a number of possible extensions and applications.The technique we outline here is not limited to the EVSor PB multiple. Itis straightforward to extend the analysis to other multiples such as price-to-cash-flows or price-to-earnings (both forward and historical). Some ofthe theoretical work for this type of extension has already been done; oth-ers are still being developed.'9 Indeed, it might be desirable to combinethe results from several different multiples to come up with a set of firmsthat are close peers based on alternative estimation procedures. We be-lieve this composite approach will enhance the precision and objectivityof

19 Ohlson and Nuettner-Nauroth [2000] is a good example, in which the price-to-forward-earnings ratio is explicitly modeled.

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TABLE 9PredictionRegressionsor Technologyirms

This table provides average estimated coefficients from the following prediction regressions:EVSi,+k= at 8 ,tC ,i, + I i,t PBi, +k= at + jj=1 j=1

where k= 0, 1, 2, 3. Only firms in the technology, biotechnology, and telecommunication sectors avariable is the enterprise-value-to-sales ratio (EVS).In Panel B, the dependent variable is the price-to-harmonic mean of the industryEVSbased on current year (k = 0), but excluding the target firm; ISEVS,firms matched on size after controlling for industry; WEVS, he firm's warranted EVS,determined usregressions and current year accounting and market-based variables; COMP, he harmonic mean of theand ICOMP,the harmonic mean of the actual EVSfor the four closest firms matched on WEVS fterdefined analogously, replacing EVS with PB. Table values represent the time-series average of the cobottom row reports the average adjusted r-square of the annual regressions.PanelA:Enterprise-value-to-sales

CurrentyearEVS One yearahead EVS TwoyearaheaInter 0.71 0.72 0.28 0.16 0.16 0.64 0.65 0.26 0.11 0.13 0.46 0.47 0.06 -IEVS 1.07 0.99 0.05 -0.29 -0.32 1.10 1.00 0.28 -0.02 -0.10 1.24 1.16 0.48ISEVS 0.06 0.03 0.00 0.02 0.09 0.05 0.03 0.05 0.07 0.06COMP 0.97 0.08 0.77 -0.07 0.73 -WEVS 1.11 0.83 1.03 0.71ICOMP 0.39 0.33r-sq 13.39 14.45 45.88 56.38 58.23 13.91 14.42 35.65 45.50 46.73 13.89 14.31 31.62PanelB:Book-value-to-sales

CurrentyearPB One yearahead PB Twoyear aheInter 0.90 0.82 0.29 0.17 0.24 0.80 0.73 0.37 0.13 0.26 0.61 0.57 0.23IPB 1.19 1.02 0.30 -0.09 -0.14 1.24 0.92 0.46 0.15 0.05 1.34 1.02 0.66ISPB 0.17 0.13 0.09 0.08 0.31 0.29 0.28 0.28 0.29 0.28COMP 0.80 0.25 0.51 0.09 0.41WPB 0.87 0.92 0.69 0.51ICOMP 0.21 0.31r-sq 8.80 9.65 28.27 36.70 37.93 6.91 8.43 15.41 19.59 21.45 7.09 7.73 11.40

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434 S. BHOJRAJ ND C. M. C. LEEmultiples-based valuation methods, and bring much needed discipline toequity valuation.Financial analysts and valuation experts often operate under conflictingincentives.20 If a more objective and conceptually defensible technique forselecting comparable firms becomes widely accepted, the onus will be onan analyst tojustify the selection of firms that depart significantly from thenorm. Our point is that any normative approach to selecting comparablefirms should reflect the fundamental concepts that underpin equity valu-ation. We do not regard our model as in any sense "optimal." However,we believe that an industry-based approach with firm-specific adjustmentsis a sensible first attempt at empirically capturing these some key conceptsfrom valuation theory. Future work might consider variables that capturethe quality of earnings or other value relevant attributes not considered inthis study.These results seem to have further potential for development as a decisionaid for financial analysisand investors. Experimental evidence suggests thatanalysts may focus on more salient firms within an industry when selectingcomparables. As in the case of Guidant Inc. (Appendix C), it is likely thatour approach will nominate suitable peer firms that do not come immedi-ately to mind to an analyst. A main advantage of market multiples is theirconvenience in common practice, particularlyin valuing private firms. It istherefore important that any tool developed from this research be relativelyeasy to use. The technique outlined here is fairlysimple to implement.The procedure would involve estimating warrantedEVSand PBratios (orwarranted price-to-earnings and other ratios) for a population of currentlytraded firms. Aft