Bhojraj Lee Paper

Accounting Research Center, Booth School of Business, University of Chicago Who Is My Peer? A Valuation-Based Approach to the Selection of Comparable Firms Author(s): Sanjeev Bhojraj and Charles M. C. Lee Source: Journal of Accounting Research, Vol. 40, No. 2, Studies on Accounting, Entrepreneurship and E-Commerce (May, 2002), pp. 407-439 Published by: Blackwell Publishing on behalf of Accounting Research Center, Booth School of Business, University of Chicago Stable URL: http://www. jstor. org/stable/3542390 . Accessed: 15/01/2011 08:35 Your use of the JSTOR archive indicates your acceptance of JSTORs Terms and Conditions of Use, available at . http://www. jstor. org/page/info/about/policies/terms. jsp. JSTORs Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. 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A Valuation-Based Approach to the Selection of Comparable Firms SANJEEV BHOJRAJ AND CHARLES M. C. LEE* Received4January2001;accepted4 September2001 ABSTRACT This study presents a general approach for selecting comparable firms in market-based research and equity valuation. Guided by valuation theory, we develop a warrantedmultiple for each firm, and identify peer firms as those having the closest warranted multiple. We test this approach by examining the efficacy of the selected comparable firms in predicting future (one- to three-year-ahead) enterprise-value-to-sales and price-to-book ratios. Our tests encompass the general universe of stocks as well as a sub-population of socalled new economy stocks. We conclude that comparable firms selected in this manner offer sharp improvements over comparable firms selected on the basis of other techniques. 1. Introduction Accounting-based market multiples are easily the most common technique in equity valuation. These multiples are ubiquitous in the reports and recommendations of sell-side financial analysts, and are widely used in *Johnson Graduate School of Management, Cornell University. We thank Bhaskaran Swaminathan, as well as workshop participants at the Australian Graduate School of ManConferagement, Cornell University, Indiana University, the 2001 Journal ofAccountingResearch 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 International Inc. 407 of of 2002 Copyright University Chicagoon behalfof the Institute Professional Accounting, ? , 408 S. BHOJRAJ C. M. C. LEE AND investment bankers fairness opinions (e. g. , DeAngelo [1990]). They also appear in valuations associated with initial public offerings (IPOs), leveraged buyout transactions, seasoned equity offerings (SEOs), and other merger and acquisition (M) activities. Even advocates of projected discounted cash flow (DCF) valuation methods frequently resort to using market multiples when estimating terminal values. Despite their widespread usage, little theory is available to guide the application of these multiples. With a few exceptions, the accounting and finance literature contains little evidence on how or why certain individual multiples, or certain comparable firms, should be selected in specific contexts. Some practitioners even suggest that the selection of comparable firms is essentially an art form that should be left to professionals. 2 Yet the degree of subjectivityinvolved in their application is discomforting from a scientific perspective. Moreover, the aura of mystique that surrounds this technique limits its coverage in financial analysis courses, and ultimately threatens its credibility as a serious alternative in equity valuation. In this study, we re-examine the theoretical underpinnings for the use of market multiples in equity valuation, and develop a systematic approach for the selection of comparable firms. Our premise is that the popularity of market-based valuation multiples stems from their function as a classic satisficingdevice (Simon [1997]). In using multiples to value firms, analysts forfeit some of the benefits of a more complete, but more complex, pro forma analysis. In exchange, they obtain a convenient valuation heuristic that produces satisfactory results without incurring extensive time and effort costs. In fact, we believe it is possible to compensate for much of the information these multiples fail to capture through the judicious selection of comparable firms. Our aim is to develop a more systematic technique for doing so, through an appeal to valuation theory. Specifically, we argue that the choice of comparable firms should be a function of the variables that drive cross-sectional variation in a given valuation multiple. For example, in the case of the enterprise-value-to-sales multiple, comparable firms should be selected on the basis of variables that drive cross-sectional differences in this ratio, including expected profitability, growth, and the cost-of-capital. 3 In this spirit, we use variables nominated by valuation theory and recent advances in estimating the implied cost-of-capital (i. . , Gebhardt, Lee, and Swaminathan [2001]) to develop a 1 For example, Kim and Ritter [1999] discuss the use of multiples in valuing IPOs. Kaplan and Ruback [1995] examine alternative valuation approaches, including multiples, in highly levered 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) ratio because the former is conceptually s uperior when firms are differentially levered (we thank the referee for pointing this out). We also report results for the price-to-book (PB) ratio. We focus on these two ratios because of their applicability to loss firm, which are particularly important among the so-called new economy (tech, biotech, and telecommunication) stocks. However, our approach is general, and can be applied to any of the widely used valuation multiples. WHO IS MYPEER? 409 warrantedmultiple for each firm based on large sample estimations. We then identify a firms peers as those firms having the closest warranted valuation multiple. Our procedures result in two end products. First, we produce warranted multiples for each firmn-that is, a warranted enterprise-value-to-sales (WEVS)and a warranted price-to-book (WPB)ratio. These warranted multiples are based on systematic variations in the observed multiples in crosssection over large samples. The warranted multiples themselves are useful for valuation purposes, because they incorporate the effect of cross-sectional variations in firm growth, profitability, and cost-of-capital. Second, by ranking firms according to their warranted multiples, we generate a list of peer firms for each target firm. For investors and analysts who prefer to conduct equity valuation using market multiples, this approach suggests a more objective method for identifying comparable firms. For researchers, our approach suggests a new technique for selecting control firms, and for isolating a variable of particular interest. Recent methodology studies have demonstrated that characteristic-matched control samples provide more reliable inferences in market-based research (e. . , Barber and Lyon [1997], Lyon et al. [1999]). Our study extends this line of research by presenting a more precise technique for matching sample firms based on characteristics identified by valuation theory. Our approach is designed to accommodate both profitable and loss firms, which have become pervasive in the so called new economy. In short, the methodology developed in this paper can be useful whenever the choice of control firms plays a prominent role in the research design of a market-related study. We test our approach by examining the efficacy of the selected comparable firms in predicting future (one- to three-year-ahead) EVSand PB ratios. 4Our tests encompass the general universe of stocks as well as a sub-population of new economy stocks from the tech, biotech, and telecommunication sectors. Our results show that comparable firms selected in this manner offer sharp improvements over comparable firms selected on the basis of other techniques, including industry and size matches. The improvement is most pronounced among the so-called new economy stocks. The main message from this study is that the choice of comparable firms can be made more systematic and less subjective through the application of valuation theory. In the case of the EVSmultiple, our approach almost triples the adjusted r-squares obtained from using simply industry or industry-size matched selections. The PB multiple is more difficult to predict in general, but our approach still more than doubles the adjusted r-square relative to industry or industry-size matched selections. Interestingly, we find that using the actual multiples from the best comparable firms is generally better than using the warranted multiple itself. Moreover, the choice of comparable 4We forecast future multiples because we do not regard the current stock price as necessarily the best benchmark for assessing valuation accuracy. As discussed later, forecasting future multiples is not equivalent to forecasting future prices or returns. 410 s. BHOJRAJAND C. M. C. LEE firms is, to some extent, dependent on the market multiple under consideration-the best firms for the EVSratio are not necessarily the best firms for the PB ratio. While we illustrate our approach using these two ratios, 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 relation to the existing literature. In section 3, we develop the theory that underpins our analysis. In section 4, we discuss sample selection, research design and estimation procedures. Section 5 reports our empirical results, and section 6 concludes with a discussion of the implications of our findings. . 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 forecasts of sales growth rates, profit margins, and asset efficiency ratios. In these settings, we typically appeal to comparable firms from the same industry as a source of reference. Second, in multiples-based valuation, the market multiples of comparable firms are u sed to infer the market value of the target firm. Third, in empirical research, academics seek out comparable firms as a research design device for isolating a variable of particular interest. Our paper is focused primarily on the second and third needs for comparable firms. 5 Given their widespread popularity among practitioners, market multiples based valuation has been the subject of surprisingly few academic studies. Three recent studies that provide some insights on this topic are Kim and Ritter (KR;[1999]), Liu, Nissim, and Thomas (LNT; [1999]), and Baker and Ruback (BR; [1999]). All three examine the relative accuracy of alternative multiples in different settings. KR uses alternative multiples to value initial public offers (IPOs), while LNT and BR investigate the more general context of valuation accuracy relative to current stock prices. KRand LNT both find that forward earnings perform much better than historical earnings. LNT shows that in terms of accuracy relative to current prices, the performance of forward earnings is followed by that of historical earnings measures, cash flow measures, book value, and finally, sales. In addition, Baker and Ruback [1999] discuss the advantages of using harmonic means-that is, the inverse of the average of inversed ratios-when aggregating common market multiples. None of these studies address the choice of comparable firms beyond noting the usefulness of industry groupings. 5 Our technique is not directly relevant to the first situation, because it does not match firms on the basis of a single attribute (such as sales growth, or profit margin). Instead, our approach matches firms on the basis of a set of variables suggested by valuation theory. Our paper also does not address the trivial case whereby a firm is its own comparable. As we point out later, in multiples-based valuation of public firms, a firms own lagged multiple is often the most useful empirical proxy for its current multiple. WHO IS MYPEER? 411 Closer to this study are three prior studies that either investigate the effect of comparable firm selection on multiple-based valuation, or examine the determinants cross-sectional variations in certain multiples. Boatsman and Baskin [1981] compare the accuracy of value estimated based on earningsto-price (EP) multiples of firms from the same industry. They find that, relative to randomly chosen firms, valuation errors are smaller when comparable firms are matched on the basis of historical earnings growth. Similarly, Zarowin [1990] examines the cross-sectional determinants of EPratios. He shows forecasted growth in long-term earnings is a dominant source of variation in these ratios. Other factors, such as risk, historical earnings growth, forecasted short-term growth, and differences in accounting methods, seem to be less important. Finally,Alford [1992] examines the relative valuation accuracy of EPmultiples when comparable firms are selected on the basis of industry, size, leverage, and earnings growth. He finds that valuation errors decline when the industry definition used to select comparable firms is narrowed to twoor three-digit SIC codes, but that there is no further improvement when a four-digit classification is used. He also finds that after controlling for industry membership, further controls for firm size, leverage, and earnings growth do not reduce valuation errors. Several stylized facts emerge from these studies. First, the choice of which multiple to use affects accuracy results. In terms of accuracy relative to current prices, forecasted earnings perform relativelywell (KR,LNT); the priceto-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 ratios is unclear, with studies reporting conflicting results (Zarowin [1999], Alford [1992], Boatsman and Baskin [1981]), but forecasted growth rates are important (Zarowin [1999]). Other measures, including risk-basedmetrics (leverage and size) do not seem to provide much additional explanatory power for E/P ratios. Our study is distinct from these prior studies in several respects. First, our approach is more general, and relies more heavily on valuation theory. This theory guides us in developing a regression model that estimates a warranted multiple for each firm. We then define a firms peers as those firms with the closest warranted market multiple to the target firm, as identified by our model. The advantage of a regression-based approach is that it allows us to simultaneously control for the effect of various explanatory variables. For example, some firms might have higher current profitability, but lower future growth prospects, and higher cost-of-capital. This approach allows us to consider the simultaneous effect of all these variables, and to place appropriate weights on each variable based on empirical relations established in large samples. Our empirical results illustrate the advantage of this approach. Contrary to the mixed results in prior studies, we find that factors related to profitability, growth, and risk, are strongly and consistently correlated with the EVS 412 S. BHOJRAJ C. M. C. LEE AND and PB ratios. Collectively, factors that relate to profitability, growth, and risk, play an important role in explaining cross-sectional variations of these multiples. In fact, we find that variables related to firm-specific profitability, forecasted growth and risk are more important than industry membership and firm size in explaining a firms future EVSand PB ratios. Second, we employ recent advances in the empirical estimation of cost-ofcapital (i. e. , Gebhardt et al. [2001]) to help identify potential explanatory variables for estimating our model of warranted market multiples. The risk metrics examined in prior studies are relatively simple, and the results are mixed. We follow the technique in Gebhardt et al. [2001] to secure additional explanatory variables that are associated with cross-sectional determinants of a firms implied cost-of-capital. Several of these factors turn out to be important in explaining EVSand PB ratios. Third, we do not assume that the current stock price of a firm is the best estimate of firm value. Prior studies compare the valuation derived by the multiples to a stocks current price to determine the valuation error. In effect, these studies assume that the current stock price is the appropriate normative benchmark by which to judge a multiples performance. Under this assumption, it is impossible to derive an independent valuation using multiples that is useful for identifying over- or under-valued stocks. Our less stringent assumption of market efficiency is that a firms current price is a noisy proxy for the true, but unobservable intrinsic value, defined as the present value of expected dividends. Moreover, due to arbitrage, price converges to value over time. As a result, price and various alternative estimates of value based on accounting fundamentals will be co-integrated over time. 6 Under this assumption, we estimate a warrantedmultiple that differs from the actual multiple implicit in the current price. Consistent with this philosophy, we test the efficacy of alternative estimated multiples by comparing their predictive power for a firms future multiples (e. g. , its one-, two-, or three-year-ahead EVSand 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]) focus solely on the EP ratio. A limitation of these studies is that they do not pertain to loss firms. This limitation has become more acute in recent years, as many technology, biotechnology, and telecommunication firms have reported negative earnings. 6 For a more formal statistical model of this co-integrated relationship between price and alternative 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 interest is 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]. WHO IS MY PEER? 413 Appendix A provides an indication of the magnitude of the problem. This appendix reports descriptive statistics for a sample of 3,515 firms from NYSE/AMEX/NASDAQ as of 5/29/2000. To be included, a firm must be U. S. domiciled (i. e. , not an ADR), have a market capitalization of over $100 million, and fundamental data for the trailing 12 months (i. . , not a recent IPO). Based on aggregate net income from the most recent four quarters, we divide the sample into profitable firms (78% of sample) and loss firms (22% of sample). Panel A reports the percentage of these firms that have positive EBIT,Operating Income, EBITDA, Gross Margin, Sales, One-year-ahead forecasted earnings (FY1), and book value. This panel shows that only 40% of the loss firms have positive operating income, only 47% have positive EBITDA, and only 34% have positive FY1forecasts. In fact, only 87% of the loss firms have positive gross margins. The only reliably positive accounting measures are sales (100%) and book value (94%). Clearly, these loss firms are difficult to value. However, they are also difficult to ignore. Panel B reports the distribution of realized returns in the past six months (11/31/99 to 5/29/00) separately 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 a high-stake game that constitutes a substantial proportion of the universe of traded stocks in the United States. Our study uses the two most reliably positive multiples (EVSand PB). Liu, Nissim, and Thomas [1999] show that these two ratios are relatively poor performers in terms of their valuation accuracy. We demonstrate that by choosing an appropriate set of comparable firms, the accuracy of these ratios can be improved sharply. In particular, we demonstrate the incremental usefulness of the technique for a sub-population of new economy stocks from the technology, telecom, and biotechnology sectors. 3. Development the Theory of The valuation literature discusses two broad approaches to estimating shareholder value. The first is direct valuation, in which firm value is estimated directly from its expected cash flows without appeal to the current price of other firms. Most direct valuations are based on projected dividends and/or earnings, and involve a present value computation of future cash flow 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 relative valuation 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 not appropriate for most going concerns. 414 s. BHOJRAJAND C. M. C. LEE which firm value estimates are obtained by examining the pricing of comparableassets. This approach involves applying an accounting-based market 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 value estimate. In relative valuation, an analyst applies the market multiple from a comparable firm to a target firms corresponding accounting number: Our estimated price = (Their market multiple) X (Our accounting number). In so doing, the analyst treats the accounting number in question as a summary statistic for the value of the firm. Assuming our firm in its current state deservesthe same market multiple as the comparable firm, this procedure allows us to estimate what the market would pay for our firm. Which firm(s) deservethe same multiple as our target firm? Valuation theory helps to resolve this question. In fact, explicit expressions for most of the most commonly used valuation multiples can be derived using little more than the dividend discount model and a few additional assumptions. For example, the residual income formula allows us to re-express the discounted dividend model in terms of the price-to-book ratio:10 * PB, Et[(ROEt+i re)Bt+i-l] (1 + re)i Bt i=1 (1) Bt where Pt* is the present value of expected dividends at time t, B, = book value 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 equity for period t + i. This equation shows that a firms price-to-book ratio is a function of its expected ROEs, its cost-of-capital, and its future growth rate in book value. Firms that have similar price-to-book ratios should have present values of future residual income (the infinite sum in the right-hand-side of equation (1)) that are close to each other. In the same spirit, it is not difficult to derive the enterprise-value-to-sales ratio in terms of subsequent profit margins, growth rates, and the cost of capital. In the case ofa stable growth firm, the enterprise-value-to-salesratio can be expressed as: EV7 Et(PMxkx(1 + g)) _ (r- g) St where EVZ is total enterprise value (equity plus debt) at time t, St = total 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 pricing theory. Designed for pricing traded assets with finite lives, this approach encounters significant measurement 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 new economy stocks. 10See Feltham and Ohlson [1995] or Lee [1999] and the references therein for a discussion of this model. See Damodaran [1994; page 245] for a similar expression. WHO IS MYPEER? 415 time t; PM is operating profit margin (earnings before interest); k is a constant payout ratio (dividends and debt servicing costs as a percentage of earnings; alternatively, it is sometimes called one minus the plow-back rate); r = weighted average cost of capital; and g is a constant earnings growth rate. In the more general case, we can model the firms growth in terms of an initial period (say n years) of high growth, followed by a period of more stable growth in perpetuity. Under this assumption, a firms enterprise-valueto-sales ratio can be expressed as: (1+ EVt St EtPMxkx rL? gl)(1- ((1 + gg)n/(l r + r)n)) (1 + gi) n(l + g2) 1 (1+g1)n(1+ g2) nir- (1+r g ]ii (3) where EV7 is the total enterprise value (debt plus equity) at time t, St = total sales at time t; Et[. = expectation based on information available at 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 for n years; and g2 is the constant growth rate applicable from period n+ 1 onwards. Equation (3) shows that a firms warranted enterprise-value-to-sales ratio is 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 market value of equity and d ebt approximates the present value of expected cash flows, these variables should explain a ignificant portion of the cross-sectional variation in the EVS ratio. In the tests that follow, we employ a multiple regression model to estimate the warranted EVSand PB ratios for each firm. The explanatory variables we use in the model are empirical proxies for the key 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 the cross-sectional variation in the EVSand PBratios. Our goal is to develop a reasonably parsimonious model that produces a warrantedmultiple (WEVS or WPB)for each firm. These warranted multiples reflect the large sample relation between a firms EVS (or PB) ratio and variables that should explain cross-sectional variations in the ratio. The estimated WEVS(or WPB) becomes the basis of our comparable firm analysis. 4. 1 ESTIMATING THE WARRANTED RATIOS We use all firms in the intersection of (a) the merged COMPUSTATindustrial and research files, and (b) the I/B/E/S historical database of analyst earnings forecasts, excluding ADRs and REITs. We conduct our analysis as of June 30th of each year for the period 1982-1998. To be included 416 AND s. BHOJRAJ C. M. C. LEE n the analysis a firm must have at least one consensus forecast of longterm growth available during the 12 months endedJune 30th. In the event that more than one consensus forecast was made in any year, the most recent forecast is used. We use accounting information for each firm as of the most recent fiscal year end date, and stock prices as of the end of June. To facilitate estimation of a r obust model, we drop firms with prices below $3 per share and sales below $100 million. We eliminate firms with negative book value (defined as common equity), and any firms with missing price or accounting data needed for the estimation regression. 2We require that all firms belong in an industry (based on two-digit SIC codes) with at least five member firms. In addition we eliminate firms in the top and bottom one percent of all firms ranked by EVS, PB, Rnoa, Lev, Adjpm,and Adjgroeach year (these variables are defined below). The number of remaining firms in the sample range from 741 (in 1982) to 1,498 (in 1998). For each firm, we secure nine explanatory variables. We are guided in the choice of these variables by the valuation equations discussed earlier, and several practical implementation principles. First, we wish to construct a model that can be applied to private as well as public firms, we therefore avoid using the market value of the target firm in any of the explanatory variables. Second, in the spirit of the contextual fundamental analysis (e. g. , see Beneish, Lee, and Tarpley [2000]), we anchor our estimation procedure on specific industries. In other words, we use the mean industry market multiples as a starting point, and adjust for key firm-specific characteristics. 3 Finally, to the extent possible, we try to use similar variables for estimating EVSand PB. Our goal is to generate relatively simple models that capture the key theoretical constructs of growth, risk, and profitability. Specifically, our model includes the following variables, which are also summarized and described in more detail in Appendix B: IndevsThe harmonic mean of the enterprise-value-to-salesmultiple for all the firms with the same two-digit SIC code. For example, for the 1982 regression, 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 industrywide factors, such as profit margins and growth rates, and we expect it to be positively correlated with current year firm-specific EVS and PB ratios. Indpb-The harmonic mean of the price-to-book ratio for all firms in the same industry. This variable controls for industry-wide factors that affect the PB ratio. In addition, Gebhardt et al. [2001] show firms with higher PB 12 The two exceptions are research and development expense and long-term debt. Missing data in these two fields are assigned a value of zero. 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]). WHO IS MYPEER? 417 ratios have lower implied costs of capital. To the extent that industries with lower implied costs-of-capital have higher market multiples, we expect this variable to be positively correlated with EVSand PB ratios. AdjpmThe industry-adjusted profit margin. We comput e this variable as the difference between the firms profit margin and the median industry profit margin. In each case, the profit margin is defined as a firms operating profit divided by its sales. Theory suggests this variable should be positively correlated with current year EVSratios. where Dum is 1 if Adjpm LosspmThisvariable is computed as Adjpm*Dum, is less than or equal to zero, and 0 otherwise. Used in conjunction with Adjpm,this variable captures the differential effect of profit margin on the P/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, controlling for Adjpm,this variable should be negatively correlated with EVSand PB ratios. AdjgroIndustry-adjusted growth forecasts. This variable is computed as the difference between a firms consensus earnings growth forecast (from IBES) and the industry median of the same. Higher growth firms merit higher EVSand PB ratios. LevBook leverage. This variable is computed as the total long-term debt scaled by the book value of common equity. In univariate tests, Gebhardt et al. [2001] shows that firms with higher leverage have higher implied costsof-capital. However, controlling for market leverage, they find that book leverage is not significant in explaining implied cost-of-capital. We include this variable for completeness, in case it captures elements of cross-sectional risk not captured by the other variables. Rnoa-Return on net operating asset. This variable is a firms operating profit scaled by its net operating assets. Penman [2000] recommends this variable as a measure of a firms core operation profitability. In our context, having already controlled for profit margins, this variable also serves as a control for a firms asset turnover. We expect it to be positively correlated with the EVSand PB ratios. RoeReturn on equity. This variable is net income before extraordinary items scaled by the end of period common equity. Conceptually, this variable should provide a better profitability proxy in the case of the PB ratio. We use this variable in place of Rnoa as an alternative measure of profitability when conducting the PB regression. Rd-Total research and development expenditures divided by sales. Firms with higher RD expenditures tend to have understated current profitability relative to future profitability. To the extent that this variable captures profitability growth beyond the consensus earnings forecast growth rate, we expect it to be positively correlated with the EVSand PB ratios. In addition to these nine explanatory variables, we also tested three other variables-a dividend payout measure (actual dividends scaled by 418 S. BHOJRAJ AND C. M. C. LEE total assets), an asset turnover measure, and a measure of the standard deviation of the forecasted growth rate. The first two variables add little to the explanatory power of the model. The standard deviation measure (suggested by Gebhardt et al. 2001] as a determinant of the cost-ofcapital) contributed marginally, but was missing for a significant number of observations. Moreover, this measure would be unavailable for private firms. For these reasons, we excluded all three variables from our final model. To recap, our research design involves estimating a series of annual cross-sectional regressions of either the EVSor PB ratio on ei ght explanatory variables. The estimated coefficients from last years regressions are used, in conjunction with each firms current year information, to generate a prediction of the firms current and future ratio. We refer to this prediction as a firms warrantedmultiple (WEVSor WPB). This warranted multiple becomes the basis for our identification of comparable firms in subsequent tests. STATISTICS 4. 2 DESCRIPTIVE Table 1 presents annual summary statistics on the two dependent and nine explanatory variables. The overall average EVS of 1. 20 (median of 0. 94) and average PB of 2. 26 (median of 1. 84) are comparable to prior studies (e. g. , LNT, BB), although our sample size is considerably larger due to the inclusion of loss firms. This table also reveals some trends in the key variables over time. Consistent with prior studies (e. g. Frankel and Lee [1999]) we observe an increase over time in the accounting-based multiples (EVS, PB, Indps, and Indpb) and total RD expenditures (Rd). This non-stationarity in the estimated coefficients could be attributable to systematic changes in the composition of firms over time. For example, the increased importance of the RD variable could reflect the ris ing prominence of technology firms in the sample. The accounting-based rates of return (Rnoa and Roe) and book leverage (Lev) are relatively stable over time. As expected, the industry-adjustedvariables (Adjpm,Losspm,and Adjgro) have mean and median measures close to zero. Overall, this table indicates that the key input variables for our analysis make economical sense. Table 2 presents the average annual pairwise correlation coefficients between these variables. The upper triangle reports Spearman rank correlation coefficients; the lower triangle reports Pearson correlation coefficients. As expected, EVSis positively correlated with the industry enterprise-value-tosales ratio (Indevs) and price-to-book ratio (Indpb). It is also positively correlated with industry-adjusted measures of a firms profit margin (Adjpm) and expected growth rate (Adjgro). It is negatively correlated with book leverage (Lev), and positively correlated with accounting rates of return (Rnoa and Roe), as well as RD expense (Rd). To a lesser degree, EVS is also positively correlated with profit margin among loss firms (Losspm). The results are similar for the PB ratio. All the correlation coefficients WHO IS MY PEER? TABLE 1 StatisticsofEstimationVariables Summary 419 This table provides information on the mean and median of the variables used in the annual estimation regressions. All accounting variables are from the most recent fiscal year end publicly available byJune 30th. Market values are as of June 30th. EVSis the enterprise value to sales ratio, computed as the market value common equity plus long-term debt, divided by sales. PB is the price to book ratio. Indevsis the industry harmonic mean of EVSbased on two-digit SIC codes. Indpbis the industry harmonic mean of PB. Adjpmis the difference between the firms profit margin and the industry profit margin, where profit margin is defined as operating profit divided by sales. Losspmis Adjpm* indicator variable, where the indicator variable is 1 if profit is margin 0 and 0 otherwise. Adjgro the difference between the analysts consensus forecast of the firms long-term growth and the industry average. Lev is the total long-term debt scaled by book value of stockholders equity. Rnoa is operating profit scaled by net operating assets. Rd is the firms RD expressed as a percentage of net sales. year 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 mean median mean median mean median mean median mean median mean median mean median mean median mean median mean median mean median mean median mean median mean median mean median mean median mean median EVS 0. 3 0. 50 0. 98 0. 77 0. 84 0. 69 0. 88 0. 73 1. 07 0. 88 1. 22 1. 00 1. 09 0. 90 1. 07 0. 89 1. 09 0. 89 1. 10 0. 87 1. 15 0. 94 1. 22 1. 02 1. 20 1. 00 1. 36 1. 07 1. 49 1. 13 1. 51 1. 20 1. 59 1. 24 PB 1. 11 0. 93 1. 82 1. 48 1. 46 1. 26 1. 72 1. 46 2. 14 1. 82 2. 31 1. 92 1. 97 1. 70 2. 02 1. 70 1. 99 1. 64 1. 93 1. 54 2. 13 1. 76 2. 48 2. 04 2. 31 1. 98 2. 49 2. 08 2. 75 2. 24 2. 87 2. 41 3. 06 2. 55 Indevs Indpb Adjpm 0. 50 0. 006 0. 92 0. 000 0. 50 0. 92 1. 57 0. 76 0. 002 1. 59 0. 77 0. 000 1. 34 0. 69 0. 001 0. 000 1. 30 0. 72 0. 70 1. 45 0. 004 1. 30 0. 000 0. 72 0. 001 0. 85 1. 7 0. 000 0. 86 1. 69 0. 95 1. 95 -0. 002 0. 95 0. 000 1. 82 1. 69 0. 85 0. 002 0. 80 1. 61 0. 000 0. 84 1. 79 0. 003 0. 76 1. 63 0. 000 0. 83 1. 69 0. 002 0. 79 1. 49 0. 000 1. 65 0. 003 0. 80 1. 39 0. 000 0. 69 0. 87 1. 71 0. 005 0. 78 0. 000 1. 52 0. 90 1. 91 0. 002 0. 000 0. 86 1. 76 0. 89 0. 006 2. 02 0. 86 1. 91 0. 000 0. 95 0. 007 2. 06 0. 93 0. 000 2. 02 1. 01 0. 009 2. 18 0. 98 1. 99 0. 000 0. 005 1. 02 2. 12 1. 07 0. 000 2. 01 1. 09 0. 004 2. 20 0. 000 1. 08 2. 05 Losspm 0. 000 0. 000 -0. 003 0. 000 -0. 004 0. 000 -0. 002 0. 000 -0. 004 0. 000 -0. 007 0. 000 -0. 004 0. 000 -0. 03 0. 000 -0. 004 0. 000 -0. 002 0. 000 -0. 004 0. 000 -0. 002 0. 000 -0. 002 0. 000 -0. 001 0. 000 -0. 002 0. 000 -0. 003 0. 000 -0. 004 0. 000 Adjgro 0. 50 0. 00 0. 21 -0. 05 0. 44 -0. 01 0. 66 0. 00 0. 30 -0. 04 0. 18 -0. 10 0. 29 0. 00 0. 69 0. 00 0. 58 -0. 08 0. 45 -0. 12 0. 23 -0. 19 0. 55 -0. 09 0. 49 -0. 15 0. 73 0. 00 0. 40 -0. 13 0. 36 -0. 17 0. 43 0. 00 Lev 0. 45 0. 36 0. 49 0. 38 0. 43 0. 33 0. 44 0. 32 0. 50 0. 34 0. 54 0. 40 0. 56 0. 43 0. 57 0. 41 0. 61 0. 44 0. 59 0. 45 0. 59 0. 42 0. 58 0. 39 0. 58 0. 36 0. 56 0. 38 0. 58 0. 37 0. 61 0. 36 0. 63 0. 38 Rnoa 20. 85 19. 62 17. 8 16. 18 17. 85 16. 93 19. 96 18. 82 17. 58 16. 41 17. 27 16. 00 19. 05 17. 68 19. 90 18. 54 19. 77 17. 97 19. 00 16. 93 17. 86 15. 97 19. 80 17. 22 20. 08 17. 47 21. 66 18. 72 22. 19 18. 93 21. 56 18. 97 22. 84 20. 24 Roe 14. 39 14. 77 11. 88 12. 82 12. 04 13. 00 13. 49 14. 32 11. 45 12. 92 10. 63 12. 22 12. 61 12. 93 13. 90 14. 71 13. 29 13. 51 11. 91 12. 55 10. 31 11. 29 11. 87 12. 39 11. 57 12. 37 13. 48 13. 18 12. 57 13. 08 12. 46 12. 89 12. 31 12. 76 Rd 1. 23 0. 14 1. 33 0. 09 1. 51 0. 08 1. 66 0. 05 1. 75 0. 00 1. 94 0. 00 1. 83 0. 00 1. 94 0. 00 1. 86 0. 00 1. 96 0. 00 2. 03 0. 00 1. 9 0. 00 1. 90 0. 00 1. 77 0. 00 2. 01 0. 00 2. 01 0. 00 2. 25 0. 00 Pooled mean 1. 20 2. 26 median 0. 94 1. 84 0. 88 0. 81 1. 83 1. 72 0. 004 -0. 003 0. 44 0. 000 0. 000 -0. 05 0. 56 20. 00 12. 35 1. 86 0. 38 17. 96 13. 01 0. 00 are in the expected direction. Except for the correlation between Rnoa and Roe (which do not appear in the same estimation regression), none of the average pairwise correlation coefficients exceed 0. 60. These results suggest that the explanatory variables are not likely to be redundant. 420 S. BHOJRAJAND C. M. C. LEE TABLE 2 Correlation between EstimationVariables This table provides the correlation between the variables. The upper triangle reflects the Spearman correlation estimates; the lower triangle reflects the Pearson correlation coefficients. All accounting variables are based on the most recent fiscal year end information publicly available byJune 30th. Market values are as of June 30th. EVSis the enterprise value to sales ratio, computed as the market value common equity plus long-term debt, divided by sales. PB is the price to book ratio. Indevsis the industry harmonic mean of EVSbased on two-digit SIC codes. Indpbis the industry harmonic mean of PB. Adjpmis the difference between the firms profit margin and the industry profit margin, where profit margin is defined as operating profit divided by sales. Losspmis Adjpm*indicator variable, where the indicator variable is 1 if profit is margin 0 and 0 otherwise. Adjgro the difference between the analysts consensus forecast of the firms long-term growth and the industry average. Lev is the total long-term debt scaled by book value of stockholders equity. Rnoa is operating profit scaled by net operating assets. Rd is the firms RD expressed as a percentage of net sales. Average Correlation (Pearson/Spearman) EVS EVS PB Indevs PB 0. 52 Indevs Indpb 0. 51 0. 16 0. 09 0. 33 0. 35 0. 35 -0. 06 -0. 02 0. 04 0. 02 -0. 01 -0. 05 0. 08 -0. 09 -0. 02 0. 25 0. 03 0. 14 0. 10 0. 06 Adjpm Losspm Adjgro Lev Rnoa Roe 0. 54 0. 08 0. 21 -0. 07 0. 21 0. 28 0. 38 0. 14 0. 60 0. 59 0. 29 -0. 20 -0. 07 0. 04 -0. 01 0. 06 -0. 01 0. 05 0. 15 -0. 03 0. 06 -0. 04 -0. 14 0. 26 0. 06 -0. 17 0. 54 0. 55 0. 26 0. 06 -0. 03 0. 32 0. 28 0. 26 0. 04 0. 04 -0. 01 0. 10 0. 09 -0. 35 -0. 16 0. 02 -0. 12 -0. 02 0. 51 0. 07 -0. 24 0. 75 0. 32 0. 50 0. 38 0. 07 -0. 12 0. 66 0. 06 -0. 10 0. 09 -0. 23 -0. 03 -0. 6 Rd 0. 17 0. 08 0. 19 0. 11 0. 03 -0. 05 -0. 02 -0. 27 0. 03 -0. 03 0. 47 0. 50 0. 04 0. 15 0. 28 Indpb 0. 33 Adjpm 0. 59 0. 09 Losspm 0. 06 0. 29 Adjgro 0. 22 Lev -0. 03 -0. 07 Rnoa 0. 54 0. 22 0. 48 Roe 0. 23 Rd 0. 09 0. 24 5. Empirical Results 5. 1 MODEL ESTIMATION Table 3 presents the results of annual cross-sectional regressions for each year from 1982 to 1998. The dependen t variable is the enterprise-value-tosales ratio (EVS). The eight independent variables are as described in the previous section. Table values represent estimated coefficients, with accompanying p-values presented in parentheses. Reported in the right columns are adjusted r-squares and the number of observations per year. The last two rows report the average coefficient for each variable, as well as a Newey-West autocorrelation adjusted t-statisticon the mean of the time series of annual estimated coefficients. The results from this table indicate that a consistently high proportion of the cross-sectional variation in the EVS ratio is captured by the eight explanatory variables. The annual adjusted r-squares average 72. 2%, and range from a low of 66. 1% to a high of 76. 5%. The strongest six explanaRnoa, nd RD) have the same tory variables (Indevs,Adjpm,Losspm, Adjgro, directional sign in each of 17 annual regressions, and are individually significant at less than 1%. Indpbis positively correlated with EVS in 11 out of 17 years, and is significant at the 5% level. Controlling for Indpb,book WHO IS MY PEER? TABLE 3 Annual EstimationRegressions Warranted for Enterprise-Value-to-Sales This table reports the res ults from the following annual estimation regression: 8 421 EVSi,t = at + j=1 jtCj,i,t + Li,t where the dependent variable, EVS,is the enterprise value to sales 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; Indpbis the industry harmonic mean of the price-to-book ratio; Adjpmis the difference between the firms profit margin and the industry profit margin, is where profit margin is defined as operating profit divided by sales; Losspm Adjpm indicator variable, where the indicator variable is 1 if profit margin 0 and 0 otherwise; Adjgrois the difference between the analysts consensus forecast of the firms long-term growth rate and the industry average; Lev is long-term debt scaled by book equity; Rnoa is operating profit as a percent of net operating assets; and Rd is RD expense as a percentage of sales. P-values are provided in parentheses. The last row represents the time-series average coefficients along with Newey-Westautocorrelation corrected t-statistics. The adjusted r-square (r-sq) and number of firms (# obs) are also reported. Year Intercept 1982 -0. 0623 (0. 13 5) 1983 -0. 0883 (0. 121) 1984 0. 0192 (0. 699) 1985 0. 1337 (0. 002) 1986 0. 0225 (0. 706) 1987 0. 1899 (0. 007) 1988 0. 1774 (0. 0) 1989 -0. 0455 (0. 347) 1990 0. 1083 (0. 027) 1991 0. 2321 (0. 00) 1992 0. 2064 Indevs 1. 2643 (0. 00) 1. 3531 (0. 00) 1. 2778 (0. 00) 1. 2231 (0. 00) 1. 3202 (0. 00) 1. 0908 (0. 00) 1. 0759 (0. 00) 1. 1264 (0. 00) 1. 1263 (0. 00) 1. 0740 (0. 00) 0. 8277 1. 0169 (0. 00) 1. 0027 (0. 00) 1. 0355 (0. 00) 1. 1690 (0. 00) 1. 1714 (0. 00) 1. 0157 (0. 00) 1. 1277 (0. 00) Indpb 0. 1648 (0. 00) -0. 0301 (0. 342) -0. 0015 (0. 964) -0. 0152 (0. 604) 0. 0047 (0. 856) -0. 0324 (0. 339) -0. 0097 (0. 63) 0. 0828 (0. 00) 0. 0322 (0. 019) 0. 0256 (0. 079) 0. 1150 0. 0579 (0. 097) 0. 0027 (0. 913) -0. 0211 (0. 512) 0. 0430 (0. 141) 0. 0366 (0. 264) 0. 1561 (0. 0) 0. 0360 (0. 031) Adjpm 6. 3052 (0. 00) 8. 1343 (0. 00) 6. 9266 (0. 00) 7. 9394 (0. 00) 9. 4308 (0. 00) 9. 8090 (0. 00) 8. 6458 (0. 00) 8. 4475 (0. 00) 9. 3485 (0. 00) 10. 4789 (0. 00) 10. 2810 Losspm -2. 8510 ( 0. 119) -5. 3800 (0. 00) -4. 2894 (0. 00) -4. 0951 (0. 00) -6. 2424 (0. 00) -6. 8296 (0. 00) -6. 9959 (0. 00) -5. 3691 (0. 00) -6. 0607 (0. 00) -6. 9779 (0. 00) -7. 9414 Adjgro 0. 0117 (0. 00) 0. 0392 (0. 00) 0. 0209 (0. 00) 0. 0177 (0. 00) 0. 0316 (0. 00) 0. 0363 (0. 00) 0. 0267 (0. 00) 0. 0225 (0. 00) 0. 0346 (0. 00) 0. 0316 (0. 00) 0. 0329 Lev 0. 0665 (0. 007) 0. 1414 (0. 00) 0. 0707 (0. 012) 0. 0238 (0. 351) -0. 0246 (0. 325) 0. 608 (0. 035) 0. 0228 (0. 27) 0. 0143 (0. 409) -0. 0381 (0. 065) -0. 0430 (0. 06) -0. 0567 Rnoa -0. 0091 (0. 00) -0. 0049 (0. 004) -0. 0088 (0. 00) -0. 0089 (0. 00) -0. 0080 (0. 00) -0. 0041 (0. 014) -0. 0054 (0. 00) -0. 0032 (0. 01) -0. 0037 (0. 005) -0. 0053 (0. 00) -0. 0037 Rd 0. 0194 (0. 00) 0. 0463 (0. 00) 0. 0197 (0. 00) 0. 0153 (0. 00) 0. 0118 (0. 01) 0. 0319 (0. 00) 0. 0281 (0. 00) 0. 0127 (0. 00) 0. 0191 (0. 00) 0. 0134 (0. 00) 0. 0157 0. 0253 (0. 00) 0. 0254 (0. 00) 0. 0680 (0. 00) 0. 0244 (0. 00) 0. 0313 (0. 00) 0. 0229 (0. 00) 0. 0253 (0. 00) R-sq # Obs 74. 40 741 70. 80 73. 45 74. 66 71. 11 66. 84 75. 44 74. 58 73. 54 76. 45 71. 63 71. 1 748 771 797 799 856 787 813 829 855 902 978 (0. 00) 1993 1994 1995 1996 1997 1998 All 0. 1811 (0. 004) 0. 2698 (0. 00) 0. 3148 (0. 00) 0. 0713 (0. 249) 0. 1192 (0. 048) -0. 0269 (0. 683) 0. 1072 (0. 007) (0. 00) (0. 00) (0. 00) (0. 00) (0. 00) (0. 004) (0. 008) (0. 00) 11. 4266 -6. 4058 (0. 00) (0. 00) 10. 6165 -7. 1717 (0. 00) (0. 00) 11. 9432 -9. 2245 (0. 00) (0. 00) 11. 3311-10. 6464 (0. 00) (0. 00) 12. 5771 -7. 5521 (0. 00) (0. 00) 13. 0309-10. 1430 (0. 00) (0. 00) 9. 8043 -6. 7162 (0. 00) (0. 00) 0. 0333 -0. 0129 -0. 0045 (0. 00) (0. 515) (0. 00) 0. 0312 0. 0219 -0. 0060 (0. 00) (0. 202) (0. 00) 0. 0419 0. 0100 -0. 0069 (0. 00) (0. 618) (0. 0) 0. 0623 0. 0001 -0. 0023 (0. 00) (0. 996) (0. 121) 0. 0452 0. 0201 -0. 0032 (0. 00) (0. 278) (0. 011) 0. 0421 0. 0362 -0. 0006 (0. 00) (0. 069) (0. 637) 0. 0330 0. 0184 -0. 0052 (0. 00) (0. 235) (0. 00) 73. 19 1102 75. 37 1190 66. 05 1341 71. 75 1440 66. 65 1498 72. 19 16447 422 AND C. M. C. LEE s. BHOJRAJ leverage (Lev) is not significantly correlated with EVS. Collectively, these results show that growth, profitability, and risk factors are incrementally important in explaining EVSratios, even after controlling for industry means. Note that the estimated coefficients on several of the key explanatory variables change systematicallyover time. For example, the estimated coefficient on the industry adjusted profit margin (Adjpm)and forecasted growth rate (Adjgro)both trend upwards over time, while the coefficient on the industry enterprise-value-to-sales ratio (Indevs) shows some decline in recent years. These patterns imply that, in forecasting future EVSratios, the estimated coefficients from the most recent year is likely to perform better than a rolling average of past years. In subsequent analyses, we use the estimated coefficients from the prior years regression to forecast current years warranted multiple. Table 4 reports the results of annual cross-sectional regressions for the PB ratio. The explanatory variables are the same as for the EVS regression in table 3, except for the replacement of Rnoa with Roe. Table 4 shows that all the variables except Lev contribute significantly to the explanation of PB. The coefficient on Indps is reliably negative. Otherwise, the variables are correlated with PB in the same direction as expected. Overall, the model is less successful at explaining PB than at explaining EVS. Nevertheless, the average adjusted r-square is still 51. 2%, ranging from a low of 32. 8% to a high of 61. 0%. FUTURE RATIOS 5. 2 FORECASTING Recall that our goal is to identify comparable firms that will help us to forecast a target firms future price-to-sales multiples. In this section, we examine the efficacy of the warranted multiple approach in achieving this goal. Specifically, we examine the relation between a firms future EVS and PB ratios, and a number of ex ante measures based on alternative definitions of comparable firms. The key variables in this analysisare defined below. EVSn and PBn, where n = 0, 1, 2, and 3-The current, one-, two-, and three-year-ahead EVSand PB ratios. These are our dependent variables. IEVS and IPBThe harmonic mean of the industry EVS and PB ratios, respectively. Industry membership is defined in terms of two-digit SIC codes. ISEVSand ISPBThe harmonic mean of the actual EVSand PB ratios for the four firms from the same industry with the closest market capitalization. and WPBThe warranted EVSand PB ratios. These variables are WEVS computed using the estimated coefficients from the prior years regression (tables 3 and 4), and accounting or market-based variables from the current year. COMPActual EVS (or PB) ratio for the closest comparable firms. This variable is the harmonic mean of the actual EVS (or PB) ratio of the four closest firms based on their warranted multiple. To construct this variable, WHO IS MY PEER? 423 TABLE 4 Price-to-Book Annual EstimationRegressions Warranted for This table reports the results from the following annual estimation regression: 8 PBi,t = at + E j=1 j,tCj,i,t + ti,t where the dependent variable, PB, is the price-to-book ratio as ofJune 30th of each year. The eight explanatory variables are as follows: Indevsis the industry harmonic mean of EVSbased on two-digit SIC codes; Indpbis the industry harmonic mean of the price-to-book ratio; Adjpm is the difference between the firms profit margin and the industry profit margin, where profit margin is defined as operating profit divided by sales; Losspmis AdjpmeDum, where Dum is 1 if profit margin 0 and 0 otherwise; Adjgrois the difference between the analysts consensus forecast of the firms long-term growth rate and the industry average; Lev is long-term debt scaled by book equity; Roe is net income before extraordinary items as a percent of book equity; and Rd is RD expense as a percentage of sales. The p-values are provided below each of the coefficients in parentheses. The last row represents the time-series average coefficients along with Newey-Westautocorrelation corrected t- statistics. The adjusted r-square (r-sq) and number of firms (# obs) are also reported. Year Intercept Indevs 1 982 -0. 2990 -0. 6056 (0. 00) (0. 00) 1983 -0. 3434 -0. 5129 (0. 00) (0. 001) 1984 -0. 1065 -0. 1806 (0. 143) (0. 099) 1985 -0. 3518 -0. 2882 (0. 00) (0. 09) 1986 0. 0998 -0. 3548 (0. 319) (0. 005) 1987 0. 0632 -0. 6468 (0. 584) (0. 00) 1988 0. 0568 -0. 5150 (0. 566) (0. 00) 1989 -0. 3306 -0. 5790 (0. 001) (0. 00) 1990 -0. 4592 -0. 9002 (0. 00) (0. 00) 1991 0. 0459 -0. 9010 (0. 613) (0. 00) 0. 1797 -0. 6645 1992 (0. 098) (0. 00) 1993 0. 2426 -0. 5925 (0. 111) (0. 00) 1994 -0. 0187 -0. 4753 1995 -0. 3095 (0. 008) 1996 -0. 0713 (0. 569) 1997 0. 1104 (0. 402) 1998 0. 0247 (0. 87) All -0. 0863 (0. 169) -0. 2491 (0. 00) -0. 3475 (0. 00) -0. 3565 (0. 00) -0. 3666 (0. 00) -0. 5021 (0. 00) Indpb 1. 1601 (0. 00) 1. 1696 (0. 00) 0. 9401 (0. 00) 1. 0448 (0. 00) 0. 9866 (0. 00) 1. 0956 (0. 00) 0. 8393 (0. 00) 1. 269 (0. 00) 1. 3508 (0. 00) 1. 0963 (0. 00) 1. 0051 (0. 00) 0. 7907 (0. 00) 1. 0234 0. 9481 (0. 00) 1. 0319 (0. 00) 0. 8816 (0. 00) 1. 0553 (0. 00) 1. 0321 (0. 00) Adjpm Losspm 2. 0331 -6. 2544 (0. 00) (0. 00) 3. 2891-11. 9301 (0. 00) (0. 00) 2. 0887 -5. 9880 (0. 00) (0. 00) 3. 0154 -8. 6571 (0. 00) (0. 00) 3. 6912 -6. 4419 (0. 00) (0. 00) 6. 0189 -9. 8553 (0. 00) (0. 00) 2. 0184 -9. 9218 (0. 00) (0. 00) 2. 6023-15. 3872 (0. 00) (0. 00) 1. 9280-10. 8096 (0. 00) (0. 00) 3. 0820-10. 7620 (0. 00) (0. 00) 3. 5272-12. 3146 (0. 00) (0. 00) 1. 6280-13. 7791 (0. 005) (0. 00) 3. 1253 -9. 8989 4. 3329 -9,7318 (0. 00) (0. 00) 4. 0730-13. 0282 (0. 00) (0. 0) 3. 8790-13. 5652 (0. 00) (0. 00) 3. 7902 -7. 1481 (0. 00) (0. 00) 3. 1837-10. 3220 (0. 00) (0. 00) Adjgro 0. 0371 (0. 00) 0. 1147 (0. 00) 0. 0527 (0. 00) 0. 0568 (0. 00) 0. 0883 (0. 00) 0. 0881 (0. 00) 0. 0694 (0. 00) 0. 0576 (0. 00) 0. 0815 (0. 00) 0. 0744 (0. 00) 0. 0781 (0. 00) 0. 0939 (0. 00) 0. 0834 Lev Roe -0. 2245 0. 0402 (0. 00) (0. 00) -0. 1545 0. 0541 (0. 01) (0. 00) -0. 2302 0. 0397 (0. 00) (0. 00) 0. 0585 -0. 2694 (0. 00) (0. 00) -0. 3075 0. 0542 (0. 00) (0. 00) 0. 0583 0. 0459 (0. 221) (0. 00) -0. 0675 0. 066 6 (0. 083) (0. 00) -0. 0474 0. 0574 (0. 176) (0. 00) -0. 0663 0. 0644 (0. 073) (0. 00) 0. 0683 -0. 1227 (0. 001) (0. 00) 0. 018 0. 0593 (0. 969) (0. 00) 0. 1131 0. 0828 (0. 02) (0. 00) 0. 1650 0. 0521 0. 0735 (0. 00) 0. 0649 (0. 00) 0. 0837 (0. 00) 0. 0674 (0. 00) 0. 0608 (0. 00) Rd 0. 0418 (0. 00) 0. 0627 (0. 00) 0. 0314 (0. 00) 0. 0013 (0. 845) 0. 0053 (0. 528) 0. 0323 (0. 001) 0. 0266 (0. 001) 0. 0111 (0. 122) 0. 0144 (0. 08) -0. 0052 (0. 477) 0. 0203 (0. 007) 0. 0468 (0. 00) 0. 0436 0. 0742 (0. 00) 0. 0147 (0. 133) 0. 0248 (0. 006) 0. 0341 (0. 00) 0. 0282 (0. 00) R-sq # Obs 55. 78 832 60. 99 57. 83 59. 15 56. 55 852 319 956 954 52. 97 1019 54. 15 52. 19 940 999 53. 16 1023 54. 88 1041 48. 51 1089 46. 82 1188 44. 96 1349 53. 52 1447 42. 76 1628 43. 00 1723 32. 2 1828 51. 18 19187 (0. 881) (0. 00) (0. 00) (0. 00oo)(0. 00) (0. 00) (0. 00) (0. 00) (0. 00) 0. 0908 0. 0409 (0. 284) (0. 00) 0. 1221 0. 1303 (0. 00) (0. 006) 0. 0948 0. 1596 (0. 00) (0. 00) 0. 0852 0. 2276 (0. 00) (0. 00) 0. 0805 -0. 0349 (0. 00) (0. 511) 424 s. BHOJRAJAND C. M. C. LEE we rank all the firms each year on the basis of their WEVS(or WPB), and compute the harmonic mean of the actual EVS (or PB) for these firms. ICOMPActual EVS(or PB) ratio for the closest comparable firms within the industry. This variable is the harmonic mean of the actual EVS (or PB) ratio of the four firms within the industrywith the closest warranted multiple. Essentially, this is the COMP variable with the firms constrained to come from the same industry. In short, we compute five different EVS (or PB) measures for each firm based on alternative methods of selecting comparable firms. IEVS and ISEVS(or, IPB and ISPB) correspond to prior studies that control for industry 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 PB ratios. As an illustration, Appendix C presents selection details for Guidant Corporation (GDT), a manufacturer of medical devices. This appendix illustrates the set of firms in the same two-digit SIC code, which are identified as peers of Guidant based on data as of April 30, 2001. Panel A reports the Panel B reports the closest firms based six closest firms based on WEVS, on WPB. We reviewed this list with a professional analyst who covers this sector. She agreed with most of the selections but questioned the absence of 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 STJ in comparison to those of the firms listed. Table 5 reports the results for a series of forecasting regressions. In panel 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 the future. In each case, we regress the future market multiple on various ex ante measures based on alternative definitions of comparable firms. 14 The table values represent the estimated coefficient for each variable averaged across 14 (n= 3) to 17 (n= 0) annual cross-sectional regressions. The bottom row reports the average adjusted r-square of the annual regressions for each model. These results show that the harmonic mean of the industry-matched firms explains 17. 5% (three-year-ahead) to 22. 9% (current year) of the crosssectional variation in future EVSratios. Including the mean EVS ratio from the closest four firms matched on size increases the adjusted r-squaresonly marginally, so that collectively IEVSand ISEVSexplain 18% to 23% of the variation in future EVSratios. These results confirm prior evidence on the usefulness of industry-based comparable firms. However, they also show that 14Even for the current year (n= 0), the warranted multiples are based on estimated coefficients from the prior years regression. Therefore, the models that involve warranted multiples are all forecasting regressions. TABLE 5 Prediction Regressions This table provides average estimated coefficients from the following prediction regressions: + EVSi,t+k = at + s j= j, tCji,t + I-i,t ES PBi,t+k = at + j=1 where k =0, 1, 2, 3. In Panel A, the dependent variable is the enterprise-value-to-sales ratio (EVS). I ratio (PB). The expanatory variables are: IEVS,the harmonic mean of the industry EVSbased on cur the harmonic mean of the actual EVS for the four closest firms matched on size after controlling for using the coefficients derived from last years estimation regressions and current year accounting and and ICOMP,the harmonic mean of the the actual EVS for the four closest firms matched on WEVS; after controlling for industry. The variables for Panel B are defined analogously, replacing EVSwith P coefficients from annual cross-sectional regressions. The bottom row reports the average adjusted r-sq Panel A: Enterprise-value-to-sales Currentyear EVS 0. 00 Inter 0. 24 0. 06 0. 00 0. 22 IEVS 1. 19 0. 08 -0. 27 -0. 26 1. 02 0. 16 0. 14 0. 16 0. 13 ISEVS COMP 0. 89 0. 16 0. 98 0. 83 WEVS 0. 33 ICOMP r-sq 22. 94 23. 46 54. 71 61. 68 62. 99 Panel B: Book-value-to-sales Current year PB 0. 07 -0. 06 -0. 07 Inter 0. 40 0. 5 IPB 1. 04 1. 19 0. 26 -0. 09 -0. 07 0. 07 ISPB 0. 16 0. 11 0. 10 0. 81 0. 35 COMP 0. 77 0. 71 WPB 0. 44 ICOMP r-sq 11. 80 12. 34 35. 21 41. 94 43. 20 One year ahead EVS 0. 01 0. 01 0. 07 0. 23 1. 05 0. 16 -0. 17 -0. 16 0. 14 0. 14 0. 12 0. 12 0. 83 0. 13 0. 80 0. 93 0. 27 21. 24 46. 14 51. 97 53. 23 One year ahead PB 0. 40 0. 15 0. 04 1. 00 0. 38 0. 12 0. 18 0. 14 0. 13 0. 65 0. 29 0. 59 8. 02 19. 91 22. 94 0. 24 1. 19 0. 27 1. 18 Two year ah 0. 0. 25 1. 06 0. 0. 0. 13 0. 20. 75 18. 37 18. 79 40. 0. 46 1. 17 0. 05 0. 12 0. 10 0. 51 0. 40 23. 38 0. 57 1. 16 Two year a 0. 50 0. 0. 96 0. 0. 0. 21 0. 7. 62 5. 01 5. 47 12. 426 S. BHOJRAJAND C. M. C. LEE he valuation accuracy of industry-based EVS ratios leaves much to be desired. In fact, industry-size based comparable firms explain less than 20% of the variation in two-year-aheadEVSratios. The predictive power of the model increases sharply with the inclusion of variables based on the warranted EVSratio (WEVS). average, a model that On includes IEVS,ISEVS,and COMPexplains over 40% of the cross-sectional variation in two-ye ar-ahead EVS ratios. Including WEVSin the model increases the average adjusted r-square on the two-year-aheadregressions to the actual WEVS ratio 45. 5%. Moreover, even after controlling for WEVS, of the closest comparable firms (COMPor ICOMP)is incrementally useful in predicting future EVSratios. It appears that comparable firms selected on the basis of their WEVS adds to the prediction of future EVSratios even after controlling for WEVS itself. COMPand ICOMPyield similar results. A model that includes IEVS,ISEVS,WEVS, ICOMPexplains between 63. 0% and (current year) and 43. 1% (three-year-ahead) of the variation in future EVS ratios. 5 Panel B reports forecasting regressions for PB. Compared to EVS,a much smaller proportion of the variation in PB is captured by these models. In the current year, the combination of IPB and ISPB explains only 12. 3% of the variation in PB. The inclusion of WPBand ICOMPincreases the adjusted r-square to 43. 2%. In future years, the explanatory power of all the models declines sharply. However, over all forecast horizons, models based on warranted multiples explain more than twice the variation in future PB ratios as compared to the industry-size matched model. The rapid decay in the explanatory power of the PB model is a possible concern with these results. Either PB ratios are difficult to forecast, or our model is missing some key forecasting variables. To shed light on this issue, we report below the serial correlation in annual EVSand PB ratios. Table values in the chart below are average Pearson correlation coefficients between the current years ratio, and the same ratio one, two, or three years later. Average Correlation Coefficient EVS1 EVSO PBO 0. 87 EVS2 0. 79 EVS3 0. 73 PB1 0. 72 PB2 0. 56 PB3 0. 44 These results show that with a one-year lag, EVSis serially correlated at 0. 7, suggesting an r-square of around 76%. With a three-year lag, EVSis serially correlated at 0. 73, suggesting an r-square of 53%. Similarly,with a one-year lag, PB is serially c orrelated at 0. 72, suggesting an r-square of 52%. With 5 We also conducted year-by-year analysis to examine the stability of these results over time. We find that a model that includes IEVS,ISEVS,WEVS, and ICOMPis extremely consistent in predicting future EVSratios. All four variables are incrementally important in predicting future EVSratios in each fore