MBA 520 Module Six Forecasting Model Questions The questions that follow and the article Comparing the Accuracy and Explainability of Dividend, Free Cash Flow, and Abnormal Earnings Equity Value Estimates will inform your completion of milestone III. An understanding of the models in this assignment will assist you in hypothesizing the incremental impact of a new investment project for the company. The understanding of these models will contribute to your ability to look toward the future when considering the direction of an organization. Prompt Once you have read the article “Comparing the Accuracy and Explainability of Dividend, Free Cash Flow, and Abnormal Earnings Equity Value Estimates” and Chapters 6 and 7 of your text, review and complete the questions below. Use the article and your text to inform your responses to the questions below. Assignment Questions: 1. For models 2, 2a, and 2b:   What is the best way to minimize the weighted average cost of capital? What is the effect of the weighted average cost of capital on the market value? 2. For models 3, 3a, and 3b:  What is the relationship between book value of equity and time t-1 and the market value of the equity? 3. Discuss model 4 and expand on the importance and the meaning of the market risk premium. 4. In your own words, what are the main conclusions for this article, and what could be improved upon in its analysis? Accounting Research Center, Booth School of Business, University of Chicago Comparing the Accuracy and Explainability of Dividend, Free Cash Flow, and Abnormal Earnings Equity Value Estimates Author(s): Jennifer Francis, Per Olsson and Dennis R. Oswald Source: Journal of Accounting Research, Vol. 38, No. 1 (Spring, 2000), pp. 45-70 Published by: Wiley on behalf of Accounting Research Center, Booth School of Business, University of Chicago Stable URL: http://www.jstor.org/stable/2672922 Accessed: 26-05-2016 13:05 UTC Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://about.jstor.org/terms JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Accounting Research Center, Booth School of Business, University of Chicago, Wiley are collaborating with JSTOR to digitize, preserve and extend access to Journal of Accounting Research This content downloaded from 198.246.186.26 on Thu, 26 May 2016 13:05:27 UTC All use subject to http://about.jstor.org/terms Journal of Accounting Research Vol. 38 No. 1 Spring 2000 Printed in US.A. Comparing the Accuracy and Explainability of Dividend, Free Cash Flow, and Abnormal Earnings Equity Value Estimates JENNIFER FRANCIS,* PER OLSSON,t AND DENNIS R. OSWALD: 1. Introduction This study provides empirical evidence on the reliability of intrinsic value estimates derived from three theoretically equivalent valuation models: the discounted dividend (DIV) model, the discounted free cash flow (FCO) model, and the discounted abnormal earnings (AE) model. We use Value Line (VL) annual forecasts of the elements in these models to calculate value estimates for a sample of publicly traded firms fol- lowed by Value Line during 1989-93.1 We contrast the reliability of value *Duke University; tUniversity of Wisconsin; London Business School. This research was supported by the Institute of Professional Accounting and the Graduate School of Business at the University of Chicago, by the Bank Research Institute, Sweden, and Jan Wallanders och Tom Hedelius Stiftelse for Samhallsvetenskaplig Forskning, Stockholm, Sweden. We appreciate the comments and suggestions of workshop participants at the 1998 EAA meetings, Berkeley, Harvard, London Business School, London School of Eco- nomics, NYU, Ohio State, Portland State, Rochester, Stockholm School of Economics, Tilburg, and Wisconsin, and from Peter Easton, Frank Gigler, Paul Healy, Thomas Hemmer, Joakim Levin, Mark Mitchell, Krishna Palepu, Stephen Penman, Richard Ruback, Linda Vincent, Terry Warfield, and Jerry Zimmerman. I We collect third-quarter annual forecast data over a five-year forecast horizon for all December year-end firms followed by VL in each of the years 1989-93. After excluding firms with missing data, the final sample contains between 554 and 607 firms per year (2,907 observations in the pooled sample). 45 Copyright ?, Institute of Professional Accounting, 2000 This content downloaded from 198.246.186.26 on Thu, 26 May 2016 13:05:27 UTC All use subject to http://about.jstor.org/terms 46 JOURNAL OF ACCOUNTING RESEARCH, SPRING 2000 estimates in terms of their accuracy (defined as the absolute price scaled difference between the value estimate and the current security price) and in terms of their explainability (defined as the ability of value estimates to explain cross-sectional variation in current security prices). In theory, the models yield identical estimates of intrinsic values; in practice, they will differ if the forecasted attributes, growth rates, or dis- count rates are inconsistent.2 Although by documenting significant dif- ferences across DIM FCF, and AE value estimates our results speak to the consistency question, our objective is to present a pragmatic exercise comparing the reliability of these value estimates, recognizing that the forecasts underlying them may be inconsistent. That is, we try to replicate the typical situation facing an investor using a valuation model to calculate an estimate of the intrinsic value of a firm. Under this view, the empirical work addresses which series of forecasts investors seem to use to value equity securities. The results show that AE value estimates perform significantly better than DIV or FCF value estimates. The median absolute prediction error for the AE model is about three-quarters that of the FCF model (30% versus 41%) and less than one-half that of the DIVmodel (30% versus 69%). Further, AE value estimates explain 71% of the variation in current prices compared to 51% (35%) for DIV (FCF) value estimates. We conclude that AEvalue estimates dominate value estimates based on free cash flows or dividends. Further analyses explore two explanations for the superiority of AE value estimates. AEvalue estimates may be superior to DIVand FCFvalue estimates when distortions in book values resulting from accounting procedures and accounting choices are less severe than forecast errors and measurement errors in discount rates and growth rates. This effect is potentially large for our sample, as indicated by the high proportion of AE value estimates represented by book value of equity (72% on average) and the high proportion of FCF and DIV value estimates repre- sented by terminal values (82% and 65%, on average, versus 21% for AE value estimates).3 Value estimates may also differ when the precision and the predictability of the fundamental attributes themselves differ. 4 Ceteris paribus, more precise and more predictable attributes should result in more reliable value estimates. Tests of these conjectures suggest that the greater reliability of AE value estimates is driven by the ability of 2For example, inconsistencies arise if the attributes violate clean surplus, if discount rates violate the assumptions of no arbitrage, unlimited borrowing, and lending at the rate of return, or if growth rates are not constant (i.e., the firm is not in steady state). 3We focus on the terminal value calculation because it is likely the noisiest component of the value estimate, reflecting errors in forecasting the attribute itself, the growth rate, and the discount factor. 4We define precision as the absolute difference between the predicted value of an attribute and its realization, scaled by share price. We define predictability as the ease with which market participants can forecast the attribute, and we measure this construct as the standard deviation of historical year-to-year percentage changes in the attribute. This content downloaded from 198.246.186.26 on Thu, 26 May 2016 13:05:27 UTC All use subject to http://about.jstor.org/terms COMPARING EARNINGS EQUITY VALUE ESTIMATES 47 book value to explain a large portion of intrinsic value and, perhaps, by the greater precision and predictability of AE forecasts. Moreover, neither accounting discretion nor accounting conservatism has a significant impact on the reliability of AEvalue estimates, suggesting that the superiority of the AE measure is robust to differences in firms' accounting practices and policies. To our knowledge, this is the first study to provide large-sample evidence on the relative performance of these models using individual se- curity value estimates based on forecast data. As discussed in section 2, Penman and Sougiannis [1998] (henceforth PS) provide empirical evaluations of these models for a large sample of firms, for portfolio value estimates based on realized attributes. The forecast versus realization dis- tinction is important because realizations contain unpredictable components which may confound comparisons of the valuations models (which are based on expectations).5 PS use a portfolio design to average out the unpredictable components of the valuation errors, whereas the use of forecasts avoids this problem entirely and permits a focus on individual securities' valuation errors. Another important difference between the two studies concerns the performance metrics: bias in PS and accuracy and explainability in our study. PS focus on bias (we believe) because their portfolio approach is better suited to describing the relation between value estimates and observed prices for the market as a whole. Specifically, under a mean bias criterion, positive and negative prediction errors offset within and across portfolios to yield estimates of the net amount that portfolio value estimates deviate from observed prices. In our individual security setting, we have no reason to believe that individual shareholders care about net prediction errors or care more (or less) about over- versus undervaluations of the same amount. Thus, we believe accuracy rather than bias better reflects the loss function of an investor valuing a given security. Explainability is also an open question in an individual security setting but is not well motivated in a portfolio setting where the random assignment of securities to portfolios and the aggregation of value estimates and observed prices within the portfolio significantly reduce the variation in these variables. Our final analysis links the two studies by examining whether, for our sample, their design yields the same results as our approach. We draw the same conclusion as PS concerning bias in portfolio prediction errors based on realizations: AEvalue estimates have smaller (in absolute terms) 5Realizations and forecasts also differ because realizations generally adhere to clean surplus, but forecasted attributes may not. Over two-thirds of the sample forecasts adhere to clean surplus in years 0, 1, and 3 but not in years 2, 4, and 5 because of the assumptions used to construct a series of five-year forecasts (described in section 3). We do not believe the differences across value estimates documented in this study are driven by violations of clean surplus both because the violations of clean surplus are modest relative to the documented absolute prediction errors and because we find similar patterns when we repeat our analyses using a one-year forecast horizon and include only those securities' forecasts which adhere to clean surplus. This content downloaded from 198.246.186.26 on Thu, 26 May 2016 13:05:27 UTC All use subject to http://about.jstor.org/terms 48 J. FRANCIS, P. OLSSON, AND D. R. OSWALD bias than FCF or DIV value estimates. However, when forecasts rather than realizations are used to calculate value estimates, this ordering depends on the assumed growth rate: for g= 0% we find the same ranking, but for g = 4% we find that FCF value estimates have the smallest (absolute) bias, followed by AE and DJVvalue estimates.6 In terms of accuracy, we find that AE value estimates generally outperform FCF and DIV value estimates regardless of whether forecasts or realizations are used. Absolute prediction errors are, however, significantly (at the .00 level) smaller when forecasts rather than realizations are used to calculate value estimates. The forecast versus realization distinction is also important for comparing DIV and FOF value estimates. While we find that FEF value estimates based on realizations are more biased than DIV value estimates based on realizations (consistent with PS), we also find that FCFvalue estimates based on forecasts dominate DIVvalue estimates based on forecasts in terms of both bias and accuracy. Section 2 describes the three valuation models and reviews the results of prior studies' investigations of estimates derived from these models. Section 3 describes the sample and data and presents the formulations of the DIV, FCF, and AE models we estimate. The empirical tests and results are reported in section 4, and section 5 reports the results of applying PS's design to our sample firms. Section 6 summarizes the results and concludes. 2. Valuation Methods 2.1 MODELS The three equity valuation techniques considered in this paper build on the notion that the market value of a share is the discounted value of the expected future payoffs generated by the share. Although the three models differ with respect to the payoff attribute considered, it can be shown that (under certain conditions) the models yield theoretically equivalent measures of intrinsic value. The discounted dividend model, attributed to Williams [1938], equates the value of a firm's equity with the sum of the discounted expected dividend payments to shareholders over the life of the firm, with the terminal value equal to the liquidating dividend: T DIV tF 1 (1+rE)t (1) where: VDIV = market value of equity at time F; F = valuation date; 6For all other growth rates examined (2%, 6%, 8%, and 10%), we find that AEvalue estimates dominate FCFand DIVvalue estimates in terms of accuracy and smallest absolute bias. This content downloaded from 198.246.186.26 on Thu, 26 May 2016 13:05:27 UTC All use subject to http://about.jstor.org/terms COMPARING EARNINGS EQUITY VALUE ESTIMATES 49 DJVt = forecasted dividends for year t; rE = cost of equity capital; and T = expected end of life of the firm (often T -o). (For ease of notation, firm subscripts and expectation operators are suppressed. All variables are to be interpreted as time F expectations for firm j.) The discounted free cash flow model substitutes free cash flows for dividends, based on the assumption that free cash flows provide a better representation of value added over a short horizon. Free cash flows equal the cash available to the firm's providers of capital after all re- quired investments. In this paper, we follow the FCF model specified by Copeland, Koller, and Murrin [1994]:7 T C - ECE + ECMSF - DF - PSF (2) VF t=1 (1+rwAcdt FCFt = (SALESt - OPEXPt - DEPEXPt) (1-I) + DEPEXPt - A WCt - CAPEXPt (2 a) rWACC = WD(l -)rD + wpSrpS + WErE (2b) where: VFCF = market value of equity at time F; SALESt = sales revenues for year t; OPEXPt = operating expenses for year t; DEPEXPt = depreciation expense for year t; AWCt = change in working capital in year t; CAPEXPt = capital expenditures in year t; ECMSt = excess cash and marketable securities at time t;8 Dt = market value of debt at time t; PSt = market value of preferred stock at time t; rWACC = weighted average cost of capital; rD = cost of debt; rps = cost of preferred stock; WD = proportion of debt in target capital structure; WpS = proportion of preferred stock in target capital structure; WE = proportion of equity in target capital structure; and X = corporate tax rate. The discounted abnormal earnings model is based on valuation techniques introduced by Preinreich [1938] and Edwards and Bell [1961], 7The FCF measure specified in equation (2a) is similar to Copeland, Koller, and Murrin's [1994] specification except we omit the change in deferred taxes because VL does not forecast this item. 8Excess cash and marketable securities (ECMS) are the short-term cash and investments that the company holds over and above its target cash balances. This content downloaded from 198.246.186.26 on Thu, 26 May 2016 13:05:27 UTC All use subject to http://about.jstor.org/terms 50 J. FRANCIS, P. OLSSON, AND D. R. OSWALD and further developed by Ohlson [1995]. The AE model assumes an accounting identity-the clean surplus relation (3b) -to express equity values as a function of book values and abnormal earnings:9 T AEt AE BE t=1 (1 + rE)t + (3) AEt = Xt- rEBt-I (3a) Bt = Bt-I+XI-DVt (3b) where: VI'E = market value of equity at time F; AEt = abnormal earnings in year t; Bt = book value of equity at end of year t; and Xt = earnings in year t. 2.2 PRIOR RESEARCH COMPARING ESTIMATES OF INTRINSIC VALUES Several studies investigate the ability of one or more of these valuation methods to generate reasonable estimates of market values. Kaplan and Ruback [1995] provide evidence on the ability of discounted cash flow estimates to explain transaction values for a sample of 51 firms en- gaged in high leverage transactions.10 Their results indicate that the median cash flow value estimate is within 10O% of the market price, and that cash flow estimates significantly outperform estimates based on compa- rables or multiples approaches. Frankel and Lee [1995; 1996] find that the AE value estimates explain a significantly larger portion of the variation in security prices than value estimates based on earnings, book val- ues, or a combination of the two. In addition to these horse races (which pit theoretically based value estimates against one or more atheoretically based, but perhaps best practice, value estimates), there are at least two studies which contrast the el- ements of, or the value estimates from, the DIV FCF, and/or AE models. Bernard [1995] compares the ability of forecasted dividends and forecasted abnormal earnings to explain variation in current security prices. Specifically, he regresses current stock price on current year, one-year- ahead, and the average of the three- to five-year-ahead forecasted dividends and contrasts the explanatory power of this model with the explanatory power of the regression of current stock price on current book value and current year, one-year-ahead and the average of three- to five- year-ahead abnormal earnings forecasts. He finds that dividends explain 29% of the variation in stock prices, compared to 68% for the combination of current book value and abnormal earnings forecasts. Penman and Sougiannis [1998] also compare dividend, cash flow, and abnormal 9 Clean surplus requires that any change in book value must flow through earnings. The exception is dividends, which are defined net of capital contributions. 10 Transaction value equals the sum of the market value of common stock and preferred stock, book value of debt not repaid as part of the transaction, repayment value of debt for debt repaid, and transaction fees; less cash balances and marketable securities. This content downloaded from 198.246.186.26 on Thu, 26 May 2016 13:05:27 UTC All use subject to http://about.jstor.org/terms COMPARING EARNINGS EQUITY VALUE ESTIMATES 51 earnings-based value estimates using infinite life assumptions. Using realizations of the payoff attributes as proxies for expected values at the valuation date, they estimate intrinsic values for horizons of T = 1 to T = 10 years, accounting for the value of the firm after time Tusing a terminal value calculation. Regardless of the length of the horizon, PS find that AE value estimates have significantly smaller (in absolute terms) mean signed prediction errors than do FCF value estimates, with DIV value estimates falling in between. Our study extends previous investigations by comparing individual securities' DI, FCF, and AE value estimates calculated using ex ante data for a large sample of publicly traded firms. In addition to evaluating value estimates in terms of their accuracy (absolute deviation between the value estimate and market price at the valuation date, scaled by the latter), we contrast their ability to explain cross-sectional variation in current market prices. Both metrics assume that forecasts reflect all available information and that valuation date securities prices are efficient with respect to these forecasts. Under the accuracy metric, value estimates with the smallest absolute forecast errors are the most reliable. The explainability tests-which compare value estimates in terms of their ability to explain cross-sectional variation in current market prices-control for systematic over- or underestimation by the valuation models." 3. Data and Model Specification Our analyses require data on historical book values (from Compustat), market prices (from CRSP), and proxies for the market's expectations of the fundamental attributes (from VL). VL data are preferred to other analyst forecast sources (such as IIBIEIS or Zacks) because VL reports contain a broader set of variables forecast over longer horizons than the typical data provided by sell-side analysts. In particular, VL reports divi- dend, earnings, book value, revenue, operating margin, capital expenditure, working capital, and income tax rate forecasts for the current year (t = 0), the following year (t = 1), and "3-5 years ahead."''2 Because the valuation models require projected attributes for each period in the forecast horizon, we assume that three- to five-year forecasts apply to all years in that interval (results are not sensitive to this assumption). Also, because VL does not- report two-year-ahead forecasts, we set year 2 fore- casts equal to the average of the one-year-ahead and the three-year- ahead forecast. We use data from third-quarter VL reports because this is the first time data are reported for the complete five-year forecast " In the OLS regression, bias is captured both by the inclusion of an intercept and by allowing the coefficient relating the value estimate to current market price to deviate from a theoretical value of one (bias which is correlated with the value estimate itself). Rank regressions implicitly control for bias by using the ranks of the variables rather than the values of the variables. 12 In contrast, IIBIEIS and Zacks contain, at most, analysts' current-year and one-yearahead earnings forecasts (annual and quarterly) and an earnings growth rate. This content downloaded from 198.246.186.26 on Thu, 26 May 2016 13:05:27 UTC All use subject to http://about.jstor.org/terms 52 J. FRANCIS, P. OLSSON, AND D. R. OSWALD horizon; these reports have calendar dates ranging from F = July 1 to September 30 (incrementing weekly) for each sample year, 1989-93. Fi- nally, we restrict our analysis to December year-end firms to simplify calculations. VL publishes reports on about 1,700 firms every 13 weeks; 800-900 of these firms have December year-ends. Because VL does not forecast all of the inputs to the three valuation models for all firms (e.g., they do not forecast capital expenditures for retail firms), the sample is reduced to those firms with a complete set of forecasts. This requirement ex- cludes about 250-300 firms each year, leaving a pooled sample of 3,085 firm-year observations (a firm appears at most once each year). Missing Compustat and CRSP data reduce the sample to 2,907 firm-year observations, ranging from 554 to 607 firms annually. The sample firms are large, with a mean market capitalization of $2.6 billion and a mean beta of 0.97. Most of the sample firms are listed on either the NYSE or the AMEX (82%), with the remainder trading on the NASDAQ For each valuation model, we discount the forecasted fundamental attributes to date F We adjust both for the horizon of the forecast (e.g., three years for a three-year-ahead forecast) and for a part-year factor, f (f equals the number of days between F and December 31, divided by 365), to bring the current-year estimate back to the forecast date. We es- timate discount rates using the following industry cost of equity model:'3 rE = rf + P[E(rm) - rf] (4) where: rE = industry-specific discount rate; rf = intermediate-term Treasury bond yield minus the historical premium on Treasury bonds over Treasury bills (Ibbotson and Sinquefield [1993]); = estimate of the systematic risk for the industry to which firm j belongs. Industry betas are calculated by averaging the firmspecific betas of all sample firms in each two-digit SIC code. Firm-specific betas are calculated using daily returns over fiscal year t- 1; E(rm) - rf = market risk premium = 6%.14 For a given firm and valuation date, we assume rE(rwAcc for the FCF model) is constant across the forecast horizon. The average cost of equity for the pooled sample is about 13%. The rwAcc calculation requires estimates of rD, rps, capital structure (WD, wps, and WE), and ECMS. The cost of debt is measured as the ratio of the VL reported interest on long-term 13Fama and French [1997] argue that industry costs of equity are more precise than firm-specific costs of equity. Results using firm-specific discount rates yield similar inferences and are not reported. 14 SiX percent is advocated by Stewart [1991] and is similar to the 5-6% geometric mean risk premium recommended by Copeland, Koller, and Murrin [1994]. We obtain qualitatively similar results using the arithmetic average market risk premium. This content downloaded from 198.246.186.26 on Thu, 26 May 2016 13:05:27 UTC All use subject to http://about.jstor.org/terms COMPARING EARNINGS EQUITY VALUE ESTIMATES 53 debt to the book value of long-term debt; the cost of preferred stock is proxied by the VL reported preferred dividends divided by the book value of preferred stock.'5 We set the pretax upper bound on the cost of debt and the cost of preferred stock equal to the industry cost of equity, and we set the pretax lower bound equal to the risk-free rate (results are not sensitive to these boundary conditions). Following Copeland, Koller, and Murrin [1994, pp. 241-42] we develop long-term target cap- ital weights for the rWAcc formula rather than use the weights implied by the capital structure at the valuation date.'6 For the pooled sample, the mean cost of debt is 9.3%, the mean cost of preferred stock is 10.3%, and the mean weighted average cost of capital is 11.8%. Based on Copeland, Koller, and Murrin's [1994, p. 161] suggestion that short-term cash and investments above 0.5-2% of sales revenues are not necessary to support operations, we define ECMS as cash and marketable securities in excess of 2% of revenues. We compute two terminal values for each valuation model, TVFUND, where FUND = DIV EU', or A. Both terminal values discount into perpetuity the stream of forecasted fundamentals after T = 5; the first specification assumes these fundamentals do not grow; the second as- sumes they grow at 4%.17 If the forecasted T = 5 fundamental is negative, we set the terminal value to zero based on the assumption that the firm will not survive if it continues to generate negative cash flows or negative abnormal earnings (dividends cannot be less than zero). (The results are not sensitive to this assumption.) Because we draw similar in- ferences from the results based on the no growth and the 4% growth assumptions, we discuss only the latter but report both sets of results in the tables.18 15 VL reports book values of long-term debt and preferred stock as of the end of quarter 1. The results are not affected if we use Compustat data on book values of debt and preferred stock at the end of quarter 2. In theory, we should use the market values of debt and preferred stock, but these data are not available. 16 Specifically, we use Value Line's long-term (three- to five-year-ahead) predictions to infer the long-term capital structure. We use the long-term price-earnings ratio multiplied by the long-term earnings prediction to calculate the implied market value of equity five years hence. For debt, we use VL's long-term prediction of the book value of debt. For preferred stock, we assume that it remains unchanged from the valuation date. The equity weight in the WACC formula, WE, is then given by WE = implied equity value/ (implied equity value + forecasted debt + current book value of preferred stock). The debt and preferred stock weights are calculated similarly. 17 The growth rate is often assumed to equal the rate of inflation. Consistent with Kaplan and Ruback [1995] and Penman and Sougiannis [1998], we use a 4% growth rate. We draw similar conclusions using growth rates of 2%, 6%, 8%, and 10%. '8We also examine a terminal value equal to VL's long-term price projection (equal to the VL three- to five-year-ahead price-earnings ratio multiplied by the three- to five-yearahead earnings forecast). All models perform extremely well using the inferred price terminal value, with absolute (signed) prediction errors of 16-24% (5-14%) and adjusted R2s of .77 to .91. Although the magnitudes of the differences are smaller, we find that AE value estimates dominate FCF value estimates and perform at least as well as DIV value estimates. Because long-term price forecasts are not available for most firms, we focus on the more common scenario where terminal values must be calculated. This content downloaded from 198.246.186.26 on Thu, 26 May 2016 13:05:27 UTC All use subject to http://about.jstor.org/terms 54 J. FRANCIS, P. OLSSON, AND D. R. OSWALD Discounted dividend model specification: 5 VDIV = (1 + rE)-f .5D1V0 + E (1 + rE)( tf )DIVt t= 1 + (1 + rE) (5 +f)TVDv (5) For the pooled sample, the average forecasted dividends for the second half of the current year and the next five years are, on average, $0.36, $0.76, $0.91, $1.05, $1.05, and $1.05. The mean terminal value estimates for the pooled sample are $8.24 and $12.68 for the no growth and 4% growth specifications, respectively.'9 Discounted free cash flow specification: 5 VFF F = (1 + rWAcc) 7.5FCF0 + E (1 + rWACC) ')FCFit t=1 + ( 1 + rWACC~~~~~~~~~L on u R cL 8 cL u 11l 0.000 .0 o X O 0 t X 2 E _ on nOO Ln0~~~~~~~~~~~~~~~\ =gge -e -z g~~~~~~~~~~~~~~~~~\ 0\ ~~~ Q ~ 6 6 .S ~ ~~~ ~ >o "t o ~~~~~~~~~~~~~~~~~ ~~~~~~ El S .~ 2 ~~~~~~~~~ b -C'G ~~ 666 666~~~~~a 66 066 14 u S 2 W ;4 < U U g g g g g g t < t ON ONt- " on O a tE ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1 m Q Q C. C - -0 t~~~~~~~~~~~~~~~~~~~~e > dI SI;DO :t.om dIXtI.0 t QO - u Lu u C Q CC) ) 00 C) C ~~~tk 7 e k . b q k m r l ~ ~ ~ ~0 ~ ~ ~ ~ ~, ~ ~ ~ ~< j C~~~~~~~~~ ) c~~~~~~~~~~~~~~~~~~~~~~~~ L ) n ~ ~0 i~~~~~~~~~~0 ? 0 in r C) C) m > > in *- 4> - 11 11 C) 0 11 i 11 ?n t X 0 | ,0; t t 3 t t; 3 tm ; | t ;t 23 t | >3 1 uD 4~ E o; =; b This content downloaded from 198.246.186.26 on Thu, 26 May 2016 13:05:27 UTC All use subject to http://about.jstor.org/terms F 0 ? b.O 68 J. FRANCIS, P. OLSSON, AND D. R. OSWALD regardless of whether the portfolio or individual security approach is used. This difference is particularly striking for FCFvalue estimates where the median VFC-based on realizations is zero, reflecting the fact that most of the sample portfolios (20 of 30, not reported) had negative realized mean free cash flows. The smaller ex post value estimates are also con- sistent with the results in table 6 which show that, for our sample, realizations fell short of analysts' expectations by a wide margin. Second, comparisons of observed prices with both ex ante and ex post value estimates indicate that ex ante value estimates dominate ex post value estimates: for all models, ex ante values have significantly (at the .00 level) smaller bias and are more accurate than comparable ex post values. Third, using either smallest absolute bias or smallest absolute prediction error as the performance criterion, the realization-portfolio results show that AE value estimates dominate DIV and FCF value estimates. In con- trast, the forecast-portfolio results depend on the growth rate: for g= 0%, VAE dominates VDV and VFC-in terms of bias and accuracy, but for g = 4%, VFC-dominates.38 This disparity between the bias and the accuracy results observed for FCF value estimates (for g = 4%) highlights the effect that variation in the value estimates has on the performance metric. When the variability in value estimates is retained-as it is when individual securities rather than portfolios are valued-the results (far right columns of table 7) show that AE value estimates consistently dominate FCF and DIV estimates in terms of accuracy. We draw the following inferences from these results. The conclusion that AE value estimates dominate FCF or DIV value estimates is fairly robust to the level of aggregation (portfolio versus individual securities), the type of data (realizations versus forecasts), and the performance metric (bias versus accuracy). We find, however, that the levels of bias and accuracy are significantly (at the .00 level) smaller when forecasts rather than realizations are used to calculate value estimates. The fore- cast versus realization distinction is also important for conclusions con- cerning FCF and DfVvalue estimates. Consistent with PS, we find that ex post FCF value estimates are more biased than ex post DIV value estimates; however, ex ante FCF value estimates dominate ex ante DIVvalue estimates in terms of both bias and accuracy. 6. Summary and Conclusions This paper compares the reliability of value estimates from the dis- counted dividend model, the discounted free cash flow model, and the discounted abnormal earnings model. Using a sample of five-year forecasts for nearly 3,000 firm-year observations over 1989-93, we find that 38 See n. 6 for results based on other growth rates. This content downloaded from 198.246.186.26 on Thu, 26 May 2016 13:05:27 UTC All use subject to http://about.jstor.org/terms COMPARING EARNINGS EQUITY VALUE ESTIMATES 69 the AE value estimates are more accurate and explain more of the varia- tion in security prices than do FCF or DfVvalue estimates. Our explorations of the sources of the relative superiority of the AE model show that the greater reliability of AE value estimates is likely driven by the sufficiency of book value of equity as a measure of intrinsic value, and perhaps by the greater precision and predictability of abnormal earnings. Our analysis of whether accounting discretion enhances or detracts from the performance of the AE model indicates no difference in the accuracy of AE estimates between firms exercising high versus low accounting discretion, although there is some evidence that AE value estimates explain more of the variation in current market prices for high discretion firms than for low discretion firms. We also find no evidence that AE value estimates are less reliable for firms with high versus low R&D expenditures. Together these findings indicate no empirical basis for concerns that accounting practices (such as immediate expensing of R&D or the flexibility afforded by accruals) result in inferior estimates of market equity value. Our results are more consistent with the argument that the articulation of clean surplus financial statements ensures that value estimates are unaffected by conservatism or accrual practices. We conclude there is little to gain-and if anything something to lose-from selecting dividends or free cash flows over abnormal earnings as the fundamental attribute to be valued. Together with the fact that earnings are by far the most consistently forecasted attribute, our results suggest little basis for manipulating accounting data (for example, to general estimates of free cash flows) when earnings forecasts and book values are available. 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