We investigate the number of and reasons for errors and questionable judgments that sell-side equity analysts make in constructing and executing discounted cash flow (DCF) equity valuation models. For a sample of 120 DCF models detailed in reports issued by U.S. brokers in 2012 and 2013, we estimate that analysts make a median of three theory-related and/or execution errors and four questionable economic judgments per DCF. Recalculating analysts’ DCFs after correcting for major errors changes analysts’ mean valuations and target prices by between −2 and 14 % per error. Based on face-to-face interviews with analysts and those who oversee them, we conclude that analysts’ DCF modeling behavior is semi-sophisticated in the sense that analysts genuinely make mistakes regarding certain aspects of correctly valuing equity but also respond rationally to the incentives they face, particularly the reality that they are not directly compensated for being textbook DCF correct.
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For example, Tham and Velez-Pareja (2004) list nine errors they propose users might make in DCF models but provide no evidence on how empirically common or important the mistakes are. Mauboussin (2006, pp. 2, 5) details a “list of the most frequent  errors we see in DCF models” identified from “various sell-side reports” but does not report sample statistics nor the economic significance of the errors. Petersen and Plenborg (2009) study three general and nonpublic valuation spreadsheets they obtained from Danish brokers. Fernandez (2013) classifies 119 types of errors in corporate valuations performed by financial analysts, investment banks, and financial consultants.
For example, it is often the case that the boilerplate sections of the required disclosures at the end of the analyst report will say words to the effect that “We employ numerous valuation methodologies which include, but are not limited to, price-to-earnings multiples, enterprise value to earnings before interest, taxes, and depreciation (EBITDA), book value, free cash flow yield, discounted cash flow, and relative valuation,” but there is no recognizable DCF model provided in the report itself.
In unreported multivariate logit regressions, the results of which are available from the authors on request, we additionally assessed whether DCF-model firms differ systematically from (1) the merged CRSP/Compustat population, (2) firms covered by Investext reports, and (3) the subset of Investext firms covered by the same brokers as DCF-model firms. Consistent with the proposition that analysts supply DCF valuations when DCF valuations are of most value to investors, we find that relative to the merged CRSP/Compustat population, DCF-model firms are reliably larger (greater analyst following and higher market caps), more intangible intensive (smaller total assets, faster growing), and harder to value using P/E multiples (negative net income). We also observe that, relative to firms covered by Investext reports and relative to the subset of Investext firms covered by the same brokers as our DCF-model firms, DCF-model firms are reliably larger (higher market caps), more intangible intensive (smaller total assets), and are harder to value using P/E multiples (negative net income).
The DCF-to-all-investors equity valuation model in Fig. 2 is stylized in that it is a condensed version of what we assume to be 100 % correct, namely the DCF-to-all-investors valuation model detailed by Lundholm and Sloan in their book Equity Valuation and Analysis with eVal (3rd edition, 2013, especially pp. 154–155; p. 225; pp. 239–243). We adopt a less than fully correct DCF valuation model against which to grade analysts for two main reasons. First, most of the differences detailed here are likely to occur infrequently and to be economically small. Second, it is rare for analysts to include the items represented by these differences in their models, and we wish to avoid biasing our study in favor of concluding that analysts construct and execute DCF valuation models in an unsophisticated manner. Thus, if analysts are aware of the differences but rationally choose to exclude them because they are infrequent and immaterial, then we would risk biasing our assessment of analyst sophistication toward concluding that analysts are unsophisticated if we include the differences in our grading template. Conversely, if analysts are not aware that the differences exist but we grade analysts under the presumption that they should be aware, then we would risk concluding that analysts are unsophisticated based on a large number of economically small aspects of DCF modeling and execution rather than on economically or theoretically important errors.
The differences that we itemize between our stylized model and that of Lundholm and Sloan are as follows. We explicate the differences because if an analyst’s DCF model does not conform to Lundholm and Sloan’s assumed 100 % correct model but does conform to our reduced model, we do not grade the analyst as having made an error or questionable judgment.
We do not include a line for the change in deferred taxes after taxes on EBIT. Some analysts address the deferred tax effect of the line taxes on EBIT by forecasting cash taxes on EBIT instead of (book) taxes on EBIT.
We do not include lines for non-operating income (loss) or extraordinary items & discontinued operations after the depreciation & amortization add-back line after NOPAT.
We do not include lines for increase in investments, purchase of intangibles, increase in other assets, increase in other liabilities, or clean surplus plug after the CAPEX line.
We do not include the cost of preferred stock or the cost of minority interest in calculating WACC.
We do not mark the firm’s financial assets and liabilities to their market values.
We ignore company warrants and ascribe no value to the conversion options embedded in convertible bonds.
We address the contingent equity claim of employee stock options by (leniently) only grading the analyst as having made an error if the analyst arrived at the equity value per share by dividing the dollar equity value of the firm by outstanding common shares, and then only if the difference between basic and fully diluted common shares as of the most recent fiscal period before the report date exceeded 3 % of common shares outstanding.
We do not include information about year T + 1 in Fig. 2, even though a 100 % correct DCF model should show year T + 1 to prove out to the reader that steady state has been achieved (Levin and Olsson 2000; Lundholm and Sloan 2013). We do not grade analysts as having made an error if they do not show year T + 1 data, although we do grade them with regard to the economic plausibility of the implied rates of growth in key financial statement variables and ratios in year T.
Given the time-consuming nature of this task and the importance of transferring the data in a uniformly high-quality manner, all data transfer from the hard copy into the Excel template was done by one of the authors.
In a few cases, an analyst report contains more than one DCF model, typically because the analyst presents multiple DCF-based valuation scenarios for the same firm. When this occurs, we input and use the scenario associated with the target price most emphasized by the analyst.
We emphasize that, in contrast to analyst reports where target prices are not linked with explicit valuations or are imperfectly linked to associated multiples-based valuations, in our sample there is an almost 100 % correspondence between analysts’ target prices and analysts’ DCF valuations. Thus, for the 115 sample reports where there is both a target price and a DCF equity value, the median target price per share and the median DCF equity value per share are both $34.40, and the Pearson correlation between target prices and DCF equity values is 0.999.
A post-terminal year perpetual growth rate of −100 % is how we code free cash flows that are assumed by the analyst to cease after the terminal year. An example of this can be found in the report on Gilead Sciences issued by Deutsche Bank on Nov. 13, 2012.
In doing so, we propose that we likely underestimate the true total number of errors and questionable judgments made by analysts in their DCF valuation models, both observed and unobserved combined.
We view 5 % as conservative in grading errors for the projected rate of growth in post-terminal year free cash flows because 5 % is 2 % larger than the value assumed by Lundholm and Sloan in Equity Valuation and Analysis with eVal (2013, 3rd ed., p. 174), the source of our assumed 100 % correctly structured and executed DCF-to-all-investors equity valuation model. Lundholm and Sloan state that they use 3 % as the default terminal value for sales growth (and therefore free cash flows also). Their reasoning is that “[h]istorically, the annual growth rate in the U.S. economy, as measured by the nominal GDP growth rate, has averaged around 6 %, composed of roughly 4 % real growth and 2 % price inflation. However, the financial crisis of 2007–2008 sent both real growth and inflation plummeting into negative territory, albeit briefly. The long-term forecasts from the Congressional Budget Office and the Federal Reserve at the end of 2010 put real growth at 2–3 % and inflation at 1–2 %. So, in most cases a terminal sales growth rate forecast should fall between 3 and 5 % … We use 3 % as the default terminal value for Sales Growth in eVal.” Also, our sample of analyst reports is from 2012–2013, very close in time to 2010. If we use Lundholm and Sloan’s cutoff of 3 %, then we estimate a much larger analyst error rate of 32 %.
One reason for the high rate of our grading questionable judgments in cash is that at least one large brokerage in our dataset instructs its analysts to treat all cash as a financial asset and not to attempt to extract an estimate of operating cash. Thus our estimated questionable judgment rate of 95 % with regard to analysts’ treatment of cash may overstate the degree to which they would make a questionable judgment if left to themselves.
Examples of adjustments to enterprise value that we define as questionable judgments include adding more cash or financial assets (or subtracting materially more or less debt or financial liabilities) than shown on the firm’s balance sheet at the effective valuation date, adding rather than subtracting debt, not adjusting for noncontrolling interest or preferred stock when shown on the firm’s balance sheet at the valuation date, adding assets or subtracting liabilities that we judge to be operating rather than financial in nature, and subtracting a public market discount.
In untabulated supplementary analysis, we also estimated OLS regressions of the number of analysts’ errors and questionable judgments on proxies for analyst sophistication, analyst effort, and economic and strategic factors. However, perhaps due to our small sample size, noise in our proxies, or both, our regressions yielded only weak and inconsistent evidence of cross-sectional predictability.
We are extremely grateful to all those we interviewed. The interviews were conducted under the requirement that the identities of the investment banks and participants would be kept confidential.
A similar statement was made by a managing director at investment bank B: “We see a lot of overoptimistic revenue growth rates [from analysts] at the terminal year. Ditto for excessive turns and margins. We see this an awful lot.”
A corroborating statement was made by a managing director at investment bank B: “At [investment bank B], nothing is mandated to be a certain way in analysts’ [DCF] models…. Analysts have complete autonomy.”
In support of his statement, the managing director showed the author conducting the interview a two-page document that summarized the dimensions on which analysts are evaluated and compensated. The only section in the document that pertained to valuation was toward the bottom of the second page under the heading “Stock Picking,” but the director explained that that section had no direct tie to the competency with which price targets or valuations were determined.
These statements agree with the ranking of stock selection in Table 1 of Bradshaw (2011), which reports the decline in the importance of stock selection from second out of eight dimensions in Institutional Investor Ranking Surveys in 1998 to 11th out of 12 dimensions in 2005. Similar data are provided by Groysberg and Healy (2013, pp. 37–43).
We define ROE as annual net income divided by end-of-year shareholder equity.
This would not necessarily be true for a sample heavily concentrated in intangible intensive firms such as pharmaceuticals or a sample tilted toward newly listed firms. For such firms, the expensing required of most intangible assets under U.S. GAAP, combined with successful intangible-intensive companies being those that create natural monopolies for themselves, might reasonably lead to ROEs that both increased toward the terminal year and, at the terminal year, were higher than RE (Lundholm and Sloan 2013, ch. 4).
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We appreciate the helpful comments of two anonymous referees, Amir Amel-Zadeh, Gavin Cassar, Jenny Chu, Peter Joos, Kalin Kolev, Ed Maydew, Michael Mauboussin, Nathan Sharp, Lakshmanan Shivakumar, Richard Sloan, Simon Taylor, Jake Thomas, Irem Tuna, Geoff Whittington, Florin Vasvari, Rantala Ville, workshop participants at Cambridge University, London Business School, UNC–Chapel Hill, the 2014 Yale Accounting Conference, and the 2014 Helsinki Finance Conference. We especially appreciate the confidential and insightful conversations we had with analysts and MDs at two top-tier U.S. investment banks.
Description of disclosure quality scores calculated for 120 DCF models in analyst reports taken from Investext, Jan. 2012–Dec. 2013
Panel A: Explanation of how disclosure quality scores are computed
Regarding forecasted financial statements: 3 (1) points are awarded for each annual full (mini) B/S, I/S, and SCF forecasted by the analyst. The sum is then divided by 3 × 3 × T, where T is the number of years ahead that the terminal year lies. Since T sometimes exceeds the number of years for which the analyst is forecasting future financial statements, the disclosure quality score for forecasted financial statements can exceed 100 %. Also, because T may not be shown in the analyst’s DCF model (e.g., the analyst simply states what WACC is and what their estimated EQVALPS is), there are some reports for which the score cannot be calculated
Regarding the deriving of FCF: 1 point is awarded for each of the following 10 lines that are explicitly or implicitly forecasted by the analyst in hir or her DCF-to-all-investors model: EBITDA, depreciation and amortization, EBIT, taxes on EBIT, NOPAT, depreciation and amortization (again), annual change in working capital, after-tax operating cash flows, CAPEX, and FCFs. The sum is then divided by 10. An explicit forecast occurs when the analyst writes down a number for a given line. An implicit forecast occurs when the analyst does not write down a number for a given line but the number for the given line can be deduced from other lines the analyst has explicitly forecasted
Regarding WACC: 1 point is awarded for each of the 11 components used in calculating WACC per panel C of Table 3. The sum is then divided by 11
Regarding converting FCF to EQVALPS, 1 point is awarded for each of the following 12 items when explicitly shown on the analyst’s DCF: horizon year (max. of 1 point), present value (PV) of FCF in each individual year in forecast horizon (max. of 1 point), total PV of all forecasted FCFs, terminal value, PV of terminal value, enterprise value, cash, debt, equity value, shares used to deflate equity value, EQVALPS, and date to which the forecasted EQVALPS applies. The sum is then divided by 12
Panel B: Descriptive statistics on the individual DCF disclosure quality scores and for the equally weighted DCF total disclosure quality score
Disclosure quality score for
10th pctile (%)
50th pctile (%)
90th pctile (%)
Forecasted financial statements
Converting FCF to EQVALPS
Total disclosure quality score (equally-weighted avg. of A–D)
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Green, J., Hand, J.R.M. & Zhang, X.F. Errors and questionable judgments in analysts’ DCF models. Rev Account Stud 21, 596–632 (2016). https://doi.org/10.1007/s11142-016-9352-4