The Power Of Numbers: Base-Ten Threshold Effects In Reported Revenue

Derrald Stice
Hong Kong University of Science & Technology

Earl K Stice
Brigham Young University

Han Stice
University of Florida, Fisher School of Accounting

Lorien Stice-Lawrence
University of North Carolina at Chapel Hill

March 29, 2016

Abstract:

We provide evidence that managers have a revealed preference for reporting total revenue numbers just above base-ten thresholds (i.e., “round” numbers) of the form N × 10^K. Examples are $10 million (1 × 10^7) and $4 billion (4 × 10^9). Our finding is consistent with a literature in psychology demonstrating that humans are susceptible to a cognitive bias associated with base-ten reference points. However, we also document several rational explanations for this revenue management behavior on the part of managers. First, analyst revenue forecasts also exhibit this regularity, especially in early forecasts when greater uncertainty can potentially induce analysts to rely to a greater extent on heuristics, suggesting that managers may be managing reported revenue numbers to meet externally-determined base-ten-influenced benchmarks. In addition, the effect that we document is stronger for firms that face greater pressure to report high revenue growth, while firms that exceed base-ten revenue thresholds for the first time benefit from increased press coverage. Finally, we show that the revenue growth needed to stretch for a base-ten threshold is not sustainable; firms that just exceed base-ten thresholds have lower subsequent revenue growth. Given that managers engage in extra, and, on average, unsustainable efforts to increase revenues to reach base-ten thresholds, our results suggest that revenue manipulation is even more pervasive than previously documented and that lenders, investors, auditors, and regulators should apply an extra degree of skepticism when a reported revenue number just exceeds a base-ten threshold.

The Power Of Numbers: Base-Ten Threshold Effects In Reported Revenue – Introduction

The existence of salient numbers, or cognitive reference points, at base-ten thresholds (i.e., “round” numbers) has been well documented in the psychology literature. These base-ten thresholds take the general form of N × 10^K, where N and K are integers. Examples are $1 million (1 × 10^6), $300 million (3 × 10^8), $7 billion (7 × 10^9), and so forth. Gabor and Granger (1966) and Rosch (1975) conclude that humans use numbers that are factors of ten as reference points when evaluating all other numbers. Schindler and Wiman (1989) suggest that round numbers are easier to remember and come to mind more readily, and Tversky and Kahneman (1973) find that when making decisions individuals give excess weight to information that is easily retrieved from memory. In this paper, we study the extent to which firms manage their reported accounting numbers in order to report revenue just above base-ten thresholds, and we provide evidence on some of the motivations and consequences associated with firms engaging in this revenue management behavior.

Managers may desire to report revenues above a base-ten threshold for several reasons. Research in psychology and marketing demonstrates that consumers view prices ending in 99 cents to be substantially lower than prices just one cent above (Brenner and Brenner 1982). This same cognitive bias may lead investors to value a company with $99 million in revenue substantially lower than an otherwise-similar company with $100 million in revenue. Additionally, a cognitive bias among investors, analysts, and business reporters may lead to an increase in visibility for firms reaching a base-ten threshold point. Firms that report revenues that meet or just beat a base-ten threshold may be more likely to capture the attention of investors and the financial press. This increase in attention could then lead to a net increase in buying by individual investors and a net increase in coverage by the media (Odean 1998; Barber and Odean 2008).

These human perception explanations imply that there could be a disproportionate number of firms reporting revenue just above rather than just below base-ten thresholds as a result of opportunistic actions by managers exploiting a cognitive bias of investors, analysts, and business reporters. If this cognitive bias is prevalent among financial market participants, it would be rational for a manager to expend money and effort to reach a base-ten revenue threshold in order to attract more market attention or to enhance firm valuation. Possible consequences of this threshold-reaching revenue management behavior by managers are that reported revenues falling in these base-ten-related regions could be less reliable because they are more susceptible to strategic reporting by managers and could also be less persistent because they are achieved through unsustainable real activities or accruals management.

Base-Ten Threshold

Empirically, we use approximate randomization techniques to show that firms are significantly more likely to report revenues just above base-ten thresholds ($10 million, $200 million, $7.0 billion, and so forth) than just below them. This base-ten revenue threshold effect exists independent of the reporting currency; our results hold for firms reporting in U.S. dollars and for firms reporting in a variety of non-U.S. currencies. We also find that the base-ten threshold effect exists in analysts’ forecasts of revenue and this effect is strongest in the earliest revenue forecasts, made when uncertainty about future revenues is the highest. This suggests that part of managers’ motivation to beat base-ten revenue thresholds may be a rational response to meet important external benchmarks. Additionally, we find that firms which reach the $500 million or $1 billion revenue thresholds for the first time experience an increase in news coverage relative to the prior year and to a matched control sample, again indicating that rational managers have an incentive to reach a base-ten revenue threshold in order to increase firm visibility. We also find that this revenue threshold effect is stronger for firms with high past and expected future revenue growth (firms for which revenue growth is often a key performance indicator). Lastly, we find that threshold-reaching firms experience lower revenue growth in the subsequent year compared to a control sample, suggesting that the increased revenue growth needed to reach a base-ten threshold is not sustainable.

Our study has important implications for practitioners and academics. First, we document the existence of a base-ten threshold effect in reported revenues. Although prior research has documented a preference for base-ten thresholds in reported earnings (Carslaw 1988; Thomas 1989), this result has not previously been documented with respect to revenue, an important metric in its own right. After earnings, revenues are the accounting number most widely followed by investors and analysts (Rees and Sivaramakrishnan 2007), and revenues have long been known to contain incremental information content beyond earnings (Swaminathan and Weintrop 1991; Davis 2002; Jegadeesh and Livnat 2006). Additionally, revenues are closely tied to future firm growth, and Ghosh et al. (2005) find that increases in earnings that are accompanied by revenue growth tend to be more persistent. However, recent research such as Dichev et al. (2013) has stressed the “one number” mentality of managers who focus on bottom line net income as the single most important number for internal decision-making and external reporting. With such a mentality, managers might care about reported revenue only to the extent that it impacts bottom-line net income. Our results provide evidence that the level of reported revenue itself is an important reporting metric to managers, independent of the contribution of revenue to overall income, and that the level of the reported revenue number is an object of strategic management.

Base-Ten Threshold

Base-Ten Threshold

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