Description
In this study, we exploit the unique reporting requirements for employee stock options to provide large
sample evidence on the accuracy of footnote disclosures related to a specific complex estimate, the fair
value of options granted. We first document the frequency and magnitude of differences between (1) the
reported weighted-average fair value of options granted and (2) the calculated option fair value using the
disclosed weighted-average valuation model inputs and the Black-Scholes option pricing model. In a
sample of 23,358 firm-year observations between 2004 and 2011, we find that 23.9 percent have reported
and calculated option fair values that differ by more than ten percent, and that these differences
are sticky and are frequently significant as a percentage of net income. We also find that fair value
differences are larger for firms that (1) exhibit anomalous stock option footnote disclosures that likely
result from disclosure errors, (2) have more complex and hence error-prone stock option programs, and
(3) have lower quality financial reporting. Taken together this evidence is consistent with large fair value
differences that are primarily due to unintentional errors in the stock option footnote disclosures. To
document the consequences of these fair value differences, we provide evidence that errors in the reported
fair values prevent financial statement users from using the reported values to reliably estimate
future stock option expense for many firms. Consistent with this result, we also find that analyst forecasts
are less accurate and more disperse for firms with larger fair value differences.
The accuracy of disclosures for complex estimates: Evidence from
reported stock option fair values
*
Brian Bratten
a
, Ross Jennings
b, *
, Casey M. Schwab
c
a
Gatton College of Business & Economics, University of Kentucky, 423FB&E, Lexington, KY, 40506, USA
b
McCombs School of Business, University of Texas at Austin, B6400, Austin, TX, 78712, USA
c
Terry College of Business, University of Georgia, 242 Brooks Hall, Athens, GA, 30602, USA
a r t i c l e i n f o
Article history:
Received 30 May 2014
Received in revised form
2 July 2015
Accepted 2 September 2015
Available online xxx
Keywords:
Employee stock options
Fair values
Disclosure quality
Complex estimates
a b s t r a c t
In this study, we exploit the unique reporting requirements for employee stock options to provide large
sample evidence on the accuracy of footnote disclosures related to a speci?c complex estimate, the fair
value of options granted. We ?rst document the frequency and magnitude of differences between (1) the
reported weighted-average fair value of options granted and (2) the calculated option fair value using the
disclosed weighted-average valuation model inputs and the Black-Scholes option pricing model. In a
sample of 23,358 ?rm-year observations between 2004 and 2011, we ?nd that 23.9 percent have re-
ported and calculated option fair values that differ by more than ten percent, and that these differences
are sticky and are frequently signi?cant as a percentage of net income. We also ?nd that fair value
differences are larger for ?rms that (1) exhibit anomalous stock option footnote disclosures that likely
result from disclosure errors, (2) have more complex and hence error-prone stock option programs, and
(3) have lower quality ?nancial reporting. Taken together this evidence is consistent with large fair value
differences that are primarily due to unintentional errors in the stock option footnote disclosures. To
document the consequences of these fair value differences, we provide evidence that errors in the re-
ported fair values prevent ?nancial statement users from using the reported values to reliably estimate
future stock option expense for many ?rms. Consistent with this result, we also ?nd that analyst forecasts
are less accurate and more disperse for ?rms with larger fair value differences.
© 2015 Elsevier Ltd. All rights reserved.
1. Introduction
As the use of fair values and other complex estimates in ?nancial
reporting has increased, regulators, the media, and researchers
have expressed concerns about the reporting and auditing of these
estimates (SEC, 2003; PCAOB, 2011; Bratten, Gaynor, McDaniel,
Montague, & Sierra, 2013; Rapoport, 2013; Grif?th, Hammersley,
& Kadous, 2015). These estimates are often accompanied by foot-
note disclosures providing the earliest information to ?nancial
statement users about the calculation of the estimates and howthe
estimates impact net income. Despite the importance of these
supporting disclosures, there is virtually no research on their
accuracy.
In this study, we conduct a comprehensive examination of
footnote disclosures related to a speci?c complex estimate, the fair
value of employee stock options granted. We focus on stock option
disclosures to exploit the unique reporting requirements for stock
options that, unlike disclosures for other estimates, require
disclosure of not only the calculation outputdthe estimated fair
value of employee stock options granteddbut also the calculation
inputs and the method of calculation. These requirements allow us
to evaluate the internal consistency of these disclosures by
comparing the disclosed fair value to a calculated fair value based
on the ?rm's disclosed inputs and the Black-Scholes valuation
*
We gratefully acknowledge helpful comments from Mark Peecher (editor), two
anonymous reviewers, Steve Baginiski, John Campbell, Preeti Choudhary, Dain
Donelson, Theodore Goodman, Jackie Hammersley, John McInnis, Laura Wang, Teri
Yohn, Yong Yu, and workshop participants at Miami University, the University of
Toronto, the 2014 FARS midyear meeting, and the 2014 AAA annual meeting. Brian
Bratten acknowledges the ?nancial support of the Von Allmen School of Accoun-
tancy and the Gatton College of Business and Economics. Ross Jennings acknowl-
edges the ?nancial support of the Deloitte & Touche Professorship of Accounting
and the McCombs School of Business. Casey Schwab acknowledges the ?nancial
support of the Terry College of Business and the J.M. Tull School of Accounting. We
also acknowledge the excellent research assistance of Philip Chung, Anne Ehinger,
Ying Huang, Jonathan Ross, and Russell Williamson.
* Corresponding author.
E-mail address: [email protected] (R. Jennings).
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Accounting, Organizations and Society xxx (2015) 1e18
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model. Speci?cally, we construct a measure that we refer to as the
“fair value difference” that equals the absolute value of the differ-
ence between the reported and calculated fair values, scaled by the
calculated fair value. We use this measure to investigate both the
accuracy of these disclosures and the consequences of inaccurate
disclosures. Our analyses proceed in three stages.
In the ?rst stage, we document the frequency and materiality of
“large” fair value differences (greater than ten percent). We focus
on large differences because small differences can occur when
multiple grants are issued in the same year and the inputs vary
across grants. In our sample of 23,358 ?rm-year observations be-
tween 2004 and 2011, we ?nd that 5573 observations (23.9
percent) have large differences between the reported and calcu-
lated fair values. For observations with large differences, 69.5
percent of the differences are greater than one percent of reported
income. These results suggest the potential for a signi?cant number
of material errors in a high pro?le ?nancial statement footnote.
In the second stage, we conduct analyses to determine whether
unintentional disclosure errors are the primary source of these fair
value differences. We ?rst evaluate Compustat footnote data and
uncover two anomalies in the stock option disclosure that suggest
possible errors. Speci?cally, we ?nd that 1109 ?rm-year observa-
tions (4.7 percent of the sample) disclose a reported fair value for
their options granted equal to the exercise price of the options, a
virtual impossibility without a disclosure error. We also ?nd that
1932 ?rm-year observations (10.8 percent of the 17,959 ?rm-year
observations for which we have disclosure data from the prior
year) disclose the same volatility, risk-free-rate, exercise price, or
option grant date fair value for option grants in consecutive years,
an unlikely occurrence. For both of these anomalies, the fair value
difference is larger for observations exhibiting the anomaly, sug-
gesting that disclosure errors are a likely source of at least some of
the fair value differences.
To provide further evidence that fair value differences represent
disclosure errors, we then conduct a multivariate analysis to
determine whether fair value differences are associated with the
complexity of the ?rm's stock option program and with ?rm
reporting and operating environment characteristics that suggest
low quality ?nancial reporting. We ?nd that ?rms have larger fair
value differences when they have more complex, and likely more
error-prone, stock option programs. Speci?cally, ?rms exhibit
larger fair value differences when they grant relatively more op-
tions to rank-and-?le employees, have higher rates of cancellations,
have larger changes in their employee base, split their stock during
the current year, or make more extensive use of options. We also
?nd that fair value differences are larger when ?nancial reporting
quality is lower. Speci?cally, fair value differences are larger inyears
in which stock option expense is disclosed rather than expensed
and for ?rms that have an internal control weakness, have an ac-
counting restatement, do not use a Big 4 auditor, or do not have a
chief accounting of?cer as one of its most highly compensated
executives. Finally, we ?nd that fair value differences are larger for
?rms that have less developed accounting systems or operate in a
more complex reporting environment. Speci?cally, ?rms making a
corporate acquisition in the current year, as well as smaller and
younger ?rms, exhibit larger fair value differences.
Although these results suggest that, on average, large fair value
differences result from unintentional disclosure errors, we also
consider several alternative explanations for the fair value differ-
ences that do not involve unintentional disclosure errors. Based on
an analysis of hand-collected data for 200 ?rm-year observations
with large fair value differences, we ?nd that 20 large fair value
differences are due to data entry errors in the Compustat database.
For the remaining 180 observations, we ?nd that at most 30 of the
fair value differences are potentially attributable to a combination
of (1) use of a valuation model other than the Black-Scholes model,
(2) options issued ineor out-of-the-money, (3) discounts for post-
vesting restrictions, and (4) disclosure of ranges for valuation
model inputs when midpoints are poor proxies for the weighted
averages of these inputs. Collectively, these analyses suggest that a
substantial majority of large fair value differences are likely
attributable to unintentional disclosure errors.
In our third stage, we investigate potential consequences of
inaccurate footnote disclosures by examining howthese errors map
into future share-based compensation expense and impact ana-
lysts' earnings forecasts. We ?nd that the relation between ex-
pected option expense based on reported fair values and future
reported share-based compensation expense is declining in the
absolute fair value difference. This result indicates that, on average,
reported fair values are measured with increasing error as the ab-
solute fair value difference increases. We also ?nd that the calcu-
lated fair value is positively and signi?cantly related to the future
expense after controlling for the reported fair value. This result
indicates that the calculated fair value is used to compute option
expense for many ?rms and the reported fair value is incorrect.
These results suggest that footnote disclosure errors likely impair
investors' abilities to predict future option expense. Focusing on
analysts' forecasts, we ?nd a positive and signi?cant relation be-
tween absolute fair value differences and both absolute forecast
errors and forecast dispersion. These results indicate that analysts'
forecasts are negatively affected by the stock option footnote errors
represented by the absolute fair value differences.
Taken together, the results reported in this paper provide evi-
dence that a substantial number of ?rms have errors in their stock
option footnote. As such, this study makes several contributions for
regulators, ?nancial statement users and researchers. First, for
regulators, our evidence suggests that material errors occur in stock
option footnote disclosures that result in disclosed information that
is either not relevant or not faithfully representative. This is espe-
cially important given that PCAOB guidance recommends that audit
?rms conduct the same comparison of reported and calculated fair
values that we conduct in this study (PCAOB, 2006, p. 26). Further,
these ?ndings validate concerns that “fair value determinations
based on unobservable inputs are particularly challenging for au-
ditors” (PCAOB, 2009, p. 5) and that auditors are not adequately
evaluating all of the inputs into an estimate for the collective
impact on the estimate (PCAOB, 2011; Peecher, Schwartz, &
Solomon, 2007; Grif?th et al. 2015). The fact that the errors we
identify can be detected with little effort leaves open the question
of the extent of errors in more dif?cult-to-verify disclosures of
complex estimates.
Second, for ?nancial statements users, our evidence on the ac-
curacy of the stock option footnote disclosure is important because
these disclosures provide the earliest information about the
magnitude of stock option expense in future years. Indeed, one of
the FASB's objectives for employee stock option footnote disclo-
sures is to “enable users of the ?nancial statements to under-
stand… the effect of compensation cost arising from share-based
payment arrangements on the income statement” (ASC 718-10-50-
1). Substantial differences between the disclosed and calculated fair
values that cannot be reconciled based on information provided in
the footnote leave ?nancial statement users with no guidance on
which value is a more accurate measure of the grant date fair value
and, thus, which value to use to estimate future option expense.
Third, this study contributes to prior research. Prior studies
examine either material but infrequent errors (i.e., restatements) or
general measures of ?nancial reporting quality (e.g., internal con-
trol weaknesses, accruals quality). Unlike these studies, we exploit
the unique reporting requirements for stock options to provide
large sample evidence on the incidence and materiality of errors in
B. Bratten et al. / Accounting, Organizations and Society xxx (2015) 1e18 2
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values, Accounting, Organizations and Society (2015),http://dx.doi.org/10.1016/j.aos.2015.09.001
a common ?nancial statement disclosure that are not publicly
disclosed by the ?rm. This study also contributes to the literature
examining stock option disclosures. Unlike prior studies which
generally investigate bias in the selection of valuation model inputs
(e.g., Aboody, Barth, & Kasznik, 2006; Hodder, Mayew, McAnally, &
Weaver, 2006; Bartov, Mohanram, & Nissim, 2007; Johnston, 2006;
Choudhary, 2011) and the valuation model (Bratten, Jennings, &
Schwab, 2015), we examine the accuracy of those disclosures by
examining whether the reported stock option fair value is inter-
nally consistent with the disclosed valuation inputs and model.
Note that selection of biased inputs alone would not result in the
fair value differences we document as long as the fair value of
options granted is consistently computed using those biased inputs.
Thus, our study complements prior literature to provide a detailed
analysis of the estimation and ?nancial reporting of employee stock
option fair values.
2. The fair value difference and the likelihood of
unintentional disclosure errors
2.1. The fair value difference
ASC 718-10-50 requires ?rms to disclose the number and
weighted-average grant date fair value of options granted during
the year. Firms are also required to disclose the valuation method
(e.g., the Black-Scholes model) and the valuation model inputs used
to estimate the fair value of these options. The valuation model
inputs include the weighted-average exercise price, expected life,
expected volatility, expected dividend yield, risk-free rate, and
discount for post-vesting restrictions. To meet these disclosure
requirements, ?rms must track and report a considerable amount
of information, creating ample opportunities for error.
In this study, we use the required stock option footnote disclo-
sures to compare two alternative measures of the fair value of
employee stock options granted in the current year. The ?rst is the
weighted-average fair value of options granted as reported in the
?rm's notes to their ?nancial statements. We refer to this value as
the reported fair value (FV
Reported
). The second is the calculated fair
value based on the weighted-average valuation model inputs dis-
closed in the ?rm's notes to their ?nancial statements and the
Black-Scholes option pricing model. We refer to this value as the
calculated fair value (FV
Calculated
).
1
We then use these values to
compute a ?rm's “fair value difference” (FV
Difference
), the difference
between the ?rm's reported and calculated fair values, scaled by
the calculated fair value [(FV
Reported
e FV
Calculated
)/FV
Calculated
].
It is unlikely that these fair value differences result from pur-
poseful earnings management for several related reasons. First, to
knowingly report incorrect fair values or option model inputs in the
stock option footnote would likely be an SEC violation and risk
serious negative consequences. Second, management is likely to
derive little to no gain from knowingly reporting incorrect fair
values or option model inputs because such misreporting by itself
would not affect reported expense unless the ?rm also used the
incorrect information reported in the footnote disclosure to
compute stock option expense, a further SEC violation. Third,
fraudulently manipulating the valuation of stock options granted is
likely not even necessary given ?ndings in prior research that ?rms
are able to decrease reported option expense (and thus manage
earnings upwards) by exercising discretion when selecting both the
valuation model (Bratten et al., 2015) and valuation model inputs
(Aboody et al., 2006; Bartov et al., 2007; Choudhary, 2011; Hodder
et al., 2006; Johnston, 2006). These actions may push the bound-
aries of legitimate reporting, but fall short of illegal activity. Finally,
as we discuss below, we ?nd that the fair value differences are
skewed toward positive (expense-increasing) values, which would
permanently decrease net income since overstated stock option
expense does not later reverse through net income like most ac-
cruals. For these reasons we focus on the absolute value of FV
Dif-
ference
, which we label AbsFV
Difference
, and investigate whether these
absolute fair value differences are due to unintentional disclosure
errors or have alternative, non-error explanations.
Minor differences between the reported and calculated fair
values can occur when valuation model inputs vary across multiple
equal-weighted option grants during the year because the Black-
Scholes model is non-linear in most valuation model inputs (life,
volatility, dividend yield, and risk-free rate). When these inputs
vary across grants, the weighted-average fair value from the model
(the reported fair value) will not equal the calculated fair value
based on the weighted-average inputs (the calculated fair value).
However, as the examples we present in Appendix A demonstrate,
using weighted-average valuation inputs to compute an option fair
value is not likely to produce a fair value difference that is more
than a few percent as long as the different grants are relatively
equally-weighted. We address the potential for larger fair value
differences that can arise frommultiple grants that are not equally-
weighted in detail below.
2.2. The likelihood of unintentional disclosure errors
To meet the stock option disclosure requirements each ?rm
must successfully track multiple variables, often for multiple stock
option grants, input these variables into a complex non-linear
formula and compute and report weighted averages for the
various inputs and the outputs. The steps involved in preparing
these footnote disclosures range from simple (e.g., if the exercise
price for the option equals the closing stock price on the grant date,
?nd that price) to more complex (e.g., estimate the expected life of
an option given the previous exercise behavior of employees, the
changes in employee pro?les, the economic environment and the
terms of the current options granted). There are ample opportu-
nities for error throughout this process. For example, an accountant
preparing the footnote disclosure may compute a weighted-
average as a simple average or not correctly incorporate the effect
of a stock split in the middle of the year. Alternatively, an accoun-
tant may incorrectly report the exercise price of options granted as
the fair value of the options granted.
2
Two additional features of the ?nancial reporting process in the
stock option setting increase the likelihood of errors. First, ?rms
often engage external valuation consultants to estimate stock op-
tion fair values and other complex estimates because management
lacks the necessary expertise to perform these estimates internally.
This lack of valuation expertise can be problematic given man-
agement is still responsible for accurately preparing the footnote
disclosures related to the estimated stock option fair values. Based
on interviews of auditors and a reviewof PCAOB inspection reports,
Grif?th et al. (2015) argue that a division of knowledge between
auditors and valuation experts is a root cause of challenges arising
when auditing complex estimates because auditors do not have
1
When computing FV
Calculated
, we assume the current market price of the un-
derlying stock on the grant day is equal to the disclosed option exercise price. This
is consistent with prior research that suggests “virtually all” ?rms issue options that
are at the money (Bebchuk et al., 2002; Chang et al., 2013; Hall & Murphy, 2002).
2
We report below that many ?rms do indeed report the exercise price as the fair
value of the options granted. As further evidence of the inherent complexity in
accounting for employee stock options, a PricewaterhouseCoopers guide (PwC,
2013) on how to account for stock-based compensation is 362 pages.
B. Bratten et al. / Accounting, Organizations and Society xxx (2015) 1e18 3
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suf?cient valuation knowledge to engage in the necessary critical
analysis of management or specialist models. Similar issues likely
exist for managers who prepare the stock option disclosures and
choose to engage an external valuation consultant to assist in the
valuation of stock options rather than acquiring the requisite
knowledge to understand and perform the valuation themselves.
Second, many ?rms rely on internal spreadsheets when ac-
counting for stock options. Panko and Ordway (2005) summarize
evidence from several sources and report that spreadsheets are
ubiquitous in ?nancial reporting by U.S. ?rms. Moreover, prior
empirical studies examining spreadsheet accuracy ?nd that the
majority of spreadsheets examined have signi?cant errors. Powell,
Baker, and Lawson (2008) cite studies by KPMG and Coopers &
Lybrand in which both ?rms found that 91 percent of the spread-
sheets they examined had a signi?cant error.
3
Various strategies are available to reduce or eliminate these
errors. Indeed, testing spreadsheets is one focus of the imple-
mentation of SarbaneseOxley Act section 404 internal controls
requirements (PwC, 2004). However, studies suggest that such
systematic testing of spreadsheets is not common (Caulkins,
Morrison, & Weidenmann, 2007; Leon, Kalbers, Coster, &
Abraham, 2012). In fact, Deloitte (2009) surveyed over 3000 pro-
fessionals during a 2008 webcast on balancing spreadsheet risks
and found that 70.1 percent of respondents indicated that spread-
sheets were relied on for critical portions of the business, but only
33.9 percent indicated that their ?rm had specialized techniques to
ensure the spreadsheets were functioning properly.
In addition, PCAOB audit guidance recommends that for com-
panies using the Black-Scholes model “the auditor should verify
that the company is using the correct formula and recalculate the
fair value” (PCAOB, 2006, p. 26). Following this recommendation for
each stock option grant should help detect many unintentional
errors at the grant level. However, if this recommendation is not
also followed after combining multiple grants, unintentional errors
can still go undetected in the weighted-average footnote
disclosures.
2.3. An example
Before empirically testing the likelihood of unintentional
disclosure errors, we provide an example based on a ?rm in our
sample reporting an option fair value equal to the option's exercise
price, a likely disclosure error. In their Form 10-K for the ?scal year
ended December 31, 2010, Hughes Communications disclosed that
both the fair value of options granted and the exercise price of
options granted equaled $53.67 for 2008, $16.77 for 2009 and
$28.99 for 2010. In contrast, the calculated fair values based on the
disclosed inputs for those years equal $24.26 for 2008, $7.25 for
2009 and $11.79 for 2010, resulting in an AbsFV
Difference
greater than
100 percent in each year. It seems likely that either (1) the reported
fair value is in error and grossly overstates the fair value for options
granted during the year or (2) the exercise price is in error so that
the calculated fair value understates the fair value of the options
granted during the year.
To determine which of these two possibilities is true, we use the
reported fair values and the calculated fair values to estimate future
expense and compare these estimates with the actual expense re-
ported by Hughes Communications. Hughes' disclosures indicate
that 2008 is the ?rst year they issue stock options and that they
made one grant per year in 2008, 2009 and 2010, about four
months into the year. We assume that (a) options granted in the
current year vest over four years with two-thirds of a year occurring
in the grant year, (b) 100,500 options are granted in 2009 (net of
options retired), and (c) forfeitures in 2008 relate to options gran-
ted in 2008, forfeitures in 2009 relate half to options granted in
2008 and half to options granted in 2009, and forfeitures in 2010
relate one third to each of the current and preceding two years.
Using these assumptions and the reported fair values, we estimate
option expense for 2008, 2009, and 2010 to be $4.9 million, $7.7
million, and $10.4 million, respectively. These estimates are much
greater than the actual stock option expense reported by Hughes of
$2.0 million, $3.5 million, and $4.3 million for these three years. In
contrast, using these same assumptions and the calculated fair
values, we estimate option expense for 2008, 2009, and 2010 to be
$2.2 million, $3.5 million, and $4.6 million, respectively. These es-
timates are very close to those reported by Hughes for their actual
option expense, and indicate that Hughes used the calculated value,
not the reported value, to compute future option expense.
4
A ?nancial statement user relying on the reported fair value of
options granted to estimate stock option expense would have had
an error relative to a forecast based on the calculated fair value of
$2.7 ($5.8) million in 2008 (2010), which was nearly 30 (25) percent
of their net income of $9.3 ($23.0) million.
5
This analysis indicates
that the reported fair values in Hughes stock option footnotes are
not consistent with reported stock option expense, and that a
?nancial statement user relying on reported stock option fair values
would be misled.
3. The sample and descriptive statistics
Our sample is drawn from the Compustat database for ?scal
years 2004e2011 and includes all ?rms incorporated in the United
States with available data to compute the fair value difference
(FV
Difference
). We begin in 2004 because this is the ?rst year for
which Compustat contains detailed information on the weighted-
average fair value of employee stock option grants during the cur-
rent year as well as the weighted-average inputs to the Black-
Scholes pricing model used to value the current year's option
grants.
6
This provides us with an initial sample of 25,439 obser-
vations. We then require the additional explanatory variables used
in our multivariate analysis, resulting in our main sample of 23,358
?rm-year observations. For some of our analyses, we also require
lagged Compustat data or analyst forecast data from I/B/E/S,
reducing our sample for these analyses. The sample construction is
detailed in Table 1.
Panel A of Table 2 reports descriptive statistics for the reported
fair value (FV
Reported
), the calculated fair value (FV
Calculated
), the fair
value difference (FV
Difference
), the absolute value of the fair value
difference (AbsFV
Difference
), and measures of the materiality of
3
To con?rm that spreadsheets are used to prepare stock option footnote dis-
closures, we asked ?ve senior partners at four major audit ?rms how commonly
spreadsheets are used to prepare stock option footnote disclosures. Three partners
responded “very common,” one responded “virtually universal,” and one responded
“common.”
4
The Hughes example provides anecdotal evidence of a disclosure error. This
example is unique because Hughes has a short history of option grants and clearly
discloses both the timing of the grants and the subsequent actual stock option
expense. Our ability to perform this calculation is much more limited for the ma-
jority of ?rms that have long-standing option programs and do not separately
disclose stock option expense.
5
In 2009, the forecast error based on the calculated value is $4.2 million less than
the forecast error based on the reported fair value, and Hughes reported a loss of
$51.6 million. As a percentage of assets, these forecast errors are 0.24 percent, 0.35
percent and 0.45 percent in 2008, 2009, and 2010, respectively.
6
The Black-Scholes inputs necessary to compute the calculated value of options
granted include life (Compustat OPTLIFE), volatility (OPTVOL), dividend yield
(OPTDR), risk-free rate (OPTRFR), and the exercise price (OPTPRCGR), which we
assume to be equal to the market price of the underlying stock on the grant date.
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AbsFV
Difference
. The distribution of the signed difference (FV
Difference
) is
centered near zero (median ¼ À0.001) but also includes many fair
value differences far from zero. In addition, the mean FV
Difference
(0.055) is signi?cantly positive (p-value < 0.01, untabulated), indi-
cating the distribution is skewed toward positive values. As dis-
cussed above, this distribution is more consistent with
unintentional error than managerial manipulation because manip-
ulation to lower option expense would result in a FV
Difference
distri-
bution skewed toward negative values (i.e., FV
Reported
< FV
Calculated
).
Panel A also reports that the mean AbsFV
Difference
is 11.9 percent.
As a point of reference, this is much larger than the mean error
reported in prior research in auditing. For example, Durney, Elder
and Glover (2014) examine 160 post-SOX audit sampling applica-
tions and report a mean error (computed as the absolute difference
between management's reported value and the auditor's proposed
value, scaled by management's reported value) of 0.2 percent. They
also report a mean error for ten studies conducted prior to SOX of
3.08 percent.
We also report in Table 2 that 23.9 percent of ?rm-year obser-
vations have an AbsFV
Difference
greater than ten percent. In some of
our analyses, we divide the sample into two groups: those with
AbsFV
Difference
greater than ten percent (the “high group”) and those
with AbsFV
Difference
less than ten percent (the “low group”). We
focus on ?rm-year observations with AbsFV
Difference
greater than ten
percent because these differences are more likely due to errors than
to some alternative explanation. If we lower (raise) the threshold
for “large” differences to ?ve (20) percent, then AbsFV
Difference
is
“large” for 33.2 (15.4) percent of the ?rms in our sample.
We next evaluate the materiality of these absolute differences.
Materiality
Income
(Materiality
Asset
) equals the absolute value of the
annual difference between the reported and calculated fair values
multiplied by the number of options granted, scaled by the absolute
value of net income (scaled by total assets). Average Materi-
ality
Income
(Materiality
Asset
) equals 7.9 (0.7) percent. Moreover,
Materiality
Income
(Materiality
Asset
) exceeds one percent for 24.6 (6.7)
percent of the sample. These statistics suggest that AbsFV
Difference
is
material for many ?rms.
Panel B of Table 2 presents univariate statistics for materiality
after partitioning the sample into high and lowAbsFV
Difference
groups.
Materiality
Income
(Materiality
Asset
) is greater than one percent for 69.5
(25.3) percent of ?rm-year observations in high AbsFV
Difference
group
relative to 10.5 (0.8) percent of observations in the low group, and
greater than?ve percent for 37.0(7.2) percent of observations inhigh
group relative to 2.4 (0.1) percent in the low group.
Panel C of Table 2 presents the distribution of AbsFV
Difference
over
time. The percentage of observations with AbsFV
Difference
greater
than ten percent declines from 32.6 percent in 2004 to 17.2 percent
in 2011. The largest decline, from 29.6 percent in 2005 to 22.6
percent in 2006, coincides with recognition of the fair value of
options granted on the income statement. The last two columns of
Panel C present the percentage of observations with an AbsFV
Dif-
ference
greater than one percent of net income for the high and low
AbsFV
Difference
groups, respectively. For the high (low) group this
percentage declines from 77.7 (16.6) percent in 2004 to 67.9 (8.3)
percent in 2011. Despite this decrease, a substantial portion of the
sample still exhibits a material difference between reported and
calculated fair values in the ?nal year of our study period.
Finally, we examine whether the large fair value differences are
one-time events or recur through time for individual companies
using a subsample (12,052 ?rm-year observations) with data
available to compute AbsFV
Difference
for three consecutive years. The
?rst column of panel D reports that for this sample 22.3 percent of
the ?rm-year observations in the ?rst year are in the high AbsFV-
Difference
group and 41.4(21.8) percent of these observations are still
in the high group in the second year (both the second and third
years). Random assignment of ?rms to the high and low groups in
subsequent years based on the frequency in the current year would
produce 22.3 percent of the current-year high group still in the high
group in the second year, and 5.0 percent (0.223 Â0.223) still in the
high group in both the second and third years. Thus, we observe
nearly twice the expected frequency in the second year and more
than four times the expected frequency in the third year.
7
The
second and third columns of panel D present results separately for
observations with positive and negative fair value differences in the
?rst year. The results are very similar to those reported for the
combined sample, with somewhat greater stickiness for positive
fair value differences.
Taken together, these results suggest that large fair value differ-
ences are not randomevents, but recur withthesame signacross time
for many ?rms. In the next section we investigate whether the fair
value differences are likely due to unintentional reporting errors
arising from complex option programs, lower quality ?nancial
reporting, and challenging accounting environments. We also inves-
tigate alternative potential explanations for fair value differences that
do not necessarily suggest the presence of disclosure errors.
Table 1
Sample selection.
Data restrictions N Used in table(s)
Primary Sample
Starting Compstat sample of U.S. Firms from ?scal years 2004e2011 with data to compute AbsFV
Difference
(i.e., FVOPTGR, OPTLIFE, OPTVOL, OPTDR, OPTRFR, OPTPRCGR)
25,439
Less ?rms without data to compute deteriminants of AbsFV
Difference
À2081 23,358 2, 3, 4
Future share-based compensation expense sample
Starting sample (i.e., Primary sample) 23,358
Less ?rms without data to compute share-based compensation expense À16 23,342
Less ?rms without AbsFV
Difference
in year t-1 À5504 17,838 7
Less ?rms without AbsFV
Difference
in year t-2 À4557 13,281 7
Analyst forecast accuracy and dispersion sample
Starting sample (i.e., Primary sample) 23,358
Less pre-SFAS 123R observations À6563 16,795
Less ?rms without I/B/E/S data to compute current and lagged forecast errors À7496 9299
Less ?rms without data to compute additional control variables À2672 6627 8
Less ?rms without I/B/E/S data to compute current and lagged forecast dispersion À887 5740 8
Detailed variable de?nitions are presented in Appendix C.
7
We also estimated the “persistence” of absolute fair value differences by
regressing ?rms' AbsFV
Difference
in year t on their AbsFV
Difference
in year t-1. The co-
ef?cient on the prior-year AbsFV
Difference
is positive and signi?cant (b ¼ 0.3338; p-
value < 0.01), providing evidence that AbsFV
Difference
exhibits some persistence from
one year to the next.
B. Bratten et al. / Accounting, Organizations and Society xxx (2015) 1e18 5
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4. Do large fair value differences result from disclosure
errors?
In this section, we conduct a variety of analyses to determine
whether the fair value differences documented above appear to
result from disclosure errors.
4.1. Direct evidence of disclosure errors
The most direct evidence we provide comes fromtwo anomalies
in the stock option footnote itself that suggest a disclosure error.
First, we observe that 1109 ?rm-year observations (4.7 percent of
the sample) disclose a reported fair value equal to the exercise price
of the options granted. While not mathematically impossible, the
option fair value will not equal the exercise price unless one or
more of the other model inputs are both incorrect and highly un-
usual. For example, in the Hughes Communications example dis-
cussed above, both of these values could be correct only if the
weighted-average volatility was 340 percent, the expected life
was 230 years, or the weighted-average risk-free rate was 500
percent. As such, this equality suggests an incorrect transfer of data
from a spreadsheet or other source to the footnote. The mean
Table 2
Univariate statistics: the magnitude and materiality of fair value differences.
Panel A: basic univariate statistics
Variable N Mean P5 P10 Q1 Median Q3 P90 P95
FV
Reported
23,358 7.369 0.460 0.930 2.360 5.260 9.790 15.390 19.400
FV
Calculated
23,358 7.180 0.456 0.905 2.304 5.086 9.579 15.023 18.960
% of sample % of sample
FV
Difference
FV
Difference
Variable N Mean P5 P10 Q1 Median Q3 P90 P95 10%
FV
Difference
23,358 0.055 À0.199 À0.095 À0.016 À0.001 0.018 0.217 0.549 9.6% 14.2%
% of sample
AbsFV
Difference
Variable N Mean P5 P10 Q1 Median Q3 P90 P95 >10%
AbsFV
Difference
23,358 0.119 0.001 0.001 0.004 0.017 0.091 0.326 0.578 23.9%
% of sample % of sample
Materiality Materiality
Variable N Mean P5 P10 Q1 Median Q3 P90 P95 >1% >5%
Materiality
Income
23,358 0.079 0.000 0.000 0.000 0.001 0.010 0.056 0.151 24.6% 10.7%
Materiality
Asset
23,358 0.007 0.000 0.000 0.000 0.000 0.001 0.005 0.016 6.7% 1.8%
Panel B: materiality univariate statistics in high and low AbsFV
Difference
subsamples
Variable AbsFV
Difference
>¼ 10% subsample AbsFV
Difference
1% >5% N Mean Median >1% >5%
Materiality
Income
5574 0.298 0.028 69.5% 37.0% 17,784 0.010 0.001 10.5% 2.4%
Materiality
Asset
5574 0.028 0.002 25.3% 7.2% 17,784 0.001 0.000 0.8% 0.1%
Panel C: absolute fair value differences (AbsFV
Difference
) over Time
Year N Mean P5 P10 Q1 Median Q3 P90 P95 Full sample AbsFV
Diff
>¼10% AbsFV
Diff
10% >1% >1%
2004 2902 0.194 0.001 0.001 0.005 0.029 0.165 0.487 0.870 32.6% 77.7% 16.6%
2005 3481 0.147 0.001 0.002 0.006 0.026 0.131 0.420 0.707 29.6% 74.9% 14.1%
2006 3259 0.110 0.001 0.001 0.005 0.016 0.081 0.312 0.516 22.6% 69.1% 11.5%
2007 3169 0.113 0.001 0.001 0.005 0.016 0.087 0.305 0.545 23.1% 69.1% 9.8%
2008 2945 0.111 0.001 0.001 0.004 0.018 0.088 0.307 0.572 23.2% 62.0% 8.9%
2009 2710 0.104 0.001 0.001 0.003 0.014 0.076 0.303 0.539 21.8% 62.1% 7.2%
2010 2566 0.081 0.000 0.001 0.003 0.011 0.052 0.223 0.416 17.8% 63.8% 7.3%
2011 2326 0.073 0.000 0.001 0.003 0.011 0.050 0.211 0.402 17.2% 67.9% 8.3%
All Years 23,358 0.119 0.001 0.001 0.004 0.017 0.091 0.326 0.578 23.9% 69.5% 10.5%
Panel D: stickiness of fair value differences in subsample with three consecutive years of data availability (N ¼ 12,052)
Large absolute diff. Large positive diff. Large negative diff.
AbsFV
Difference
> 10% FV
Difference
> 10% FV
Difference
< À10%
% of subsample with large differences in the ?rst year 22.3% 10.7% 11.6%
% of ?rst-year large differences with a large difference in the second year 41.4% 51.2% 32.3%
% of ?rst-year large differences with a large difference in the second and third year 21.8% 23.5% 13.8%
The sample includes ?rm-year observations from 2004 to 2011 with suf?cient disclosure information to re-calculate the fair value of stock options granted, and to estimate
Equation (1). FV
Difference
equals the difference between the reported (FV
Reported
) and calculated (FV
Calculated
) fair value of stock options granted, scaled by the calculated fair value
(FV
Calculated
). FV
Reported
equals OPTFVGR as reported by Compustat. FV
Calculated
is the calculated fair value based on the Black-Scholes valuation model and the disclosed valuation
model inputs reported by Compustat. AbsFV
Difference
equals the absolute value of FV
Difference
. Materiality
Income
(Materiality
Asset
) equals the ratio of absolute value of the difference
between the reported and calculated stock option fair values multiplied by the number of option granted to net income (total assets) [Abs(FV
Reported
e FV
Calculated
)*# Options
Granted/Net Income] ([Abs(FV
Reported
- FV
Calculated
)*# Options Granted/Assets]). Panel D is limited to a subsample of ?rms for which there are at least three consecutive ?rm-
year observations.
B. Bratten et al. / Accounting, Organizations and Society xxx (2015) 1e18 6
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absolute fair value difference is 59.3 (8.9) percent for observations
for which the reported fair value equals (does not equal) the ex-
ercise price. These means are signi?cantly different (p-
value < 0.01).
Second, among 17,959 ?rm-year observations with available
data, we observe that 1932 observations (10.8 percent of this sub-
sample) exhibit a “repeat disclosure” in which they disclose the
same volatility, risk-free rate, exercise price, or grant date fair value
for option grants in consecutive years. While it is not impossible for
these values to be the same from one year to the next, these values
are generally expected to vary from year to year, so a repeated
disclosure for one of these values may indicate that a value was not
properly updated. For observations with (without) a repeat
disclosure, the mean absolute fair value difference is 13.0 percent
(9.5 percent). These means are signi?cantly different (p-
value
In this study, we exploit the unique reporting requirements for employee stock options to provide large
sample evidence on the accuracy of footnote disclosures related to a specific complex estimate, the fair
value of options granted. We first document the frequency and magnitude of differences between (1) the
reported weighted-average fair value of options granted and (2) the calculated option fair value using the
disclosed weighted-average valuation model inputs and the Black-Scholes option pricing model. In a
sample of 23,358 firm-year observations between 2004 and 2011, we find that 23.9 percent have reported
and calculated option fair values that differ by more than ten percent, and that these differences
are sticky and are frequently significant as a percentage of net income. We also find that fair value
differences are larger for firms that (1) exhibit anomalous stock option footnote disclosures that likely
result from disclosure errors, (2) have more complex and hence error-prone stock option programs, and
(3) have lower quality financial reporting. Taken together this evidence is consistent with large fair value
differences that are primarily due to unintentional errors in the stock option footnote disclosures. To
document the consequences of these fair value differences, we provide evidence that errors in the reported
fair values prevent financial statement users from using the reported values to reliably estimate
future stock option expense for many firms. Consistent with this result, we also find that analyst forecasts
are less accurate and more disperse for firms with larger fair value differences.
The accuracy of disclosures for complex estimates: Evidence from
reported stock option fair values
*
Brian Bratten
a
, Ross Jennings
b, *
, Casey M. Schwab
c
a
Gatton College of Business & Economics, University of Kentucky, 423FB&E, Lexington, KY, 40506, USA
b
McCombs School of Business, University of Texas at Austin, B6400, Austin, TX, 78712, USA
c
Terry College of Business, University of Georgia, 242 Brooks Hall, Athens, GA, 30602, USA
a r t i c l e i n f o
Article history:
Received 30 May 2014
Received in revised form
2 July 2015
Accepted 2 September 2015
Available online xxx
Keywords:
Employee stock options
Fair values
Disclosure quality
Complex estimates
a b s t r a c t
In this study, we exploit the unique reporting requirements for employee stock options to provide large
sample evidence on the accuracy of footnote disclosures related to a speci?c complex estimate, the fair
value of options granted. We ?rst document the frequency and magnitude of differences between (1) the
reported weighted-average fair value of options granted and (2) the calculated option fair value using the
disclosed weighted-average valuation model inputs and the Black-Scholes option pricing model. In a
sample of 23,358 ?rm-year observations between 2004 and 2011, we ?nd that 23.9 percent have re-
ported and calculated option fair values that differ by more than ten percent, and that these differences
are sticky and are frequently signi?cant as a percentage of net income. We also ?nd that fair value
differences are larger for ?rms that (1) exhibit anomalous stock option footnote disclosures that likely
result from disclosure errors, (2) have more complex and hence error-prone stock option programs, and
(3) have lower quality ?nancial reporting. Taken together this evidence is consistent with large fair value
differences that are primarily due to unintentional errors in the stock option footnote disclosures. To
document the consequences of these fair value differences, we provide evidence that errors in the re-
ported fair values prevent ?nancial statement users from using the reported values to reliably estimate
future stock option expense for many ?rms. Consistent with this result, we also ?nd that analyst forecasts
are less accurate and more disperse for ?rms with larger fair value differences.
© 2015 Elsevier Ltd. All rights reserved.
1. Introduction
As the use of fair values and other complex estimates in ?nancial
reporting has increased, regulators, the media, and researchers
have expressed concerns about the reporting and auditing of these
estimates (SEC, 2003; PCAOB, 2011; Bratten, Gaynor, McDaniel,
Montague, & Sierra, 2013; Rapoport, 2013; Grif?th, Hammersley,
& Kadous, 2015). These estimates are often accompanied by foot-
note disclosures providing the earliest information to ?nancial
statement users about the calculation of the estimates and howthe
estimates impact net income. Despite the importance of these
supporting disclosures, there is virtually no research on their
accuracy.
In this study, we conduct a comprehensive examination of
footnote disclosures related to a speci?c complex estimate, the fair
value of employee stock options granted. We focus on stock option
disclosures to exploit the unique reporting requirements for stock
options that, unlike disclosures for other estimates, require
disclosure of not only the calculation outputdthe estimated fair
value of employee stock options granteddbut also the calculation
inputs and the method of calculation. These requirements allow us
to evaluate the internal consistency of these disclosures by
comparing the disclosed fair value to a calculated fair value based
on the ?rm's disclosed inputs and the Black-Scholes valuation
*
We gratefully acknowledge helpful comments from Mark Peecher (editor), two
anonymous reviewers, Steve Baginiski, John Campbell, Preeti Choudhary, Dain
Donelson, Theodore Goodman, Jackie Hammersley, John McInnis, Laura Wang, Teri
Yohn, Yong Yu, and workshop participants at Miami University, the University of
Toronto, the 2014 FARS midyear meeting, and the 2014 AAA annual meeting. Brian
Bratten acknowledges the ?nancial support of the Von Allmen School of Accoun-
tancy and the Gatton College of Business and Economics. Ross Jennings acknowl-
edges the ?nancial support of the Deloitte & Touche Professorship of Accounting
and the McCombs School of Business. Casey Schwab acknowledges the ?nancial
support of the Terry College of Business and the J.M. Tull School of Accounting. We
also acknowledge the excellent research assistance of Philip Chung, Anne Ehinger,
Ying Huang, Jonathan Ross, and Russell Williamson.
* Corresponding author.
E-mail address: [email protected] (R. Jennings).
Contents lists available at ScienceDirect
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j ournal homepage: www. el sevi er. com/ l ocat e/ aoshttp://dx.doi.org/10.1016/j.aos.2015.09.001
0361-3682/© 2015 Elsevier Ltd. All rights reserved.
Accounting, Organizations and Society xxx (2015) 1e18
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values, Accounting, Organizations and Society (2015),http://dx.doi.org/10.1016/j.aos.2015.09.001
model. Speci?cally, we construct a measure that we refer to as the
“fair value difference” that equals the absolute value of the differ-
ence between the reported and calculated fair values, scaled by the
calculated fair value. We use this measure to investigate both the
accuracy of these disclosures and the consequences of inaccurate
disclosures. Our analyses proceed in three stages.
In the ?rst stage, we document the frequency and materiality of
“large” fair value differences (greater than ten percent). We focus
on large differences because small differences can occur when
multiple grants are issued in the same year and the inputs vary
across grants. In our sample of 23,358 ?rm-year observations be-
tween 2004 and 2011, we ?nd that 5573 observations (23.9
percent) have large differences between the reported and calcu-
lated fair values. For observations with large differences, 69.5
percent of the differences are greater than one percent of reported
income. These results suggest the potential for a signi?cant number
of material errors in a high pro?le ?nancial statement footnote.
In the second stage, we conduct analyses to determine whether
unintentional disclosure errors are the primary source of these fair
value differences. We ?rst evaluate Compustat footnote data and
uncover two anomalies in the stock option disclosure that suggest
possible errors. Speci?cally, we ?nd that 1109 ?rm-year observa-
tions (4.7 percent of the sample) disclose a reported fair value for
their options granted equal to the exercise price of the options, a
virtual impossibility without a disclosure error. We also ?nd that
1932 ?rm-year observations (10.8 percent of the 17,959 ?rm-year
observations for which we have disclosure data from the prior
year) disclose the same volatility, risk-free-rate, exercise price, or
option grant date fair value for option grants in consecutive years,
an unlikely occurrence. For both of these anomalies, the fair value
difference is larger for observations exhibiting the anomaly, sug-
gesting that disclosure errors are a likely source of at least some of
the fair value differences.
To provide further evidence that fair value differences represent
disclosure errors, we then conduct a multivariate analysis to
determine whether fair value differences are associated with the
complexity of the ?rm's stock option program and with ?rm
reporting and operating environment characteristics that suggest
low quality ?nancial reporting. We ?nd that ?rms have larger fair
value differences when they have more complex, and likely more
error-prone, stock option programs. Speci?cally, ?rms exhibit
larger fair value differences when they grant relatively more op-
tions to rank-and-?le employees, have higher rates of cancellations,
have larger changes in their employee base, split their stock during
the current year, or make more extensive use of options. We also
?nd that fair value differences are larger when ?nancial reporting
quality is lower. Speci?cally, fair value differences are larger inyears
in which stock option expense is disclosed rather than expensed
and for ?rms that have an internal control weakness, have an ac-
counting restatement, do not use a Big 4 auditor, or do not have a
chief accounting of?cer as one of its most highly compensated
executives. Finally, we ?nd that fair value differences are larger for
?rms that have less developed accounting systems or operate in a
more complex reporting environment. Speci?cally, ?rms making a
corporate acquisition in the current year, as well as smaller and
younger ?rms, exhibit larger fair value differences.
Although these results suggest that, on average, large fair value
differences result from unintentional disclosure errors, we also
consider several alternative explanations for the fair value differ-
ences that do not involve unintentional disclosure errors. Based on
an analysis of hand-collected data for 200 ?rm-year observations
with large fair value differences, we ?nd that 20 large fair value
differences are due to data entry errors in the Compustat database.
For the remaining 180 observations, we ?nd that at most 30 of the
fair value differences are potentially attributable to a combination
of (1) use of a valuation model other than the Black-Scholes model,
(2) options issued ineor out-of-the-money, (3) discounts for post-
vesting restrictions, and (4) disclosure of ranges for valuation
model inputs when midpoints are poor proxies for the weighted
averages of these inputs. Collectively, these analyses suggest that a
substantial majority of large fair value differences are likely
attributable to unintentional disclosure errors.
In our third stage, we investigate potential consequences of
inaccurate footnote disclosures by examining howthese errors map
into future share-based compensation expense and impact ana-
lysts' earnings forecasts. We ?nd that the relation between ex-
pected option expense based on reported fair values and future
reported share-based compensation expense is declining in the
absolute fair value difference. This result indicates that, on average,
reported fair values are measured with increasing error as the ab-
solute fair value difference increases. We also ?nd that the calcu-
lated fair value is positively and signi?cantly related to the future
expense after controlling for the reported fair value. This result
indicates that the calculated fair value is used to compute option
expense for many ?rms and the reported fair value is incorrect.
These results suggest that footnote disclosure errors likely impair
investors' abilities to predict future option expense. Focusing on
analysts' forecasts, we ?nd a positive and signi?cant relation be-
tween absolute fair value differences and both absolute forecast
errors and forecast dispersion. These results indicate that analysts'
forecasts are negatively affected by the stock option footnote errors
represented by the absolute fair value differences.
Taken together, the results reported in this paper provide evi-
dence that a substantial number of ?rms have errors in their stock
option footnote. As such, this study makes several contributions for
regulators, ?nancial statement users and researchers. First, for
regulators, our evidence suggests that material errors occur in stock
option footnote disclosures that result in disclosed information that
is either not relevant or not faithfully representative. This is espe-
cially important given that PCAOB guidance recommends that audit
?rms conduct the same comparison of reported and calculated fair
values that we conduct in this study (PCAOB, 2006, p. 26). Further,
these ?ndings validate concerns that “fair value determinations
based on unobservable inputs are particularly challenging for au-
ditors” (PCAOB, 2009, p. 5) and that auditors are not adequately
evaluating all of the inputs into an estimate for the collective
impact on the estimate (PCAOB, 2011; Peecher, Schwartz, &
Solomon, 2007; Grif?th et al. 2015). The fact that the errors we
identify can be detected with little effort leaves open the question
of the extent of errors in more dif?cult-to-verify disclosures of
complex estimates.
Second, for ?nancial statements users, our evidence on the ac-
curacy of the stock option footnote disclosure is important because
these disclosures provide the earliest information about the
magnitude of stock option expense in future years. Indeed, one of
the FASB's objectives for employee stock option footnote disclo-
sures is to “enable users of the ?nancial statements to under-
stand… the effect of compensation cost arising from share-based
payment arrangements on the income statement” (ASC 718-10-50-
1). Substantial differences between the disclosed and calculated fair
values that cannot be reconciled based on information provided in
the footnote leave ?nancial statement users with no guidance on
which value is a more accurate measure of the grant date fair value
and, thus, which value to use to estimate future option expense.
Third, this study contributes to prior research. Prior studies
examine either material but infrequent errors (i.e., restatements) or
general measures of ?nancial reporting quality (e.g., internal con-
trol weaknesses, accruals quality). Unlike these studies, we exploit
the unique reporting requirements for stock options to provide
large sample evidence on the incidence and materiality of errors in
B. Bratten et al. / Accounting, Organizations and Society xxx (2015) 1e18 2
Please cite this article in press as: Bratten, B., et al., The accuracy of disclosures for complex estimates: Evidence from reported stock option fair
values, Accounting, Organizations and Society (2015),http://dx.doi.org/10.1016/j.aos.2015.09.001
a common ?nancial statement disclosure that are not publicly
disclosed by the ?rm. This study also contributes to the literature
examining stock option disclosures. Unlike prior studies which
generally investigate bias in the selection of valuation model inputs
(e.g., Aboody, Barth, & Kasznik, 2006; Hodder, Mayew, McAnally, &
Weaver, 2006; Bartov, Mohanram, & Nissim, 2007; Johnston, 2006;
Choudhary, 2011) and the valuation model (Bratten, Jennings, &
Schwab, 2015), we examine the accuracy of those disclosures by
examining whether the reported stock option fair value is inter-
nally consistent with the disclosed valuation inputs and model.
Note that selection of biased inputs alone would not result in the
fair value differences we document as long as the fair value of
options granted is consistently computed using those biased inputs.
Thus, our study complements prior literature to provide a detailed
analysis of the estimation and ?nancial reporting of employee stock
option fair values.
2. The fair value difference and the likelihood of
unintentional disclosure errors
2.1. The fair value difference
ASC 718-10-50 requires ?rms to disclose the number and
weighted-average grant date fair value of options granted during
the year. Firms are also required to disclose the valuation method
(e.g., the Black-Scholes model) and the valuation model inputs used
to estimate the fair value of these options. The valuation model
inputs include the weighted-average exercise price, expected life,
expected volatility, expected dividend yield, risk-free rate, and
discount for post-vesting restrictions. To meet these disclosure
requirements, ?rms must track and report a considerable amount
of information, creating ample opportunities for error.
In this study, we use the required stock option footnote disclo-
sures to compare two alternative measures of the fair value of
employee stock options granted in the current year. The ?rst is the
weighted-average fair value of options granted as reported in the
?rm's notes to their ?nancial statements. We refer to this value as
the reported fair value (FV
Reported
). The second is the calculated fair
value based on the weighted-average valuation model inputs dis-
closed in the ?rm's notes to their ?nancial statements and the
Black-Scholes option pricing model. We refer to this value as the
calculated fair value (FV
Calculated
).
1
We then use these values to
compute a ?rm's “fair value difference” (FV
Difference
), the difference
between the ?rm's reported and calculated fair values, scaled by
the calculated fair value [(FV
Reported
e FV
Calculated
)/FV
Calculated
].
It is unlikely that these fair value differences result from pur-
poseful earnings management for several related reasons. First, to
knowingly report incorrect fair values or option model inputs in the
stock option footnote would likely be an SEC violation and risk
serious negative consequences. Second, management is likely to
derive little to no gain from knowingly reporting incorrect fair
values or option model inputs because such misreporting by itself
would not affect reported expense unless the ?rm also used the
incorrect information reported in the footnote disclosure to
compute stock option expense, a further SEC violation. Third,
fraudulently manipulating the valuation of stock options granted is
likely not even necessary given ?ndings in prior research that ?rms
are able to decrease reported option expense (and thus manage
earnings upwards) by exercising discretion when selecting both the
valuation model (Bratten et al., 2015) and valuation model inputs
(Aboody et al., 2006; Bartov et al., 2007; Choudhary, 2011; Hodder
et al., 2006; Johnston, 2006). These actions may push the bound-
aries of legitimate reporting, but fall short of illegal activity. Finally,
as we discuss below, we ?nd that the fair value differences are
skewed toward positive (expense-increasing) values, which would
permanently decrease net income since overstated stock option
expense does not later reverse through net income like most ac-
cruals. For these reasons we focus on the absolute value of FV
Dif-
ference
, which we label AbsFV
Difference
, and investigate whether these
absolute fair value differences are due to unintentional disclosure
errors or have alternative, non-error explanations.
Minor differences between the reported and calculated fair
values can occur when valuation model inputs vary across multiple
equal-weighted option grants during the year because the Black-
Scholes model is non-linear in most valuation model inputs (life,
volatility, dividend yield, and risk-free rate). When these inputs
vary across grants, the weighted-average fair value from the model
(the reported fair value) will not equal the calculated fair value
based on the weighted-average inputs (the calculated fair value).
However, as the examples we present in Appendix A demonstrate,
using weighted-average valuation inputs to compute an option fair
value is not likely to produce a fair value difference that is more
than a few percent as long as the different grants are relatively
equally-weighted. We address the potential for larger fair value
differences that can arise frommultiple grants that are not equally-
weighted in detail below.
2.2. The likelihood of unintentional disclosure errors
To meet the stock option disclosure requirements each ?rm
must successfully track multiple variables, often for multiple stock
option grants, input these variables into a complex non-linear
formula and compute and report weighted averages for the
various inputs and the outputs. The steps involved in preparing
these footnote disclosures range from simple (e.g., if the exercise
price for the option equals the closing stock price on the grant date,
?nd that price) to more complex (e.g., estimate the expected life of
an option given the previous exercise behavior of employees, the
changes in employee pro?les, the economic environment and the
terms of the current options granted). There are ample opportu-
nities for error throughout this process. For example, an accountant
preparing the footnote disclosure may compute a weighted-
average as a simple average or not correctly incorporate the effect
of a stock split in the middle of the year. Alternatively, an accoun-
tant may incorrectly report the exercise price of options granted as
the fair value of the options granted.
2
Two additional features of the ?nancial reporting process in the
stock option setting increase the likelihood of errors. First, ?rms
often engage external valuation consultants to estimate stock op-
tion fair values and other complex estimates because management
lacks the necessary expertise to perform these estimates internally.
This lack of valuation expertise can be problematic given man-
agement is still responsible for accurately preparing the footnote
disclosures related to the estimated stock option fair values. Based
on interviews of auditors and a reviewof PCAOB inspection reports,
Grif?th et al. (2015) argue that a division of knowledge between
auditors and valuation experts is a root cause of challenges arising
when auditing complex estimates because auditors do not have
1
When computing FV
Calculated
, we assume the current market price of the un-
derlying stock on the grant day is equal to the disclosed option exercise price. This
is consistent with prior research that suggests “virtually all” ?rms issue options that
are at the money (Bebchuk et al., 2002; Chang et al., 2013; Hall & Murphy, 2002).
2
We report below that many ?rms do indeed report the exercise price as the fair
value of the options granted. As further evidence of the inherent complexity in
accounting for employee stock options, a PricewaterhouseCoopers guide (PwC,
2013) on how to account for stock-based compensation is 362 pages.
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suf?cient valuation knowledge to engage in the necessary critical
analysis of management or specialist models. Similar issues likely
exist for managers who prepare the stock option disclosures and
choose to engage an external valuation consultant to assist in the
valuation of stock options rather than acquiring the requisite
knowledge to understand and perform the valuation themselves.
Second, many ?rms rely on internal spreadsheets when ac-
counting for stock options. Panko and Ordway (2005) summarize
evidence from several sources and report that spreadsheets are
ubiquitous in ?nancial reporting by U.S. ?rms. Moreover, prior
empirical studies examining spreadsheet accuracy ?nd that the
majority of spreadsheets examined have signi?cant errors. Powell,
Baker, and Lawson (2008) cite studies by KPMG and Coopers &
Lybrand in which both ?rms found that 91 percent of the spread-
sheets they examined had a signi?cant error.
3
Various strategies are available to reduce or eliminate these
errors. Indeed, testing spreadsheets is one focus of the imple-
mentation of SarbaneseOxley Act section 404 internal controls
requirements (PwC, 2004). However, studies suggest that such
systematic testing of spreadsheets is not common (Caulkins,
Morrison, & Weidenmann, 2007; Leon, Kalbers, Coster, &
Abraham, 2012). In fact, Deloitte (2009) surveyed over 3000 pro-
fessionals during a 2008 webcast on balancing spreadsheet risks
and found that 70.1 percent of respondents indicated that spread-
sheets were relied on for critical portions of the business, but only
33.9 percent indicated that their ?rm had specialized techniques to
ensure the spreadsheets were functioning properly.
In addition, PCAOB audit guidance recommends that for com-
panies using the Black-Scholes model “the auditor should verify
that the company is using the correct formula and recalculate the
fair value” (PCAOB, 2006, p. 26). Following this recommendation for
each stock option grant should help detect many unintentional
errors at the grant level. However, if this recommendation is not
also followed after combining multiple grants, unintentional errors
can still go undetected in the weighted-average footnote
disclosures.
2.3. An example
Before empirically testing the likelihood of unintentional
disclosure errors, we provide an example based on a ?rm in our
sample reporting an option fair value equal to the option's exercise
price, a likely disclosure error. In their Form 10-K for the ?scal year
ended December 31, 2010, Hughes Communications disclosed that
both the fair value of options granted and the exercise price of
options granted equaled $53.67 for 2008, $16.77 for 2009 and
$28.99 for 2010. In contrast, the calculated fair values based on the
disclosed inputs for those years equal $24.26 for 2008, $7.25 for
2009 and $11.79 for 2010, resulting in an AbsFV
Difference
greater than
100 percent in each year. It seems likely that either (1) the reported
fair value is in error and grossly overstates the fair value for options
granted during the year or (2) the exercise price is in error so that
the calculated fair value understates the fair value of the options
granted during the year.
To determine which of these two possibilities is true, we use the
reported fair values and the calculated fair values to estimate future
expense and compare these estimates with the actual expense re-
ported by Hughes Communications. Hughes' disclosures indicate
that 2008 is the ?rst year they issue stock options and that they
made one grant per year in 2008, 2009 and 2010, about four
months into the year. We assume that (a) options granted in the
current year vest over four years with two-thirds of a year occurring
in the grant year, (b) 100,500 options are granted in 2009 (net of
options retired), and (c) forfeitures in 2008 relate to options gran-
ted in 2008, forfeitures in 2009 relate half to options granted in
2008 and half to options granted in 2009, and forfeitures in 2010
relate one third to each of the current and preceding two years.
Using these assumptions and the reported fair values, we estimate
option expense for 2008, 2009, and 2010 to be $4.9 million, $7.7
million, and $10.4 million, respectively. These estimates are much
greater than the actual stock option expense reported by Hughes of
$2.0 million, $3.5 million, and $4.3 million for these three years. In
contrast, using these same assumptions and the calculated fair
values, we estimate option expense for 2008, 2009, and 2010 to be
$2.2 million, $3.5 million, and $4.6 million, respectively. These es-
timates are very close to those reported by Hughes for their actual
option expense, and indicate that Hughes used the calculated value,
not the reported value, to compute future option expense.
4
A ?nancial statement user relying on the reported fair value of
options granted to estimate stock option expense would have had
an error relative to a forecast based on the calculated fair value of
$2.7 ($5.8) million in 2008 (2010), which was nearly 30 (25) percent
of their net income of $9.3 ($23.0) million.
5
This analysis indicates
that the reported fair values in Hughes stock option footnotes are
not consistent with reported stock option expense, and that a
?nancial statement user relying on reported stock option fair values
would be misled.
3. The sample and descriptive statistics
Our sample is drawn from the Compustat database for ?scal
years 2004e2011 and includes all ?rms incorporated in the United
States with available data to compute the fair value difference
(FV
Difference
). We begin in 2004 because this is the ?rst year for
which Compustat contains detailed information on the weighted-
average fair value of employee stock option grants during the cur-
rent year as well as the weighted-average inputs to the Black-
Scholes pricing model used to value the current year's option
grants.
6
This provides us with an initial sample of 25,439 obser-
vations. We then require the additional explanatory variables used
in our multivariate analysis, resulting in our main sample of 23,358
?rm-year observations. For some of our analyses, we also require
lagged Compustat data or analyst forecast data from I/B/E/S,
reducing our sample for these analyses. The sample construction is
detailed in Table 1.
Panel A of Table 2 reports descriptive statistics for the reported
fair value (FV
Reported
), the calculated fair value (FV
Calculated
), the fair
value difference (FV
Difference
), the absolute value of the fair value
difference (AbsFV
Difference
), and measures of the materiality of
3
To con?rm that spreadsheets are used to prepare stock option footnote dis-
closures, we asked ?ve senior partners at four major audit ?rms how commonly
spreadsheets are used to prepare stock option footnote disclosures. Three partners
responded “very common,” one responded “virtually universal,” and one responded
“common.”
4
The Hughes example provides anecdotal evidence of a disclosure error. This
example is unique because Hughes has a short history of option grants and clearly
discloses both the timing of the grants and the subsequent actual stock option
expense. Our ability to perform this calculation is much more limited for the ma-
jority of ?rms that have long-standing option programs and do not separately
disclose stock option expense.
5
In 2009, the forecast error based on the calculated value is $4.2 million less than
the forecast error based on the reported fair value, and Hughes reported a loss of
$51.6 million. As a percentage of assets, these forecast errors are 0.24 percent, 0.35
percent and 0.45 percent in 2008, 2009, and 2010, respectively.
6
The Black-Scholes inputs necessary to compute the calculated value of options
granted include life (Compustat OPTLIFE), volatility (OPTVOL), dividend yield
(OPTDR), risk-free rate (OPTRFR), and the exercise price (OPTPRCGR), which we
assume to be equal to the market price of the underlying stock on the grant date.
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AbsFV
Difference
. The distribution of the signed difference (FV
Difference
) is
centered near zero (median ¼ À0.001) but also includes many fair
value differences far from zero. In addition, the mean FV
Difference
(0.055) is signi?cantly positive (p-value < 0.01, untabulated), indi-
cating the distribution is skewed toward positive values. As dis-
cussed above, this distribution is more consistent with
unintentional error than managerial manipulation because manip-
ulation to lower option expense would result in a FV
Difference
distri-
bution skewed toward negative values (i.e., FV
Reported
< FV
Calculated
).
Panel A also reports that the mean AbsFV
Difference
is 11.9 percent.
As a point of reference, this is much larger than the mean error
reported in prior research in auditing. For example, Durney, Elder
and Glover (2014) examine 160 post-SOX audit sampling applica-
tions and report a mean error (computed as the absolute difference
between management's reported value and the auditor's proposed
value, scaled by management's reported value) of 0.2 percent. They
also report a mean error for ten studies conducted prior to SOX of
3.08 percent.
We also report in Table 2 that 23.9 percent of ?rm-year obser-
vations have an AbsFV
Difference
greater than ten percent. In some of
our analyses, we divide the sample into two groups: those with
AbsFV
Difference
greater than ten percent (the “high group”) and those
with AbsFV
Difference
less than ten percent (the “low group”). We
focus on ?rm-year observations with AbsFV
Difference
greater than ten
percent because these differences are more likely due to errors than
to some alternative explanation. If we lower (raise) the threshold
for “large” differences to ?ve (20) percent, then AbsFV
Difference
is
“large” for 33.2 (15.4) percent of the ?rms in our sample.
We next evaluate the materiality of these absolute differences.
Materiality
Income
(Materiality
Asset
) equals the absolute value of the
annual difference between the reported and calculated fair values
multiplied by the number of options granted, scaled by the absolute
value of net income (scaled by total assets). Average Materi-
ality
Income
(Materiality
Asset
) equals 7.9 (0.7) percent. Moreover,
Materiality
Income
(Materiality
Asset
) exceeds one percent for 24.6 (6.7)
percent of the sample. These statistics suggest that AbsFV
Difference
is
material for many ?rms.
Panel B of Table 2 presents univariate statistics for materiality
after partitioning the sample into high and lowAbsFV
Difference
groups.
Materiality
Income
(Materiality
Asset
) is greater than one percent for 69.5
(25.3) percent of ?rm-year observations in high AbsFV
Difference
group
relative to 10.5 (0.8) percent of observations in the low group, and
greater than?ve percent for 37.0(7.2) percent of observations inhigh
group relative to 2.4 (0.1) percent in the low group.
Panel C of Table 2 presents the distribution of AbsFV
Difference
over
time. The percentage of observations with AbsFV
Difference
greater
than ten percent declines from 32.6 percent in 2004 to 17.2 percent
in 2011. The largest decline, from 29.6 percent in 2005 to 22.6
percent in 2006, coincides with recognition of the fair value of
options granted on the income statement. The last two columns of
Panel C present the percentage of observations with an AbsFV
Dif-
ference
greater than one percent of net income for the high and low
AbsFV
Difference
groups, respectively. For the high (low) group this
percentage declines from 77.7 (16.6) percent in 2004 to 67.9 (8.3)
percent in 2011. Despite this decrease, a substantial portion of the
sample still exhibits a material difference between reported and
calculated fair values in the ?nal year of our study period.
Finally, we examine whether the large fair value differences are
one-time events or recur through time for individual companies
using a subsample (12,052 ?rm-year observations) with data
available to compute AbsFV
Difference
for three consecutive years. The
?rst column of panel D reports that for this sample 22.3 percent of
the ?rm-year observations in the ?rst year are in the high AbsFV-
Difference
group and 41.4(21.8) percent of these observations are still
in the high group in the second year (both the second and third
years). Random assignment of ?rms to the high and low groups in
subsequent years based on the frequency in the current year would
produce 22.3 percent of the current-year high group still in the high
group in the second year, and 5.0 percent (0.223 Â0.223) still in the
high group in both the second and third years. Thus, we observe
nearly twice the expected frequency in the second year and more
than four times the expected frequency in the third year.
7
The
second and third columns of panel D present results separately for
observations with positive and negative fair value differences in the
?rst year. The results are very similar to those reported for the
combined sample, with somewhat greater stickiness for positive
fair value differences.
Taken together, these results suggest that large fair value differ-
ences are not randomevents, but recur withthesame signacross time
for many ?rms. In the next section we investigate whether the fair
value differences are likely due to unintentional reporting errors
arising from complex option programs, lower quality ?nancial
reporting, and challenging accounting environments. We also inves-
tigate alternative potential explanations for fair value differences that
do not necessarily suggest the presence of disclosure errors.
Table 1
Sample selection.
Data restrictions N Used in table(s)
Primary Sample
Starting Compstat sample of U.S. Firms from ?scal years 2004e2011 with data to compute AbsFV
Difference
(i.e., FVOPTGR, OPTLIFE, OPTVOL, OPTDR, OPTRFR, OPTPRCGR)
25,439
Less ?rms without data to compute deteriminants of AbsFV
Difference
À2081 23,358 2, 3, 4
Future share-based compensation expense sample
Starting sample (i.e., Primary sample) 23,358
Less ?rms without data to compute share-based compensation expense À16 23,342
Less ?rms without AbsFV
Difference
in year t-1 À5504 17,838 7
Less ?rms without AbsFV
Difference
in year t-2 À4557 13,281 7
Analyst forecast accuracy and dispersion sample
Starting sample (i.e., Primary sample) 23,358
Less pre-SFAS 123R observations À6563 16,795
Less ?rms without I/B/E/S data to compute current and lagged forecast errors À7496 9299
Less ?rms without data to compute additional control variables À2672 6627 8
Less ?rms without I/B/E/S data to compute current and lagged forecast dispersion À887 5740 8
Detailed variable de?nitions are presented in Appendix C.
7
We also estimated the “persistence” of absolute fair value differences by
regressing ?rms' AbsFV
Difference
in year t on their AbsFV
Difference
in year t-1. The co-
ef?cient on the prior-year AbsFV
Difference
is positive and signi?cant (b ¼ 0.3338; p-
value < 0.01), providing evidence that AbsFV
Difference
exhibits some persistence from
one year to the next.
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4. Do large fair value differences result from disclosure
errors?
In this section, we conduct a variety of analyses to determine
whether the fair value differences documented above appear to
result from disclosure errors.
4.1. Direct evidence of disclosure errors
The most direct evidence we provide comes fromtwo anomalies
in the stock option footnote itself that suggest a disclosure error.
First, we observe that 1109 ?rm-year observations (4.7 percent of
the sample) disclose a reported fair value equal to the exercise price
of the options granted. While not mathematically impossible, the
option fair value will not equal the exercise price unless one or
more of the other model inputs are both incorrect and highly un-
usual. For example, in the Hughes Communications example dis-
cussed above, both of these values could be correct only if the
weighted-average volatility was 340 percent, the expected life
was 230 years, or the weighted-average risk-free rate was 500
percent. As such, this equality suggests an incorrect transfer of data
from a spreadsheet or other source to the footnote. The mean
Table 2
Univariate statistics: the magnitude and materiality of fair value differences.
Panel A: basic univariate statistics
Variable N Mean P5 P10 Q1 Median Q3 P90 P95
FV
Reported
23,358 7.369 0.460 0.930 2.360 5.260 9.790 15.390 19.400
FV
Calculated
23,358 7.180 0.456 0.905 2.304 5.086 9.579 15.023 18.960
% of sample % of sample
FV
Difference
FV
Difference
Variable N Mean P5 P10 Q1 Median Q3 P90 P95 10%
FV
Difference
23,358 0.055 À0.199 À0.095 À0.016 À0.001 0.018 0.217 0.549 9.6% 14.2%
% of sample
AbsFV
Difference
Variable N Mean P5 P10 Q1 Median Q3 P90 P95 >10%
AbsFV
Difference
23,358 0.119 0.001 0.001 0.004 0.017 0.091 0.326 0.578 23.9%
% of sample % of sample
Materiality Materiality
Variable N Mean P5 P10 Q1 Median Q3 P90 P95 >1% >5%
Materiality
Income
23,358 0.079 0.000 0.000 0.000 0.001 0.010 0.056 0.151 24.6% 10.7%
Materiality
Asset
23,358 0.007 0.000 0.000 0.000 0.000 0.001 0.005 0.016 6.7% 1.8%
Panel B: materiality univariate statistics in high and low AbsFV
Difference
subsamples
Variable AbsFV
Difference
>¼ 10% subsample AbsFV
Difference
1% >5% N Mean Median >1% >5%
Materiality
Income
5574 0.298 0.028 69.5% 37.0% 17,784 0.010 0.001 10.5% 2.4%
Materiality
Asset
5574 0.028 0.002 25.3% 7.2% 17,784 0.001 0.000 0.8% 0.1%
Panel C: absolute fair value differences (AbsFV
Difference
) over Time
Year N Mean P5 P10 Q1 Median Q3 P90 P95 Full sample AbsFV
Diff
>¼10% AbsFV
Diff
10% >1% >1%
2004 2902 0.194 0.001 0.001 0.005 0.029 0.165 0.487 0.870 32.6% 77.7% 16.6%
2005 3481 0.147 0.001 0.002 0.006 0.026 0.131 0.420 0.707 29.6% 74.9% 14.1%
2006 3259 0.110 0.001 0.001 0.005 0.016 0.081 0.312 0.516 22.6% 69.1% 11.5%
2007 3169 0.113 0.001 0.001 0.005 0.016 0.087 0.305 0.545 23.1% 69.1% 9.8%
2008 2945 0.111 0.001 0.001 0.004 0.018 0.088 0.307 0.572 23.2% 62.0% 8.9%
2009 2710 0.104 0.001 0.001 0.003 0.014 0.076 0.303 0.539 21.8% 62.1% 7.2%
2010 2566 0.081 0.000 0.001 0.003 0.011 0.052 0.223 0.416 17.8% 63.8% 7.3%
2011 2326 0.073 0.000 0.001 0.003 0.011 0.050 0.211 0.402 17.2% 67.9% 8.3%
All Years 23,358 0.119 0.001 0.001 0.004 0.017 0.091 0.326 0.578 23.9% 69.5% 10.5%
Panel D: stickiness of fair value differences in subsample with three consecutive years of data availability (N ¼ 12,052)
Large absolute diff. Large positive diff. Large negative diff.
AbsFV
Difference
> 10% FV
Difference
> 10% FV
Difference
< À10%
% of subsample with large differences in the ?rst year 22.3% 10.7% 11.6%
% of ?rst-year large differences with a large difference in the second year 41.4% 51.2% 32.3%
% of ?rst-year large differences with a large difference in the second and third year 21.8% 23.5% 13.8%
The sample includes ?rm-year observations from 2004 to 2011 with suf?cient disclosure information to re-calculate the fair value of stock options granted, and to estimate
Equation (1). FV
Difference
equals the difference between the reported (FV
Reported
) and calculated (FV
Calculated
) fair value of stock options granted, scaled by the calculated fair value
(FV
Calculated
). FV
Reported
equals OPTFVGR as reported by Compustat. FV
Calculated
is the calculated fair value based on the Black-Scholes valuation model and the disclosed valuation
model inputs reported by Compustat. AbsFV
Difference
equals the absolute value of FV
Difference
. Materiality
Income
(Materiality
Asset
) equals the ratio of absolute value of the difference
between the reported and calculated stock option fair values multiplied by the number of option granted to net income (total assets) [Abs(FV
Reported
e FV
Calculated
)*# Options
Granted/Net Income] ([Abs(FV
Reported
- FV
Calculated
)*# Options Granted/Assets]). Panel D is limited to a subsample of ?rms for which there are at least three consecutive ?rm-
year observations.
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absolute fair value difference is 59.3 (8.9) percent for observations
for which the reported fair value equals (does not equal) the ex-
ercise price. These means are signi?cantly different (p-
value < 0.01).
Second, among 17,959 ?rm-year observations with available
data, we observe that 1932 observations (10.8 percent of this sub-
sample) exhibit a “repeat disclosure” in which they disclose the
same volatility, risk-free rate, exercise price, or grant date fair value
for option grants in consecutive years. While it is not impossible for
these values to be the same from one year to the next, these values
are generally expected to vary from year to year, so a repeated
disclosure for one of these values may indicate that a value was not
properly updated. For observations with (without) a repeat
disclosure, the mean absolute fair value difference is 13.0 percent
(9.5 percent). These means are signi?cantly different (p-
value