Do firms understate stock option-based compensation expense disclosed under SFAS 123?

Abstract

Focusing on the four key option pricing model inputs—expected option life, expected stock price volatility, expected dividend yield, and the risk-free interest rate for the expected life of the option—this study finds that firms understate option value estimates and, thus, stock-based compensation expense disclosed under SFAS 123. As predicted based on incentives and opportunities for management to understate SFAS 123 expense, the understatement of option value estimates is increasing in proxies for the magnitude of the expense, is greater for firms with weaker corporate governance, and, to a lesser extent, is increasing in the excessiveness of executive pay. The findings are strongest for the expected option life and expected stock price volatility input assumptions, consistent with firms’ greater latitude in determining these inputs. We find weaker evidence of understatement associated with the expected dividend yield assumption, and none for the interest rate assumption, consistent with these inputs being less amenable to discretion. Taken together, our findings raise some concern that the exercise of management discretion adversely affects the overall reliability of SFAS 123 expense.

The objective of this study is to determine whether firms understate stock-based compensation expense that is disclosed but not recognized under Statement of Financial Accounting Standards (SFAS) No. 123 (Financial Accounting Standards Board, FASB, 1995, hereafter SFAS 123 expense). SFAS 123 expense relates to employee compensation in the form of stock options. It is based on estimates of the grant-date values of options granted to employees, which depend on expectations about the future. Although SFAS 123 provides guidance relating to factors firms should consider in making these estimates, substantial opportunity for managerial discretion remains. We focus on the key inputs to option value estimates—assumptions of expected option life from grant to exercise and expected stock price volatility, expected dividend yield, and the risk-free interest rate for the expected life of the option. SFAS 123 requires disclosure of these assumptions, which permits us to investigate whether managerial discretion reflected in the assumptions varies predictably with incentives and opportunity for firms to understate SFAS 123 expense.

We identify two incentives for firms to understate SFAS 123 expense and, thus, option value estimates. The first relates to increasing investors’ perceptions of the firm’s profitability. Prior research and anecdotal evidence are consistent with users of financial statements viewing SFAS 123 expense as an expense of the firm. If, consistent with this view, managers believe that understating SFAS 123 expense will cause investors to perceive profitability to be higher than they otherwise would, firms have incentives to understate it. The second relates to decreasing any perceived excessiveness of compensation paid to the firm’s executives. The executive compensation literature documents that managers often attempt to minimize perceptions that their compensation, particularly that related to stock options, is excessive. Thus, we predict that the understatement of firms’ disclosed option value estimates increases with the magnitude of stock option-based compensation expense and the perceived excessiveness of executive pay. We also consider management’s opportunity to understate SFAS 123 expense by considering the strength of the firm’s corporate governance structure. We predict that firms with weaker corporate governance have more understatement of disclosed option value estimates.

Our first set of tests focuses on determining whether proxies for firms’ incentives and opportunity to understate SFAS 123 expense can explain firms’ disclosed option value estimates, after controlling for an estimate of option values that we calculate using option pricing model inputs we determine following the guidelines in SFAS 123. Differences between firms’ disclosed option value estimates and our calculated option values arise only from differences between firms’ disclosed input assumptions, which are potentially subject to discretion, and the input assumptions we determine, which are not. Detecting a significant negative relation between disclosed option values and our experimental variables indicates that the understatement of option value estimates and, thus, SFAS 123 expense is larger for firms with greater incentives and opportunity to do so.

Our proxy for the magnitude of stock option-based compensation expense is the number of options granted during the year multiplied by our calculated option value, deflated by number of shares outstanding. Our proxy for excessive executive pay is, following prior research, the residual from a regression of Chief Executive Officer (CEO) annual compensation on proxies for firm size, performance, growth, risk, and industry membership. Our proxy for corporate governance is based on the governance score compiled by the Investor Responsibility Research Center (IRRC).

To implement our tests, we hand collect disclosures relating to stock option-based compensation for firms in the Standard and Poors (S&P) 500, S&P 400 mid-capitalization, and S&P 600 small-capitalization indices. We collect option pricing model inputs used by the firm in estimating the value of its granted options, the resulting option value estimates, and other items related to the firm’s employee stock options. Our sample comprises 3,368 firm-year observations from 1996 to 2001 with all of the data we require for our tests.

We find that firms’ disclosed option value estimates significantly understate the option values that we calculate. As predicted, we also find that the understatement increases with our proxies for the magnitude of stock option-based compensation expense and weaker corporate governance. These findings indicate that the extent to which firms understate option value estimates through their combined discretion in assumed expected option life, expected stock price volatility, expected dividend yield, and the risk-free interest rate is larger for firms that have greater incentives and opportunity to do so.

Our second set of tests focuses on determining which of the four option pricing model inputs are associated with firms’ understatement of option value estimates. For each input, we calculate option value estimates using the assumption we determine for that input and the firms’ disclosed assumptions for the other three inputs. Thus, differences between disclosed option values and our calculated option values arise only from differences between the particular disclosed input assumption, which is potentially subject to discretion, and the input assumption we determine, which is not.

For expected option life, we find a significant association between the understatement of option value estimates and the magnitude of stock option-based compensation expense, perceived excessiveness of executive pay, and weaker corporate governance. For expected stock price volatility, we find a significant association for the magnitude of stock option-based compensation expense and weaker corporate governance. For expected dividend yield, we find a significant association only for corporate governance; for the interest rate assumption, we find no association between the understatement of option value estimates and our experimental variables.

The stronger findings for expected option life and expected volatility are consistent with firms’ having latitude in determining these input assumptions. The weaker findings for expected dividend yield and the interest rate assumption are not unexpected given that the ability of firms to manage these two input assumptions is limited by the existence of publicly available benchmarks for determining them. Benchmarks for expected option life and expected stock price volatility are less well established, making understating these input assumptions a potentially more fruitful way of understating SFAS 123 expense.

Results from additional analyses reveal corroborating inferences. First, we find identical inferences when we focus on whether our experimental variables explain the difference between the disclosed option value and the option value we calculate. Second, we find identical inferences when we focus on the input assumptions themselves, rather than the resulting estimated option value. Third, we find identical inferences when we use the number of options granted as an alternative proxy for stock option-based compensation expense.

The paper proceeds as follows. The next section summarizes the financial reporting for employee stock option-based compensation, and Sect. 3 discusses firms’ incentives and opportunity to understate SFAS 123 expense. Section 4 outlines the research design and Sect. 5 describes the data and descriptive statistics. Section 6 presents our findings and Sect. 7 concludes.

1 Financial reporting for stock option-based compensation

Accounting for stock option-based compensation is specified in Accounting Principles Board Opinion (APB) No. 25 (APB, 1973) and SFAS 123. Under APB 25, stock option-based compensation expense is based on the difference at the measurement date between the stock price and option exercise price. Because for most fixed option grants the exercise price equals the stock price at the date of grant, the expense under APB 25 typically equals zero. Under SFAS 123, the expense is calculated based on the option’s fair value at grant date, and is not adjusted for subsequent changes in value. SFAS 123 expense is grant-date option value multiplied by the number of granted options, amortized over the vesting period. To capture the fact that some employees terminate employment before the end of the vesting period, firms can either recognize forfeitures as they occur, or use the number of options expected to vest.

SFAS 123 permits firms to apply the measurement provisions in APB 25 or SFAS 123; almost all firms apply APB 25. ¹ If a firm measures the expense under APB 25, SFAS 123 requires disclosure of pro forma net income, which is what net income would have been had SFAS 123 expense been recognized. Other required disclosures include the number of options granted, vesting period, estimated value of options granted, and the inputs the firm used to estimate option values, i.e., option exercise price, expected option life, expected stock price volatility, expected dividend yield, and the risk-free interest rate for the expected option life. ²

In estimating grant date option values, SFAS 123 requires use of the expected life of the option, rather than its contractual term, because employee stock options are nontransferable and, thus, employees systematically exercise them early (Huddart & Lang, 1996). SFAS 123 states that in estimating expected option life, a firm should consider the option vesting period, the average length of time similar grants have been outstanding, and expected stock price volatility. In estimating expected stock price volatility, a firm should consider historical volatility for the most recent period that is commensurate with expected option life. In estimating expected dividends, a firm should consider historical dividends, and its expectations about changes in dividends over the expected option life. The risk-free interest rate is to be the implied yield currently available on zero-coupon U.S. government issues with a remaining term equal to the expected option life.

Because option value estimates depend on expectations about the future, SFAS 123 creates an opportunity for the exercise of management discretion. SFAS 123 states that expectations are to be based on past experience, modified to reflect ways in which currently available information indicates the future is reasonably expected to differ from the past. Despite guidance in SFAS 123 relating to factors firms should consider in making these assumptions, significant room for discretion remains. In particular, estimated option values depend on assumptions of expected option life from grant to exercise, future stock price volatility, and future dividends, and the risk-free interest rate. Moreover, there is no ex post verification of the grant-date option values used in the calculation of SFAS 123 expense. That is, unlike for other accruals, there is no mechanism in the accounting system that subsequently reveals whether the option value estimates are reasonable or adjusts them for errors in their estimation. This susceptibility to discretion has raised concerns that SFAS 123 expense is not reliably estimable. ³

The accounting treatment of stock option-based compensation has been one of the most controversial in the FASB’s history and received further attention following the recent wave of accounting scandals and the collapse of the stock-compensation-intensive technology sector. In 2004, the FASB revisited SFAS 123 and amended it to require recognition of stock-based compensation expense (FASB, 2004). In the same year, the International Accounting Standards Board issued a similar standard (IASB, 2004). Despite the considerable attention to stock option-based compensation in recent years, there is little evidence on how management discretion affects the reliability of the expense disclosed under SFAS 123. ⁴

2 Incentives and opportunity to understate SFAS 123 expense

Our main research question is whether firms understate SFAS 123 expense by understating option value estimates. We identify two incentives for firms to do so. The first relates to increasing investors’ perceptions of the firm’s profitability. Even though SFAS 123 expense is not recognized, prior research finds evidence consistent with financial statement users viewing SFAS 123 expense as an expense of the firm. Because SFAS 123 expense relates to employee compensation, firms’ operating income can be overstated if the expense is not included. ⁵ In particular, Aboody (1996) finds a significant negative relation between share price and researcher-estimated values of outstanding employee stock options, and Aboody et al. (2004a) finds a significant negative relation between share prices and SFAS 123 expense. To the extent managers believe that understating SFAS 123 expense increases their firms’ perceived profitability, they have incentives to do so. ⁶ Such incentives could be related to equity valuation effects associated with SFAS 123 expense or to implicit contracts based on pro forma net income. ⁷ Thus, we predict that the understatement of firms’ disclosed option value estimates increases with the magnitude of stock option-based compensation expense.

Our directional prediction differs from many other earnings management studies that predict some firms have incentives to decrease earnings and, therefore, to increase expenses. These studies typically focus on accounting-based contractual provisions that provide incentives to decrease earnings in particular circumstances. However, underlying these earnings-decreasing predictions typically is the accruals-reversal feature of accounting. With accruals-reversal, exercising discretion to decrease earnings in one period results in increased earnings in a subsequent period. For example, managers with nonlinear cash bonus plans may have incentives to maximize their compensation by selecting earnings-decreasing discretionary accruals in the current period, knowing that such discretionary accruals will reverse in subsequent periods, thereby increasing earnings in those periods (e.g., Healy, 1985).

The accruals-reversal feature of accounting is not present in the case of SFAS 123 expense. Unlike for other accruals, grant-date option value estimates are not subsequently adjusted for any discretion exercised in their estimation; once grant-date option values are determined, they are not changed in subsequent periods. Thus, exercising discretion in estimating option value estimates cannot be used to shift income across periods. ⁸ As a consequence, management incentives identified in prior research to decrease earnings do not apply to SFAS 123 expense. For example, without the prospects of a subsequent earnings reversal, the incentives for managers to understate earnings in response to nonlinear bonus plans are essentially nullified.

The second incentive for firms to understate SFAS 123 expense relates to decreasing perceived excessiveness of executive pay. The executive compensation literature finds that although managers make financial reporting and disclosure decisions that increase their compensation (e.g., Aboody & Kasznik, 2000; Healy, 1985), they also attempt to minimize investors’ perception of its magnitude. ⁹ Murphy (1999) surveys the executive compensation literature and notes that higher perceived pay levels impose costs on executives by inviting scrutiny and criticism from the media, labor unions, institutional investors, and shareholder groups. Some of these costs are non-pecuniary and some are pecuniary, e.g., an increased likelihood of employment termination or reduced pay in future periods. These costs likely are greater for executives whose compensation is perceived as excessive. ¹⁰

Executives whose compensation could be perceived as excessive likely are more concerned about attracting media and investor attention if their firms disclose high levels of SFAS 123 expense. Relatedly, Dechow, Hutton, and Sloan (1996) finds a significant relation between the use of stock options in top executive compensation and the likelihood the firm submitted a comment letter opposing the FASB’s proposal to recognize SFAS 123 expense. This proxy is the primary variable explaining firms’ positions on the proposal. Thus, we expect that the extent to which firms understate SFAS 123 expense increases in the perceived excessiveness of executive pay.

We will not find evidence that firms understate SFAS 123 expense if managers do not believe that understating the expense will either increase perceived firm profitability or decrease the perceived excessiveness of executive pay. Managers might believe that investors and other users of the financial statements do not view SFAS 123 expense as an expense of the firm, or ignore it. Managers also might believe that financial statement users see through the effects of exercised discretion. ¹¹ Finally, as with all financial statement amounts, SFAS 123 expense is subject to audit, regulatory enforcement, and scrutiny by investor groups, resulting in costs associated with managing it. Although it is difficult to quantify these costs, we presume firms do not have unlimited opportunity to manage option value estimates. Therefore, we will not find evidence that firms understate the SFAS 123 expense if the cost of doing so exceeds any potential benefits.

To capture some of the cross-sectional variation in firms’ opportunity to manage financial statement amounts, we consider the relation between the understatement of option value estimates and the firm’s corporate governance. We expect that firms with weaker corporate governance have more opportunity to understate option values. This prediction is consistent with Dechow, Sloan, and Sweeney (1996), which finds that firms are more likely to manipulate earnings, as evidenced by SEC accounting enforcement actions, if they have weak corporate governance. It also is consistent with Klein (2002), which shows that boards of directors that are structured to be more independent of the CEO are more effective in monitoring financial accounting decisions.

3 Research design

Our first set of tests focuses on determining whether our proxies for firms’ incentives and opportunity to understate SFAS 123 expense explain firms’ disclosed option value estimates, after controlling for calculated option values that are not subject to discretion. In particular, we base our inferences on the following equation:

$$ \begin{aligned} \hbox{OPTVAL}_{it} &= \sum\limits_{N=1}^{33}{\alpha_{0N}\hbox{INDUSTRY}_{\rm Nit}} + \sum\limits_{Y=1996}^{2001}{\alpha_{0Y}\hbox{YR}_{Yit}} + \alpha_1 \hbox{OPTVAL}\_\hbox{CALC}_{it} \\ & \beta_1 \hbox{COMPX}_{it} +\beta_2 \hbox{RESCOMP}_{it} + \beta_3 \hbox{GOV}_{it} + K^{*} \hbox{CONTROLS}_{it} +\varepsilon_{1{it}} . \end{aligned} $$

(1)

OPTVAL is the estimated value of each option granted by the firm, as disclosed under SFAS 123. OPTVAL_CALC is an option value estimate we calculate using the Black and Scholes (1973) option pricing formula based on option pricing model inputs that we determine, as described below. Because OPTVAL is based on firms’ expectations of option life, future stock price volatility, and future dividend yield, and the risk-free interest rate over the expected option life, it reflects any discretion firms exercise in determining these inputs. In contrast, OPTVAL_CALC is not affected by discretion. Thus, estimating (1) permits us to test whether the effects of discretion in firms’ inputs are associated with incentives and opportunity to understate SFAS 123 expense, as reflected in our experimental variables described below, COMPX, RESCOMP, and GOV. CONTROLS is a vector of control variables, which also are described below. INDUSTRY _N (YR _Y ) is an indicator variable that equals one if the firm is in industry N (the observation is from year Y), and zero otherwise. Subscripts i and t denote firms and years. ¹²

Our proxy for the magnitude of stock option-based compensation expense is COMPX, the number of options granted during the year multiplied by OPTVAL_CALC and deflated by shares outstanding at the end of the year. We do not use SFAS 123 expense itself as the proxy because it is a function of the disclosed option value estimates, which are the focus of our tests. Our proxy for excessive executive pay is RESCOMP. Following Murphy (1996), Yermack (1998), and Baker (1999), RESCOMP is the residual from a regression of total annual CEO compensation on proxies for firm size, performance, growth, risk, and industry membership, as described in the Appendix. Our proxy for corporate governance is based on the governance score compiled by the IRRC. The IRRC score is based on 23 corporate governance provisions that measure shareholders’ rights (see Gompers, Metrick, & Ishii, 2003). GOV is an indicator variable that equals one if the firm’s IRRC governance score is above the sample median, i.e., with weaker corporate governance, and zero otherwise. ¹³ We predict that the coefficients on COMPX, RESCOMP, and GOV are negative.

We estimate OPTVAL_CALC using proxies for the four key option pricing model inputs, following the guidelines outlined in SFAS 123. In particular, in place of the firm’s disclosed expected volatility assumption, VOL, which is an input for the disclosed option value estimate, OPTVAL, we use historical volatility estimated over a period equal to expected option life, VOL_HIST. SFAS 123 states that when determining expected volatility, a firm should consider historical volatility for the most recent period that is commensurate with expected option life. Similarly, in place of the firm’s disclosed expected dividend assumption, DIV, we use dividend yield measured over the prior year, DIV_HIST; SFAS 123 states that in estimating future dividends, firms should consider its dividend yield history. In place of the firm’s interest rate assumption, INT, we use the grant-year average yield on zero coupon U.S. Treasury Bills with a term equal to expected option life, INT_HIST, as suggested by SFAS 123.

In place of the firm’s expected option life assumption, LIFE, we use LIFE_PRED, the predicted value from a regression of LIFE on four instrumental variables. The first is the option vesting period. SFAS 123 states that expected option life should depend on the vesting period. The next two are the number of options cancelled during the year deflated by the sum of options outstanding at the end of the year and options cancelled during the year, and the number of options exercised during the year deflated by the sum of options outstanding at the end of the year and options exercised during the year. SFAS 123 states that a firm should consider the average length of time similar grants have been outstanding in the past. ¹⁴ The fourth is the percent of options granted to the top five executives. We expect that such options have longer expected lives than do options granted to other employees. ¹⁵

We use an instrumental variables approach for LIFE because there is no single proxy that captures expected option life well. The advantage of using an instrumental variables approach is that multiple dimensions of expectations can be taken into account. The disadvantage is that mean differences between the disclosed amounts and amounts not subject to discretion are not preserved. As evidenced by the correlation coefficients reported in Table 2, for the other three inputs, VOL, DIV, and INT, highly correlated single-variable proxies are available. Thus, we use them rather than using an instrumental variables approach.

Our second set of tests focuses on determining which of the option pricing model inputs are associated with firms’ incentives and opportunity to understate SFAS 123 expense. We base our inferences on estimating four versions of (1), one for each of the inputs, LIFE, VOL, DIV, and INT. In particular, for each input, we calculate OPTVAL_CALC^INPUT using the assumption we determine for the input in question and the disclosed assumptions for the other three inputs. For example, for LIFE, we calculate OPTVAL_CALC^LIFE using LIFE_PRED, VOL, DIV, and INT. For VOL, we calculate OPTVAL_CALC^VOL using VOL_HIST, LIFE, DIV, and INT. Thus, differences between OPTVAL and OPTVAL_CALC^INPUT reflect only differences between the particular disclosed input assumption, which is potentially subject to discretion, and the input assumption we determine, which is not.

In particular, we estimate the following equations:

$$ \begin{aligned} \hbox{OPTVAL}_{it} &= \sum\limits_{N=1}^{33}{\alpha_{0N}\hbox{INDUSTRY}_{Nit}}\,+\,\sum\limits_{Y=1996}^{2001}{\alpha_{0Y}\hbox{YR}_{Yit}}\,+\,\alpha_1 \hbox{OPTVAL}\_\hbox{CALC}^{\rm LIFE}_{it} \\ & \beta_1 \hbox{COMPX}_{it}\,+\,\beta_2 \hbox{RESCOMP}_{it}\,+\,\beta_3 \hbox{GOV}_{it}\,+\,K^{*} \hbox{CONTROLS}^{\rm LIFE}_{it}\,+\,\varepsilon_{2ait}. \\ \end{aligned} $$

(2a)

$$ \begin{aligned} \hbox{OPTVAL}_{it} &= \sum\limits_{N=1}^{33}{\alpha_{0N}\hbox{INDUSTRY}_{Nit}}\,+\,\sum\limits_{Y=1996}^{2001}{\alpha_{0Y}YR_{Yit}}\,+\,\alpha_1 \hbox{OPTVAL}\_\hbox{CALC}^{\rm VOL}_{it} \\ & \beta_1 \hbox{COMPX}_{it}\,+\,\beta_2 \hbox{RESCOMP}_{it}\,+\,\beta_3 \hbox{GOV}_{it}\,+\,K^{*} \hbox{CONTROLS}^{\rm VOL}_{it}\,+\,\varepsilon_{2bit}. \\ \end{aligned} $$

(2b)

$$ \begin{aligned} \hbox{OPTVAL}_{it} &= \sum\limits_{N=1}^{33}{\alpha_{0N} \hbox{INDUSTRY}_{Nit}}\,+\,\sum\limits_{Y=1996}^{2001}{\alpha_{0Y} \hbox{YR}_{Yit}}\,+\,\alpha_1 \hbox{OPTVAL}\_\hbox{CALC}^{\rm DIV}_{it} \\ & \beta_1 \hbox{COMPX}_{it}\,+\,\beta_2 \hbox{RESCOMP}_{it}\,+\,\beta_3 \hbox{GOV}_{it}\,+\,K^{*} \hbox{CONTROLS}^{\rm DIV}_{it}\,+\,\varepsilon_{2cit}. \end{aligned} $$

(2c)

$$ \begin{aligned} \hbox{OPTVAL}_{it} &= \sum\limits_{N=1}^{33}{\alpha_{0N} \hbox{INDUSTRY}_{Nit}}\,+\,\sum\limits_{Y=1996}^{2001}{\alpha_{0Y} \hbox{YR}_{Yit}}\,+\,\alpha_1 \hbox{OPTVAL}\_\hbox{CALC}^{\rm INT}_{it} \\ & \beta_1 \hbox{COMPX}_{it}\,+\,\beta_2 \hbox{RESCOMP}_{it}\,+\,\beta_3 \hbox{GOV}_{it}\,+\,K^{*} \hbox{CONTROLS}^{\rm INT}_{it}\,+\,\varepsilon_{2dit}. \\ \end{aligned} $$

(2d)

Equations 1 and 2a–d each includes a vector of control variables, CONTROLS and CONTROLS,^INPUT which comprises variables that are intended to mitigate measurement error in our calculated option value associated with using proxies for expected option life, expected volatility, expected dividend yield, and the risk-free interest rate. The controls also are intended to control for firm characteristics that could explain differences in option values unrelated to our predictions. Because Eqs. 1 and 2a–d test for the effects of discretion in different inputs, the control variables differ across equations. We do not predict the sign of the relation between OPTVAL and the control variables.

CONTROLS, CONTROLS,^LIFE CONTROLS,^VOL and CONTROLS^DIV each includes the natural logarithm of market value of equity, SIZE, because larger firms likely are more well-established and so are likely to have longer expected option lives, lower volatility, and higher dividend yields. Each also includes the book-to-market ratio, BM, and sales growth over the prior year, GROWTH, because firms with more growth, i.e., lower BM and higher GROWTH, might have less stable workforces and, thus, shorter option lives, and likely have higher volatility and lower dividend yields. Each also includes the number of options outstanding at the beginning of the year as a percentage of shares outstanding at the end of the year, OPT_OUT, as a control for unspecified factors related to firms’ propensity to issue stock options to employees. For example, firms with higher stock price volatility tend to rely more extensively on stock options for compensation. ¹⁶ Each also includes stock price volatility over the prior year, 1YR_VOL^PRE as a proxy for the firm’s volatility. We do this because SFAS 123 and Huddart and Lang (1996) suggest that firms with more volatile stock prices likely have shorter option lives. ¹⁷ Also, firms might consider volatility from recent periods to be more indicative of future volatility than that from earlier periods. Finally, it is likely that firms with lower volatility pay higher dividends. CONTROLS^INT does not include variables capturing firm characteristics because, unlike the other three inputs, INT relates to market interest rates, not firm-specific characteristics.

CONTROLS,^VOL CONTROLS,^DIV and CONTROLS^INT each includes LIFE because expected volatility, expected dividend yield, and the risk-free interest rate depend on the firm’s assumption about expected option life—each is to reflect expectations over a future period equal to expected option life. Generally, the longer expected option life, the firm is likely to be less volatile and pay more dividends. The risk-free interest rate depends on expected option life because of term structure effects. CONTROLS includes an expected option life variable for the same reasons. However, it includes LIFE_PRED rather than LIFE because Eq. 1 is designed to test for discretion in all input assumptions, including LIFE. Thus, controlling for LIFE in Eq. 1 would confound our tests. Equations 2b–d are designed to test for discretion in expected volatility, expected dividend yield, and the risk-free rate, respectively, not expected option life. We do not include a control for expected life in Eq. 2a because expected option life is the variable of interest in that equation.

CONTROLS and CONTROLS^VOL each also includes stock price volatility over the subsequent year, 1YR_VOL^POST. We do so to mitigate measurement error in OPTVAL_CALC and OPTVAL_CALC^VOL associated with using VOL_HIST as a proxy for expected volatility. Equations 1 and 2b are designed to test for discretion in the expected volatility assumption and realized future volatility is a proxy for expected volatility. ¹⁸ We do not include 1YR_VOL^POST in Eqs. 2a, c because OPTVAL_CALC^LIFE and OPTVAL_CALC^DIV do not depend on VOL_HIST. CONTROLS^VOL also includes DIV_HIST because firms with lower dividends tend to have higher volatility. This is the same reason we include 1YR_VOL^PRE in CONTROLS^DIV. ¹⁹

4 Data and descriptive statistics

4.1 Data

Our sample comprises firms in the S&P 500, S&P 400 mid-capitalization, and S&P 600 small-capitalization indices with stock option-based compensation plans. We include firms from these three indices because we seek to test our predictions on a broad sample of firms—these indices represent over 50% of the total market capitalization of the US equity markets and comprise large, medium, and small firms. ²⁰ Also, firms in these indices are those included in the Execucomp database, from which we obtain our executive compensation data. We identify a firm as having a stock option-based compensation plan if the firm has a nonzero number of shares reserved for stock option plans (Compustat data item # 215), or if Execucomp identifies the firm as having options outstanding to at least one of its top five executives. Of the 1,175 firms that meet these criteria, 980 have financial statements available on EDGAR and disclose SFAS 123 expense. The final sample comprises 3,368 firm-year observations relating to 887 firms with all data required for our tests.

We hand collect data relating to stock option-based compensation in fiscal years 1996 through 2001 from firms’ financial statement footnotes. We collect the fair value of granted options, option vesting period, and inputs for the option pricing model. Many firms disclose ranges of these inputs across multiple grants within the year; we use the mid-point of the range. We also collect the number and exercise prices of options granted, exercised, and cancelled. We obtain other financial statement data from Compustat and stock price data from CRSP.

4.2 Descriptive statistics

Table 1 presents the industry composition of the sample. It reveals that sample firms represent many industries. Although the distribution differs somewhat from the Compustat population, no single industry represents 10% or more of the sample. The industry breakdown in table 1 is the basis on which we determine INDUSTRY.

Table 1 Industry classification for sample of 887 firms from the S&P 500, S&P 400 mid-capitalization, and S&P 600 small-capitalization indices

Table 2 presents descriptive statistics, in panel A, relating to the variables that we use in our tests, and correlation coefficients, in panel B, for some of our key variables. Regarding information disclosed under SFAS 123, Table 2, panel A, reveals that the mean (median) disclosed value of options granted, OPTVAL, is $10.36 ($9.68) per option, which compares with an untabulated exercise price of $29.65 ($26.32). The mean (median) option value estimate calculated based on option pricing model inputs that we determine, OPTVAL_CALC, is $11.07 ($9.83) per option. Untabulated statistics reveal that for 58% of our observations OPTVAL is less than OPTVAL_CALC. The untabulated mean (median) difference between OPTVAL and OPTVAL_CALC reveals that, on average, firms understate option value estimates under SFAS 123 by approximately 5.5% (7.6%), which is significantly different from zero. ²¹ The focus of our tests is determining whether the extent of understatement is associated with the incentives and opportunity to manage the estimates.

Table 2 Descriptive statistics and correlation coefficients for sample of 3,368 firm-year observations over the 1996 to 2001 period, relating to 887 firms from the S&P 500, S&P 400 mid-capitalization, and S&P 600 small-capitalization indices

The mean (median) LIFE is 5.55 (5.09) years, which is considerably less than the typical 10-year contractual life, consistent with employees exercising options early. By construction because of the instrumental variables approach, LIFE_PRED has the same mean (median) as LIFE. The mean (median) VOL is 37.00% (33.00%), which is similar to the 36.93% (33.20%) of VOL_HIST, and the mean (median) DIV is 1.27% (0.90%), which is similar to the 1.25% (0.91%) of DIV_HIST; the p-values for the differences in means (medians) are 0.63 (0.29) for volatility and 0.19 (0.99) for dividends. These statistics do not indicate that managers understate expected volatility or overstate expected dividend yield relative to historical levels. The mean (median) INT is 5.68% (5.79%), which is somewhat lower than the 5.71% (5.86%) of INT_HIST; the p-values for the differences are 0.01 (0.72).

Regarding the other factors, the shorter-horizon volatility measures, 1YR_VOL^PRE, which has a mean (median) of 44.25% (39.43%), and 1YR_VOL^POST, which has a mean (median) of 47.55% (41.90%), are higher than longer-horizon volatility, VOL_HIST. The mean (median) SIZE is 7.72 (7.68). The mean (median) BM is 0.47 (0.37) and GROWTH is 12.70% (8.27%), indicating sample firms have relatively high growth. The mean (median) OPT_OUT indicates that firms’ outstanding options average 7.34% (5.78%) of total shares outstanding.

Regarding our proxies for the magnitude of stock option-based compensation expense, excessive executive pay, and corporate governance, the mean (median) value of all options granted during the year per share, COMPX, is 0.28 (0.17). Because it is a regression residual, mean RESCOMP is 0.00 by construction. The mean (median) of GOVSCORE, the IRRC corporate governance measure, is 8.89 (9.00), indicating that, on average, firms have nine of the 23 provisions comprising the measure.

Regarding correlations between the variables, Table 2, panel B, reveals that, as expected, many variables are significantly correlated with each other. The highest correlations are among variables representing similar constructs; the Pearson (Spearman) correlation between VOL and VOL_HIST is 0.85 (0.87), DIV and DIV_HIST is 0.80 (0.93), and INT and INT_HIST is 0.70 (0.68). ²² The Pearson (Spearman) correlation between LIFE and LIFE_PRED is somewhat lower, 0.33 (0.35), which is not unexpected given that we use an instrumental variables approach to construct LIFE_PRED.

5 Findings

5.1 Using the Black–Scholes formula to calculate option values

Our tests rely on attributing differences between OPTVAL and OPTVAL_CALC to differences in the inputs to the option pricing model. In particular, we seek to test whether the firm’s input assumptions reflect the predicted exercise of discretion, by constructing our own input assumptions that do not reflect discretion. OPTVAL is disclosed by the firm; we calculate OPTVAL_CALC using the Black–Scholes option pricing formula. However, SFAS 123 does not require use of a particular option pricing model and many firms do not disclose which model they use. Thus, differences between OPTVAL and OPTVAL_CALC could be attributable to our use of the Black–Scholes formula, not differences in input assumptions. Also, firms with multiple option grants within a year disclose only ranges of option values and input assumptions across these grants. In these cases, we define LIFE, VOL, DIV, and INT as the mid-points of the range. Doing so could result in differences between OPTVAL and OPTVAL_CALC that are unrelated to discretion. Moreover, in these cases, OPTVAL is the average option value for the firm in a particular year. Given that option values are nonlinear in the inputs, even if the mid-points of the ranges of assumptions reasonably reflect the inputs, the resulting option value might not equal OPTVAL.

Thus, before estimating (1) and (2a–d) to test our predictions, we assess the extent of these potential estimation problems. Specifically, we use the Black–Scholes formula and LIFE, VOL, DIV, and INT as inputs to calculate option value. We then compare this calculated option value to OPTVAL. Untabulated summary statistics from a regression of OPTVAL on this option value reveal that its estimated coefficient is 1.002 (indistinguishable from one with p-value of 0.71), and an adjusted R ² of 99.7%. These statistics provide strong evidence that our use of the Black–Scholes formula and mid-points of ranges of input assumptions are unlikely to affect our inferences.

5.2 Primary findings

Table 3 presents our findings relating to estimating (1), which tests for discretion associated with the combined effect of all four inputs, as reflected in disclosed option value estimates, OPTVAL. It reveals, as expected, that the option value calculated using our proxies for the four key inputs, OPTVAL_CALC, is highly significant in explaining OPTVAL (t = 115.96).

Table 3 Summary statistics from a regression of option value estimates used in the calculation of SFAS 123 expense on proxies for firms’ incentives and opportunity to understate SFAS 123 expense and control variables

Consistent with predictions, Table 3 also reveals that our proxies for the magnitude of stock option-based compensation expense, excessive executive pay, and corporate governance are negatively associated with OPTVAL. Although the coefficient RESCOMP is not significantly different from zero (t = −1.43), the coefficients on COMPX and GOV are significantly negative (t = −6.74 and  −4.13). These findings indicate that the extent to which firms make input assumptions that result in lower option value estimates is larger for firms with greater incentives and opportunity to do so.

Table 4 presents regression summary statistics from estimating (2a–d), which focus on the effects of each input assumption considered separately. Table 4, panel A, relates to (2a), which focuses on the effects of LIFE. Consistent with Table 3, it reveals that OPTVAL_CALC^LIFE is highly significant in explaining OPTVAL (t = 168.61). Recall that the only difference between OPTVAL_CALC^LIFE and OPTVAL is that we use LIFE_PRED to calculate OPTVAL_CALC^LIFE, whereas firms use LIFE to calculate OPTVAL.

Table 4 Summary statistics from a regression of option value estimates used in the calculation of SFAS 123 expense on proxies for firms’ incentives and opportunity to understate SFAS 123 expense and control variables

Consistent with predictions, Table 4, panel A, reveals that our proxies for the magnitude of stock option-based compensation expense, excessive executive pay, and corporate governance all are significantly negatively associated with OPTVAL, after controlling for OPTVAL_CALC^LIFE and the other control variables. The t-statistics associated with the coefficients on COMPX, RESCOMP, and GOV are  −7.36,  −2.36, and  −2.63. These findings indicate that, as predicted, firms assume an expected option life that results in lower option value estimates when they have greater incentives and opportunity to do so. Table 4, panel B, presents summary statistics from (2b), which focuses on the effects of VOL. It reveals that OPTVAL_CALC^VOL is highly significant in explaining OPTVAL (t = 175.12). Panel B also reveals that, as predicted, firms’ assumptions of expected stock price volatility are significantly associated with COMPX (t = −3.56) and GOV (t = −2.70). However, it reveals no significant relation with RESCOMP (t = 0.33).

Table 4, panel C, presents summary statistics from (2c), which focuses on DIV. Consistent with the findings relating to LIFE and VOL, OPTVAL_CALC^DIV is highly significant in explaining OPTVAL (t = 364.96). Also, firms’ assumptions of expected dividend yield are significantly negatively associated with GOV (t = −1.83), consistent with firms exercising discretion in determining DIV to understate option value estimates when corporate governance is weaker. However, panel C reveals no significant relation with COMPX or RESCOMP (t = −0.18 and  −0.99). Finally, Table 4, panel D, presents summary statistics from (2d), which focuses on INT. In contrast to the findings for LIFE, VOL, and DIV, but not unexpectedly, panel D reveals no evidence that firms use the interest rate assumption to understate option value estimates. In particular, it reveals that the coefficients on COMPX, RESCOMP, and GOV are all insignificantly different from zero (t = 0.67, 0.21, and  −1.21).

5.3 Additional analyses

5.3.1 [OPTVAL–OPTVAL_CALC] as the dependent variable

Equations 1 and 2a–d include variations of OPTVAL_CALC as a control variable. This permits us to interpret the coefficients on our experimental variables, i.e., COMPX, RESCOMP, and GOV, as relating to differences between OPTVAL and OPTVAL_CALC resulting from differences in input assumptions. An alternative specification is to use [OPTVAL–OPTVAL_CALC] as the dependent variable. This specification restricts the coefficient on OPVAL_CALC to equal one; in the primary specification its coefficient is unrestricted. In this alternative specification, our proxy for stock option-based compensation expense, COMPX^†, is the number of options granted during the year multiplied by their average exercise price and deflated by shares outstanding at the end of the year, rather than COMPX. We do not use COMPX because it depends on OPTVAL_CALC, which is part of the dependent variable in this specification. Exercise price is highly positively correlated with option value, but is not mechanically related.

Table 5, panel A, presents summary statistics associated with total option value, analogous to Table 3. It reveals inferences similar to those in Table 3, except that the coefficient on RESCOMP is significantly negative in the Table 5 specification. In particular, COMPX^†, RESCOMP, and GOV are significantly negatively related to differences between OPTVAL and OPTVAL_CALC (t = −12.06,  −1.77, and  −4.01).

Table 5 Summary statistics from a regression of [OPTVAL–OPTVAL_CALC] on proxies for firms’ incentives and opportunity to understate SFAS 123 expense and control variables

Table 5, panel B, presents summary statistics associated with each of the inputs separately, analogous to Table 4, panels A–D. All inferences in Table 5, panel B, are the same as in table 4, except that COMPX^† and GOV are significantly negatively related to DIV in the Table 5 specification. Specifically, relating to LIFE, Table 5, panel B, reveals that COMPX†, RESCOMP, and GOV are all significantly negatively related to differences between OPTVAL and OPTVAL_CALC^LIFE (t = −8.10,  −2.69, and  −2.48). Relating to VOL, Table 5, panel B, reveals that COMPX^† and GOV are significantly negatively related to differences between OPTVAL and OPTVAL_CALC^VOL (t = −5.57 and  −2.75) and RESCOMP is not (t = 0.21). Relating to DIV, COMPX^† and GOV are significantly negatively related to differences between OPTVAL and OPTVAL_CALC^DIV (t =  −2.15 and  −1.78) and RESCOMP is not (t =  −0.83). Relating to INT, COMPX^†, RESCOMP, and GOV are not significantly related to differences between OPTVAL and OPTVAL_CALC^INT (t =  −0.91, 0.01, and  −1.36).

5.3.2 Inputs as the dependent variables

Our primary tests focus on the effects on option value of discretion in the option pricing model input assumptions. We do this because our predictions relate to incentives to manage option value and stock option-based compensation expense, which depends on option value. Because of this, we test our predictions on the combined effect of discretion in all of the inputs. Also, the effect on option value of discretion in each input assumption is nonlinear, in ways that differ across the inputs. Yet, it is the inputs that are the subject of managerial discretion. Thus, we also estimate Eqs. 2a–d using the inputs, i.e., LIFE, VOL, DIV, and INT, as the dependent variables.

Table 6 presents the findings. It reveals inferences that are similar to those in Table 4. Specifically, table 6 reveals that COMPX and GOV are significantly negatively related to LIFE (t =  −7.26 and  −2.73). However, in contrast to table 4, panel A, RESCOMP is negatively related to LIFE, but not significantly so (t = −1.57). ²³ Table 6 also reveals that, consistent with Table 4, COMPX and GOV are significantly negatively related to VOL (t = −3.27 and  −5.42) and RESCOMP is not (t = −1.32). Again consistent with Table 4, only GOV is significantly negatively related to DIV (t = −2.17), and none of the three experimental variables is significantly related to INT (t = −0.98,  −0.96, and 0.97). ²⁴

Table 6 Summary statistics from a regression of the SFAS 123 disclosed input assumptions used in the calculation of option value estimates on proxies for firms’ incentives and opportunity to understate SFAS 123 expense and control variables

5.3.3 Number of options granted

The number of options granted, OPT_GRANT, is an alternative proxy for stock option-based compensation expense that does not depend on option values. We do not use OPT_GRANT in our primary tests because it is possible that OPT_GRANT and OPTVAL are negatively correlated not because of the factors we posit, but because firms tend to grant fewer options when option values are higher (Core & Guay, 2001). Although (1) and (2a–d) include OPTVAL_CALC as an explanatory variable, which permits interpreting the coefficient on OPT_GRANT as the association between OPTVAL and OPT_GRANT after controlling for the unmanaged value of options granted, it is possible that some mechanical correlation remains. However, untabulated findings reveal that our inferences are unaffected if we use OPT_GRANT in place of COMPX in our estimating equations. In particular, the coefficients on OPT_GRANT are significantly negative in (1), (2a), and (2b) (t = −3.42,  −3.88, and  −1.64), and not significantly different from zero in (2d) (t = −1.33). In contrast to Table 4, but consistent with predictions, the coefficient is significantly negative in (2c) (t = −2.00).

6 Summary and concluding remarks

Focusing on the four key option pricing model inputs—expected option life, expected stock price volatility, expected dividend yield, and the risk-free interest rate for the expected life of the option—this study finds that firms understate estimates of option values and, thus, SFAS 123 expense. Our findings indicate that firms with higher stock option-based compensation expense, firms that have CEOs with perceived excessive pay, and firms with weaker corporate governance assume expected option life, expected stock price volatility, and expected dividend yield that result in significantly lower option value estimates. These three assumptions all depend on firm-specific characteristics, making them candidates for exercise of discretion. We find no evidence that firms use the risk-free interest rate assumption to understate option value estimates, consistent with this assumption depending primarily on market interest rates. The understatement of option value estimates we document is unlikely to be attributable to firms adjusting option value estimates to better reflect their assessment of the value of the options. Rather, it suggests managerial opportunism.

These findings have implications for our understanding of the financial reporting for stock option-based compensation expense. In particular, our findings are consistent with firms managing a disclosed earnings amount; prior literature focuses on recognized earnings. This suggests managers believe that even though SFAS 123 expense is disclosed but not recognized, it is relevant to financial statement users. More importantly, our findings suggest that some concerns about the overall reliability of SFAS 123 expense are not unwarranted. We leave it to standard setters to determine whether the effects of discretion on reliability are sufficient to cause them concern and, if so, how such effects can be mitigated.

Our study is silent on the potential implications of changing the accounting treatment of SFAS 123 expense from footnote disclosure to expense recognition. Although expense recognition would likely provide managers with greater incentives to understate the expense, it would also likely increase costs related to audit, regulatory enforcement, and scrutiny by investor groups associated with doing so.

Appendix: Estimation of excessive CEO compensation

Testing the prediction that perceived excessive executive pay motivates firms to understate SFAS 123 expense requires a measure of excessive pay. Our benchmark is the predicted value from a regression of annual CEO compensation on variables identified in prior research as explaining CEO compensation, particularly firm size, performance, growth, risk, and industry membership. We interpret the regression residual, RESCOMP, as perceived excessive compensation, and use it as a proxy for the excessiveness of executive pay.

Consistent with Smith and Watts (1992) and Core, Holthausen, and Larcker (1999), among others, we expect that larger firms with growth opportunities and complex operations demand higher-quality managers, leading to higher CEO compensation. Consistent with Core et al. (1999) we use sales, SALES, as a proxy for size and complexity, book-to-market ratio, BM, and 1-year sales growth, GROWTH, as proxies for growth opportunities and investment opportunity set. We also include two measures of firm performance, return on assets, ROA, and annual stock return, RET. We control for stock price volatility, 1YR_VOL^PRE, because prior studies find a positive relation between volatility and CEO compensation (see, e.g., Cyert, Kang, Kumar, & Shah, 1997). We also control for industry and year effects. The estimation equation is:

$$ \begin{aligned} \log(\hbox{CEO}\_\hbox{COMP})_{it} &= \sum\limits_{N=1}^{33}{\theta_{0I} \hbox{INDUSTRY}_{Nit}}\,+\,\sum\limits_{Y=1996}^{2001}{\alpha_{0Y} \hbox{YR}0_{Yit}}\,+\,\theta_1 \log(\hbox{SALES})_{it}\,+\,\theta_2 \hbox{BM}_{it} \\ &\,+\,\theta_3 \hbox{GROWTH}_{it}\,+\,\theta_4 \hbox{ROA}_{it}\,+\,\theta_5 \hbox{RET}_{it}\,+\,\theta_6 \hbox{1YR}\_\hbox{VOL}^{\rm PRE}_{it}\,+\,\varepsilon _{A1it} \end{aligned} $$

(3)

CEO_COMP is total annual CEO compensation, measured as the sum of cash salary, bonus payments, restricted stock awards, and stock option grants, as estimated and reported by Execucomp. ²⁵ All other variables are as defined in the text, and log denotes logarithm. ²⁶

To estimate (3), we use robust regression and pool all firm-year observations with available data. Untabulated summary statistics reveal that all of the coefficients are consistent with predictions and prior research. In particular, the coefficients on log(SALES), GROWTH, ROA, RET, and 1YR_VOL^PRE are significantly positive (t = 68.45, 7.14, 2.39, 2.42, and 12.54), and that on BM is significantly negative (t = −19.05). Many industry intercepts are significantly different from zero and from each other, indicating significant across-industry variation in CEO compensation. The regression explains 61% of the variation in CEO compensation. This explanatory power is the same as that of the analogous equation in Baker (1999) and considerably more than the 16% for the three-factor model in Yermack (1998).