# SFAS No. 123 stock-based compensation expense and equity market values.

ABSTRACT: This study investigates the relation between share price and stock-based compensation expense that is disclosed but not recognized under SFAS No. 123, after controlling for net income, equity book value, and expected earnings growth. Our instrumental variables approach controls for the mechanical relation between share price and option values. We find that investors view SFAS No. 123 expense as an expense of the firm, and as sufficiently reliable to be reflected in their valuation assessments. Findings based on annual returns indicate SFAS No. 123 expense reflects on a timely basis changes in investor-perceived costs associated with stock-based compensation.I. INTRODUCTION

The objective of this study is to understand the relation between equity market values and stock-based employee compensation expense that is disclosed, but not recognized in net income, under Statement of Financial Accounting Standards (SFAS) No. 123 (Financial Accounting Standards Board 1995; hereafter "SFAS No. 123 expense"). Accounting for stock-based compensation, particularly employee stock options, has long been a controversial financial reporting issue, generating heated debate among managers, auditors, investors, capital market regulators, and accounting standard setters. The controversy focuses on whether the value of employee stock options is an expense of the firm, and, if it is, whether it can be measured reliably enough for expense recognition. Our findings indicate that investors view SFAS No. 123 expense as an expense of the firm that is measured with sufficient reliability to be reflected in their valuation assessments.

The FASB, among others, believe that the value of stock-based compensation is an expense that should be recognized in net income (FASB 1995). It argues that issuing stock options transfers claims on equity from existing shareholders to employees, diluting existing shareholders' interests. Because employees provide services to the firm, the value of the transferred ownership claims represents a cost of generating earnings. (1) Opponents to recognition argue that stock-based compensation is a transaction among shareholders and, therefore, is not an expense of the firm. They also argue that the value of employee stock options cannot be measured reliably because extant option value estimation technology is not suitable for employee options, the FASB's method of calculating the expense is inappropriate, and estimation of option values requires exercise of substantial management discretion. They also argue that stock options align more closely employees' incentives and those of existing shareholders, resulting in benefits that increase current and future earnings and offset the cost of dilution.

We test the relation between share price and SFAS No. 123 expense, incremental to net income, equity book value, and expected earnings growth. To the extent that benefits associated with option incentive effects are reflected in net income, equity book value, and expected earnings growth, and that investors view SFAS No. 123 expense as an expense of the firm, which measures with sufficient reliability costs associated with stock-based compensation, we predict a negative relation between the expense and share price. Because benefits associated with stock-based compensation likely are reflected in expected earnings growth or net income and equity book value, our tests are not designed to determine the net costs and benefits associated with stock-based compensation. Instead, our objective is to assess the value-relevance of SFAS No. 123 expense. Our tests are joint tests of relevance and reliability. We will detect a significant negative relation between share price and SFAS No. 123 expense only if the expense is relevant to investors and measured with sufficient reliability to be reflected in their valuation assessments. (2)

To obtain data for our tests, we hand collect disclosures relating to stock-based compensation for 1996 through 1998, for a sample of firms in the Standard & Poor's (S&P) 500, S&P 400 mid-capitalization, and S&P 600 small-capitalization indices. Under SFAS No. 123, firms can calculate recognized compensation expense relating to these options based on their grant date fair value or on the difference between the firm's stock price at grant date and the option exercise price, which typically equals zero. If a firm chooses the zero expense alternative, as most firms do, it must disclose pro forma net income, i.e., net income under the grant date fair value alternative. We collect pro forma net income, option pricing model inputs used by the firm in estimating the value of its granted options, the resulting option fair value, and other items related to the firm's stock options.

Option pricing theory indicates that option values, a primary determinant of SFAS No. 123 expense, are a positive function of the price of the underlying share, even when the option's intrinsic value equals zero. This results in a relation between share price and SFAS No. 123 expense that is unrelated to the hypothesized relation between share price and stock-based compensation expense as a component of net income (hereafter, the "mechanical relation"). Thus, we use an instrumental variables approach to construct our stock-based compensation expense variable. The instruments include option pricing model inputs, vesting period, and number of options granted, all of which are disclosed by firms as inputs to their calculation of stock-based compensation expense, as well as net income, equity book value, and expected earnings growth. The option pricing model inputs used as instruments are expected stock return volatility, expected option life, expected dividend yield, and expected risk-free interest rate.

We find a significant negative relation between our stock-based compensation expense variable and share price. This finding indicates that investors view SFAS No. 123 expense as an expense of the firm, after controlling for benefits associated with options as reflected in net income, equity book value, and expected earnings growth. The negative relation between our stock-based compensation expense variable and share price also indicates that, despite the large amount of discretion managers have with respect to the estimation of SFAS No. 123 expense, it is sufficiently reliably measured to be reflected in investors' valuation assessments. (3) Consistent with the share price findings, we also find a significant negative relation between returns and change in our stock-based compensation expense variable, incremental to net income, change in net income, and change in expected earnings growth. This finding indicates that SFAS No. 123 expense reflects on a timely basis changes in investor-perceived costs associated with stock-based compensation. It also indicates that our share price findings are not attributable to intertemporally constant correlated omitted variables.

Bell et al. (BLMY 2002) investigate the relation between share price and SFAS No. 123 expense. Our findings differ from those of BLMY. After implementing an instrumental variables approach similar to ours and controlling for benefits associated with the options, BLMY find an insignificant relation between share price and their stock-based compensation expense variable for a sample of profitable computer software firms. BLMY conjecture that the difference between their findings and ours most likely is attributable to sample differences. We investigate this conjecture. Consistent with BLMY, we find an insignificant relation between share price and our stock-based compensation expense variable for computer software firms. More importantly, we find that BLMY's inferences are not generalizable to broader samples of firms, including profitable firms in a variety of industries and firms in knowledge-based industries beyond computer software.

The remainder of the paper proceeds as follows. Section II provides the background of financial reporting for stock-based compensation and related prior research. Section III outlines our research design and Section IV describes the data and presents descriptive statistics. Section V presents our findings, Section VI offers additional analyses, and Section VII concludes.

II. BACKGROUND

Accounting for Employee Stock-Based Compensation

Accounting for stock-based compensation is specified in Accounting Principles Board Opinion (APB) No. 25 (APB 1973) and SFAS No. 123. Under APB No. 25, stock-based compensation expense is the difference at the measurement date between the share price and option exercise price, times the number of options. The measurement date is the date at which the exercise price and number of options are known and, thus, for fixed option grants the measurement date is the grant date. Most companies grant employee stock options with a fixed exercise price that equals share price at date of grant. Thus, under APB No. 25 stock-based compensation expense equals zero.

Under SFAS No. 123, stock-based compensation expense is based on option fair values at the measurement date. Option values are calculated using an option pricing model that takes into account the option exercise price, the share price, the option's expected life, expected dividend yield, expected risk-free interest rate, and expected stock price volatility. SFAS No. 123 expense is recognized over the vesting period; as the expense is recognized, so is equity. (4)

Recognizing that extant option pricing models were not designed to value options with terms that typify employee options, SFAS No. 123 specifies modifications to be made. In particular, employee options typically are nontransferable, which results in early exercise (Huddart and Lang 1996). Thus, SFAS No. 123 specifies that the option's expected life is used, rather than its contractual life. Employee options also typically are subject to vesting conditions, and SFAS No. 123 specifies that total stock-based compensation expense only relates to options that ultimately vest. SFAS No. 123 offers firms a choice of how to accomplish this. First, firms can estimate the number of options expected to vest and use that number in calculating the expense. This estimate is updated each period and effects of changes in it are reflected in the period of change's and future periods' expense. Second, firms can calculate the expense based on the total number of options granted, and adjust the expense in subsequent periods as options are forfeited.

SFAS No. 123 permits firms to apply the measurement provisions in APB No. 25 or those in SFAS No. 123. If a firm measures compensation expense under APB No. 25, it must disclose, among other items, pro forma net income, which is net income if stock-based compensation expense had been measured under SFAS No. 123. Almost all firms apply the measurement provisions of APB 25. The disclosure of pro forma net income permits us to calculate SFAS No. 123 expense. Other required disclosures include number of options granted and exercised, vesting period, estimated fair value of options granted, and inputs to the option fair value calculation, i.e., option exercise price and expected option life, dividend yield, risk-free interest rate, and stock price volatility.

The debate surrounding the issuance of SFAS No. 123 has been one of the most politically controversial in the FASB's history. Opponents argued for footnote disclosure rather than recognition in part because they claimed it was not possible to measure reliably stock-based compensation expense. Their reliability concerns stem from three sources. The first is the questionable applicability to employee stock options of extant option pricing models, including the appropriateness of the commonly used Black-Scholes formula and SFAS No. 123's requirement to use expected option life to take account of non-transferability. The second is SFAS No. 123's expense attribution method, including the choice of how to account for forfeitures and attribution of the expense to the vesting period. The FASB and the International Accounting Standards Board are developing new standards for stock-based compensation and considering how to alleviate reliability concerns arising from these sources. The third is the ability of managers, who actively fought issuance of SFAS No. 123, to exercise their discretion so as to limit the standard's effectiveness (see Aboody et al. 2003). This study's objective is to determine whether the combined effects of these reliability problems are sufficient to render SFAS No. 123 expense valuation irrelevant.

Related Research

After controlling for the mechanical relation between option values and share price, Aboody (1996) finds a significant negative relation between share price and the value of outstanding employee stock options calculated using researcher estimates of inputs to an option pricing model. Because we seek to study the relation between share price and SFAS No. 123 expense, our tests focus on those amounts. Aboody's (1996) evidence indicates that a researcher can reliably estimate the value of outstanding options and that value is reflected in share price. However, only by using amounts disclosed under SFAS No. 123 can we test whether measurement error inherent in the SFAS No. 123 calculation of effects of management discretion exercised in determining the amounts is sufficient to eliminate the value-relevance of SFAS No. 123 expense.

More recently, BLMY investigate the relation between share price and SFAS No. 123 expense, but only for 85 profitable firms in the computer software industry. BLMY document a positive association between share price and SFAS No. 123 expense for these firms. However, BLMY obtain these inferences without controlling for the mechanical relation between share price and option values. After controlling for this mechanical relation, BLMY find a negative, but insignificant relation between share price and their stock-based compensation expense variable. These findings are consistent with SFAS No. 123 expense lacking relevance and reliability and with profitable computer software firms being different from other firms. BLMY conjecture that the second reason is why its findings differ from ours. We investigate this conjecture in Section VI. Consistent with BLMY, in a pooled specification we find an insignificant relation between share price and our stock-based compensation expense variable for profitable computer software firms. However, we find that BLMY's inferences are not generalizable to separate-year estimation or to broader samples of firms, including profitable firms in other industries and firms in knowledge-based industries beyond computer software. (5)

Our study also relates to Hanlon et al. (HRS 2003), who find a significant positive relation between future operating earnings and the Black-Scholes value of stock option grants to the top five executives. HRS interpret this finding as evidence of a net benefit to firms from granting stock options to top executives. As HRS point out, our study differs in that we do not seek to determine the net benefit of stock-based compensation. Also, we focus on the expense associated with options granted to all employees, not only the top five executives, which could affect the net benefit calculus.

III. RESEARCH DESIGN

We focus our tests on the following equation:

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Pis share price, BV is equity book value, NI is net income, LTG is mean year-end analyst I/B/E/S earnings growth forecast, and COMPX is net income minus pro forma net income disclosed under SFAS No. 123, all measured at fiscal year-end. BV, NI, and COMPX are deflated by number of shares outstanding. (6) [IND.sub.N] is an indicator variable that equals 1 if the firm is in industry N, and 0 otherwise; i and t denote firms and years. We estimate all equations using robust regression. (7)

Equation (1) is consistent with Ohlson (1995), where COMPX is a component of net income. (8) We include LTG in Equation (1) because Liu and Ohlson (2000) and Ohlson (2001) show that expected future abnormal earnings are reflected in equity price before they are reflected in equity book value and net income (see also Barth et al. 1998). LTG is analysts' forecast of annual growth in operating earnings, which does not include SFAS No. 123 expense, over the firm's next full business cycle, which generally is between three and five years. Thus, LTG can capture benefits associated with stock-based compensation not yet reflected in net income, but not the related cost. Also, because SFAS No. 123 expense and growth likely are correlated, omitting LTG from (1) could affect our inferences relating to COMPX (Skinner 1996). Based on prior research, we predict [[alpha].sub.1], [[alpha].sub.2], and [[alpha].sub.3] are positive. If investors view SFAS No. 123 expense as an expense of the firm, and to the extent that any associated benefits are reflected in net income, equity book value, and expected earnings growth, we predict [[alpha].sub.4] is negative.

Option pricing theory indicates that the values of stock options are a positive function of the price of the underlying share, even when the option's intrinsic value equals 0. (9) Thus, there is a mechanical relation between share price and SFAS No. 123 expense (Aboody 1996). Although P is share price at fiscal year end and the price affecting the option values comprising COMPX is price at the option grant date, the two prices are highly positively correlated. (10) Failure to consider the effects of this correlation could bias upward COMPX's coefficient in Equation (1). Thus, following Aboody (1996), we use an instrumental variables approach to purge COMPX of this correlation.

Specifically, we replace COMPX in Equation (1) with COMPX *, which is the predicted value from a regression of COMPX on instruments that we expect to be highly correlated with SFAS No. 123 expense, but uncorrelated with the error in Equation (1) that arises because of COMPX's mechanical relation with P. Recall from Section II that COMPX is based on option value at grant date times the number of options, recognized over the vesting period. Thus, the instruments are the option pricing inputs sample firms use in calculating COMPX, i.e., expected stock price volatility, VOL, expected option life, LIFE, expected risk-free interest rate, INT, and expected dividend yield, DIV, as well as the number of options granted, OPT_GRANT, and the percentage of options vesting each year, VEST. (11) The instruments also include BV, NI, LTG, and [IND.sub.N], the other explanatory variables in Equation (1). (12)

To investigate whether SFAS No. 123 expense reflects on a timely basis changes in investor-perceived costs associated with stock-based compensation, we estimate:

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

where RET is annual share return, and [DELTA] denotes annual change. All variables are deflated by share price at the beginning of year t.

We estimate all equations separately by year because SFAS No. 123 applies to options granted after December 15, 1995, which results in a phase-in period. That is, in 1996, COMPX relates to options granted in 1996, whereas in 1997 (1998) it relates to options granted in 1997 and 1996 (1998, 1997, and 1996). Because COMPX aggregates the amortization of the value of options granted in each year, we use the average over time of the instrumental variables. (13)

IV. DATA AND DESCRIPTIVE STATISTICS

We collect data for firms in the S&P 500 index and firms in the S&P mid-capitalization and small-capitalization indices with substantial stock-based compensation plans. To identify firms with substantial plans, we rank firms in the latter two indices based on the ratio of the number of shares reserved for stock options to the number of shares outstanding and select 600 firms with the largest ratios for which 1998 financial statements are available through EDGAR. Combining these firms with the S&P 500 firms results in a sample of 756, 767, and 751 observations in 1998, 1997, and 1996 with data required for our tests.

We hand collect data relating to stock-based compensation from firms' 1998 financial statement footnotes. Specifically, we collect pro forma net income, fair value of granted options, option vesting period, and inputs for the option pricing model. When firms disclose ranges of these inputs across multiple option grants within the year, we use the median of the range. We also hand collect the number of options granted, outstanding, and exercisable, and the average exercise price for each category. We obtain other data from Compustat.

Table 1 presents the industry composition of the sample in Panel A, descriptive statistics for variables in Panel B, and correlations among the variables in Panel C. Panel A reveals that sample firms represent many industries. Although the distribution differs somewhat from the Compustat population, no single industry represents 10 percent of more of the sample.

Table 1, Panel B, reveals that, on average, sample firms' share price, P, substantially exceeds equity book value, BV. if also reveals that the mean (median) of SFAS No. 123 expense, COMPX, is $0.11, $0.09, and $0.07 ($0.08, $0.06, and $0.04) in 1998, 1997, and 1996. The increase over time is consistent with the phase-in provisions of SFAS No. 123. These amounts are not inconsequential relative to the mean (median) net income, NI, of $1.31, $1.74, and $1.87 ($1.33, $1.55, and $1.61). Analyst forecasts of earnings growth, LTG, are consistent across years, with mean and median of about 15 percent.

Table 1, Panel B, indicates that the mean (median) number of options granted as a percentage of outstanding shares, OPT_GRANT, is approximately 3 percent (2 percent) in each year. Yearly grants of this magnitude can result in substantial share dilution. In 1998, 1997, and 1996, the means (medians) of the fair value of granted options, FVOPT, are $11.37, $10.06, and $8.40 ($10.21, $8.98, and $7.34) and mean (median) share prices are $35.15, $39.29, and $35.85 ($30.00, $35.00, and $31.75). Table 1, Panel C, reveals that P is significantly positively correlated with FVOPT and COMPX, but not significantly correlated with COMPX *. These correlations are consistent with a positive mechanical relation between option value and share price, which the instrumental variables approach effectively mitigates.

V. PRIMARY FINDINGS

Table 2 presents summary statistics from Equation (1) estimated using SFAS No. 123 expense, COMPX. We present these findings as a benchmark to assess the effect of the mechanical relation between share price and option values on the relation between share price and SFAS No. 123 expense. As predicted, the coefficients on BV and NI are significantly positive in all three years, as is the coefficient on LTG in 1996 and 1997. (14) However, contrary to predictions, the coefficient on COMPX is insignificantly different from 0 in all three years (coefficient (t): 2.90 (0.69), -4.39 (-1.03), and 6.20 (1.24)). (15) These results are inconclusive as to whether investors view SFAS No. 123 expense as a reliably measured expense of the firm. However, the Hausman-Taylor (1981) test rejects the null hypothesis of no correlation between COMPX and the error in Equation (1) (p-value < 0.001), indicating the coefficient estimates from this regression likely are biased and inconsistent.

Table 3 presents summary statistics from regressions of COMPX on the instrumental variables used to construct COMPX *. It reveals that the adjusted [R.sup.2]s are 0.64, 0.60, and 0.57 in 1998, 1997, and 1996, indicating the instruments explain a large portion of the variation in COMPX. The coefficients on VOL, OPT_GRANT, VEST, BV, NI, and LTG (DIV) generally are significantly positive (negative) as expected; the coefficients on the other instruments are insignificantly different from 0.

Table 4 presents summary statistics from Equation (1) estimated using COMPX *. It reveals, as expected and consistent with Table 2, that the coefficients on BV, NI, and LTG are significantly positive in all three years. The coefficient magnitudes and significance are similar to those in Table 2 (except for the coefficient on LTG in 1998), indicating that using COMPX * in place of COMPX has little effect on these variables. However, in striking contrast to Table 2, the coefficient on COMPX * is negative in all three years, and significantly so in 1998 and 1997 (t = -5.89, -5.09, and -0.84). (16) These findings are consistent with the insignificant coefficients on COMPX in Table 2 being attributable to the mechanical relation between share price and option values. More importantly for our research question, the findings indicate that, after controlling for option benefits as reflected in net income, equity book value, and forecasted earnings growth, investors view SFAS No. 123 expense as an expense of the firm. The negative relation between COMPX * and share price also suggests that SFAS No. 123 expense is measured with sufficient reliability to be associated with investors' firm valuation assessments. We investigate potential bias in the estimated COMPX * coefficient in Section VI.

Table 5 presents summary statistics from Equation (2), which are consistent with those in Table 4. In particular, as predicted, the coefficient on the change in SFAS No. 123 expense, ACOMPX *, is significantly negative in 1998 and 1997 (t = -2.64 and -2.70). (17) Also as predicted, the coefficients on NI, [DELTA]NI, and [DELTA]LTG are significantly positive in both years, except for that on [DELTA]LTG in 1998. These findings reveal that increases in SFAS No. 123 expense are associated with decreases in share price, after controlling for net income and changes in net income and expected earnings growth. These findings also reveal that SFAS No. 123 expense reflects on a timely basis changes in investor-perceived costs associated with stock-based compensation. They also indicate our Table 4 findings are not attributable to bias caused by intertemporally constant correlated omitted variables.

VI. ADDITIONAL ANALYSES

Comparison with Bell et al. (2002)

After controlling for the mechanical relation between share price and option values, and the benefits associated with option incentive effects, BLMY find an insignificant relation between share price and SFAS No. 123 expense (BLMY, Table 9). BLMY conjecture that the difference between this finding and our finding of a significant negative relation most likely is attributable to sample differences. BLMY's sample comprises 85 profitable computer software firms; our sample comprises firms in many industries that are not necessarily profitable.

We first determine whether our inferences are affected by not focusing only on profitable firms. Table 6, Panel A, presents findings from limiting our sample to firms with positive NI and BV. It reveals that the coefficients on COMPX * are significantly negative in 1998 and 1997, as in Table 4, and in 1996 (t = -3.20, -3.54, and -2.57). To facilitate comparison with BLMY, we also present findings from a pooled estimation, in which COMPX * has a significant negative coefficient (t = -3.91). These findings are inconsistent with lack of profitability driving the inferences in Table 4.

BLMY conjecture that their finding an insignificant relation between share price and SFAS No. 123 expense, after controlling for benefits of stock-based compensation, is specific to knowledge-based firms. Thus, Table 6, Panel B, presents findings using only profitable software firms in our sample (SIC = 737). BLMY's inferences are based on pooling observations across the three years. Findings from the pooled estimation in Table 6, Panel B, reveal the same inferences as in BLMY. In particular, the coefficient on COMPX * is negative, but insignificantly different from 0 (t = -0.58). These findings indicate that the difference between our findings and BLMY's results from sample, not estimation specification, differences. Panel B also presents findings from separate-year estimations. Although one should interpret these findings cautiously because of the small sample sizes, they reveal COMPX *'s coefficient differs across years; it is significantly negative in 1998 and 1997, and insignificant in 1996 (t = -1.68, -2.94, and 0.54). Thus, pooling observations across SFAS No. 123 phase-in years can affect inferences.

To investigate further BLMY's conjecture relating to knowledge-based firms, Table 6, Panel C, presents findings based on using profitable firms from a broader set of knowledge-based industries. (18) It reveals inferences consistent with Table 4, i.e., the coefficient on COMPX * is significantly negative in 1998 and 1997 (t = -2.15 and -4.28) and insignificant in 1996 (t = 0.99). It also is significantly negative in the pooled specification (t = -2.31). These findings do not support the conjecture that the relation between SFAS No. 123 expense and share price is insignificant for knowledge-based firms.

BLMY focus on firms in knowledge-based industries because such firms often are heavy users of stock-based compensation. To investigate whether SFAS No. 123 expense has less of a negative relation with share price when stock-based compensation is higher, we estimate Equation (1) using COMPX * and include its squared term, [COMPX *.sup.2], as an explanatory variable. (19) Consistent with the conjecture, untabulated findings reveal a significant negative relation with COMPX * for all three years (t = -6.39, -4.03, and -1.86) and a significant positive relation with [COMPX *.sup.2] (t = 4.50, 2.01, and 1.61). To determine whether the incremental valuation effect of COMPX * is significantly negative even for large stock-based compensation expense, we estimate Equation (1) permitting the coefficient on COMPX * to vary by deciles of SFAS No. 123 expense. Untabulated findings reveal that, consistent with the nonlinear specification, the coefficient on COMPX * declines in absolute value almost monotonically across deciles in all three years. More importantly, the coefficient is significantly negative for all deciles in 1998 and 1997 and for four deciles in 1996, including the second largest.

Stock-Based Compensation Expense and Expected Earnings Growth

The significant negative coefficient on COMPX * in Table 4 is consistent with costs associated with stock-based compensation. However, a primary reason firms issue stock options is to align employees' interests with those of shareholders and motivate the employees to work to increase firm value. (20) To the extent there is a relation between stock-based compensation and current and future firm performance, BV, NI, and, LTG in Equation (1) could act as a control for these incentive effects. To determine whether expected earnings growth reflects benefits associated with stock-based compensation, we estimate Equation (1) using COMPX * and omitting expected earnings growth, LTG. (21) To the extent SFAS No. 123 expense reflects not only costs associated with stock-based compensation, but also benefits as reflected in positive valuation effects of expected earnings growth, these positive valuation effects will attenuate the negative relation between SFAS No. 123 expense and share price when the estimation equation excludes LTG. (22)

Table 7 presents the findings and reveals, as expected, that the coefficients on COMPX * are attenuated relative to those in Table 4 (-42.95, -21.05, and 13.72 in Table 7; -57.54, -49.31, and -10.21 in Table 4). Consistent with Table 4, the coefficients are significantly negative for 1998 and 1997 (t = -5.19 and -2.39), and insignificant in 1996 (t = 1.17). Because SFAS No. 123 expense for 1997 (1998) pertains to option grants no more than two (three) years prior to the date of the valuation equation, these results indicate that a noticeable portion of the benefits associated with stock-based compensation is reflected in net income and equity book value within a few years subsequent to the grant. (23) This also is consistent with SFAS No. 123 expense, which is calculated by amortizing stock-based compensation cost over the vesting period, not being grossly mismatched with recognized associated benefits.

Nonlinearity in Option Values

Our primary tests focus on whether COMPX *'s coefficient is significantly negative. An alternative benchmark is the coefficient on NI, although one might expect the coefficient on COMPX to be somewhat larger than that on NI, which comprises transitory and non-transitory components. Consistent with this, COMPX *'s coefficients in Table 4 are large relative to those on NI (-57.54, -49.31, and -10.21, compared with 3.32, 6.72, and 7.25); untabulated tests reveal the coefficients on COMPX * and NI differ significantly in 1998 and 1997, but not in 1996. (24)

Option pricing formulas are nonlinear in the inputs and COMPX is not additive in the number of options granted of vesting period, whereas the instrumental variables specification is linear in the instruments. An instrumental variables approach is necessary because not all inputs necessary to calculate COMPX are disclosed, e.g., estimates of the number of options expected to vest, components of COMPX attributable to options granted in each year, and any reload options or other changes to outstanding options that affect COMPX. However, using a linear specification could result in inefficient or biased estimates of COMPX *'s coefficient, to the extent omitted nonlinear effects are correlated with the explanatory variables.

Thus, we estimate total grant date value of options granted during the year that is not dependent on share price. Specifically, we calculate Black and Scholes (1973) option values, using each firm's disclosed valuation inputs, i.e., VOL, LIFE, INT, and DIV, and set share price and exercise price both equal to the sample mean price in each year. For each firm-year we calculate the total grant date option value by multiplying this "equal price" option value by number of options granted during the year. We then estimate Equation (1) using this variable, [GRANT_VAL.sup.EP], in place of COMPX. The advantage of this approach is that it obviates the need for the instrumental variables approach. The disadvantage is that the approach is limited to total grant date option values; we do not have information to reconstruct SFAS No. 123 expense.

Table 8, Panel A, presents the findings. It reveals that, as expected and consistent with Table 4, the coefficients on BV, NI, and LTG are significantly positive in all three years. More importantly, the coefficient on [GRANT_VAL.sup.EP] is negative in all three years, and significantly so in 1998 and 1997 (t = -5.55 and -3.72; t = -0.01 in 1996). These findings indicate that our primary inferences are not attributable to error induced by the linear instrumental variables equation, and are consistent with the instrumental variables approach controlling for bias induced by the mechanical relation between share price and option values.

The coefficient on [GRANT_VAL.sup.EP] in Table 8, Panel A, is substantially smaller than that on COMPX * in Table 4. This finding is consistent with the coefficient on COMPX * being sensitive to the linearity imposed by the instrumental variables approach. It also is consistent with [GRANT_VAL.sup.EP] reflecting the total value of options granted during the current year, whereas COMPX * is based on the sum of total value of options granted over the current and prior years amortized over the options' vesting periods. To distinguish between these explanations, Table 8, Panel B, presents findings from Equation (1) estimated using GRANT_VAL * in place of [GRANT_VAL.sup.EP]. GRANT_VAL * is FVOPT * multiplied by OPT_GRANT, where FVOPT * is the predicted value from a regression of FVOPT on VOL, LIFE, INT, DIV, BV, NI, and LTG. Thus, the difference between Panels A and Bis that we use equal price option values in Panel A and instrumental variables estimated option values in Panel B. The findings in Panel B are similar to those in Panel A, indicating that the linear instrumental variables approach does not drive our findings.

Options Outstanding

If COMPX * is correlated with the total value of options outstanding, omitting the latter from Equation (1) could bias COMPX *'s coefficient (Soffer 2000; Li 2003). To investigate this possibility, we include in Equation (1) OUT_VAL *, which is the total value of options outstanding after removing its mechanical relation with share price using the same approach we use to calculate GRANT_VAL *. We estimate option values using the Black and Scholes (1973) formula and the firm's disclosed option pricing model inputs and weighted average exercise price of options outstanding. (25) Untabulated findings reveal, as expected, that the coefficients on OUT_VAL * are significantly negative in all three years (t = -1.71, -2.43, and -4.81). More importantly for our research question, the findings also reveal that our inferences relating to SFAS No. 123 expense are robust to including OUT_VAL *. The coefficients on COMPX * are significantly negative in 1998 and 1997, as in Table 4, and in 1996 (t = -4.03, -4.42, and -4.38). (26)

Our estimation equations do not include SFAS No. 123 expense related to options granted prior to SFAS No. 123's effective date. Thus, we permit COMPX *'s coefficient to differ for firms with exercisable options as a fraction of options outstanding above the sample median. Exercisable options are vested and, thus, likely issued before SFAS No. 123 became effective. To the extent BV, NI, and LTG reflect more of the incentive effects of older options, we predict that COMPX *'s coefficient is more negative for firms with more exercisable options. Consistent with this, untabulated findings reveal that the incremental coefficient on COMPX * is negative in 1998 and 1997, and significantly so in 1998 (t = -1.90).

Number of Options Granted as a Choice Variable

If a firm grants a specified dollar value of options, the firm might grant fewer options as its share price rises (Core and Guay 2001). If so, there could be a negative relation between share price and number of options granted that could confound our inferences. Consistent with this possibility, Table 1 reveals that the correlation between share price and number of options granted is significantly negative. However, findings in this section reveal that our inferences are not affected by potential endogeneity between share price and number of options granted.

First, the correlation between stock returns and change in number of options granted is insignificant; Pearson (Spearman) correlation p-values are 0.28 (0.34) for 1998 and 0.40 (0.64) for 1997. (27) These correlations are inconsistent with firms changing number of options granted as share price changes. Second, we estimate Equation (1) including OPT_GRANT. Untabulated findings reveal that COMPX *'s coefficient is negative in all three years (t = -7.69, -9.89, and -4.82). Interestingly, OPT_GRANT's coefficient is positive in all three years, and significantly so in 1998 and 1997, which is inconsistent with firms with higher share prices granting fewer options. Third, we estimate the instrumental variables equation after deflating COMPX by OPT_GRANT, and omitting OPT_GRANT from the set of instruments. We then estimate Equation (1) including OPT_GRANT and using this modified COMPX *. Untabulated findings indicate that the coefficient on the modified COMPX * is significantly negative in all three years (t = -8.31, -9.82 and -4.38), consistent with our primary findings. The coefficient on OPT_GRANT is insignificantly negative in all three years.

VII. SUMMARY AND CONCLUDING REMARKS

This study investigates the relation between share price and stock-based compensation expense that is disclosed, but not recognized in net income, under SFAS No. 123, after controlling for net income, equity book value, and expected earnings growth. We use an instrumental variables approach for our stock-based compensation variable in an attempt to eliminate the mechanical relation between share price and SFAS No. 123 expense attributable to the fact that option values, a primary determinant of SFAS No. 123 expense, are a positive function of the price of the underlying share.

Taken together, our findings indicate that investors view stock-based compensation as an expense of the firm, and that SFAS No. 123 expense measures this cost sufficiently reliably to be reflected in their valuation assessments. Moreover, our findings based on annual stock returns indicate that SFAS No. 123 expense reflects on a timely basis changes in investor-perceived costs associated with stock-based compensation. We also find that a noticeable portion of the benefits associated with stock-based compensation is reflected in net income and equity book value within a few years subsequent to grant. Given that the vesting period for sample firms averages less than three years, this finding suggests that recognition of stock-based compensation expense over the vesting period, as required by SFAS No. 123, results in an expense that is not severely mismatched with recognized associated benefits.

Our study is silent on the potential implications of changing the financial reporting of stock-based compensation expense from disclosure in the footnotes to recognition. Expense recognition might provide managers with greater incentives to understate option value estimates thereby increasing their firms' reported profitability. To the extent this is the case, our inferences related to the perceived reliability of disclosed but unrecognized SFAS No. 123 expense may not be generalizable to an expense recognition regime. We leave to standard setters the determination of whether stock-based compensation expense is reliable enough to be recognized in financial statements.

TABLE 1 Industry Classification, Descriptive Statistics, and Correlations Panel A: Industry Classification Frequency in Frequency in Sample Compustat Ratio of n %(1) % (2) (1) to (2) Industry Agriculture, Mining 34 4.43 4.06 1.1 Construction 8 1.05 1.15 0.9 Food, Tobacco 22 2.87 2.13 1.4 Textile, Apparel 14 1.83 1.30 1.4 Lumber, Furniture 13 1.69 0.90 1.9 Paper 19 2.48 0.90 2.7 Printing 24 3.13 1.24 2.5 Chemicals 65 8.47 5.39 1.6 Rubber, Plastics 15 1.96 1.52 1.4 Leather, Glass 8 1.05 0.80 1.3 Metal Industries 35 4.56 2.48 1.8 Machinery 49 6.39 5.40 1.2 Electrical Equipment 50 6.52 6.61 1.0 Transportation Equipment 27 3.52 1.68 2.1 Instruments 38 4.95 5.02 1.0 Misc. Manufacturing 9 1.17 1.02 1.1 Transportation Services 17 2.22 2.22 1.0 Communications 12 1.56 4.10 0.4 Utilities 28 3.65 2.88 1.3 Durables-Wholesale 17 2.22 2.32 0.9 Nondurables-Wholesale 12 1.56 1.46 1.1 Retail 19 2.48 1.35 1.9 Apparel Stores 15 1.96 1.05 1.8 Eating and Drinking 12 1.56 1.49 1.0 Misc. Retail 12 1.56 1.80 0.9 Banks 45 5.87 11.54 0.5 Insurance Services 34 4.43 3.16 1.4 Lodging 7 0.91 0.70 1.3 Business Services 43 5.61 13.05 0.4 Entertainment 9 1.17 1.81 0.6 Health Services 12 1.56 1.66 0.9 Other Services 8 1.05 1.89 0.6 Others 35 4.56 5.92 0.8 Total Number of Firms 767 100 100 Panel B: Descriptive Statistics 1998 1997 Mean Median Std. Dev. Mean Median Std. Dev. P 35.15 30.00 23.39 39.29 35.00 22.91 BV 12.40 10.52 8.58 13.34 11.13 9.94 NI 1.31 1.33 2.14 1.74 1.55 1.94 LTG 15.22 14.50 6.08 15.25 14.00 6.23 COMPX 0.11 0.08 0.11 0.09 0.06 0.09 VOL 32.59 29.53 13.37 31.68 29.00 13.15 LIFE 5.61 5.33 1.81 5.66 5.25 2.74 INT 5.87 5.87 0.44 6.12 6.15 0.42 DIV 1.32 1.03 1.34 1.32 1.00 1.38 OPT-GRANT 2.75 1.76 3.08 2.82 1.81 3.55 VEST 42.23 33.00 26.52 42.45 33.00 26.79 FVOPT 11.37 10.21 6.86 10.06 8.98 5.97 COMPX * 0.09 0.08 0.06 0.07 0.06 0.05 N 756 767 1996 Mean Median Std. Dev. P 35.85 31.75 21.39 BV 13.87 11.21 10.15 NI 1.87 1.61 1.90 LTG 15.28 14.00 6.97 COMPX 0.07 0.04 0.08 VOL 31.61 28.40 13.34 LIFE 5.61 5.10 1.72 INT 6.13 6.13 0.99 DIV 1.40 1.07 1.44 OPT-GRANT 3.13 1.94 3.88 VEST 42.49 33.00 26.78 FVOPT 8.40 7.34 5.13 COMPX * 0.05 0.04 0.04 N 751 Panel C: Pearson (Spearman) Correlations in Upper (Lower) Triangle P BV NI LTG COMPX VOL LIFE P 0.40 0.62 -0.21 0.41 -0.52 0.06 BV 0.37 0.49 -0.47 0.01 -0.39 0.07 N1 0.47 0.46 -0.34 -0.06 -0.45 0.11 LTG -0.13 -0.40 -0.22 0.33 0.59 -0.15 COMPX 0.16 -0.03 -0.09 0.34 0.39 -0.12 VOL -0.42 -0.36 -0.34 0.57 0.46 -0.16 LIFE 0.03 0.04 0.05 -0.11 -0.10 -0.17 INT -0.01 -0.06 0.04 0.03 0.00 0.00 0.12 DIV 0.25 0.31 0.26 -0.56 -0.32 -0.61 0.11 OPT_GRANT -0.18 -0.16 -0.27 0.31 0.62 0.52 -0.18 VEST 0.20 0.16 0.07 -0.27 -0.09 -0.31 -0.04 FVOPT 0.65 0.31 0.39 0.12 0.29 -0.05 0.15 COMPX * -0.09 0.00 -0.15 0.46 0.69 0.61 -0.19 INT DIV OPT-GRANT VEST FVOPT COMPX * P 0.06 0.35 -0.23 0.35 0.68 -0.07 BV -0.03 0.34 -0.20 0.17 0.33 0.02 N1 0.04 0.34 -0.27 0.20 0.30 -0.14 LTG 0.03 -0.63 0.37 -0.27 0.11 0.46 COMPX 0.02 -0.36 0.63 -0.06 0.24 0.68 VOL 0.02 -0.70 0.50 -0.39 -0.06 0.55 LIFE 0.23 0.15 -0.19 -0.08 0.08 -0.20 INT -0.06 -0.02 -0.09 0.05 0.00 DIV -0.03 -0.42 0.33 -0.09 -0.49 OPT-GRANT -0.04 -0.35 -0.26 -0.11 0.78 VEST -0.10 0.29 -0.20 0.07 -0.15 FVOPT 0.10 -0.05 -0.10 0.18 0.08 COMPX * -0.02 -0.44 0.90 -0.14 0.14 P is year-end share price. BV is year-end equity book value. NI is annual net income. LTG is year-end I/B/E/S mean analyst earnings growth forecast. COMPX is unrecognized stock-based compensation expense, i.e., net income minus the pro forma net income disclosed under SFAS No. 123. BV, NI, and COMPX are deflated by number of shares outstanding. VOL is expected stock price volatility, expressed in percentage form. LIFE is expected option life. INT is expected risk-free interest rate, expressed in percentage form. DIV is expected dividend yield, expressed in percentage form. OPT_GRANT is number of options granted as a percentage of number of shares outstanding. VEST is the percentage of options vesting each year. FVOPT is the weighted average value of options granted during the year. VOL. LIFE, INT. DIV, OPT-GRANT, VEST, and FVOPT are disclosed under SFAS No. 123. COMPX * is fitted value from a regression of COMPX on VOL, LIFE, INT, DIV. OPT-GRANT, VEST, BV, NI, LTG, and IND, Correlations significantly different from 0 at p-values less than 5 percent are in boldface type. TABLE 2 Summary Statistics from Regressions of Share Price on Book Value of Equity, Net Income, Analyst Earnings Growth Forecast, and SEAS No. 123 Stock-Based Compensation Expense [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] 1998 1997 Variable Pred Coefficient t-statistic Coefficient BV + 0.77 10.80 0.75 NI + 3.80 11.39 6.97 LTG + 0.07 0.73 0.49 COMPX - 2.90 0.69 -4.39 N 756 767 Adj. [R.sup.2] 0.53 0.71 1997 1996 Variable t-statistic Coefficient t-statistic BV 9.52 0.50 8.30 NI 17.16 7.29 19.68 LTG 6.14 0.42 5.82 COMPX -1.03 6.20 1.24 N 751 Adj. [R.sup.2] 0.72 P is year-end share price. BV is year-end equity book value. NI is net income. LTG is year-end I/B/E/S mean analyst earnings growth forecast. COMPX * is unrecognized stock-based compensation expense, i.e., net income minus pro forma net income disclosed under SFAS No. 123. BV, NI, and COMPX are deflated by number of shares outstanding. IND, equals I if the firm is in industry N (based on the 33 industries in Table 1 Panel A), and 0 otherwise. i and t denote firm and years. Coefficients are estimated using robust regression. The industry-specific intercepts are untabulated. t-statistics are based on White (1980) heteroscedasticity-consistent standard errors. TABLE 3 Summary Statistics from Regressions of SFAS No. 123 Stock-Based Compensation Expense on Instrumental Variables [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] 1998 1997 Variable Pred Coefficient t-statistic Coefficient VOL + 0.09 4.95 0.10 LIFE + 0.01 0.76 0.01 INT + 0.11 0.54 -0.37 DIV - -0.28 -1.97 -0.28 OPT_GRANT + 1.43 19.49 1.08 VEST + 0.02 3.94 0.02 BV + 0.01 8.75 0.01 NI + 0.01 1.86 0.01 LTG + 0.01 5.41 0.01 N 756 767 Adj. [R.sup.2] 0.64 0.60 1997 1996 Variable t-statistic Coefficient t-statistic VOL 6.19 0.10 7.59 LIFE 0.39 -0.01 -2.02 INT -1.33 0.01 0.16 DIV -2.47 -0.01 -0.03 OPT-GRANT 18.04 0.84 15.64 VEST 3.58 0.03 6.62 BV 6.22 0.01 2.68 NI 1.29 0.01 3.75 LTG 1.54 -0.01 -0.58 N 767 751 Adj. [R.sup.2] 0.57 COMPX is unrecognized stock-based compensation expense. i.e., net income minus the pro fbrnra net income disclosed under SFAS No. 123. VOL is expected stock price volatility. LIFE is expected option life. INT is expected risk-free interest rate. DIV is expected dividend yield. OPT-GRANT is number of options granted during the year. VEST is the percentage of options vesting each year. COMPX, VOL, LIFE, INT, DIV. OPT_GRANT. and VEST are disclosed under SFAS No. 123. BV is year-end equity book value. NI is net income. LTG is year-end I/B/E/S mean analyst earnings growth forecast. COMPX OPT_GRANT, BV, and NI are deflated by number of shares outstanding at the end of the year. IN[D.sub.N] equals 1 if the firm is in industry N (based on the 33 industries in Table 1, Panel A). and 0 otherwise. i and t denote firm and years. Coefficients are estimated using robust regression. The industry-specific intercepts are untabulated. t-statistics are based on White (1980) heteroscedasticity-consistent standard errors. TABLE 4 Summary Statistics from Regressions of Share Price on Book Value of Equity, Net Income, Analyst Earnings Growth Forecast, and the SEAS No. 123 Expense Variable Derived from the Instrumental Variable Approach [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] 1998 1997 Variable Pred Coefficient t-statistic Coefficient BV + 0.91 12.74 0.84 NI + 3.32 10.01 6.72 LTG + 0.33 3.44 0.63 COMPX * - -57.54 -5.89 -49.31 N 756 767 Adj. [R.sup.2] 0.54 0.72 1997 1996 Variable t-statistic Coefficient t-statistic BV 10.98 0.51 8.52 NI 17.05 7.25 19.80 LTG 7.72 0.47 6.42 COMPX * -5.09 -10.21 -0.84 N 751 Adj. [R.sup.2] 0.72 P is year-end share price. BV is year-end equity book value. NI is net income. LTG is year-end I/B/E/S mean analyst earnings growth forecast. IND, equals I if the firm is in industry N (based on the 33 industries in Table 1, Panel A), and 0 otherwise. COMPX * is fitted value from a regression of unrecognized stock-based compensation expense, i.e., net income minus pro forma net income disclosed under SEAS No. 123, COMPX, on VOL, expected stock price volatility, LIFE, expected option life, INT, expected risk-free interest rate. DIV, expected dividend yield, OPT-GRANT, number of options granted deflated by number of shares outstanding, VEST, percentage of options vesting each year, BV, NI, LTG, and IND,. BV, NI, and COMPX * are deflated by number of shares outstanding at the end of the year. i and t denote firm and years. Coefficients are estimated using robust regression. The industry-specific intercepts are untabulated. t-statistics are based on White (1980) heteroscedastieity-consistent standard errors. TABLE 5 Summary Statistics from Regressions of Stock Return on Net Income, Change in Net Income, Change in Analyst Earnings Growth Forecast, and Change in the SFAS No. 123 Expense Variable Derived from the Instrumental Variable Approach [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] 1998 Variable Pred Coefficient t-statistic NI + 0.52 3.23 [DELTA]NI + 0.39 2.37 [DELTA]LTG + 0.04 1.03 [DELTA]COMPX * - 13.85 -2.64 N 748 Adj. [R.sup.2] 0.23 1997 Variable Coefficient t-statistics NI 0.72 4.80 [DELTA]NI 0.89 4.24 [DELTA]LTG 0.33 4.19 [DELTA]COMPX * -14.95 -2.70 N 751 Adj. [R.sup.2] 0.33 RET is annual stock return. NI is net income. LTG is year-end I/B/E/S mean analyst earnings growth forecast. INDN equals 1 if the firm is in industry N (based on the 33 industries in Table 1, Panel A), and 0 otherwise. COMPX * is fitted value from a regression of unrecognized stock-based compensation expense, i.e., net income minus pro farina net income disclosed under SFAS No. 123, COMPX, on VOL, expected stock price volatility, LIFE, expected option life, INT, expected risk-free interest rate, DIV, expected dividend yield, OPT-GRANT, number of options granted deflated by number of shares outstanding, VEST, percentage of options vesting each year, BV, NI, LTG, and INDN. NI, and COMPX * are deflated by market value of equity at the beginning of the year. A denotes annual change. i and r denote firm and years. Coefficients are estimated using robust regression. The industry-specific intercepts are untabulated. t-statistics are based on White (1980) heteroscedasticity-consistent standard errors. TABLE 6 Summary Statistics from Regressions of Share Price on Book Value of Equity, Net Income, Analyst Earnings Growth Forecast, and the SEAS No. 123 Expense Variable Derived from the Instrumental Variable Approach 1998 1997 Variable Pred Coefficient t-statistic Coefficient Panel A: Sample Firms with Positive Net Income and Equity Book Value BV + 0.49 5.74 0.42 NI + 9.79 17.30 10.91 LTG + 0.45 3.81 0.66 COMPX * - -38.54 -3.20 -36.82 N 612 664 Adj. [R.sup.2] 0.71 0.77 Panel B: Software Firms with Positive Net Income and Equity Book Value Intercept ? 3.16 0.51 30.80 BV + 1.44 2.07 -1.31 NI + 14.96 3.67 17.88 LTG + 0.32 1.37 0.44 COMPX * - -39.12 -1.68 -126.70 N 22 22 Adj. [R.sup.2] 0.79 0.65 Panel C: Sample Firms from Knowledge-Based Industries with Positive Net Income and Equity Book Value BV + 0.19 3.50 0.17 NI + 24.25 10.46 15.66 LTG + 0.77 2.45 0.44 COMPX * - -52.43 -2.15 -31.95 N 88 101 Adj. [R.sup.2] 0.76 0.75 1997 1996 Variable t-statistics Coefficient t-statistics Panel A: Sample Firms with Positive Net Income and Equity Book Value BV 4.68 0.41 5.81 NI 21.10 9.31 19.90 LTG 6.96 0.60 6.71 COMPX * -3.54 -43.13 -2.57 N 666 Adj. [R.sup.2] 0.78 Panel B: Software Firms with Positive Net Income and Equity Book Value Intercept 1.81 -13.41 -1.39 BV -1.39 1.31 1.74 NI 3.70 8.35 2.77 LTG 1.70 1.20 3.05 COMPX * -2.94 21.40 0.54 N 26 70 Adj. [R.sup.2] 0.84 0.62 Panel C: Sample Firms from Knowledge-Based Industries with Positive Net Income and Equity Book Value BV 2.97 0.38 3.11 NI 11.38 14.07 10.67 LTG 2.20 0.02 0.10 COMPX * -4.28 12.77 0.99 N 101 Adj. [R.sup.2] 0.75 Pooled Variable Coefficient t-statistics Panel A: Sample Firms with Positive Net Income and Equity Book Value BV 0.42 8.89 NI 9.76 32.90 LTG 0.52 9.25 COMPX * -24.06 -3.91 N 1,942 Adj. [R.sup.2] 0.71 Panel B: Software Firms with Positive Net Income and Equity Book Value Intercept 0.96 0.15 BV 0.72 1.61 NI 13.14 6.93 LTG 0.64 3.00 COMPX * -9.86 -0.58 N 70 Adj. [R.sup.2] 0.62 Panel C: Sample Firms from Knowledge-Based Industries with Positive Net Income and Equity Book Value BV 0.22 3.31 NI 14.65 16.03 LTG 0.24 1.61 COMPX * -19.13 -2.31 N 298 Adj. [R.sup.2] 0.69 P is year-end share price. BV is year-end equity book value. NI is net income. LTG is year-end I/B/E/S mean analyst earnings growth forecast. IND,, equals 1 if the firm is in industry N (based on the 33 industries in Table 1, Panel A), and 0 otherwise. COMPX * is fitted value from a regression of unrecognized stock-based compensation expense, i.e., net income minus pro forma net income disclosed under SEAS No. 123, COMPX, on VOL, expected stock price volatility, LIFE. expected option life, INT, expected risk-free interest rate, DIV, expected dividend yield, OPT-GRANT, number of options granted deflated by number of shares outstanding, VFST, percentage of options vesting each year, BV, NI, LTG, and IN[D.sub.N], BV, NI, and COMPX * are deflated by number of shares outstanding at the end of the year. i and t denote firm and years. Knowledge-based industries include Drugs (Compustat four-digit SIC codes 2833-2836), Computers (3570-3577), Electronics (3600-3674), Software (7370-7379), and R&D Services (8731-8734). Coefficients are estimated using robust regression. The industry-specific intercepts are untabulated. t-statistics are based on White (1980) heteroscedasticity-consistent standard errors. TABLE 7 Summary Statistics from Regressions of Share Price on Book Value of Equity, Net Income, and the SFAS No. 123 Expense Variable Derived from the Instrumental Variable Approach [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] 1998 1997 Variable Pred Coefficient t-statistic Coefficient BV + 0.81 11.82 0.70 NI + 3.38 10.19 6.45 COMPX * - -42.95 -5.19 -21.05 N 756 767 Adj. [R.sup.2] 0.53 0.70 1997 1996 Variable t-statistic Coefficient t-statistic BV 9.73 0.45 7.50 NI 15.00 6.84 18.78 COMPX * -2.39 13.72 1.17 N 767 751 Adj. [R.sup.2] 0.70 P is year-end share price. BV is year-end equity book value. NI is net income. IND, equals 1 if the firm is in industry N (based on the 33 industries in Table 1, Panel A), and 0 otherwise. COMPX * is fitted value from a regression of unrecognized stock-based compensation expense. i.e., net income minus pro forma net income disclosed under SFAS No. 123, COMPX, on VOL, expected stock price volatility, LIFE, expected option life, INT. expected risk-free interest rate, DIV, expected dividend yield, OPT-GRANT, number of options granted deflated by number of shares outstanding, VEST, percentage of options vesting each year, BV, Nl, LTG, and IN[D.sub.n], where LTG is year-end I/B/E/S mean analyst earnings growth forecast. BV, NI, and COMPX * are deflated by number of shares outstanding at the end of the year. i and t denote firm and years. Coefficients are estimated using robust regression. The industry-specific intercepts are untabulated. t-statistics are based on White (1980) heteroscedasticity-consistent standard errors. TABLE 8 Summary Statistics from Regressions of Share Price on Book Value of Equity, Net Income, Analyst Earnings Growth Forecast, and Value of Options Granted, Purged of Its Mechanical Relation with Share Pricess Panel A: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] 1998 1997 Variable Pred Coefficient t-statistic Coefficient BV + 0.79 11.32 0.76 NI + 3.35 9.90 6.74 LTG + 0.20 2.25 0.55 GRANT_VA[L.sup.EP] - -5.05 -5.55 -4.08 N 756 767 Adj. [R.sup.2] 0.54 0.71 Panel B: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] 1998 1997 Variable Pred Coefficient t-statistic Coefficient BV + 0.83 11.71 0.78 Nl + 3.50 10.36 7.08 LTG + 0.20 2.24 0.52 GRANT_VAL * - -8.91 -4.37 -6.08 N 756 767 751 Adj. [R.sup.2] 0.53 0.71 0.72 Panel A: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] 1997 1996 Variable t-statistic Coefficient t-statistic BV 10.08 0.50 8.43 NI 16.81 7.25 19.44 LTG 6.94 0.44 6.06 GRANT_VA[L.sup.EP] -3.72 -0.01 -0.01 N 751 Adj. [R.sup.2] 0.72 Panel B: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] 1997 1996 Variable t-statistic Coefficient t-statistic BV 8.90 0.50 8.24 Nl 16.59 7.25 19.57 LTG 5.48 0.43 5.70 GRANT_VAL * -2.18 0.57 0.25 N 751 Adj. [R.sup.2] 0.72 P is year-end share price. BV is year-end equity book value. NI is net income. LTG is year-end I/B/E/S mean analyst earnings growth forecast. IND, equals 1 if the firm is in industry N (based on the 33 industries in Table 1, Panel A), and 0 otherwise. i and t denote firm and years. GRANT-VA[L.sup.EP] is estimated total grant-date value of options granted during the year that is not dependent on share price. It is measured based on Black and Scholes (1973) option values, using the firm's disclosed valuation inputs, i.e., VOL, expected stock price volatility, LIFE, expected option life, INT, expected risk-free interest rate, and DIV, expected dividend yield, while setting share price and exercise price both equal to the sample mean price in each year. Total grant-date option value is then cal culated by multiplying this "equal price" option value by number of options granted. GRANT_VAL * is FVOPT * multiplied by OPT-GRANT, number of options granted during the year, where FVOPT * is the predicted value from a regression of FVOPT the fair value of options granted, on VOL, LIFE, INT, DIV. BV. NI, LTG, and INT, DIV, BV, NI, GRANT_VA[L.sup.EP], and GRANT_VAL * are deflated by number of shares outstanding at the end of the year. Coefficients are estimated using robust regression. The industry-specific intercepts are untabulated. t-statistics are based on White (1980) heteroscedasticity-consistent ,tandard errors.

We appreciate the helpful comments and suggestions from workshop participants at Cambridge University, Carnegie Mellon University, Columbia University, The University of New South Wales Australian Graduate School of Management Research Camp, and Stanford Accounting Summer Camp, Bill Beaver, Jules Cassel, Greg Clinch, Ken Peasnell, Stephen Penman, Ken Singleton, Richard Sloan, Michael Williams, and two anonymous reviewers. We also appreciate the research assistance of Hung-Ken Chien and Kazbi Kothavala. We appreciate funding by the GSB Faculty Trust Fellowship, Stanford University Graduate School of Business.

Editor's note: This paper was accepted by Terry Sheviin, Senior Editor

(1) Consistent with this view, Standard & Poor's includes SFAS No. 123 expense in "core earnings," which it introduced as a standard, comparable number that reflects ongoing operating earnings (Business Week 2002).

(2) Our tests are based on the assumption that the marginal investor is rational and share prices aggregate investors' consensus beliefs. See Barth et al. (2001) and Holthausen and Watts (2001) for discussion of the assumptions underlying value-relevance research and its interpretation. (3) For evidence on the extent to which firms understate SFAS No. 123 expense, see Aboody et al. (2003).

(4) Under the SFAS No. 123 exposure draft, an intangible asset and equity would be recognized equal to the total value of options granted, with the asset amortized over the vesting period. Under SFAS No. 123, no asset is recognized. Thus, equity and assets would have been higher under the exposure draft approach; the net income effect is the same.

(5) Using disclosures in 1996 and not controlling for the mechanical relation between share price and option value, Rees and Stott (1998) find a significant positive relation between SFAS No. 123 expense and share price and returns. Using only 1996 disclosures for firms in seven industries, Chamberlain and Hsieh (1999) find a negative relation.

(6) All our inferences are robust to using total assets as an alternative deflator.

(7) The robust regression procedure begins by calculating Cook's D statistic and excluding observations with D > 1. Then, the regression is re-estimated, weights for each observation are calculated based on absolute residuals, and the estimation is repeated using the weighted observations (Berk 1990). Our inferences are unaffected by using ordinary least squares estimation.

(8) Equation (1) does not include in BV an adjustment for COMPX because SFAS No. 123 expense results in a debit to retained earnings and a credit to "paid in capital-stock options." However, because COMPX is net of tax, the debit is smaller than the credit, with the difference recognized as a deferred tax asset. Because the tax provision is not disclosed, we consider the tax effect as a cross-sectional constant embedded in COMPX's coefficient. Our inferences are unaffected if we adjust BV for deferred taxes, assuming a 35 percent tax rate. Also, our inferences are unaffected if we adjust BV to exclude options, including related tax effects.

(9) This can be seen by taking the derivative of the Black and Scholes (1973) option pricing formula with respect to share price, and setting the exercise price equal to the share price.

(10) Untabulated Pearson (Spearman) correlations between P and share price at option grant date, i.e., the option exercise price, for 1998, 1997, and 1996 are 0.78, 0.56, and 0.60 (0.84, 0.70, and 0.64), all of which are significant.

(11) Aboody (1996) uses as instruments the number of options outstanding, granted over the prior ten years. Our more comprehensive set of instruments likely increases the power of our tests (Skinner 1996). Using as instruments firms' option pricing inputs preserves in COMPX * any effects of management discretion. Also, as Table 1, Panel C indicates, the correlation between price and model inputs, particularly VOL and DIV, is high, albeit not as high as the correlation between price and option fair value, FVOPT, the variable with the potential mechanical relation problem. To the extent these instruments are correlated with the error in Equation (1) arising from COMPX's mechanical relation with P, the instrumental variables approach might not eliminate the coefficient bias. Thus, we test whether the error from estimating Equation (1) with COMPX * is correlated with the instruments (Griliches and Intriligator 1983), and find it is correlated with VOL. Our inferences are unaffected if we exclude VOL from the set of instruments.

(12) As is standard in instrumental variables estimation, the most efficient estimates are obtained by using as instruments variables intended to capture the endogenous variable, COMPX, as well as all other independent variables in the system of equations, i.e., BV, NI, and LTG. Including these other independent variables reflects the notion that share price is the variable we are attempting to remove from COMPX. Thus, the first-stage regression needs to include variables that are instruments for share price as well as for COMPX. Because Equation (1) posits that BV, NI, and LTG explain share price incremental to COMPX, they are likely candidates for instruments, in addition to the variables that capture COMPX, i.e., VOL, DIV, INT, LIFE, OPT_GRANT, and VEST.

(13) For 1998 we use the average over 1996 through 1998, for 1997 we use the average over 1996 and 1997, and for 1996 we use the 1996 amounts. Our inferences are unaffected by using the contemporaneous variable amounts.

(14) The term significant refers to statistical significance at the 0.05 level or less based on a one-tailed test for signed predictions and a two-tailed test otherwise. All t-statistics are calculated based on White (1980) standard errors.

(15) Our inferences are unaffected by estimating all valuation equations permitting the coefficient on NI to differ for firms with negative NI, and to defining NI as income before extraordinary items and discontinued operations.

(16) We also estimate Equation (1) in a pooled cross-sectional regression with fixed-year and fixed-industry effects. Untabulated results indicate the coefficient on COMPX * is -24.06 and the t-statistic is -4.47.

(17) Because data necessary to compute COMPX for 1995 are not disclosed, we are unable to estimate Equation (2) for 1996. Also, Table 4 reveals that the coefficient on COMPX * varies across years, suggesting that estimating Equation (2) using [DELTA]COMPX * could affect our inferences (Landsman and Magliolo 1988). Thus, we estimate Equation (2) using instead COMPX *, and [COMPX*.sub.t-1]. Untabulated findings reveal that our inferences are unaffected. In particular, the coefficients on COMPX *, are significantly negative, and that on [COMPX*.sub.t-1] is significantly positive in the 1998 equation and insignificantly different from 0 in the 1997 equation.

(18) Following Kasznik and Ley (1995), knowledge-based industries include Drugs (four-digit SIC codes 2833-2836), Computers (3570-3577), Electronics (3600-3674), Software (7370-7379), and R&D Services (8731-8734).

(19) Hanlon et al. (2003) estimate an analogous specification when testing for a nonlinear relation between future operating performance and the value of options granted to the top five executives.

(20) Consistent with incentive effects, the extant literature documents an association between executive stock-based compensation and firm performance (e.g., Murphy 1985; Lambert and Larcker 1987; DeFusco et al. 1990; Jensen and Murphy 1990; Lambert et al. 1993; Hanlon et al. 2003). However, recent studies question whether the benefits associated with stock-based compensation are related to incentive effects or to sorting (Lazear 2001) or retention (Oyer 2001; Oyer and Scheafer 2002) effects. We do not examine the nature of benefits associated with stock-based compensation, but presume that any such benefits are reflected in recognized or expected profitability.

(21) Consistent with this, Table 1, Panel C, indicates COMPX * is significantly positively correlated with LTG (Pearson (Spearman) correlation = 0.46 (0.46)). The correlation between COMPX and LTG also is significantly positive but smaller (0.33 (0.34)). Our inferences in this section are insensitive to using COMPX in place of COMPX *.

(22) Our analyses are not intended to determine whether higher stock-based compensation results in higher expected growth in earnings. Firms with high growth opportunities might grant more stock options to employees. However, establishing that stock-based compensation and the valuation effects of expected earnings growth are positively related lends support to claims that stock-based compensation is associated with an intangible asset. It also lends support to claims that because employees are not obligated to render services, the intangible asset is not recognizable under the FASB's Conceptual Framework because these expected future earnings are not probable future benefits controlled by the firm as a result of past transactions and events (FASB 1995, [paragraph] 92-96).

(23) As time lengthens between option grant date and the valuation equation date, more benefits associated with incentive effects of past years' option grants are realized in NI and BV. Consistent with this, COMPX *'s coefficient is significantly more negative for 1998 than for 1997 (t = 1.69) and 1996 (t = 2.81); the coefficient for 1997 is more negative than for 1996, but not significantly so (t = 1.26). This coefficient pattern also is consistent with investors gradually incorporating the expense into their valuation assessments subsequent to SFAS No. 123's issuance in 1995.

(24) The increase in COMPX *'s coeffieient from 1996 to 1998 is not consistent with potential mechanical effects of the SFAS,No. 123 phase-in, which would result in a decrease. However, it is consistent with benefits of stock-based compensation being reflected in BV and NI as time increases between grant date and the valuation equation date. Because firms' vesting periods differ, there also can be phase-in effects in the separate-year estimations. Thus, we estimate Equation (1) permitting COMPX * 's coefficient to vary with VEST. Our inferences are unaffected.

(25) Firms receive a tax deduction for nonqualified stock options equal to the intrinsic value of the options at exercise date (Soffer 2000). Because OUT_VAL * includes intrinsic value and time value it likely is positively correlated with intrinsic value. Thus, any expected tax benefit will be reflected in its valuation coefficient.

(26) An alternative approach is to use as the dependent variable the sum of the value of outstanding options and share price. This approach eliminates the concern about the mechanical relation between share price and the value of options outstanding. Untabulated statistics from this specification reveal the same inferences as from Table 4.

(27) Moreover, the correlation between number of options granted and annual returns is small. The Pearson (Spearman) correlation is 0.02 (-0.01) in 1998 and -0.02 (0.03) in 1997; p-values all > 0.70.

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David Aboody

University of California, Los Angeles

Mary E. Barth

Ron Kasznik

Stanford University

Submitted March 2003

Accepted September 2003

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Author: | Aboody, David; Barth, Mary E.; Kasznik, Ron |
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Publication: | Accounting Review |

Date: | Apr 1, 2004 |

Words: | 12788 |

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