Abstract
We use a residual income valuation framework to compare equity valuation implications of four approaches to employee stock options (ESOs) accounting: APB 25 “recognize nothing”, SFAS 123 (revised) “recognize ESO expense”, FASB Exposure Draft “recognize and expense ESO asset” and “recognize ESO asset and liability”. Theoretical analysis shows only grant date recognition of an asset and liability, and subsequent marking-to-market of the liability, results in accounting numbers that capture the dilution effects of ESOs on current shareholder value. Out-of-sample equity market value prediction tests and in-sample comparisons of model explanatory power also support the “recognize ESO asset and liability” method.
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Notes
For a published version of the results, see Christensen and Feltham (2003, ch. 9).
The data needed for the APB 25 and SFAS 123 (revised) approaches are readily available from SFAS 123 mandated disclosures, whereas the additional items needed to implement the Exposure Draft and particularly the Asset and Liability approaches have to be approximated by the external analyst, with attendant greater risks of measurement errors.
There are some minor differences between the accounting methods required to be used in income recognition by IFRS 2 and required to be used in the footnote disclosures under SFAS 123.
Consistent with this, Hanlon et al. (2003) finds a positive empirical relation between ESO grants to the firm’s top five executives and future earnings.
Most ESOs are granted at-the-money. What follows ignores the issue of whether the options have an exercise price that is different to the market value of the underlying shares at grant date since incorporating this possibility merely complicates the analysis without adding anything significant.
ESO expense is the annual amount needed to amortize the off-balance sheet fair valued ESO asset over the vesting period of the ESO.
A possible refinement to this procedure would be to follow the proposal by Ohlson and Penman (2005) that the change in option value be separated into an interest expense component and the residual component, in the expectation that the former is the predictable element and the other is the pure windfall.
For simplicity, we ignore the possibility that the employee might exercise earlier as it makes no difference to the accounting.
Again for simplicity, we ignore any tax implications.
Other academic researchers (Kirschenheiter et al., 2003, 2004; Ohlson & Penman, 2005) and investment analysts (Credit Suisse First Boston, 2004b) make a related observation regarding Method 4’s theoretical superiority regarding accounting ESO dilution to that provided by Christensen and Feltham (2003).
The difference between these two methods is not in the recognition of comprehensive income, but rather as shown in section 1.4, the different balance sheet treatment in Method 3 results in a measure of residual income that yields an interpretable residual income-based valuation estimate whereas Method 2 does not.
Ohlson and Penman (2005) recommends additional accounting entries for Method 4 beyond those set out in Table 1. As well as charging ESO expense to net income, the paper also charges against net income an imputed interest expense based on the beginning-of-period fair value of the ESOs. This interest expense is deducted from (added to) the loss (gain) from any increase (decrease) in the value of the ESOs during the period. That gain or loss is then included in other comprehensive income. The interest expense can be thought of as the predictable element in the change in the value of the ESOs and the remaining gain or loss as the unpredictable element. Ohlson and Penman (2005) also advocates “truing up” net income over time, either by transferring the accumulated gains and losses into net income at the end of the life of each option, or spreading the accumulated amounts into net income over time, thereby smoothing out items that have low persistence. We do not consider these refinements in our theoretical analysis because they do not change the valuations in our model.
We make this assumption to simplify the exposition. Since none of the accounting methods under consideration involves immediate recognition of options that might be granted in the future, nothing is gained by introducing such complications. We return to the valuation implications of this simplification at the end of Section “Dividend-based valuation”.
Note that our analysis is cast in terms of total dollar amounts rather than per share amounts. Our purpose in focusing on dollar amounts is primarily to avoid irrelevant complications such as the need to model the ESOs as warrants (Li & Wong, 2005), and hence to sidestep the endogeneity problem arising from the mutual dependence, at the per share level, of stock and ESO values.
The exercise proceeds are a source of capital to the firm. To avoid irrelevant complications, we make the standard Miller and Modigliani (1961) type of assumption that the firm is following an optimal investment strategy such that an additional dollar of X results in a dollar increase in dividends, leaving the total value of the firm unchanged. We make an equivalent assumption regarding m’s employment contract. An increase in X will result in the ESO being worth less to m, but we assume that this would be offset by an increase in straight salary such that both m’s utility and the value of e’s shares are unchanged.
We make this assumption because, in practice, during our sample period, all sample firms use the APB 25 method. When we conduct our empirical tests, we impose the four ESO accounting methods on the data. It is therefore important that our theoretical analysis does not incorporate the effects of ESO accounting methods on managerial behavior.
We can see from Eq. (9) that the dilution correction needed to get the correct market value per share requires \(\frac{{MV}_0^{e}}{n^{e}} = \frac{{MV}_0^{e} + {OPV}_0}{n^{e} + n^{m}}\). This requirement implies that \(\frac{n^{m}}{n^{e}}=\frac{{OPV}_0}{{MV}_0^{e}}\). Current accounting rules for computing EPS makes an adjustment based on option intrinsic values instead of their fair values. As a result, fully diluted EPS will be biased upwards. Core et al. (2002) make a similar observation.
A natural alternative approach would be to use the abnormal earnings growth (AEG) model developed by Ohlson and Juettner-Nauroth (2005) as it does not assume that clean surplus accounting is employed and can easily handle changes in the numbers of shares in issue. It can readily be shown that when net income is measured under any of the four ESO accounting approaches considered in this paper the AEG model will produce a value estimate equal to MV e0 +OPV 0, if dividends are defined on a total net dividends basis. Furthermore, if dividends are defined on a per share basis then the AEG value will always equal MV e0 , regardless of the basis on which the accounting is done. As we shall see, this is not always the case with the RIV model. While this makes the AEG model a potentially extremely useful model for many practical investment purposes, it means it is not a suitable engine for obtaining insights into how equity market value reflects ESO transactions. For the present study, an advantage of the RIV model is that it makes use of both balance sheet and income statement items, whereas the balance sheet is superfluous in the AEG model.
This result is not simply an artifact of our assumption that amortization is charged on a straight-line basis. Any allocation scheme that assigns the proportion δ t of OPV 0 as ESO expense in period t and satisfies the conditions that all 0 ≤ δ t ≤ 1 such that \(\sum\limits_{t=1}^T {\delta _t} =1\) will result in a value for MV 20 that falls somewhere between MV e0 and MVE e0 +OPV 0. This follows from the fact that any discounted sum of ESO expense charges must result in \(\sum\limits_{t=1}^T {\frac{\delta _t}{(1+r)^t}}<1{if} r>0\)
A parallel can be drawn here with the use of simple multiples of accounting numbers that loom large in professional publications and that research has shown can often out-perform valuation methods that have more theoretical support (e.g., Liu, Nissim, & Thomas, 1999). This still leaves open the possibility, of course, that the rankings might be different again if the measures were combined with other sources of information available to investors.
This might not happen if the items in question were included as part of book value of equity or residual income, because then the ESO items would be constrained to have the same valuation coefficients as other components of book value and residual income. Based on the findings in Barth et al. (2005), disaggregation of balance sheet and income statement components should improve out-of-sample predictions. However, our comparisons are not between aggregated and disaggregated accounting numbers but rather between equations that include or exclude ESO items that could have predictive power in their own right.
Although Barth and Kallapur (1996) provides convincing reasons to estimate cross-sectional equity valuation models similar to ours using unscaled data, there are several additional reasons to avoid estimating our equations on a per share basis. First, our theoretical analysis suggests that equations using different accounting methods for ESOs require different share amounts as scalars. This would amount to throwing away the baby with the bath water in that we could no longer carry out any meaningful tests of the valuation effects of different methods of accounting for ESOs. Second, per share deflation for all but Method 4 would require estimating additional shares relating to ESOs based on option fair value. This would needlessly introduce the potential of additional measurement error in the affected models. Nonetheless, we also estimate our equations using two deflators, sales and total assets, to address the possibility that our findings are sensitive to scale bias arising from estimation using unscaled data.
Following prior research (e.g., Barth, Beaver, Hand, & Landsman, 1999), the different versions of Eqs. (22) and (23) that we estimate include intercepts and error terms to allow for the average valuation effects of unmodeled other information. We acknowledge that omission of unmodeled other information variables could bias the coefficients of the included variables.
The jack-knife procedure assumes that parameter estimates are generated from a randomly collected sample and that observations in the sample are independent.
We thank Jim Ohlson for suggesting we compare the four accounting methods using this approach.
Bell et al. (2002) point out that although defining residual income based on net income before extraordinary items and discontinued operations violates the clean surplus assumption in Ohlson (1995), it eliminates potentially confounding effects of large one-time items and is consistent with prior empirical research (e.g., Barth et al., 1999, 2005; Dechow, Hutton, & Sloan, 1999; Hand & Landsman, 2005). Ohlson (1999, p. 160) concludes that this approach is justified in empirical work because one-time items are likely to have limited forecasting ability.
In particular, we set the r equal to r f + β × 0.06, where r f is the prevailing 3-month t-bill rate at the beginning of each fiscal year and 0.06 is an estimate of the market risk premium, r m -r f . Our estimate of the market risk premium is similar to the estimate of the long-run equity risk premium in Ibbotson Associates (2005) over our sample period.
There are two additional inconsistencies in the measurement of equity book value and residual income for all but Methods 1 and 2. The first arises from the fact that OPTIONEXPENSE is on an after-tax basis, and we ignore income tax effects in our measurement of equity book value under Methods 3 and 4. In principle, equity book value under these two methods should reflect the same accumulated before-tax OPTIONEXPENSE charge. The second is that OPTIONEXPENSE reflects adjustments for anticipated forfeitures, but book equity under Methods 3 and 4 cannot be adjusted appropriately because we do not have details of the forfeitures.
Li and Wong (2005) point out that Black-Scholes estimates of ESO fair values result in the overstatement of ESO expense compared to the amount that would be obtained using a warrant pricing model. To the extent that our use of Black-Scholes fair value estimates creates measurement error in option expense, option equity, and option liabilities, this will reduce our ability to distinguish between the models’ relative forecasting ability.
Following Bell et al. (2002), we require positive beginning owner’s equity to ensure that the firm’s cost of capital in calculating abnormal earnings (r BVE t-1) is positive. Also for the case of the firm-specific equity cost of capital sample, we also require non-missing data for beta.
Note the larger sample sizes for Table 4 estimations relative to the 1,354 and 1,204 firm-year observations used for cross-accounting method comparisons in Tables 5 and 6 reflects the fact that Table 4 only requires data needed to estimate Eq. (23a) for Method 1, the APB 25 method.
Details are available from the authors on request.
We consider t-statistics with associated two-sided p-values less than 0.05 as statistically significant.
Inferences based on estimations in which sales and total assets are used as deflators are similar to those based on the reported findings in Table 5.
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Acknowledgments
The authors are grateful to Jack Ciesielski of R.G. Associates, Inc., for providing the employee stock option data used in this study, and to the Center for Finance and Accounting Research, University of North Carolina, Republic of China National Science Council (Project no. NSC93-2416-H-002-026), and the Financial Services Exchange for providing financial support. The authors thank workshop participants at the 2005 Review of Accounting Studies Conference, particularly David Aboody (discussant) and Jim Ohlson, and the two anonymous reviewers and Stephen Penman, the editor, for helpful comments. The paper also benefited from comments received at the 2004 European Accounting Association Congress, the 2004 London Business School Accounting Symposium, the 2004 University of Minnesota Empirical Accounting Research Conference, Brigham Young University, City University of London, Dartmouth College, University of North Carolina, National Taiwan University, Ohio State University, and Penn State University.
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Landsman, W.R., Peasnell, K.V., Pope, P.F. et al. Which approach to accounting for employee stock options best reflects market pricing?. Rev Acc Stud 11, 203–245 (2006). https://doi.org/10.1007/s11142-006-9008-x
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DOI: https://doi.org/10.1007/s11142-006-9008-x
Keywords
- Equity valuation
- Employee stock options
- ESO asset and liability
- ESO expense
- Residual income
- Mark-to-market