asset value. In particular, as the value of the firm’s assets exceeds the value of debt by a larger margin, the sensitivity of debt value to changes in asset value approaches zero and the sensitivity of equity value to changes in asset value approaches one (Merton, 1974). Therefore, if the sensitivity to changes in asset value of the value of employee stock options is more similar to equity than it is to debt, then the sensitivity of option value to changes in asset value should be closer to one (zero) for firms further from (closer to) debt default. As a test of this relation, we present evidence on the sensitivity of the change in the value of liabilities, ∆MVL, equity, ∆MVE, and employee stock options, ∆MVO, to changes in the value of assets, ∆MVA, for firms with different distances to default on their debt. We also provide evidence on the expected return on options, RET_OPT.
We base our estimates of option value and expected return on the approach in Daves and Ehrhardt (2007), as outlined in Appendix B. Daves and Ehrhardt (2007) shows how to compute capital components’ values and required returns using only market observables. Specifically, using EQUITYVOL, common shares outstanding, and employee stock option disclosure data from Compustat, we first simultaneously solve equations (B3) through (B6) in Appendix B to
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obtain estimates of option value and the partial derivative of option value with respect to share price. We then input those estimates, combined with share price, ECC, and the risk-free interest rate, into equation (B6) in the Appendix to obtain an estimate of the return on options,
RET_OPT. To estimate the values of assets and liabilities, we use the procedure described in Barth, Hodder, and Stubben (2008), which builds on Merton (1974) and Hillegeist et al. (2004).
Given observed equity value and historical stock return volatility, we invert the Merton (1974) model to estimate the value of assets, which is then used to estimate the value of liabilities.
For purposes of comparison, we also estimate the value of employee stock options using the Black-Scholes (1973) option pricing formula, based on inputs from the employee stock option disclosure data from Compustat; namely, average exercise price, expected stock return volatility, risk-free interest rate, expected dividend yield, and time to maturity. We follow Landsman et al. (2006) to estimate the average life for options outstanding.
Table 4, Panel A, presents distributional statistics for and Panel B presents correlations between the variables we construct. We refer to the Daves and Ehrhardt (2007) estimate of the value of employee stock options as the D-E value, and the Black-Scholes (1973) estimate as the B-S value, both scaled by market value of common equity. The estimation methods differ most with respect to their treatment of dilution and leverage.23
23 The Black-Scholes (1973) option pricing model is frequently used by firms to estimate the value of employee options at the grant date (Aboody, Barth, and Kasznik 2006; Landsman et al. 2006). The binomial pricing model is another common method used to estimate option value. As commonly applied, neither of these methods adjusts for the effects of dilution or considers debt in the capital structure. Appendix A shows how the binomial model can be adjusted for dilution and leverage.
How large differences are is an empirical question. Panel A reveals that the mean B-S value of employee options is 6% of the market value of common equity and the mean D-E value is 4%. These statistics indicate that the Black-Scholes (1973) formula results in values of employee stock options that are overstated by approximately 50% when dilution is ignored. Consistent with the greater risk of employee stock
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options, the mean expected return on options, RET_OPT, of 22% is substantially higher than the mean expected equity cost of capital, ECC, of 13%.
Additional descriptive statistics presented in Panel B reveal that B-S value and D-E value are positively correlated, although not highly (Corr. = 0.14). Panel B also reveals that, contrary to theory, B-S value is negatively correlated with BETA (Corr. = –0.20). This is not the case for D-E value, which is positively correlated with BETA (Corr. = 0.17). B-S value is positively correlated with LEVERAGE (Corr. = 0.08) and D-E value is negatively correlated with
LEVERAGE (Corr. = –0.26). Neither value estimate is highly correlated with equity volatility, EQUITYVOL.24
Table 5 presents statistics that enable us to assess the sensitivity to changes in asset value of equity value, liability value, and employee option value as the distance to default increases.
Panel A presents the median ratio of the change in the values of equity, debt, and options to the change in asset value by distance-to-default quintile. We define distance to default as the excess of asset market value over liability book value, scaled by the market value of assets. As
expected, Panel A reveals that the unit change in equity value per unit change in asset value monotonically decreases as the distance to default increases (0.98 for quintile 5 to 0.73 for quintile 1). Also as expected, Panel A reveals the opposite for debt—that is, the unit change in debt value per unit change in asset value monotonically increases as the distance to default increases (–0.02 for quintile 5 to 0.25 for quintile 1). These relations are consistent with Merton
Consistent with theory, the D-E required return on options, RET_OPT, is positively correlated with BETA (Corr. = 0.12). RET_OPT is positively correlated with EQUITYVOL by construction. Overall, the statistics in Table 4 indicate that D-E value and RET_OPT are consistent with the theory from which they are derived.
24 Recall that the value of a warrant is increasing in the volatility of firm assets and decreasing in leverage. Leverage increases the volatility of equity but not necessarily the volatility of assets. Therefore, the value of warrants is not necessarily increasing in the volatility of common equity.
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(1974), which shows that as the probability of default increases toward certainty, debt holders become claimants on the firm’s assets and, thus, effectively equity holders.
More importantly for our research question, as predicted, Panel A reveals that the change in D-E value exhibits a convex pattern that is similar to that of equity value and opposite that of debt value. Namely, D-E value decreases monotonically in the change in asset value as the distance to default decreases (0.06 for quintile 5 to 0.01 for quintile 1). To test whether these patterns are significant, we estimate the relation between each of the value sensitivities and distance to default. Table 5, Panel B, presents the findings. It reveals that the sensitivity of common equity value and option value to changes in asset value each is significantly positive (t
= 5.16 for equity value and 8.67 for option value). In contrast, the sensitivity of liability value to changes in asset value is significantly negative (t = –5.24).
Taken together, the findings in Table 5 provide corroborative evidence that employee stock options share more in common with equity than with debt. This, too, suggests that options would be more appropriately classified as equity, not liabilities, for financial reporting purposes.