A Superfield for Every Dash-Chromotopology

The recent classification scheme of so-called adinkraic off-shell supermultiplets of N-extended worldline supersymmetry without central charges finds a combinatorial explosion. Completing our earlier efforts, we now complete the constructive proof that all of these trillions or more of supermultiplets have a superfield representation. While different as superfields and supermultiplets, these are still super-differentially related to a much more modest number of minimal supermultiplets, which we construct herein.Comment: 13 pages, integrated illustration

Diluted Earnings Per Share Overstatement Bias: Including Unrecognized Employee Compensation In Proceeds From Assumed Exercise Of Employee Stock Options Under The Treasury Stock Method

Generally accepted accounting principles (GAAP) require firms to recognize compensation expense under the fair value method in the case of employee stock options. Straight line amortization of the options grant date fair value must be recognized as expense over the service period which decreases the earnings per share numerator. For diluted earnings per share (EPS), GAAP requires using the treasury stock method, where proceeds from assumed stock option exercise is used to purchase treasury shares at the average for the period price. Exercise proceeds include the exercise price plus unrecognized future employee compensation. For profitable firms, exercise is assumed if dilutive - more shares are assumed issued than are reacquired for the treasury which increases the diluted EPS denominator. These requirements are consistent across US GAAP and International Financial Reporting Standards. This paper tests whether including unrecognized employee compensation in proceeds from the assumed exercise of employee stock options under the treasury stock method is appropriate. A simple multi period model that assumes a risk free environment with complete certainty is applied. This study contributes to the literature by demonstrating that future unrecognized employee compensation should not be included in proceeds from the assumed exercise of stock options under the treasury stock method. Doing so consistently causes diluted EPS overstatement, and in certain instances causes assumed exercise of in the money options to be antidilutive, which results in complete exclusion from the diluted EPS calculation. This research extends the employee stock option work of Doran (2005 and 2008) that found: 1) Compensation expense recognized over the employee service period should equal the periodic annuity amount that provides the options grant date fair value, and 2) Treasury shares should be assumed purchased at the higher end of period stock price

Employee Stock Options And Diluted Earnings Per Share

At the time of this writing, SFAS No.123 (1995) prescribes GAAP in accounting for employee stock options.  It allows firms to choose either the intrinsic or fair value method in determining the amount of compensation expense recognized for employee stock options.  The choice of method affects the numerator of the earnings per share (EPS) calculation.   The FASB recently issued a revised SFAS No. 123 (2004) which will require uniform application of the fair value method.  GAAP also requires that the denominator for the diluted EPS calculation be increased for incremental shares under the treasury stock method.  SFAS 128 requires the treasury stock method be applied where the proceeds from the assumed exercise of options are used to acquire shares of the firm’s outstanding stock at the average market price for the period.  Previous to SFAS No. 128, APB Opinion No. 15 required that the higher of average or period ending stock price be used in determining the number of shares reacquired with the proceeds from the assumed exercise of stock options.  This paper develops a simple one period model that assumes a risk free environment with complete certainty conditions in testing the accuracy of EPS calculated under GAAP using the fair value method vs. the intrinsic value method.   The results indicate that EPS reported under the intrinsic value method are overstated, and further indicate that a combination of both the fair value method and the treasury stock method is needed in calculating diluted EPS.  This fair value and treasury stock method combination is shown to not “double count” the stock option’s impact upon EPS.  The results also indicate a slight misstatement of diluted EPS under the fair value method when applying the treasury stock method requirements of SFAS No. 128.  Correct EPS results when shares are assumed reacquired for the treasury at the higher year ending price, consistent with superseded APB 15.  However, the diluted EPS misstatement is so slight that the FASB’s rationale for always requiring the use of average period price seems likely to be justified.  The findings of this research support the requirements of SFAS No. 123 (revised 2004) and SFAS No. 128

Methodological Choices In Detecting Divergent Earnings: An Extension

Divergent earnings are those that differ from expected.  Doran (2000) provides evidence that nonparametric tests based upon rank values are superior to parametric alternatives in detecting divergent earnings.  He also finds that deflator choice (i.e., forecasted earnings or market price of the stock) is of little importance when superior nonparametric methods are used.  This study extends the efforts of Doran (2000) by testing for benefit derived from the common research method of deflating earnings data.  The data used here is the same as used by Doran (2000), where Value Line is the source of all earnings data.  One hundred independent two sample tests are performed between a positive earnings group and a matched control group.  The tests are performed with various levels (1%, 3%, 5%, 7%, and 10 %) of positive actual earnings introduced.  Failure to reject the null hypothesis of no positive earnings divergence indicates the existence of Type II error (determined using the nonparametric Mann Whitney test).  The Mann Whitney test was performed on the undeflated data, and the same data deflated by: 1) forecasted earnings, and 2) market price of the stock.  Difference in frequency of type II error is determined using the Chi-square test.  The results generally indicate no significant difference in the ability to identify abnormal divergent earnings when utilizing deflated data.  Statistical tests are found here to be at least as powerful when undeflated earnings data are used.  There is weak evidence supporting the notion that deflating earnings data inhibits the ability to detect abnormal earnings.  These findings indicate that the common practice of deflating earnings data is unnecessary, and may actually weaken the power of statistical tests.  &nbsp

A Note On Accounting For Employee Stock Options When Reporting Diluted Earnings Per Share Under The Treasury Stock Method

Firms must currently apply the fair value method in determining the amount of employee compensation incurred in the case of employee stock options.  Current GAAP also requires that for purposes of calculating diluted earnings per share (EPS), the treasury stock method be applied where the assumed proceeds from exercise of the optioned shares is used to purchase shares of the firm’s stock at its average market price of the earnings period.  These incremental shares increase the denominator for purposes of calculating diluted EPS.  These requirements are consistent across the pronouncements of the Financial Accounting Standards Board (FASB) and the International Accounting Standards Board (IASB).  This study extends the work of Doran (2005) and Doran (2008).  These previous studies found that applying the treasury stock method where shares are assumed purchased at the average for the period price (instead of end of year price) understates the number of incremental shares (the denominator), which overstates diluted EPS.  However, these previous works assumed that no shares were actually purchased for the treasury during the earnings period.  The FASB indicates one reason that the average for the period price is appropriate is because if treasury shares purchases were to occur, “the shares would be purchased at various prices, not at the price at the end of the period.”  This study tests the notion that the average for the period price is appropriate under circumstances where the firm actually purchases shares for the treasury at its average market price during the earnings period.  This paper employs a simple one period model that assumes a risk free environment with complete certainty.  The model allows comparison of computed EPS with an a priori known, correct amount.  Consistent with Doran (2005) and Doran (2008), the results here again indicate that assuming purchase of treasury shares at their average market price of the earnings period understates the EPS denominator which results in EPS overstatement.  Correct diluted EPS is derived when the shares assumed purchased under the treasury stock method are acquired at the higher period ending market price.&nbsp

Employee Stock Options And Diluted Earnings Per Share: An Extension

Firms must currently apply the fair value method in determining the amount of employee compensation incurred in the case of employee stock options.   The amount of such compensation is required to be measured as fair value of the equity instrument at the grant date, with compensation expense recognized over the service period under the straight-line method.  This compensation expense affects the numerator for purposes of calculating earnings per share (EPS) under generally accepted accounting principles (GAAP).  Current GAAP also requires that for purposes of calculating diluted EPS, the treasury stock method be applied where the assumed proceeds from exercise of the optioned shares is used to purchase shares of the firm’s stock at its average market price of the earnings period.  These incremental shares increase the denominator for purposes of calculating diluted EPS.  These requirements are consistent across the pronouncements of the Financial Accounting Standards Board (FASB) and the International Accounting Standards Board (IASB).  This study extends the work of Doran (2005) where a single period model was assumed and found: 1. Application of the fair value method does not double count the impact of compensation recognized, and 2. Applying the treasury stock method where shares are assumed purchased at the average for the period price (instead of end of year price) understates the number of incremental shares (the denominator), which overstates diluted EPS.  This paper employs a simple multi period model that assumes a risk free environment with complete certainty in testing the accuracy of GAAP compliant diluted EPS in the case of employee stock options.  Consistent with Doran (2005) the results here again indicate that assuming purchase of treasury shares at their average market price of the earnings period understates the EPS denominator. The results of this study also indicate that the reported employee compensation expense is understated.  The observed cause of this numerator error is treating the “payment” for the option (employee service) as if it was received in full at the grant date - as a lump sum (like inventory or some other asset), rather than being received ratably over the employee service period – as an annuity.  Each of these findings contributes to the observed overstatement of diluted EPS.  Correct diluted EPS is observed when the employee service is treated as being received ratably over the service period, and the shares assumed purchased as treasury stock are acquired at the higher period ending market price.  The amount of diluted EPS overstatement under both FASB and IASB standards is directly related to the length of the term of the option

Methodological Choices In Detecting Divergent Earnings

This paper empirically tests for methodological superiority in detecting divergent earnings (the difference between actual and expected earnings).  Divergent earnings are generated using Value Line forecasted and reported earnings data.  Two hundred random samples of 100 cases each are drawn.    One hundred independent two sample tests are performed with 0%, 1%, 3%, 5%, 7%, and 10 % positive earnings introduced.  The two sample tests are performed using both parametric (t test), and nonparametric (Mann Whitney test) statistics.  They are performed on the “divergent earnings” data deflated by: 1) forecasted earnings , and 2) the market price of the stock.  The results indicate that the superior alternative is nonparametric statistical methods based upon ranks, and the deflator choice under these nonparametric methods is of little consequence

Early Dark Energy Cosmologies

We propose a novel parameterization of the dark energy density. It is particularly well suited to describe a non-negligible contribution of dark energy at early times and contains only three parameters, which are all physically meaningful: the fractional dark energy density today, the equation of state today and the fractional dark energy density at early times. As we parameterize Omega_d(a) directly instead of the equation of state, we can give analytic expressions for the Hubble parameter, the conformal horizon today and at last scattering, the sound horizon at last scattering, the acoustic scale as well as the luminosity distance. For an equation of state today w_0 < -1, our model crosses the cosmological constant boundary. We perform numerical studies to constrain the parameters of our model by using Cosmic Microwave Background, Large Scale Structure and Supernovae Ia data. At 95% confidence, we find that the fractional dark energy density at early times Omega_early < 0.06. This bound tightens considerably to Omega_early < 0.04 when the latest Boomerang data is included. We find that both the gold sample of Riess et. al. and the SNLS data by Astier et. al. when combined with CMB and LSS data mildly prefer w_0 < -1, but are well compatible with a cosmological constant.Comment: 6 pages, 3 figures; references added, matches published versio