ࡱ> 5@ bjbj22 qXX)O64.{{{hz{L{,.(&Lrrrrrr$6Rd%rr%rr:ooorrooos6?Wr =0 To determine which of the two competing market to book ratios, MBND and MBDIL, is a better proxy for the predicted market to book ratio, MBP, we also estimate a confidence interval for MBP. We compute the proportion of observations for which each of the two competing market to book ratios is closer to the MBP. Obviously, when one of the two market to book ratios is included within the confidence interval while the other is outside the interval, the former is said to be closer to MBP. In the case where both ratios are included in the confidence interval, we measure which one is closer (in absolute value) to the mean of MBP. When both ratios are outside the confidence interval, we posit that the one closer to one of boundaries is the closer to MBP. Exhibit 2 summarizes all the possible cases, based on the location of MBND and MBDIL relative to the boundaries of the confidence interval of MBP. It also assigns each of these cases into two groups for which either MBND or MBDIL is a better surrogate of the predicted ratio MBP. Our null hypothesis is that the proportion of cases where MBND is closer to MBP (denoted P(MBND)) is greater than the proportion of cases where MBDIL is closer to MBP (denoted P(MBDIL)). To the extent that the accounting CSE does not represent the expected dilution to market participants, i.e., that market participants essentially ignore the accounting CSE, we expect: H2: P(MBND)>P(MBDIL) Exhibit 2 CaseLocation of MBDIL and MBND Relatively to the Confidence Interval of MBP Better Proxy for MBP (MBND or MBDIL)1MBNDUBOUNDMBDIL if (LBOUND-MBND)>(MBDIL-UBOUND), MBND otherwise4LBOUNDABS(MBDIL-MBP), MBND otherwise5LBOUND3%). We then also report ERND and ERDIL for firms with a dilution ratio in excess of 4%. We repeat these reports for firms with DIL greater than 5%, 6%, etc., until 10%. This allows us to test the sensitivity of the hypothesis to various levels of assumed dilution. The medians of ERND and ERDIL are reported in Table 3. (Insert Table 3 about here) Table 3 shows that the median ERND is negative for all levels of dilution, and statistically different from zero for DIL greater then 6%. These results are consistent with the first part of the hypothesis that ERND is less or equal to zero. Furthermore, the median ERND increases in absolute value as the dilution cut-off increases, indicating that the no-dilution M/B further deviates from MBP the higher is the dilution level. Also, the percentage of observations that are negative increases monotonically with the dilution level. The median of ERDIL is positive and significant for dilution levels below 7%, positive but insignificant for 7%, and negative but insignificantly different from zero for higher dilution levels. These results are also consistent with the null hypothesis that the market ignores accounting CSE for low dilution levels. Note further that the percentage of positive observations declines monotonically with the levels of dilution, possibly because CSE are ignored by market participants for lower levels of dilution but not for higher dilution levels. Overall, we find that for low levels of dilution, ERND is not significantly different from zero and that ERDIL is positive and significant. For high levels of dilution, ERND is significantly negative and ERDIL is not different from zero. These results suggest that market participants do (do not) take into account the possible effect of dilution due to CSE for low (high) levels of dilution. Hence, for low (high) level of dilution MBND (MBDIL) may be a better proxy for the intrinsic market to book. A second test we use is not based singly on the mean of the predicted MBP, but takes into account its variance as well. This is based on the 95% and the 90% confidence intervals of MBP. We examine what percentage of the observations on MBND and MBDIL fall outside the confidence interval, and which measure is closer to the interval boundary. Also, we examine those observations of MBND and MBDIL that fall within the confidence interval, and again test which one is closer to the mean MBP (the middle of the confidence interval). This is carried out in Table 4 for the dilution cut-off level of 3%. (Insert Table 4 about here) Table 4 reveals that 79% (73%) of both MBND and MBDIL fall within the 95% (90%) confidence interval. Since the MBP is estimated from the coefficients obtained for the sample of no-dilution firms, the 95% confidence interval is supposed to contain 95% of the MBND if market participants ignore accounting CSE completely, or 95% of the MBDIL if market participants incorporate the accounting CSE completely in market prices. Table 4 reveals that 80.8% of the MBND fall within the 95% confidence interval (cases 4a, 4b, and 5), whereas only 79.3% of the MBDIL fall within the confidence interval (cases 2, 4a, and 4b). Thus, for a surprisingly large proportion of the firms, the confidence interval does not contain either MBND or MBDIL. In 4.4% of the sample cases, both are below the lower boundary of the 95% confidence interval, and in 14.2% of the sample cases, both MBND and MBDIL are above the upper boundary. That is, the market tends to deviate from the confidence interval by assigning a higher market value to dilution firms more often than a lower value. This is more consistent with market participants who ignore accounting CSE than a market which incorporates all accounting CSE. We can now examine two additional proportions in Table 4 that may indicate whether the MBND is more consistent with the data, or whether MBDIL is. The first is the proportion of cases in Table 4 where MBDIL is indicated in Table 4 to be closer to MBP. In Table 4, this includes cases 1, 2, 3a, and 4a, or a total of 48.6% for the 95% confidence interval. This proportion is indicated by PDIL in the first row of Table 5. The second is the proportion of cases where (i) both MBDIL and MBND fall within the confidence interval, and (ii) MBDIL is closer to the mean MBP, indicated by PDILW_95% and PDILW_90%, for the 95% and 90% confidence interval, respectively, in Table 5. These proportions are summarized in Table 5 for various levels of dilution. (Insert Table 5 about here) As can be seen in the table, the proportion of observations that indicate that the market ignores accounting CSE (PDIL<50%) applies for levels of dilution below 6%. Above 6%, market participants seem to set security prices more in accordance with accounting CSE than without. For the firms where both MBND and MBDIL fall within the confidence interval, we find that the market price is set more consistently with accounting CSE at all dilution levels, and that this conclusion is monotonically stronger with increasing levels of dilution. However, the table also indicates that the proportion of observations which fall outside the confidence interval actually increases as the dilution levels increase. Thus, the cumulative evidence provided in the study indicates that the market seems to ignore, or at least to not fully incorporate the accounting CSE in determining the price per share for low levels of dilution. For high levels of dilution, the market seems to set the security price in a manner that is more consistent with the potential dilution of the accounting CSE. Sensitivity Analysis: We repeated the tests in the study assuming that 2% and 4% level of dilutions are the cut-off points between dilution and no-dilution firms. The results point generally in the same direction as those reported in the study. One of the selection criteria required that the common shares outstanding will not change between the beginning and end of the year by more than 3%. We experimented with 2% and 4%, without any material effects on the results. V. Summary and Conclusions: This study examines whether stock market participants seem to incorporate into the price per share the potential dilution due to accounting CSE. The study shows that if market participants do incorporate the accounting CSE in setting the price per share, the market value of equity should be calculated through a multiplication of the price per share by the sum of outstanding shares and accounting CSE. In practice, market professionals ignore accounting CSE in calculations of the market value of equity. The study shows that for low levels of dilution (typically below 6-7%), the market seems to set security prices in a manner that ignores accounting CSE. For higher levels of dilution, the market seems to set the price in a manner that is consistent with the assumption that the accounting CSE will be converted. These results provide mixed signals about the ability of accountants to assess correctly the potential dilution due to CSE. It seems that for low levels of dilution, market participants ignore the accounting CSE, or assess a low probability for their conversion. For these low levels of dilution, it is also possible that market participants do not bother with the precise incorporation of the accounting CSE, because the effect is not material enough, indicating a minor market inefficiency. However, stock market participants seem to agree with the accounting professions calculation of CSE for high levels of dilution, either because the probability of conversion is closer to that assessed by the market, or because ignoring CSE will result in a market inefficiency that will be too large. The study points out two implications, one for finance professionals, and the other for accounting regulators. Finance professionals seem justified in ignoring accounting CSE when they calculate the market value of equity for firms with low levels of potential dilution of accounting CSE. However, when the firm has high levels of dilution, the calculation of the market value should incorporate accounting CSE. Similarly, when earnings or other items are calculated on a per share basis, finance professionals can use outstanding shares for low levels of dilution, but should use outstanding shares plus CSE for firms with high levels of dilution. The study also finds that the FASBs approach to the calculation and presentation of Basic and Diluted EPS seems to be justified. As a matter of fact, for low levels of dilution, market participants are better off using Basic EPS, or just the number of shares used to calculate it (which incorporates changes in outstanding shares during the year). However, for firms with high levels of dilution, Diluted EPS and the number of shares used to calculate it seem to be more appropriate. Allowing users to employ whichever number they prefer seem to be superior to the Primary EPS computation that required the assumption of conversion of CSE. Table 1 The Number of Industries, Number of Dilution and The Number of No-Dilution Firms YearNo. of IndustriesNo. of No-Dilution FirmsNo. of Dilution FirmsTotal No. of Firms862746856524873154971620883058782669893156488652903261980699913265285737923356412268693335801377179438701171872954071617489096379242601184Total692413268250 The table is based on 3% as the cut-off for dilution; firms with dilution ratios below 3% are classified as no-dilution, whereas firms with dilution ratios above 3% are classified as dilution firms. Table 2 Financial Ratios And Variables For Dilution And No-Dilution Firms YearM/B ratioE/B ratioE/P ratioDilutionNo-DilutionDilutionNo-DilutionDilutionNo-Dilution862.21.70.1500.0370.0600.029872.41.50.1650.0570.0700.039882.41.70.1690.0630.0730.042892.81.80.1590.0610.0640.039902.41.30.1540.0450.0780.053912.71.70.1480.0310.0630.028922.72.10.1530.0580.0620.033933.12.30.1440.0580.0530.030942.92.00.1540.0680.0610.038953.12.30.1520.0580.0500.032962.92.10.1470.0820.0560.043Mean2.71.90.1540.0560.0630.037M/B Market value at the end of year t divided by the book value at the end of year t-1. E/B- Earnings at the end of year t divided by the book value at the end of year t-1. E/P- Earnings at the end of year t divided by the stock price at the end of year t. YearB/B ratioGrowth DilutionNo-DilutionDilutionNo-Dilution861.1521.02722.210.4871.1641.03922.58.2881.1661.03528.914.0891.1431.03428.913.3901.1531.02027.611.5911.1561.00416.36.4921.1491.02814.76.9931.1431.04016.26.2941.1451.03017.611.1951.1681.05919.813.6961.1321.05321.314.3Mean1.1521.03321.510.5B/B- Book value at the end of year t divided by the book value at the end of year t-1. Growth average growth of revenues (in percent) over the period t-2 to t. Table 3 Median Differences between the Calculated and Predicted M/B Ratios for Dilution Firms at different Dilution Levels ERNDERDILDILNMedianSignif.% Negat.MedianSignif.% Posit.3%1326-0.0330.50252%0.0750.00153%4%937-0.0670.98154%0.0650.00153%5%681-0.0600.82054%0.0960.00154%6%477-0.1710.16556%0.0290.04551%7%361-0.2220.03458%0.0140.21050%8%287-0.2640.00461%-0.0370.65649%9%231-0.3840.00063%-0.0810.71446%10%192-0.4580.00165%-0.1260.53345% Notes: ERDIL is the difference between the calculated M/B ratio, assuming full dilution of CSE, and the predicted M/B ratio, estimated from the no-dilution group of firms in the same industry and year. ERND is the difference between the calculated M/B ratio, using only the outstanding shares, and the predicted M/B ratio, estimated from the no-dilution group of firms in the same industry and year. N is the sample size. Signif. represents the significance level of the one-sample Wilcoxon statistic that the median is equal to zero. % Negative is the percentage of observation with negative ERND. % Positive is the percentage of observation with positive ERDIL. Bold table entries are statistically significant at the 5% level or better. 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