Ethan Frome - New York University



The Calculation of Earnings Per Share and Market Value of Equity: Should Common Stock Equivalents Be Included?

By

Joshua Livnat and Dan Segal

Leonard N. Stern School of Business

New York University

40 W. 4th St.

NY NY 10012

(212) 998-0022

jlivnat@stern.nyu.edu

dsegal@stern.nyu.edu

First Draft: March 1999

Current Draft: March 27, 2003

The Calculation of Earnings Per Share and Market Value of Equity: Should Common Stock Equivalents Be Included?

Abstract

Most stock market participants calculate the market value of equity through a multiplication of the price per share by the number of outstanding shares. This study shows that this practice is inconsistent with the assumption that the market price per share incorporates the potential dilution due to outstanding financial instruments that can be converted to common stocks (common stock equivalents, CSE). If the market price incorporates all CSE, the market value of equity (including contingent equity) should be calculated through the multiplication of price per share by the sum of outstanding shares and shares that will be issued upon dilution.

Information about CSE can be found by examining all the financial instruments of a firm that can potentially be converted into common stock. However, one easily accessible source for the CSE is the accounting calculation of Earnings Per Share (EPS), where the accounting profession follows a rigid set of rules to calculate the potential dilution in the number of outstanding shares due to CSE. This study examines how close are the accounting CSE to those inferred by market participants in their determination of market prices. Our results indicate that the market and the accounting CSE converge for firms with high levels of potential dilution due to CSE, but not for low levels of potential dilution (below 5-6%). Thus, the FASB standard on EPS (FASB, 1997) that requires the disclosure of Basic EPS (with the assumption of zero CSE) and Diluted EPS (with the assumption of all CSE), enables market users to select the number of shares they deem most appropriate for the firm’s level of potential dilution.

The Calculation of Earnings Per Share and Market Value of Equity: Should Common Stock Equivalents Be Included?

In a recent pronouncement regarding Earnings Per Share (EPS), the Financial Accounting Standards Board (FASB) now requires the disclosure of Basic and Diluted EPS, instead of the previously required Primary and Fully Diluted EPS (FASB, 1997). While one motive for the change was to conform EPS calculations to the majority of countries and international standards, the FASB has also wanted to supply users of financial statements with two extreme EPS figures – one with no dilution and one with full dilution. This change was intended to help investors to better assess the effect of potential dilution than that achieved under Primary EPS, which required the inclusion of Common Stock Equivalents (CSE) in the computation.

The calculation of EPS may be important for market participants who rely on such measures as the Price/Earnings (P/E) ratio to value and select securities for their portfolios. It is also important for calculating the market value of equity[1], because it provides a comprehensive and easily accessible source about the potential dilution in the number of outstanding shares due to conversion of CSE. Currently, the market value of equity is typically calculated as the price per share times the number of outstanding shares. When asked whether the market value of equity should be calculated by the total number of shares that would be issued when CSE are converted into common stock, most academics respond that the current price per share already takes into account these dilutive shares. As we shall show below, if the price per share indeed incorporates the expected dilutive shares, the market value of equity should be based not only on outstanding shares, but also on the expected dilutive shares. As a matter of fact, calculating the market value of equity by using only outstanding shares is theoretically inconsistent with the assumption that the market price per share incorporates the potential dilution.

The number of shares used to calculate Primary (or Diluted) EPS can be employed to assess the accounting profession’s estimate of the additional shares that would be issued if all CSE are converted to common stock. If the market assessment of the potentially dilutive shares corresponds exactly to the CSE calculations of the accounting profession, the number of shares used to calculate EPS can be utilized to calculate the correct market value of equity. The calculation of EPS then has implications for applied finance, as well as security analysis, through the calculation of market value of equity and various per share amounts.

The purpose of this study is to examine whether market participants seem to use only the outstanding shares, or also the dilution caused by CSE, in determining security prices. If the accounting procedures underlying EPS calculations are also used by market participants to determine security prices, the market values will incorporate the dilution due to CSE as reported by accountants. On the other hand, if market participants use other procedures to incorporate the effects of dilution on security prices, the accounting methods used to calculate EPS will produce market value calculations that should be different from those determined by market participants.

Our results show that, for firms with low levels of dilution (below 5-6%), market participants seem to ignore the possible effect of dilution caused by accounting CSE on market prices, and seem to only consider the number of outstanding shares. For firms with higher dilution levels, investors appear to incorporate the possibility of dilution when they set the price per share, and the accounting CSE seem to correspond to those assumed by market participants when prices are set. These results indicate that the accounting procedures underlying the calculations of dilution are only partially shared by market participants. Our findings indicate that the market perceptions of the adverse consequences of dilution increase with the dilution level. Furthermore, our results seem to support the FASB’s conclusion to replace Primary EPS with Basic EPS, which is based solely on outstanding shares, essentially providing users the two scenarios of no accounting CSE and full dilution due to accounting CSE. Users can then choose the scenario that they deem more appropriate for the specific firm, according to its level of potential dilution.

The next section provides a conceptual perspective for the pricing of shares in the market when CSE can dilute outstanding shares. It also describes how we test whether market prices seem to incorporate the dilution due to accounting CSE. The third section describes the research design employed in the study, while the fourth section describes the sample and discusses the results. The last section summarizes our findings and concludes the paper.

II. Background and Conceptual Perspective

The accounting profession required the computation and disclosure of EPS by a rigid set of rules as part of Accounting Principles Board (APB) Opinion No. 15 (APB, 1969). Under this standard, firms were required to report Primary EPS and Fully-Diluted EPS in their financial statements, where both measures included the potential dilution of common stock equivalents, which are defined as such securities that are presently not common stock, but can become common stock upon conversion. CSE include convertible bonds, convertible preferred stocks, stock options and warrants, contingent shares, and similar instruments. APB Opinion No. 15 required the inclusion of CSE in computation of Primary EPS if their effect was dilutive. It also specified the rules that determine when an instrument is classified as a CSE, sometimes only at inception of the instument, without further adjustments to reflect changes in the probability of conversion to common stock. Fully-Diluted EPS was based on assumptions about conversion of all potentially dilutive financial instruments, and resulted in a lower EPS number than Primary EPS.

In 1997, the FASB issued its Statement No. 128 (FASB, 1997), which requires firms to calculate and disclose Basic EPS and Diluted EPS, where Basic EPS does not contain any dilution due to CSE, and Diluted EPS includes the dilutive effects of all CSE. In its explanation for this change, the FASB stated:

“The Board decided to replace primary EPS with basic EPS for the following reasons:

a. Presenting undiluted and diluted EPS data would give users the most factually supportable range of EPS possibilities. The spread between basic and diluted EPS would provide information about an entity’s capital structure by disclosing a reasonable estimate of how much potential dilution exists.

b. Use of a common international EPS statistic has become even more important as a result of database-oriented financial analysis and the internationalization of business and capital markets.

c. The notion of common stock equivalents as used in primary EPS is viewed by many as not operating effectively in practice, and “repairing” it does not appear to be a feasible option.

d. The primary EPS computation is complex, and there is some evidence that the current guidance is not well understood and may not be consistently applied.

e. If basic EPS were to replace primary EPS, the criticisms about the arbitrary methods by which common stock equivalents are determined would no longer be an issue. If entities were required to disclose the details of their convertible securities, the subjective determination of the likelihood of conversion would be left to individual users of financial statements (FASB 1997, Par. 89)”.

In fact, the FASB has explicitly stated that providing investors with both Basic and Diluted EPS will enable them to assess the two extreme scenarios of no dilution and that of full dilution, an option not available when only Primary EPS figures were disclosed. Users can use this information to determine any number in between, which would reflect their assessments of potential dilution.

In a similar manner, users of financial statements can calculate other per share data, as well as total market value of equity using their assessments of the total number of common shares. Since the future cash flows of the firm from its investment projects are probably unaffected directly by the existence of CSE, the economic market value of equity (including contingent equity) should not be related to the CSE. However, the price per common share is affected by the assessment of dilution due to CSE, since the total market value of equity (including contingent equity) is divided over more shares. Thus, the practical calculation of market value of equity, i.e., the number of shares times the price per share, should be affected by the existence (and probability) of dilution due to CSE. This provides the linchpin between the EPS calculation and the calculation of market value of equity.

Prior Studies Relating to Calculations of EPS:

Most of the research studies concerning EPS calculation and disclosure can be categorized into two broad areas: (1) criticism of the arbitrary methods used to calculate Earning Per Share, and (2) the information content of the various earnings per share measures.

The criticism concerning EPS calculations centered mainly around the rule that determines when convertible bonds and warrants are deemed common stock equivalents. The APB postulated that convertible debt should be considered CSE if, on the date of issuance, the cash yield on the bond was less than 2/3 of the bank prime interest rate at the time of issuance.

Frank and Weygandt [1970] suggest that the method of determining convertible debt as CSE has three theoretical weaknesses. The first refers to the term structure of interest rates. Since interest rates are varying and volatile, a low yield on a convertible debt as compared to the existing prime rate may be a reflection of a change in the relationship between short- and long-term rates. The second refers to the credit risk of the company that issues the debt. Riskier companies issue bonds with higher cash yields. Since the benchmark of the prime interest rate applies to all companies regardless of their risk, the likelihood that convertible debt will be treated as CSE may be negatively correlated with the company’s risk. The third refers to the permanent classification of the convertible debt as CSE or straight debt. This classification may be irrelevant when later conditions have changed (e.g., by a dramatic change in the stock price) to such extent that the probability of conversion has been dramatically altered. Curry [1971] suggests a dual method of accounting for convertible debt in order to overcome the shortcomings of the method required by APB Opinion No. 15. He proposes that companies with convertible debt will present two Earnings Per Share (EPS) numbers based on the assumptions of conversion and non-conversion. Vigeland [1981] argues that, based on financial theory, one can specify ex-ante when voluntary conversion can occur and can estimate the probability of occurrence. Thus, it is possible to identify possible dates of dilution and estimate their likelihood. Gibson and Williams [1973], and Bierman [1986] also contend that the criteria for determining common stock equivalents are not meaningful.

With respect to the second area of EPS research, most studies examined the information content of the different measures of EPS by investigating which measure explains more of the variability in security returns. Rice [1978] computed the cumulative abnormal return (CAR) around the time of the first reports under Opinion 15 for two portfolios: one which consists of companies that reported Fully Diluted EPS (FDEPS) in the first financial report after the commencement date of Opinion 15. The second portfolio consists of firms that did not report FDEPS. He then compares the pattern of the two CARs and finds that they started to differ a year before the opinion became mandatory. Based on his findings, he concludes that the information content of FDEPS is value relevant to investors. Millar, Nunthirapakorn and Courtenay [1987] find that Basic Earnings Per Share (BEPS) exhibits stronger correlation with stock returns than either PEPS or FDEPS. They conclude that among the three measures of earnings, Primary EPS (PEPS) and FDEPS are the least informative. Jenings, LeClere and Thompson [1997], and Balsam and Lipka [1998] compare the extent to which BEPS, PEPS and FDEPS explain the variation in stock prices. They find that FDEPS explains better the variation in stock prices than both BEPS and PEPS, and that PEPS is superior to BEPS in their sample. Deberg and Murdoch [1994] examine whether FDEPS contains more information than PEPS. They find that PEPS and FDEPS, as well as price-earnings ratios computed using PEPS and FDEPS, are highly correlated. They conclude that both figures contain essentially the same information. Kross, Chapman and Strand [1980] assess whether FDEPS has any incremental value for security prices beyond PEPS. They also find that there is no difference between PEPS and FDEPS in the degree of association with both risk levels, measured as beta, and unexpected security returns.

The above studies seem to point out inconclusive results about the superiority of any one of the three EPS figures. Most studies indicate that there is no material difference in the information content of PEPS and FDEPS, but that the FDEPS has more value relevance to investors than BEPS, since it explains better the variations in stock prices. This suggests that investors take into account the possibility of dilution when they price securities.

The above studies attempted to distinguish among the various EPS measures, and indirectly examine whether stock prices incorporate the dilutive effects of CSE. Our study will address this question directly through the use of valuation models. Also, our study will examine the potential value relevance of accounting CSE for different levels of potential dilution, an issue which most of the prior studies ignored.

The Calculation of Market value of Equity:

The calculation of a firm’s market value is one of the most fundamental tasks in security analysis and investment management. For example, ratio analysis includes the market-to-book ratio, which is the ratio of market value of equity to book value of equity. Investment managers often categorize their holdings as large-capitalization stocks, mid-capitalization stocks, or small-capitalization stocks. Further, market values are also used as weights in many indices, such as the S&P 500 Index. In all of the above, the capitalization is based on the market value of the firm’s equity.

The calculation of a firm’s market value seems to be straightforward -- the number of outstanding shares times the price per share. Recently, however, there has been some debate about the correct market value of a firm, and, in particular, whether the computation should also include the potentially dilutive options, warrants, convertible preferred stocks, convertible bonds, etc. This debate became more heated with the frequent practice of granting stock options to employees in high-technology firms, and with the large increases in stock prices in recent years, which made the conversion of stock options to common stocks more probable (Scism and Bank, 1998).

In practice, most market participants use the following definition of market value of equity (capitalization):

Market capitalization

The price of a stock multiplied by the total number of shares outstanding. Also, the market's total valuation of a public company. (The Nasdaq Stock Market Glossary, emphasis added)

Standard & Poors uses the market value of a firm’s equity in constructing its famous value-weighted S&P 500 Index. The market value is determined based only on the number of shares outstanding:

“How is the S&P 500 Index calculated?

The S&P 500 Index is calculated using a base-weighted aggregate

methodology, meaning the level of the Index reflects the total market value of all 500 component stocks relative to a particular base period. Total market value is determined by multiplying the price of its stock by the number of shares outstanding.”(Standard & Poors, emphasis added)

Similarly, Value Line defines Market Capitalization as:

Market Capitalization

“The recent price of a stock multiplied by the number of common shares outstanding.” (The Value Line Investment Survey, Glossary, emphasis added)

In addition to market capitalization, Value Line provides detailed analysis on specific companies. The analysis includes numerous per share ratios, such as, Sales, “Cash Flow”, Earnings, etc., all of which are based on the number of outstanding shares.

These examples show that the prevalent calculation of market value of equity does not account for the potential dilution in the number of outstanding shares due to CSE. However, since the number of shares used to calculate Primary EPS has been reported in the financial statements of firms, market participants could have calculated a second market value of equity figure, through the multiplication of price per share by the number of shares used to calculate Primary EPS.

In fact, for each firm, market participants could have obtained two competing market values of equity; the first based only on the number of outstanding common shares (the no-dilution market value), and the second based on the diluted number of shares (the dilution market value). However, only one of these of competing market values is “correct”, that is, gives a more accurate estimate of the market value of equity as perceived by investors when they determine the price per share. To determine which of these two measures is the “correct” market value of equity, consider the following analysis.

Conceptual Analysis:

In an efficient market, investors should determine the price per share by using their assessments of future cash flows and the expected number of shares, which includes outstanding shares and the expected number of additional shares due to CSE. To illustrate the process and the associated issues, we use the following artificial example.

Example:

Consider a firm with $100 cash and no other assets or liabilities, with a book value of equity of $100. There are 10 shares outstanding, as well as 10 options with an exercise price of zero, which are exercisable over a period of ten years, beginning immediately.

The market value of the firm’s assets is $100, the cash on hand. The correct market price per common share should be $5 ($100/20), because the options should be deemed as exercised for valuation purposes (the probability of exercise is one). If the market completely ignores the options, the price per outstanding common share will be $10 ($100/10). To the extent that market participants assume that not all options will be exercised, or that not all options will be exercised immediately, the market price will range between $5 and $10 per common share. At $6 per share, market participants either assume a high probability of conversion (but less than one), or are almost correct in setting the market price. At $9 per share, market participants are either almost entirely incorrect in setting the price, or attributing a low probability of conversion to the stock options.

The following exhibit shows the market value of the firm (and the market to book ratio) if one only uses outstanding shares (no dilution), and if one uses also dilutive shares (dilution):

Exhibit 1

|Market |MV |MV |M/B |M/B |

|Price |(no dilution) |(dilution) |(no dilution) |(dilution) |

|$5 |$50($5x10) |$100($5x20) |0.5 |1.0 |

|(correct price) | |(correct MV) | |(correct M/B) |

|$6 |$60 |$120 |0.6 |1.2 |

|(almost correct price) | | | | |

|$9 |$90 |$180 |0.9 |1.8 |

|(almost entirely incorrect| | | | |

|price) | | | | |

|$10 |$100($10x10) |$200($10x20) |1.0 |2.0 |

|(incorrect price) |(correct MV) | |(correct M/B) | |

The M/B ratio should be one, because both the market and book value of equity are $100. Note that the correct market value (of $100) is obtained in one of two cases: (i) the market has priced the stock (correctly) at $5/share, and we (correctly) use the potential dilution (i.e. 20 shares) in calculating the market value. Or (ii) the market (incorrectly) ignored the dilution completely, and we (incorrectly) use only the outstanding shares in calculating the market value. Obtaining the correct market value in the first case is intuitively simple –the market priced the stock correctly, and we correctly used the potential dilution in the calculation of market value. Obtaining the correct market value in the second case is less intuitive – it results from making two errors which cancel each other; the market prices the stock incorrectly and we ignore dilution in calculating market values. Note that similar results obtain for the market to book ratio in the exhibit.

Another feature seen in the exhibit is that if we calculate the market value of the firm without allowing for dilution, i.e., using only the outstanding shares, the calculated market value is likely to understate the correct market value. To the extent that stock prices incorporate some dilution (even a small amount as in the case of a price of $9/share), the calculated market value is below the correct market value of $100. In contradistinction, if we calculate the market value by assuming full dilution (20 shares), we are likely to overstate the market value of the firm. As long as the market does not adjust the price to reflect full dilution (even with a price of $6/share), the calculated market value will exceed the correct market value of $100. Similar results obtain for the M/B ratio, where the ratio will be understated if we calculate the market value with no dilution, and will be overstated if we allow for dilution in calculating the market value.

In practice, determining the price per share is a complex process, which includes two stages. In the first stage, investors assess the total market value of the firm’s equity (and contingent equity) based upon its future cash flows. In the second stage, investors assess the expected number of shares that are used to calculate the price per share. The expected number of shares includes the number of currently outstanding shares, plus the expected additional shares due to conversion of CSE. The expected additional shares due to CSE may be based on various assumptions about the probability of conversion of CSE to common shares, as well as on potential applications of the increased cash flows from conversion.[2] The calculations that underlie Primary EPS or Diluted EPS reflect one potential way of assessing the expected number of common shares for determining the price per share. Whether the accounting methods used to calculate EPS are similar to those used by the market to assess the expected number of shares (and the price per share), is an empirical question which we examine below.

III. Research design

The research question we examine is whether the price per common share incorporates the potential dilution of the number of outstanding shares due to CSE. We address this question by determining which market value, the dilution or no-dilution market value, deviates further from the “theoretical” (intrinsic) market value. We estimate the intrinsic market value using Ohlson’s (1995) valuation model, which is based on the assumption that the share price equals the present value of future dividends. The intrinsic market value (to both current equity holders and any contingent equity holders) is, therefore, independent of the capital structure of the firm, and of the possibility of dilution. This independence enables us to assess which estimate of market value of equity is a better proxy for the intrinsic value.

Ohlson (1995) shows that the firm’s market value is a linear function of its book value (BV) of equity and the present value of expected abnormal accounting earnings. If abnormal earnings follow a specific generating process, the market value can be written as:

MVt = BVt + (Xta (1)

where MVt is the market value of equity at the end of period t, Xta is the abnormal accounting earnings during period t, and BVt is the book value of equity at the end of period t. The abnormal accounting earnings is defined as:

Xta = Xt – (Rf-1) BVt-1 (2)

where Xt is reported earnings during period t, and Rf is one plus the risk free rate, assuming risk neutrality. Substituting (2) into (1) gives:

MVt = BVt + (( Xt – (Rf-1)BVt-1)

Scaling by BVt-1 to control for size gives:

MVt/BVt-1 = -((Rf-1) + BVt/ BVt-1 + ( Xt/BVt-1 (3)

This model has been extensively used in the literature for both cross-sectional analysis and time-series analysis. However, when it is applied in cross-sectional analysis, a third independent variable is usually added to allow for differences in growth rates of firms – growth firms should have higher M/B ratios than value firms. To account for the differences in the growth rates, we estimate the following model:

MB = (tj + (1tjBB + (2tjEB + (3tjGROWTH + (tj (4)

where MB is the ratio of market value of equity at the end of period t to book value of equity at the end of period t-1, BB is book value of equity at the end of year t divided by book value of equity at the end of year t-1, EB is earnings at the end of year t divided by book value of equity at the end of year t-1, GROWTH is the average annual growth in sales over the period from t-2 to t, ( is the disturbance term, which is assumed to be independent, homoscedastic and Normally distributed. The subscript j stands for industry j, since this equation is estimated separately for each 4-digit SIC industry.

We estimate the dilution ratio (DIL) for each firm in a given year as follows:

DILt = NSEPSt/(0.5 NSOUTt + 0.5 NSOUTt-1)

Where NSEPS is the number of shares used to calculate Primary earnings per share, and NSOUT is the number of outstanding common shares. If the firm has no common stock equivalents, and if the weighted average number of outstanding shares can be estimated by the simple average of outstanding shares at the beginning and end of year t, then the dilution ratio is one. The dilution ratio will be greater than one if the firm has common stocks equivalents. To eliminate the bias in the analysis due to cases where firms issued or repurchased common stocks during the first or last months of the year, we restricted our analysis to those firms where the number of outstanding shares did not change during the year by more than 3%[3].

To estimate the intrinsic market value of firms with significant potential dilution, we first partition the sample based on the dilution ratio DIL into two groups: dilution firms and no dilution firms. We assume that firms with a dilution ratio below 3% are firms with no significant dilution (no dilution firms), whereas firms with dilution ratios above 3% are considered to have significant dilution (dilution firms). The cutoff of 3% stems from APB Opinion 15 (APB, 1969), which states that “any reduction of less than 3% in the aggregate need not be considered as dilution in the computation and presentation of earnings per share data as discussed throughout this Opinion”. We repeat the tests in this study using 2% and 4% cut-off with no major differences in the results.

We then estimate the coefficients of the model (Equation 4) for all the no-dilution firms in a given year and given industry. We use the estimated coefficients to predict the intrinsic (predicted from the regression equation (4)) market to book ratio for all the dilution firms in the same year and industry. The predicted market to book ratio should be independent of the dilution ratio, and should represent the “theoretical” market to book ratio given the expected future cash flows of the firm.

Using the dilution ratio (DIL) and the predicted market to book ratio, we compute the following variables for the sample firms with significant (above 3%) potential dilution:

MBND (Market to Book, No Dilution) – the market to book ratio, where the market value is computed based only on the number of outstanding shares at the end of year t.

MBDIL (Market to Book, Dilution) – market to book ratio, where the market value is calculated based on the dilutive number of shares. MBDIL is computed as the price per share (at the end of year t) times the number of common shares outstanding times the dilution ratio, DIL, divided by book value of equity.

MBP (Predicted market to book ratio) – is the predicted market to book ratio of dilution firms (using the coefficients estimated for all the no-dilution firms in the same year and industry).

ERND – the difference between the predicted market to book ratio and the no dilution market to book ratio, ERND = MBND – MBP

ERDIL - the difference between the predicted market to book ratio and the dilution market to book ratio, ERDIL = MBDIL – MBP

We expect MBND to be the lower bound of the predicted market to book ratio (MBP) since the market value MBND is calculated using only the outstanding shares, and the market price per share is likely to include the expected number of CSE that will be converted to common stock. Conversely, we expect MBDIL to be the upper bound of the predicted market to book ratio, since the market value MBDIL incorporates all CSE, where the price per share may include only a portion of the CSE. Thus, our first test is of the following hypothesis:

H1: ERND=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

|Case |Location of MBDIL and MBND Relatively to the |Better Proxy for MBP (MBND or MBDIL) |

| |Confidence Interval of MBP | |

|1 |MBND ................
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