Professor Paul Zarowin - NYU Stern School of Business

Financial Reporting and Analysis - B10.2302/C10.0021 - Class Notes

Earnings Per Share (EPS)
Calculating EPS is important, because of its linkage to equity valuation (i.e., a share's value is based on the amount of earnings accruing to it). When the firm has no potentially dilutive securities (this is called a simple capital structure), the calculation of EPS (available to common stockholders) is:
Basic EPS = net income - preferred stock dividends
weighted average # of common shares outstanding

This is called Basic EPS. For a firm that has a simple capital structure, even if the # of shares outstanding changes during the year (this can happen due to a stock split or a stock dividend, or if the firm issues new shares or repurchases outstanding shares) calculating Basic EPS is also easy. Just use in the denominator above the weighted average # of shares outstanding, weighting each # of shares by the fraction of the year it was in effect. RCJ show an example of the basic EPS calculation with weighted average # of shares on pages 751-752.

The primary complication in computing EPS is when a firm has potentially dilutive securities (this is called a complex capital structure). These are securities such as convertible bonds, convertible preferred stock, stock options and stock warrants that are not common stock now, but have the right to be converted into common stock. They are potentially dilutive, because when converted, they increase the number of shares outstanding, and this often dilutes (lowers) EPS.

Note that conversion might increase EPS. This is called anti-dilutive. This can happen, because while conversion increases the number of shares outstanding (lowering EPS by raising the denominator), conversion also raises the EPS numerator. If the numerator effect is greater than the denominator effect, EPS will rise. The numerator rises, because if convertible preferred stock is converted, there are no preferred stock dividends. If convertible bonds are converted, there is no interest expense, so net income goes up.

Since accounting is conservative, the effect of conversion on EPS must be shown if it is dilutive even though the potentially dilutive securities have not been converted into common stock. If the effect is anti-dilutive, it is not shown. Thus, firms with potentially dilutive securities will usually show 2 EPS numbers, basic EPS and diluted EPS; diluted EPS will be shown only if conversion is dilutive. That is, diluted EPS assumes that only dilutive securities are converted or exercised (included in the EPS calculation), including exercise of all dilutive options and warrants. It assumes that anti-dilutive securities are not converted/exercised (not included in the EPS calculation). Thus, diluted EPS is a conservative measure of the earnings accruing to each share.
Calculating the Effect of Conversion/Exercise - Dilutive or Not?
Thus, it is essential to know whether each security's conversion or exercise is dilutive or anti-dilutive. To know whether conversion or exercise will dilute EPS, first calculate Basic EPS as defined above. This is the benchmark against which to judge whether conversion or exercise is dilutive or anti-dilutive. Then, calculate the effect on EPS of exercising options and warrants. Finally, calculate the effect on EPS of conversion of convertible bonds and preferred stock.

Common Stock Options and Warrants: The effects of these are calculated first, because they affect only the EPS denominator; they do not affect the EPS numerator. Thus, if they increase (decrease) the number of shares in the denominator, they must be dilutive (anti-dilutive). As pointed out above, conversion of bonds and preferred stock increases the denominator, but might still be anti-dilutive.

The test for whether options and warrants are dilutive or not is called the treasury stock method. It is called this, because the calculation assumes that all proceeds from exercise of options and warrants are used to repurchase treasury shares. In effect, the exercise gives the firm cash and increases the number of shares outstanding; the repurchase uses this cash to decrease the number of shares outstanding. The test is: after both exercise and repurchase, are shares outstanding increased or decreased? If increased, the EPS denominator rises, so EPS declines (is diluted). If decreased, the EPS denominator falls, so EPS rises (is anti-dilutive). The rule is: if the exercise price is less (greater) than the market price of the stock, the option or warrant is dilutive (anti-dilutive).

For example, assume that there are 10 options outstanding to purchase shares at an exercise price of $10 per share, when the market price is $20. Exercise increases shares outstanding by 10 and gives the firm $100. The firm uses the $100 to repurchase 5 shares, leaving an increase of 5 shares. This is dilutive. If the market price is $5, the firm can repurchase 20 shares, leaving 10 fewer shares outstanding. This is anti-dilutive. An intuitive way to think about this is: no one would exercise if exercise price > market price, so you would not calculate the effect (it must be anti-dilutive). The market price is the average common stock share price during the year.

Convertible Bonds and Convertible Preferred Stock: The test for whether convertible securities are dilutive or not is called the if converted method, because it calculates diluted EPS as if the convertibles were converted. The EPS figure that includes the effects of all dilutive options and warrants becomes the new benchmark to judge whether conversion of convertible securities is dilutive or anti-dilutive. The easiest way to determine whether they are dilutive or not is first to rank all the convertible securities by the conversion ratio: increase in numerator ÷ increase in denominator. In effect, this ratio is the effect on EPS of the conversion. For example, if conversion would increase the numerator by $100 and increase the denominator by 40 shares, the ratio is 100/40 = 2.5. If EPS before conversion is greater (less) than 2.5, then conversion must lower (raise) EPS, so the security is dilutive (anti-dilutive). Conversion amounts to calculating a weighted average of the pre-conversion EPS and the conversion ratio.

Starting with the new benchmark, take the convertible with the lowest conversion ratio (most dilutive) and, if it is dilutive, calculate a new EPS. This new (lower, by construction) EPS becomes the new benchmark to judge whether the convertible with the next lowest conversion ratio is dilutive or not. Keep going and stop when you reach a convertible that is anti-dilutive. Note that the benchmark changes as each additional dilutive security is included in the EPS calculation. Of course, it might be the case that all convertibles for a given firm are anti-dilutive. In this case, none of them are included in the diluted EPS calculation.

For example, if the diluted EPS before convertibles is $1.25, and the lowest conversion ratio is 1.5, then all of the convertibles are anti-dilutive. If the diluted EPS before convertibles is $1.25, and the conversion ratios of three convertibles are 1.0, 1.4, and 1.5, only the first one is dilutive.

It is important to point out that ROE is superior to EPS as a performance measure, because EPS ignores the amount of capital required to generate the earnings. This can affect cross-firm comparisons, as the analysis of a given firm over time. For example, a firm can improve its EPS by repurchasing common shares (no effect on net income, but fewer shares outstanding).