© 2000 John Petroff
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© 2000 John Petroff |
For valuation of shares by investors, earnings per share is the most useful statistic. Earnings per share (EPS) is simply net profit after tax PAT divided by the number of shares subscribed issued and outstanding N
An adjustment is required if the number of outstanding shares has varied over the year as a result of stock dividends, stock splits, exercised stock options, issue of new shares or stock repurchase by the corporation. In that case, a weighted average of shares outstanding is used in the denominator where the weights are the number of days in the year during which each different quantity of the shares that have been outstanding (except in case of stock dividends or stock splits, in which case the change is retroactive to the beginning of the fiscal year).
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Earnings per share will be calculated first using Timken's data. From Table T-6.1 , The Timken Company Income Statements 1997-99, we take the net profits after tax for 1999 of $ 62,624 millions. Since Timken does not have preferred shares, this amount is available to common shareholders. Note #3 of the notes to consolidated financial statements reveals that the number of share authorized, issued and outstanding was calculated as a weighted average of 61,795,162 for the year 1999. Earnings per share are EPS = 62,624,000 / 61,795,162 = $1.01 |
Net profit after tax must be reduced if there are preferred shares, or other senior shares, that give title to fixed dividends DPS. The statistic is then called earnings per common stock EPSCS
EPSCS = (PAT - DPS ) / Average(N)
Extraordinary items, discontinued operations and the cumulative effect of accounting changes must be taken out of EPS and reported on a per share basis separately. For instance, this would be observed if a corporation closed a significant part of its operation because of expropriation or a catastrophe. Again, the purpose is to show what are considered normal operating results separate from what is not. Note that if the definition of what is normal operation changes in a given year, the firm should also want to show a restatement of results and EPS for prior years.
Much more significant adjustments are required in earnings per share for any corporations that has a complex capital structure, that is, one which has securities or agreements that allow conversion into or purchase of common shares. Such securities are called potential common shares for the purpose of earnings per share calculation. These potential common shares may cause company earnings to be diluted (i.e. reduced by being divided among a larger number of shares). Since 1997, American corporations must report two calculations of earnings per share: basic and diluted.
a)- Basic earnings per share
Basic earnings per share BEPS is calculated exactly as earnings per common stock above.
BEPS = (PAT - DPS ) / Average(N)
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For a second example for EPS calculation we take Delta Air Lines which has a complex capital structure. Net after tax profit for 1999 of $ 1,1101 millions is obtained from Table T-6.11, Delta Air Lines Income Statement. Delta distributed $ 11 millions of preferred stock dividends, leaving $ 1,090 millions of income available to common shareholders. Note #14 to financial statements indicates that the weighted average number of shares outstanding was 142,900,000 for the year. Basic earnings per share in 1999 were therefore BEPS = 1,090,000,000 / 142,900,000 = 7.6277 or $ 7.63 |
b)- Diluted earnings per share
Diluted earnings per share are calculated only if the company has a profit from continuing operations. If it has a loss, the diluted earnings per share is identical to the basic earnings per share.
Diluted earnings per share is calculated by i) adding back to profit after tax in the numerator the amount(s) distributed to potential common shares, and ii) adding those potential common shares to the weighted average of common shares in the denominator, as long as the potential common shares have a dilutive effect (i.e. again, if it decreases the basic earnings per share). An incremental per share effect is calculated for each group of potential common shares. Incremental per share effects are ranked, and added one by one, in decreasing order, to basic earnings per share (i.e. adding payments in numerator, and adding number of potential common shares in weighted average of shares), until there is no dilutive effect from remaining potential common shares.
The following is a list of the most
important types of potential common shares
- bonds with right to convert into common stock,
- preferred stock with right to convert into common stock,
- rights distributed to existing shareholders giving them a preemptive
right to purchase a number (or fraction) of common shares at a
stated exercise price,
- warrants attached to bonds giving bondholders the right to acquire
a number (or fraction) of common shares at a stated exercise price,
- securities of subsidiaries that can be converted into parent's
shares,
- stock options entitling certain employees (most often key executives)
to purchase common stock at a low price,
- contingent shares that the corporation is committed to issue
at some future date or when certain conditions are met.
For potential common shares such as warrants, that require payment or subscription, the amount received by the corporation is considered to be used to purchase treasury stock (i.e. reducing the shares outstanding). Convertible securities are included as "if-converted" (i.e. the convertible security is assumed converted). Convertible securities outstanding at the beginning of the year, are assumed converted for the entire year. Convertible securities issued during the year, are assumed to be converted on the date of their issue, and the per share incremental effect is calculated by dividing the actual income paid to holders of those securities (net of tax), by the time weighted average of these potential common shares. For these and other details pertaining to the calculation of earnings per share of US corporations, one should consult Financial Accounting Standards Statements 128 and 129, "Earnings per Share", issued by the Financial Accounting Standards Board in 1997, or the International Accounting Standard No. 33, issued by the IASC at the same time with similar content.
The note to financial statements of the corporation, where basic and diluted earnings per share derivation is presented, must show the potential common shares that were no included in the diluted earnings per share because their effect was not dilutive.
Thus, for the potential common shares PCS that are dilutive both numerator and denominator of EPS are modified. The interest paid on such bonds IPCS (net of income tax) is added back into profit PAT, Dividends DPS on preferred stock that is not dilutive are deducted from profit, as they were for basic earnings per share. (But dividends on preferred stock that is dilutive are not deducted from profits.) For the denominator, the number of common shares is increased by the potential common shares PCS. Then, if among the potential common shares PCS, there are potential common shares that require payment to exercise subscription rights, such payment is considered to reduce the common shares outstanding by the number of treasury stock TSPCS that would be purchased with the proceeds. The formula for diluted earnings per share DEPS is
DEPS = ( PAT + IPCS-DPS ) / Average( N + PCS - TSPCS)
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We continue with Delta Air Lines to demonstrate the calculation of diluted earnings per share. We start with the same net after tax profit of $ 1,101 millions and weighted average common shares outstanding of 142,900,000 for 1999. Net after tax profit is reduced by the preferred stock dividend distributed on preferred stock that is not convertible in the amount of $ 4 millions, leaving $ 1,097 millions available to common shareholders. The number of common shares is increased by 4,700,000 shares from exercise of stock options and by 4,700,000 from conversion of Series B ESOP convertible preferred stock, for a total of 152,300,000. Diluted earnings per share is then DEPS = 1,097,000,000 / 152,300,000 = 7.2029 or $7.20 |
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Prior to 1997, in annual reports of American corporations, one may find three calculations of earnings per share: earnings per share of corporations without complex capital structure, and primary earnings per share and fully-diluted earnings per share for corporations with complex capital structure. The primary earnings per share was calculated by dividing net after tax profits PAT by the number of shares outstanding N plus common stock equivalents CSE. Common stock equivalents were the shares that the corporation would have to issue when holders of securities or agreements (e.g. convertible bonds, warrants, stock options) exercise their rights of conversion to or acquisition of common stock (i.e. same as potential common shares). The value of these CSE securities or agreements stemmed essentially from the conversion rights. In other words, a holder of such CSE had an economic incentive to convert (e.g. the market price of a common stock was higher than the exercise price of the right) anytime he/she wished. The holder of a CSE might, however, actually postpone conversion in order to take advantage of the dual benefits from holding on to the CSE. For instance, most preferred stock is convertible into common stock often on a one-for-one basis, and increases, therefore, in value in step with common stock, but holding on to the preferred stock gives guaranteed dividends while not losing the right to convert, and avoiding the risk of price decline: so, postponing conversion is logical. The diluted earnings per share was calculated by adding to the denominator (N + CSE), all other shares that may have to be issued because of conversion rights and other commitments, even if the exercise of these conversion rights was not economically justifiable then, and as long as the effect was dilutive. As the wording suggests, the fully-diluted earnings per share was reported to show the minimum earning a common share would be entitled to, and is similar to diluted earnings per share as it is defined today. The new rules simplify somewhat the calculation, but above all remove the ambiguity of determining whether conversion is economically justifiable or not. |
When EPS is used to calculate a stock value, for instance, with the help of earnings multiple, it is the basic earnings per share that is used. The earnings per share figure can be compared over time, but cannot be compared to other companies because it is still an absolute amount. Next, we study ratios that are relative measures.
See review questions Q-13B2.1 through Q-13B2.16.
See research assignment R-13B2.1.
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