# Anti dilutive securities and EPS

## Definition and explanation

In the computation of EPS, situations are encountered in which the inclusion of the effects of a potentially dilutive security actually produces a higher per share figure. This effect is known as antidilution. In this article, three particular aspects of antidilution are discussed in more detail.

### Opposite effects on EPS before and after extraordinary items

Under certain conditions, it is possible that the savings per share from a potentially dilutive security can be less than the EPS before extraordinary items but greater than the EPS after extraordinary items. Despite this result, the anti-dilutive security be included in the calculation of fully diluted EPS.

### Example

For example, suppose that the Sample Company reports $7,000,000 ordinary income and a $3,200,000 extraordinary loss. It has an issue of preferred stock on which it paid $1,000,000 of dividends and which is convertible to 400,000 common shares. The preferred is not considered to be equivalent to common. If there were 1,400,000 outstanding common shares, these EPS calculations would be made:

Even though the fully diluted EPS is larger than the primary EPS, both results must be disclosed.

### Losses

When an ordinary loss occurs for a year, all potential savings from conversions and all potential increases in the number of shares are anti-dilutive because the loss per share is reduced by including them. That is, the fully diluted loss per share would be smaller than the primary loss per share, and this result would not be consistent with the ‘ ‘worst case” assumption.

### Example

For example, suppose that Sample Company has a $7,000,000 operating loss and 1,400,000 outstanding shares, such that there is a $5 loss per share. If warrants equivalent to 100,000 common shares are outstanding, including them would change the result to $7,000,000 / 1,500,000, or a loss of only $4.67 per share. If bonds convertible to 200,000 shares offered interest savings of $400,000, the result would be $6,600,000 / 1,600,000, or a loss of $4.13 per share. Thus, neither of these potentially dilutive securities (or any others) would be included in the calculation of EPS, even if they were common stock equivalents.

### Multiple dilutive securities

When more than two potentially dilutive securities exist, anti-dilutive effects can be more difficult to detect. The easiest approach to obtaining the most diluted EPS involves ranking the securities from most to least dilutive in terms of the savings per common share that would have been achieved if the shares had been issued. Then, each is brought into the calculation of primary or fully diluted EPS until it is reduced to the smallest possible figure.

### Example

To demonstrate, assume that the Sample Company has reported net income of $1,000,000 divided among 100,000 shares adjusted for common stock equivalents. Further, suppose that these convertible bonds are outstanding:

From these facts, it can be seen that each of the bonds and all of them together appear to be dilutive of the $10 primary earnings per share. If all of them are included, the EPS result is $1,715,000 / 370,000, or $4.64 per share.

To determine if this point is maximum dilution, alternate calculations can be made bringing in the savings and new shares in order from the most to the least dilutive. Including only group A produces the result of $1,080,000 / 180,000, or $6 per share. This number is still larger than the total figure and the next group can be brought in.

Group B will be dilutive because its saving per share ($1.25) is less than the last diluted EPS result. Including it produces $1,205,000 / 280,000, or $4.30 per share.

Group C will not be dilutive because its savings per share of $4.50 is larger than the $4.30 just obtained. Thus, the $4.30 figure is the smallest fully diluted figure and should be reported on Sample’s income statement. As verification, including groups A, B, and C produces $1,385,000 / 320,000, or $4.33.