Weighted average of outstanding shares

Explanation

In order for the denominator to be consistent with the numerator, it should reflect in earning power brought about by issuances of new shares or retirements of old shares. For example, if the denominator included all of a group of new shares issued late in the year, it would not be consistent with the earnings derived from the resources available to the firm throughout the entire year.

Consequently, GAAP requires the use of an average number of shares outstanding as the starting point for all denominators. Further, the number of shares used in computing the average are to be weighted by that fraction of the year that they were actually outstanding.

When the number of outstanding shares is changed by a stock dividend or split, the firm’s earning power is not affected. However, a stock dividend or split does have the effect of creating a new “type” of common share in the sense that the percentage of ownership per share is altered. Consequently, the treatment of stock dividends and splits is different from the one given to issuances of shares in exchange for assets or services.

Specifically, the amount of actual shares outstanding must be altered to what it would have been if the split or dividend had occurred at the beginning of the year. This adjustment is made if the split or dividend occurs during the year or even after the end of the year. Thus, the denominator is expressed in terms of the type of common share existing at the financial statement release date rather than the one existing when the earnings were achieved.

How to Calculate weighted average of outstanding shares?

The calculations of the weighted average under several situations are presented in the following series of examples.

Example 1

Assume that the Sample Company had 100,000 shares of common stock outstanding on January 1, 20×1, that 20,000 shares were issued for cash on April 1, 20×1, and that 12,000 shares were retired on September 1, 20×1 The ending total of shares can be calculated as follows:

weighted average of outstanding shares

The shares can be grouped according to the length of time that they were outstanding. In this case, group 1 consists of 100,000 shares that were outstanding for the entire year, while groups 2 and 3 are included in the 20,000 shares issued on April 1. Group 2 is the 8,000 shares outstanding from April 1 to the end of the year and group 3 is the 12,000 shares outstanding from April 1 to August 31 The weighting of each group by the fraction of the year it was outstanding is shown in this table.

weighted average of outstanding shares example

Thus, the situation during the year was equivalent to having 111,000 shares outstanding throughout the year.

Example 2

For this example, assume the same events as above and add a two-for-one stock split on July 1. Thus, the shares outstanding after that date (and retired on September 1) are not the same as those that existed prior to that date. Before grouping the shares, they all must be converted to the same type. This table shows the calculations:

weighted average of outstanding shares example

Group 1 consists of 200,000 split shares that effectively were outstanding all year. Of the 40,000 split shares issued on April 1, group 2 consists of 28,000 that were outstanding until the end of the year and group 3 consists of the 12,000 that were retired on September 1. The calculation of the weighted average is shown below.

weighted average of outstanding shares example

Example 3

If the July 1, 20×1, split is assumed to have occurred instead on February 1, 20×2 (before the income statement for 20×1 is published), the shares used in the denominator must be adjusted for the change as follows:

weighted average of outstanding shares example

In this case, group 1 consists of 200,000 shares deemed to have been outstanding from January 1 to December 31. Of the 40,000 split shares issued on April 1, group 2 consists of 16,000 considered to have been outstanding from April 1 to December 31 and group 3 is composed of 24,000 that were outstanding from April 1 to August 31 The weighted average is found as follows:

weighted average of outstanding shares example

In this case, the same result could have been achieved by multiplying the 111,000 shares from example 1 by a factor of 2. This shortcut approach would be used for adjusting the average outstanding shares for earlier years covered by comparative statements.

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