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In order to simplify the presentation of EPS numbers, GAAP allows a firm to not disclose effects of dilution when the result is immaterial. Rather than leave that judgment to individual accountants, the GAAP specified a 3 percent limitation. A firm should determine if its fully diluted EPS figure is less than or equal to 97 percent of simple EPS. If it is, then both primary and fully diluted EPS are to be disclosed. If the fully diluted EPS is more than 97 percent of the simple EPS, only the simple EPS result needs to be reported.

It should be noted that the materiality test is not mandatory but only a voluntary guideline. Thus, it need not be complied with if the firm does not wish to do so or if there is material dilution in one year but not the other when comparative statements are presented.

### Facts

From these facts, we can proceed to perform the calculations necessary to provide the EPS information required.

## Calculations

### Weighted average

There are three groups of common shares: group 1 consists of 800,000 shares that were outstanding from January 1 to December 31; group 2 consists of 420,000 that were outstanding from March 1 to December 31 and group 3 consists of 48,000 shares that were outstanding from August 1 to December 31. Schedule 1 shows the calculation of the weighted average which is used in Example to calculate the EPS figures.

### Warrants

All of the warrants outstanding at the end of 20×4 are exercisable within the next five years and have exercise prices ($30 and $45) below the last quarter’s market value. Consequently, all of them are to be considered as dilutive for primary and fully diluted EPS. The treasury stock method can be applied without concern for the 20 percent test because cash produced upon exercise would be insufficient for acquiring more than 253,600 shares (20 percent of the year-end total of 1,268,000 shares).

Schedule 2 shows the calculation of the effect of the warrants on the denominator of primary EPS. Because groups B and C were not outstanding throughout the whole year, it is necessary to use the average market value for the period that the warrants were outstanding and to weight the number of incremental share by the fraction of the year that the warrants were in effect. Group B was outstanding for seven months, and group C for only four months. The total of 21,726 equivalent shares is added to the denominator for primary EPS in below example.

Schedule 3 shows the calculation of the effect of the warrants on the denominator of fully diluted EPS. Because group B and C were exercised during the year, it is necessary to use the market value of the stock for the date on which they were exercised (even though the average market value is higher) and to weight the number of incremental shares by the fraction of the year that the warrants were in effect. Because the year-end market value ($49) was higher than the average for the year ($46), it is used for groups A and D. The total of 24,117 equivalent shares is added to the denominator for fully diluted EPS in below example.

### Convertible preferred shares

Because the convertible preferred stock cannot be converted until six years after December 31, 20×4, there is no need to test for its equivalency to common stock or to assume its conversion for the computation of primary EPS. Thus, the only effect on primary EPS is the deduction of the declared dividends of $168,750 from the numerator.

For fully diluted EPS, conversion should be assumed because it can take place within the next 10 years. The numerator thus does not show any adjustment for dividends. Because the preferred shares were outstanding for only three-fourths of 20×4, the denominator is increased by only three-fourths of the 200,000 common shares that would have been issued if conversion had taken place. Thus, 150,000 shares are added to the denominator in below example.

### Convertible debenture bonds

The convertible bonds are exercisable within five years and need to be tested for equivalency. Their cash yield of 5 percent equals their nominal rate because they were issued at face This rate is below 51/3 percent (two-thirds of the prime rate of 8 percent); therefore, the bonds are considered to be equivalent to common stock. Consequently, conversion is assumed for both primary and fully diluted EPS. The calculation of the numerator adjustment is seen below:

The denominators are both increased by 60,000 shares (see below example).

### Contingent issuance agreement

At the end of 20×4, Example Company had not met the condition stated in the contingent issuance agreement of annual income of $2,500,000. Consequently, the agreement should be considered only for fully diluted EPS.

In making the calculation, it is necessary to assume that the income actually reached the stated level, after considering the interest savings that would have been achieved if the bonds had been converted. The adjustment to the numerator is calculated as follows:

The denominator is increased by 160,000 shares.