Warrants are the instruments that give the right to the holder to buy stock shares of issuing company at a fixed price until the expiry. Warrants are similar to options.


Stock warrants (options) have obvious potential for diluting the percentage ownership of existing shares; however, not all warrants have the same potential for immediate impact. Accordingly, GAAP allows the firm to exclude from its EPS calculations those warrants that are not reasonably expected to become shares of common stock. Specifically, the accountant should not include warrants in the calculation of primary EPS if they cannot be exercised within five years. As part of the “worst case” approach, warrants are excluded from the fully diluted EPS only if they cannot be exercised within 10 years.

Further, warrants should be excluded if market conditions indicate that they are unlikely to be exercised. To provide guidance, warrants should be included in calculations only if: The market price of the common stock obtainable has been in excess of the exercise price for substantially all of three consecutive months ending with the last month of the period to which the earnings per share data relate.

Warrants that pass these two tests (exercisability and the market test) are assumed to have been exercised. Once this assumption is made, consideration needs to be given to identifying what the firm would have done with the cash that it would have received if the warrants had been exercised.

The treasury stock method

Without suggesting that any firm would ever actually use cash received from warrants to do so, EPS should be calculated as if the cash was used to acquire treasury stock. There are two effects on EPS from this assumption. First, the numerator is left unchanged as treasury stock purchases would not affect net income. Second, the impact of the assumed exercise on the denominator is reduced because the purchased shares counteract the effect of the new shares assumed to have been issued.


For example, assume that the Sample Company has outstanding 20,000 stock warrants, each of which allows the holder to buy one share for $100. Thus, if it is assumed that all 20,000 warrants are exercised, the company would have $2,000,000 available to spend. If the market value of the shares is $125 per share, Sample would be able to buy 16,000 shares ($2,000,000 / $125). Consequently, there would be an assumed increase in the denominator of only 4,000 shares (20,000 newly issued shares less 16,000 treasury shares acquired).

The formula for computing the net increase in shares is:

Formula of calculating EPS warrants

If the market value of the shares is closer to the exercise price, the effect is greatly diminished. For example, if the market value is only $102 per share, Sample can buy back19,608 shares with the exercise proceeds ($2,000,000 / $102). Thus only 392 new shares would be added to the denominator.

If the market value of the stock is below the exercise price, the company would be able to buy back more shares than it would have issued because of the warrants, and the denominator would decrease. Because this result would, in turn, produce a larger EPS, such warrants are antidilutive and should not be considered.

For example, if Sample Company’s stock is worth only $86 per share, the $2,000 000 could be used to acquire 23,256 treasury shares, a quantity which would exceed the 20,000 new shares and reduce the number outstanding by 3,256 shares.

A brief reflection, furthermore, would show that the warrants would not be exercised if the holder could buy the stock more cheaply on the market.

Primary EPS

In applying the treasury stock method for calculating primary EPS, the market value used to find the incremental shares should be the average market value for the covered period. Assume the following facts for Sample Company:

Warrants of primary eps example

The exercise of the warrants would have produced $10,000,000 cash (100,000 x $100), which would have been used to buy back 80,000 shares at $125. Thus, the denominator would have been increased by 20,000 shares. This table illustrates the calculation of EPS:

Calculating Primary EPS Warrants

Fully diluted EPS

As part of the “worst case” approach, the calculation of the effect of warrants on fully diluted EPS be based on the end-of-the-year market value of the shares, if it is higher than the average for the year This change has the effects of (1) reducing the number of treasury shares that could have been purchased, (2) increasing the number of incremental shares, and (3) further reducing the EPS.

Using the same data as above, but inserting a year-end market value of $152 per share, it can be seen that Sample could buy back only 65,789 shares of treasury stock with the $10,000,000 of assumed proceeds from the exercise of the warrants ($10,000,000 / $152). Consequently, the net increase in the denominator is 34,211 (100,000 – 65,789). These calculations would be made:

Calculating fully diluted EPS Warrants

The 20 percent limit

As a limit on the treasury stock method, it should be used only for an assumed acquisition of up to 20 percent of the end-of-the-year outstanding shares. Any assumed proceeds remaining after that acquisition should be assumed to have been used to retire debt and then to acquire interest-bearing securities. In the event that this point is reached, the calculation of EPS also includes an increase of earnings through reduced interest expense or increased interest income. There also is a more significant impact on the denominator as fewer shares are assumed to have been purchased back.


Assume that Sample Company has warrants outstanding for the issuance of 150,000 shares at $100 each and that the average market value per share is $125. Thus, if exercising is assumed, there would be $15 000,000 cash on hand. This quantity is enough to acquire 120,000 shares of treasury stock; however, there are only 420,000 shares outstanding, with the result that only 20 percent, or 84,000 shares, can be purchased. The net result would be an increase in the number of shares by 66,000. This purchase would use up only $10,500,000 of the $15,000,000 proceeds and the difference of $4,500,000 have to be applied.

If debt totaling $2,500,000 and bearing 11 percent interest could be retired with the assumed proceeds, Sample would save $275,000 of interest expense (0.11 X $2,500,000). However, this expense would have been deductible on the tax return so the company must further assume that more income taxes would have to be paid. If the incremental tax rate is 45 percent, Sample would have had to pay another $123,750 and the net savings would be $151,250.

The purchase of treasury stock and retirement of the debt would have used only $13,000,000 of the $15,000,000 proceeds. If the rate was 8 percent, the company would have earned additional income of $160,000 but would have incurred an additional 45 percent tax expense of $72 000. The additional $88,000 would be added to net income to find the pro forma earnings for the year. The calculation of simple and primary EPS is shown below:

20 percent method of calculating EPS

If the year-end market value of the common stock was greater than average, fully diluted EPS would be calculated with an assumed larger outlay for the treasury shares with less cash available for retiring debt and acquiring securities.

Changes in warrants

Special consideration must be given when warrants are exercised, issued, or allowed to lapse during the year. Warrants actually exercised produce shares that are included in the weighted average from the date of issue. The warrants are considered as common stock equivalents for the partial period prior to their exercising, and the incremental shares produced by the treasury stock method are weighted by the fraction of the year that the warrants were outstanding.


For example, assume that 10,000 warrants are exercised on March 31 at $10 per share when the market value is $12 per share. Thus, the incremental number of shares is the 10,000 new shares less the 8,333 treasury shares, or 1,667. Then, this number is weighted by the fraction of 3/12 for the three months that the warrants were outstanding. The 10,000 shares actually outstanding are weighted by 9/12 for the nine months from March 31 to December 31.

For newly issued warrants, the treasury stock method is applied as if they were exercised at the date of issuance. Then, the incremental shares are weighted by the fraction of the year that the warrants were outstanding. For example, assume that 10,000 warrants are issued on July 31 for a purchase of shares at $10 each and the market value is $12 per share.

Exercise would have produced $100,000 of cash, which would have been used to purchase 8,333 shares. The 1,667 incremental shares would be weighted by 5/12 for the five months from August through December. In the event that the 20 percent limit is exceeded, interest savings or income would be calculated only for the fraction of the year that they would have been realized.

If warrants are canceled or otherwise become ineffective during the year, the treasury stock method should be applied and the resulting incremental shares should be weighted by the fraction of the year during which they are outstanding.

This procedure generally would not be needed for warrants that lapse because lapsing normally occurs only when the exercise price exceeds the market value per share. In this case, the effect of including the warrants in EPS would be anti-dilutive.

Stock subscriptions

Uncollected stock subscriptions are essentially the same as warrants for EPS calculations because the subscriber can obtain shares by paying in the balance owed. Thus, the unpaid balance is like the exercise price of a warrant and the accountant should treat the subscription in the same way that warrants are treated, including the application of the treasury stock method.

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