Question

CA16-6 WRITING (EPS, Antidilution) Brad Dolan, a stockholder of Rhode Corporation, has asked you, the firm’s accountant, to explain why his stock warrants were not included in diluted EPS. In order to explain this situation, you must briefly explain what dilutive securities are, why they are included in the EPS calculation, and why some securities are antidilutive and thus not included in this calculation.

Rhode Corporation earned \(228,000 during the period, when it had an average of 100,000 shares of common stock outstanding. The common stock sold at an average market price of \)25 per share during the period. Also outstanding were 30,000 warrants that could be exercised to purchase one share of common stock at $30 per warrant.

Instructions

Write Mr. Dolan a 1–1.5-page letter explaining why the warrants are not included in the calculation.

Short answer

Warrants are not included in the earnings per share calculationbecause these are anti-dilutive securities.

Step-by-step solution

Definition of Diluted Earnings per Share

The financial metric that calculates the earnings per share, assuming that all investors will convert their convertible debt securities into equity security, is diluted earnings per share.

Letter for explaining why warrants are not included in the calculation of diluted earnings per share

Dear Mr. Dolan

Earnings per share are the metric that will provide information about the profit generated for each common share outstanding. It is calculated using the following formula:

$\mathbf{Earnings}\mathbf{}\mathbf{per}\mathbf{}\mathbf{share}\mathbf{=}\frac{\mathbf{Net}\mathbf{}\mathbf{income}\mathbf{-}\mathbf{Preferred}\mathbf{}\mathbf{dividend}\mathbf{}}{\mathbf{Common}\mathbf{}\mathbf{shares}\mathbf{}\mathbf{outstanding}}$

Some corporations have different varieties of shares outstanding such as convertible bonds, convertible preferred stock, and stock options. Such shares are convertible into common stock and therefore have a dilutive effect on the earnings per share.

Analysts believe that financial statements must provide fair and true information to their users. Therefore, basic EPS calculation includes only common shares outstanding while dilutive EPS calculation includes dilutive securities also. Basic EPS uses only shares outstanding, while dilutive earnings per share assume that all convertible securities are converted into shares.

Some of the securities are anti-dilutive, inflating the value of earnings per share rather than diluting it. Therefore, these securities are excluded from the calculation of earnings per share.

Now taking the above situation:

If 30,000 warrants are exercised at $30, it will not increase the outstanding shares by 30,000; rather, it will dilute the EPS. The company will retire the shares of treasury stock from the proceeds received.

$\begin{array}{rcl}\mathbf{Retired}\mathbf{}\mathbf{shares}& \mathbf{=}& \frac{\mathbf{Outstanding}\mathbf{}\mathbf{warrants}\mathbf{\times }\mathbf{Par}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{warrant}}{\mathbf{Par}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{treasury}\mathbf{}\mathbf{stock}}\\ & \mathbf{=}& \frac{\mathbf{30}\mathbf{,}\mathbf{000}\mathbf{\$}\mathbf{30}}{\mathbf{\$}\mathbf{25}}\\ & \mathbf{=}& \mathbf{36}\mathbf{,}\mathbf{000}\end{array}$

Therefore, the company can repurchase 36,000 shares using the proceeds received from the exercise of warrants. This process will increase the outstanding shares by 30,000 and decrease them by 36,000. Therefore, the total outstanding shares will reduce by 6,000 shares. Due to a reduction in the denominator, earnings per share will increase, and the aim of exercising the warrant will remain unachieved. Therefore, these warrants are anti-dilutive and will not be included in calculating earnings per share.

Regards,

Accountant