# Computing the denominator of diluted earnings per share

I'm practicing for CFA level 1, and I faced this question. I don't understand the last part (802 − 481 = 321) because I understand that a company doesn't realize options of its own shares, if you are the owner of those options, you realize them at 6, get those 4812 dollars, buy 481 shares at price \$10. So:

1. Those shares are purchased in the market (if not where?), then why would the company need to issue more shares?
2. The question seems to assume the company has those options. Is this actually possible? It doesn't make sense to me that the company has options (why would it have them in the first place?)
3. Why is the 802 - 481 actually mean? If I realize those 802 options, and buy the 481 shares, it's actually fewer shares than options. I just don't get it.

Assume that the exercise price of an option is 6, and the average market price of the stock is 10. Assuming 802 options are outstanding during the entire year, the number of shares to be added to the denominator of diluted earnings per share (EPS) is closest to:

Answer Proceeds from the exercise of the options would be:

(802)(6) = 4,812

The number of shares that could be repurchased with the proceeds at the average price is:

4,812 / 10 = 481.2

The additional number of shares the company would need to issue to fulfill the stock options is:

802 − 481 = 321

I think your misunderstanding arises from who is holding the options. The options are not held by the company itself but by others, e.g. employees, who received the options as a form of compensation.

The option holders will exercise the options paying exercise price of 6 and receiving one stock for each option from the company. The payments by the option holders earn the company $$6 \times 802 = 4,812$$. The company can use this to buy $$4,812 / 10 = 481.2$$ shares in the open market. However, the companies needs to give the option holders 802 stocks in total. Therefore, they need to come up with $$802 - 481 = 321$$ shares. The company can do this in two ways:

1. Buy these in the open market but this requires financing; or
2. Create new shares

Apparently, in this question, the second option is chosen and 321 shares are created, leading to dilution of the existing shareholders.

• This is called treasury stock method in accounting (IFRS). Worked example 2 from Deloitte's IAS plus website shows this too. For the CFA, make sure you also study what chapter asks what concept. Else you will find it hard to know what is asked sometimes. Sep 5, 2021 at 23:37