# 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

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: