# Understanding the earnings and shares in the commentary

I'm reading The Intelligent Investor, commentary on chapter 11, and quote:

AOL Time Warner, for example, reported in the front of its annual report that it had 4.5 billion shares of common stock outstanding as of December 31, 2002. But a footnote in the bowels of the report reveals that the company had issued options on 657 million more shares. So AOL’s future earnings will have to be divided among 15% more shares. You should factor in the potential flood of new shares from stock options whenever you estimate a company’s future value.

My question is,

1. If these options are issued on existing shares, it would already take `0.657/4.5=14.6%` of AOL's earnings, why would the author emphasize it?
2. If these options are converted to new shares, it should take `0.657/(4.5+0.657)=12.7%` of AOL's earnings, but the author claims to be 15%.

Does anyone know what the author means?

• The author doesn’t say that the options will take 15% of earnings, he or she says that they will increase the number of shares by 15%. Those aren’t the same thing — increasing the number of shares by 15% means the new shares take 13% of the earnings, 1 - 1/1.15. Dec 24, 2022 at 2:14

`657M/4500M = 0.146`. Rounding up it's `0.15`, or `15%` of the `4.5B` shares outstanding. The options are not issued on the outstanding shares, they're issued on treasury shares which the company would sell if the option is executed (making them outstanding at that time).