Convertible Debt - Diluted EPS

What is the logic/intuition on adding the After Tax Interest on Convertible Debt back to the Net Income in the numerator? I mean, I get why the interest payments that now do not have to be made is added back in, but why after tax? Implicity I suppose this means that the corporation has to now pay taxes on this amount, whereas if they simply paid it out as interest to debt holders they would not? Is it that simple? And since I have your attention on this topic, can someone explain how stock options work from the corporate side? What I mean is, say I am awarded a stock option as compensation. Do these shares actually exist at the moment that I am awarded the option? Or are they new issues once I exercise the option… or something else?

Yep, its that simple. You’re looking for the after tax return and as you said, if that amount were not paid out as interest, it would be taxed. Also, the share’s don’t exist yet. They are issued when you exercise. MDD