Diluted EPS question

Question

Hi all.. I thought I had this calculation down and am now seemingly struggling to get it figured out once again. Here is the question below.

The following Financial information is available at the end of the year:

Net Income: 1,000,000
Common stock Outstanding: 250,000
Preferred Stock (Series A): 12,000 - Nonconvertible, cumulative; pays a dividend of $4 per share
Preferred Stock (Series B): 30,000 - convertible, pays a dividend of $7.50 per share and convertible into 2.5 common shares each.

Calculate Diluted eps.

The answer shows Basic EPS is 2.91 from (1,000,000-48,000-225,000)/250,000

The diluted EPS is 2.93 (1,000,000-48,000)/(250,000+75,000)

Diluted exceeds basic so its anti-dilutive.

Could someone please help me answer this question?

Why, if the second preferred stock is anti-dilutive, ie (7.5*30,000)/(2.5*30,000)=3 is it included in the calculation of the weighted average shares outstanding, but the dividend isn't added back into the numerator, since you wouldn't be paying it, if converted? All of the books I have show that if it is anti-dilutive, than it is saying to ignore it, or if dilutive, then add dividends to numerator, and converted shares to denominator. Does it always occur, that if preferred is antidilutive, it is included in the denominator, but not the numerator?

Thank you for any assistance!
Paul

Sophie Macon · Answer

Hey @pcweldon‌ , I don't fully follow your question.

As you can see from the Basic EPS calculation, preferred dividends of 225,000 was subtracted. In the case of diluted EPS, preferred dividends are not paid (as it's assumed converted into stock), hence the equation becomes (in this case) = (Net income less non-convertible shares dividends) / (WASO+new shares for convertible stock).

The convertible preferred stock's dividend is in fact 'added' back to the numerator (vs. basic eps, that's why you don't see any subtraction of that here since as you say it's converted to stock). Does this make sense?

pcweldon · Answer

oh my... that's embarrassing... thank you very much! I'm going to go with the, "I needed someone else to explain it for it to make sense" excuse! Thanks again Sophie!