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I'm confused about how to calculate diluted earnings per share. As far as I know, for any type of EPS, one must divide the earnings attributable to relevant shareholders by the weighted average number of shares.

I was studying this topic from a source and was bombarded with different types of shares and earnings. Shares - common, diluted, preferred. Earnings - basic earnings, diluted earnings.

It's mentioned that diluted earnings uses:

  1. diluted shares or the no. of shares that would hypothetically be outstanding if potentially dilutive claims on common shares (e.g. stock options/convertible bonds) were exercised/converted.
  2. an appropriately adjusted profit/loss attributable to common shareholders.

Question: regarding point 1, do we use only the no. of diluted shares or add the number of diluted shares to the no. of common shares? How do we "adjust" the PnL as indicated in point 2?

Secondly, what exactly is "basic earnings" - Is it the PnL attributable ONLY to common shareholders (and NOT preferred shareholders)?

The main source of my confusion is an example in which I saw 4 types of EPS - basic earnings per ordinary share, basic earnings per preferred share, diluted earnings per ordinary share, diluted earnings per preferred share. According to the definition of diluted EPS given in the source, (point 2) we "adjust" PnL attributable to common shareholders.

For diluted earnings per preferred share, shouldn't we "adjust" PnL attributable to preferred shareholders?

Apologies for the flurry of questions but I'm very much confused.

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So in regards to your first question, you add the impact of diluted shares to the number of common shares if you are calculating Diluted EPS. You adjust the PnL (numerator) by assuming that any and all conversions happened at the beginning of the year. So if you have convertible preferred shares, do not subtract preferred dividends from profit in the numerator because you assume the convertible preferred shares were converted to common and thus not awarded their preferred dividend.

Second question: Basic earnings is exactly as you describe it. It is the earnings available to common shareholders ONLY. In that case, you do subtract any preferred dividends from your profit in the numerator.

The 4 types of EPS you mention involve manipulating the denominator as well as the numerator. Whatever EPS you decide to measure, you want to think about the availability of profits. So, if calculating basic EPS per common share, you want to subtract any dividends that will not be available to common shareholders (which are preferred dividends). For the denominator, frame your thinking as "what types of shares am I dividing these available profits against?". In the case of basic EPS per common share, you simply want your weighted average of common shares outstanding. If you had 10M common shares outstanding last year, and 15M this year, your denominator is 12.5M.

For a complex capital structure, this can get a little murky as you can have warrants, options, convertible debt, etc. It involves a combination of the "assume converted" method along with what is called the "treasury stock" method. Intuitively, the treasury stock method looks something like this: Your average share price was $10 a year and you had 100 warrants outstanding (worth 1 share each) exercisable at $5 per share. That means, if exercised, you will receive 100*$5 = $500. Take the $500 you received / avg share price of $10 = 50 additional common shares. You add these 50 shares to the denominator. - Investopedia for reference

Edit: I cannot stress the importance of the sanity check when doing ANY calculation related to security analysis. It is really easy to get caught up in the formulas and forget what it is you are actually trying to do. Before you calculate X type of EPS, ask yourself "does the numerator (earnings) accurately reflect the money available to the type of shares I am using?" and "Does the denominator (shares) accurately reflect the type and amount of shares I want"?

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