Work out earnings per share on a basic and a diluted basis

CFA® Level I · Financial Statement Analysis · Analyzing Income Statements · FSA.1.e

The idea

Basic earnings per share divides income available to common shareholders — net income less preferred dividends — by the weighted average number of common shares outstanding, weighted by the portion of the year each tranche was outstanding. Diluted earnings per share assumes that dilutive convertible securities and options were exercised: convertible preferred adds back its dividend and its shares, convertible debt adds back after-tax interest and its shares, and options add net new shares under the treasury stock method. A security is included only if it reduces earnings per share; antidilutive securities are excluded.

Formulas

Basic earnings per share

basic EPS = (net income − preferred dividends) ÷ weighted average shares outstanding

net income: profit after tax for the period
preferred dividends: dividends declared on preferred stock, which belong to somebody else
weighted average shares outstanding: shares weighted by the part of the year they were outstanding for

Preferred dividends come out because earnings per share is per common share. The weighting matters whenever shares were issued or bought back mid-year; a split is treated as though it had always been in place.

Diluted earnings per share

diluted EPS = (net income − preferred dividends) ÷ (weighted average shares outstanding + dilutive shares)

net income: profit after tax, adjusted for anything the conversion itself would change
preferred dividends: excluded where the preferred is itself convertible and assumed converted
weighted average shares outstanding: the basic denominator
dilutive shares: the extra shares that would exist if options, warrants and convertibles were exercised

Only securities that would lower EPS are counted — an antidilutive one is left out, so diluted EPS is never above basic. It answers what the earnings would be if everyone with a claim on shares took it.

A practice question

From the question bank, with the reason each wrong option is wrong.

What is the denominator of basic earnings per share?

The weighted average number of common shares outstanding — correct
The number of shares outstanding at year endWhy not: Shares issued in the final month did not fund a full year of earnings. Counting them in full understates what each share earned.
The total of common and preferred sharesWhy not: Preferred shares have their own fixed claim, which is removed from the numerator as a dividend. They do not share in the residual.

Weighting by time outstanding matches the share count to the period in which the earnings were generated.

A harder one

How is convertible debt treated in diluted earnings per share?

Its interest is deducted twiceWhy not: It is added *back*, not deducted again: if the debt had converted there would have been no interest to pay.
Both numerator and denominator adjust — correct
Only the conversion shares are addedWhy not: That takes the dilution without the offsetting benefit. Conversion removes the interest expense too, so the numerator rises as well as the denominator.

After-tax interest is added back to the numerator and the conversion shares to the denominator. If the debt had converted there would be no interest expense and more shares, so both sides of the ratio must reflect the assumed conversion.

The hardest tier

Why must an antidilutive security be excluded from diluted earnings per share?

Because the holder would not convert — correct
Because it is excluded from basic earnings per share as wellWhy not: So is every potential share, dilutive or not. Basic counts only shares actually outstanding, so this does not distinguish the antidilutive case.
Because its conversion price is unknownWhy not: The conversion terms are known and disclosed. It is what those terms imply — a higher earnings per share on conversion — that causes the exclusion.

Including it would overstate the figure the measure is meant to floor. Diluted earnings per share is a worst case rather than an average of scenarios, and a conversion that would improve the figure is one that would not happen.

In the app: 12 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.

Take the free diagnostic →