Diluted EPS: The Control Number Almost Everyone Reaches for Wrongly

The dilution test in IAS 33 is run against one specific number, and it is not the one most people reach for. Paragraph 42 requires an entity to use profit or loss from continuing operations attributable to the parent entity as the control number.

Not total profit. Not profit including discontinued operations. And not tested separately for discontinued operations. The FRC has picked this up in review work, so it is a real-world failure rather than only an exam one.

The principle

Paragraphs 30 to 32 set the objective. Diluted EPS shows each ordinary share's interest in performance as if every dilutive potential ordinary share had already converted. Both halves of the fraction move: earnings are increased by the after-tax dividends and interest that would no longer arise, and the share count is increased by the weighted average number of additional ordinary shares that would have been outstanding.

Paragraph 33 sets out the numerator adjustments, all on an after-tax basis: any dividends or other items relating to dilutive potential ordinary shares that were deducted in arriving at the numerator; any interest recognised in the period relating to them; and — the limb everyone forgets — any other changes in income or expense that would result from the conversion.

That third limb matters more than its length suggests. If conversion removes interest expense, anything else keyed to profit moves with it: a profit-related employee bonus scheme, a royalty calculated on profit, a management charge. The knock-on is part of the adjustment, not a refinement to be ignored.

Paragraph 36 handles the denominator: the basic weighted average, plus the shares issuable on conversion of all dilutive potential ordinary shares, which are deemed to have been converted at the start of the period or at their date of issue if later.

A worked example: convertible debt

Profit attributable to ordinary equity holders is 1,000,000 and the weighted average number of ordinary shares is 2,000,000, so basic EPS is 0.50.

The entity has 2,000,000 of 5 per cent convertible bonds in issue for the whole year, convertible into 400,000 ordinary shares. The tax rate is 25 per cent.

Interest for the year is 2,000,000 at 5 per cent, which is 100,000. The post-tax saving on conversion is 100,000 less 25 per cent, so 75,000. That is the numerator adjustment.

Diluted numerator: 1,000,000 plus 75,000 equals 1,075,000. Diluted denominator: 2,000,000 plus 400,000 equals 2,400,000. Diluted EPS is 1,075,000 divided by 2,400,000, which is 0.4479.

Check that it is dilutive before using it: 0.4479 is below basic EPS of 0.50, so it is. The quicker test is the incremental one — 75,000 of extra earnings divided by 400,000 of extra shares gives 0.1875 per incremental share, well below basic EPS, which is what makes the instrument dilutive.

The tax gross-down is where this goes wrong in practice. Interest on a liability is deductible, so eliminating it costs tax. Adding back the full 100,000 rather than 75,000 inflates the numerator and understates the dilution — which is the wrong direction for a measure whose purpose is to show the worst case.

The same instrument, antidilutive

Change two numbers and the answer reverses. Suppose the bonds were 2,000,000 of 12 per cent convertible debt, convertible into only 100,000 shares.

Interest is 240,000, and post-tax 180,000. The incremental test: 180,000 divided by 100,000 is 1.80 per incremental share, which is far above basic EPS of 0.50. So the instrument is antidilutive and must be excluded.

Prove it by including it anyway: 1,180,000 divided by 2,100,000 gives 0.5619, which is higher than basic EPS. Paragraph 43 is explicit that potential ordinary shares are antidilutive when their conversion would increase earnings per share, and paragraph 41 that they are treated as dilutive when, and only when, conversion would decrease earnings per share or increase loss per share from continuing operations.

So an expensive convertible that converts into few shares usually raises EPS on conversion, and gets left out. Diluted EPS is not a calculation of what would happen if everything converted. It is a calculation of what would happen if everything that hurts converted.

Which is why the sequence matters

Where an entity has several series of potential ordinary shares, each must be considered separately and in sequence from the most dilutive to the least. The reason is arithmetic: including a mildly dilutive instrument after a strongly dilutive one can turn the mild one antidilutive, because the comparison is against the running diluted figure rather than against basic EPS. Test them in the wrong order and you will include something you should have excluded.

Three rules that catch people out

Each period is computed from scratch. Paragraph 37 requires dilutive potential ordinary shares to be determined independently for each period presented. Year-to-date diluted EPS is not the weighted average of the interim diluted EPS figures — it is recomputed. Anyone reporting half-yearly under IAS 34 should know that the full-year number will not reconcile to the sum of the interims, and that this is correct rather than an error.

Instruments converted during the year straddle both measures. Under paragraph 38, potential ordinary shares are weighted for the period they were outstanding, and shares actually converted during the period count in diluted EPS up to the conversion date and in basic EPS thereafter.

Assume the holder's best terms. Where more than one basis of conversion exists, paragraph 39 requires the most advantageous conversion rate or exercise price from the standpoint of the holder. Not the most likely one, and not the one management expects.

One further point for groups: under paragraph 40, potential ordinary shares issued by a subsidiary, joint venture or associate to parties outside the group are included where they are dilutive to the reporting entity. Dilution does not stop at the parent's own instruments.

Why the control number is the thing to get right

Return to where this started, because it governs everything above.

If an entity has discontinued operations, the dilution test is still run against continuing operations attributable to the parent. An instrument that looks antidilutive against total profit may be dilutive against continuing operations, and the standard requires the continuing-operations answer. Using the wrong control number does not merely produce a different diluted EPS — it can produce the wrong population of instruments, because the include-or-exclude decision flips.

Both basic and diluted EPS then have to be presented with equal prominence, for every period presented. For the basic calculation and the share-change mechanics, see our practical guide to IAS 33, and for the bonus and rights issue adjustments that reshape the denominator, our guide to the bonus versus rights issue mistake.