The diluted EPS formula
Diluted EPS = (profit for ordinary shareholders + earnings added back) ÷ (weighted average shares + incremental shares)
Diluted EPS answers the question: what would EPS be if every option, warrant and convertible that would reduce EPS had already become an ordinary share? Instruments that would raise EPS are antidilutive and are ignored, so diluted EPS is never higher than basic EPS. The steps below follow the general principles of IAS 33 and ASC 260, which agree on the mechanics shown here.
Step 1: basic EPS
Basic EPS is the starting point and the first line of the sequence: profit attributable to ordinary shareholders ÷ weighted average ordinary shares = 12,000,000 ÷ 20,000,000 = USD 0.60. The profit is already after the 720,000 preference dividend, because that money belongs to the preference shareholders. Shares issued or bought back during the year count only for the months they were outstanding.
Worked example: diluted EPS with options, warrants, bonds and preference shares
A fictional company with four kinds of potential ordinary shares (yellow inputs). Rows 2 to 5 calculate the earnings added and the incremental shares of each instrument with the treasury stock and if-converted methods. Rows 16 to 19 add them one at a time, most dilutive first, and row 20 picks diluted EPS.
| A | B | C | D | E | F | |
|---|---|---|---|---|---|---|
| 1 | Instrument | Number or face | Exercise / conv. price | Earnings added | Incremental shares | Earnings per incr. share |
| 2 | Options | 1,200,000 | 15.00 | 0 | 480,000 | 0.000 |
| 3 | Warrants | 800,000 | 28.00 | 0 | 0 | excluded |
| 4 | Convertible bonds | 10,000,000 | 10.00 | 300,000 | 1,000,000 | 0.300 |
| 5 | Convertible preference | 9,000,000 | 9.00 | 720,000 | 1,000,000 | 0.720 |
| 6 | ||||||
| 7 | Profit for ordinary shareholders (after preference dividends) | 12,000,000 | ||||
| 8 | Weighted average ordinary shares | 20,000,000 | ||||
| 9 | Average market price | 25.00 | ||||
| 10 | ||||||
| 11 | Bond interest expense | 400,000 | ||||
| 12 | Tax rate | 25% | ||||
| 13 | Preference dividend | 720,000 | ||||
| 14 | ||||||
| 15 | Step | Earnings | Shares | EPS | Dilutive? | |
| 16 | Basic EPS | 12,000,000 | 20,000,000 | 0.6000 | ||
| 17 | + options and warrants | 12,000,000 | 20,480,000 | 0.5859 | Yes | |
| 18 | + convertible bonds | 12,300,000 | 21,480,000 | 0.5726 | Yes | |
| 19 | + convertible preference | 13,020,000 | 22,480,000 | 0.5792 | No | |
| 20 | Diluted EPS (lowest in the sequence) | 0.5726 | ||||
| 21 | Dilution vs basic EPS | 4.6% | ||||
| 22 | Wrong: all instruments in, no antidilution test | 0.5792 | ||||
- E2
=MAX(0,B2-B2*C2/$B$9)Treasury stock method: incremental shares from options - D4
=B11*(1-B12)If-converted: after-tax interest added back - E4
=B4/C4If-converted: new shares from the bonds - F4
=IF(E4=0,"excluded",D4/E4)Earnings per incremental share - D17
=B17/C17EPS after options and warrants - E19
=IF(D19<D18,"Yes","No")Antidilution test for the preference shares - D20
=MIN(D16:D19)Diluted EPS: the lowest EPS in the sequence
Fictional company and illustrative figures. The steps follow the general principles of IAS 33 and ASC 260. Tabellab is not affiliated with the IASB or the FASB, and this is not accounting advice.
Step 2: options and warrants, the treasury stock method
Assume the options are exercised and the company uses the cash to buy back its own shares at the average market price of the year. Only the difference is new:
- Exercise proceeds: 1,200,000 × USD 15 = USD 18,000,000
- Shares bought back: 18,000,000 ÷ USD 25 = 720,000
- Incremental shares: 1,200,000 − 720,000 = 480,000
In one formula: =MAX(0,B2-B2*C2/$B$9). The warrants have an exercise price of USD 28, above the average price of USD 25. The buyback would exceed the new shares, so they are out of the money and add 0. Options add shares but no earnings, so their earnings per incremental share is 0 and they always come first. EPS after options: 12,000,000 ÷ 20,480,000 = USD 0.5859.
Step 3: convertible bonds, the if-converted method
Assume the bonds were converted at the start of the year. The USD 10,000,000 of bonds convert at USD 10 per share into 1,000,000 new shares, and the company no longer pays the interest. Interest is tax-deductible, so add back the after-tax amount: 400,000 × (1 − 25%) = USD 300,000.
The bonds earn 300,000 ÷ 1,000,000 = USD 0.30 per incremental share, less than the current EPS of 0.5859, so they dilute: (12,000,000 + 300,000) ÷ (20,480,000 + 1,000,000) = USD 0.5726. Use the interest expense in profit or loss, which can be higher than the coupon when the bond was issued at a discount.
Step 4: preference shares and the antidilution test
The convertible preference shares would convert into 1,000,000 ordinary shares, and the 720,000 preference dividend would no longer be paid, so it is added back. That is USD 0.72 per incremental share, more than the 0.5726 reached after the bonds. Adding them would raise EPS to 0.5792, so they are antidilutive and stay out.
That is why the order matters. Rank the instruments by earnings per incremental share, lowest first (options 0, bonds 0.30, preference 0.72), add them one at a time and stop when EPS rises. Diluted EPS is the lowest EPS in the sequence, here =MIN(D16:D19) = 0.5726. Adding everything at once would report 0.5792 and overstate diluted EPS.
Reporting diluted EPS
Companies present basic and diluted EPS on the face of the income statement, usually to two decimals: USD 0.60 and USD 0.57 here. A few points to watch:
- Instruments issued during the year are weighted by the months they existed, exactly like ordinary shares.
- Under IAS 33 the dilution test uses profit from continuing operations as the control number. With a loss from continuing operations, potential shares are antidilutive and diluted EPS equals basic EPS.
- Under US GAAP, after ASU 2020-06, convertible debt is generally included with the if-converted method.
- Share options also create an expense in profit or loss. The Black-Scholes option expense guide shows how that number is measured.
Common mistakes
- The year-end share price in the treasury stock method. The buyback uses the average market price of the period, not the closing price.
- Pre-tax interest added back. Saving the interest also raises the tax bill. Add back 400,000 × (1 − 25%) = 300,000, not 400,000.
- Out-of-the-money options included. When the exercise price is above the average price, the instrument is antidilutive and adds 0 shares, never a negative number.
- All instruments added at once. Including the preference shares gives 0.5792 instead of 0.5726. Add instruments in order of earnings per incremental share and stop when EPS rises.
- Preference dividends forgotten in basic EPS. Basic EPS uses profit after preference dividends, and only convertible preference shares get their dividend added back in diluted EPS.
- No time-weighting. Options granted on 1 July count for 6 of 12 months. Using the full number overstates the dilution.
Frequently asked questions
What is the difference between basic and diluted EPS?
Basic EPS divides profit for ordinary shareholders by the weighted average shares outstanding. Diluted EPS also counts the shares that options, warrants and convertibles would create, but only if they lower EPS.
How do you calculate diluted EPS with stock options?
Use the treasury stock method: incremental shares = options − options × exercise price ÷ average market price. Add them to the denominator. The numerator does not change.
What does antidilutive mean?
An instrument is antidilutive if including it would increase EPS or reduce a loss per share. Antidilutive instruments are left out of diluted EPS, for example options whose exercise price is above the average share price.
Can diluted EPS be higher than basic EPS?
No. Instruments that would raise EPS are excluded, so diluted EPS is at most equal to basic EPS. With a loss from continuing operations, diluted EPS usually equals basic EPS.