CFA Level I Exam · Analyzing Income Statements

Basic and Diluted EPS: How to Calculate Them

Updated 7 October 2026 · Fact-checked

Basic EPS = (net income − preferred dividends) ÷ weighted average ordinary shares outstanding. Diluted EPS adds the effect of dilutive securities: convertibles use the if-converted method, and options and warrants use the treasury stock method. Include a security only if it lowers EPS.

Understand Earnings per Share (Basic and Diluted)

Earnings per share (EPS) tells you how much profit belongs to each ordinary share. It is the most quoted per-share number and the base for the P/E ratio. Only ordinary shareholders count, so you remove claims that rank ahead of them, such as preferred dividends.

Basic EPS uses only the shares that exist today. Because shares are issued and bought back during the year, you use the weighted average number outstanding, not the year-end count. A share outstanding for six months counts as half a share.

Diluted EPS asks: what if every security that could become an ordinary share did so? Convertible bonds, convertible preferred shares, stock options and warrants can all add shares. Diluted EPS shows the worst-case EPS for current owners. It is never higher than basic EPS, because you only include securities that are dilutive.

Each security has its own method. If-converted method: assume conversion at the start of the period (or issue date, if later). Add the shares to the denominator and add back the related cost to the numerator: after-tax interest for convertible bonds, or preferred dividends for convertible preferred. Treasury stock method (options and warrants): assume the options are exercised and the cash received is used to buy back shares at the average market price. Only the net new shares are added.

A stock split or stock dividend is applied retroactively to all periods, as if it had always existed. This is different from an issue of shares for cash, which is weighted from its date.

Key formulas to remember

Basic EPS: Basic EPS = (Net income − Preferred dividends) ÷ Weighted average ordinary shares outstanding; Deduct preferred dividends declared on non-cumulative preferred, or for the period on cumulative preferred, whether or not declared.
Weighted average shares: Σ (shares outstanding × fraction of period outstanding); Restate for splits and stock dividends as if they happened at the start of the earliest period shown.
Diluted EPS (general): Diluted EPS = [(Net income − Preferred dividends) + Preferred dividends on convertible preferred + Convertible debt interest × (1 − t)] ÷ [Weighted average shares + Shares from conversion of preferred + Shares from conversion of debt + Net shares from options]; Include an item only if it reduces EPS.
If-converted: convertible bonds: Numerator add-back = Interest × (1 − tax rate); Denominator add = shares from conversion; Assume conversion at the start of the period or at issue date if later.
Treasury stock method: Net new shares = Options × (Average price − Exercise price) ÷ Average price; Options with an exercise price above the average market price are antidilutive and are ignored.

How to solve Earnings per Share (Basic and Diluted) questions

Work in a fixed order so you do not miss an adjustment. The same order works for any basic or diluted EPS question.

1Find the weighted average ordinary shares. Apply any split or stock dividend to all earlier share counts first, then time-weight issues and buybacks.
2Compute the numerator for basic EPS: net income minus preferred dividends. Calculate basic EPS.
3List every potentially dilutive security: convertible bonds, convertible preferred, options, warrants.
4Apply the right method to each. If-converted for convertibles: add back after-tax interest or preferred dividends, and add the conversion shares. Treasury stock method for options: add the net new shares only.
5Test each security for dilution. Compute its effect per incremental share (add-back ÷ new shares). Options and warrants are dilutive only when the average market price is above the exercise price. Those in-the-money options have a zero add-back, so their ratio is zero and you test them first. Options with an exercise price above the average price are antidilutive, so exclude them even though their add-back is zero. Then test the convertibles, starting with the lowest ratio. Include a security only if its ratio is below the EPS so far, and update EPS after each one you include.
6Add the dilutive items to the numerator and denominator and compute diluted EPS.
7Check that diluted EPS is not above basic EPS.

Quickest way: Fast path for diluted EPS in a three-option MCQ

When to use it: Use this when the question gives one or two dilutive securities and you have about 90 seconds.

Compute basic EPS first. The answer for diluted EPS must be lower, so you can discard any option equal to or above basic EPS.
For a convertible bond, compute add-back ÷ new shares. If that is below basic EPS, it is dilutive. If it is above, ignore the bond.
For options, check price first. If the average price is not above the exercise price, ignore them.
Do the final division once. On the BA II Plus, enter the numerator, press ÷, enter the denominator, press =.
Quick check: the answer should sit between the incremental ratio and basic EPS.

Common mistakes in Earnings per Share (Basic and Diluted)

Using year-end shares instead of the weighted average.
The balance sheet shows year-end shares, so it feels like the obvious number.
Fix: Always time-weight issues and buybacks by months outstanding divided by 12.
Time-weighting a stock split.
Students treat a split like a cash share issue.
Fix: A split or stock dividend is applied to the whole period and prior periods. Multiply earlier share counts by the split factor and do not weight by date.
Adding back pre-tax interest on convertible bonds.
The interest figure is given and the tax step is forgotten.
Fix: Add back interest × (1 − tax rate). Conversion removes the interest expense and its tax shield.
Adding all options as new shares under the treasury stock method.
Students forget the assumed buyback.
Fix: Add only the net shares: options × (average price − exercise price) ÷ average price.
Including an antidilutive security.
Students assume every convertible must be included.
Fix: Include it only if it lowers EPS. Options with an exercise price above the average price, or convertibles whose add-back per share exceeds basic EPS, are excluded.
Forgetting to subtract preferred dividends in basic EPS.
Net income is the first number listed.
Fix: Subtract preferred dividends before dividing by ordinary shares. Then add them back only in the if-converted method for convertible preferred.

Worked examples

Example 1

A company reports net income of $12,000,000 and paid preferred dividends of $1,500,000. It had 5,000,000 ordinary shares at the start of the year, issued 1,200,000 shares on 1 April, and repurchased 400,000 shares on 1 October. Basic EPS is closest to: A) $1.77, B) $1.81, C) $1.88

Show the solution

Shares at start: 5,000,000 for the full year = 5,000,000.
Issue on 1 April: 1,200,000 × 9/12 = 900,000.
Buyback on 1 October: 400,000 × 3/12 = 100,000 to remove.
Weighted average = 5,000,000 + 900,000 − 100,000 = 5,800,000.
Numerator = 12,000,000 − 1,500,000 = 10,500,000.
Basic EPS = 10,500,000 ÷ 5,800,000 = 1.8103.

Answer: Basic EPS is about $1.81 per share. The answer is B.

Example 2

A company has net income of $9,000,000, no preferred stock and 6,000,000 weighted average shares. It has $10,000,000 of 5% convertible bonds, convertible into 400,000 shares, and 300,000 options with an exercise price of $20. The average share price is $25. The tax rate is 30%. Diluted EPS is closest to: A) $1.40, B) $1.45, C) $1.50

Show the solution

Basic EPS = 9,000,000 ÷ 6,000,000 = $1.50.
Convertible bonds: interest = 5% × 10,000,000 = 500,000. After tax = 500,000 × 0.70 = 350,000. New shares = 400,000.
Incremental ratio for bonds = 350,000 ÷ 400,000 = $0.875. This is below $1.50, so the bonds are dilutive.
Options: net new shares = 300,000 × (25 − 20) ÷ 25 = 60,000. They add no numerator amount, so they are dilutive.
Numerator = 9,000,000 + 350,000 = 9,350,000.
Denominator = 6,000,000 + 400,000 + 60,000 = 6,460,000.
Diluted EPS = 9,350,000 ÷ 6,460,000 = 1.4474.

Answer: Diluted EPS is about $1.45, below basic EPS of $1.50 as it must be. The answer is B.

Exam tips

Always compute basic EPS first. In a three-option MCQ, any diluted answer at or above basic EPS can be eliminated.
Read the dates carefully. Decide at once whether each change is a cash issue (time-weight it) or a split or stock dividend (apply to the whole period).
For options, check average price against exercise price before doing any arithmetic. If the exercise price is higher, the options drop out.
Watch for the tax rate in convertible bond questions. After-tax interest is the add-back.
Questions may give several securities. Test options that are in the money first, since their add-back is zero. Options with an exercise price above the average price are antidilutive and drop out. Then test the convertible with the lowest add-back per incremental share.

Practice questions from Analyzing Income Statements

Earnings per Share (Basic and Diluted) in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Earnings per Share (Basic and Diluted): frequently asked questions

What is the difference between basic EPS and diluted EPS?

Basic EPS uses only ordinary shares actually outstanding, weighted over the period. Diluted EPS also assumes that dilutive securities such as convertibles, options and warrants are converted or exercised. Diluted EPS is equal to or lower than basic EPS.

How does the treasury stock method work?

You assume options are exercised and the exercise cash is used to buy back shares at the average market price. The net new shares are options × (average price − exercise price) ÷ average price. Options with an exercise price above the average price are ignored.

When do I use the if-converted method?

Use it for convertible bonds and convertible preferred shares. Assume conversion at the start of the period. Add the shares to the denominator and add back after-tax interest or preferred dividends to the numerator.

How do stock splits affect weighted average shares?

Splits and stock dividends are applied retroactively to all periods presented. You multiply the earlier share counts by the split factor and do not time-weight the split. A cash share issue, by contrast, is weighted from its issue date.