FAR · Financial reporting · 6 practice questions
How to Calculate Basic and Diluted EPS
Compute basic EPS from income available to common and weighted-average common shares, then include only dilutive securities. Below: a worked calculation that subtracts preferred dividends, weights shares, and adds options before convertible bonds.
Try one first
Hint
First determine income available to common (consider current-year cumulative preferred dividends). Then compute time-weighted average common shares, remember to apply the 2-for-1 split retrospectively to all prior periods before weighting.
Answer D. Income available to common = net income − current-year cumulative preferred dividend = $1,200,000 − (5,000 × $50 × 8%) = $1,180,000. Apply the 2-for-1 split retrospectively: Jan-Mar = 100,000 → 200,000 for 3 months; Apr-Aug = 120,000 → 240,000 for 5 months; Sep-Oct = 110,000 → 220,000 for 2 months; Nov-Dec = 220,000 for 2 months. Weighted-average shares = (200,000×3 + 240,000×5 + 220,000×4) / 12 = 223,333.33. Basic EPS = $1,180,000 ÷ 223,333.33 = $5.28 (rounded to nearest cent).
Why not A: Tempting because ignoring the Sep 1 repurchase (i.e., treating Apr-Dec as 240,000 shares after the split) inflates the weighted-average denominator; (200,000×3 + 240,000×9)/12 = 230,000 shares, giving EPS ≈ $5.13. It's wrong because the Sep 1 treasury repurchase reduces shares outstanding beginning Sept. 1 and must be reflected in the time-weighted denominator.
Why not B: Tempting because failing to subtract the current-year cumulative preferred dividend raises the numerator, 1,200,000 ÷ 223,333.33 ≈ $5.37. It's wrong because for cumulative preferred stock the current year's dividend (5,000 × $50 × 8% = $20,000) is deducted from net income when computing income available to common even if not declared.
Why not C: Tempting because using the year-end post-split share count (220,000) is the simplest approach, 1,180,000 ÷ 220,000 = $5.36. It's incorrect because EPS requires time-weighted average shares for the year, and stock splits must be applied retrospectively to prior periods.
Worked example
Maple Co. reports net income of $1,680,000 and $30,000 of current-year cumulative preferred dividends, undeclared. Common shares were 300,000 on January 1; 100,000 were issued July 1. All year, 40,000 options had a $30 exercise price and $40 average market price. Convertible bonds outstanding all year would add 40,000 shares and save $30,000 of after-tax interest. There are no discontinued operations.
| 1 | Income available to common$1,680,000 - $30,000 | $1,650,000 |
| 2 | Weighted-average common shares(300,000 × 6/12) + (400,000 × 6/12) | 350,000 shares |
| 3 | Basic EPS$1,650,000 ÷ 350,000 | $4.71 |
| 4 | Incremental option shares40,000 - (40,000 × $30 ÷ $40) | 10,000 shares |
| 5 | EPS after options$1,650,000 ÷ (350,000 + 10,000) | $4.58 |
| 6 | Test convertible bonds$30,000 ÷ 40,000 = $0.75; $0.75 < $4.58 | Dilutive: add $30,000 and 40,000 shares |
| 7 | Diluted EPS($1,650,000 + $30,000) ÷ (350,000 + 10,000 + 40,000) | $4.20 |
Maple reports basic EPS of $4.71 and diluted EPS of $4.20.
Check: Options add 10,000 shares and no income; bonds add $0.75 per new share, below the $4.58 EPS after options.
Key points
- Cash issuances and treasury-share repurchases affect weighted-average shares only from their transaction dates.
- Apply stock splits and stock dividends retroactively to all periods presented, including those occurring after year-end but before statement issuance.
- Deduct declared noncumulative preferred dividends, but do not deduct prior-year cumulative dividend arrears again.
- Use income from continuing operations available to common to test dilution.
How the exam traps you
- Ignoring cumulative preferred dividends because none were declared. Subtract the full current-year cumulative dividend requirement, whether declared or not.
- Using ending shares or weighting a stock split only from its effective date. Time-weight actual share changes, then apply the split factor retroactively.
- Adding every potential share without testing dilution. Add dilutive options first; test convertibles against EPS after earlier dilutive securities.
Question 2
Hint
Focus on whether EPS is required for each income statement period presented, not on whether the statements are annual or interim.
Answer B. For a public entity, basic and diluted earnings per share are presented for each period for which an income statement is shown. In interim reporting, that includes both the quarterly period and the year-to-date period, along with comparable prior-year periods if those income statements are presented. Because Northgate has common stock and dilutive options, both basic and diluted EPS are required.
Why not A: This is tempting because candidates sometimes assume interim reports require less detail, but public entities must present both basic and diluted EPS for each income statement period shown, not just basic EPS.
Why not C: This distractor appeals to the idea that year-to-date information can be inferred from quarterly data. It is incorrect because EPS must be shown for each separate statement of operations period presented, including the year-to-date interim period.
Why not D: This is tempting if a candidate remembers that options affect diluted EPS but forgets that diluted EPS does not replace basic EPS; public entities generally present both basic and diluted EPS on the face of the income statement.
Question 3
Hint
Tie EPS presentation to the income statement periods shown in the interim filing, not just to the latest quarter.
Answer D. For a public company, basic and diluted earnings per share must be presented for each period for which an income statement is presented. When an interim filing includes both quarterly (three-month) and year-to-date (six-month) income statements, EPS (basic and diluted) is required for each of those periods. The facts here say securities are dilutive in each period, so both basic and diluted EPS should be shown for all periods presented.
Why not A: This is tempting because candidates often focus on the current quarter in a Form 10-Q, but it is incorrect: EPS must be presented for every income statement period shown, so you cannot show only the quarter when the year-to-date periods are also presented.
Why not B: This distractor appeals to the idea that year-to-date amounts are more comprehensive, but it is wrong: presenting YTD amounts does not eliminate the requirement to present EPS for the separate quarterly periods when those are also included.
Why not C: This may seem plausible because diluted EPS can be more complex, but there is no blanket exemption for diluted EPS in interim filings. If diluted EPS is applicable (i.e., not antidilutive), both basic and diluted EPS must be shown for each period.
Question 4
Hint
Separate two issues: first compute income available to common shareholders, then decide which EPS captions a public company must show on the face of the income statement.
Answer D. For basic EPS, income available to common shareholders equals the reported amount less cumulative preferred dividends (which are deducted for EPS purposes even if not declared). Continuing-operations EPS = ($6,200,000 - $400,000) / 1,000,000 = $5.80. Net-income EPS = ($5,000,000 - $400,000) / 1,000,000 = $4.60. Public companies must present EPS for income from continuing operations and net income on the face of the income statement.
Why not A: This choice presents net income EPS and the discontinued-component EPS but omits continuing-operations EPS, which is specifically required on the face of the income statement for a public company.
Why not B: This answer fails to deduct the cumulative preferred dividend from the continuing-operations numerator. The preferred dividend reduces income available to common shareholders for both continuing operations and net income, so $6.20 overstated.
Why not C: Although companies disclose per-share amounts for discontinued operations, the face of the income statement must show EPS for continuing operations and net income. Providing continuing-operations EPS and only the discontinued-component EPS (instead of net income EPS) does not meet the face-of-statement requirement.
Question 5
Hint
In basic EPS, ask which preferred dividends are considered applicable to the current year. The declaration requirement is not the same for cumulative and noncumulative preferred stock.
Answer B. Basic EPS numerator = net income less preferred dividends applicable to the period. Current-year dividends on cumulative preferred stock (50,000 × $3 = $150,000) are deducted whether or not declared; noncumulative preferred dividends are deducted only if declared (30,000 × $2 = $60,000). Net income of $1,200,000 minus $210,000 of preferred dividends equals $990,000.
Why not A: This ignores preferred dividends entirely. It's wrong because the declared noncumulative dividend and the current-year cumulative dividend (even if not declared) both reduce income available to common.
Why not C: This reflects deducting only the $60,000 declared noncumulative dividend. It's a common partial-rule error; current-year cumulative dividends of $150,000 must also be subtracted even though they were not declared.
Why not D: This reflects deducting only the cumulative preferred dividend ($150,000) and omitting the declared noncumulative dividend. It's wrong because the declared $60,000 noncumulative dividend also reduces income available to common.
Question 6
Hint
Focus on whether a stock split changes only future share counts or also the comparability of prior-period per-share data.
Answer A. Stock splits are reflected retroactively in earnings per share for all periods presented. That treatment applies even when the split occurs after the reporting period but before the financial statements are issued. Restating both comparative periods ensures per-share data are comparable on the new share basis.
Why not B: This is tempting because the split happened after Year 1, but EPS is adjusted for comparability across all periods presented, not just the most recent year.
Why not C: While some post-period events are disclosed rather than recognized, a stock split affecting per-share amounts requires retroactive adjustment of EPS for all presented periods rather than mere disclosure.
Why not D: This distractor assumes only shares outstanding at the balance-sheet date matter, but for EPS presentation a stock split is treated as if it occurred at the beginning of the earliest period presented, so prior-period EPS is restated.
Common questions
Do you subtract cumulative preferred dividends if not declared?
Yes. Subtract the full current-year cumulative dividend requirement; prior-year arrears paid this year do not reduce this year's numerator again.
How do stock splits affect weighted-average shares for EPS?
First time-weight actual share changes, then multiply by the split factor. Restate all periods presented, including for a split after year-end but before the financial statements are issued.
How do you calculate diluted EPS with options and convertible bonds?
Options add only incremental shares under the treasury-stock method. Convertible bonds add after-tax interest and conversion shares, but only if they lower EPS from continuing operations after earlier dilutive securities.
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