Chapter 45 – Diluted Earnings per Share

Context & Key Definitions

• Earnings per share (EPS) communicates the portion of a company’s profit/loss attributable to each common share holder.
  • Investors routinely use EPS in price–earnings (P/E) valuation and to benchmark profitability among peers.
• Two EPS figures are required for publicly-accountable enterprises under IAS 33:
  • Basic EPS – actual per-share performance for the period.
  • Diluted EPS – hypothetical “worst-case” per-share performance assuming all potential common shares (PCS) that are dilutive are converted.
• Non-public entities reporting under IFRS are not required to present EPS (no ASPE guidance).
• PCS = contracts/instruments that can become common shares, e.g. convertible bonds, convertible preferred shares, employee stock options, warrants, contingently issuable shares.
  • Dilutive PCS lower EPS.
  • Anti-dilutive PCS increase EPS or reduce loss per share; they are ignored in diluted EPS.

Diluted EPS: Purpose & Formula

• Purpose: portray the lowest possible EPS a shareholder could experience if every dilutive instrument becomes a share today.
• IFRS formula (IAS 33):
  • (\text{Diluted EPS}) = \dfrac{\text{Net earnings available to common shareholders} + \text{Income effect of dilutive PCS}}{\text{WACSO} + \text{Share effect of dilutive PCS}}
  • Key terms:
  • Income effect (numerator adjustment) – after-tax interest/dividends avoided if PCS convert.
  • Share effect (denominator adjustment) – incremental shares issued on conversion/exercise.
  • Always apply the same split/stock-dividend restatements used in Basic EPS.

Four-Step Calculation Process

• IAS 33 prescribes a four-step approach executed after Basic EPS is computed.

Step 1 – Identify PCS

• Examine contracts, debt, equity, employee compensation, acquisition agreements, etc.
• Common PCS:
  • Convertible bonds (debt ➜ shares at preset ratio).
  • Convertible preferred shares (equity ➜ common shares).
  • Stock options & warrants (right to buy shares at exercise price).
  • Contingently issuable shares triggered by performance or events.

Step 2 – Compute Incremental EPS for each PCS class

• \text{Incremental EPS} = \dfrac{\text{Income impact}}{\text{Share impact}}
• Purpose: test whether security is dilutive (incremental EPS < current EPS) or anti-dilutive.

a) Convertible Bonds (if-converted method)

• Income impact: \text{Carrying value} \times \text{Effective rate} \times (1 - \text{Tax rate})
  • When issued at premium/discount use effective-interest expense, not coupon.
  • Prorate for months outstanding.
• Share impact: additional common shares issued on conversion, prorated by time outstanding.
• Example (Danforth Inc.):
  • 1{,}000{,}000 \times 5\% \times (1-0.25) = 37{,}500 income impact.
  • 25,000 shares impact ⇒ Incremental EPS = 1.50.
  • Issued 8/12 of year ⇒ 25{,}000 income, 16{,}667 shares, still 1.50 EPS.

b) Convertible Preferred Shares

• Income impact depends on dividend policy:
  • Cumulative: include annual dividend whether declared or not.
  • Non-cumulative: include only if declared.
  • Dividends are not tax-deductible ⇒ no tax adjustment.
• Share impact: shares obtained on conversion, prorated for time.
• Example (Danforth):
  • Class A (cumulative): 50{,}000 income, 100{,}000 shares ⇒ 0.50.
  • Class B (non-cum, declared): 25{,}000 income, 125{,}000 shares ⇒ 0.20.
  • If issued 2/12 of year ⇒ 8{,}333 / 16{,}667 = 0.50.

c) Stock Options & Warrants (treasury-stock method)

• Only in-the-money options considered (exercise price < average market price).
• Income impact = 0 (no interest/dividends paid).
• Share impact:
  • Equivalent to shares issued minus shares hypothetically repurchased with exercise proceeds.
  • Formula: \text{Options} \times \dfrac{\text{Market price} - \text{Exercise price}}{\text{Market price}}
• Always dilutive (incremental EPS = 0 if in the money).
• Example (Danforth):
  • 2,000 options, P{avg}=25,\;P{ex}=20 ⇒ 2{,}000\times\dfrac{25-20}{25}=400 shares.
  • Incremental EPS = 0.
• Example (Quitzau’s Fishing):
  • Series A: 10,000 unvested, P{ex}=15, P{avg}=18 ⇒ 1,667 shares.
  • Series B: 5,000 vested, P_{ex}=17 ⇒ 278 shares.
  • Series C: P{ex}=20 > P{avg}=18 ⇒ out-of-money ⇒ anti-dilutive, exclude.

Step 3 – Rank Incremental EPS (Most ➜ Least Dilutive)

• Order PCS ascending by incremental EPS; 0 always ranks first.
• If two classes share identical incremental EPS, relative order immaterial.
• Compare each incremental EPS to Basic EPS; if higher, security already anti-dilutive and can be excluded before Step 4.
• Example (Danforth): ranking
  1. Stock options (0)
  2. Class B preferred (0.20)
  3. Class A preferred (0.50)
  4. Convertible bond (1.50)
  • Basic EPS = 3.66, so all are initially considered dilutive.
• Example (RGE): convertible bonds’ incremental EPS 3.50 > basic 2.50 ⇒ anti-dilutive, remove before Step 4.

Step 4 – Successively Recompute Provisional EPS

1. Start with Basic EPS (earnings ÷ WACSO).
2. Add most dilutive PCS; update numerator & denominator to obtain provisional EPS.
3. Compare next PCS’s incremental EPS to new provisional EPS.
4. If incremental EPS < provisional, include PCS; otherwise stop (remaining PCS are anti-dilutive).
5. Continue until all PCS processed or a PCS fails the test.
6. Last provisional EPS = Diluted EPS.

• Example (Danforth):
  • Basic = 3.66.
  • Add options ⇒ 3.65.
  • Add Class B ⇒ 2.73.
  • Add Class A ⇒ 2.34.
  • Add bond ⇒ 2.30 (final). If bond incremental EPS had been 2.50, stop at 2.34.
• Example (Sati’s Kennel):
  • Basic 1.51; add option A 1.49; add bonds 1.47; stop (preferred 1.50 is anti-dilutive now).

Complicating Factors & Special Situations

Contingently Issuable Shares

• Shares issuable if future event/performance triggers.
  • Affect Basic EPS only after conditions satisfied.
  • For Diluted EPS, treat as PCS from period start; include shares that would be issued if period ended today.
• Example (Roland): 50,000 shares became issuable Aug 31. Basic EPS includes 4/12 of shares; Diluted EPS includes them from Jan 1 for entire year.

Basic EPS Negative (Loss per Share)

• IAS 33: PCS are dilutive only if they reduce EPS or increase loss per share.
• When basic EPS < 0, adding income or shares moves figure toward zero (less negative) ⇒ anti-dilutive.
• Result: Diluted EPS = Basic EPS when a loss.
• Example (Abacus): loss -1.00. Options (incremental EPS 0) & bonds (0.42) both reduce loss magnitude ⇒ anti-dilutive; report loss per share -1.00 basic = diluted.

PCS Converted During the Period

• After actual conversion date, post-conversion effects already in Basic EPS.
• For Diluted EPS, add pre-conversion fraction to simulate conversion at period start.
  • E.g., bond converts Dec 1: add 11/12 interest saving & 11/12 shares in Step 2 computation.

Multiple Conversion Options

• Use scenario generating highest share impact / lowest incremental EPS (most dilutive).

Stock Splits & Share Dividends After Year-End but Before Authorization

• Recalculate all presented Basic & Diluted EPS retroactively as if split occurred at start of earliest period shown.

Other Comprehensive Income (OCI)

• Ignored in EPS; only profit or loss attributable to common shareholders considered.

Error Corrections & Accounting Policy Changes

• When prior periods restated, restate Basic & Diluted EPS comparatives consistently.

Presentation & Disclosure Requirements (IAS 33)

Presentation on Statement of Comprehensive Income (SCI)

• Must show (to nearest cent):
  • Basic EPS from continuing operations.
  • Diluted EPS from continuing operations (even if same as basic; may be combined on one line if identical).
  • If discontinued operations present: basic & diluted EPS for those, either on face or in notes.
• Show regardless of positive or negative values.

Disclosures in Notes

• Reconciliation of numerator: profit or loss ➜ earnings used for basic ➜ earnings used for diluted.
• Reconciliation of denominator: WACSO for basic ➜ effect of PCS ➜ diluted WACSO.
• Description of PCS that could dilute EPS in future but were anti-dilutive in current period.
• Details of significant share transactions after year-end that would materially affect future EPS (issues, conversions, redemptions, new options, etc.).
• Precision rule: EPS rounded to whole cent (5.40, not 5.4 or 5.401).

Quick Reference: Formulas & Shortcuts

• Basic EPS: \dfrac{\text{Net earnings avail. to common}}{\text{WACSO}}.
• Incremental EPS (general): \dfrac{\text{Income impact}}{\text{Share impact}}.
• Treasury-stock share impact: \text{Options}\times \dfrac{P{avg}-P{ex}}{P_{avg}}.
• Convertible bond income impact: \text{Interest expense}\times(1-\text{Tax rate}).
• Convertible preferred income impact: cumulative or declared dividend (no tax effect).
• Diluted EPS determination: start basic, add PCS in rank order until incremental EPS > provisional EPS.

Practical & Ethical Implications

• Preparers must avoid manipulation: classifying anti-dilutive instruments as dilutive or vice-versa misleads investors.
• Users should remember diluted EPS is hypothetical and may never be realized; conversion privileges might expire or remain unexercised.
• Analysts compare trends in basic vs. diluted EPS to infer potential future dilution risk and capital structure flexibility.