Stock Split, Convertible Bonds, Options, and RSUs in EPS
Halcyon Corp. reports net income of $1,800,000 for 20X5. On 1 January, 500,000 common shares were outstanding. Halcyon issued 120,000 shares for cash on 1 April and purchased 60,000 treasury shares on 1 July. On 1 October, it declared a 2-for-1 stock split. Throughout the year, Halcyon had $2,000,000 of 6% convertible bonds outstanding, issued at par; each $1,000 bond is convertible into 50 common shares, adjusted for the split. Halcyon also had 100,000 stock options outstanding with an exercise price of $25. The average market price of the common shares was $30, and the year-end price was $35. On 1 November, Halcyon modified options held by 10,000 employees, reducing the exercise price from $25 to $18; the modification increased the options' fair value by $3 each. Halcyon also has 50,000 restricted stock units that vest on 31 December 20X7 if the employees remain employed; management expects the service condition to be met. The tax rate is 25%.
1. Compute basic EPS for 20X5.
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Weighted-average shares must reflect the 2-for-1 split retroactively for all periods before the split. Pre-split weighted average:
- 1 January–31 March: 500,000 × 3/12 = 125,000
- 1 April–30 June: 620,000 × 3/12 = 155,000
- 1 July–30 September: 560,000 × 3/12 = 140,000
- 1 October–31 December: 1,120,000 × 3/12 = 280,000 Total pre-split equivalent = 700,000. Multiply by 2 for the split = 1,400,000 weighted-average shares.
Basic EPS = $1,800,000 / 1,400,000 = $1.2857, or $1.29 rounded. The treasury shares reduce the count from the July purchase date; they are not retroactively removed before purchase. The April issuance is weighted for nine months. The split does not change total equity, only the number of shares.
2. Compute diluted EPS. Address the convertible bonds, the options, and the RSUs.
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Convertible bonds: after-tax interest = $2,000,000 × 6% × (1 - 25%) = $90,000. Incremental shares = 2,000 bonds × 50 = 100,000. Incremental EPS = $90,000 / 100,000 = $0.90, which is below basic EPS of $1.2857, so the bonds are dilutive.
Options: use the treasury stock method at the $30 average market price. For 90,000 unmodified options at $25: assumed proceeds $2,250,000; shares repurchased $2,250,000/$30 = 75,000; incremental shares = 15,000. For 10,000 modified options at $18: proceeds $180,000; repurchased 6,000; incremental = 4,000. Total option dilution = 19,000 shares.
Diluted numerator = $1,800,000 + $90,000 = $1,890,000. Diluted denominator = 1,400,000 + 100,000 + 19,000 = 1,519,000. Diluted EPS = $1,890,000 / 1,519,000 = $1.244.
RSUs: because only a service condition remains and it is expected to be met, the 50,000 RSUs are potentially dilutive. Include them using the treasury stock method, with assumed proceeds equal to unrecognized compensation cost (and related tax effects), not simply adding 50,000 shares. If unrecognized compensation cost is zero, the incremental shares would be 50,000 and diluted EPS would be $1,890,000 / 1,569,000 = $1.205.
3. How should the 1 November option modification affect compensation expense and diluted EPS?
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The modification reduces the exercise price from $25 to $18 and increases fair value by $3 per option. Measure the incremental compensation cost as the fair value immediately after the modification minus the fair value immediately before, multiplied by the number of modified options. That amount is recognized over the remaining requisite service period, or immediately if the options are already vested. The $3 increase is a compensation cost, not a direct adjustment to the EPS numerator, except for any income tax effect.
For diluted EPS, treat the modified options under their new terms. The 10,000 modified options produce 4,000 incremental shares at the $18 exercise price, compared with 1,667 incremental shares at $25, an additional 2,333 dilutive shares. The unmodified 90,000 options continue at $25 and produce 15,000 incremental shares. Do not retroactively restate prior-period EPS for the modification; apply the new terms from the modification date. If the modification were antidilutive, exclude the incremental shares.