Earnings Per Share with Share-Based Payments and Convertible Bonds
On 1 January 20X5, Zeta Co. had 1,000,000 ordinary shares outstanding. On 1 April 20X5, Zeta issued 200,000 new shares for cash. On 1 July 20X5, Zeta granted 100,000 share options to employees, exercisable at CU10 per share. The fair value of each option at grant date is CU3. The options vest over 2 years (service condition). The average market price of Zeta's shares during 20X5 was CU12. Zeta also has CU500,000 of 5% convertible bonds, issued at par on 1 January 20X4. The bonds are convertible into 100,000 ordinary shares. The interest expense recognized for the bonds in 20X5 was CU25,000. The tax rate is 30%. Zeta's profit for the year ended 31 December 20X5 is CU800,000. Zeta uses IFRS and applies IAS 33. The share options are not yet vested at 31 December 20X5, but Zeta expects all options to vest.
1. Calculate the basic earnings per share (EPS) for 20X5. Show the weighted average number of shares.
Read the worked answer
Basic EPS = (Profit or loss attributable to ordinary shareholders) / (Weighted average number of ordinary shares outstanding).
Profit for 20X5 = CU800,000. There are no preference dividends, so profit attributable to ordinary shareholders = CU800,000.
Weighted average number of shares:
- 1,000,000 shares outstanding from 1 Jan to 31 Mar (3 months): 1,000,000 × 3/12 = 250,000
- 1,200,000 shares (after issue of 200,000 on 1 April) outstanding from 1 Apr to 31 Dec (9 months): 1,200,000 × 9/12 = 900,000 Total weighted average shares = 250,000 + 900,000 = 1,150,000.
Basic EPS = 800,000 / 1,150,000 = CU0.6957 per share (rounded to CU0.70).
Note: The share options are potential ordinary shares and are not included in basic EPS. They are considered for diluted EPS.
2. Calculate the diluted earnings per share (EPS) for 20X5. Assume the convertible bonds are dilutive and the share options are dilutive. Show all workings.
Read the worked answer
Diluted EPS = (Profit attributable to ordinary shareholders + after-tax interest on convertible bonds) / (Weighted average shares + shares from assumed conversion of bonds + incremental shares from options).
First, assess dilution:
- Convertible bonds: Interest expense = CU25,000. After-tax = 25,000 × (1 - 0.30) = CU17,500. Shares from conversion = 100,000. Impact on EPS = 17,500 / 100,000 = CU0.175 per share. Since this is less than basic EPS (0.6957), the bonds are dilutive.
- Share options: 100,000 options with exercise price CU10. Average market price CU12. Incremental shares = options - (options × exercise price / average market price) = 100,000 - (100,000 × 10/12) = 100,000 - 83,333 = 16,667 shares. These are included in diluted EPS from the date of grant (1 July 20X5). Since they are granted on 1 July, we need to weight them for the period outstanding: 6 months (1 July to 31 Dec). So weighted incremental shares = 16,667 × 6/12 = 8,333.5 ≈ 8,334.
Now, calculate diluted EPS: Numerator: 800,000 + 17,500 = CU817,500. Denominator: Weighted average shares (1,150,000) + shares from bonds (100,000) + incremental shares from options (8,334) = 1,258,334.
But careful: The bonds were outstanding for the entire year, so the 100,000 shares are included for the full year. The options are included only for the period they were outstanding (6 months). So denominator = 1,150,000 + 100,000 + 8,334 = 1,258,334.
Diluted EPS = 817,500 / 1,258,334 = CU0.6497 per share (rounded to CU0.65).
However, we must check the order of dilution: The options are potentially dilutive and should be included first? Actually, IAS 33 requires that potential ordinary shares are considered in sequence from most dilutive to least dilutive. But since both are dilutive, we include both. The calculation above includes both. But we need to ensure that the inclusion of options does not make the bonds antidilutive. Since diluted EPS with both is 0.65, which is less than basic EPS, both are dilutive. So the answer is CU0.65.
Alternatively, if we consider the options first: diluted EPS with options only = 800,000 / (1,150,000 + 8,334) = 800,000 / 1,158,334 = 0.6907. Then including bonds: (800,000+17,500)/(1,158,334+100,000) = 817,500/1,258,334 = 0.6497. So same result.
Thus, diluted EPS = CU0.65.