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Share-based compensation | 12 Months Ended
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Dec. 31, 2024
Share-Based Payment Arrangement [Abstract] |
Share-based compensation | 17. Share-based compensation Share-based compensation relates primarily to awards granted under the 2014 Performance Share Plan (PSP) and the Company’s Savings-related Share Option Schemes. The expense, net of estimated forfeitures, is reflected in Operating income in the Consolidated Statements of Income. The share-based compensation for these plans for the years ended December 31 was:
in $ millions | 2024 | 2023 | 2022
Performance Share Plan expense | 123 | 120 | 97
Share Option expense | 2 | 3 | 3
Total share-based compensation | 125 | 123 | 100
2014 Performance Share Plan The PSP authorizes the granting of conditional awards or nil-cost options (right to acquire shares during an exercise period without cost to the participant). The number of shares authorized under the PSP during the years ended December 31, 2024, 2023 and 2022 did not exceed 10% of the issued share capital at that time. Under the PSP, the Company has granted performance stock units (PSUs) to its employees. PSUs provide an employee with the right to receive shares of the Company’s stock, subject to fulfillment of certain market, performance and service conditions over a vesting period. The performance conditions are as follows for the 2024, 2023 and 2022 PSUs: 20% of each award made is subject to Total Shareholder Return (TSR) performance measured against a tailored peer group; 20% is subject to a RONA metric; 15% is subject to ESG metrics; with the remaining 45% subject to a cumulative cash flow metric. Performance for the awards is assessed over a three-year period. The details of the awards granted under the PSP for the year ended December 31, 2024 were:
| Number of shares | Weighted average grant date fair value
| Shares in whole numbers | Amounts in $ | Amounts in €
Outstanding at beginning of year | 9,816,619 | 41.56 |  | 37.90 |
Granted | 1,856,679 | 79.52 |  | 73.85 |
Forfeited | (294,689) | 46.12 |  | 41.44 |
Vested | (3,080,029) | 40.93 |  | 34.97 |
Outstanding at end of year | 8,298,580 | 50.11 |  | 46.89 |
During fiscal years 2023 and 2022, the weighted average grant date fair values were $48.55 (€45.57) and $36.29 (€34.50), respectively. The fair value of (i) the portion of awards subject to a cash flow performance metric; (ii) the portion of awards subject to a RONA metric; (iii) the portion of awards subject to ESG metrics; and (iv) the portion of awards with no performance conditions which are subject to a two-year service period; was calculated as the Company’s closing share price at the date the award was granted. The fair value assigned to the portion of awards subject to a TSR performance metric was calculated using the Monte Carlo simulation model, at the grant date, taking account of peer group TSR, volatilities and correlations together with the following assumptions:
| 2024 | 2023 | 2022
Risk-free interest rate (%) | 4.44 |  | 3.16 |  | 0.51 |
Expected volatility (%) | 30.3 |  | 28.9 |  | 36.9 |
The expected volatility was determined using a historical sample of the Company’s daily share prices over a period equal to the expected term. The risk-free interest rate is based on the U.S. Treasury bond yield at the grant date with a maturity period equal to the expected term. During the years ended December 31, 2024, 2023 and 2022, 3,080,029 shares vested having a fair value of $256 million; 2,985,299 shares vested having a fair value of $147 million, and 3,084,926 shares vested having a fair value of $123 million, respectively. At December 31, 2024, unrecognized compensation expense related to the awards was $183 million, which will be recognized over the remaining weighted average vesting period of 1.22 years. 2010 and 2021 Savings-related Share Option Schemes In April 2021, shareholders approved the adoption of the 2021 Savings-related Share Option Schemes (Share Option Schemes), which replaced the schemes approved by shareholders in May 2010. The number of shares authorized under the Share Option Schemes during the years ended December 31, 2024, 2023 and 2022 did not exceed 10% of the issued share capital at that time. Under the Share Option Schemes, participants may save up to €500/Stg£500 per month from their net salaries, for a fixed term of three or five years (the savings period). Within a period of six months after the end of the savings period, they have the option to buy shares of the Company at a discount of up to 15% of the market price on the date of invitation of each savings contract. Under the Share Options Schemes, 236,581, 86,520 and 402,645 shares of the Company were purchased at a weighted average price of $28.68, $26.82 and $25.24 respectively, during the years ended December 31, 2024, 2023, and 2022. At December 31, 2024, the total unrecognized stock-based compensation expense related to the Share Option Schemes was $1 million and is expected to be recognized over a weighted average period of 1.13 years. The fair values assigned to options issued under the Share Option Schemes were calculated in accordance with the trinomial valuation methodology. The assumptions used to determine the fair value of the options issued under the Share Options Schemes with three-year and five-year savings periods at December 31 were:
|  | 2022
|  |  | 3-year | 5-year
Risk-free interest rate (%) |  |  | 2.08 |  | 2.24 |
Expected dividend payments over the expected life (€) |  |  | 4.06 | 7.05
Expected volatility (%) |  |  | 26.4 |  | 24.2 |
Expected life term (years) |  |  | 3 | 5
There were no options granted during the years ended December 31, 2024, and 2023. The expected volatility was determined using a historical sample of 37 month-end Company share prices in respect of the three-year savings-related share options and 61 month-end share prices in respect of the five-year savings-related share options. The expected lives of the options are based on historical data and are therefore not necessarily indicative of exercise patterns that may materialize. Other than the assumptions listed above, no other features of options grants were factored into the determination of fair value. The terms of the options issued under the Share Option Schemes do not contain any market conditions.

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