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Share-based awards | 9 Months Ended
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Sep. 30, 2021
Share-based Payment Arrangement [Abstract] |
Share-based awards | Share-based awards Share Options The following table summarizes option activity for the nine months ended September 30, 2021:
| Options Outstanding Number of Shares |  | Weighted Average Exercise Price |  |  |  | Weighted Average Remaining Contractual Life
Outstanding at December 31, 2020 | 553,746 |  |  | $ | 108.53 |  |  |  |  | 4.86
Assumed through business combinations (a) | 2,177,130 |  |  | $ | 108.78 |  |  |  |  |
Granted | 100,299 |  |  | $ | 177.76 |  |  |  |  |
Exercised | (913,743) |  |  | $ | 113.87 |  |  |  |  |
Canceled/expired | (32,784) |  |  | $ | 132.25 |  |  |  |  |
Outstanding at September 30, 2021 | 1,884,648 |  |  | $ | 109.50 |  |  |  |  | 5.66
Exercisable at September 30, 2021 | 1,095,429 |  |  | $ | 90.80 |  |  |  |  | 4.72
(a) Represents stock options issued as replacement awards in connection with the Merger. The Company issues ordinary shares for all options exercised. The total amount of fully vested share options which remained outstanding at September 30, 2021 was 1,095,429. Fully vested share options at September 30, 2021 have an average remaining contractual term of 4.72 years, an average exercise price of $90.80. Fair value of Stock Options Assumptions The weighted average fair value of options granted during the nine months ended September 30, 2021 and September 30, 2020 was calculated using the Black-Scholes option pricing model. The weighted average grant date fair values and assumptions used were as follows:
| Nine Months Ended
| September 30, 2021 |  | September 30, 2020
Weighted average grant date fair value | $ | 49.15 |  |  | $ | 42.43 |
Assumptions: |  |  |
Expected volatility | 30 | % |  | 30 | %
Dividend yield | — | % |  | — | %
Risk-free interest rate | 0.78 | % |  | 0.57 | %
Expected life | 5 years |  | 5 years
The weighted average fair value of options assumed on the date of the Merger was calculated using the Black-Scholes option pricing model. The weighted average fair values on the date of the Merger and assumptions used were as follows:
| July 1, 2021
Weighted average grant date fair value | $ | 107.21 |
Assumptions: |
Expected volatility | 30 | %
Dividend yield | — | %
Risk-free interest rate | 0.56 | %
Expected life | 3.5 years
Expected volatility is based on the historical volatility of our common stock over a period equal to the expected term of the options; the expected life represents the weighted average period of time that options granted are expected to be outstanding given consideration to vesting schedules and our historical experience of past vesting and termination patterns. The risk-free rate is based on the U.S. government zero-coupon bonds yield curve in effect at time of the grant for periods corresponding with the expected life of the option. Restricted Share Units and Performance Share Units On April 30 2019, the Company approved the 2019 Consultants and Directors Restricted Share Unit Plan (the “2019 Consultants RSU Plan”), which was effective as of May 16, 2019, pursuant to which the Compensation and Organization Committee of the Company’s Board of Directors may select any consultant, adviser or non-executive Director retained by the Company, or a Subsidiary to receive an award under the plan. 250,000 ordinary shares have been reserved for issuance under the 2019 Consultants RSU Plan. The awards are at par value and vest over a service period. Awards granted to non-executive directors during 2019, 2020 and 2021 vest over twelve months. The Company has awarded RSUs and PSUs to certain key individuals of the Group. The following table summarizes RSU and PSU activity for the nine months ended September 30, 2021:
| PSU Outstanding Number of Shares |  | PSU Weighted Average Grant Date Fair Value |  |  | RSU Outstanding Number of Shares |  | RSU Weighted Average Grant Date Fair Value
Outstanding at December 31, 2020 | 159,641 |  |  | $ | 137.64 |  |  |  | 341,424 |  |  | $ | 145.77 |
Assumed through business combinations (a) | — |  |  | $ | — |  |  |  | 589,517 |  |  | $ | 206.71 |
Granted | 55,444 |  |  | $ | 177.77 |  |  |  | 159,796 |  |  | $ | 210.64 |
Shares vested | (44,132) |  |  | $ | 115.61 |  |  |  | (441,328) |  |  | $ | 186.03 |
Forfeited | (4,777) |  |  | $ | 115.61 |  |  |  | (48,441) |  |  | $ | 180.74 |
Outstanding at September 30, 2021 | 166,176 |  |  | $ | 159.11 |  |  |  | 600,968 |  |  | $ | 190.56 |
(a) Represents RSUs issued as replacement awards in connection with the Merger. The fair value of PSUs vested for the nine months ended September 30, 2021 totaled $5.1 million (full year 2020: $5.3 million). The fair value of RSUs vested for the nine months ended September 30, 2021 totaled $82.1 million (full year 2020: $14.3 million). The PSUs vest based on service and specified EPS targets over the periods 2019 – 2021, 2020 – 2022 and 2021 - 2023. Depending on the amount of EPS from 2019 to 2023, up to an additional 83,088 PSUs may also be granted. Non-cash stock compensation expense Non-cash stock compensation expense for the three and nine months ended September 30, 2021 and September 30, 2020 has been allocated as follows:
| Three Months Ended |  | Nine Months Ended
| September 30, 2021 |  | September 30, 2020 |  | September 30, 2021 |  | September 30, 2020
| (in thousands) |  | (in thousands)
Direct costs | $ | 8,787 |  |  | $ | 2,284 |  |  | $ | 13,822 |  |  | $ | 6,472 |
Selling, general and administrative | 17,568 |  |  | 4,687 |  |  | 27,133 |  |  | 13,685 |
Transaction and integration-related expenses | 73,836 |  |  | — |  |  | 73,836 |  |  | — |
| $ | 100,191 |  |  | $ | 6,971 |  |  | $ | 114,791 |  |  | $ | 20,157 |

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- Definition The entire disclosure for share-based payment arrangement. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -URI http://asc.fasb.org/topic&trid=2228938 + Details
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