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Share Capital | 12 Months Ended
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Dec. 31, 2023 | Dec. 31, 2022
Equity [Abstract] |  |
Share Capital | 15. Share Capital The authorized and outstanding share capital of the Company is below. Class A Common Stock There are 1.0 billion shares of Class A Common Stock authorized, of which 118.5 million shares were issued and outstanding as of December 31, 2023. Each share of Class A Common Stock carries one vote and represents an economic interest in the Company. Class C Common Stock There are 250.0 million shares of Class C Common Stock authorized, of which 151.6 million shares were issued and outstanding as of December 31, 2023. Each share of Class C Common Stock carries one vote and does not represent an economic interest in the Company. Each share of Class C Common Stock is paired with a corresponding common unit of OpCo (each such paired share of Class C Common Stock and common unit of OpCo, a “Paired Unit”). Each holder of Paired Units may, at its option, exchange such Paired Units for shares of Class A Common Stock on a one-to-one basis (i.e., one Paired Unit for one share of Class A Common Stock). In the year ended December 31, 2023, holders of the Paired Units exchanged 9.3 million Paired Units for the same number of shares of Class A Common Stock. Class A Common Stock Repurchases The Company may purchase shares of Class A Common Stock under its stock repurchase program (the “Repurchase Program”) as well as repurchases outside of the Repurchase Program. On March 1, 2023, the Company’s board of directors (the “Board”) authorized an extension and a $125.0 million increase in the size of the Repurchase Program to an aggregate of $250.0 million, with any previous purchases under the Repurchase Program continuing to count against that limit. The Repurchase Program, as amended, will expire on March 1, 2026. Under the Repurchase Program, share repurchases may be made at our discretion from time to time in open market transactions at prevailing market prices, including through trading plans that may be adopted in accordance with Rule 10b5-1 of the Securities Exchange Act of 1934, as amended, in privately negotiated transactions, or through other means. The timing and number of shares repurchased under the Repurchase Program will depend on a variety of factors, including the performance of our stock price, general market and economic conditions, regulatory requirements, the availability of funds, and other considerations we deem relevant. The Repurchase Program may be suspended, modified or discontinued at any time without prior notice. Our Board will review the Repurchase Program periodically and may authorize adjustments of its terms. During the year ended December 31, 2023, 9.9 million shares of Class A Common Stock were repurchased pursuant to the Repurchase Program at an aggregate value, excluding fees, of $59.5 million. These shares were repurchased at an average price of $6.00 per share. The remaining value of shares of Class A Common Stock permitted to be repurchased under the Repurchase Program was $138.6 million as of December 31, 2023. In addition to the repurchases under the Repurchase Program, on May 23, 2023, the Company repurchased 23.3 million shares of Class A Common Stock from certain affiliates of AlpInvest Partners B.V. at a price of $6.43 per share, for an aggregate total repurchase price of $150.0 million. Employee Stock Purchase Plan The Company’s 2023 Employee Stock Purchase Plan (the “ESPP”) was approved by stockholders and adopted by the Board in 2023. A total of 3.0 million shares of Class A Common Stock was reserved for sale under the ESPP to eligible employees as defined in the plan. Under the ESPP, eligible employees can elect to withhold up to 15% of their earnings, subject to certain maximums, to purchase shares of Class A Common Stock on certain plan-defined dates. The purchase price for each offering period is 92.5% of the fair market value of shares of Class A Common Stock at the end of the offering period. The plan is considered compensatory resulting in the fair value of the discount being expensed over the service period. The total number of shares authorized that remained available to be issued was 2.9 million as of December 31, 2023. During the year ended December 31, 2023, there were no material expenses incurred by the Company related to the ESPP and contributions to the ESPP were nominal. Stock-based Awards The Company’s stock-based awards outstanding consist of restricted stock units, restricted stock and stock appreciation rights (“SAR awards”). The total number of shares authorized that remained available to be issued for future awards was 6.5 million as of December 31, 2023 and 12.9 million as of December 31, 2022. For the years ended December 31, 2023, 2022, and 2021, the Company recognized total stock-based compensation expense related to all stock compensation awards of $51.2 million, $36.7 million, and $75.0 million, respectively. The related income tax benefit for the years ended December 31, 2023, 2022, and 2021 was $13.0 million, $4.1 million, and $5.3 million, respectively. The following tables summarize stock-based activity of awards authorized under our employee stock incentive plans and awards (such as inducement awards) and other share-based commitments that have met the requirements to be issued separate from shareholder-approved stock incentive plans. The following table summarizes information about time-based and performance-based restricted stock and restricted stock unit awards:
| Time-Based Awards |  | Performance-Based Awards |  |
| Shares |  | Weighted Average Grant Date Fair Value |  | Shares |  | Weighted Average Grant Date Fair Value |  |  |  |
Balance at December 31, 2022 | 6,269 |  |  | $ | 7.07 |  |  | 2,386 |  |  | $ | 7.74 |  |  |  |  |
Granted | 6,595 |  |  | 7.19 |  |  | 1,328 |  |  | 7.24 |  |  |  |  |
Vested | (5,479) |  |  | 7.00 |  |  | — |  |  | — |  |  |  |  |
Forfeited | (213) |  |  | 7.25 |  |  | (3) |  |  | 5.01 |  |  |  |  |
Balance at December 31, 2023 | 7,172 |  |  | $ | 7.23 |  |  | 3,711 |  |  | $ | 7.56 |  |  |  |  |
The weighted average grant date fair value of time-based awards granted in 2022 and 2021 was $7.38 and $5.51, respectively. The weighted average grant date fair value of performance-based awards granted in 2022 and 2021 was $8.68 and $7.03, respectively. The vesting of the performance-based awards is contingent primarily upon the Company meeting certain cumulative revenue and earnings targets, primarily three years, and continued employment through the vesting date. The term of the time-based awards is generally three years with vesting generally one to three years. The vesting period of the time-based and performance-based awards is generally commensurate with the requisite service period. The total fair value of restricted stock and restricted stock unit awards, which vested during the years ended December 31, 2023, 2022, and 2021, was $38.4 million, $77.3 million, and $1.5 million respectively. At December 31, 2023, the weighted average remaining contractual life for time-based and performance-based awards was 0.67 and 1.33 years, respectively. At December 31, 2023, the unrecognized compensation expense for time-based awards was $21.3 million and will be recognized over a weighted average period of 0.67 years. At December 31, 2023, the unrecognized compensation expense for performance-based awards was $12.3 million and will be recognized over a weighted average period of 1.33 years. The following table summarizes information about SAR awards:
| SAR Awards
| Shares |  | Weighted Average Grant Date Fair Value |  | Weighted Average Exercise Price
Balance at December 31, 2022 | 4,845 |  |  | $ | 2.78 |  |  | $ | 4.57 |
Granted | 225 |  |  | 2.23 |  |  | 6.79 |
Forfeited | — |  |  | — |  |  | — |
Exercised | (1,948) |  |  | 3.02 |  |  | 2.93 |
Balance at December 31, 2023 | 3,122 |  |  | $ | 2.59 |  |  | $ | 5.74 |
The weighted average grant date fair value of SAR awards granted in 2021 was $2.39. There were no SAR awards granted in 2022. We use the Black-Scholes option-pricing model to estimate the fair value of SAR awards. The grant date fair value of the SAR awards granted in 2021 ranged from $2.20 to $3.66 per share. The assumptions used to value the SAR awards granted in 2021 were as follows: expected life ranging from 2.8 to 4 years, risk free interest rate of approximately 1.0%, expected volatility ranging from 35.5% to 38.1%, and dividend yield of 0%. The grant date fair value of the SAR awards granted in 2023 ranged from $2.10 to $2.35 per share. The assumptions used to value the SARS granted in 2023 were as follows: expected life ranging from 3 to 4 years, risk free interest rate of approximately 4.6%, expected volatility ranging from 34.6% to 36.7%, and dividend yield of 0%. These SAR awards vest in 1 to 3 years. The vesting period of these awards is generally commensurate with the requisite service period. The term of these awards is 5 years. Certain of the Company’s SAR awards are settled in cash. These awards are liability classified and remeasured at each reporting period. As of December 31, 2023, the assumptions for the Black-Scholes model for these awards were as follows: expected life ranging from 0 to 3 years, risk free interest rate of approximately 5%, expected volatility ranging from 26.7% to 42.1%, and dividend yield of 0.0%. The remaining term of these awards as of December 31, 2023, ranges from approximately 0.2 years to 4 years. During the year ended December 31, 2023, certain SAR awards were modified from equity to cash settled. The SAR awards were fair valued on the date of modification, reclassed from equity to liability and resulted in incremental stock-based compensation expense of $4.4 million. For the year ended December 31, 2023, 0.5 million SAR awards vested. As of December 31, 2023, 2.4 million SAR awards vested and were exercisable. The total intrinsic value of SAR awards exercised during the years ended December 31, 2023 and 2022 was $8.1 million and $0.1 million, respectively. There were no SAR awards exercised during the year ended December 31, 2021. As of December 31, 2023, the aggregate intrinsic value of the SAR awards outstanding was $5.3 million and the weighted average remaining contractual life for these awards was 1.02 years. As of December 31, 2023, the aggregate intrinsic value of the SAR awards exercisable was $5.3 million and the weighted average remaining contractual life for these awards was 0 years. The weighted average exercise price of SAR awards exercisable as of December 31, 2023 was $5.12. At December 31, 2023, the unrecognized compensation expense for these awards was $0.4 million, to be recognized over a weighted average period of 1.02 years. Subsidiary Awards Certain of the Company’s subsidiaries grant awards to their employees providing them with an equity interest in the respective subsidiary (the “profits interests awards”). The profits interests awards generally provide the employee the right, but not the obligation, to sell its profits interest in the subsidiary to the Company based on a performance-based formula and, in certain cases, receive a profit share distribution. The profits interests awards are settled in cash and the corresponding liability was $20.3 million and $21.0 million at December 31, 2023 and 2022, respectively and is included as a component of Accruals and other liabilities and Other liabilities on the Consolidated Balance Sheets. The change in the profits interest liabilities for the years ended December 31, 2023 and 2022 was an increase of $3.9 million and a decrease of $4.2 million, respectively and was recorded as stock-based compensation in Cost of Services within the Statements of Operations. | 12.3 million

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