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Shareholders' equity | 3 Months Ended
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Mar. 31, 2021
Equity [Abstract] |
Long-term incentive compensation | Shareholders' equity Stock-based compensation During the three months ended March 31, 2021, the Company granted 706 restricted and performance stock units with an aggregate grant-date fair value of $77,279 and a weighted-average expected life of approximately 3.5 years and 132 stock-settled stock appreciation rights with an aggregate grant-date fair value of $4,250 and a weighted-average expected life of approximately 4.5 years. As of March 31, 2021, the Company had $230,270 in total estimated but unrecognized stock-based compensation expense under the Company's equity compensation and employee stock purchase plans. The Company expects to recognize this expense over a weighted average remaining period of 1.5 years.
Share repurchases | Share repurchases The following table summarizes the Company's common stock repurchases during the three months ended March 31, 2021 and 2020:
| Three months ended March 31, 2021 |  | Three months ended March 31, 2020
| Shares repurchased |  | Amount paid |  | Average paid per share |  | Shares repurchased |  | Amount paid |  | Average paid per share
Open market repurchases | 2,949 |  |  | $ | 322,333 |  |  | $ | 109.28 |  |  | 4,052 |  |  | $ | 303,139 |  |  | $ | 74.81 |
The Company repurchased 991 shares of its common stock for $108,892 at an average cost of $109.91 per share subsequent to March 31, 2021 through April 28, 2021. Effective on December 10, 2020, the Company's Board of Directors (Board) terminated all remaining prior share repurchase authorizations available to the Company and approved a new share repurchase authorization of $2,000,000. As of April 28, 2021, the Company had a total of $1,498,730 available under the current authorization for additional share repurchases. Although this share repurchase authorization does not have an expiration date, the Company remains subject to share repurchase limitations including under the terms of its current senior secured credit facilities.

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