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Shareholders' equity
 6 Months Ended
Jun. 30, 2021
Equity [Abstract]  
Long-term incentive compensation Shareholders' equity
Stock-based compensation
During the six months ended June 30, 2021, the Company granted 714 restricted and performance stock units with an aggregate grant-date fair value of $78,287 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 June 30, 2021, the Company had $204,649 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 1.4 years.
Share repurchases
Share repurchases
The following table summarizes the Company's common stock repurchases during the three and six months ended June 30, 2021 and 2020:
Three months ended June 30,Six months ended June 30,
Open market repurchases:2021202020212020
Shares2,070 — 5,019 4,052 
Amount paid$240,897 $— $563,230 $303,139 
Average paid per share$116.38 $— $112.21 $74.81 
The Company repurchased 890 shares of its common stock for $107,199 at an average cost of $120.50 per share subsequent to June 30, 2021 through August 2, 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 August 2, 2021, the Company had a total of $1,259,527 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.