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Shareholders' equity
 9 Months Ended
Sep. 30, 2021
Equity [Abstract]  
Long-term incentive compensation Shareholders' equity
Stock-based compensation
During the nine months ended September 30, 2021, the Company granted 722 restricted and performance stock units with an aggregate grant-date fair value of $79,214 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 September 30, 2021, the Company had $179,110 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 1.3 years.
Share repurchases
Share repurchases
The following table summarizes the Company's common stock repurchases during the three and nine months ended September 30, 2021 and 2020:
Three months ended September 30,Nine months ended September 30,
2021202020212020
Open market repurchases:
Shares2,731 250 7,750 4,302 
Amount paid$336,217 $21,259 $899,447 $324,398 
Average paid per share$123.14 $85.04 $116.06 $75.40 
Tender offer:
Shares— 7,982 — 7,982 
Amount paid(1)
$— $704,180 $— $704,180 
Average paid per share$— $88.22 $— $88.22 
Total:
Shares2,731 8,232 7,750 12,284 
Amount paid$336,217 $725,439 $899,447 $1,028,578 
Average paid per share$123.14 $88.13 $116.06 $83.73 
(1)Represents the aggregate amount paid for shares repurchased pursuant to the Company's 2020 tender offer for its shares during the three and nine months ended September 30, 2020, including its clearing price of $88.00 per share plus related fees and expenses of $1,792.
The Company repurchased 1,229 shares of its common stock for $139,538 at an average cost of $113.54 per share subsequent to September 30, 2021 through October 27, 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 October 27, 2021, the Company had a total of $890,970 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.