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Stock compensation plans (Tables)
 12 Months Ended
Dec. 31, 2021
Share-based Payment Arrangement, Noncash Expense [Abstract]  
Summary of Share-based Compensation Activity
The following table summarizes the share-based compensation activity:
202120202019
Share-based compensation expense$22,937 $20,739 $26,940 
Total income tax benefit recognized for share-based compensation arrangements10,912 21,958 21,121 
Net excess tax benefit6,355 17,549 15,380 
Weighted-Average Assumptions used to Estimate Fair Value of Options Granted
The fair value of options granted in 2021, 2020 and 2019 was estimated at the date of grant using a Black-Scholes option pricing model. The following weighted-average assumptions were used:
 202120202019
Risk-free interest rate0.67 %1.16 %2.44 %
Expected life of option5.01 years5.00 years4.99 years
Expected dividend yield0.34 %0.39 %0.47 %
Expected volatility30.03 %23.98 %23.92 %
Summary of Stock Option Activity
The following table summarizes the option activity during 2021:
Shares Subject to OptionsWeighted Average Exercise PriceWeighted Average Remaining Contractual Life In Years
Aggregate
Intrinsic
Value
Outstanding, beginning of the year1,157,315 $195.57 
Granted108,686 403.99 
Exercised(125,143)175.90 
Forfeited or expired(32,859)334.14 
Outstanding, end of the year1,107,999 214.13 5.11$136,520 
Exercisable, end of the year908,854 $181.31 4.37$135,036 
Weighted-Average Assumptions used to Estimate Fair Value of Non-Vested Shares Granted The following weighted-average assumptions were used:
202120202019
Risk-free interest rate0.28 %1.07 %2.41 %
Expected dividend yield0.34 %0.38 %0.46 %
Summary of Non-Vested Restricted Stock Unit Activity
The following table summarizes the non-vested restricted stock unit activity during 2021:
Number of
Non-Vested
Shares
Weighted
Average
Grant-Date
Fair Value
Weighted
Average
Remaining
Contractual
Life
Aggregate
Intrinsic
Value
Outstanding, beginning of the year150,812 $293.10 
Granted59,210 398.59 
Vested(50,098)260.32 
Forfeited(24,546)334.38 
Outstanding, end of the year135,378 $343.89 1.2$44,469