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Stock compensation plans (Tables)
12 Months Ended
Dec. 31, 2022
Share-Based Payment Arrangement, Noncash Expense [Abstract]  
Summary of Share-based Compensation Activity The following table summarizes the share-based compensation activity:
202220212020
Share-based compensation expense$27,224 $22,937 $20,739 
Total income tax benefit recognized for share-based compensation arrangements6,824 10,912 21,958 
Net excess tax benefit1,292 6,355 17,549 
Weighted-Average Assumptions used to Estimate Fair Value of Options Granted
The fair value of options granted in 2022, 2021 and 2020 was estimated at the date of grant using a Black-Scholes option pricing model. The following weighted-average assumptions were used:
 202220212020
Risk-free interest rate1.56 %0.67 %1.16 %
Expected life of option5.03 years5.01 years5.00 years
Expected dividend yield0.41 %0.34 %0.39 %
Expected volatility30.09 %30.03 %23.98 %
Summary of Stock Option Activity
The following table summarizes the option activity during 2022:
Shares Subject to OptionsWeighted Average Exercise PriceWeighted Average Remaining Contractual Life In Years
Aggregate
Intrinsic
Value
Outstanding, beginning of the year1,107,999 $214.13 
Granted156,918 330.03 
Exercised(27,518)95.07 
Forfeited or expired(8,551)359.54 
Outstanding, end of the year1,228,848 230.58 4.77$66,774 
Exercisable, end of the year990,842 $201.19 3.84$66,746 
Weighted-Average Assumptions used to Estimate Fair Value of Non-Vested Shares Granted The following weighted-average assumptions were used:
202220212020
Risk-free interest rate1.57 %0.28 %1.07 %
Expected dividend yield0.42 %0.34 %0.38 %
Summary of Non-Vested Restricted Stock Unit Activity
The following table summarizes the non-vested restricted stock unit activity during 2022:
Number of
Non-Vested
Shares
Weighted
Average
Grant-Date
Fair Value
Weighted
Average
Remaining
Contractual
Life
Aggregate
Intrinsic
Value
Outstanding, beginning of the year135,378 $343.89 
Granted85,780 323.35 
Vested(51,831)290.75 
Forfeited(21,359)352.06 
Outstanding, end of the year147,968 $349.42 1.5$36,970