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Stock Options and Other Share-Based Compensation (Tables)
12 Months Ended
Dec. 31, 2022
Share-Based Payment Arrangement [Abstract]  
Fair market values of stock options and stock appreciation rights granted The fair market values of stock options and stock appreciation rights granted in 2022, 2021 and 2020 were measured on the date of grant using the Black-Scholes option-pricing model with the following weighted-average assumptions:
Year ended December 31
202220212020
Expected term in years1
6.96.86.6
Volatility2
31.3 %31.1 %20.8 %
Risk-free interest rate based on zero coupon U.S. treasury note
1.79 %0.71 %1.50 %
Dividend yield5.0 %6.0 %4.0 %
Weighted-average fair value per option granted$23.56 $12.22 $13.00 
1    Expected term is based on historical exercise and post-vesting cancellation data.
2    Volatility rate is based on historical stock prices over an appropriate period, generally equal to the expected term.
Summary of option activity
A summary of option activity during 2022 is presented below:
Shares (Thousands)Weighted-Average
 Exercise Price
Averaged Remaining Contractual Term (Years)Aggregate Intrinsic Value
Outstanding at January 1, 202277,399 $108.10 
Granted3,870 $132.69 
Exercised(55,275)$105.56 
Forfeited(729)$208.46 
Outstanding at December 31, 202225,265 $114.61 6.62$1,794 
Exercisable at December 31, 202216,421 $117.20 5.18$1,178