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Stock Options and Other Share-Based Compensation (Tables)
12 Months Ended
Dec. 31, 2023
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 2023, 2022 and 2021 were measured on the date of grant using the Black-Scholes option-pricing model with the following weighted-average assumptions:
 
             Year ended December 31  
     
  2023   
       2022        2021   
Expected term in years
1
  
 
6.4    
 
     6.9        6.8   
Volatility
2
  
 
32.5 %
 
     31.3      31.1 
Risk-free interest rate based on zero coupon U.S. treasury note
  
 
3.43 %
 
     1.79      0.71 
Dividend yield
  
 
3.5 %
 
     5.0      6.0 
Weighted-average fair value per option granted
  
$
   45.82   
     $    23.56      $    12.22   
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 2023 is presented below:
 
      Shares (Thousands)     
Weighted-Average
Exercise Price
       Averaged Remaining
Contractual Term (Years)
       Aggregate Intrinsic Value  
Outstanding at January 1, 2023
     25,265        $  114.61            
Granted
     2,122        $  179.08            
Exercised
     (2,538      $  104.30            
Forfeited
     (474      $  246.61            
Outstanding at December 31, 2023
     24,375        $  118.72          5.14          $     934   
Exercisable at December 31, 2023
     18,438        $  113.38          4.11          $     791