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Share Based Compensation (Tables)
12 Months Ended
Dec. 31, 2023
Share-Based Payment Arrangement [Abstract]  
Weighted Average Fair Value and Assumptions
The following table shows the weighted-average fair value for our stock options and the assumptions we used to estimate fair value:
202320222021
Weighted-average estimated fair value$41.06 $34.77 $29.56 
Quarterly dividend rate$0.55 $0.52 $0.50 
Expected term of stock options, in years4.24.34.3
Risk-free interest rate3.7 %1.6 %0.3 %
Dividend yield1.9 %2.0 %2.2 %
Expected stock price volatility35.4 %35.0 %34.4 %
Present value of dividends
$8.57 $8.58 $8.61 
Data With Respect to Stock Options SARs Activity
The following table shows information about outstanding stock options for the year ended December 31, 2023:

Number of Stock Options
(in thousands)
Weighted-Average Exercise Price
Outstanding at beginning of the year1,001$82.04 
Granted190113.28 
Exercised(193)72.25 
Forfeited/Cancelled(1)104.61 
Outstanding at end of the year99789.85 
Vested and exercisable at end of the year63380.12 
Schedule of Share-Based Compensation, Aggregate Intrinsic Value and Weighted Average Remaining Contractual Term
The following table shows the aggregate intrinsic value of stock options and stock appreciation rights exercised in 2023, 2022, and 2021, and the weighted-average remaining contractual term and aggregate intrinsic value of stock options and stock appreciation rights outstanding and vested as of December 31, 2023:
Stock Options and Stock Appreciation RightsWeighted-Average Remaining Contractual Term
(in years)
Aggregate Intrinsic Value
(in millions)
Exercised in 2021$22.5
Exercised in 202213.4 
Exercised in 20239.0 
Outstanding at December 31, 2023 (a)3.830.3
Vested and exercisable at December 31, 20232.825.4 
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(a) As of December 31, 2023, 997,281 stock options and 0 stock appreciation rights were outstanding.
Schedule of Share-Based Compensation, Restricted Stock Units and Performance Shares Award Activity
The following table shows information about restricted stock units and performance shares for the year ended December 31, 2023:

Number of Share Units Outstanding (in thousands)Weighted-Average Grant-Date Fair Value
Restricted Stock Units:
Nonvested at beginning of the year108 $90.47 
Granted33 113.39 
Vested(41)77.87 
Forfeited— 108.10 
Nonvested at end of the year100 103.19 
Performance Shares:
Nonvested at beginning of the year73 $94.79 
Granted37 113.28 
Net increase due to estimated performance30 100.33 
Vested(43)87.57 
Nonvested at end of the year97 106.89