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Stockholders' Equity
 6 Months Ended
Jun. 30, 2024
Stockholders' Equity Note [Abstract]  
Stockholders' Equity
(3) Stockholders' Equity
Dividends
On July 11, 2024, our board of directors declared a quarterly dividend of $0.39 per share of common stock to be paid in cash on August 23, 2024 to shareholders of record at the close of business on July 26, 2024.
The following table presents the cash dividends either paid previously or declared by our board of directors for future payment on a per share basis:
20242023
First quarter$0.39 $0.35 
Second quarter0.39 0.35 
Third quarter0.39 0.35 
Fourth quarter0.35 
Fourth quarter (special)0.38 
Total$1.17 $1.78 
Stock Options
The following tables summarize the details of options granted under our stock option plans that were outstanding as of June 30, 2024, and the assumptions used to value those grants. All such grants were effective at the close of business on the date of grant.
 Options
Granted		Option Exercise
Price		Closing Stock Price on Date
of Grant		June 30, 2024
Date of GrantOptions
Outstanding		Options
Exercisable
January 2, 2024814,912 $64.00 $63.550 791,482 50,717 
January 3, 20231,071,943 $48.00 $47.400 928,955 201,513 
January 3, 2022713,438 $62.00 $61.980 575,395 223,661 
January 4, 2021741,510 $48.00 $47.650 538,824 271,200 
January 2, 2020902,263 $38.00 $37.230 597,803 387,378 
January 2, 20191,316,924 $26.00 $25.705 619,843 483,463 
January 2, 20181,087,936 $27.50 $27.270 468,772 393,326 
January 3, 20171,529,578 $23.50 $23.475 375,430 331,582 
April 19, 20161,690,880 $23.00 $22.870 137,696 137,696 
Total9,869,384 5,034,200 2,480,536 
Date of GrantRisk-free
Interest Rate		Expected Life of
Option in Years		Expected
Dividend
Yield		Expected
Stock
Volatility		Estimated Fair
Value of Stock
Option
January 2, 20243.8 %5.002.2 %28.44 %$15.87 
January 3, 20234.0 %5.002.6 %29.58 %$11.62 
January 3, 20221.3 %5.001.7 %28.52 %$13.68 
January 4, 20210.4 %5.002.0 %29.17 %$9.57 
January 2, 20201.7 %5.002.4 %25.70 %$6.81 
January 2, 20192.5 %5.002.9 %23.96 %$4.40 
January 2, 20182.2 %5.002.3 %23.45 %$5.02 
January 3, 20171.9 %5.002.6 %24.49 %$4.20 
April 19, 20161.3 %5.002.6 %26.34 %$4.09 
All of the options in the tables above vest and become exercisable over a period of up to eight years. Generally, each option will terminate approximately 10 years after the grant date.
The fair value of each share-based option is estimated on the date of grant using a Black-Scholes valuation method that uses the assumptions listed above. The risk-free interest rate is based on the U.S. Treasury rate over the expected life of the option at the time of grant. The expected life is the average length of time over which we expect the employee groups will exercise their options, net of forfeitures, which is based on historical experience with similar grants. The dividend yield is estimated over the expected life of the option based on our current dividend payout, historical dividends paid, and expected future cash dividends. Expected stock volatilities are based on the movement of our stock price over the most recent historical period equivalent to the expected life of the option.
Compensation expense equal to the grant date fair value is recognized for all of these awards over the vesting period. The stock-based compensation expense for the six-month periods ended June 30, 2024 and 2023 was $4.0 and $3.8, respectively, while the second quarter of 2024 and 2023 was $2.0 and $1.9, respectively. Unrecognized stock-based compensation expense related to outstanding unvested stock options as of June 30, 2024 was $22.9 and is expected to be recognized over a weighted average period of 4.43 years. Any future changes in estimated forfeitures will impact this amount.
Income Per Share
The following tables present a reconciliation of the denominators used in the computation of basic and diluted income per share and a summary of the options to purchase shares of common stock which were excluded from the diluted income per share calculation because they were anti-dilutive:
 Six-month PeriodThree-month Period
Reconciliation2024202320242023
Basic weighted average shares outstanding572,457,897 571,033,444 572,576,300 571,138,039 
Weighted shares assumed upon exercise of stock options1,645,549 1,724,032 1,537,308 1,752,121 
Diluted weighted average shares outstanding574,103,446 572,757,476 574,113,608 572,890,160 
 Six-month PeriodThree-month Period
Summary of Anti-dilutive Options Excluded2024202320242023
Options to purchase shares of common stock1,262,947 2,244,555 1,261,870 1,866,320 
Weighted average exercise prices of options$63.17 52.17 $63.17 52.96 
Any dilutive impact summarized above related to periods when the average market price of our stock exceeded the exercise price of the potentially dilutive stock options then outstanding.