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Stockholders' Equity
 3 Months Ended
Mar. 31, 2021
Stockholders' Equity Note [Abstract]  
Stockholders' Equity
(3) Stockholders' Equity
Dividends
On April 12, 2021, our board of directors declared a quarterly dividend of $0.28 per share of common stock to be paid in cash on May 25, 2021 to shareholders of record at the close of business on April 26, 2021. Since 2011, we have paid quarterly cash dividends, and in 2020, we paid a special cash dividend late in the year. Our board of directors currently intends to continue paying quarterly cash dividends, provided that any future determination as to payment of dividends will depend on the financial condition and results of operations of the company and such other factors as are deemed relevant by the board of directors.
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:
20212020
First quarter$0.28 $0.25 
Second quarter$0.28 $0.25 
Third quarter$0.25 
Fourth quarter$0.25 
Fourth quarter (special)$0.40 
Total$0.56 $1.40 
Stock Options
The following tables summarize the details of options granted under our stock option plans that were outstanding as of March 31, 2021, and the assumptions used to value these grants. All such grants were effective at the close of business on the date of grant.
 Options
Granted		Option Exercise
(Strike) Price		Closing Stock Price on Date
of Grant		March 31, 2021
Date of GrantOptions
Outstanding		Options
Exercisable
January 4, 2021741,510 $48.00 $47.650 734,323 26,643 
January 2, 2020902,263 $38.00 $37.230 865,298 24,964 
January 2, 20191,316,924 $26.00 $25.705 1,118,034 351,964 
January 2, 20181,087,936 $27.50 $27.270 837,605 395,067 
January 3, 20171,529,578 $23.50 $23.475 904,791 525,801 
April 19, 20161,690,880 $23.00 $22.870 888,322 562,764 
April 21, 20151,786,440 $21.00 $20.630 586,137 340,577 
April 22, 20141,910,000 $28.00 $25.265 323,400 170,900 
April 16, 2013410,000 $27.00 $24.625 28,964 10,226 
April 17, 20122,470,000 $27.00 $24.505 20,750 20,750 
Total13,845,531 6,307,624 2,429,656 

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 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 
April 21, 20151.3 %5.002.7 %26.84 %$3.68 
April 22, 20141.8 %5.002.0 %28.55 %$4.79 
April 16, 20130.7 %5.001.6 %37.42 %$6.33 
April 17, 20120.9 %5.001.4 %39.25 %$6.85 
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 ten 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, 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 three-month periods ended March 31, 2021 and 2020 was $1.5 and $1.6, respectively. Unrecognized stock-based compensation expense related to outstanding unvested stock options as of March 31, 2021 was $16.6 and is expected to be recognized over a weighted average period of 4.41 years. Any future changes in estimated forfeitures will impact this amount.
Earnings Per Share
The following tables present a reconciliation of the denominators used in the computation of basic and diluted earnings per share and a summary of the options to purchase shares of common stock which were excluded from the diluted earnings per share calculation because they were anti-dilutive:
 Three-month Period
Reconciliation20212020
Basic weighted average shares outstanding574,336,112 573,904,156 
Weighted shares assumed upon exercise of stock options2,210,857 1,414,674 
Diluted weighted average shares outstanding576,546,969 575,318,830 
 Three-month Period
Summary of Anti-dilutive Options Excluded20212020
Options to purchase shares of common stock711,977 891,290 
Weighted average exercise prices of options$48.00 38.00 
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.