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Stockholders' Equity
9 Months Ended
Sep. 30, 2021
Stockholders' Equity Note [Abstract]  
Stockholders' Equity
(3) Stockholders' Equity
Dividends
On October 11, 2021, our board of directors declared a quarterly dividend of $0.28 per share of common stock to be paid in cash on November 23, 2021 to shareholders of record at the close of business on October 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$0.28 $0.25 
Fourth quarter$0.28 $0.25 
Fourth quarter (special)$0.40 
Total$1.12 $1.40 
Stock Options
The following tables summarize the details of options granted under our stock option plans that were outstanding as of September 30, 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
September 30, 2021
Date of GrantOptions
Outstanding
Options
Exercisable
January 4, 2021741,510 $48.00 $47.650 715,053 26,643 
January 2, 2020902,263 $38.00 $37.230 848,066 24,964 
January 2, 20191,316,924 $26.00 $25.705 1,035,830 285,098 
January 2, 20181,087,936 $27.50 $27.270 763,921 337,067 
January 3, 20171,529,578 $23.50 $23.475 750,260 380,596 
April 19, 20161,690,880 $23.00 $22.870 693,029 498,611 
April 21, 20151,786,440 $21.00 $20.630 441,398 278,570 
April 22, 20141,910,000 $28.00 $25.265 224,937 149,953 
April 16, 2013410,000 $27.00 $24.625 13,696 13,696 
Total11,375,531 5,486,190 1,995,198 

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 
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 nine-month periods ended September 30, 2021 and 2020 was $4.3 and $4.3, respectively. Unrecognized stock-based compensation expense related to outstanding unvested stock options as of September 30, 2021 was $14.0 and is expected to be recognized over a weighted average period of 4.11 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:
 Nine-month PeriodThree-month Period
Reconciliation2021202020212020
Basic weighted average shares outstanding574,637,254 573,673,031 574,973,196 573,913,929 
Weighted shares assumed upon exercise of stock options2,291,000 1,797,201 2,286,643 2,203,402 
Diluted weighted average shares outstanding576,928,254 575,470,232 577,259,839 576,117,331 
 Nine-month PeriodThree-month Period
Summary of Anti-dilutive Options Excluded2021202020212020
Options to purchase shares of common stock680,227 852,728 688,410 — 
Weighted average exercise prices of options$48.00 38.00 $48.00 — 
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.