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Stockholders' Equity | 9 Months Ended
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Sep. 30, 2022
Stockholders' Equity Note [Abstract] |
Stockholders' Equity | (3) Stockholders' Equity Dividends On October 12, 2022, our board of directors declared a quarterly dividend of $0.31 per share of common stock to be paid in cash on November 23, 2022 to shareholders of record at the close of business on October 27, 2022. Since 2011, we have paid quarterly cash dividends, and in 2020, we paid a special cash dividend late in the year. 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:
| 2022 |  | 2021
First quarter | $ | 0.31 |  |  | $ | 0.28 |
Second quarter | $ | 0.31 |  |  | $ | 0.28 |
Third quarter | $ | 0.31 |  |  | $ | 0.28 |
Fourth quarter | $ | 0.31 |  |  | $ | 0.28 |
Total | $ | 1.24 |  |  | $ | 1.12 |
Stock Options The following tables summarize the details of options granted under our stock option plans that were outstanding as of September 30, 2022, 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, 2022
Date of Grant |  |  |  | Options Outstanding |  | Options Exercisable
January 3, 2022 | 713,438 |  |  | $ | 62.00 |  |  | $ | 61.980 |  |  | 689,415 |  |  | 53,355 |
January 4, 2021 | 741,510 |  |  | $ | 48.00 |  |  | $ | 47.650 |  |  | 676,305 |  |  | 26,643 |
January 2, 2020 | 902,263 |  |  | $ | 38.00 |  |  | $ | 37.230 |  |  | 774,842 |  |  | 266,832 |
January 2, 2019 | 1,316,924 |  |  | $ | 26.00 |  |  | $ | 25.705 |  |  | 942,372 |  |  | 411,536 |
January 2, 2018 | 1,087,936 |  |  | $ | 27.50 |  |  | $ | 27.270 |  |  | 693,780 |  |  | 420,712 |
January 3, 2017 | 1,529,578 |  |  | $ | 23.50 |  |  | $ | 23.475 |  |  | 675,420 |  |  | 516,344 |
April 19, 2016 | 1,690,880 |  |  | $ | 23.00 |  |  | $ | 22.870 |  |  | 498,563 |  |  | 375,563 |
April 21, 2015 | 1,786,440 |  |  | $ | 21.00 |  |  | $ | 20.630 |  |  | 363,211 |  |  | 286,051 |
April 22, 2014 | 1,910,000 |  |  | $ | 28.00 |  |  | $ | 25.265 |  |  | 137,868 |  |  | 137,868 |
Total | 11,678,969 |  |  |  |  |  |  | 5,451,776 |  |  | 2,494,904 |
Date of Grant | Risk-free Interest Rate |  | Expected Life of Option in Years |  | Expected Dividend Yield |  | Expected Stock Volatility |  | Estimated Fair Value of Stock Option
January 3, 2022 | 1.3 | % |  | 5.00 |  | 1.7 | % |  | 28.52 | % |  | $ | 13.68 |
January 4, 2021 | 0.4 | % |  | 5.00 |  | 2.0 | % |  | 29.17 | % |  | $ | 9.57 |
January 2, 2020 | 1.7 | % |  | 5.00 |  | 2.4 | % |  | 25.70 | % |  | $ | 6.81 |
January 2, 2019 | 2.5 | % |  | 5.00 |  | 2.9 | % |  | 23.96 | % |  | $ | 4.40 |
January 2, 2018 | 2.2 | % |  | 5.00 |  | 2.3 | % |  | 23.45 | % |  | $ | 5.02 |
January 3, 2017 | 1.9 | % |  | 5.00 |  | 2.6 | % |  | 24.49 | % |  | $ | 4.20 |
April 19, 2016 | 1.3 | % |  | 5.00 |  | 2.6 | % |  | 26.34 | % |  | $ | 4.09 |
April 21, 2015 | 1.3 | % |  | 5.00 |  | 2.7 | % |  | 26.84 | % |  | $ | 3.68 |
April 22, 2014 | 1.8 | % |  | 5.00 |  | 2.0 | % |  | 28.55 | % |  | $ | 4.79 |
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, 2022 and 2021 was $4.4 and $4.3, respectively, and the third quarter of 2022 and 2021 was $1.4 and $1.4, respectively. Unrecognized stock-based compensation expense related to outstanding unvested stock options as of September 30, 2022 was $15.8 and is expected to be recognized over a weighted average period of 4.23 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 Period |  | Three-month Period
Reconciliation | 2022 |  | 2021 |  | 2022 |  | 2021
Basic weighted average shares outstanding | 574,667,188 |  |  | 574,637,254 |  |  | 573,019,381 |  |  | 574,973,196 |
Weighted shares assumed upon exercise of stock options | 1,912,011 |  |  | 2,291,000 |  |  | 1,724,550 |  |  | 2,286,643 |
Diluted weighted average shares outstanding | 576,579,199 |  |  | 576,928,254 |  |  | 574,743,931 |  |  | 577,259,839 |
| Nine-month Period |  | Three-month Period
Summary of Anti-dilutive Options Excluded | 2022 |  | 2021 |  | 2022 |  | 2021
Options to purchase shares of common stock | 1,343,160 |  |  | 680,227 |  |  | 1,340,567 |  |  | 688,410 |
Weighted average exercise prices of options | $ | 55.23 |  |  | 48.00 |  |  | $ | 55.22 |  |  | 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. Translation Adjustment Upon Merger of Foreign Subsidiary Retained earnings for the nine-month period ended September 30, 2022, includes $0.9 of historical cumulative translation upon the merger of a foreign subsidiary recognized in March 2022.

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