On January 16, 2020, our board of directors declared a quarterly dividend of $0.25 per share of common stock to be paid in cash on February 28, 2020 to shareholders of record at the close of business on January 31, 2020. We paid aggregate annual dividends per share of $0.87, $0.77, and $0.64 in 2019, 2018, and 2017, respectively.

Effective January 2, 2020, the compensation committee of our board of directors granted to our employees options to purchase a total of 877,299 shares of our common stock at an exercise strike price of $38.00 per share. The closing stock price on the effective date of the grant was $37.23 per share. On the same date, certain of our non-employee directors elected to forgo all or a portion of the 2020 annual cash retainer in exchange for options to acquire a total of 24,964 shares of our common stock at an exercise price of $38.00 per share.

The following tables summarize the details of options granted under our stock option plans that were still outstanding as of December 31, 2019, 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 (Strike) Price		Closing Stock Price on Date of Grant		December 31, 2019
Date of Grant	Options Granted	Option Exercise (Strike) Price		Closing Stock Price on Date of Grant		Options Outstanding	Options Exercisable
January 2, 2019	1,316,924	$	26.00	$	25.705	1,279,842	29,010
January 2, 2018	1,087,936	$	27.50	$	27.270	1,019,440	42,370
January 3, 2017	1,529,578	$	23.50	$	23.475	1,197,606	332,132
April 19, 2016	1,690,880	$	23.00	$	22.870	1,220,524	447,166
April 21, 2015	1,786,440	$	21.00	$	20.630	833,593	444,589
April 22, 2014	1,910,000	$	28.00	$	25.265	599,128	357,268
April 16, 2013	410,000	$	27.00	$	24.625	97,472	58,722
April 17, 2012	2,470,000	$	27.00	$	24.505	547,112	440,310
April 19, 2011	820,000	$	17.50	$	15.890	12,500	12,500
Total	13,021,758					6,807,217	2,164,067



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 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
April 16, 2013	0.7	%	5.00	1.6	%	37.42	%	$	6.33
April 17, 2012	0.9	%	5.00	1.4	%	39.25	%	$	6.85
April 19, 2011	2.1	%	5.00	1.6	%	39.33	%	$	5.60

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 nine 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



	Options Outstanding		Exercise Price⁽¹⁾		Remaining Life⁽²⁾
Outstanding as of January 1, 2019	7,999,264		$	24.765	5.61
Granted	1,316,924		$	26.000	9.00
Exercised	(2,325,073	)	$	25.150
Cancelled/forfeited	(183,898	)	$	24.630
Outstanding as of December 31, 2019	6,807,217		$	24.890	6.09
Exercisable as of December 31, 2019	2,164,067		$	24.510	4.30



	Options Outstanding		Exercise Price⁽¹⁾		Remaining Life⁽²⁾
Outstanding as of January 1, 2018	7,897,816		$	24.140	5.89
Granted	1,087,936		$	27.500	9.00
Exercised	(620,766	)	$	21.655
Cancelled/forfeited	(365,722	)	$	24.430
Outstanding as of December 31, 2018	7,999,264		$	24.765	5.61
Exercisable as of December 31, 2018	3,108,756		$	25.530	3.69

The total intrinsic value of stock options exercised during the years ended December 31, 2019, 2018, and 2017 was $20.2, $4.2, and $6.9, respectively. The intrinsic value represents the difference between the exercise price and fair value of the underlying shares at the date of exercise.

At December 31, 2019, there was $13.1 of total unrecognized stock-based compensation expense related to outstanding unvested stock options granted under the employee stock option plan. This expense is expected to be recognized over a weighted average period of 3.82 years. Any future change in estimated forfeitures will impact this amount. The total grant date fair value of stock options vested under our employee stock option plan during 2019, 2018, and 2017 was $5.9, $5.3, and $4.2, respectively.



	2019	2018		2017
Balance at beginning of year	571,803,838	575,183,072		578,323,848
Stock options exercised	2,325,073	620,766		659,224
Purchases of common stock	—	(4,000,000	)	(3,800,000	)
Balance at end of year	574,128,911	571,803,838		575,183,072

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 calculation because they were anti-dilutive:



Reconciliation	2019	2018	2017
Basic weighted average shares outstanding	573,202,152	573,933,834	576,416,870
Weighted shares assumed upon exercise of stock options	1,239,476	391,694	268,596
Diluted weighted average shares outstanding	574,441,628	574,325,528	576,685,466



Summary of Anti-dilutive Options Excluded	2019		2018	2017
Options to purchase shares of common stock	—		3,159,514	7,048,802
Weighted average exercise prices of options	$	—	27.510	24.925

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.