On January 19, 2021, our board of directors declared a quarterly dividend of $0.28 per share of common stock to be paid in cash on March 3, 2021 to shareholders of record at the close of business on February 3, 2021. We paid aggregate annual cash dividends per share of $1.40, $0.87, and $0.77 in 2020, 2019, and 2018, respectively.

Effective January 4, 2021, the compensation committee of our board of directors granted to our employees options to purchase a total of 714,867 shares of our common stock at an exercise strike price of $48.00 per share. The closing stock price on the effective date of the grant was $47.65 per share. On the same date, certain of our non-employee directors elected to forgo all or a portion of the 2021 annual cash retainer in exchange for options to acquire a total of 26,643 shares of our common stock at an exercise price of $48.00 per share.

The following tables summarize the details of options granted under our stock option plans that were still outstanding as of December 31, 2020, 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, 2020
Date of Grant				Options Outstanding	Options Exercisable
January 2, 2020	902,263	$38.00	$37.230	874,112	24,964
January 2, 2019	1,316,924	$26.00	$25.705	1,221,248	25,010
January 2, 2018	1,087,936	$27.50	$27.270	886,679	270,457
January 3, 2017	1,529,578	$23.50	$23.475	988,415	378,747
April 19, 2016	1,690,880	$23.00	$22.870	930,043	589,137
April 21, 2015	1,786,440	$21.00	$20.630	596,622	350,526
April 22, 2014	1,910,000	$28.00	$25.265	337,550	185,050
April 16, 2013	410,000	$27.00	$24.625	32,340	13,602
April 17, 2012	2,470,000	$27.00	$24.505	47,748	47,748
Total	13,104,021			5,914,757	1,885,241


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, 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
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

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.


	Options Outstanding	Exercise Price(1)		Remaining Life(2)
Outstanding as of January 1, 2020	6,807,217	$	24.890	6.09
Granted	902,263	$	38.000	9.00
Exercised	(1,630,664)	$	25.180
Cancelled/forfeited	(164,059)	$	27.640
Outstanding as of December 31, 2020	5,914,757	$	26.730	6.22
Exercisable as of December 31, 2020	1,885,241	$	24.230	4.71


	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

The total intrinsic value of stock options exercised during the years ended December 31, 2020, 2019, and 2018 was $26.7, $20.2, and $4.2, 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, 2020, there was $12.6 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 3.87 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 2020, 2019, and 2018 was $6.1, $5.9, and $5.3, respectively.


	2020	2019	2018
Balance at beginning of year	574,128,911	571,803,838	575,183,072
Stock options exercised	1,630,664	2,325,073	620,766
Purchases of common stock	(1,600,000)	—	(4,000,000)
Balance at end of year	574,159,575	574,128,911	571,803,838

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	2020	2019	2018
Basic weighted average shares outstanding	573,778,761	573,202,152	573,933,834
Weighted shares assumed upon exercise of stock options	1,893,193	1,239,476	391,694
Diluted weighted average shares outstanding	575,671,954	574,441,628	574,325,528


Summary of Anti-dilutive Options Excluded	2020		2019	2018
Options to purchase shares of common stock	846,041		—	3,159,514
Weighted average exercise prices of options	$	38.00	—	27.51

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.