(3) Stockholders' Equity

Dividends

On October 9, 2018, our board of directors declared a dividend of $0.40 per share of common stock to be paid in cash on November 21, 2018 to shareholders of record at the close of business on October 24, 2018. Since 2011, we have paid quarterly dividends. Our board of directors intends to continue paying quarterly 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 dividends either paid previously or declared by our board of directors for future payment on a per share basis:



	2018		2017
First quarter	$	0.37	0.32
Second quarter	0.37		0.32
Third quarter	0.40		0.32
Fourth quarter	0.40		0.32
Total	$	1.54	1.28

Stock Options

The following tables summarize the details of options granted under our stock option plan that were still outstanding as of September 30, 2018, 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, 2018
Date of Grant	Options Granted	Option Exercise (Strike) Price		Closing Stock Price on Date of Grant		Options Outstanding	Options Exercisable
January 2, 2018	541,786	$	55.00	$	54.54	525,525	21,185
January 3, 2017	764,789	$	47.00	$	46.95	683,528	—
April 19, 2016	845,440	$	46.00	$	45.74	706,116	—
April 21, 2015	893,220	$	42.00	$	41.26	630,784	130,318
April 22, 2014	955,000	$	56.00	$	50.53	519,750	314,000
April 16, 2013	205,000	$	54.00	$	49.25	91,249	57,506
April 17, 2012	1,235,000	$	54.00	$	49.01	828,750	716,250
April 19, 2011	410,000	$	35.00	$	31.78	52,850	40,350
April 20, 2010	530,000	$	30.00	$	27.13	33,150	33,150
Total	6,380,235					4,071,702	1,312,759



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, 2018	2.2	%	5.00	2.3	%	23.45	%	$	10.03
January 3, 2017	1.9	%	5.00	2.6	%	24.49	%	$	8.40
April 19, 2016	1.3	%	5.00	2.6	%	26.34	%	$	8.18
April 21, 2015	1.3	%	5.00	2.7	%	26.84	%	$	7.35
April 22, 2014	1.8	%	5.00	2.0	%	28.55	%	$	9.57
April 16, 2013	0.7	%	5.00	1.6	%	37.42	%	$	12.66
April 17, 2012	0.9	%	5.00	1.4	%	39.25	%	$	13.69
April 19, 2011	2.1	%	5.00	1.6	%	39.33	%	$	11.20
April 20, 2010	2.6	%	5.00	1.5	%	39.10	%	$	8.14

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 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, 2018 and 2017 was $3.8 and $4.0, respectively. Unrecognized stock-based compensation expense related to outstanding unvested stock options as of September 30, 2018 was $14.9 and is expected to be recognized over a weighted average period of 4.07 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	2018	2017	2018	2017
Basic weighted average shares outstanding	287,263,379	288,451,470	287,006,910	287,456,943
Weighted shares assumed upon exercise of stock options	195,029	140,104	256,312	121,100
Diluted weighted average shares outstanding	287,458,408	288,591,574	287,263,222	287,578,043



	Nine-month Period			Three-month Period
Summary of Anti-dilutive Options Excluded	2018		2017	2018		2017
Options to purchase shares of common stock	1,597,342		3,881,605	1,534,795		3,848,126
Weighted average exercise price of options	$	55.02	49.21	$	55.02	49.18

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.