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Stockholders' Equity
 6 Months Ended
Jun. 30, 2017
Stockholders' Equity Note [Abstract]  
Stockholders' Equity
(3) Stockholders' Equity
Dividends
On July 11, 2017, our board of directors declared a dividend of $0.32 per share of common stock. This dividend is to be paid in cash on August 23, 2017 to shareholders of record at the close of business on July 26, 2017. Since 2011, we have paid quarterly dividends. Our board of directors expects to continue paying quarterly dividends, provided the future determination as to payment of dividends will depend on the financial needs of the Company and such other factors as 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:
 
2017
 
2016
First quarter
$
0.32

 
0.30

Second quarter
0.32

 
0.30

Third quarter
0.32

 
0.30

Fourth quarter


 
0.30

Total
$
0.96

 
1.20


Stock Options
The following tables summarize the details of options granted under our stock option plan that were still outstanding as of June 30, 2017, 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
 
June 30, 2017
Date of Grant
 
 
 
Options
Outstanding
 
Options
Exercisable
January 3, 2017
764,789

 
$
47.00

 
$
46.95

 
747,772

 
—

April 19, 2016
845,440

 
$
46.00

 
$
45.74

 
771,432

 
—

April 21, 2015
893,220

 
$
42.00

 
$
41.26

 
712,290

 
—

April 22, 2014
955,000

 
$
56.00

 
$
50.53

 
582,500

 
116,250

April 16, 2013
205,000

 
$
54.00

 
$
49.25

 
110,000

 
57,250

April 17, 2012
1,235,000

 
$
54.00

 
$
49.01

 
965,125

 
778,603

April 19, 2011
410,000

 
$
35.00

 
$
31.78

 
73,800

 
48,800

April 20, 2010
530,000

 
$
30.00

 
$
27.13

 
110,300

 
84,050

April 21, 2009
790,000

 
$
27.00

 
$
17.61

 
224,150

 
224,150

Total
6,628,449

 
 
 
 
 
4,297,369

 
1,309,103


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, 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

April 21, 2009
1.9
%
 
5.00
 
1.0
%
 
38.80
%
 
$
3.64


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 six-month periods ended June 30, 2017 and 2016 was $2.8 and $1.7, respectively. Unrecognized stock-based compensation expense related to outstanding unvested stock options as of June 30, 2017 was $17.2 and is expected to be recognized over a weighted average period of 4.58 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:
 
Six-month Period
 
Three-month Period
Reconciliation
2017
 
2016
 
2017
 
2016
Basic weighted average shares outstanding
288,948,734

 
288,863,482

 
288,655,020

 
288,918,945

Weighted shares assumed upon exercise of stock options
150,582

 
268,820

 
133,943

 
200,525

Diluted weighted average shares outstanding
289,099,316

 
289,132,302

 
288,788,963

 
289,119,470


 
 
Six-month Period
 
Three-month Period
Summary of Anti-dilutive Options Excluded
2017
 
2016
 
2017
 
2016
Options to purchase shares of common stock
3,603,850

 
2,941,864

 
3,897,177

 
3,253,343

Weighted average exercise price of options
$
49.81

 
50.39

 
$
49.18

 
49.91


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.