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Share-Based Compensation (Tables)
 12 Months Ended
Dec. 31, 2017
Disclosure of Compensation Related Costs, Share-based Payments [Abstract]  
Summary of Weighted Average Assumptions Used for Options Granted
The following weighted average assumptions were used for options granted:
 
Years Ended December 31,
 
2017
 
2016
 
2015
Expected life (in years)
6.0

 
6.0

 
6.0

Expected volatility
28.1
%
 
29.3
%
 
28.3
%
Risk-free interest rate
2.0
%
 
1.8
%
 
1.7
%
Expected forfeiture rate
—
%
 
—
%
 
1.7
%
Summary of Share-Based Compensation Expense Related to Share-Based Awards
The following table summarizes share-based compensation expense related to share-based awards which is recorded in the statements of comprehensive income:
 
Years Ended December 31,
 
2017
 
2016
 
2015
Cost of software services, maintenance and subscriptions
$
9,415

 
$
6,548

 
$
3,380

Selling, general and administrative expenses
27,933

 
23,199

 
16,802

Total share-based compensation expenses
37,348

 
29,747


20,182

Tax benefit
(40,624
)
 
(30,059
)
 
(5,986
)
Net (increase) decrease in net income
$
(3,276
)
 
$
(312
)

$
14,196
Stock Option Activity
Other information pertaining to option activity was as follows during the twelve months ended December 31:
 
2017
 
2016
 
2015
Weighted average grant-date fair value of stock options granted
$
55.56

 
$
46.89

 
$
45.17

Total intrinsic value of stock options exercised
137,699

 
103,703

 
149,542

Options granted, exercised, forfeited and expired are summarized as follows:
 
Number of
Shares
 
Weighted
Average Exercise
Price
 
Weighted
Average
Remaining
Contractual Life
(Years)
 
Aggregate
Intrinsic Value
Outstanding at December 31, 2014
5,537

 
$
44.61

 
 
 
 

Granted
747

 
145.71

 
 
 
 

Exercised
(1,118
)
 
20.71

 
 
 
 

Forfeited
(2
)
 
19.61

 
 
 
 

Outstanding at December 31, 2015
5,164

 
64.43

 
 
 
 

Granted
846

 
147.25

 
 
 
 

Exercised
(827
)
 
28.43

 
 
 
 

Forfeited
(27
)
 
95.33

 
 
 
 

Outstanding at December 31, 2016
5,156

 
83.64

 
 
 
 
Granted
824

 
176.26

 
 
 
 
Exercised
(1,113
)
 
44.80

 
 
 
 

Forfeited
(50
)
 
134.83

 
 
 
 

Outstanding at December 31, 2017
4,817

 
107.91

 
7
 
$
334,940

Exercisable at December 31, 2017
2,355

 
78.40

 
6
 
$
232,366