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Stock-Based Compensation (Tables)
 12 Months Ended
Dec. 31, 2017
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]  
Stock-Based Compensation Expense
Total stock-based compensation expense recognized for the years ended December 31, 2017, 2016 and 2015 is as follows:
 
 
Year Ended December 31,
(in thousands, except per share amounts)
 
2017
 
2016
 
2015
Cost of sales:
 
 
 
 
 
 
Software licenses
 
$
969

 
$
701

 
$
745

Maintenance and service
 
2,533

 
1,578

 
1,868

Operating expenses:
 
 
 
 
 
 
Selling, general and administrative
 
30,817

 
15,990

 
17,153

Research and development
 
18,835

 
15,078

 
14,185

Stock-based compensation expense before taxes
 
53,154

 
33,347

 
33,951

Related income tax benefits
 
(20,503
)
 
(10,538
)
 
(11,656
)
Stock-based compensation expense, net of taxes
 
$
32,651

 
$
22,809

 
$
22,295

Net impact on earnings per share:
 
 
 
 
 
 
Basic earnings per share
 
$
(0.38
)
 
$
(0.26
)
 
$
(0.25
)
Diluted earnings per share
 
$
(0.38
)
 
$
(0.26
)
 
$
(0.24
)
Summary Of Stock Options
Information regarding stock option transactions is summarized below:
 
 
Year Ended December 31,
 
 
2017
 
2016
 
2015
(options in thousands)
 
Options
 
Weighted-
Average
Exercise
Price
 
Options
 
Weighted-
Average
Exercise
Price
 
Options
 
Weighted-
Average
Exercise
Price
Outstanding, beginning of year
 
3,136

 
$
56.37

 
3,986

 
$
51.07

 
4,932

 
$
48.76

Granted
 
—

 
$
—

 
260

 
$
94.38

 
57

 
$
88.10

Issued pursuant to acquisitions
 
—

 
$
—

 
—

 
$
—

 
8

 
$
12.26

Exercised
 
(956
)
 
$
49.78

 
(1,082
)
 
$
45.57

 
(975
)
 
$
40.52

Forfeited
 
(10
)
 
$
80.92

 
(28
)
 
$
72.07

 
(36
)
 
$
70.15

Outstanding, end of year
 
2,170

 
$
59.17

 
3,136

 
$
56.37

 
3,986

 
$
51.07

Vested and Exercisable, end of year
 
1,930

 
$
55.11

 
2,762

 
$
51.80

 
3,539

 
$
48.29

 
 
 
2017
 
2016
 
2015
Weighted-Average Remaining Contractual Term (in years)
 
 
 
 
 
 
Outstanding
 
4.10

 
4.62

 
4.85

Vested and Exercisable
 
3.57

 
4.04

 
4.53

Aggregate Intrinsic Value (in thousands)
 
 
 
 
 
 
Outstanding
 
$
191,895

 
$
113,822

 
$
165,131

Vested and Exercisable
 
$
178,456

 
$
112,379

 
$
156,487
Information Regarding Stock Options Outstanding
Information regarding stock options outstanding as of December 31, 2017 is summarized below:
(options in thousands)
 
Options Outstanding
 
Options Exercisable
Range of Exercise Prices
 
Options
 
Weighted-
Average
Remaining
Contractual
Life (years)
 
Weighted-
Average
Exercise
Price
 
Options
 
Weighted-
Average
Exercise
Price
$5.91 - $40.89
 
437

 
1.74
 
$
32.01

 
434

 
$
32.15

$48.97 - $55.30
 
392

 
2.80
 
$
49.11

 
392

 
$
49.11

$58.67
 
492

 
3.85
 
$
58.67

 
492

 
$
58.67

$61.68 - $95.09
 
849

 
6.05
 
$
78.06

 
612

 
$
72.35
Stock Options [Member]  
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]  
Assumptions To Estimate Fair Value Of Stock Awards
The table below presents the weighted average input assumptions used and resulting fair values for options granted or issued in business combinations during each respective year:
 
 
Year Ended December 31,
 
 
2016
 
2015
Risk-free interest rate
 
1.19% to 1.93%
 
1.18% to 1.65%
Expected dividend yield
 
—%
 
—%
Expected volatility
 
24%
 
25%
Expected term
 
5.7 years
 
5.6 years
Weighted-average fair value per share
 
$23.96
 
$30.83
Restricted Stock Units (RSUs) [Member]  
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]  
Assumptions To Estimate Fair Value Of Stock Awards
The table below represents the assumptions used in the Monte Carlo simulation model to determine the fair value of the restricted stock units during each respective year:
 
Year Ended December 31,
Assumptions used in Monte Carlo lattice pricing model
2017
 
2016
 
2015
Risk-free interest rate
1.5%
 
1.0%
 
1.1%
Expected dividend yield
—%
 
—%
 
—%
Expected volatility—ANSYS stock price
19%
 
21%
 
23%
Expected volatility—NASDAQ Composite Index
15%
 
16%
 
14%
Expected term
2.8 years
 
2.8 years
 
2.8 years
Correlation factor
0.70
 
0.65
 
0.60