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Stock-Based Compensation (Tables)
12 Months Ended
Dec. 31, 2020
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, 2020, 2019 and 2018 is as follows:
 Year Ended December 31,
(in thousands, except per share amounts)202020192018
Cost of sales:
Maintenance and service13,626 8,494 5,224 
Operating expenses:
Selling, general and administrative73,491 60,639 47,099 
Research and development58,498 47,057 31,023 
Stock-based compensation expense before taxes145,615 116,190 83,346 
Related income tax benefits(56,485)(47,454)(34,518)
Stock-based compensation expense, net of taxes$89,130 $68,736 $48,828 
Net impact on earnings per share:
Basic earnings per share$(1.04)$(0.82)$(0.58)
Diluted earnings per share$(1.02)$(0.80)$(0.57)
Summary of Stock Options
Information regarding stock option transactions is summarized below:
 Year Ended December 31,
 202020192018
(options in thousands)OptionsWeighted-
Average
Exercise
Price
OptionsWeighted-
Average
Exercise
Price
OptionsWeighted-
Average
Exercise
Price
Outstanding, beginning of year984 $67.49 1,484 $62.80 2,170 $59.17 
Granted $ — $— — $— 
Exercised(336)$54.43 (495)$53.53 (679)$50.92 
Forfeited $ (5)$64.21 (7)$86.28 
Outstanding, end of year648 $74.26 984 $67.49 1,484 $62.80 
Vested and Exercisable, end of year648 $74.26 924 $65.71 1,347 $59.69 
Nonvested $ 60 $94.77 137 $93.44 
 
202020192018
Weighted Average Remaining Contractual Term (in years)
Outstanding2.933.183.55
Vested and Exercisable2.932.953.14
Nonvested0.006.717.60
Aggregate Intrinsic Value (in thousands)
Exercised$78,269 $72,098 $78,648 
Outstanding$187,679 $186,926 $118,908 
Vested and Exercisable$187,679 $177,111 $112,133 
Nonvested $ $9,815 $6,775 
Compensation Expense - Stock Options (in thousands)
$1,030 $1,709 $2,006 
Summary of Types of Awards and Vesting Conditions The following table summarizes the types of awards and vesting conditions:
AwardVesting PeriodVesting Condition
Restricted stock units with a service condition onlyThree yearsContinued employment through the vesting period. One third vests annually.
Restricted stock units with an operating performance and service conditionThree yearsOperating performance metrics as defined at the beginning of each sub-performance period and subject to continued employment.
Restricted stock units with a market and service condition
Three years
Our performance measured by total stockholder return relative to the Nasdaq Composite Index for the performance period and subject to continued employment through the vesting period.
Summary of Restricted Stock Units
Information regarding all employee RSU transactions is summarized below:
 Year Ended December 31,
 202020192018
(RSUs in thousands)RSUsWeighted-
Average
Grant Date Fair Value
RSUsWeighted-
Average
Grant Date Fair Value
RSUsWeighted-
Average
Grant Date Fair Value
Nonvested, beginning of year1,618 $165.26 1,522 $129.96 1,361 $100.66 
Granted(1)
501 $256.47 843 $192.37 681 $163.67 
Performance adjustment - awards with market condition(2)
18 $191.76 12 $120.96 10 $78.71 
Performance adjustment - awards with performance condition(2)
(10)$279.08 62 $176.89 66 $162.64 
Vested(742)$158.13 (704)$125.84 (524)$101.38 
Forfeited(62)$193.28 (117)$140.43 (72)$125.29 
Nonvested, end of year1,323 $201.98 1,618 $165.26 1,522 $129.96 
(1) Includes all RSUs granted during the year. RSUs with operating performance conditions are issued annually and have one performance cycle or three sub-performance cycles. Performance conditions are assigned near the beginning of each performance cycle or sub-performance cycle, as applicable, and awards are reflected as grants at the target number of units at that time.
(2) RSUs with a market or performance condition are granted at target and vest based on achievement of the market or operating performance and service conditions. The actual number of RSUs issued may be more or less than the target RSUs depending on the achievement of the market or operating performance conditions.
Employee Stock Option  
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]  
Information Regarding Stock Options Outstanding
Information regarding stock options outstanding as of December 31, 2020 is summarized below:
(options in thousands)Options Outstanding & Exercisable
Range of Exercise PricesOptionsWeighted-
Average
Remaining
Contractual
Life (years)
Weighted-
Average
Exercise
Price
$12.26 - $24.4213 0.40$22.10 
$58.67167 0.86$58.67 
$67.44226 1.85$67.44 
$78.56 - $95.09242 5.48$94.15 
Restricted Stock Units (RSUs)  
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]  
Assumptions to Estimate Fair Value of Stock Awards The determination of the fair values of the awards was affected by the grant date and several variables, each of which has been identified in the chart below:
Year Ended December 31,
Assumptions used in Monte Carlo lattice pricing model202020192018
Risk-free interest rate0.7%2.5%2.4%
Expected dividend yield—%—%—%
Expected volatility—Ansys stock price25%23%21%
Expected volatility—Nasdaq Composite Index18%16%15%
Expected term2.8 years2.8 years2.8 years
Correlation factor0.770.710.65
Weighted average fair value per share$245.08$238.99$191.76
Diversified Deferred Stock Award  
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]  
Summary of Stock Awards To Non-Employee Directors
Information regarding deferred stock awards to non-employee Directors is summarized below:
Year Ended December 31, 2020
DiversifiedUndiversifiedTotal
Deferred Awards Outstanding, beginning of year5,598 60,081 65,679 
Shares Diversified1,400 (1,400) 
Deferred Awards Outstanding, end of year6,998 58,681 65,679 
Year Ended December 31, 2019
DiversifiedUndiversifiedTotal
Deferred Awards Outstanding, beginning of year12,250 120,449 132,699 
Shares Diversified13,348 (13,348)— 
Shares Issued Upon Retirement(20,000)(47,020)(67,020)
Deferred Awards Outstanding, end of year5,598 60,081 65,679 
Year Ended December 31, 2018
DiversifiedUndiversifiedTotal
Deferred Awards Outstanding, beginning of year29,500 159,599 189,099 
Shares Diversified6,105 (6,105)— 
Shares Issued Upon Retirement(23,355)(33,045)(56,400)
Deferred Awards Outstanding, end of year12,250 120,449 132,699 
Director Restricted Stock Units  
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]  
Summary of Stock Awards To Non-Employee Directors
Information regarding RSU awards to non-employee Directors is summarized below:

 Year Ended December 31,
 202020192018
(RSUs in thousands)BOD RSUsWeighted-
Average
Grant Date Fair Value
BOD RSUsWeighted-
Average
Grant Date Fair Value
BOD RSUsWeighted-
Average
Grant Date Fair Value
Nonvested, beginning of year9,688 $187.53 13,632 $165.71 18,018 $123.38 
Granted9,664 $253.40 11,259 $187.53 13,632 $165.71 
Vested(10,704)$193.35 (14,287)$166.71 (18,018)$123.38 
Forfeited(577)$253.93 (916)$187.53 — $— 
Nonvested, end of year8,071 $253.93 9,688 $187.53 13,632 $165.71