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Share-Based Compensation (Tables)
6 Months Ended
Jun. 30, 2023
Share-Based Payment Arrangement [Abstract]  
Disclosure of Share-Based Compensation Arrangements by Share-Based Payment Award
The following table presents the effects of share-based compensation expense in the Condensed Consolidated Statements of Operations during the periods presented (in thousands):
Three months ended June 30,Six months ended June 30,
2023202220232022
Cost of revenues$94 $142 $170 $226 
Sales and marketing1,038 1,106 1,962 1,675 
Research, development, and engineering958 852 1,741 1,481 
General and administrative7,127 5,603 13,746 11,038 
Total share-based compensation expense$9,217 $7,703 $17,619 $14,420 
Market-Based Restricted Stock Awards, Valuation Assumptions
The weighted-average fair values of market-based restricted stock units granted have been estimated utilizing the following assumptions:
June 30, 2023June 30, 2022
Underlying stock price at valuation date$77.80 $99.32 
Expected volatility32.0 %36.7 %
Risk-free interest rate4.1 %1.8 %
Restricted Stock and Restricted Stock Unit Award Activity
Restricted stock award activity for the six months ended June 30, 2023 is set forth below:
SharesWeighted-Average
Grant-Date
Fair Value
Nonvested at January 1, 2023311,281 $59.90 
Vested(47,484)$78.37 
Nonvested at June 30, 2023
263,797 $57.71 
  
Restricted stock unit activity for the six months ended June 30, 2023 is set forth below:
Number of
Shares
Weighted-Average
Remaining
Contractual
Term (in years)
Aggregate
Intrinsic
Value
Outstanding at January 1, 2023464,354 
Granted458,765 
Vested(67,892)
Canceled(5,401)
Outstanding at June 30, 2023849,826 3.2$59,538,810 
Vested and expected to vest at June 30, 2023710,196 2.9$49,756,330 
Schedule of Employee Stock Purchase Plan, Valuation Assumptions
The shared-based compensation expense related to the Purchase Plan has been estimated utilizing the following weighted-average assumptions:
June 30, 2023June 30, 2022
Risk-free interest rate
4.7%1.5%
Expected term (in years)
0.50.5
Expected volatility
35.8%41.6%