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Share-Based Compensation (Tables)
3 Months Ended
Mar. 31, 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 March 31,
20232022
Cost of revenues$76 $84 
Sales and marketing924 569 
Research, development and engineering783 629 
General and administrative6,619 5,435 
Total share-based compensation$8,402 $6,717 
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:
March 31, 2023March 31, 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 three months ended March 31, 2023 is set forth below:
SharesWeighted-Average
Grant-Date
Fair Value
Nonvested at January 1, 2023311,281 $59.90 
Vested(36,380)$100.41 
Nonvested at March 31, 2023
274,901 $58.43 
  
Restricted stock unit activity for the three months ended March 31, 2023 is set forth below:
Number of
Shares
Weighted-Average
Remaining
Contractual
Term (in years)
Aggregate
Intrinsic
Value
Outstanding at January 1, 2023464,354 
Granted439,220 
Vested(53,299)
Canceled(1,401)
Outstanding at March 31, 2023848,874 3.4$66,508,434 
Vested and expected to vest at March 31, 2023705,218 3.2$54,788,467