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Share-Based Compensation (Tables)
 6 Months Ended
Jun. 30, 2024
Share-Based Payment Arrangement [Abstract]  
Disclosure of Share-Based Compensation Arrangements by Share-Based Payment Award
The following table presents 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,
2024202320242023
Direct costs
$62 $94 $123 $170 
Sales and marketing1,093 1,038 1,851 1,962 
Research, development, and engineering1,071 958 2,161 1,741 
General, administrative, and other related costs
9,374 7,127 16,337 13,746 
Total share-based compensation expense$11,600 $9,217 $20,472 $17,619 
Market-Based Restricted Stock Awards, Valuation Assumptions
The assumptions used in determining the weighted-average fair values of PSUs granted during the periods presented are as follows:
Six months ended June 30,
20242023
Underlying stock price at valuation date$66.88 $77.80 
Expected volatility32.9 %32.0 %
Risk-free interest rate4.3 %4.1 %
Restricted Stock and Restricted Stock Unit Award Activity
Restricted stock award activity for the six months ended June 30, 2024 is set forth below:
RSAs
PSAs
Number of
Shares
Weighted Average
Grant Date
Fair Value
Number of
Shares
Weighted Average
Grant Date
Fair Value
Nonvested at January 1, 202495,718$70.17 163,181$36.27 
Vested(37,501)71.21 — — 
Forfeited
(154)77.75 — — 
Nonvested at June 30, 2024
58,063 $69.48 163,181 $36.27 
  
Restricted stock unit activity for the six months ended June 30, 2024 is set forth below:
RSUs
PSUs
Number of
Shares

Weighted Average Grant Date Fair Value
Number of Shares (1)
Weighted Average Grant Date Fair Value
Outstanding at January 1, 2024506,425 $88.36 270,772 $77.09 
Granted390,284 66.22308,970 87.17
Vested(129,013)84.13— — 
Forfeited
(24,386)79.82(15,364)78.91 
Outstanding at June 30, 2024743,310 $78.13 564,378 $82.55 
(1)Represents the number of shares at 100% achievement.