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Stock-Based Compensation (Tables)
3 Months Ended
Mar. 31, 2023
Summary of Stock-Based Compensation Expense The following table summarizes the Company’s stock-based compensation expense (in thousands):
    
Three Months Ended
March 31,
 
    
2023
    
2022
 
Stock appreciation rights
   $ 215      $ 154  
Time-based restricted stock and restricted stock units
     935        847  
Performance-based restricted stock and restricted stock units
     724        1,158  
Employee stock purchase plan
     98        67  
    
 
 
    
 
 
 
Total stock-based compensation
   $ 1,972      $ 2,226  
    
 
 
    
 
 
 
Summary of Assumptions Used to Estimate Fair Value of Each SAR
The fair value of each SAR is estimated on the date of grant using a Black-Scholes option-pricing formula. For SARs issued in the three months ended March 31, 2023, and March 31, 2022, the data and assumptions shown in the following table were used:
 
    
Three Months Ended

March 31, 2023
   
Three Months Ended

March 31, 2022
 
Weighted-average fair value of grants
   $ 27.19     $ 33.90  
Dividend yield
     0     0
Average risk-free interest rate
     4.0     1.9
Expected term (years)
     5       5  
Expected volatility
     49.5     44.9
Summary of Stock-Based Compensation Grants
The following table summarizes the Company’s stock-based compensation grants for the three months ended March 31, 2023:
 
    
Stock Awards Granted
    
Weighted-Average

Grant Price

Per Share
 
Time-based restricted stock units
     76,698      $ 56.75  
Performance-based restricted stock units (a)
     96,013      $ 56.79  
Stock appreciation rights
     51,916      $ 56.80  
 
(a)
Includes 11,059 of target performance-based restricted stock unit awards granted during the three months ended March 31, 2023, and adjustments of 1,413, and 9,646 to grants due to the actual performance level achieved for restricted stock and restricted stock units awarded in 2021, and 2020, respectively.