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Stock-Based Compensation (Tables)
9 Months Ended
Sep. 30, 2022
Summary of Stock-Based Compensation Grants
The following table summarizes the Company’s stock-based compensation grants for the nine months ended September 30, 2022:
 
    
Stock Awards Granted
    
Weighted-Average

Grant Price

Per Share
 
Time-based restricted stock units
     56,818      $ 56.18  
Performance-based restricted stock units (a)
     72,152      $ 76.14  
Stock appreciation rights
     32,971      $ 82.01  
 
(a)
Includes 47,072 of target performance-based restricted stock unit awards granted during the nine months ended September 30, 2022, and adjustments of 8,160, 11,684, and 5,236 to grants due to the actual performance level achieved for restricted stock and restricted stock units awarded in 2021, 2020, and 2019, respectively.
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 nine months ended September 30, 2022, and September 30, 2021, the data and assumptions shown in the following table were used:
 
    
Nine Months Ended

September 30, 2022
   
Nine Months Ended

September 30, 2021
 
Weighted-average fair value of grants
   $ 33.9     $ 51.84  
Dividend yield
     0     0
Average risk-free interest rate
     1.9     0.6
Expected term (years)
     5       5  
Expected volatility
     44.85     58.7
Summary of Stock-Based Compensation Expense The following table summarizes the Company’s stock-based compensation expense (in thousands):
 
    
Three Months Ended
September 30,
    
Nine Months Ended
September 30,
 
    
2022
    
2021
    
2022
    
2021
 
Stock appreciation rights
   $ 196      $ 94      $ 547      $ 352  
Time-based restricted stock and restricted stock units
     1,012        692        2,818        2,133  
Performance-based restricted stock and restricted stock units
     (1,012      1,047        (5      3,487  
Employee stock purchase plan
     52        54        171        223  
    
 
 
    
 
 
    
 
 
    
 
 
 
Total stock-based compensation
   $ 248      $ 1,887      $ 3,531      $ 6,195