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Stock Compensation (Tables)

12 Months Ended

Dec. 31, 2021

Stock Compensation

Schedule of valuation assumptions used for valuation of fair value of stock compensation granted

We utilized the Black-Scholes valuation model for estimating the fair value of the stock options granted, with the following weighted-average assumptions:

​	​	​	​	​	​	​	​	​	​	​	​	​	​
​	​	Employee Stock Options					​	Employee Stock Purchase Plan					​
​	​	For the year ended December 31,					​	For the year ended December 31,					​
​		2021		2020		2019		2021		2020		2019	​
Average risk-free interest rates	​	0.62	%	0.80	%	2.27	%	0.40	%	0.17	%	1.82	%
Average expected life (in years)	​	5.01	​	4.98	​	5.27	​	0.50	​	0.50	​	0.50	​
Volatility	​	39	%	40	%	45	%	33	%	45	%	31	%
Weighted-average fair value (in dollars)	​	29.03	​	32.65	​	32.38	​	18.02	​	19.13	​	14.04	​

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- Definition

Tabular disclosure of the significant assumptions used during the year to estimate the fair value of employee stock options plan and employee stock purchase plans, including, but not limited to: (a) expected term, (b) expected volatility of the entity's shares, (c) expected dividends, (d) risk-free rate(s), and (e) discount for post-vesting restrictions.

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