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Stock-Based Compensation
 12 Months Ended
Dec. 31, 2021
Share-based Payment Arrangement [Abstract]  
Stock-Based Compensation Stock-Based Compensation
Stock Plans
The Company’s stock-based awards that result in compensation expense consist of stock options and restricted stock units (RSUs). As of December 31, 2021, the Company had 15,640,000 shares available for grant under its stock plans. Stock options are granted with an exercise price equal to the market value of the Company’s common stock at the grant date and generally vest over four or five years based on continuous employment and expire ten years from the grant date. RSUs generally vest upon three years of continuous employment or incrementally over such three-year period. Participants are not entitled to dividends on RSUs.
Stock Options
The following table summarizes the Company’s stock option activity:
Shares
(in thousands)		Weighted-
Average
Exercise
Price		Weighted-
Average
Remaining
Contractual
Term
(in years)		Aggregate
Intrinsic Value
(in thousands)
Outstanding as of December 31, 20208,970 $44.73 
Granted564 88.62 
Exercised(1,694)37.70 
Forfeited or expired(230)50.34 
Outstanding as of December 31, 20217,610 $49.38 6.57$222,053 
Exercisable as of December 31, 20213,442 $39.87 5.45$130,448 
Options vested or expected to vest as of 
 December 31, 2021 (1)		7,134 $48.66 6.49$212,746 
(1) In addition to the vested options, the Company expects a portion of the unvested options to vest at some point in the future. Options expected to vest are calculated by applying an estimated forfeiture rate to the unvested options.
The fair values of stock options granted in each period presented were estimated using the following weighted-average assumptions:
 Year Ended December 31,
 202120202019
Risk-free rate1.3 %1.4 %2.7 %
Expected dividend yield0.27 %0.41 %0.39 %
Expected volatility39 %37 %37 %
Expected term (in years)6.06.05.3
Risk-free rate
The risk-free rate was based on a treasury instrument whose term was consistent with the contractual term of the option.
Expected dividend yield
Generally, the current dividend yield is calculated by annualizing the cash dividend declared by the Company’s Board of Directors and dividing that result by the closing stock price on the grant date. 
Expected volatility
The expected volatility was based on a combination of historical volatility of the Company’s common stock over the contractual term of the option and implied volatility for traded options of the Company’s stock.
Expected term
The expected term was derived from the binomial lattice model from the impact of events that trigger exercises over time.
The weighted-average grant-date fair value of stock options granted was $33.79 in 2021, $19.62 in 2020, and $18.62 in 2019.
The total intrinsic value of stock options exercised was $80,369,000 in 2021, $166,796,000 in 2020, and $90,762,000 in 2019. The total fair value of stock options vested was $45,328,000 in 2021, $45,998,000 in 2020, and $38,974,000 in 2019.
Restricted Stock Units (RSUs)
The following tables summarizes the Company's RSU activity:
Shares
(in thousands)		Weighted-Average
Grant Date Fair Value
Nonvested as of December 31, 2020554 $51.27 
Granted335 87.03 
Vested(16)57.31 
Forfeited or expired(50)58.47 
Nonvested as of December 31, 2021823 $65.26 
The fair value of RSUs is determined based on the observable market price of the Company's stock on the grant date less the present value of expected future dividends. The weighted-average grant-date fair value of RSUs granted in 2020 and 2019 was $52.09 and $48.61, respectively. There were 16,000 RSUs that vested in 2021, and no RSUs that vested in 2020 and 2019.
Stock-Based Compensation Expense
The Company stratifies its employee population into two groups: one consisting of senior management and another consisting of all other employees. The Company currently applies an estimated forfeiture rate of 8% to all unvested options for senior management and a rate of 12% for all other employees. Each year during the first quarter, the Company revises its forfeiture rate. This resulted in a decrease to compensation expense of $255,000 in 2021, an increase to compensation expense of $1,787,000 in 2020, and a decrease to compensation expense of $499,000 in 2019.
As of December 31, 2021, total unrecognized compensation expense related to non-vested stock-based awards, including stock options and RSUs, was $47,690,000, which is expected to be recognized over a weighted-average period of 1.4 years.
The total stock-based compensation expense and the related income tax benefit recognized was $43,774,000 and $6,764,000, respectively, in 2021, $42,661,000 and $6,569,000, respectively, in 2020, and $45,589,000 and $7,756,000, respectively, in 2019. Stock-based compensation expense recognized in 2020 included credits of $1,401,000 relating to grants cancelled as a result of the Company's workforce reduction in the second quarter of 2020. No compensation expense was capitalized in 2021, 2020, or 2019.
The following table presents the stock-based compensation expense by caption for each period presented on the Consolidated Statements of Operations (in thousands):
 Year Ended December 31,
 202120202019
Cost of revenue$1,345 $1,365 $1,504 
Research, development, and engineering13,535 13,387 15,748 
Selling, general, and administrative28,894 27,909 28,337 
$43,774 $42,661 $45,589