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Stock-Based Compensation Expense
 9 Months Ended
Oct. 02, 2022
Share-Based Payment Arrangement [Abstract]  
Shareholders' Equity and Share-based Payments Stock-Based Compensation Expense
Stock Plans
The Company’s stock-based awards that result in compensation expense consist of stock options, restricted stock units ("RSUs"), and performance restricted stock units ("PRSUs"). As of October 2, 2022, the Company had 13,748,000 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 upon continuous service and expire ten years from the grant date. RSUs generally vest upon three or four years of continuous employment or incrementally over such three or four-year period. PRSUs generally vest upon three years of continuous employment and achievement of performance criteria established by the Compensation Committee of our Board of Directors on or prior to the grant date. Participants are not entitled to dividends on RSUs or PRSUs.
Stock Options
The following table summarizes the Company’s stock option activity for the nine-month period ended October 2, 2022:
Shares
(in thousands)		Weighted-
Average
Exercise
Price		Weighted-
Average
Remaining
Contractual
Term (in years)		Aggregate
Intrinsic
Value
(in thousands)
Outstanding as of December 31, 20217,610 $49.38 
Granted1,399 59.79 
Exercised(158)41.83 
Forfeited or expired(170)58.01 
Outstanding as of October 2, 20228,681 $51.03 6.40$22,376 
Exercisable as of October 2, 20224,335 $43.54 5.08$22,334 
Options vested or expected to vest as of October 2, 2022 (1)8,189 $50.48 6.27$22,375 
 (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:
 Three-months EndedNine-months Ended
 October 2, 2022October 3, 2021October 2, 2022October 3, 2021
Risk-free rate2.7 %1.4 %2.1 %1.3 %
Expected dividend yield0.54 %0.28 %0.44 %0.27 %
Expected volatility37 %39 %37 %39 %
Expected term (in years)6.47.15.56.0
Risk-free rate
The risk-free rate was based upon 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 upon 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 values of stock options granted during the three-month and nine-month periods ended October 2, 2022 were $18.81 and $21.40, respectively, and during the three-month and nine-month periods ended October 3, 2021 were $35.64 and $33.78, respectively.
The total intrinsic values of stock options exercised for the three-month and nine-month periods ended October 2, 2022 were $516,000 and $3,615,000, respectively, and for the three-month and nine-month periods ended October 3, 2021 were $21,415,000 and $75,363,000, respectively. The total fair values of stock options vested for the three-month and nine-month periods ended October 2, 2022 were $1,159,000 and $27,882,000, respectively, and for the three-month and nine-month periods ended October 3, 2021 were $1,498,000 and $38,928,000, respectively.
Restricted Stock Units (RSUs)
The following table summarizes the Company's RSUs activity for the nine-month period ended October 2, 2022:
Shares
(in thousands)		Weighted-Average
Grant Date Fair Value
Nonvested as of December 31, 2021823 $65.26 
Granted691 58.44 
Vested(141)65.33 
Forfeited or expired(61)65.18 
Nonvested as of October 2, 20221,312 $61.67 
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 values of RSUs granted during the three-month and nine-month periods ended October 2, 2022 were $47.12 and $58.44, respectively, and during the three-month and nine-month periods ended October 3, 2021 were $86.34 and $87.38, respectively. There were 67,000 and 141,000 RSUs that vested during the three-month and nine-month periods ended October 2, 2022, respectively, and 0 and 15,000 that vested during the three-month and nine-month periods ended October 3, 2021, respectively.
Performance Restricted Stock Units (PRSUs)
The following table summarizes the Company's PRSUs activity for the nine-month period ended October 2, 2022:
Shares
(in thousands)		Weighted-Average
Grant Date Fair Value
Nonvested as of December 31, 2021— $— 
Granted33 62.49 
Vested— — 
Forfeited or expired— — 
Nonvested as of October 2, 202233 $62.49 
No PRSUs were granted or vested during the three-month period ended October 2, 2022. No PRSUs were granted or vested during the three-month and nine-month periods ended October 3, 2021.
The fair value of PRSUs is calculated using the Monte Carlo simulation model to estimate the probability of satisfying the service and market conditions stipulated in the award grant.
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 annual forfeiture rate of 7% to all stock-based awards for senior management and a rate of 12% for all other employees. Each year during the first quarter, the Company revises its forfeiture rate based on updated estimates of employee turnover. This resulted in an increase to compensation expense of $1,536,000 in 2022 and a decrease to compensation expense of $255,000 in 2021.
As of October 2, 2022, total unrecognized compensation expense related to non-vested equity awards, including stock options, RSUs, and PRSUs, was $68,089,000, which is expected to be recognized over a weighted-average period of 1.6 years.
The total stock-based compensation expense and the related income tax benefit recognized for the three-month period ended October 2, 2022 were $13,366,000 and $2,133,000, respectively, and for the nine-month period ended October 2, 2022 were $41,419,000 and $6,496,000, respectively. The total stock-based compensation expense and the related income tax benefit recognized for the three-month period ended October 3, 2021 were $10,614,000 and $1,637,000, respectively, and for the nine-month period ended October 3, 2021 were $33,353,000 and $5,101,000, respectively. No compensation expense was capitalized as of October 2, 2022 or December 31, 2021.
The following table presents the stock-based compensation expense by caption for each period presented on the Consolidated Statements of Operations (in thousands):
 Three-months EndedNine-months Ended
 October 2, 2022October 3, 2021October 2, 2022October 3, 2021
Cost of revenue$468 $366 $1,513 $965 
Research, development, and engineering4,209 3,091 12,508 10,158 
Selling, general, and administrative8,689 7,157 27,398 22,230 
$13,366 $10,614 $41,419 $33,353