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Stock-Based Compensation Expense
 6 Months Ended
Jul. 04, 2021
Share-based Payment Arrangement [Abstract]  
Stock-Based Compensation Expense Stock-Based Compensation Expense
Stock Plans
The Company’s stock-based awards that result in compensation expense consist of stock options and restricted stock units ("RSUs"). As of July 4, 2021, the Company had 15,692,000 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 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 for the six-month period ended July 4, 2021:
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 
Granted469 89.19 
Exercised(1,167)38.51 
Forfeited or expired(171)50.95 
Outstanding as of July 4, 20218,101 $48.07 6.91$298,370 
Exercisable as of July 4, 20213,652 $38.46 5.72$168,497 
Options vested or expected to vest as of July 4, 2021 (1)7,474 $47.27 6.81$281,063 
 (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 EndedSix-months Ended
 July 4, 2021June 28, 2020July 4, 2021June 28, 2020
Risk-free rate1.5 %1.6 %1.3 %1.6 %
Expected dividend yield0.31 %0.43 %0.27 %0.43 %
Expected volatility39 %37 %39 %37 %
Expected term (in years)7.16.05.86.0
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 six-month periods ended July 4, 2021 were $32.07 and $33.47, respectively, and during the three-month and six-month periods ended June 28, 2020 were $19.13 and $18.52, respectively.
The total intrinsic values of stock options exercised for the three-month and six-month periods ended July 4, 2021 were $11,621,000 and $53,948,000, respectively, and for the three-month and six-month periods ended June 28, 2020 were $39,359,000 and $53,814,000, respectively. The total fair values of stock options vested for the three-month and six-month periods ended July 4, 2021 were $1,830,000 and $37,430,000, respectively, and for the three-month and six-month periods ended June 28, 2020 were $1,287,000 and $37,951,000, respectively.
Restricted Stock Units (RSUs)
The following table summarizes the Company's RSUs activity for the six-month period ended July 4, 2021:
Shares
(in thousands)		Weighted-Average
Grant Date Fair Value
Nonvested as of December 31, 2020554 $51.27 
Granted296 87.46 
Vested(15)56.61 
Forfeited or expired(27)54.60 
Nonvested as of July 4, 2021808 $64.31 
The weighted-average grant-date fair values of RSUs granted during the three-month and six-month periods ended July 4, 2021 were $75.98 and $87.46, respectively, and during the three-month and six-month periods ended June 28, 2020 were $56.97 and $51.53, respectively. There were 13,000 and 15,000 RSUs that vested during the three-month and six-month periods ended July 4, 2021, respectively. There were no RSUs that vested during the three-month and six-month periods ended June 28, 2020.
Stock-Based Compensation Expense
The Company segments 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 8% 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 a decrease to compensation expense of $255,000 in 2021 and an increase to compensation expense of $1,787,000 in 2020.
As of July 4, 2021, total unrecognized compensation expense related to non-vested equity awards, including stock options and RSUs, was $63,625,000, which is expected to be recognized over a weighted-average period of 1.8 years.
The total stock-based compensation expense and the related income tax benefit recognized for the three-month period ended July 4, 2021 were $10,730,000 and $1,651,000, respectively, and for the six-month period ended July 4, 2021 were $22,739,000 and $3,464,000, respectively. The total stock-based compensation expense and the related income tax benefit recognized for the three-month period ended June 28, 2020 were $8,018,000 and $1,277,000, respectively, and for the six-month period ended June 28, 2020 were $22,808,000 and $3,841,000, respectively. Stock-based compensation expense recognized for the three-month and six-month periods ended June 28, 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 as of July 4, 2021 or December 31, 2020.
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 EndedSix-months Ended
 July 4, 2021June 28, 2020July 4, 2021June 28, 2020
Cost of revenue$351 $363 $599 $717 
Research, development, and engineering3,064 2,401 7,067 7,767 
Selling, general, and administrative7,315 5,254 15,073 14,324 
$10,730 $8,018 $22,739 $22,808