Stock-Based Compensation Expense

The Company’s share-based payments that result in compensation expense consist of stock option grants and restricted stock awards. As of September 30, 2018, the Company had 20,246,002 shares available for grant. 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. Vesting of restricted stock awards may be based on continuing employment and/or achievement of pre-established performance goals and objectives. Vesting for performance-based restricted stock awards and time-based restricted stock awards must not be less than one year and three years, respectively; however, awards with time-based vesting may become vested incrementally over such three-year period.

The following table summarizes the Company’s stock option activity for the nine-month period ended September 30, 2018:



	Shares (in thousands)		Weighted- Average Exercise Price		Weighted- Average Remaining Contractual Term (in years)	Aggregate Intrinsic Value (in thousands)
Outstanding as of December 31, 2017	12,726		$	25.24
Granted	2,318		55.66
Exercised	(1,434	)	18.06
Forfeited or expired	(429	)	33.24
Outstanding as of September 30, 2018	13,181		$	31.11	7.48	$	329,301
Exercisable as of September 30, 2018	4,327		$	20.14	6.01	$	154,377
Options vested or expected to vest as of September 30, 2018 (1)	11,916		$	29.99	7.37	$	310,772

(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 Ended				Nine-months Ended
	September 30, 2018		October 1, 2017		September 30, 2018		October 1, 2017
Risk-free rate	2.9	%	2.4	%	2.9	%	2.4	%
Expected dividend yield	0.32	%	0.39	%	0.32	%	0.39	%
Expected volatility	39	%	41	%	39	%	41	%
Expected term (in years)	5.4		5.1		5.3		5.3

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 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 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 estimated forfeiture rate. This resulted in an increase to compensation expense of $1,283,000 in 2018 and a decrease to compensation expense of $673,000 in 2017.

The weighted-average grant-date fair values of stock options granted during the three-month periods ended September 30, 2018 and October 1, 2017 were $22.52 and $14.80, respectively. The weighted-average grant-date fair values of stock options granted during the nine-month periods ended September 30, 2018 and October 1, 2017 were $21.70 and $14.97, respectively.

The total intrinsic values of stock options exercised for the three-month periods ended September 30, 2018 and October 1, 2017 were $17,985,000 and $28,462,000, respectively. The total intrinsic values of stock options exercised for the nine-month periods ended September 30, 2018 and October 1, 2017 were $50,975,000 and $100,913,000, respectively. The total fair values of stock options vested for the three-month periods ended September 30, 2018 and October 1, 2017 were $997,000 and $844,000, respectively. The total fair values of stock options vested for the nine-month periods ended September 30, 2018 and October 1, 2017 were $27,557,000 and $19,557,000, respectively.

As of September 30, 2018, total unrecognized compensation expense related to non-vested stock options was $50,387,000, which is expected to be recognized over a weighted-average period of 1.61 years.

The following table summarizes the Company's restricted stock activity for the nine-month period ended September 30, 2018:



	Shares (in thousands)		Weighted-Average Grant Fair Value		Aggregate Intrinsic Value (in thousands)
Nonvested as of December 31, 2017	20		$	17.03
Granted
Vested	(20	)	17.03		993
Forfeited or expired
Nonvested as of September 30, 2018	—		$	—	$	—

The fair values of restricted stock awards granted were determined based upon the market value of the Company's common stock at the time of grant. The initial cost was then amortized over the period of vesting until the restrictions lapsed. These restricted shares became fully vested in 2018. Participants were entitled to dividends on the restricted stock awards, but only received those amounts if the shares vested. The sale or transfer of these shares was restricted during the vesting period.

The total stock-based compensation expense and the related income tax benefit recognized for the three-month period ended September 30, 2018 were $9,143,000 and $1,654,000, respectively, and for the three-month period ended October 1, 2017 were $8,026,000 and $2,639,000, respectively. The total stock-based compensation expense and the related income tax benefit recognized for the nine-month period ended September 30, 2018 were $31,339,000 and $5,608,000, respectively, and for the nine-month period ended October 1, 2017 were $23,355,000 and $7,661,000, respectively. No compensation expense was capitalized as of September 30, 2018 or December 31, 2017.

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 Ended				Nine-months Ended
	September 30, 2018		October 1, 2017		September 30, 2018		October 1, 2017
Cost of revenue	$	544	$	520	$	1,898	$	1,404
Research, development, and engineering	3,197		2,765		11,166		8,090
Selling, general, and administrative	5,402		4,741		18,275		13,861
	$	9,143	$	8,026	$	31,339	$	23,355