The Company’s share-based payments that result in compensation expense consist of stock option grants and restricted stock awards. As of June 30, 2019, the Company had 17,363,952 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.



	Shares (in thousands)		Weighted- Average Exercise Price		Weighted- Average Remaining Contractual Term (in years)	Aggregate Intrinsic Value (in thousands)
Outstanding as of December 31, 2018	13,789		$	31.73
Granted	2,821		51.37
Exercised	(1,239	)	21.32
Forfeited or expired	(606	)	40.27
Outstanding as of June 30, 2019	14,765		$	36.00	7.42	$	207,599
Exercisable as of June 30, 2019	5,867		$	25.12	5.95	$	138,370
Options vested or expected to vest as of June 30, 2019 (1)	13,214		$	34.65	7.25	$	201,420

(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				Six-months Ended
	June 30, 2019		July 1, 2018		June 30, 2019		July 1, 2018
Risk-free rate	2.7	%	2.9	%	2.7	%	2.9	%
Expected dividend yield	0.39	%	0.32	%	0.39	%	0.32	%
Expected volatility	37	%	39	%	37	%	39	%
Expected term (in years)	5.2		5.4		5.3		5.3

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.

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.

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 9% 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 a decrease to compensation expense of $499,000 in 2019 and in increase to compensation expense of $1,283,000 in 2018.

The weighted-average grant-date fair values of stock options granted during the three-month periods ended June 30, 2019 and July 1, 2018 were $18.68 and $21.63, respectively. The weighted-average grant-date fair values of stock options granted during the six-month periods ended June 30, 2019 and July 1, 2018 were $18.59 and $21.62, respectively.

The total intrinsic values of stock options exercised for the three-month periods ended June 30, 2019 and July 1, 2018 were $14,220,000 and $4,902,000, respectively. The total intrinsic values of stock options exercised for the six-month periods ended June 30, 2019 and July 1, 2018 were $36,799,000 and $32,991,000, respectively. The total fair values of stock options vested for the three-month periods ended June 30, 2019 and July 1, 2018 were $887,000 and $887,000, respectively. The total fair values of stock options vested for the six-month periods ended June 30, 2019 and July 1, 2018 were $30,859,000 and $26,560,000, respectively.

As of June 30, 2019, total unrecognized compensation expense related to non-vested stock options was $66,645,000, which is expected to be recognized over a weighted-average period of 1.88 years.

The total stock-based compensation expense and the related income tax benefit recognized for the three-month period ended June 30, 2019 were $10,967,000 and $1,813,000, respectively, and for the three-month period ended July 1, 2018 were $9,002,000 and $1,607,000, respectively. The total stock-based compensation expense and the related income tax benefit recognized for the six-month period ended June 30, 2019 were $23,248,000 and $4,035,000, respectively, and for the six-month period ended July 1, 2018 were $22,196,000 and $3,954,000, respectively. No compensation expense was capitalized as of June 30, 2019 or December 31, 2018.

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				Six-months Ended
	June 30, 2019		July 1, 2018		June 30, 2019		July 1, 2018
Cost of revenue	$	329	$	557	$	780	$	1,354
Research, development, and engineering	3,550		3,154		8,017		7,969
Selling, general, and administrative	7,088		5,291		14,451		12,873
	$	10,967	$	9,002	$	23,248	$	22,196