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 March 31, 2019, the Company had 16,956,452 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.

The following table summarizes the Company’s stock option activity for the three-month period ended March 31, 2019:



	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	2,761		51.49
Exercised	(717	)	20.03
Forfeited or expired	(139	)	41.73
Outstanding as of March 31, 2019	15,694		$	35.65	7.63	$	255,322
Exercisable as of March 31, 2019	6,289		$	24.86	6.17	$	166,524
Options vested or expected to vest as of March 31, 2019 (1)	13,860		$	34.21	7.46	$	244,429

(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
	March 31, 2019		April 1, 2018
Risk-free rate	2.7	%	2.9	%
Expected dividend yield	0.39	%	0.32	%
Expected volatility	37	%	39	%
Expected term (in years)	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 9% to all unvested options for senior management and a rate of 12% for all other employees. The Company revised its estimated forfeiture rates in the three-month period ended March 31, 2019, resulting in a decrease to compensation expense of $499,000. The Company also revised its estimated forfeiture rates in the three-month period ended April 1, 2018, resulting in an increase to compensation expense of $1,283,000.

The weighted-average grant-date fair values of stock options granted during the three-month periods ended March 31, 2019 and April 1, 2018 were $18.59 and $21.62, respectively.

The total intrinsic values of stock options exercised for the three-month periods ended March 31, 2019 and April 1, 2018 were $22,579,000 and $28,088,000, respectively. The total fair values of stock options vested for the three-month periods ended March 31, 2019 and April 1, 2018 were $29,972,000 and $25,674,000, respectively.

As of March 31, 2019, total unrecognized compensation expense related to non-vested stock options was $75,985,000, which is expected to be recognized over a weighted-average period of 2.14 years.

The total stock-based compensation expense and the related income tax benefit recognized for the three-month period ended March 31, 2019 were $12,281,000 and $2,222,000, respectively, and for the three-month period ended April 1, 2018 were $13,194,000 and $2,347,000, respectively. No compensation expense was capitalized as of March 31, 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
	March 31, 2019		April 1, 2018
Cost of revenue	$	451	$	797
Research, development, and engineering	4,467		4,815
Selling, general, and administrative	7,363		7,582
	$	12,281	$	13,194