Stock-Based Compensation

Stock Option Plans

The Company’s share-based payments that result in compensation expense consist of stock option grants and restricted stock awards. As of December 31, 2018, the Company had 19,578,752 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 of 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:



	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	2,997		52.67
Exercised	(1,493	)	17.94
Forfeited or expired	(441	)	33.59
Outstanding as of December 31, 2018	13,789		$	31.73	7.36	$	146,270
Exercisable as of December 31, 2018	4,556		$	20.94	5.85	$	82,716
Options vested or expected to vest as of December 31, 2018 (1)	12,499		$	30.60	7.23	$	141,643

(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:



	Year Ended December 31,
	2018		2017		2016
Risk-free rate	2.9	%	2.4	%	1.7	%
Expected dividend yield	0.35	%	0.40	%	0.83	%
Expected volatility	39	%	41	%	41	%
Expected term (in years)	5.4		5.4		5.6

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 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 forfeiture rate. This resulted in an increase to compensation expense of $1,283,000 in 2018, a decrease to compensation expense of $673,000 in 2017, and an increase to compensation expense of $334,000 in 2016.

The weighted-average grant-date fair value of stock options granted was $20.84 in 2018, $15.59 in 2017, and $6.33 in 2016.

The total intrinsic value of stock options exercised was $52,629,000 in 2018, $136,672,000 in 2017, and $55,580,000 in 2016. The total fair value of stock options vested was $31,106,000 in 2018, $21,519,000 in 2017, and $18,114,000 in 2016.

As of December 31, 2018, total unrecognized compensation expense related to non-vested stock options was $49,229,000, which is expected to be recognized over a weighted-average period of 1.56 years.

The following table summarizes the Company's restricted stock activity:



	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 December 31, 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 is then amortized over the period of vesting until the restrictions lapse. These restricted shares were fully vested in 2018. Participants are entitled to dividends on restricted stock awards, but only receive those amounts if the shares vest. The sale or transfer of these shares is restricted during the vesting period.

The total stock-based compensation expense and the related income tax benefit recognized was $41,090,000 and $7,317,000, respectively, in 2018, $31,942,000 and $10,473,000, respectively, in 2017, and $20,558,000 and $6,747,000, respectively, in 2016. No compensation expense was capitalized in 2018, 2017, or 2016.

The following table presents the stock-based compensation expense by caption for each period presented on the Consolidated Statements of Operations (in thousands):



	Year Ended December 31,
	2018		2017		2016
Cost of revenue	$	2,447	$	1,881	$	1,052
Research, development, and engineering	14,578		11,022		6,271
Selling, general, and administrative	24,065		19,039		13,235
	$	41,090	$	31,942	$	20,558