Stock-Based Compensation Expense

6 Months Ended

Jun. 30, 2019

Share-based Payment Arrangement [Abstract]

Stock-Based Compensation Expense. The stock-based compensation expense before income tax expense for the three and six months ended June 30, 2019 and 2018 consisted of the following (in thousands):



	Three Months Ended June 30,				Six Months Ended June 30,
	2019		2018		2019		2018
Cost of sales	$	355	$	232	$	607	$	416
Research and development	281		147		473		271
Selling, general and administrative	1,887		1,186		3,209		2,134
Stock-based compensation expense before taxes	$	2,523	$	1,565	$	4,289	$	2,821

We recognize stock-based compensation expense (net of a forfeiture rate) for those awards which are expected to vest on a straight-line basis over the requisite service period. We estimate the forfeiture rate based on our historical experience and expectations about future forfeitures. As of June 30, 2019, the total remaining unrecognized compensation cost related to non-vested stock options, net of expected forfeitures, was approximately $32.4 million and was expected to be recognized over a weighted average period of 3.32 years.

During the three and six-month periods ended June 30, 2019, we granted stock-based awards representing 190,000 and approximately 1.1 million shares of our common stock, respectively. During the three and six-month periods ended June 30, 2018, we granted stock-based awards representing 200,000 and 692,002 shares of our common stock, respectively. We use the Black-Scholes methodology to value the stock-based compensation expense for options. In applying the Black-Scholes methodology to the option grants, the fair value of our stock-based awards granted was estimated using the following assumptions for the periods indicated below:



	Six Months Ended June 30,
	2019	2018
Risk-free interest rate	1.90% - 2.56%	2.63% - 2.77%
Expected option term	3.0 - 5.0 years	5.0 years
Expected dividend yield	—	—
Expected price volatility	28.66% - 33.69%	34.06% - 34.32%

The average risk-free interest rate is determined using the U.S. Treasury rate in effect as of the date of grant, based on the expected term of the stock options. We determine the expected term of the stock options using the historical exercise behavior of employees. The expected price volatility was determined using a weighted average of daily historical volatility of our stock price over the corresponding expected option term and implied volatility based on recent trends of the daily historical volatility. For options with a vesting period, compensation expense is recognized on a straight-line basis over the service period, which corresponds to the vesting period.