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Stock-Based Compensation Expense | 9 Months Ended
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Sep. 30, 2018
Disclosure of Compensation Related Costs, Share-based Payments [Abstract] |
Stock-Based Compensation Expense | Stock-Based Compensation Expense. Stock-based compensation expense before income tax expense for the three and nine months ended September 30, 2018 and 2017, consisted of the following (in thousands):
| Three Months Ended September 30, |  |  |  | Nine Months Ended September 30, |  |
| 2018 |  | 2017 |  | 2018 |  | 2017
Cost of sales | $ | 241 |  | $ | 189 |  | $ | 657 |  | $ | 453
Research and development | 141 |  | 110 |  | 412 |  | 262
Selling, general and administrative | 1,291 |  | 893 |  | 3,425 |  | 2,168
Stock-based compensation expense before taxes | $ | 1,673 |  | $ | 1,192 |  | $ | 4,494 |  | $ | 2,883
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 September 30, 2018, the total remaining unrecognized compensation cost related to non-vested stock options, net of expected forfeitures, was approximately $20.7 million and is expected to be recognized over a weighted average period of 3.25 years. During the three-month period ended September 30, 2018, we did not grant any new stock-based awards. During the nine-month period ended September 30, 2018, we granted stock-based awards representing 692,002 shares of our common stock. During the three and nine-month periods ended September 30, 2017, we granted stock-based awards representing 20,000 and approximately 1.3 million 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:
| Nine Months Ended September 30, |  |
| 2018 |  | 2017
Risk-free interest rate | 2.63% - 2.77% |  | 1.77% - 1.83%
Expected option life | 5.0 years |  | 5.0 years
Expected dividend yield | — |  | —
Expected price volatility | 34.06% - 34.32% |  | 33.81% - 34.07%
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 life 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.

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- Definition The entire disclosure for compensation-related costs for equity-based compensation, which may include disclosure of policies, compensation plan details, allocation of equity compensation, incentive distributions, equity-based arrangements to obtain goods and services, deferred compensation arrangements, employee stock ownership plan details and employee stock purchase plan details. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -URI http://asc.fasb.org/topic&trid=2228938 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 505 -SubTopic 50 -URI http://asc.fasb.org/subtopic&trid=2208855 + Details
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