12.   Stock-Based Compensation Expense. Stock-based compensation expense before income tax expense for the three and nine-month periods ended September 30, 2022 and 2021 consisted of the following (in thousands):

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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.

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Nonqualified Stock Options

During the nine-month periods ended September 30, 2022 and 2021, we granted stock options representing 203,606 and 656,350 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:

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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 award. We determine the expected term of 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 awards 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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As of September 30, 2022, the total remaining unrecognized compensation cost related to non-vested stock options was $22.0 million, which was expected to be recognized over a weighted average period of 2.3 years.

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Stock-Settled Performance-Based Restricted Stock Units (“Performance Stock Units”)

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During the nine-month periods ended September 30, 2022 and 2021, we granted performance stock units to certain of our executive officers which represent up to 120,710 and 128,883 shares of our common stock, respectively. Conversion of the performance stock units occurs at the end of the relevant performance periods, or one year after the agreement date, whichever is later. The conversion ratio is based upon attaining targeted levels of free cash flow (“FCF”) and relative shareholder return as compared to the Russell 2000 Index (“rTSR”), as defined in the award agreements.

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We use Monte-Carlo simulations to estimate the grant-date fair value of the performance stock units linked to total shareholder return. The fair value of each performance stock unit was estimated as of the grant date using the following assumptions for awards granted in the periods indicated below:

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The risk-free interest rate of return was determined using the U.S. Treasury rate at the time of grant with a term equal to the expected term of the award. The expected volatility was based on the weighted average volatility of our stock price and the average volatility of our compensation peer group's stock price. The expected dividend yield was assumed to be zero because, at the time of the grant, we had no plans to declare a dividend.

Compensation expense is recognized using the grant-date fair value for the number of shares that are probable of being awarded based on the performance conditions. Each reporting period, this probability assessment is updated, and cumulative adjustments are recorded based on the level of FCF that is expected to be achieved. At the end of the performance period, cumulative expense is calculated based on the actual level of FCF achieved. As of

September 30, 2022, the total remaining unrecognized compensation cost related to stock-settled performance stock units was $6.5 million, which is expected to be recognized over a weighted average period of 1.7 years.

Liability Awards

During the nine-month periods ended September 30, 2022 and 2021, we granted liability awards to our Chief Executive Officer with total target cash incentives, each in the amount of $1.0 million. These awards entitle him to a target cash payment based upon attaining targeted levels of FCF and rTSR, as defined in the award agreements. Settlement generally occurs based upon the same performance metrics, vesting period, and performance period as our performance stock units.

The fair value of these awards is remeasured at each reporting period until the awards are settled. These awards are classified as liabilities and reported in accrued expenses and other long-term obligations within our consolidated balance sheet. As of September 30, 2022, the total remaining unrecognized compensation cost related to cash-settled performance-based share-based awards was $2.7 million, which is expected to be recognized over a weighted average period of 1.9 years.

Restricted Stock Units

During the nine-month periods ended September 30, 2022 and 2021, we granted restricted stock units to our non-employee directors representing 30,500 and 26,226 shares of our common stock, respectively. The expense recognized for restricted stock units is equal to the closing stock price on the date of grant, which is recognized over the vesting period. Restricted stock units granted to each director are subject to such director’s continued service through the vesting date, which is one year from the date of grant. As of September 30, 2022, the total remaining unrecognized compensation cost related to restricted stock units was $1.2 million, which will be recognized over the remaining vesting period.