17. STOCK-BASED COMPENSATION PLANS

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As of June 30, 2022, we had approximately 6 million shares remaining under the stock-based compensation plans available for grant. Option awards have a maximum contractual term of 10 years and generally must have an exercise price at least equal to the market price of our common stock on the date the option award is granted. Outstanding stock-based awards generally vest annually over a three-year period or in total at the end of a three-year period. Certain performance share unit awards vest in total at the end of a two-year period.

The compensation cost from continuing operations under the stock-based compensation plans for our Company and Huntsman International were as follows (dollars in millions):

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The total income tax benefit recognized in the condensed consolidated statements of operations for us and Huntsman International for stock-based compensation arrangements was $7 million and $1 million for the six months ended June 30, 2022 and 2021, respectively.

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Stock Options

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The fair value of each stock option award is estimated on the date of grant using the Black-Scholes valuation model that uses the assumptions noted in the following table. Expected volatilities are based on the historical volatility of our common stock through the grant date. The expected term of options granted was estimated based on the contractual term of the instruments and employees’ expected exercise and post-vesting employment termination behavior. The risk-free rate for periods within the contractual life of the option was based on the U.S. Treasury yield curve in effect at the time of grant. The assumptions noted below represent the weighted average of the assumptions utilized for stock options granted during the periods.

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A summary of stock option activity under the stock-based compensation plans as of June 30, 2022 and changes during the six months then ended is presented below:

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As of June 30, 2022, there was approximately $3 million of total unrecognized compensation cost related to nonvested stock option arrangements granted under the stock-based compensation plans. That cost is expected to be recognized over a weighted-average period of approximately 1.2 years. 

The total intrinsic value of stock options exercised during the six months ended June 30, 2022 and 2021 was approximately $12 million and $8 million, respectively. Cash received from stock options exercised during both of the six months ended June 30, 2022 and 2021 was approximately $6 million. The cash tax benefit from stock options exercised during both of the six months ended June 30, 2022 and 2021 was approximately $2 million.

Nonvested Shares

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Nonvested shares granted under the stock-based compensation plans consist of restricted stock and performance share unit awards, which are accounted for as equity awards, and phantom stock, which is accounted for as a liability award because it can be settled in either stock or cash. The fair value of each restricted stock and phantom stock award is estimated to be the closing stock price of Huntsman’s stock on the date of grant.

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We grant two types of performance share unit awards. For one type of performance share unit award, the performance criteria are total stockholder return of our common stock relative to the total stockholder return of a specified industry peer group for the three-year performance periods. The fair value of each performance share unit award is estimated using a Monte Carlo simulation model that uses various assumptions, including an expected volatility rate and a risk-free interest rate. For the six months ended June 30, 2022 and 2021 , the weighted-average expected volatility rate was 43.5% and 44.8%, respectively, and the weighted average risk-free interest rate was 1.67% and 0.2%, respectively. For the performance share unit awards granted during the six months ended June 30, 2022 and 2021, the number of shares earned varies based upon the Company achieving certain performance criteria over a three-year performance period.

During the first quarter of 2022, we began issuing a second type of performance award, which also includes a market condition. The performance criteria are our corporate free cash flow achieved relative to targets set by management, modified for the total stockholder return of our common stock relative to the total stockholder return of a specified industry peer group for the two-year performance period. The fair value of each performance share unit award is estimated using a Monte Carlo simulation model that uses various assumptions, including an expected volatility rate and a risk-free interest rate. For the six months ended  June 30, 2022, the weighted-average expected volatility rate was 37.9% and the weighted average risk-free interest rate was 1.43%. For the performance share unit awards granted during the six months ended June 30, 2022, the number of shares earned varies based upon the Company achieving certain performance criteria over a two-year performance period.

A summary of the status of our nonvested shares as of June 30, 2022 and changes during the six months then ended is presented below:

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As of June 30, 2022, there was approximately $54 million of total unrecognized compensation cost related to nonvested share compensation arrangements granted under the stock-based compensation plans. That cost is expected to be recognized over a weighted-average period of approximately 1.9 years. The value of share awards that vested during the six months ended June 30, 2022 and 2021 was approximately $32 million and $18 million, respectively.

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