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Capital Stock and Equity Compensation | 9 Months Ended
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Sep. 30, 2023
Share-Based Payment Arrangement, Noncash Expense [Abstract] |
Capital Stock and Equity Compensation | Capital Stock and Equity Compensation Equity Compensation Performance-Based Restricted Stock Units As of September 30, 2023, we had performance-based restricted stock units from 2023 and 2021 outstanding. These awards generally cliff vest at the end of a three-year measurement period. However, employees whose employment terminates during the measurement period due to death, disability, or, in certain cases, retirement may receive a pro-rata payout based on the number of days they were employed during the measurement period. Participants are eligible to be awarded shares ranging from 0% to 200% of the original award amount, based on certain defined performance measures. The outstanding awards have one measurement criterion: the three-year total shareholder return (TSR) on our capital stock as compared to that of a specified group of peer companies. The TSR measurement criterion of the awards is considered a market condition. As such, the fair value of this measurement criterion was determined on the grant date using a Monte Carlo simulation valuation model. We recognize compensation expense on all of these awards on a straight-line basis over the vesting period with no changes for final projected payout of the awards. We account for forfeitures as they occur. The following table sets forth the assumptions used in the Monte Carlo calculation for each material award granted in 2023:
| February 9, 2023
Expected volatility | 53.2%
Expected term (in years) | 2.9
Risk-free interest rate | 4.08%
Expected volatility – In determining expected volatility, we have considered a number of factors, including historical volatility. Expected term – We use the vesting period of the award to determine the expected term assumption for the Monte Carlo simulation valuation model. Risk-free interest rate – We use an implied “spot rate” yield on U.S. Treasury Constant Maturity rates as of the grant date for our assumption of the risk-free interest rate. Expected dividend yield – We do not currently pay dividends on our capital stock; therefore, a dividend yield of 0% was used in the Monte Carlo simulation valuation model. A summary of activity of the outstanding performance-based restricted stock units for the nine months ended September 30, 2023 is presented below:
| Performance-Based Restricted Stock Units
Awards outstanding as of December 31, 2022 | 65,513 |
Awards granted | 50,551 |
Stock issued | (8,775) |
Awards cancelled | (31,943) |
Awards outstanding as of September 30, 2023 | 75,346 |
We recognized $1.3 million and $1.1 million of compensation expense for performance-based restricted stock units for the three months ended September 30, 2023 and 2022, respectively. We recognized $2.6 million and $3.3 million of compensation expense for performance-based restricted stock units for the nine months ended September 30, 2023 and 2022, respectively. Time-Based Restricted Stock Units As of September 30, 2023, we had time-based restricted stock unit awards from 2023, 2022, 2021 and 2020 outstanding. The outstanding awards all ratably vest on the first, second and third anniversaries of the original grant date. However, employees whose employment terminates during the measurement period due to death, disability, or, in certain cases, retirement may receive a pro-rata payout based on the number of days they were employed subsequent to the last grant anniversary date. Each time-based restricted stock unit represents a right to receive one share of Rogers’ capital stock at the end of the vesting period. The fair value of the award is determined by the market value of the underlying stock price at the grant date. We recognize compensation expense on all of these awards on a straight-line basis over the vesting period. We account for forfeitures as they occur. A summary of activity of the outstanding time-based restricted stock units for the nine months ended September 30, 2023 is presented below:
| Time-Based Restricted Stock Units
Awards outstanding as of December 31, 2022 | 124,284 |
Awards granted | 67,094 |
Stock issued | (43,254) |
Awards cancelled | (24,296) |
Awards outstanding as of September 30, 2023 | 123,828 |
We recognized $2.5 million and $2.4 million of compensation expense for time-based restricted stock units for the three months ended September 30, 2023 and 2022, respectively. We recognized $7.1 million and $7.0 million of compensation expense for time-based restricted stock units for the nine months ended September 30, 2023 and 2022, respectively. Deferred Stock Units We grant deferred stock units to non-management directors. These awards are fully vested on the date of grant and the related shares are generally issued on the 13-month anniversary of the grant date unless the individual elects to defer the receipt of those shares. Each deferred stock unit results in the issuance of one share of Rogers’ capital stock. The grant of deferred stock units is typically done annually during the second quarter of each year. The fair value of the award is determined by the market value of the underlying stock price at the grant date. A summary of activity of the outstanding deferred stock units for the nine months ended September 30, 2023 is presented below:
| Deferred Stock Units
Awards outstanding as of December 31, 2022 | 6,850 |
Awards granted | 8,100 |
Stock issued | (6,850) |
Awards outstanding as of September 30, 2023 | 8,100 |
We recognized no compensation expense for deferred stock units for the three months ended September 30, 2023 and 2022, respectively. We recognized $1.2 million and $1.3 million of compensation expense for the nine months ended September 30, 2023, and 2022, respectively.

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