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Capital Stock and Equity Compensation | 6 Months Ended
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Jun. 30, 2020
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 June 30, 2020, we had performance-based restricted stock units from 2020, 2019, and 2018 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 2020 and 2019:
| February 12, 2020 |  | June 3, 2019 |  | February 7, 2019
Expected volatility | 41.0% |  | 39.7% |  | 36.7%
Expected term (in years) | 2.9 |  | 2.6 |  | 2.9
Risk-free interest rate | 1.41% |  | 1.78% |  | 2.43%
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 six months ended June 30, 2020 is presented below:
| Performance-Based Restricted Stock Units
Awards outstanding as of December 31, 2019 | 106,943 |
Awards granted | 87,244 |
Stock issued | (75,486) |
Awards forfeited | (4,962) |
Awards outstanding as of June 30, 2020 | 113,739 |
We recognized $1.3 million and $1.1 million of compensation expense for performance-based restricted stock units for the three months ended June 30, 2020 and 2019, respectively. We recognized $2.7 million and $2.0 million of compensation expense for performance-based restricted stock units for the six months ended June 30, 2020 and 2019, respectively. Time-Based Restricted Stock Units As of June 30, 2020, we had time-based restricted stock unit awards from 2020, 2019, 2018 and 2017 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 six months ended June 30, 2020 is presented below:
| Time-Based Restricted Stock Units
Awards outstanding as of December 31, 2019 | 101,685 |
Awards granted | 58,042 |
Stock issued | (47,197) |
Awards forfeited | (3,585) |
Awards outstanding as of June 30, 2020 | 108,945 |
We recognized $1.5 million and $1.4 million of compensation expense for time-based restricted stock units for the three months ended June 30, 2020 and 2019, respectively. We recognized $3.1 million and $2.9 million of compensation expense for time-based restricted stock units for the six months ended June 30, 2020 and 2019, 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 six months ended June 30, 2020 is presented below:
| Deferred Stock Units
Awards outstanding as of December 31, 2019 | 7,150 |
Awards granted | 9,400 |
Stock issued | (5,100) |
Awards outstanding as of June 30, 2020 | 11,450 |
We recognized $1.0 million of compensation expense related to deferred stock units for the three and six months ended June 30, 2020, and $1.1 million of compensation expense for the three and six months ended June 30, 2019.

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- Definition The entire disclosure for share-based payment arrangement. + 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 + Details
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