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Stock-Based Compensation | 12 Months Ended
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Dec. 31, 2022
Share-Based Payment Arrangement [Abstract] |
Stock-Based Compensation | Stock-Based Compensation The Company’s shareholder-approved stock-based incentive compensation plans provide for the granting of awards in the form of stock options, deferred stock, restricted stock or stock appreciation rights (“SARs”). The awards may be subject to the achievement of certain performance goals as determined by the Compensation Committee designated by the Company’s Board of Directors. There have been no awards of SARs. In April 2022, the Company's shareholders approved the 2022 Stock-Based Incentive Plan (the "Plan") which allowed for a total of 2.8 million shares to be issued under future awards. At December 31, 2022, there were 4.6 million authorized shares available for future awards. Restricted and Deferred Stock Annually, the Company awards shares of restricted stock to certain senior executives in the form of time-vesting restricted stock and performance-based shares. The time-vesting restricted stock vests ratably over three years. The performance-based share awards are subject to either a market condition or a performance condition. For awards subject to a market condition, the metric is the Company’s Total Shareholder Return (“TSR”), which includes share price appreciation and dividends paid, during the three-year term of the award measured against the TSR of a peer group of companies. For awards subject to a performance condition, the metric is the Company's average return on invested capital over the three-year term. The performance-based shares cliff vest at the end of three years. The number of performance-based shares that will ultimately vest is based on the level of performance achieved, ranging between 0% and 200% of the shares originally awarded, and is settled in shares of common stock. Participants who terminate employment because of disability, death or, subject to Company approval, retirement, receive accelerated vesting of their service condition to the date of termination and, if approved, performance restrictions laps on the original vesting date. The Company also issues shares of time-vesting restricted stock to U.S. employees and deferred stock to non-U.S. employees which vest ratably over three to five years. A summary of restricted and deferred stock activity follows:
| Number of shares
Non-vested shares outstanding at January 1, 2022 | 1,284,206 |
Awarded: |
Time-vesting | 190,442 |
Performance-based | 207,212 |
Released: |
Time-vesting | (348,062) |
Performance-based | (305,492) |
Forfeitures: |
Time-vesting | (73,188) |
Performance-based | (12,283) |
Non-vested shares outstanding at December 31, 2022 | 942,835 |
The average grant-date fair value of restricted stock awarded in 2022, 2021 and 2020 follows:
| 2022 |  | 2021 |  | 2020
Time-vesting | $ | 96.29 |  |  | $ | 100.08 |  |  | $ | 70.07 |
Performance-based | 111.84 |  |  | 100.99 |  |  | 72.08 |
The fair values of the performance-based awards that include a market condition were calculated using a Monte Carlo valuation model and the following weighted average assumptions:
| 2022 |  | 2021 |  | 2020
Risk-free interest rate | 1.0 | % |  | 0.2 | % |  | 1.6 | %
Expected term (years) | 3 |  | 3 |  | 3
Expected stock price volatility | 34.8 | % |  | 35.5 | % |  | 22.0 | %
At December 31, 2022, unrecognized compensation cost related to outstanding restricted and deferred stock was $42. The weighted average period over which the expense is expected to be recognized is 2.0 years. The aggregate market value of the shares released on the vesting dates was $70 in 2022.

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