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Incentive Plans (Tables) | 12 Months Ended
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Dec. 31, 2022
Share-Based Payment Arrangement [Abstract] |
Share-Based Plans, Amounts Recognized in the Financial Statements | Amounts recognized in the financial statements with respect to share-based plans are shown in the following table:
(Thousands of dollars) | 2022 |  | 2021 |  | 2020
Compensation charged against income before income tax benefit | $ | 74,587 |  |  | $ | 43,660 |  |  | $ | 24,812 |
Related income tax benefit recognized in income | 12,710 |  |  | 7,196 |  |  | 2,672 |
Changes in PSUs and RSUs Outstanding | Changes in PSUs outstanding for each of the last three years are presented in the following table.
(Number of stock units) | 2022 |  | 2021 |  | 2020
Outstanding at beginning of year | 2,670,756 |  |  | 2,207,429 |  |  | 2,129,733 |
Granted | 595,700 |  |  | 1,156,800 |  |  | 999,700 |
Vested and issued | (654,177) |  |  | (642,473) |  |  | (429,194) |
Forfeited | (463,812) |  |  | (51,000) |  |  | (492,810) |
Outstanding at end of year | 2,148,467 |  |  | 2,670,756 |  |  | 2,207,429 |
Changes in RSUs outstanding for each of the last three years are presented in the following table.
(Number of share units) | 2022 |  | 2021 |  | 2020
Outstanding at beginning of year | 1,451,438 |  |  | 1,383,043 |  |  | 1,535,080 |
Granted | 416,492 |  |  | 573,907 |  |  | 446,848 |
Vested and issued | (462,418) |  |  | (476,012) |  |  | (271,285) |
Forfeited | (177,720) |  |  | (29,500) |  |  | (327,600) |
Outstanding at end of year | 1,227,792 |  |  | 1,451,438 |  |  | 1,383,043 |
Assumptions used in Valuation of Performance Awards Granted | The assumptions used in the valuation of the performance awards granted in 2022, 2021 and 2020 are presented in the following table.
| 2022 |  | 2021 |  | 2020
Fair value per share at grant date | $37.77 - $47.37 |  | $16.03 |  | $21.51
Assumptions |  |  |  |  |
Expected volatility | 79.00% - 81.00% |  | 74.00% |  | 39.00%
Risk-free interest rate | 1.39% - 2.85% |  | 0.18% |  | 1.40%
Stock beta | 1.195 - 1.200 |  | 1.169 |  | 0.864
Expected life | 3.0 years |  | 3.0 years |  | 3.0 years
Schedule of Stock Unit Awards | The fair value of the time-based restricted stock units awarded in 2022, 2021 and 2020 are presented in the following table.
Type of Plan | Valuation Methodology |  | 2022 |  |  | 2021 |  | 2020
Non-Employee Directors 1 | Closing Stock Price at Grant Date |  | $32.84 |  |  | $13.14 - $23.58 |  | $22.59
Long-Term Incentive Plan, 2 | Average Low/High Stock Price at Grant Date |  | $29.80 - $49.86 |  |  | 12.30 |  | 21.68
1 Under the 2021 NED Plan, RSUs granted in 2021 are scheduled to vest in February 2022. 2 The RSUs granted under the 2012 Plan will vest on the fifth anniversary of the date of grant. The RSUs granted under the 2018 and 2020 Long-Term Plan generally vest on the third anniversary of the date of grant.
Changes in Stock Options Outstanding | Changes in stock options outstanding during the last three years are presented in the following table.
| Number of Shares |  | Average Exercise Price
Outstanding at December 31, 2019 | 2,920,410 |  |  | 43.93 |
Outstanding at Exercised | (47,000) |  |  | 17.57
Outstanding at Forfeited | (825,010) |  |  | 54.85
Outstanding at December 31, 2020 | 2,048,400 |  |  | 40.14
Exercised | (170,000) |  |  | 17.57
Forfeited | (558,900) |  |  | 52.61
Outstanding at December 31, 2021 | 1,319,500 |  |  | 37.77
Exercised | (760,500) |  |  | 23.29
Forfeited | (546,000) |  |  | 49.65
Outstanding at December 31, 2022 | 13,000 |  |  | 28.51
Exercisable at December 31, 2019 | 3,182,345 |  |  | 49.10
Exercisable at December 31, 2020 | 2,048,400 |  |  | 37.88
Exercisable at December 31, 2021 | 1,319,500 |  |  | 34.25
Exercisable at December 31, 2022 | 13,000 |  |  | 28.51
Additional Information about Stock Options Outstanding | Additional information about stock options outstanding at December 31, 2022 is shown below.
|  | Options Outstanding |  | Options Exercisable
Exercisable Price |  | No. of Options |  | Avg. Life Remaining in Years |  | Aggregate Intrinsic Value |  | No. of Options |  | Avg. Life Remaining in Years |  | Aggregate Intrinsic Value
28.51 |  | 13,000 |  |  | 1.1 |  | $ | 188,565 |  |  | 13,000 |  |  | 1.1 |  | $ | 188,565 |

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