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Incentive Plans (Tables)
 12 Months Ended
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)
202220212020
Compensation charged against income before income tax benefit$74,587 $43,660 $24,812 
Related income tax benefit recognized in income12,710 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)
202220212020
Outstanding at beginning of year2,670,756 2,207,429 2,129,733 
Granted595,700 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 year2,148,467 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)
202220212020
Outstanding at beginning of year1,451,438 1,383,043 1,535,080 
Granted416,492 573,907 446,848 
Vested and issued(462,418)(476,012)(271,285)
Forfeited(177,720)(29,500)(327,600)
Outstanding at end of year1,227,792 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.
202220212020
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
1.1690.864
Expected life3.0 years3.0 years3.0 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 PlanValuation Methodology202220212020
Non-Employee Directors1
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
12.3021.68
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, 20192,920,410 43.93 
Outstanding at Exercised(47,000)17.57
Outstanding at Forfeited(825,010)54.85
Outstanding at December 31, 20202,048,400 40.14
Exercised(170,000)17.57
Forfeited(558,900)52.61
Outstanding at December 31, 20211,319,500 37.77
Exercised(760,500)23.29
Forfeited(546,000)49.65
Outstanding at December 31, 202213,000 28.51
Exercisable at December 31, 20193,182,345 49.10
Exercisable at December 31, 20202,048,400 37.88
Exercisable at December 31, 20211,319,500 34.25
Exercisable at December 31, 202213,000 28.51
Additional Information about Stock Options Outstanding
Additional information about stock options outstanding at December 31, 2022 is shown below.
Options OutstandingOptions Exercisable
Exercisable PriceNo. of
Options		Avg. Life
Remaining
in Years		Aggregate
Intrinsic
Value		No. of
Options		Avg. Life
Remaining
in Years		Aggregate
Intrinsic
Value
28.5113,000 1.1$188,565 13,000 1.1$188,565