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Incentive Plans (Tables)
 12 Months Ended
Dec. 31, 2021
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)
202120202019
Compensation charged against income (loss) before income tax benefit$43,660 24,812 50,170 
Related income tax benefit recognized in income7,196 2,672 7,389 
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)
202120202019
Outstanding at beginning of year2,207,429 2,129,733 1,660,417 
Granted1,156,800 999,700 957,600 
Vested and issued(642,473)(429,194)(331,917)
Forfeited(51,000)(492,810)(156,367)
Outstanding at end of year2,670,756 2,207,429 2,129,733 
Changes in RSUs outstanding for each of the last three years are presented in the following table.
(Number of share units)
202120202019
Outstanding at beginning of year1,383,043 1,535,080 1,538,854 
Granted573,907 446,848 409,692 
Vested and issued(476,012)(271,285)(275,738)
Forfeited(29,500)(327,600)(137,728)
Outstanding at end of year1,451,438 1,383,043 1,535,080 
Assumptions used in Valuation of Performance Awards Granted The assumptions used in the valuation of the performance awards granted in 2021, 2020 and 2019 are presented in the following table.
202120202019
Fair value per share at grant date$16.03$21.51$28.09
Assumptions
Expected volatility74.00%39.00%46.00%
Risk-free interest rate0.18%1.40%2.50%
Stock beta1.1690.8641.037
Expected life3.0 years3.0 years3.0 years
Schedule of Stock Unit Awards
The fair value of the time-based restricted stock units awarded in 2021, 2020 and 2019 are presented in the following table.
Type of PlanValuation Methodology202120202019
Non-Employee Directors1, 2
Closing Stock Price at Grant Date$
13.14 - 23.58
$22.59$21.68
Long-Term Incentive Plan3
Average High/Low Stock Price at Grant Date$12.30$21.68$28.16
1 Under the 2018 NED Plan, the RSUs granted in 2019 vest on the third anniversary of the date of grant and the RSUs granted in 2020 vest on the first anniversary of the date of grant. 
2 Under the 2021 NED Plan, RSUs granted in 2021 are scheduled to vest in February 2022.
3 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, 20183,994,595 $44.66 
Exercised(57,500)17.57 
Forfeited(1,016,685)48.29 
Outstanding at December 31, 20192,920,410 43.93 
Exercised(47,000)17.57 
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 
Exercisable at December 31, 20183,182,345 $49.10 
Exercisable at December 31, 20192,694,410 43.51 
Exercisable at December 31, 20202,048,400 37.88 
Exercisable at December 31, 20211,319,500 34.25 
Additional Information about Stock Options Outstanding
Additional information about stock options outstanding at December 31, 2021 is shown below.
Options OutstandingOptions Exercisable
Range of Exercise
Prices per Option		No. of
Options		Avg. Life
Remaining
in Years		Aggregate
Intrinsic
Value		No. of
Options		Avg. Life
Remaining
in Years		Aggregate
Intrinsic
Value
$17.00 to $30.99
773,500 1.6$3,097,563 773,500 1.6$3,097,563 
$31.00 to $50.99
546,000 0.1— 546,000 0.1— 
1,319,500 1.0$3,097,563 1,319,500 1.0$3,097,563