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Incentive Plans (Tables)
12 Months Ended
Dec. 31, 2019
Disclosure of Compensation Related Costs, Share-based Payments [Abstract]  
Share-Based Plans, Amounts Recognized
Amounts recognized in the financial statements with respect to share-based plans are shown in the following table:
(Thousands of dollars)
2019
 
2018
 
2017
Compensation charged against income (loss) before income tax benefit
$
50,170

 
34,467

 
40,365

Related income tax benefit recognized in income
7,389

 
4,383

 
5,017


Fair Value of Option Award Estimated on Date of Grant using Black-Scholes Pricing Model

2019
 
2018
 
2017
Fair value per option grant
N/A
 
N/A
 
$7.96
Assumptions
 
 
 
 
 
Dividend yield
N/A
 
N/A
 
3.60%
Expected volatility
N/A
 
N/A
 
41.00%
Risk-free interest rate
N/A
 
N/A
 
1.97%
Expected life
N/A
 
N/A
 
5.30 years

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, 2016
5,757,435

 
$
48.46

Granted at FMV
603,000

 
28.51

Exercised

 

Forfeited
(1,459,166
)
 
49.34

Outstanding at December 31, 2017
4,901,269

 
45.74

Granted at FMV

 

Exercised
(72,000
)
 
17.57

Forfeited
(834,674
)
 
53.36

Outstanding at December 31, 2018
3,994,595

 
44.66

Granted at FMV

 

Exercised
(57,500
)
 
17.57

Forfeited
(1,016,685
)
 
48.29

Outstanding at December 31, 2019
2,920,410

 
43.93

Exercisable at December 31, 2016
3,830,535

 
$
53.80

Exercisable at December 31, 2017
3,197,269

 
54.22

Exercisable at December 31, 2018
3,182,345

 
49.10

Exercisable at December 31, 2019
2,694,410

 
43.51


Additional Information about Stock Options Outstanding
Additional information about stock options outstanding at December 31, 2019 is shown below.

 
Options Outstanding
 
Options 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
 
1,033,000

 
3.5
 
$
5,365,535

 
807,000

 
3.4
 
$
5,365,535

$31.00 to $50.99
 
730,000

 
2.1
 

 
730,000

 
2.1
 

$51.00 to $65.00
 
1,157,410

 
0.5
 

 
1,157,410

 
0.5
 


 
2,920,410

 
2.0
 
$
5,365,535

 
2,694,410

 
1.8
 
$
5,365,535


Changes in Performance-Based RSU Outstanding
Changes in PSUs outstanding for each of the last three years are presented in the following table.
(Number of stock units)
2019
 
2018
 
2017
Outstanding at beginning of year
1,660,417

 
1,187,921

 
992,573

Granted
957,600

 
905,500

 
560,000

Vested and issued
(331,917
)
 
(311,866
)
 
(272,725
)
Forfeited
(156,367
)
 
(121,138
)
 
(91,927
)
Outstanding at end of year
2,129,733

 
1,660,417

 
1,187,921


Assumptions used in Valuation of Performance Awards Granted The assumptions used in the valuation of the performance awards granted in 2019, 2018 and 2017 are presented in the following table.

2019
 
2018
 
2017
Fair value per share at grant date
$28.09
 
$22.99 - $30.56
 
$24.10 – $28.28
Assumptions
 
 
 
 
 
Expected volatility
46.00%
 
48.00%
 
47.00%
Risk-free interest rate
2.50%
 
2.30%
 
1.46%
Stock beta
1.037
 
1.103
 
1.058
Expected life
3.0 years
 
3.0 years
 
3.0 years

Changes in Time-Lapse Restricted Stock and Restricted Stock Units Outstanding
Changes in RSUs outstanding for each of the last three years are presented in the following table.
(Number of share units)
2019
 
2018
 
2017
Outstanding at beginning of year
1,538,854

 
1,035,980

 
923,282

Granted
409,692

 
823,803

 
419,720

Vested and issued
(275,738
)
 
(233,456
)
 
(217,633
)
Forfeited
(137,728
)
 
(87,473
)
 
(89,389
)
Outstanding at end of year
1,535,080

 
1,538,854

 
1,035,980