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Incentive Plans (Tables) | 12 Months Ended
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Dec. 31, 2020
Share-based Payment Arrangement [Abstract] |
Summary of Amounts Recognized in Financial Statements with Respect to Share-Based Plans | Amounts recognized in the financial statements by the Company with respect to all share-based plans are shown in the following table.
|  | Years Ended December 31,
(Millions of dollars) |  | 2020 |  | 2019 |  | 2018
Compensation charged against income before income tax benefit |  | $ | 14.3 |  |  | $ | 10.5 |  |  | $ | 9.2 |
Related income tax benefit recognized in income |  | $ | 3.0 |  |  | $ | 2.2 |  |  | $ | 1.9 |
Summary of Valuation Assumptions | Following are the assumptions used by the Company to value the original awards:
| Years Ended December 31,
| 2020 |  | 2019 |  | 2018
Fair value per option grant | $ | 28.28 |  |  | $ | 20.48 |  |  | $ | 17.32 |
Assumptions |  |  |  |  |
Dividend yield | — |  |  | — |  |  | — |
Expected volatility | 28.1 | % |  | 26.8 | % |  | 27.0 | %
Risk-free interest rate | 1.5 | % |  | 2.5 | % |  | 2.4 | %
Expected life (years) | 4.7 |  | 4.5 |  | 3.9
Stock price at valuation date | $ | 106.72 |  |  | $ | 76.15 |  |  | $ | 71.00 |
Summary of Changes in Stock Options Outstanding | Changes in options outstanding for Company employees during the period from December 31, 2019 to December 31, 2020 are presented in the following table:
Options | Number of Shares |  | Weighted Average Exercise Price |  | Weighted Average Remaining Contractual Term (Years) |  | Aggregate Intrinsic Value (Millions of Dollars)
Outstanding at December 31, 2019 | 392,300 |  |  | 68.52 |  |  |  |  |
Granted | 79,200 |  |  | 105.57 |  |  |  |  |
Exercised | (148,800) |  |  | 64.21 |  |  |  |  |
Outstanding at December 31, 2020 | 322,700 |  |  | $ | 79.60 |  |  | 4.6 |  | $ | 16.5 |
Exercisable at December 31, 2020 | 110,700 |  |  | $ | 66.91 |  |  | 3.3 |  | $ | 7.1 |
Summary of Additional Stock Option Information | Additional information about stock options outstanding at December 31, 2020 is shown below:
|  | Options Outstanding | Options Exercisable
Range of Exercise Prices per Option |  | No. of Options |  | Avg. Life Remaining in Years |  | No. of Options |  | Avg. Life Remaining in Years |
$50.00 to $59.99 |  | 7,300 |  |  | 2.1 |  | 7,300 |  |  | 2.1 |
$60.00 to $69.99 |  | 69,500 |  |  | 3.1 |  | 69,500 |  |  | 3.1 |
$70.00 to $79.99 |  | 166,700 |  |  | 4.6 |  | 33,900 |  |  | 3.9 |
$80.00 to $89.99 |  | 3,600 |  |  | 6.2 |  | — |  |  |  |
$100.00 to $109.99 |  | 75,600 |  |  | 6.1 |  | — |  |  |  |
|  | 322,700 |  |  | 4.6 |  | 110,700 |  |  | 3.3 |
Summary of Restricted Stock Unit Activity | Changes in restricted stock units outstanding for Company employees during the period from December 31, 2019 to December 31, 2020 are presented in the following table:
Employee RSUs | Number of units |  | Weighted Average Grant Date Fair Value |  | Total Fair Value (Millions of Dollars)
Outstanding at December 31, 2019 | 198,915 |  |  | $ | 70.58 |  |  |
Granted | 55,734 |  |  | $ | 90.09 |  |  |
Vested and issued | (59,324) |  |  | $ | 66.31 |  |  | $ | 6.4 |
Forfeited | (12,530) |  |  | $ | 78.43 |  |  |
Outstanding at December 31, 2020 | 182,795 |  |  | $ | 77.38 |  |  | $ | 23.9 |
Changes in performance-based restricted stock units outstanding for Company employees during the period from December 31, 2019 to December 31, 2020 are presented in the following table:
Employee PSU's | Number of Units |  | Weighted Average Grant Date Fair Value |  | Total Fair Value (Millions of Dollars)
Outstanding at December 31, 2019 | 131,200 |  |  | $ | 82.98 |  |  |
Granted | 64,290 |  |  | $ | 122.95 |  |  |
Vested and issued | (65,745) |  |  | $ | 85.04 |  |  | $ | 7.0 |
Forfeited | (405) |  |  | $ | 65.75 |  |  |
Outstanding at December 31, 2020 | 129,340 |  |  | $ | 97.01 |  |  | $ | 16.9 |
Changes in restricted stock units outstanding for Company non-employee directors during the period from December 31, 2019 to December 31, 2020 are presented in the following table:
Director RSU's | Number of Units |  | Weighted Average Grant Date Fair Value |  | Total Fair Value (Millions of Dollars)
Outstanding at December 31, 2019 | 33,607 |  |  | $ | 70.68 |  |  |
Granted | 9,801 |  |  | $ | 105.33 |  |  |
Vested and issued | (12,404) |  |  | $ | 66.01 |  |  | $ | 1.3 |
Outstanding at December 31, 2020 | 31,004 |  |  | $ | 83.31 |  |  | $ | 4.1 |

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