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Stock-based Compensation (Tables) | 12 Months Ended
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Dec. 31, 2021
Share-based Compensation Arrangement by Share-based Payment Award |
Share-based Payment Arrangement, Cost by Plan | The following table summarizes stock-based compensation costs for the years ended December 31, 2021, 2020, and 2019. .
| Year Ended December 31
Millions of dollars | 2021 | 2020 | 2019
Stock-based compensation cost | $ | 214 |  | $ | 218 |  | $ | 257 |
Tax benefit | (32) |  | (35) |  | (48) |
Stock-based compensation cost, net of tax | $ | 182 |  | $ | 183 |  | $ | 209 |
Stock Options |
Share-based Compensation Arrangement by Share-based Payment Award |
Share-based Payment Arrangement, Option, Activity | The following table represents our stock options activity during 2021.
| Number of Shares (in millions) | Weighted Average Exercise Price per Share | Weighted Average Remaining Contractual Term (years) | Aggregate Intrinsic Value (in millions)
Outstanding at January 1, 2021 | 25.9 |  | $ | 40.36 |  |  |
Exercised | (0.1) |  | 23.88 |  |  |
Forfeited/expired | (1.6) |  | 41.54 |  |  |
Outstanding at December 31, 2021 | 24.2 |  | $ | 40.42 |  | 4.6 | $ | 0.5 |
Exercisable at December 31, 2021 | 21.3 |  | $ | 42.53 |  | 4.2 | $ | 0.3 |
Schedule of Share-based Payment Award, Stock Options, Valuation Assumptions | The assumptions and resulting fair values of options granted were as follows:
| Year Ended December 31
| 2021 | 2020 | 2019
Expected term (in years) | 0.00 | 5.39 | 5.31
Expected volatility | — | 33% | 31%
Expected dividend yield | — | 2.92 - 3.23% | 2.25 - 3.88%
Risk-free interest rate | — | 1.43 - 1.69% | 1.35 - 2.51%
Weighted average grant-date fair value of option | — | $5.41 | $5.91
There were no stock options granted for the year ended December 31, 2021.
Restricted Stock |
Share-based Compensation Arrangement by Share-based Payment Award |
Schedule of Share-based Payment Award, Stock Options, Valuation Assumptions | The following table represents our restricted stock awards and restricted stock units granted, vested, and forfeited during 2021. .
| Number of Shares (in millions) | Weighted Average Grant-Date Fair Value per Share
Nonvested shares at January 1, 2021 | 19.0 |  | $ | 26.32 |
Granted | 9.6 |  | 20.94 |
Vested | (5.4) |  | 30.29 |
Forfeited | (0.5) |  | 28.32 |
Nonvested shares at December 31, 2021 | 22.7 |  | $ | 23.16 |
Employee Stock Purchase Plan |
Share-based Compensation Arrangement by Share-based Payment Award |
Schedule of Share-based Payment Award, Stock Options, Valuation Assumptions | The assumptions and resulting fair values were as follows:
| Year Ended December 31
| 2021 | 2020 | 2019
Expected volatility | 69 | % | 68 | % | 34 | %
Expected dividend yield | 0.84 | % | 4.89 | % | 3.06 | %
Risk-free interest rate | 0.05 | % | 0.65 | % | 2.20 | %
Weighted average grant-date fair value per share | $ | 5.01 |  | $ | 3.18 |  | $ | 5.22 |

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- Definition Tabular disclosure for stock option plans. Includes, but is not limited to, outstanding awards at beginning and end of year, grants, exercises, forfeitures, and weighted-average grant date fair value. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (d) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (e) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (c)(1) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 + Details
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- Definition Tabular disclosure of the significant assumptions used during the year to estimate the fair value of stock options, including, but not limited to: (a) expected term of share options and similar instruments, (b) expected volatility of the entity's shares, (c) expected dividends, (d) risk-free rate(s), and (e) discount for post-vesting restrictions. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (f)(2) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 + Details
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