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Stock-based Compensation (Tables) | 12 Months Ended
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Dec. 31, 2020
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, 2020, 2019 and 2018.
| Year Ended December 31
Millions of dollars | 2020 | 2019 | 2018
Stock-based compensation cost | $ | 218 |  | $ | 257 |  | $ | 274 |
Tax benefit | (35) |  | (48) |  | (51) |
Stock-based compensation cost, net of tax | $ | 183 |  | $ | 209 |  | $ | 223 |
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 2020.
| 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, 2020 | 25.3 |  | $ | 41.58 |  |  |
Granted | 2.2 |  | 24.59 |  |  |
Forfeited/expired | (1.6) |  | 37.87 |  |  |
Outstanding at December 31, 2020 | 25.9 |  | $ | 40.36 |  | 5.4 | $ | — |
Exercisable at December 31, 2020 | 19.7 |  | $ | 44.29 |  | 4.5 | $ | — |
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
| 2020 | 2019 | 2018
Expected term (in years) | 5.39 | 5.31 | 5.27
Expected volatility | 33% | 31% | 28%
Expected dividend yield | 2.92 - 3.23% | 2.25 - 3.88% | 1.37 - 2.29%
Risk-free interest rate | 1.43 - 1.69% | 1.35 - 2.51% | 2.27 - 2.84%
Weighted average grant-date fair value of option | $5.41 | $5.91 | $11.56
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 2020.
| Number of Shares (in millions) | Weighted Average Grant-Date Fair Value per Share
Nonvested shares at January 1, 2020 | 18.1 |  | $ | 34.72 |
Granted | 8.2 |  | 16.53 |
Vested | (5.4) |  | 36.97 |
Forfeited | (1.9) |  | 33.66 |
Nonvested shares at December 31, 2020 | 19.0 |  | $ | 26.26 |
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
| 2020 | 2019 | 2018
Expected volatility | 68 | % | 34 | % | 25 | %
Expected dividend yield | 4.89 | % | 3.06 | % | 1.62 | %
Risk-free interest rate | 0.65 | % | 2.20 | % | 1.92 | %
Weighted average grant-date fair value per share | $ | 3.18 |  | $ | 5.22 |  | $ | 8.86 |

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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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