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Stock-based Compensation (Tables) | 9 Months Ended
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Sep. 30, 2020
Stock-based compensation [Abstract] |
Stock-Based Compensation | Information regarding stock-based compensation appears in the table below:
| Three Months Ended |  | Nine Months Ended
| September 30, |  | September 30,
Millions | 2020 | 2019 |  | 2020 | 2019
Stock-based compensation, before tax: |  |  |  |  |  |  |  |  |
Stock options | $ | 4 | $ | 5 |  | $ | 12 | $ | 14
Retention awards |  | 13 |  | 19 |  |  | 45 |  | 61
Total stock-based compensation, before tax | $ | 17 | $ | 24 |  | $ | 57 | $ | 75
Excess tax benefits from equity compensation plans | $ | 16 | $ | 3 |  | $ | 51 | $ | 48
Stock Options Weight Average Assumptions | The table below shows the annual weighted-average assumptions used for valuation purposes:
Weighted-Average Assumptions | 2020 | 2019
Risk-free interest rate |  | 1.5% |  | 2.5%
Dividend yield |  | 2.1% |  | 2.2%
Expected life (years) |  | 4.9 |  | 5.2
Volatility |  | 23.4% |  | 22.7%
Weighted-average grant-date fair value of options granted | $ | 32.20 | $ | 30.37
Stock Options Activity | A summary of stock option activity during the nine months ended September 30, 2020, is presented below:
| Options (thous.) | Weighted-Average ‎Exercise Price | Weighted-Average Remaining Contractual Term | Aggregate Intrinsic Value (millions)
Outstanding at January 1, 2020 | 3,502 | $ | 113.38 | 6.1 | yrs. | $ | 236
Granted | 558 |  | 176.63 |  | N/A |  | N/A
Exercised | (1,271) |  | 101.56 |  | N/A |  | N/A
Forfeited or expired | (38) |  | 161.13 |  | N/A |  | N/A
Outstanding at September 30, 2020 | 2,751 | $ | 131.01 | 6.6 | yrs. | $ | 181
Vested or expected to vest at September 30, 2020 | 2,718 | $ | 130.61 | 6.6 | yrs. | $ | 180
Options exercisable at September 30, 2020 | 1,637 | $ | 110.85 | 5.4 | yrs. | $ | 141
Stock Option Exercises | Additional information regarding stock option exercises appears in the following table:
| Three Months Ended |  | Nine Months Ended
| September 30, |  | September 30,
Millions | 2020 | 2019 |  | 2020 | 2019
Intrinsic value of stock options exercised | $ | 40 | $ | 10 |  | $ | 105 | $ | 174
Cash received from option exercises |  | 29 |  | 10 |  |  | 80 |  | 108
Treasury shares repurchased for employee taxes |  | (8) |  | (3) |  |  | (20) |  | (32)
Tax benefit realized from option exercises |  | 11 |  | 3 |  |  | 25 |  | 43
Aggregate grant-date fair value of stock options vested |  | - |  | - |  |  | 14 |  | 15
Retention Awards Activity | Changes in our retention awards during the nine months ended September 30, 2020, were as follows:
| Shares ‎(thous.) | Weighted-Average ‎Grant-Date Fair Value
Nonvested at January 1, 2020 | 1,898 | $ | 112.12
Granted | 305 |  | 185.99
Vested | (634) |  | 76.89
Forfeited | (68) |  | 140.94
Nonvested at September 30, 2020 | 1,501 | $ | 140.71
Performance Retention Awards Present Value Calculation Assumptions | The assumptions used to calculate the present value of estimated future dividends related to the February 2020 grant were as follows:
| 2020
Dividend per share per quarter | $ | 0.97
Risk-free interest rate at date of grant |  | 1.4%
Performance Based Units Activity | Changes in our performance retention awards during the nine months ended September 30, 2020, were as follows:
| Shares ‎(thous.) | Weighted-Average ‎Grant-Date Fair Value
Nonvested at January 1, 2020 | 929 | $ | 123.32
Granted | 287 |  | 166.63
Vested | (339) |  | 102.79
Unearned | (8) |  | 150.42
Forfeited | (55) |  | 143.12
Nonvested at September 30, 2020 | 814 | $ | 145.54

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