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Stock compensation plans (Tables) | 12 Months Ended
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Dec. 31, 2020
Share-based Payment Arrangement, Noncash Expense [Abstract] |
Summary of Share-based Compensation Activity | The following table summarizes the share-based compensation activity:
| 2020 |  | 2019 |  | 2018
| (Dollars in millions)
Share-based compensation expense | $ | 20.7 |  |  | $ | 26.9 |  |  | $ | 22.4 |
Total income tax benefit recognized for share-based compensation arrangements | 22.0 |  |  | 21.1 |  |  | 20.7 |
Net excess tax benefit | 17.5 |  |  | 15.4 |  |  | 15.9 |
Weighted-Average Assumptions used to Estimate Fair Value of Options Granted | The fair value of options granted in 2020, 2019 and 2018 was estimated at the date of grant using a Black-Scholes option pricing model. The following weighted-average assumptions were used:
| 2020 |  | 2019 |  | 2018
Risk-free interest rate | 1.16 | % |  | 2.44 | % |  | 2.67 | %
Expected life of option | 5.00 years |  | 4.99 years |  | 4.98 years
Expected dividend yield | 0.39 | % |  | 0.47 | % |  | 0.54 | %
Expected volatility | 23.98 | % |  | 23.92 | % |  | 22.65 | %
Summary of Stock Option Activity | The following table summarizes the option activity during 2020:
| Shares Subject to Options |  | Weighted Average Exercise Price |  | Weighted Average Remaining Contractual Life In Years |  | Aggregate Intrinsic Value
Outstanding, beginning of the year | 1,325,532 |  |  | $ | 161.91 |  |  |  |  |
Granted | 130,206 |  |  | 347.64 |  |  |  |  |
Exercised | (289,324) |  |  | 106.79 |  |  |  |  |
Forfeited or expired | (9,099) |  |  | 290.49 |  |  |  |  |
Outstanding, end of the year | 1,157,315 |  |  | 195.57 |  |  | 5.71 |  | $ | 249,979 |
Exercisable, end of the year | 903,680 |  |  | $ | 163.27 |  |  | 4.94 |  | $ | 224,388 |
Weighted-Average Assumptions used to Estimate Fair Value of Non-Vested Shares Granted | The following weighted-average assumptions were used:
| 2020 |  | 2019 |  | 2018
Risk-free interest rate | 1.07 | % |  | 2.41 | % |  | 2.41 | %
Expected dividend yield | 0.38 | % |  | 0.46 | % |  | 0.53 | %
Summary of Non-Vested Restricted Stock Unit Activity | The following table summarizes the non-vested restricted stock unit activity during 2020:
| Number of Non-Vested Shares |  | Weighted Average Grant-Date Fair Value |  | Weighted Average Remaining Contractual Life |  | Aggregate Intrinsic Value
Outstanding, beginning of the year | 177,348 |  |  | $ | 240.17 |  |  |  |  |
Granted | 52,464 |  |  | 344.70 |  |  |  |  |
Vested | (67,851) |  |  | 195.95 |  |  |  |  |
Forfeited | (10,718) |  |  | 285.37 |  |  |  |  |
Outstanding, end of the year | 151,243 |  |  | $ | 293.06 |  |  | 1.2 |  | $ | 62,236 |

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- Definition Tabular disclosure of allocation of amount expensed and capitalized for award under share-based payment arrangement to statement of income or comprehensive income and statement of financial position. Includes, but is not limited to, corresponding line item in financial statement. + 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 (h)(1) -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 S99 -Paragraph 1 -Subparagraph (SAB Topic 14.F) -URI http://asc.fasb.org/extlink&oid=115993241&loc=d3e301413-122809 Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 1 -Subparagraph (b) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5047-113901 + Details
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- Definition Tabular disclosure of the changes in outstanding nonvested restricted stock units. + 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 (c)(2) -URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901 + Details
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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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