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Share-based Payments (Tables) | 12 Months Ended
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Aug. 31, 2022
Share-Based Payment Arrangement [Abstract] |
Schedule of Share-based Compensation Recognized | Compensation expense recognized related to the awards under the current and prior equity incentive plans during the periods presented is summarized as follows (in millions):
| Year Ended August 31,
| 2022 |  | 2021 |  | 2020
Restricted stock awards and units | $ | 17.2 |  |  | $ | 15.1 |  |  | $ | 24.6 |
Stock options | 8.8 |  |  | 9.2 |  |  | 4.9 |
Performance stock units | 9.9 |  |  | 6.8 |  |  | 7.3 |
Director stock units | 1.5 |  |  | 1.4 |  |  | 1.4 |
Total share-based payment expense | $ | 37.4 |  |  | $ | 32.5 |  |  | $ | 38.2 |
Schedule of Restricted Stock Award Activity | Activity related to restricted stock awards during the periods presented was as follows (in millions, except per share data):
| Number of Shares |  | Weighted Average Grant Date Fair Value Per Share
Outstanding at August 31, 2019 | 0.4 |  | $ | 156.32 |
Granted | 0.2 |  | $ | 122.10 |
Vested | (0.1) |  | $ | 171.92 |
Forfeited | (0.1) |  | $ | 135.43 |
Outstanding at August 31, 2020 | 0.4 |  | $ | 134.68 |
Granted | 0.2 |  | $ | 108.79 |
Vested | (0.1) |  | $ | 150.44 |
Forfeited | (0.1) |  | $ | 116.33 |
Outstanding at August 31, 2021 | 0.4 |  | $ | 116.77 |
Granted | 0.1 |  | $ | 204.36 |
Vested | (0.1) |  | $ | 122.27 |
Forfeited | (0.1) |  | $ | 131.08 |
Outstanding at August 31, 2022 | 0.3 |  | $ | 144.51 |
Schedule of Stock Options, Weighted Average Assumptions | The following weighted average assumptions were used to estimate the fair value of the stock options granted in the fiscal years presented:
|  | Market Options |  |  |  | Service Options
|  | 2021 |  | 2020 |  |  |  | 2020
Dividend yield |  | 0.5% |  | 0.4% |  |  |  | 0.4%
Expected volatility |  | 36.5% |  | 33.7% |  |  |  | 33.7%
Risk-free interest rate |  | 0.7% |  | 1.5% |  |  |  | 1.3%
Expected life of options |  | 8 years |  | 7 years |  |  |  | 5 years
Weighted-average fair value of options |  | $40.45 |  | $44.74 |  |  |  | $34.22
Schedule of Stock Option Transactions | Stock option activity during the periods presented was as follows:
| Outstanding |  | Exercisable
| Number of Options (in millions) |  | Weighted Average Exercise Price |  | Number of Options (in millions) |  | Weighted Average Exercise Price
Outstanding at August 31, 2019 | 0.4 |  | $ | 146.70 |  |  | 0.3 |  | $ | 147.51 |
Granted | 0.5 |  | $ | 121.87 |  |  |  |  |
Exercised | — | * | $ | 116.36 |  |  |  |  |
Outstanding at August 31, 2020 | 0.9 |  | $ | 133.19 |  |  | 0.4 |  | $ | 151.07 |
Granted | 0.3 |  | $ | 108.96 |  |  |  |  |
Exercised | — | * | $ | 108.58 |  |  |  |  |
Outstanding at August 31, 2021 | 1.2 |  | $ | 127.98 |  |  | 0.5 |  | $ | 142.36 |
Exercised | (0.1) |  | $ | 88.94 |  |  |  |  |
Outstanding at August 31, 2022 | 1.1 |  | $ | 132.50 |  |  | 0.6 |  | $ | 143.15 |
Range of option exercise prices: |  |  |  |  |  |  |
$100.00 - $160.00 (average life - 7.1 years) | 0.9 |  | $ | 119.32 |  |  | 0.5 |  | $ | 122.70 |
$160.01 - $210.00 (average life - 3.2 years) | 0.1 |  | $ | 207.80 |  |  | 0.1 |  | $ | 207.80 |
$210.01 - $239.76 (average life - 4.1 years) | 0.1 |  | $ | 239.76 |  |  | 0.1 |  | $ | 239.76 |
___________________________ * Represents amounts of less than 0.1 million.

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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 https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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- Definition Tabular disclosure of the number and weighted-average grant date fair value for restricted stock units that were outstanding at the beginning and end of the year, and the number of restricted stock units that were granted, vested, or forfeited during the year. + 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)(1) -URI https://asc.fasb.org/extlink&oid=128089324&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 https://asc.fasb.org/extlink&oid=128089324&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 https://asc.fasb.org/extlink&oid=128089324&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 https://asc.fasb.org/extlink&oid=128089324&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 https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901 + Details
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