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Share-based Payments (Tables) | 12 Months Ended
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Aug. 31, 2024
Share-Based Payment Arrangement [Abstract] |
Schedule of Share-based Compensation Recognized | Compensation expense recognized related to our share-based payment awards during the periods presented is summarized as follows (in millions):
| Year Ended August 31,
| 2024 |  | 2023 |  | 2022
Restricted stock awards and units | $ | 23.9 |  |  | $ | 19.6 |  |  | $ | 17.2 |
Performance stock units | 18.6 |  |  | 15.2 |  |  | 9.9 |
Stock options | 2.6 |  |  | 5.7 |  |  | 8.8 |
Director stock units | 1.5 |  |  | 1.5 |  |  | 1.5 |
Total share-based payment expense | $ | 46.6 |  |  | $ | 42.0 |  |  | $ | 37.4 |
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, 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 |
Granted | 0.2 |  | $ | 175.23 |
Vested | (0.1) |  | $ | 140.85 |
Forfeited | (0.1) |  | $ | 163.37 |
Outstanding at August 31, 2023 | 0.3 |  | $ | 159.33 |
Granted | 0.2 |  | $ | 168.74 |
Vested | (0.2) |  | $ | 153.74 |
Forfeited | — | * | $ | 154.90 |
Outstanding at August 31, 2024 | 0.3 |  | $ | 167.39 |
___________________________ * Represents shares of less than 0.1 million.
Schedule of the Weighted Average Assumptions Used to Estimate Fair Value of Stock Options |
|  | 2024 |  | 2023 |  |  |  |
Dividend yield |  | —% |  | —% |  |  |  |
Expected volatility |  | 34.6% |  | 46.7% |  |  |  |
Risk-free interest rate |  | 4.9% |  | 4.5% |  |  |  |
Fair value of awards |  | $241.39 |  | $254.19 |  |  |  |
The following weighted average assumptions were used to estimate the fair value of the stock options granted in the fiscal year presented:
|  | Market Options |  |  |  |
|  | 2021 |  |  |  |  |  |
Dividend yield |  | 0.5% |  |  |  |  |  |
Expected volatility |  | 36.5% |  |  |  |  |  |
Risk-free interest rate |  | 0.7% |  |  |  |  |  |
Expected life of options |  | 8 years |  |  |  |  |  |
Weighted-average fair value of options |  | $40.45 |  |  |  |  |  |
Schedule of Performance Shares Outstanding Activity and Weighted Average Assumptions Used to Estimate Fair Value | Activity related to performance stock units 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, 2021 | 0.2 |  | $ | 109.99 |
Granted | — | * | $ | 207.02 |
Forfeited | — | * | $ | 113.51 |
Outstanding at August 31, 2022 | 0.2 |  | $ | 145.46 |
Granted | 0.1 |  | $ | 186.78 |
Vested | (0.1) |  | $ | 124.29 |
Forfeited | — | * | $ | 195.67 |
Outstanding at August 31, 2023 | 0.2 |  | $ | 171.01 |
Granted | 0.2 |  | $ | 172.98 |
Vested | (0.1) |  | $ | 91.36 |
Outstanding at August 31, 2024 | 0.3 |  | $ | 186.66 |
___________________________ * Represents shares of less than 0.1 million.
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, 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 |
Exercised | — | * | $ | 126.92 |  |  |  |  |
Forfeitures | (0.1) |  | $ | 227.15 |  |  |  |  |
Outstanding at August 31, 2023 | 1.0 |  | $ | 131.81 |  |  | 0.9 |  | $ | 135.91 |
Exercised | (0.1) |  | $ | 143.92 |  |  |  |  |
Outstanding at August 31, 2024 | 0.9 |  | $ | 130.74 |  |  | 0.9 |  | $ | 132.48 |
Range of option exercise prices: |  |  |  |  |  |  |
$100.00 - $160.00 (average life - 5.5 years) | 0.8 |  | $ | 118.70 |  |  | 0.8 |  | $ | 119.58 |
$160.01 - $210.00 (average life - 1.2 years) | — | * | $ | 207.80 |  |  | — | * | $ | 207.80 |
$210.01 - $239.76 (average life - 2.1 years) | 0.1 |  | $ | 239.76 |  |  | 0.1 |  | $ | 239.76 |
___________________________ * Represents amounts of less than 0.1 million.

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