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Share-based Payments (Tables)
12 Months Ended
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,
202220212020
Restricted stock awards and units$17.2 $15.1 $24.6 
Stock options8.8 9.2 4.9 
Performance stock units9.9 6.8 7.3 
Director stock units1.5 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, 20190.4$156.32 
Granted0.2$122.10 
Vested(0.1)$171.92 
Forfeited(0.1)$135.43 
Outstanding at August 31, 20200.4$134.68 
Granted0.2$108.79 
Vested(0.1)$150.44 
Forfeited(0.1)$116.33 
Outstanding at August 31, 20210.4$116.77 
Granted0.1$204.36 
Vested(0.1)$122.27 
Forfeited(0.1)$131.08 
Outstanding at August 31, 20220.3$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 OptionsService Options
202120202020
Dividend yield0.5%0.4%0.4%
Expected volatility36.5%33.7%33.7%
Risk-free interest rate0.7%1.5%1.3%
Expected life of options8 years7 years5 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:
 OutstandingExercisable
Number of
Options
(in millions)
Weighted Average
Exercise Price
Number of
Options
(in millions)
Weighted Average
Exercise Price
Outstanding at August 31, 20190.4$146.70 0.3$147.51 
Granted0.5$121.87   
Exercised*$116.36   
Outstanding at August 31, 20200.9$133.19 0.4$151.07 
Granted0.3$108.96   
Exercised*$108.58   
Outstanding at August 31, 20211.2$127.98 0.5$142.36 
Exercised(0.1)$88.94   
Outstanding at August 31, 20221.1$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 
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* Represents amounts of less than 0.1 million.