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Derivative Financial Instruments and Hedging Activities - Narrative (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
May 31, 2018
Feb. 28, 2018
May 31, 2017
May 31, 2018
May 31, 2017
Aug. 31, 2017
Aug. 31, 2016
Forward contracts              
Derivative [Line Items]              
Aggregate notional amount $ 2,200.0     $ 2,200.0   $ 2,100.0  
Forward contracts | Forward foreign exchange contracts | Cash flow hedging              
Derivative [Line Items]              
Aggregate notional amount $ 252.3     $ 252.3   $ 314.6  
Anticipated debt issuance | Cash flow hedging              
Derivative [Line Items]              
Aggregate notional amount             $ 200.0
Fair value of cash received for settlement of swaps   $ 17.2          
Term Loan Facility | Cash flow hedging              
Derivative [Line Items]              
Aggregate notional amount             $ 200.0
Senior Notes | 3.950% Senior Notes              
Derivative [Line Items]              
Senior Notes, stated interest rate 3.95% 3.95%   3.95%      
Cost of revenue              
Derivative [Line Items]              
Foreign currency losses $ 27.2   $ 59.8    
Cost of revenue | Forward foreign exchange contracts              
Derivative [Line Items]              
Gain recognized due to changes in fair value of derivatives $ 41.2   $ 92.2