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Debt - Narrative (Details) - USD ($)
12 Months Ended
Aug. 31, 2022
Mar. 01, 2022
Aug. 31, 2022
Aug. 31, 2021
Aug. 31, 2020
May 31, 2022
Mar. 05, 2020
Aug. 31, 2019
Mar. 29, 2019
Debt Instrument [Line Items]                  
Repayments of debt     $ 825,000,000 $ 0 $ 0        
Interest expense     $ 35,200,000 $ 8,100,000          
Weighted average interest rate 2.02%   2.02% 1.38%          
Interest rate swap agreement | Cash Flow Hedging | Designated as Hedging Instrument                  
Debt Instrument [Line Items]                  
Fixed interest rate   1.162%         0.7995%    
Line of Credit | 2019 Credit Agreement                  
Debt Instrument [Line Items]                  
Debt issuance costs               $ 900,000  
Amortization of remaining debt issuance costs   $ 400,000              
Line of Credit | 2022 Credit Agreement                  
Debt Instrument [Line Items]                  
Debt issuance costs           $ 9,500,000      
Covenants, permitted netting of unrestricted cash and cash equivalents   350,000,000.0              
Covenants, material acquisition aggregate consideration minimum   $ 200,000,000.0              
Covenants, maximum leverage ratio, potential increase   0.50              
Covenants, minimum interest coverage ratio   3.00              
Line of Credit | 2022 Credit Agreement | Beginning with fiscal quarter ending May 31, 2022                  
Debt Instrument [Line Items]                  
Covenants, required maximum leverage ratio   4.00              
Line of Credit | 2022 Credit Agreement | Beginning with fiscal quarter ending August 31, 2023                  
Debt Instrument [Line Items]                  
Covenants, required maximum leverage ratio   3.75              
Line of Credit | 2022 Credit Agreement | Beginning with fiscal quarter ending August 31, 2024                  
Debt Instrument [Line Items]                  
Covenants, required maximum leverage ratio   3.50              
Line of Credit | 2022 Credit Agreement | Term SOFR                  
Debt Instrument [Line Items]                  
Basis spread on variable rate   1.10%              
Floor interest rate   0              
Line of Credit | 2022 Credit Agreement | Term SOFR | Credit Spread Adjustment                  
Debt Instrument [Line Items]                  
Basis spread on variable rate   0.10%              
Line of Credit | 2022 Credit Agreement | Term SOFR | Interest Rate Margin                  
Debt Instrument [Line Items]                  
Basis spread on variable rate   1.00%              
Line of Credit | 2022 Credit Agreement | Daily Simple SOFR                  
Debt Instrument [Line Items]                  
Floor interest rate   0              
Line of Credit | 2022 Credit Agreement | Daily Simple SOFR | Credit Spread Adjustment                  
Debt Instrument [Line Items]                  
Basis spread on variable rate   0.10%              
Line of Credit | 2022 Credit Agreement | Daily Simple SONIA                  
Debt Instrument [Line Items]                  
Floor interest rate   0              
Line of Credit | 2022 Credit Agreement | EURIBOR                  
Debt Instrument [Line Items]                  
Floor interest rate   0              
Senior Notes                  
Debt Instrument [Line Items]                  
Debt issuance costs   $ 9,100,000              
Discount   $ 2,800,000              
Redemption price, percentage   101.00%              
Senior Notes | 2027 Notes                  
Debt Instrument [Line Items]                  
Aggregate principal amount   $ 500,000,000.0              
Stated interest rate   2.90%              
Senior Notes | 2032 Notes                  
Debt Instrument [Line Items]                  
Aggregate principal amount   $ 500,000,000.0              
Stated interest rate   3.45%              
Revolving Credit Facility | Line of Credit | 2019 Credit Agreement                  
Debt Instrument [Line Items]                  
Maximum borrowing capacity                 $ 750,000,000.0
Borrowed                 $ 575,000,000.0
Revolving Credit Facility | Line of Credit | 2022 Credit Agreement                  
Debt Instrument [Line Items]                  
Maximum borrowing capacity   $ 500,000,000.0              
Borrowed   250,000,000.0              
Maximum additional borrowings   $ 750,000,000.0              
Commitment fee percentage 0.125%                
Revolving Credit Facility | Line of Credit | 2022 Credit Agreement | Minimum                  
Debt Instrument [Line Items]                  
Commitment fee percentage   0.10%              
Revolving Credit Facility | Line of Credit | 2022 Credit Agreement | Maximum                  
Debt Instrument [Line Items]                  
Commitment fee percentage   0.25%              
Letter of Credit | Line of Credit | 2022 Credit Agreement                  
Debt Instrument [Line Items]                  
Maximum borrowing capacity   $ 100,000,000.0              
Swingline Loan | Line of Credit | 2022 Credit Agreement                  
Debt Instrument [Line Items]                  
Maximum borrowing capacity   50,000,000.0              
Term Loan | Line of Credit | 2022 Credit Agreement                  
Debt Instrument [Line Items]                  
Borrowed   1,000,000,000.0              
Aggregate principal amount   $ 1,000,000,000.0              
Scheduled amortization payments   1.25%              
Repayments of debt     $ 250,000,000.0            
Voluntary prepayments of debt     $ 237,500,000