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Long-Term Debt - Additional Information (Details) - USD ($)
$ in Millions
6 Months Ended
Aug. 31, 2023
Aug. 28, 2023
Apr. 22, 2022
Dec. 18, 2013
Mar. 31, 2024
Mar. 31, 2023
Sep. 30, 2023
Jun. 22, 2022
Debt Instrument [Line Items]                
Debt repayments         $ 0.0 $ 6.0    
Debt voluntary repayment         9.5 279.5    
Debt borrowings during the period         0.5 298.0    
Long-term debt, fair value         892.0   $ 900.1  
Receivables Financing Agreement | Wholly-owned Subsidiary                
Debt Instrument [Line Items]                
Credit agreement, maximum borrowing capacity               $ 275.0
Debt voluntary repayment         0.5 298.0    
Debt borrowings during the period         9.5 279.5    
Series B Term Loan | SOFR                
Debt Instrument [Line Items]                
Debt instrument, basis spread on variable rate     0.50%          
Series B Term Loan | ABR                
Debt Instrument [Line Items]                
Debt instrument, basis spread on variable rate     1.50%          
Credit Agreement | First Lien Credit Facility Term Loans                
Debt Instrument [Line Items]                
Credit agreement date       Dec. 18, 2013        
Debt instrument, term       7 years        
Credit agreement, maximum borrowing capacity       $ 1,460.0        
Credit Agreement | First Lien Revolving Credit Facility                
Debt Instrument [Line Items]                
Debt instrument, term       5 years        
Credit agreement, maximum borrowing capacity       $ 210.0        
Amended Credit Agreement                
Debt Instrument [Line Items]                
Percentage of prepayment premium for voluntary prepayments 1.00%              
Debt borrowings during the period   $ 450.0            
Amended Credit Agreement | First Lien Revolving Credit Facility                
Debt Instrument [Line Items]                
Debt instrument, term     5 years          
Credit agreement, maximum borrowing capacity     $ 300.0          
Amended Credit Agreement | Series B Term Loan                
Debt Instrument [Line Items]                
Debt instrument, term     7 years          
Credit agreement, maximum borrowing capacity     $ 1,200.0          
Debt instrument, original discount     $ 12.0          
Debt repayments         6.0      
Debt instrument, maturity date     Apr. 22, 2029          
Debt instrument, effective interest rate     3.42%          
Previous Revolving Credit Facility | First Lien Revolving Credit Facility                
Debt Instrument [Line Items]                
Credit agreement, maximum borrowing capacity     $ 260.0          
Letters of credits, outstanding amount         $ 42.6   $ 42.6  
Revolving Credit Facility | SOFR                
Debt Instrument [Line Items]                
Debt instrument, basis spread on variable rate     0.00%          
Revolving Credit Facility | ABR                
Debt Instrument [Line Items]                
Debt instrument, basis spread on variable rate     1.00%          
Revolving Credit Facility | ABR | Maximum                
Debt Instrument [Line Items]                
Debt instrument, basis spread on variable rate     1.50%          
Revolving Credit Facility | ABR | Minimum                
Debt Instrument [Line Items]                
Debt instrument, basis spread on variable rate     1.00%          
Revolving Credit Facility | First Lien Revolving Credit Facility                
Debt Instrument [Line Items]                
Debt instrument, term     5 years          
Credit agreement, maximum borrowing capacity     $ 300.0          
Debt instrument, maturity date     Apr. 22, 2027          
Debt voluntary repayment           $ 33.5    
Revolving Credit Facility | First Lien Revolving Credit Facility | LIBOR [Member] | Maximum                
Debt Instrument [Line Items]                
Debt instrument, basis spread on variable rate     2.50%          
Revolving Credit Facility | First Lien Revolving Credit Facility | LIBOR [Member] | Minimum                
Debt Instrument [Line Items]                
Debt instrument, basis spread on variable rate     2.00%          
Revolving Credit Facility | Series B Term Loan | SOFR | Maximum                
Debt Instrument [Line Items]                
Debt instrument, basis spread on variable rate     3.25%          
Revolving Credit Facility | Series B Term Loan | SOFR | Minimum                
Debt Instrument [Line Items]                
Debt instrument, basis spread on variable rate     3.00%          
Revolving Credit Facility | Series B Term Loan | ABR | Maximum                
Debt Instrument [Line Items]                
Debt instrument, basis spread on variable rate     2.25%          
Revolving Credit Facility | Series B Term Loan | ABR | Minimum                
Debt Instrument [Line Items]                
Debt instrument, basis spread on variable rate     2.00%