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Long-Term Debt - Additional Information (Details) - USD ($)
$ in Millions
9 Months Ended
Apr. 22, 2022
Dec. 18, 2013
Jun. 30, 2023
Jun. 30, 2022
Sep. 30, 2022
Jun. 22, 2022
Debt Instrument [Line Items]            
Debt repayments     $ 9.0 $ 1,003.3    
Debt voluntary repayment     448.0 203.0    
Debt borrowings during the period     460.0 223.7    
Long-term debt, fair value     1,353.2   $ 1,317.1  
Receivables Financing Agreement | Wholly-owned Subsidiary            
Debt Instrument [Line Items]            
Credit agreement, maximum borrowing capacity           $ 275.0
Debt voluntary repayment     460.0 224.0    
Debt borrowings during the period     448.0 203.0    
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 | 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     9.0 1,003.3    
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          
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 repayments       165.0    
Debt instrument, maturity date Apr. 22, 2027          
Debt voluntary repayment     $ 33.5 $ 165.0    
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%