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Long-Term Debt - Additional Information (Details) - USD ($)
$ in Millions
12 Months Ended
Apr. 22, 2022
Dec. 18, 2013
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Jun. 22, 2022
Dec. 31, 2021
Sep. 20, 2021
Debt Instrument [Line Items]                
Debt repayments     $ 1,006.3 $ 10.4 $ 10.4      
Loss on debt extinguishment [1]     12.6 0.0 0.0      
Debt voluntary repayment     374.4 24.6 80.0      
Debt borrowings during the period     391.7 34.5 $ 80.0      
Long-term debt, fair value     $ 1,317.1 $ 1,148.7        
Receivables Financing Agreement | Wholly-owned Subsidiary                
Debt Instrument [Line Items]                
Credit agreement, maximum borrowing capacity           $ 275.0 $ 250.0 $ 235.0
Interest period term     6 months          
Weighted average interest rate     2.40% 1.60%        
Commitment fee for unused balance of facility     0.40%          
Debt voluntary repayment     $ 392.0 $ 34.5        
Debt borrowings during the period     $ 374.4 24.6        
SOFR | Maximum | Receivables Financing Agreement | Wholly-owned Subsidiary                
Debt Instrument [Line Items]                
Debt instrument, basis spread on variable rate     170.00%          
SOFR | Minimum | Receivables Financing Agreement | Wholly-owned Subsidiary                
Debt Instrument [Line Items]                
Debt instrument, basis spread on variable rate     140.00%          
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]                
Loss on debt extinguishment $ (12.6)              
Percentage of principle balance used to calculate debt repayments amount of quarterly installments due     0.25%          
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     $ 1,006.3 $ 10.4        
Debt instrument, maturity date Apr. 22, 2029              
Debt instrument, effective interest rate 3.42%              
Weighted average interest rate     3.76% 2.65%        
Previous Revolving Credit Facility | First Lien Revolving Credit Facility                
Debt Instrument [Line Items]                
Credit agreement, maximum borrowing capacity   $ 260.0            
Line of credit facility, amount outstanding balance     $ 0.0 $ 0.0        
Letters of credits, outstanding amount     $ 49.1 52.3        
Previous Revolving Credit Facility | First Lien Revolving Credit Facility | Scenario One Depending on Leverage Ratio                
Debt Instrument [Line Items]                
Commitment fee for unused balance of facility     0.05%          
Previous Revolving Credit Facility | First Lien Revolving Credit Facility | Scenario Two Depending on Leverage Ratio                
Debt Instrument [Line Items]                
Commitment fee for unused balance of facility     0.375%          
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 $ 0.0        
Debt instrument, maturity date Apr. 22, 2027              
Weighted average interest rate     2.30% 2.30%        
Debt borrowings during the period     $ 165.0          
Revolving Credit Facility | First Lien Revolving Credit Facility | LIBOR | Maximum                
Debt Instrument [Line Items]                
Debt instrument, basis spread on variable rate 2.50%              
Revolving Credit Facility | First Lien Revolving Credit Facility | LIBOR | 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%              
[1] Represents losses on the extinguishment of debt related to Amendment No. 6 to the Credit Agreement and includes the write-off of deferred finance fees and original issue discount.