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Long-Term Debt - Additional Information (Details) - USD ($)
9 Months Ended
Feb. 21, 2019
Aug. 15, 2018
Apr. 28, 2017
Dec. 18, 2013
Jun. 30, 2020
Jun. 30, 2019
Sep. 30, 2019
Debt Instrument [Line Items]              
Debt repayments         $ 7,800,000 $ 10,400,000  
Debt borrowings during the period         70,000,000.0 10,000,000.0  
Debt voluntary repayment         70,000,000.0 10,000,000.0  
Level 2 Inputs              
Debt Instrument [Line Items]              
Long-term debt, fair value         1,155,800,000   $ 1,166,600,000
Receivables Financing Agreement | Wholly-owned Subsidiary              
Debt Instrument [Line Items]              
Credit agreement, maximum borrowing capacity $ 200,000,000.0   $ 175,000,000.0        
Debt instrument, maturity date Feb. 20, 2022   Apr. 27, 2020        
Debt borrowings during the period         80,000,000.0 115,000,000.0  
Debt voluntary repayment         50,000,000.0 $ 105,000,000.0  
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       $ 1,460,000,000.0      
Credit Agreement | First Lien Revolving Credit Facility              
Debt Instrument [Line Items]              
Debt instrument, term       5 years      
Credit agreement, maximum borrowing capacity       $ 210,000,000.0      
Amended Credit Agreement              
Debt Instrument [Line Items]              
Credit agreement date   Aug. 15, 2018          
Amended Credit Agreement | First Lien Revolving Credit Facility              
Debt Instrument [Line Items]              
Debt instrument, term   5 years          
Credit agreement, maximum borrowing capacity   $ 260,000,000.0          
Amended Credit Agreement | Series B Term Loan              
Debt Instrument [Line Items]              
Debt instrument, term   7 years          
Credit agreement, maximum borrowing capacity   $ 1,037,000,000.0          
Debt instrument, original discount   $ 2,800,000          
Debt instrument, basis spread on variable rate   2.50%          
Debt repayments         7,800,000    
Revolving Credit Facility | First Lien Revolving Credit Facility              
Debt Instrument [Line Items]              
Credit agreement, maximum borrowing capacity         210,000,000.0    
Line of credit facility, amount outstanding balance         0   $ 0
Revolving Credit Facility | First Lien Revolving Credit Facility              
Debt Instrument [Line Items]              
Credit agreement, maximum borrowing capacity   $ 260,000,000.0          
Debt repayments         70,000,000.0    
Debt instrument, maturity date   Aug. 15, 2023          
Debt borrowings during the period         $ 70,000,000.0    
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 | First Lien Revolving Credit Facility | LIBOR | Maximum              
Debt Instrument [Line Items]              
Debt instrument, basis spread on variable rate   2.50%