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Long-Term Debt - Additional Information (Details) - USD ($)
6 Months Ended
Feb. 21, 2019
Aug. 15, 2018
Apr. 28, 2017
Dec. 18, 2013
Mar. 31, 2020
Mar. 31, 2019
Sep. 30, 2019
Debt Instrument [Line Items]              
Debt repayments         $ 5,200,000 $ 7,800,000  
Debt borrowings during the period         70,000,000 10,000,000  
Debt voluntary repayment         10,000,000 10,000,000  
Level 2 Inputs              
Debt Instrument [Line Items]              
Long-term debt, fair value         1,132,800,000   $ 1,166,600,000
Receivables Financing Agreement | Wholly-owned Subsidiary              
Debt Instrument [Line Items]              
Credit agreement, maximum borrowing capacity $ 200,000,000   $ 175,000,000        
Debt instrument, maturity date Feb. 20, 2022   Apr. 27, 2020        
Debt borrowings during the period         80,000,000 85,000,000  
Debt voluntary repayment         50,000,000 $ 75,000,000  
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      
Credit Agreement | First Lien Revolving Credit Facility              
Debt Instrument [Line Items]              
Debt instrument, term       5 years      
Credit agreement, maximum borrowing capacity       $ 210,000,000      
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          
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          
Debt instrument, original discount   $ 2,800,000          
Debt instrument, basis spread on variable rate   2.50%          
Debt repayments         5,200,000    
Revolving Credit Facility | First Lien Revolving Credit Facility              
Debt Instrument [Line Items]              
Credit agreement, maximum borrowing capacity         210,000,000    
Line of credit facility, amount outstanding balance         60,000,000   $ 0
Revolving Credit Facility | First Lien Revolving Credit Facility              
Debt Instrument [Line Items]              
Credit agreement, maximum borrowing capacity   $ 260,000,000          
Debt repayments         10,000,000    
Debt instrument, maturity date   Aug. 15, 2023          
Debt borrowings during the period         $ 70,000,000    
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%