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Long-Term Debt - Additional Information (Details) - USD ($)
12 Months Ended
Feb. 21, 2019
Aug. 15, 2018
Jul. 02, 2018
Apr. 28, 2017
Dec. 18, 2013
Sep. 30, 2020
Sep. 30, 2019
Sep. 30, 2018
Sep. 30, 2017
Debt Instrument [Line Items]                  
Debt repayments           $ 10,400,000 $ 13,000,000.0 $ 1,493,900,000  
Loss on debt extinguishment [1]               25,100,000  
Debt voluntary repayment           80,000,000.0 120,000,000.0 108,700,000  
Debt borrowings during the period           80,000,000.0 120,000,000.0 115,000,000.0  
Level 2 Inputs                  
Debt Instrument [Line Items]                  
Long-term debt, fair value           $ 1,143,500,000 $ 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          
Weighted average interest rate           2.70% 4.40%    
Commitment fee for unused balance of facility           0.50%      
Debt voluntary repayment           $ 80,000,000.0 $ 120,000,000.0    
Debt borrowings during the period           $ 80,000,000.0 $ 120,000,000.0    
LIBOR | Receivables Financing Agreement | Wholly-owned Subsidiary                  
Debt Instrument [Line Items]                  
Debt instrument, basis spread on variable rate           2.00%      
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        
Debt instrument, original discount         $ 3,700,000        
Debt instrument, basis spread on variable rate         4.00%        
Debt repayments               347,100,000  
Loss on debt extinguishment               $ 19,300,000  
LIBOR floor rate           1.00%      
Weighted average interest rate               4.70% 4.10%
Credit Agreement | First Lien Credit Facility Term Loans | Prime Rate                  
Debt Instrument [Line Items]                  
Debt instrument, basis spread on variable rate           3.00%      
Credit Agreement | First Lien Credit Facility Term Loans | LIBOR                  
Debt Instrument [Line Items]                  
Debt instrument, basis spread on variable rate           3.00%      
Credit Agreement | First Lien Credit Facility Term Loans | Contractual Repayments                  
Debt Instrument [Line Items]                  
Debt repayments               $ 11,000,000.0  
Credit Agreement | First Lien Credit Facility Term Loans | Voluntary Repayments | IPO                  
Debt Instrument [Line Items]                  
Debt repayments               336,100,000  
Credit Agreement | First Lien Revolving Credit Facility                  
Debt Instrument [Line Items]                  
Debt instrument, term         5 years        
Credit agreement, maximum borrowing capacity         $ 210,000,000.0        
Amended Credit Agreement                  
Debt Instrument [Line Items]                  
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   $ 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           $ 10,400,000      
Debt instrument, maturity date   Aug. 15, 2025              
Debt instrument, effective interest rate   2.50%              
Weighted average interest rate           3.50% 4.90%    
Previous 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  
Letters of credits, issued amount           78,000,000.0 $ 94,100,000    
Letters of credits, outstanding amount           $ 78,000,000.0 $ 94,100,000    
Line of credit facility, interest rate during period           2.30% 2.50% 2.50%  
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           0.50%      
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 | IPO                  
Debt Instrument [Line Items]                  
Debt repayments     $ 55,000,000.0            
Revolving Credit Facility | First Lien Revolving Credit Facility                  
Debt Instrument [Line Items]                  
Debt instrument, term   5 years              
Credit agreement, maximum borrowing capacity   $ 260,000,000.0              
Debt repayments           $ 70,000,000.0      
Debt instrument, maturity date   Aug. 15, 2023              
Line of credit facility, amount outstanding balance             $ 0 $ 0  
Line of credit facility, interest rate during period           2.30% 2.50% 2.50%  
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%              
[1]

Represents losses on the extinguishment of debt.