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Long-Term Debt - Additional Information (Details) - USD ($)
9 Months Ended 12 Months Ended
Aug. 15, 2018
Jul. 02, 2018
Apr. 28, 2017
Dec. 18, 2013
Sep. 30, 2017
Sep. 30, 2019
Sep. 30, 2018
Sep. 30, 2017
Feb. 21, 2019
Debt Instrument [Line Items]                  
Debt repayments         $ 181,600,000 $ 143,000,000 $ 1,662,600,000    
Loss on debt extinguishment [1]             25,100,000    
Level 2 Inputs                  
Debt Instrument [Line Items]                  
Long-term debt, fair value           $ 1,166,600,000 $ 1,182,200,000    
Receivables Financing Agreement | Wholly-owned Subsidiary                  
Debt Instrument [Line Items]                  
Credit agreement, maximum borrowing capacity     $ 175,000,000           $ 200,000,000
Debt instrument, maturity date     Apr. 27, 2020            
Weighted average interest rate           4.40% 2.30%    
Commitment fee for unused balance of facility           0.50%      
Debt voluntary repayment           $ 120,000,000 $ 108,800,000    
Line of credit facility, current borrowing           120,000,000 115,000,000    
Line of credit facility, current borrowing           $ 120,000,000 115,000,000    
LIBOR | Receivables Financing Agreement | Wholly-owned Subsidiary                  
Debt Instrument [Line Items]                  
Debt instrument, basis spread on variable rate           2.00%      
Credit Agreement                  
Debt Instrument [Line Items]                  
Debt instrument, original discount       $ 3,700,000          
Debt instrument, effective interest rate       4.00%          
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          
Debt repayments             347,100,000    
Loss on debt extinguishment             $ 19,300,000    
LIBOR floor rate           1.00%      
Weighted average interest rate         4.10%   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    
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          
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                
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, effective interest rate 2.50%                
Debt repayments           $ 13,000,000      
Debt instrument, maturity date Aug. 15, 2025                
Debt instrument, basis spread on variable rate 2.50%                
Weighted average interest rate           4.90% 4.60%    
Previous 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           0 $ 0    
Letters of credits, issued amount           94,100,000 77,300,000    
Letters of credits, outstanding amount           $ 94,100,000 $ 77,300,000    
Line of credit facility, interest rate during period           2.50% 2.50% 3.00%  
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              
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                
Debt repayments           $ 10,000,000      
Debt instrument, maturity date Aug. 15, 2023                
Line of credit facility, amount outstanding balance           $ 0 $ 0    
Line of credit facility, interest rate during period           2.50% 2.50% 3.00%  
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.