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Long-Term Debt - Additional Information (Details) - USD ($)
3 Months Ended 6 Months Ended
Mar. 31, 2022
Mar. 31, 2022
Mar. 31, 2022
Mar. 31, 2021
Feb. 10, 2022
Debt Instrument [Line Items]          
Debt issuance costs incurred $ 36,700,000 $ 36,700,000 $ 36,700,000    
Unamortized debt issuance costs and discount 36,800,000 36,800,000 36,800,000    
Distribution to BD in connection with the spin-off   1,466,000,000      
Payment to BD for the consideration of assets transferred   1,266,000,000 1,266,000,000 $ 0  
Level 2 | Fair Value          
Debt Instrument [Line Items]          
Long-term debt 1,409,500,000 1,409,500,000 1,409,500,000    
Level 2 | Reported Value Measurement          
Debt Instrument [Line Items]          
Long-term debt 1,413,200,000 1,413,200,000 1,413,200,000    
Senior Notes and Term Loan B          
Debt Instrument [Line Items]          
Unamortized debt issuance costs and discount 36,800,000 36,800,000 36,800,000    
5.00% Senior Secured Notes due February 2030 | Senior Notes          
Debt Instrument [Line Items]          
Face amount         $ 500,000,000
Stated interest rate         5.00%
Interest expense   3,400,000 3,400,000    
Senior Secured Term Loan B maturing March 2029 | Secured Debt          
Debt Instrument [Line Items]          
Face amount $ 950,000,000 $ 950,000,000 $ 950,000,000    
Term 7 years        
Discount percentage 0.50% 0.50% 0.50%    
Initial draw period 3 months 3 months 3 months    
Effective interest rate 3.65% 3.65% 3.65%    
Quarterly payment as a percentage of principal 0.25%        
Discount $ 5,800,000 $ 5,800,000 $ 5,800,000    
Interest expense   1,000,000 1,000,000    
Senior Secured Term Loan B maturing March 2029 | Secured Debt | SOFR          
Debt Instrument [Line Items]          
Basis spread on variable rate 3.00%        
Variable rate floor 0.50%        
Senior Secured Revolving Credit Facility maturing 2027 | Secured Debt | Revolving Credit Facility          
Debt Instrument [Line Items]          
Term 5 years        
Maximum borrowing capacity $ 500,000,000 500,000,000 500,000,000    
Commitment fee percentage 0.25%        
Amount drawn $ 0 0 0    
Issuance costs and upfront fees 5,600,000 5,600,000 5,600,000    
Related Party Notes | Senior Notes | Parent          
Debt Instrument [Line Items]          
Face amount 200,000,000 200,000,000 200,000,000    
Discount $ 3,000,000 $ 3,000,000 $ 3,000,000