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Borrowings - Schedule of Long-term Debt (Details)
£ in Thousands, $ in Thousands
3 Months Ended 12 Months Ended
Dec. 30, 2022
USD ($)
Dec. 30, 2022
GBP (£)
Sep. 30, 2022
USD ($)
Debt Instrument [Line Items]      
Long-term Debt $ 3,434,318   $ 3,357,256
Less: Current Portion (51,643)   (50,415)
Less: Deferred Financing Fees (3,076)   (3,466)
2021 Term Loan Facility      
Debt Instrument [Line Items]      
Long-term Debt $ 987,410   $ 923,580
2021 Term Loan Facility | Base Interest Rate | Minimum      
Debt Instrument [Line Items]      
Debt instrument, basis spread on variable rate 0.00% 0.00%  
2021 Term Loan Facility | Base Interest Rate | Maximum      
Debt Instrument [Line Items]      
Debt instrument, basis spread on variable rate 0.625% 0.625%  
2021 Term Loan Facility | LIBOR      
Debt Instrument [Line Items]      
Debt instrument, basis spread on variable rate 5.76% 5.76% 4.06%
2021 Term Loan Facility | Eurocurrency Interest Rate | Minimum      
Debt Instrument [Line Items]      
Debt instrument, basis spread on variable rate 0.875% 0.875%  
2021 Term Loan Facility | Eurocurrency Interest Rate | Maximum      
Debt Instrument [Line Items]      
Debt instrument, basis spread on variable rate 1.625% 1.625%  
2020 Term Loan Facility      
Debt Instrument [Line Items]      
Long-term Debt $ 890,833   $ 882,263
Quarterly principal payment, percent of aggregate borrowings 1.25%    
Quarterly principal payment $ 9,125 £ 3,125  
2020 Term Loan Facility | Base Interest Rate | Minimum      
Debt Instrument [Line Items]      
Debt instrument, basis spread on variable rate 0.00% 0.00%  
2020 Term Loan Facility | Base Interest Rate | Maximum      
Debt Instrument [Line Items]      
Debt instrument, basis spread on variable rate 0.50% 0.50%  
2020 Term Loan Facility | LIBOR      
Debt Instrument [Line Items]      
Debt instrument, basis spread on variable rate 5.76% 5.76% 4.49%
2020 Term Loan Facility | Eurocurrency Interest Rate      
Debt Instrument [Line Items]      
Debt instrument, basis spread on variable rate 4.84% 4.84% 3.60%
2020 Term Loan Facility | Eurocurrency Interest Rate | Minimum      
Debt Instrument [Line Items]      
Debt instrument, basis spread on variable rate 0.875% 0.875%  
2020 Term Loan Facility | Eurocurrency Interest Rate | Maximum      
Debt Instrument [Line Items]      
Debt instrument, basis spread on variable rate 1.50% 1.50% 1.625%
Senior Notes, Series A      
Debt Instrument [Line Items]      
Long-term Debt $ 0   $ 190,000
Interest Rate 4.27%    
Senior Notes, Series B      
Debt Instrument [Line Items]      
Long-term Debt $ 0   180,000
Interest Rate 4.42%    
Senior Notes, Series C      
Debt Instrument [Line Items]      
Long-term Debt $ 0   130,000
Interest Rate 4.52%    
Revolving Credit Facility      
Debt Instrument [Line Items]      
Long-term Debt $ 1,610,794   $ 1,105,294
Revolving Credit Facility | SONIA Rate | Minimum      
Debt Instrument [Line Items]      
Debt instrument, basis spread on variable rate 0.875% 0.875%  
Revolving Credit Facility | SONIA Rate | Maximum      
Debt Instrument [Line Items]      
Debt instrument, basis spread on variable rate 1.625% 1.625%  
Revolving Credit Facility | Base Interest Rate | Minimum      
Debt Instrument [Line Items]      
Debt instrument, basis spread on variable rate 0.00% 0.00%  
Revolving Credit Facility | Base Interest Rate | Maximum      
Debt Instrument [Line Items]      
Debt instrument, basis spread on variable rate 0.625% 0.625%  
Revolving Credit Facility | LIBOR      
Debt Instrument [Line Items]      
Debt instrument, basis spread on variable rate 5.76% 5.76% 4.08%
Revolving Credit Facility | 2021 Term Loan Facility | SONIA Rate | Minimum      
Debt Instrument [Line Items]      
Debt instrument, basis spread on variable rate 0.875% 0.875%  
Revolving Credit Facility | 2021 Term Loan Facility | SONIA Rate | Maximum      
Debt Instrument [Line Items]      
Debt instrument, basis spread on variable rate 1.625% 1.625%  
Revolving Credit Facility | 2021 Term Loan Facility | Eurocurrency Interest Rate      
Debt Instrument [Line Items]      
Debt instrument, basis spread on variable rate 4.84% 4.84% 3.60%