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Borrowings - Schedule of Long-term Debt (Details)
$ in Thousands
9 Months Ended 12 Months Ended
Aug. 18, 2023
Feb. 16, 2023
Jun. 28, 2024
USD ($)
Sep. 29, 2023
USD ($)
Sep. 29, 2023
GBP (£)
Jun. 28, 2024
GBP (£)
Feb. 13, 2023
Debt Instrument [Line Items]              
Long-term debt     $ 2,091,456 $ 2,813,471      
Less: Current Portion     (824,060) (51,773)      
Less: Deferred Financing Fees     (12,370) (13,172)      
2021 Term Loan Facility - USD Portion              
Debt Instrument [Line Items]              
Long-term debt     $ 120,000 120,000      
2021 Term Loan Facility - USD Portion | Base Rate | Minimum              
Debt Instrument [Line Items]              
Debt instrument, basis spread on variable rate     0.00%        
2021 Term Loan Facility - USD Portion | Base Rate | Maximum              
Debt Instrument [Line Items]              
Debt instrument, basis spread on variable rate     0.625%        
2021 Term Loan Facility - GBP Portion              
Debt Instrument [Line Items]              
Long-term debt     $ 822,705 $ 794,170      
2021 Term Loan Facility - GBP Portion | Sterling Overnight Interbank Average Rate (SONIA)              
Debt Instrument [Line Items]              
Effective interest rate     6.48% 6.47%   6.48%  
2021 Term Loan Facility - GBP Portion | Sterling Overnight Interbank Average Rate (SONIA) | Minimum              
Debt Instrument [Line Items]              
Debt instrument, basis spread on variable rate     0.908% 1.658% 1.658%    
2020 Term Loan Facility              
Debt Instrument [Line Items]              
Long-term debt     $ 824,060 $ 854,246      
Quarterly principal payment, percent of aggregate borrowings       1.25%      
Quarterly principal payment       $ 9,100 £ 3,100,000    
2020 Term Loan Facility | Secured Overnight Financing Rate (SOFR)              
Debt Instrument [Line Items]              
Effective interest rate     6.69%     6.69%  
2020 Term Loan Facility | Secured Overnight Financing Rate (SOFR) | Minimum              
Debt Instrument [Line Items]              
Debt instrument, basis spread on variable rate     0.975%        
2020 Term Loan Facility | Secured Overnight Financing Rate (SOFR) | Maximum              
Debt Instrument [Line Items]              
Debt instrument, basis spread on variable rate     1.725%        
2020 Term Loan Facility | Base Rate | Minimum              
Debt Instrument [Line Items]              
Debt instrument, basis spread on variable rate     0.00%        
2020 Term Loan Facility | Base Rate | Maximum              
Debt Instrument [Line Items]              
Debt instrument, basis spread on variable rate     0.625%        
2020 Term Loan Facility | London Interbank Offered Rate (LIBOR)              
Debt Instrument [Line Items]              
Effective interest rate       6.68%      
2020 Term Loan Facility | Sterling Overnight Interbank Average Rate (SONIA)              
Debt Instrument [Line Items]              
Effective interest rate     6.48% 6.47%   6.48%  
2020 Term Loan Facility | Sterling Overnight Interbank Average Rate (SONIA) | Minimum              
Debt Instrument [Line Items]              
Debt instrument, basis spread on variable rate     0.908% 1.658% 1.658%    
5.90% Bonds | Senior Notes              
Debt Instrument [Line Items]              
Long-term debt     $ 500,000 $ 500,000      
Interest rate   5.90%         5.90%
Interest rate, increase (decrease) over period   0.35%          
5.90% Bonds | Senior Notes | First Step Up Date              
Debt Instrument [Line Items]              
Interest rate     5.90%     5.90%  
Debt instrument, basis spread on variable rate     6.025%        
Interest rate, increase (decrease) over period     0.125%        
Interest rate payable period     15 days        
5.90% Bonds | Senior Notes | Second Step Up Date              
Debt Instrument [Line Items]              
Interest rate     5.90%     5.90%  
Debt instrument, basis spread on variable rate     6.15%        
Interest rate, increase (decrease) over period     0.125%        
Interest rate payable period     15 days        
6.35% Bonds | Senior Notes              
Debt Instrument [Line Items]              
Long-term debt     $ 600,000 $ 600,000      
Interest rate 6.35%            
Interest rate, increase (decrease) over period 0.30%            
2021 Term Loan Facility - USD Portion | Secured Overnight Financing Rate (SOFR)              
Debt Instrument [Line Items]              
Effective interest rate     6.68%     6.68%  
2021 Term Loan Facility - USD Portion | Secured Overnight Financing Rate (SOFR) | Minimum              
Debt Instrument [Line Items]              
Debt instrument, basis spread on variable rate     0.975%        
2021 Term Loan Facility - USD Portion | Secured Overnight Financing Rate (SOFR) | Maximum              
Debt Instrument [Line Items]              
Debt instrument, basis spread on variable rate     1.725%        
2021 Term Loan Facility - USD Portion | London Interbank Offered Rate (LIBOR)              
Debt Instrument [Line Items]              
Effective interest rate       6.68%      
Revolving Credit Facility              
Debt Instrument [Line Items]              
Long-term debt     $ 61,121 $ 10,000   £ 0  
Revolving Credit Facility | Secured Overnight Financing Rate (SOFR)              
Debt Instrument [Line Items]              
Effective interest rate     4.90%     4.90%  
Revolving Credit Facility | Secured Overnight Financing Rate (SOFR) | Minimum              
Debt Instrument [Line Items]              
Debt instrument, basis spread on variable rate     0.975%        
Revolving Credit Facility | Secured Overnight Financing Rate (SOFR) | Maximum              
Debt Instrument [Line Items]              
Debt instrument, basis spread on variable rate     1.725%        
Revolving Credit Facility | Base Rate | Minimum              
Debt Instrument [Line Items]              
Debt instrument, basis spread on variable rate     0.00%        
Revolving Credit Facility | Base Rate | Maximum              
Debt Instrument [Line Items]              
Debt instrument, basis spread on variable rate     0.625%        
Revolving Credit Facility | London Interbank Offered Rate (LIBOR)              
Debt Instrument [Line Items]              
Effective interest rate       8.75%      
Revolving Credit Facility | Sterling Overnight Interbank Average Rate (SONIA) | Minimum              
Debt Instrument [Line Items]              
Debt instrument, basis spread on variable rate     0.908%        
Revolving Credit Facility | Sterling Overnight Interbank Average Rate (SONIA) | Maximum              
Debt Instrument [Line Items]              
Debt instrument, basis spread on variable rate     1.658%