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Borrowings - Schedule of Long-term Debt (Details)
£ in Thousands, $ in Thousands
9 Months Ended 12 Months Ended
Feb. 16, 2023
Jun. 30, 2023
USD ($)
Jun. 30, 2023
GBP (£)
Sep. 30, 2022
USD ($)
Debt Instrument [Line Items]        
Long-term debt   $ 3,145,529   $ 3,357,256
Less: Current Portion   (55,743)   (50,415)
Less: Deferred Financing Fees   (8,687)   (3,466)
2021 Term Loan Facility - USD Portion        
Debt Instrument [Line Items]        
Long-term debt   $ 200,000   $ 200,000
2021 Term Loan Facility - USD Portion | SONIA Rate        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   6.50% 6.50%  
2021 Term Loan Facility - USD Portion | SONIA Rate | Minimum        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   0.975% 0.975%  
2021 Term Loan Facility - USD Portion | SONIA Rate | Maximum        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   1.725% 1.725%  
2021 Term Loan Facility - USD Portion | LIBOR        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate       4.06%
2021 Term Loan Facility - USD Portion | Base Interest Rate | Minimum        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   0.00% 0.00%  
2021 Term Loan Facility - USD Portion | Base Interest Rate | Maximum        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   0.625% 0.625%  
2021 Term Loan Facility - GBP Portion        
Debt Instrument [Line Items]        
Long-term debt   $ 826,280   $ 723,580
2021 Term Loan Facility - GBP Portion | SONIA Rate | Minimum        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   0.908% 0.908%  
2021 Term Loan Facility - GBP Portion | SONIA Rate | Maximum        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   1.658% 1.658%  
2021 Term Loan Facility - GBP Portion | Eurocurrency Interest Rate        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   6.21% 6.21% 3.60%
2020 Term Loan Facility        
Debt Instrument [Line Items]        
Long-term debt   $ 877,532   $ 882,263
Quarterly principal payment, percent of aggregate borrowings   1.25%    
Quarterly principal payment   $ 9,125 £ 3,125  
2020 Term Loan Facility | SONIA Rate        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   6.45% 6.45%  
2020 Term Loan Facility | SONIA Rate | Minimum        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   0.975% 0.975%  
2020 Term Loan Facility | SONIA Rate | Maximum        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   1.725% 1.725%  
2020 Term Loan Facility | LIBOR        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate       4.49%
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   0.625% 0.625%  
2020 Term Loan Facility | Eurocurrency Interest Rate        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   6.21% 6.21% 3.60%
Bonds, Sustainability-Linked | Senior Notes        
Debt Instrument [Line Items]        
Long-term debt   $ 500,000   $ 0
Interest rate 5.90% 5.90%    
Interest rate, increase (decrease) over period 0.35%      
Bonds, Sustainability-Linked | Senior Notes | First Step Up Date        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   6.025% 6.025%  
Interest rate, increase (decrease) over period   0.125% 0.125%  
Interest rate payable period   15 days 15 days  
Bonds, Sustainability-Linked | Senior Notes | Second Step Up Date        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   6.15% 6.15%  
Interest rate, increase (decrease) over period   0.125% 0.125%  
Interest rate payable period   15 days 15 days  
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%    
2020 Term Loan Facility, Denominated in GDP | SONIA Rate | Minimum        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   0.908% 0.908%  
2020 Term Loan Facility, Denominated in GDP | SONIA Rate | Maximum        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   1.658% 1.658%  
Revolving Credit Facility        
Debt Instrument [Line Items]        
Long-term debt   $ 806,147   $ 1,105,294
Revolving Credit Facility | SONIA Rate        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   6.49% 6.49%  
Revolving Credit Facility | SONIA Rate | Minimum        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   0.975% 0.975%  
Revolving Credit Facility | SONIA Rate | Maximum        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   1.725% 1.725%  
Revolving Credit Facility | LIBOR        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate       4.08%
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 | Eurocurrency Interest Rate | Minimum        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   0.908% 0.908%  
Revolving Credit Facility | Eurocurrency Interest Rate | Maximum        
Debt Instrument [Line Items]        
Debt instrument, basis spread on variable rate   1.658% 1.658%