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Derivative Financial Instruments - Narrative (Details)
$ in Thousands, £ in Millions
3 Months Ended 12 Months Ended
Apr. 02, 2023
USD ($)
Jan. 01, 2023
USD ($)
Sep. 29, 2024
USD ($)
Oct. 01, 2023
USD ($)
Oct. 02, 2022
USD ($)
Sep. 30, 2018
agreement
Jan. 23, 2023
USD ($)
Dec. 28, 2022
USD ($)
Dec. 28, 2022
GBP (£)
Oct. 02, 2022
GBP (£)
Derivative [Line Items]                    
Other non-operating income     $ 0 $ 89,402 $ 19,904          
(Loss) gain on cash flow hedge valuations, net of tax     $ 0 $ (2,412) $ 11,806          
RPS Group plc                    
Derivative [Line Items]                    
Derivative, forward exchange rate         1.0852         1.0852
RPS Group PLC                    
Derivative [Line Items]                    
Derivative, forward exchange rate               1.086 1.086  
Interest Rate Swap | Cash flow hedges | Derivatives designated as hedging instruments                    
Derivative [Line Items]                    
Number of derivative agreements | agreement           5        
Fair value of interest rate swap agreements         $ 2,400          
Foreign Exchange Contract | RPS Group plc                    
Derivative [Line Items]                    
Notional amount         774,800         £ 714.0
Foreign currency forward contract, asset fair value         $ 19,900          
Foreign Exchange Contract | RPS Group PLC                    
Derivative [Line Items]                    
Notional amount               $ 775,400 £ 714.0  
Foreign currency forward contract, asset fair value             $ 109,300      
Other non-operating income $ 21,400 $ 68,000