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Derivative Financial Instruments (Details)
$ in Thousands, £ in Millions
3 Months Ended 12 Months Ended
Jan. 23, 2023
USD ($)
Jan. 01, 2023
USD ($)
Jan. 02, 2022
USD ($)
Sep. 30, 2018
agreement
Jan. 23, 2023
GBP (£)
Dec. 31, 2022
GBP (£)
Dec. 30, 2022
USD ($)
Dec. 28, 2022
USD ($)
Dec. 28, 2022
GBP (£)
Oct. 02, 2022
USD ($)
Derivative [Line Items]                    
Gain on foreign currency forward contract   $ 67,995 $ 0              
Gains (losses) on cash flow hedges recognized in comprehensive income   (89) $ 2,666              
RPS Group PLC                    
Derivative [Line Items]                    
Derivative, forward exchange rate             1.0852 1.086 1.086  
Interest Rate Swap | Designated as cash flow hedges | Derivatives designated as hedging instruments                    
Derivative [Line Items]                    
Notional amount   $ 196,900                
Number of derivative agreements | agreement       5            
Fixed rate   2.79%                
Credit to be reclassified during next twelve months   $ 2,200                
Interest Rate Swap | Designated as cash flow hedges | Derivatives designated as hedging instruments | Other current liabilities                    
Derivative [Line Items]                    
Fair value loss of interest rate swap agreements                   $ 2,400
Interest Rate Swap | Designated as cash flow hedges | Derivatives designated as hedging instruments | Other Noncurrent Assets                    
Derivative [Line Items]                    
Fair value gain of interest rate swap agreements   2,300                
Interest Rate Swap 1 | Designated as cash flow hedges | Derivatives designated as hedging instruments                    
Derivative [Line Items]                    
Notional amount   39,400                
Interest Rate Swap 2 | Designated as cash flow hedges | Derivatives designated as hedging instruments                    
Derivative [Line Items]                    
Notional amount   39,400                
Interest Rate Swap 3 | Designated as cash flow hedges | Derivatives designated as hedging instruments                    
Derivative [Line Items]                    
Notional amount   39,400                
Interest Rate Swap 4 | Designated as cash flow hedges | Derivatives designated as hedging instruments                    
Derivative [Line Items]                    
Notional amount   39,400                
Interest Rate Swap 5 | Designated as cash flow hedges | Derivatives designated as hedging instruments                    
Derivative [Line Items]                    
Notional amount   39,400                
Foreign Exchange Forward | RPS Group PLC                    
Derivative [Line Items]                    
Notional amount           £ 714.0 $ 774,800 $ 775,400 £ 714.0  
Foreign currency forward contract, asset fair value   87,900               $ 19,900
Gain on foreign currency forward contract   $ 68,000                
Foreign Exchange Forward | RPS Group PLC | Subsequent Event                    
Derivative [Line Items]                    
Notional amount | £         £ 714.0          
Gain on foreign currency forward contract $ 109,000