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Income Taxes - Narrative (Details) - USD ($)
$ in Millions
12 Months Ended
Jan. 01, 2023
Jan. 02, 2022
Jan. 03, 2021
Dec. 29, 2019
Income Taxes [Line Items]        
Loss carryforwards $ 33.4 $ 36.4    
Operating loss carryforwards, not subject to expiration $ 30.7      
U.S. statutory rate 21.00% 21.00% 21.00%  
Income tax expense (benefit) $ (7.9) $ 35.1 $ (34.0)  
Gain from insurance settlement   4.8    
Disposition of business 3.9 0.0 (6.6)  
Tax exempt life insurance cash surrender 7.8 (5.2) (4.6)  
Undistributed earnings of foreign subsidiaries 156.5      
Unrecognized tax benefits 0.5 0.6 0.5 $ 0.9
Unrecognized tax benefits that would impact effective tax rate 0.4 0.5 0.4  
Unrecognized Tax Benefits, Income Tax Penalties and Interest Expense   0.1 (0.1)  
Unrecognized tax benefits, income tax penalties and interest accrued 0.1 0.2    
Significant change in unrecognized tax benefits is reasonably possible, amount of unrecorded benefit 0.2      
Goodwill        
Income Taxes [Line Items]        
Income tax expense (benefit) (7.1)   (23.0)  
Expiring in Years 2023 to 2042        
Income Taxes [Line Items]        
Subject to expiration 2.7      
General Business Tax Credit Carryforward | Expiring In Years 2034 to 2042        
Income Taxes [Line Items]        
General business credit carryforward 177.1      
Foreign Tax Credit Carryforward | Expiring In Years 2023 to 2032        
Income Taxes [Line Items]        
General business credit carryforward 23.6      
Pro Forma        
Income Taxes [Line Items]        
Potential repatriation of foreign earnings amount 9.8      
United Kingdom        
Income Taxes [Line Items]        
Income tax expense (benefit)   (5.2)    
Persol Holdings Investment        
Income Taxes [Line Items]        
Income tax expense (benefit) $ (16.9) $ 37.3 $ (5.1)