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Income Taxes - Narrative (Details) - USD ($)
$ in Millions
12 Months Ended
Jan. 02, 2022
Jan. 03, 2021
Dec. 29, 2019
Dec. 30, 2018
Income Taxes [Line Items]        
Loss carryforwards $ 36.4 $ 33.6    
Operating loss carryforwards, not subject to expiration $ 33.8      
U.S. statutory rate 21.00% 21.00% 21.00%  
Income tax expense (benefit) $ 35.1 $ (34.0) $ 0.4  
Gain from insurance settlement 4.8      
Disposition of business 0.0 (6.6) 0.0  
Valuation allowance 19.0 20.2    
Undistributed earnings of foreign subsidiaries 167.8      
Unrecognized tax benefits 0.6 0.5 0.9 $ 1.1
Unrecognized tax benefits that would impact effective tax rate 0.5 0.4 0.8  
Unrecognized Tax Benefits, Income Tax Penalties and Interest Expense 0.1 (0.1)    
Unrecognized tax benefits, income tax penalties and interest accrued 0.2 0.1    
Significant change in unrecognized tax benefits is reasonably possible, amount of unrecorded benefit 0.2      
Goodwill        
Income Taxes [Line Items]        
Income tax expense (benefit)   (23.0)    
Expiring in Years 2022 to 2041        
Income Taxes [Line Items]        
Subject to expiration 2.6      
General Business Tax Credit Carryforward        
Income Taxes [Line Items]        
General business credit carryforward 166.5      
Foreign Tax Credit Carryforward        
Income Taxes [Line Items]        
General business credit carryforward 8.4      
State Credit Carryforward        
Income Taxes [Line Items]        
General business credit carryforward 0.1      
Pro Forma        
Income Taxes [Line Items]        
Potential repatriation of foreign earnings amount 10.8      
Mexico        
Income Taxes [Line Items]        
Deferred tax asset 3.8      
Germany        
Income Taxes [Line Items]        
Valuation allowance     3.9  
United Kingdom        
Income Taxes [Line Items]        
Income tax expense (benefit) (5.2)   (14.3)  
Persol Holdings Investment        
Income Taxes [Line Items]        
Income tax expense (benefit) $ 37.3 $ (5.1) $ 11.0