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Income taxes - Significant Portions of Deferred Tax Assets and Liabilities (Details) - USD ($)
$ in Millions
Dec. 31, 2024
Dec. 31, 2023
Dec. 31, 2022
Dec. 31, 2021
Deferred tax assets        
Tax loss carryforwards $ 787.6 $ 813.0    
Pension and postretirement benefits 196.5 183.0    
Foreign tax credit carryforwards 61.9 83.6    
Other tax credit carryforwards 29.5 29.1    
Deferred revenue 48.2 31.9    
Employee benefits and compensation 31.2 31.5    
Purchased capitalized software 18.4 19.4    
Depreciation 28.6 33.0    
Warranty, bad debts and other reserves 2.9 7.6    
Capitalized costs 9.3 9.0    
Capitalized research and development 6.7 0.0    
Other 76.0 57.6    
Total deferred tax assets, gross 1,296.8 1,298.7    
Valuation allowance (1,168.6) (1,150.1) $ (1,110.5) $ (1,226.2)
Total deferred tax assets 128.2 148.6    
Deferred tax liabilities        
Undistributed earnings of certain foreign subsidiaries 27.7 0.0    
Capitalized research and development 0.0 10.4    
Other 32.6 25.1    
Total deferred tax liabilities 60.3 35.5    
Net deferred tax assets $ 67.9 $ 113.1