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Income taxes - Significant Portions of Deferred Tax Assets and Liabilities (Details) - USD ($)
$ in Millions
Dec. 31, 2023
Dec. 31, 2022
Dec. 31, 2021
Dec. 31, 2020
Deferred tax assets        
Tax loss carryforwards $ 813.0 $ 825.5    
Postretirement benefits 183.0 149.6    
Foreign tax credit carryforwards 83.6 109.2    
Other tax credit carryforwards 29.1 32.7    
Deferred revenue 31.9 28.2    
Employee benefits and compensation 31.5 21.2    
Purchased capitalized software 19.4 16.9    
Depreciation 33.0 32.6    
Warranty, bad debts and other reserves 7.6 7.1    
Capitalized costs 9.0 6.2    
Other 57.6 49.9    
Total deferred tax assets, gross 1,298.7 1,279.1    
Valuation allowance (1,150.1) (1,110.5) $ (1,226.2) $ (1,271.5)
Total deferred tax assets 148.6 168.6    
Deferred tax liabilities        
Capitalized research and development 10.4 31.0    
Other 25.1 29.2    
Total deferred tax liabilities 35.5 60.2    
Net deferred tax assets $ 113.1 $ 108.4