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Income taxes - Significant Portions of Deferred Tax Assets and Liabilities (Details) - USD ($)
$ in Millions
Dec. 31, 2020
Dec. 31, 2019
Deferred tax assets    
Tax loss carryforwards $ 795.2 $ 841.1
Postretirement benefits 253.0 434.4
Foreign tax credit carryforwards 201.3 211.5
Other tax credit carryforwards 29.2 30.3
Deferred revenue 31.1 42.8
Employee benefits and compensation 25.3 31.2
Purchased capitalized software 24.1 31.2
Depreciation 28.2 28.1
Warranty, bad debts and other reserves 10.5 5.9
Capitalized costs 8.1 7.1
Other 52.0 27.9
Total deferred tax assets, gross 1,458.0 1,691.5
Valuation allowance (1,271.5) (1,524.7)
Total deferred tax assets 186.5 166.8
Deferred tax liabilities    
Capitalized research and development 47.4 44.7
Other 29.8 29.0
Total deferred tax liabilities 77.2 73.7
Net deferred tax assets $ 109.3 $ 93.1