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Income taxes - Significant Portions of Deferred Tax Assets and Liabilities (Details) - USD ($)
$ in Millions
Dec. 31, 2019
Dec. 31, 2018
Deferred tax assets    
Tax loss carryforwards $ 841.1 $ 860.0
Postretirement benefits 434.4 440.3
Foreign tax credit carryforwards 211.5 221.6
Other tax credit carryforwards 30.3 29.8
Deferred revenue 42.8 37.1
Employee benefits and compensation 31.2 31.1
Purchased capitalized software 31.2 22.9
Depreciation 28.1 20.1
Warranty, bad debts and other reserves 5.9 4.8
Capitalized costs 7.1 5.1
Other 27.9 30.4
Total deferred tax assets, gross 1,691.5 1,703.2
Valuation allowance (1,524.7) (1,547.5)
Total deferred tax assets 166.8 155.7
Deferred tax liabilities    
Capitalized research and development 44.7 36.1
Other 29.0 30.2
Total deferred tax liabilities 73.7 66.3
Net deferred tax assets $ 93.1 $ 89.4