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Income taxes (Tables)
12 Months Ended
Dec. 31, 2020
Income Tax Disclosure [Abstract]  
Total Income (Loss) From Continuing Operations Before Income Taxes and Provision (Benefit) for Income Taxes
Following is the total income (loss) from continuing operations before income taxes and the provision (benefit) for income taxes.
Year ended December 31,202020192018
Income (loss) from continuing operations before income taxes
United States$(316.3)$(148.4)$(125.8)
Foreign44.5 87.8 196.8 
Total income (loss) before income taxes from continuing operations$(271.8)$(60.6)$71.0 
Provision (benefit) for income taxes
Current
United States$7.3 $(17.7)$(13.6)
Foreign51.5 41.0 51.4 
Total58.8 23.3 37.8 
Deferred
Foreign(13.4)4.4 8.2 
Total provision for income taxes$45.4 $27.7 $46.0 
Reconciliation of the Provision (Benefit) for Income Taxes Following is a reconciliation of the provision (benefit) for income taxes at the United States statutory tax rate to the provision for income taxes as reported:
Year ended December 31,202020192018
United States statutory income tax provision (benefit)$(57.1)$(12.7)$14.9 
Income and losses for which no provision or benefit has been recognized78.6 23.9 19.1 
Foreign rate differential and other foreign tax expense5.9 3.2 9.5 
Income tax withholdings16.8 17.6 19.3 
Permanent items0.8 (2.5)(5.0)
Enacted rate changes(4.0)0.5 (2.3)
Change in uncertain tax positions3.6 0.2 (1.2)
Change in valuation allowances due to changes in judgment2.9 (2.3)(5.9)
Income tax credits, U.S.(2.1)(0.2)(2.4)
Provision for income taxes$45.4 $27.7 $46.0 
Significant Portions of Deferred Tax Assets and Liabilities
The tax effects of temporary differences and carryforwards that give rise to significant portions of deferred tax assets and liabilities were as follows:
As of December 31,20202019
Deferred tax assets
Tax loss carryforwards$795.2 $841.1 
Postretirement benefits253.0 434.4 
Foreign tax credit carryforwards201.3 211.5 
Other tax credit carryforwards29.2 30.3 
Deferred revenue31.1 42.8 
Employee benefits and compensation25.3 31.2 
Purchased capitalized software24.1 31.2 
Depreciation28.2 28.1 
Warranty, bad debts and other reserves10.5 5.9 
Capitalized costs8.1 7.1 
Other52.0 27.9 
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 
Other29.8 29.0 
Total deferred tax liabilities$77.2 $73.7 
Net deferred tax assets$109.3 $93.1 
Schedule of Tax Effected Tax Loss Carryforwards
At December 31, 2020, the company has tax effected tax loss carryforwards as follows:
As of December 31, 2020
U.S. Federal$317.6 
State and local200.1 
Foreign277.5 
Total tax loss carryforwards$795.2 
These carryforwards will expire as follows:
Year
2021$15.7 
202217.5 
202313.6 
202411.9 
202513.2 
Thereafter723.3 
Total$795.2 
Schedule of Tax Credit Carryforwards
The company also has available tax credit carryforwards, which will expire as follows:
Year
2021$55.9 
202238.1 
202327.0 
202422.5 
202520.7 
Thereafter66.3 
Total$230.5 
Schedule of Cash Paid for Income Taxes, Net of Refunds
Cash paid for income taxes, net of refunds was as follows:
Year ended December 31,202020192018
Cash paid for income taxes, net of refunds$24.7 $37.6 $39.1 
Reconciliation of Changes in Unrecognized Tax Benefits A reconciliation of the beginning and ending amount of unrecognized tax benefits is as follows:
Year ended December 31,202020192018
Balance at January 1$25.6 $18.9 $27.9 
Additions based on tax positions related to the current year8.5 11.1 2.6 
Changes for tax positions of prior years(0.7)(0.6)(6.1)
Reductions as a result of a lapse of applicable statute of limitations(2.3)(2.3)(2.4)
Settlements(1.8)(1.1)(1.5)
Changes due to foreign currency1.6 (0.4)(1.6)
Balance at December 31$30.9 $25.6 $18.9