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Income taxes (Tables)
12 Months Ended
Dec. 31, 2021
Income Tax Disclosure [Abstract]  
Schedule of Income (Loss) from Continuing Operations before Income Taxes and Provision (Benefit) for Income Taxes
Following is the total loss from continuing operations before income taxes and the provision (benefit) for income taxes.
Year ended December 31,202120202019
Income (loss) from continuing operations before income taxes
United States$(443.5)$(316.3)$(148.4)
Foreign(18.2)44.5 87.8 
Total income (loss) from continuing operations before income taxes$(461.7)$(271.8)$(60.6)
Provision (benefit) for income taxes
Current
United States$9.1 $7.3 $(17.7)
Foreign38.1 51.5 41.0 
Total47.2 58.8 23.3 
Deferred
Foreign(59.1)(13.4)4.4 
Total (benefit) provision for income taxes$(11.9)$45.4 $27.7 
Schedule of Reconciliation of Provision (Benefit) for Income Taxes Following is a reconciliation of the provision (benefit) for income taxes at the United States statutory tax rate to the provision (benefit) for income taxes as reported:
Year ended December 31,202120202019
United States statutory income tax provision (benefit)$(96.9)$(57.1)$(12.7)
Income and losses for which no provision or benefit has been recognized91.1 78.6 23.9 
Foreign rate differential and other foreign tax expense0.4 5.9 3.2 
Income tax withholdings13.5 16.8 17.6 
Permanent items(1.8)0.8 (2.5)
Enacted rate changes(17.1)(4.0)0.5 
Change in uncertain tax positions(0.3)3.6 0.2 
Change in valuation allowances due to changes in judgment(0.8)2.9 (2.3)
Income tax credits, U.S. (2.1)(0.2)
(Benefit) provision for income taxes$(11.9)$45.4 $27.7 
Schedule of 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 31,20212020
Deferred tax assets
Tax loss carryforwards$840.4 $795.2 
Postretirement benefits211.8 253.0 
Foreign tax credit carryforwards145.9 201.3 
Other tax credit carryforwards31.9 29.2 
Deferred revenue35.8 31.1 
Employee benefits and compensation25.8 25.3 
Purchased capitalized software24.2 24.1 
Depreciation31.6 28.2 
Warranty, bad debts and other reserves7.5 10.5 
Capitalized costs3.9 8.1 
Other46.1 52.0 
1,404.9 1,458.0 
Valuation allowance(1,226.2)(1,271.5)
Total deferred tax assets$178.7 $186.5 
Deferred tax liabilities
Capitalized research and development$43.1 $47.4 
Other29.5 29.8 
Total deferred tax liabilities$72.6 $77.2 
Net deferred tax assets$106.1 $109.3 
Schedule of Tax Effected Tax Loss Carryforwards
At December 31, 2021, the company has tax effected tax loss carryforwards as follows:
As of December 31, 2021
U.S. Federal$370.7 
State and local203.4 
Foreign266.3 
Total tax loss carryforwards$840.4 
These carryforwards will expire as follows:
Year
2022$13.8 
202313.0 
202413.0 
202515.5 
202610.3 
Thereafter502.3 
Unlimited272.5 
Total$840.4 
Schedule of Tax Credit Carryforwards
The company also has available tax credit carryforwards, which will expire as follows:
Year
2022$38.1 
202327.0 
202422.5 
202520.7 
202633.7 
Thereafter35.8 
Total$177.8 
Schedule of Cash Paid for Income Taxes, Net of Refunds
Cash paid for income taxes, net of refunds was as follows:
Year ended December 31,202120202019
Cash paid for income taxes, net of refunds$53.7 $24.7 $37.6 
Schedule of 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 31,202120202019
Balance at January 1$30.9 $25.6 $18.9 
Additions based on tax positions related to the current year3.5 8.5 11.1 
Changes for tax positions of prior years(8.8)(0.7)(0.6)
Reductions as a result of a lapse of applicable statute of limitations(2.6)(2.3)(2.3)
Settlements(0.3)(1.8)(1.1)
Changes due to foreign currency(1.1)1.6 (0.4)
Balance at December 31$21.6 $30.9 $25.6