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Income taxes (Tables)
12 Months Ended
Dec. 31, 2022
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 31,202220212020
Income (loss) from continuing operations before income taxes
United States$(177.2)$(443.5)$(316.3)
Foreign114.6 (18.2)44.5 
Total loss from continuing operations before income taxes$(62.6)$(461.7)$(271.8)
Provision (benefit) for income taxes
Current
United States$15.9 $9.1 $7.3 
Foreign34.7 38.1 51.5 
Total50.6 47.2 58.8 
Deferred
Foreign(8.3)(59.1)(13.4)
Total provision (benefit) for income taxes$42.3 $(11.9)$45.4 
Schedule of Reconciliation of Provision (Benefit) for Income Taxes Following is a reconciliation of the benefit for income taxes at the United States statutory tax rate to the provision (benefit) for income taxes as reported:
Year ended December 31,202220212020
United States statutory income tax benefit$(13.2)$(96.9)$(57.1)
Income and losses for which no provision or benefit has been recognized40.9 91.1 78.6 
Foreign rate differential and other foreign tax expense6.4 0.4 5.9 
Income tax withholdings19.7 13.5 16.8 
Permanent items(2.1)(1.8)0.8 
Enacted rate changes (17.1)(4.0)
Change in uncertain tax positions0.4 (0.3)3.6 
Change in valuation allowances(9.8)(0.8)2.9 
Income tax credits, U.S. — (2.1)
Provision (benefit) for income taxes$42.3 $(11.9)$45.4 
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 31,20222021
Deferred tax assets
Tax loss carryforwards$825.5 $840.4 
Postretirement benefits149.6 211.8 
Foreign tax credit carryforwards109.2 145.9 
Other tax credit carryforwards32.7 31.9 
Deferred revenue28.2 35.8 
Employee benefits and compensation21.2 25.8 
Purchased capitalized software16.9 24.2 
Depreciation32.6 31.6 
Warranty, bad debts and other reserves7.1 7.5 
Capitalized costs6.2 3.9 
Other49.9 46.1 
1,279.1 1,404.9 
Valuation allowance(1,110.5)(1,226.2)
Total deferred tax assets$168.6 $178.7 
Deferred tax liabilities
Capitalized research and development$31.0 $43.1 
Other29.2 29.5 
Total deferred tax liabilities$60.2 $72.6 
Net deferred tax assets$108.4 $106.1 
Summary of Valuation Allowance
Changes in the valuation allowance was as follows:
Year ended December 31,202220212020
Valuation allowance, at beginning of year$(1,226.2)$(1,271.5)$(1,524.7)
Actuarial pension adjustments70.7 99.5 41.8 
Expired net operating losses/tax credits52.3 50.0 28.9 
Foreign exchange14.8 18.4 (20.9)
Recognition of income tax benefit (expense) (i)
(43.9)(102.1)189.0 
Other21.8 (20.5)14.4 
Valuation allowance, at end of year$(1,110.5)$(1,226.2)$(1,271.5)
(i) Includes U.S pension activity of $(11.3) million, $(84.9) million and $141.7 million for the years ended December 31, 2022, 2021 and 2020, respectively.
Schedule of Tax Effected Tax Loss Carryforwards
At December 31, 2022, the company has tax effected tax loss carryforwards as follows:
As of December 31, 2022
U.S. Federal$378.6 
State and local178.0 
Foreign268.9 
Total tax loss carryforwards$825.5 
These carryforwards will expire as follows:
Year
2023$13.2 
202412.7 
202519.5 
202610.7 
202759.9 
Thereafter434.2 
Unlimited275.3 
Total$825.5 
Schedule of Tax Credit Carryforwards
The company also has available tax credit carryforwards, which will expire as follows:
Year
2023$27.0 
202422.5 
202520.7 
202633.7 
20279.5 
Thereafter28.5 
Total$141.9 
Schedule of Cash Paid for Income Taxes, Net of Refunds
Cash paid for income taxes, net of refunds was as follows:
Year ended December 31,202220212020
Cash paid for income taxes, net of refunds$49.0 $53.7 $24.7 
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 31,202220212020
Balance at January 1$21.6 $30.9 $25.6 
Additions based on tax positions related to the current year1.9 3.5 8.5 
Changes for tax positions of prior years1.2 (8.8)(0.7)
Reductions as a result of a lapse of applicable statute of limitations(5.4)(2.6)(2.3)
Settlements (0.3)(1.8)
Changes due to foreign currency(1.5)(1.1)1.6 
Balance at December 31$17.8 $21.6 $30.9