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Income taxes (Tables)
12 Months Ended
Dec. 31, 2024
Income Tax Disclosure [Abstract]  
Schedule of Income (Loss) from Continuing Operations before Income Taxes and Provision for Income Taxes
Following is the total loss before income taxes and the provision for income taxes.
Year ended December 31,202420232022
Income (loss) before income taxes
United States$(268.7)$(545.5)$(177.2)
Foreign193.4 197.7 114.6 
Total loss before income taxes$(75.3)$(347.8)$(62.6)
Provision (benefit) for income taxes
Current
United States$21.1 $8.8 $15.9 
Foreign61.2 46.0 34.7 
Total82.3 54.8 50.6 
Deferred
United States18.7 — — 
Foreign16.9 24.5 (8.3)
Total provision for income taxes$117.9 $79.3 $42.3 
Schedule of Reconciliation of Provision for Income Taxes
Following is a reconciliation of the benefit for income taxes at the United States statutory tax rate to the provision for income taxes as reported:
Year ended December 31,202420232022
U.S. statutory income tax benefit$(15.8)$(73.0)$(13.2)
Income and losses for which no provision or benefit has been recognized63.0 123.2 40.9 
Foreign rate differential and other foreign tax expense8.9 12.7 6.4 
Income tax withholdings23.0 14.0 19.7 
Additional tax expense on undistributed earnings of certain foreign subsidiaries27.3 — — 
Permanent items1.2 (3.0)(2.1)
Change in uncertain tax positions1.3 3.8 0.4 
Change in valuation allowances7.9 2.1 (9.8)
U.S. income tax benefit
 (0.6)— 
Other1.1 0.1 — 
Provision for income taxes$117.9 $79.3 $42.3 
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 31,20242023
Deferred tax assets
Tax loss carryforwards$787.6 $813.0 
Pension and postretirement benefits
196.5 183.0 
Foreign tax credit carryforwards61.9 83.6 
Other tax credit carryforwards29.5 29.1 
Deferred revenue48.2 31.9 
Employee benefits and compensation31.2 31.5 
Purchased capitalized software18.4 19.4 
Depreciation28.6 33.0 
Warranty, bad debts and other reserves2.9 7.6 
Capitalized costs9.3 9.0 
Capitalized research and development
6.7 — 
Other76.0 57.6 
1,296.8 1,298.7 
Valuation allowance(1,168.6)(1,150.1)
Total deferred tax assets$128.2 $148.6 
Deferred tax liabilities
Undistributed earnings of certain foreign subsidiaries$27.7 $— 
Capitalized research and development 10.4 
Other32.6 25.1 
Total deferred tax liabilities$60.3 $35.5 
Net deferred tax assets$67.9 $113.1 
Schedule of Valuation Allowance
Changes in the valuation allowance was as follows:
Year ended December 31,202420232022
Valuation allowance, at beginning of year$(1,150.1)$(1,110.5)$(1,226.2)
Actuarial pension adjustments24.8 84.5 70.7 
Expired net operating losses/tax credits35.2 42.9 52.3 
Foreign exchange15.5 (6.8)14.8 
Recognition of income tax benefit (expense) (i)
(56.0)(125.9)(43.9)
Other(38.0)(34.3)21.8 
Valuation allowance, at end of year$(1,168.6)$(1,150.1)$(1,110.5)
(i) Includes U.S. pension activity of $(44.8) million, ($95.9) million and ($11.3) million for the years ended December 31, 2024, 2023 and 2022, respectively.
Schedule of Tax Effected Tax Loss Carryforwards
The company has tax effected tax loss carryforwards as follows:
As of December 31, 2024
U.S. Federal$339.6 
State and local196.0 
Foreign252.0 
Total tax loss carryforwards$787.6 
These carryforwards will expire as follows:
Year
2025$20.4 
202615.1 
202719.0 
202889.9 
20294.9 
Thereafter361.0 
Unlimited277.3 
Total$787.6 
Schedule of Tax Credit Carryforwards
The company also has available tax credit carryforwards, which will expire as follows:
Year
2025$20.8 
202633.7 
20279.1 
20280.3 
20290.1 
Thereafter27.4 
Total$91.4 
Schedule of Cash Paid for Income Taxes, Net of Refunds
Cash paid for income taxes, net of refunds was as follows:
Year ended December 31,202420232022
Cash paid for income taxes, net of refunds$56.4 $63.4 $49.0 
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 31,202420232022
Balance at January 1$20.9 $17.8 $21.6 
Additions based on tax positions related to the current year2.5 4.6 1.9 
Changes for tax positions of prior years(3.4)2.6 1.2 
Reductions as a result of a lapse of applicable statute of limitations(5.8)(4.6)(5.4)
Settlements(0.5)— — 
Changes due to foreign currency(0.2)0.5 (1.5)
Balance at December 31$13.5 $20.9 $17.8