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Income taxes (Tables)
12 Months Ended
Dec. 31, 2019
Income Tax Disclosure [Abstract]  
Total Income (Loss) Before Income Taxes and Provision (Benefit) for Income Taxes
Following is the total income (loss) before income taxes and the provision (benefit) for income taxes for the three years ended December 31, 2019.
Year ended December 31,
 
2019

 
2018

 
2017

Income (loss) before income taxes
 
 
 
 
 
 
United States
 
$
(48.1
)
 
$
(53.6
)
 
$
(152.7
)
Foreign
 
87.8

 
196.8

 
80.6

Total income (loss) before income taxes
 
$
39.7

 
$
143.2

 
$
(72.1
)
Provision for income taxes
 
 
 
 
 
 
Current
 
 
 
 
 
 
United States
 
$
7.6

 
$
4.7

 
$
(42.8
)
Foreign
 
41.0

 
51.4

 
33.9

Total
 
48.6

 
56.1

 
(8.9
)
Deferred
 
 
 
 
 
 
Foreign
 
4.4

 
8.2

 
3.4

Total provision (benefit) for income taxes
 
$
53.0

 
$
64.3

 
$
(5.5
)

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,
 
2019

 
2018

 
2017

United States statutory income tax provision (benefit)
 
$
8.3

 
$
30.1

 
$
(25.2
)
Income and losses for which no provision or benefit has been recognized
 
28.2

 
22.2

 
70.3

Foreign rate differential and other foreign tax expense
 
3.2

 
9.5

 
(11.3
)
Income tax withholdings
 
17.6

 
19.3

 
16.8

Permanent items
 
(2.5
)
 
(5.0
)
 
(3.0
)
Enacted rate changes
 
0.5

 
(2.3
)
 
(0.4
)
Change in uncertain tax positions
 
0.2

 
(1.2
)
 
2.3

Change in valuation allowances due to changes in judgment
 
(2.3
)
 
(5.9
)
 
(4.6
)
Income tax credits, U.S.
 
(0.2
)
 
(2.4
)
 
(50.4
)
Provision (benefit) for income taxes
 
$
53.0

 
$
64.3

 
$
(5.5
)

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 at December 31, 2019 and 2018 were as follows:
As of December 31,
 
2019

 
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

 
 
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


Schedule of Tax Effected Tax Loss Carryforwards
At December 31, 2019, the company has tax effected tax loss carryforwards as follows:
As of December 31,
 
2019

U.S. Federal
 
$
348.2

State and local
 
247.8

Foreign
 
245.1

Total tax loss carryforwards
 
$
841.1

These carryforwards will expire as follows:
Year
 
2020
$
23.9

2021
13.5

2022
15.8

2023
13.3

2024
12.2

Thereafter
762.4

Total
$
841.1


Schedule of Tax Credit Carryforwards
The company also has available tax credit carryforwards, which will expire as follows:
Year
 
2020
$
31.5

2021
35.0

2022
38.1

2023
27.0

2024
22.5

Thereafter
87.7

Total
$
241.8


Schedule of Cash Paid for Income Taxes, Net of Refunds
Cash paid for income taxes, net of refunds, for the three years ended December 31, 2019, was as follows:
Year ended December 31,
 
2019

 
2018

 
2017

Cash paid for income taxes, net of refunds
 
$
37.6

 
$
39.1

 
$
34.3


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,
 
2019

 
2018

 
2017

Balance at January 1
 
$
18.9

 
$
27.9

 
$
35.8

Additions based on tax positions related to the current year
 
11.1

 
2.6

 
4.2

Changes for tax positions of prior years
 
(0.6
)
 
(6.1
)
 
(11.2
)
Reductions as a result of a lapse of applicable statute of limitations
 
(2.3
)
 
(2.4
)
 
(2.7
)
Settlements
 
(1.1
)
 
(1.5
)
 
(0.2
)
Changes due to foreign currency
 
(0.4
)
 
(1.6
)
 
2.0

Balance at December 31
 
$
25.6

 
$
18.9

 
$
27.9