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Income taxes (Tables)
12 Months Ended
Dec. 31, 2018
Income Tax Disclosure [Abstract]  
Total Income (Loss) Before Income Taxes and Provision for Income Taxes
Following is the total income (loss) before income taxes and the provision for income taxes for the three years ended December 31, 2018.
Year ended December 31,
 
2018

 
2017

 
2016

Income (loss) before income taxes
 
 
 
 
 
 
United States
 
$
(53.6
)
 
$
(152.7
)
 
$
(88.3
)
Foreign
 
196.8

 
80.6

 
108.8

Total income (loss) before income taxes
 
$
143.2

 
$
(72.1
)
 
$
20.5

Provision for income taxes
 
 
 
 
 
 
Current
 
 
 
 
 
 
United States
 
$
4.7

 
$
(42.8
)
 
$
6.7

Foreign
 
51.4

 
33.9

 
47.7

Total
 
56.1

 
(8.9
)
 
54.4

Deferred
 
 
 
 
 
 
Foreign
 
8.2

 
3.4

 
2.8

Total provision (benefit) for income taxes
 
$
64.3

 
$
(5.5
)
 
$
57.2

Reconciliation of the Provision 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,
 
2018

 
2017

 
2016

United States statutory income tax provision (benefit)
 
$
30.1

 
$
(25.2
)
 
$
7.2

Income and losses for which no provision or benefit has been recognized
 
22.2

 
70.3

 
65.5

Foreign rate differential and other foreign tax expense
 
9.5

 
(11.3
)
 
(21.1
)
Income tax withholdings
 
19.3

 
16.8

 
22.8

Permanent items
 
(5.0
)
 
(3.0
)
 
(4.7
)
Enacted rate changes
 
(2.3
)
 
(0.4
)
 
3.5

Change in uncertain tax positions
 
(1.2
)
 
2.3

 
0.4

Change in valuation allowances due to changes in judgment
 
(5.9
)
 
(4.6
)
 
(16.4
)
Income tax credits, U.S.
 
(2.4
)
 
(50.4
)
 

Provision (benefit) for income taxes
 
$
64.3

 
$
(5.5
)
 
$
57.2

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, 2018 and 2017 were as follows:
As of December 31,
 
2018

 
2017

Deferred tax assets
 
 
 
 
Tax loss carryforwards
 
$
860.0

 
$
837.6

Postretirement benefits
 
440.3

 
437.7

Foreign tax credit carryforwards
 
221.6

 
127.0

Other tax credit carryforwards
 
29.8

 
29.1

Deferred revenue
 
37.1

 
40.9

Employee benefits and compensation
 
31.1

 
35.2

Purchased capitalized software
 
22.9

 
22.2

Depreciation
 
20.1

 
24.5

Warranty, bad debts and other reserves
 
4.8

 
5.3

Capitalized costs
 
5.1

 
3.1

Other
 
30.4

 
39.3

 
 
1,703.2

 
1,601.9

Valuation allowance
 
(1,547.5
)
 
(1,441.1
)
Total deferred tax assets
 
$
155.7

 
$
160.8

Deferred tax liabilities
 
 
 
 
Capitalized research and development
 
$
36.1

 
$
24.3

Other
 
30.2

 
25.8

Total deferred tax liabilities
 
$
66.3

 
$
50.1

Net deferred tax assets
 
$
89.4

 
$
110.7

Schedule of Tax Effected Tax Loss Carryforwards
At December 31, 2018, the company has tax effected tax loss carryforwards as follows:
As of December 31,
 
2018

U.S. Federal
 
$
349.6

State and local
 
257.5

Foreign
 
252.9

Total tax loss carryforwards
 
$
860.0

These carryforwards will expire as follows:
Year
 
2019
$
7.7

2020
25.9

2021
14.1

2022
15.1

2023
14.3

Thereafter
782.9

Total
$
860.0

Schedule of Tax Credit Carryforwards
The company also has available tax credit carryforwards, which will expire as follows:
Year
 
2019
$
11.8

2020
24.5

2021
41.9

2022
38.1

2023
27.0

Thereafter
108.1

Total
$
251.4

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, 2018, was as follows:
Year ended December 31,
 
2018

 
2017

 
2016

Cash paid for income taxes, net of refunds
 
$
39.1

 
$
34.3

 
$
46.4

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,
 
2018

 
2017

 
2016

Balance at January 1
 
$
27.9

 
$
35.8

 
$
27.7

Additions based on tax positions related to the current year
 
2.6

 
4.2

 
2.7

Changes for tax positions of prior years
 
(6.1
)
 
(11.2
)
 
12.0

Reductions as a result of a lapse of applicable statute of limitations
 
(2.4
)
 
(2.7
)
 
(2.8
)
Settlements
 
(1.5
)
 
(0.2
)
 
(0.1
)
Changes due to foreign currency
 
(1.6
)
 
2.0

 
(3.7
)
Balance at December 31
 
$
18.9

 
$
27.9

 
$
35.8