Note 12—Income taxes:

	Years ended December 31,
	2013			2014			2015
	(In millions)
Pre-tax income (loss):
United States	$	(70.4	)	$	40.1		$	(35.3	)
Non-U.S. subsidiaries		(147.5	)		71.9			(38.5	)
Total	$	(217.9	)	$	112.0		$	(73.8	)
Expected tax expense (benefit) at U.S. federal statutory income tax rate of 35%	$	(76.3	)	$	39.2		$	(25.8	)
Non-U.S. tax rates		4.3			(4.1	)		.6
Incremental net benefit on earnings (losses) of non-U.S. and U.S. subsidiaries		(18.5	)		(2.2	)		(37.6	)
Valuation allowance		—			—			159.0
U.S. state income taxes, net		(3.4	)		4.1			(1.3	)
Adjustment to the reserve for uncertain tax positions, net		2.1			(3.7	)		.8
Nondeductible expenses		2.9			2.8			3.0
Tax rate changes		(.2	)		—			—
Other, net		(1.9	)		(3.6	)		(1.4	)
Provision for income taxes (benefit)	$	(91.0	)	$	32.5		$	97.3
Components of income tax expense (benefit):
Currently payable (refundable):
U.S. federal and state	$	9.1		$	7.4		$	7.6
Non-U.S.		(1.2	)		15.2			3.3
Total		7.9			22.6			10.9
Deferred income taxes (benefit):
U.S. federal and state		(57.9	)		3.8			(58.5	)
Non-U.S.		(41.0	)		6.1			144.9
Total		(98.9	)		9.9			86.4
Provision for income taxes (benefit)	$	(91.0	)	$	32.5		$	97.3
Comprehensive provision for income taxes (benefit) allocable to:
Net income (loss)	$	(91.0	)	$	32.5		$	97.3
Other comprehensive income (loss):
Marketable securities		5.1			(11.3	)		(4.1	)
Currency translation		5.5			(16.9	)		(17.3	)
Pension plans		14.1			(33.2	)		4.1
OPEB plans		1.0			(1.2	)		(.4	)
Interest rate swap		—			—			(1.7	)
Total	$	(65.3	)	$	(30.1	)	$	77.9

The amount shown in the above table of our income tax rate reconciliation for non-U.S. tax rates represents the result determined by multiplying the pre-tax earnings or losses of each of our non-U.S. subsidiaries by the difference between the applicable statutory income tax rate for each non-U.S. jurisdiction and the U.S. federal statutory tax rate of 35%. The amount shown on such table for incremental net tax (benefit) on earnings and losses on non-U.S. companies and U.S. subsidiaries includes, as applicable, (i) current income taxes (including withholding taxes, if applicable), if any, associated with any current-year earnings of our Chemicals Segments non-U.S. subsidiaries to the extent such current-year earnings were distributed to us in the current year, (ii) deferred income taxes (or deferred income tax benefits) associated with the current-year change in the aggregate amount of undistributed earnings of our Chemicals Segment’s Canadian subsidiary, which earnings are not subject to a permanent reinvestment plan, in an amount representing the current-year change in the aggregate current income tax that would be generated (including withholding taxes, if applicable) when such aggregate undistributed earnings are distributed to us, (iii) current U.S. income taxes (or current income tax benefit) , including U.S. personal holding company tax, as applicable, attributable to current-year income (losses) of one of Kronos’ non-U.S. subsidiaries, which subsidiary is treated as a dual resident for U.S. income tax purposes, to the extent the current-year income (losses) of such subsidiary is subject to U.S. income tax under the U.S. dual-resident provisions of the Internal Revenue Code, and (iv) certain and deferred income taxes associated with distributions and earnings from our investment in LandWell and BMI.

The components of the net deferred tax liability at December 31, 2014 and 2015 are summarized below. See Note 20.

	December 31,
	2014						2015
	Assets			Liabilities			Assets			Liabilities
	(In millions)
Tax effect of temporary differences related to:
Inventories	$	5.4		$	(5.2	)	$	3.7		$	(3.7	)
Marketable securities		—			(126.4	)		—			(98.2	)
Property and equipment		—			(109.2	)		—			(96.6	)
Accrued OPEB costs		4.8			—			4.0			—
Accrued pension costs		52.0			—			44.0			—
Currency revaluation on intercompany debt		5.6			—			18.6			—
Accrued environmental liabilities		38.8			—			39.9			—
Other deductible differences		34.7			—			45.7			—
Other taxable differences		—			(21.6	)		—			(21.7	)
Investments in subsidiaries and affiliates		—			(278.7	)		—			(238.8	)
Tax on unremitted earnings of non-U.S. subsidiaries		—			(2.6	)		—			(2.0	)
Tax loss and tax credit carryforwards		163.6			—			154.3			—
Valuation allowance		(.1	)		—			(168.9	)		—
Adjusted gross deferred tax assets (liabilities)		304.8			(543.7	)		141.3			(461.0	)
Netting of items by tax jurisdiction		(143.9	)		143.9			(140.0	)		(140.0	)
Net noncurrent deferred tax asset (liability)	$	160.9		$	(399.8	)	$	1.3		$	(321.0	)

Our acquisition of an additional ownership interest in BMI in December 2013, discussed in Note 3, increased our ownership interest in BMI from 32% to 63%. As a result, effective December 31, 2013 we no longer account for our ownership interest in BMI by the equity method of accounting but instead BMI is a consolidated subsidiary. Prior to December 31, 2013, we recognized a deferred income tax liability for the excess of our book basis over our tax basis of our investment in BMI at capital gains rates, because we did not have the ability to control BMI and hence we could assume we would only realize such excess upon a disposition of our ownership interest in BMI. Upon gaining control of BMI in December 2013, we now have the ability to control the means in which such excess would be realized, and accordingly the deferred income tax liability we now recognize for such excess is based on the assumption that we would realize such excess from dividend distributions from BMI (which are taxed at a lower rate, after considering the effect of the dividends received deduction). Our income tax benefit in 2013 includes an aggregate $11.1 million benefit (classified in the table above as part of our incremental U.S. tax on earnings of non-U.S. and non-tax group companies) related to the remeasurement of such deferred income tax liability with respect to our investment in BMI from capital gains rates to dividend received deduction rates, including the deferred income taxes related to (i) the gain from the re-measurement of our existing investment in BMI to estimated fair value and (ii) the bargain purchase gain related to the additional ownership interest in BMI acquired in December 2013.

Tax authorities are examining certain of our U.S. and non-U.S. tax returns and have or may propose tax deficiencies, including penalties and interest. Because of the inherent uncertainties involved in settlement initiatives and court and tax proceedings, we cannot guarantee that these tax matters will be resolved in our favor, and therefore our potential exposure, if any, is also uncertain. In 2011 and 2012 Kronos received notices of re-assessment from the Canadian federal and provincial tax authorities related to the years 2002 through 2004. We objected to the re-assessments and believed the position was without merit. Accordingly, we appealed the re-assessments and in connection with such appeal we were required to post letters of credit aggregating Cdn. $7.9 million (see Note 9). In 2014, the Appeals Division of the Canadian Revenue Authority ruled in our favor and reversed in their entirety such notices of re-assessment. As a result, we recognized a non-cash income tax benefit of $3.0 million related to the release of a portion of our reserve for uncertain tax positions in 2014 related to the completion of this Canadian income tax audit. In addition, the related letters of credit have been cancelled. Also during 2014, we recognized a non-cash income tax benefit of $3.1 million related to the release of a portion of our reserve for uncertain tax positions in conjunction with the completion of an audit of our U.S. income tax return for 2009. We believe we have adequate accruals for additional taxes and related interest expense which could ultimately result from tax examinations. We believe the ultimate disposition of tax examinations should not have a material adverse effect on our consolidated financial position, results of operations or liquidity.

The following table shows the changes in the amount of our uncertain tax positions (exclusive of the effect of interest and penalties) during 2013, 2014 and 2015:

	Years ended December 31,
	2013			2014			2015
	(In millions)
Unrecognized tax benefits:
Amount beginning of year	$	33.4		$	47.9		$	30.1
Net increase (decrease):
Tax positions taken in prior periods		.5			(19.6	)		(.4	)
Tax positions taken in current period		11.3			3.6			6.4
Lapse due to applicable statute of limitations		3.4			(.7	)		(6.0	)
Acquisition of BMI and LandWell		.1			—			—
Changes in currency exchange rates		(.8	)		(1.1	)		(1.3	)
Amount at end of year	$	47.9		$	30.1		$	28.8

If our uncertain tax positions were recognized, a benefit of $29.2 million, $24.2 million and $23.4 million at December 31, 2013, 2014 and 2015, respectively, would affect our effective income tax rate. We currently estimate that our unrecognized tax benefits will decrease by approximately $6.6 million during the next twelve months due to the reversal of certain timing differences and the expiration of certain statutes of limitations.

We file income tax returns in various U.S. federal, state and local jurisdictions. We also file income tax returns in various foreign jurisdictions, principally in Germany, Canada, Belgium and Norway. Our U.S. income tax returns prior to 2012 are generally considered closed to examination by applicable tax authorities. Our foreign income tax returns are generally considered closed to examination for years prior to: 2006 for Norway; 2010 for Canada; 2011 for Germany; and 2012 for Belgium.

We accrue interest and penalties on our uncertain tax positions as a component of our provision for income taxes. We accrued interest and penalties of $1.3 million during 2013 and $1.2 million during 2014 and $1.3 million during 2015, and at December 31, 2014 and 2015 we had $4.1 million and $4.2 million, respectively, accrued for interest and an immaterial amount accrued for penalties for our uncertain tax positions.

Our Chemicals Segment has substantial net operating loss (“NOL”) carryforwards in Germany (the equivalent of $683 million and $96 million for German corporate and trade tax purposes, respectively, at December 31, 2015) and in Belgium (the equivalent of $86 million for Belgian corporate tax purposes at December 31, 2015), all of which have an indefinite carryforward period. As a result, we have net deferred income tax assets recognized with respect to these two jurisdictions, primarily related to these NOL carryforwards. The German corporate tax is similar to the U.S. federal income tax, and the German trade tax is similar to the U.S. state income tax. Prior to June 30, 2015, and using all available evidence, we had concluded no deferred income tax asset valuation allowance was required to be recognized with respect to these net deferred income tax assets under the more-likely-than-not recognition criteria, primarily because (i) the carryforwards have an indefinite carryforward period, (ii) we utilized a portion of such carryforwards during the most recent three-year period, and (iii) we expected to utilize the remainder of the carryforwards over the long term. We had also previously indicated that facts and circumstances could change, which might in the future result in the recognition of a valuation allowance against some or all of such deferred income tax assets. However, as of June 30, 2015, and given our operating results during the second quarter of 2015 and our expectations at that time for our operating results for the remainder of 2015, we did not have sufficient positive evidence to overcome the significant negative evidence of having cumulative losses in the most recent twelve consecutive quarters in both our German and Belgian jurisdictions at June 30, 2015 (even considering that the carryforward period of our German and Belgium NOL carryforwards is indefinite, one piece of positive evidence). Accordingly, at June 30, 2015, we concluded that we were required to recognize a non-cash deferred income tax asset valuation allowance under the more-likely-than-not recognition criteria with respect to our German and Belgian net deferred income tax assets. Such valuation allowance aggregated $150.3 million at June 30, 2015. We recognized an additional $8.7 million non-cash deferred income tax valuation allowance under the more-likely-than-not recognition criteria during the third and fourth quarters of 2015, due to losses recognized by Kronos’ German and Belgium operations during such period. In addition to the aggregate $159.0 million increase in the deferred income tax asset valuation allowance recognized as part of the provision for income taxes in 2015, the deferred income tax asset valuation allowance also increased by an aggregate of $9.8 million in 2015 due to amounts recognized in other comprehensive loss.

We recognize deferred income taxes with respect to the excess of the financial reporting carrying amount over the income tax basis of our direct investment in Kronos common stock because the exemption under GAAP to avoid such recognition of deferred income taxes is not available to us. There is a maximum amount (or cap) of such deferred income taxes we are required to recognize with respect to our direct investment in Kronos, and we previously reached such maximum amount in the fourth quarter of 2010. Since that time and through March 31, 2015, we were not required to recognize any additional deferred income taxes with respect to our direct investment in Kronos because the deferred income taxes associated with the excess of the financial reporting carrying amount over the income tax basis of our direct investment in Kronos common stock continued to be above such cap. However, at June 30, 2015, the deferred income taxes associated with the excess of the financial reporting carrying amount over the income tax basis of our direct investment in Kronos common stock was, for the first time since the fourth quarter of 2010, below such cap, in large part due to the net loss reported by Kronos in the second quarter of 2015. Accordingly, our provision for income taxes in 2015 includes an aggregate non-cash income tax benefit of $29.3 million, recognized in the second, third and fourth quarters of, 2015, for the reduction in the deferred income taxes required to be recognized with respect to the excess of the financial reporting carrying amount over the income tax basis of our direct investment in Kronos common stock, to the extent such reduction related to our equity in Kronos’ net loss. Such amount is included in the above table of our income tax rate reconciliation for incremental net benefit on earnings and losses on non-U.S. and U.S. subsidiaries (in addition to the other items indicated above). A portion of such reduction also related to our equity in Kronos’ other comprehensive income (loss) items, and the amounts shown in the table above for income tax expense (benefit) allocated to other comprehensive income (loss) includes amounts related to our equity in Kronos’ other comprehensive income (loss) items.