Note 12—Income taxes:

	Three months ended September 30,						Nine months ended September 30,
	2014			2015			2014			2015
	(In millions)
Expected tax expense (benefit), at U.S. federal statutory income tax rate of 35%	$	18.6		$	(8.0	)	$	30.4		$	(10.5	)
Incremental net benefit on earnings and losses of non-U.S. and U.S. subsidiaries		(1.4	)		(4.6	)		(2.6	)		(32.7	)
Non-U.S. tax rates		(1.3	)		—			(3.0	)		(.6	)
Valuation allowance		─			2.3			─			152.6
Adjustment to the reserve for uncertain tax positions, net		.5			.5			(5.1	)		(2.4	)
Nondeductible expenses		.9			1.3			2.1			1.2
Domestic manufacturing credit		(.7	)		—			(.9	)		(1.0	)
Adjustment to prior year taxes		(2.0	)		—			(1.8	)
U.S. state income taxes and other, net		1.2			(1.0	)		2.0			(1.2	)
Income tax expense (benefit)	$	15.8		$	(9.5	)	$	21.1		$	105.4

Comprehensive provision for income taxes (benefit) allocable to:
Income tax expense (benefit)	$	15.8		$	(9.5	)	$	21.1		$	105.4
Other comprehensive income (loss):
Marketable securities		.1			(2.8	)		(11.1	)		(3.5	)
Interest rate swap		—			(2.6	)		—			(2.6	)
Currency translation		(8.9	)		(4.6	)		(10.5	)		(12.7	)
Pension plans		1.0			1.1			2.9			2.6
OPEB plans		(.2	)		(.1	)		(.6	)		(.5	)
Total	$	7.8		$	(18.5	)	$	1.8		$	88.7

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 Chemicals Segment’s 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 benefit on earnings and losses on non-U.S. 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 Segment’s 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 benefit) 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, and (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 our Chemicals Segment’s 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.

As previously disclosed, our Chemicals Segment has substantial net operating loss (“NOL”) carryforwards in Germany (the equivalent of $738 million and $94 million for German corporate and trade tax purposes, respectively, at December 31, 2014) and in Belgium (the equivalent of $87 million for Belgian corporate tax purposes at December 31, 2014), 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, which as discussed elsewhere in this Quarterly Report have been driven in large part by the trend of TiO₂ selling prices over such periods as well as the $21.1 million pre-tax charge recognized in the second quarter of 2015 in connection with the implementation of certain work force reductions, 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 aggregates $150.3 million at June 30, 2015. We recognized an additional $2.3 million non-cash deferred income tax valuation allowance under the more-likely-than-not recognition criteria during the third quarter of 2015, due to losses recognized by Kronos’ German and Belgium operations during such period.

As disclosed in the 2014 Annual Report, 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 the first nine months of 2015 includes an aggregate non-cash income tax benefit of $29.7 million 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. A substantial portion of such $29.7 million was recognized in the second quarter of 2015, with the remainder recognized in the third quarter. 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.

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 matters will be resolved in our favor, and therefore our potential exposure, if any, is also uncertain. 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.

During the first nine months of 2015, primarily in the first quarter, we recognized a non-cash income tax benefit of $2.4 million primarily related to the release of a portion of our reserve for uncertain tax positions due to the expiration of the applicable statute of limitations. We currently estimate that our unrecognized tax benefits will change by $6.4 million during the next twelve months related to the expiration of certain statutes of limitations.