Note 13—Income taxes:

	Three months ended June 30,						Six months ended June 30,
	2016			2017			2016			2017
	(In millions)
Expected tax benefit, at U.S. federal statutory income tax rate of 35%	$	(2.6	)	$	(39.3	)	$	(13.3	)	$	(25.4	)
Incremental net tax on earnings and losses of non-U.S., U.S. and non-tax group companies		.3			37.1			2.7			48.3
Non-U.S. tax rates		(.6	)		(2.3	)		(.4	)		(4.7	)
Valuation allowance		2.9			(157.6	)		2.9			(162.6	)
Adjustment to the reserve for uncertain tax positions, net		.4			.6			.6			1.1
Nondeductible expenses		.5			.3			.6			.8
Domestic production activities deduction		(.5	)		(1.5	)		(.8	)		(2.1	)
U.S. state income taxes		(.1	)		(4.7	)		(.5	)		(4.7	)
Other, net		(.1	)		—			(.2	)		(.1	)
Income tax expense (benefit)	$	.2		$	(167.4	)	$	(8.4	)	$	(149.4	)

Comprehensive provision for income taxes (benefit) allocable to:
Income tax expense (benefit)	$	.2		$	(167.4	)	$	(8.4	)	$	(149.4	)
Other comprehensive income (loss):
Marketable securities		.4			(.3	)		.2			(.5	)
Currency translation		(1.0	)		16.4			1.8			18.1
Interest rate swap		(.6	)		(.3	)		(2.7	)		.1
Pension plans		.9			2.2			1.7			3.1
OPEB plans		(.2	)		(.1	)		(.4	)		(.2	)
Total	$	(.3	)	$	(149.5	)	$	(7.8	)	$	(128.8	)

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 on earnings and losses on non-U.S. and non-tax group companies 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, (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, (iv) deferred income taxes associated with our direct investment in Kronos (beginning in the second quarter of 2015) and (v) current and deferred income taxes associated with distributions and earnings from our investment in LandWell and BMI.

Kronos has substantial net operating loss (NOL) carryforwards in Germany (the equivalent of $638 million for German corporate purposes and $71 million for German trade tax purposes at December 31, 2016) and in Belgium (the equivalent of $93 million for Belgian corporate tax purposes at December 31, 2016), all of which have an indefinite carryforward period. As a result, we have net deferred income tax assets 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 Belgian 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 at such date. We recognized an additional non-cash deferred income tax asset valuation allowance during the second half of 2015 due to losses recognized by our German and Belgian operations during such period. During 2016, we recognized an aggregate $2.2 million non-cash tax benefit as the result of a net decrease in such deferred income tax valuation allowance, as the impact of utilizing a portion of our German NOLs during such period more than offset the impact of additional losses recognized by our Belgian operations during such period. Such valuation allowance aggregated approximately $173 million at December 31, 2016 ($153 million with respect to Germany and $20 million with respect to Belgium). During the first six months of 2017, we recognized an aggregate non-cash income tax benefit of $12.7 million as a result of a net decrease in such deferred income tax asset valuation allowance, due to utilizing a portion of both the German and Belgian NOLs during such period, including $7.7 million in the second quarter of 2017. At June 30, 2017, we concluded we now have sufficient positive evidence under the more-likely-than-not recognition criteria to support reversal of the entire valuation allowance related to our German and Belgian operations. As discussed below, a large portion of the remaining valuation allowance is reversed as of June 30, 2017, but a portion of the remaining valuation allowance will be reversed during the second half of 2017. Such sufficient positive evidence at June 30, 2017 includes, among other things, the existence of cumulative profits in the most recent twelve consecutive quarters (Germany) or profitability in recent quarters during which such profitability was trending upward throughout such period (Belgium), the ability to demonstrate future profitability in Germany and Belgium for a sustainable period, and the indefinite carryforward period for the German and Belgian NOLs. Accordingly, our income tax benefit in the second quarter of 2017 includes an aggregate non-cash income tax benefit of $149.9 million related to such reversal at June 30, 2017 ($141.9 million related to Germany, and $8.0 million related to Belgium). Such second quarter 2017 income tax benefit associated with reversal of the German and Belgian valuation allowance excludes the non-cash income tax benefit of $7.7 million, also recognized in the second quarter, as discussed above. In addition to the above amounts, our deferred income tax asset valuation allowance increased by $9.5 million during the first six months of 2017 as a result of changes in currency exchange rates, which was recognized as part of other comprehensive income (loss).

In accordance with the ASC 740-270 guidance regarding accounting for income taxes at interim dates, the amount of the valuation allowance reversed at June 30, 2017 ($149.9 million) relates to our change in judgment regarding the realizability of the related deferred income tax asset as it relates to future years (i.e. 2018 and after). A change in judgment regarding the realizability of deferred tax assets as it relates to the current year is considered in determining the estimated annual effective tax rate for the year. Accordingly, of the aggregate $173 million deferred income tax asset valuation allowance recognized at December 31, 2016, approximately $163 million has been reversed through June 30, 2017, and the remaining $20 million (which relates to the expected level of profitability of our German and Belgian operations in calendar 2017) will be reversed during the third and fourth quarters of 2017 (such aggregate reversal amount includes the $9.5 million increase to our deferred income tax asset valuation allowance as a result of changes in currency exchange rates recognized as part of other comprehensive income (loss).

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. As a result of ongoing audits in certain jurisdictions, in 2008 Kronos filed Advance Pricing Agreement Requests with the tax authorities in the U.S., Canada and Germany. These requests have been under review with the respective tax authorities since 2008 and prior to 2016, it was uncertain whether an agreement would be reached between the tax authorities and whether we would agree to execute and finalize such agreements. During 2016, Contran, as the ultimate parent of our U.S. Consolidated income tax group, executed and finalized an Advance Pricing Agreement with the U.S. Internal Revenue Service and our Canadian subsidiary executed and finalized an Advance Pricing Agreement with the Competent Authority for Canada (collectively, the “U.S.-Canada APA”) effective for tax years 2005 - 2015. Pursuant to the terms of the U.S.-Canada APA, the U.S. and Canadian tax authorities agreed to certain prior year changes to taxable income of Kronos’ U.S. and Canadian subsidiaries. As a result of such agreed-upon changes, Kronos’ Canadian subsidiary incurred a cash income tax payment of approximately CAD $3 million (USD $2.3 million) related to the U.S.-Canada APA, but such payment was fully offset by previously provided accruals. We currently expect the Advance Pricing Agreement between Canada and Germany (collectively, the “Canada-Germany APA”) to be executed and finalized within the next twelve months. We believe we have adequate accruals to cover any cash income tax payment which might result from the finalization of the Canada-Germany APA, and accordingly we do not expect the execution of such APA to have a material adverse effect on our consolidated financial position, results of operations or liquidity.

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. During the second, third and fourth quarters of 2015, we recognized an aggregate $29.3 million non-cash income tax benefit 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 in 2015. We recognized a non-cash income tax expense of $6.5 million in 2016 (including $3.4 million in the first six months of 2016) for the increase 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 income (loss) in such periods. Our provision for income taxes in the first six months of 2017 includes a non-cash income tax expense of $39.5 million for the increase 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 income in such period. Such amount is included in the above table of our income tax rate reconciliation for incremental net tax on earnings and losses on non-U.S. and non-tax group companies (in addition to the other items included in such line item in the rate reconciliation, as indicated above). A portion of such increase (decrease) with respect to the excess of the financial reporting carrying amount over the income tax basis of our direct investment in Kronos common stock during 2015, 2016 and 2017 related to our equity in Kronos’ other comprehensive income (loss) items, and the amounts shown in the above table for income tax expense (benefit) allocated to other comprehensive income (loss) includes amounts related to our equity in Kronos’ other comprehensive income (loss) items.

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. We currently estimate that our unrecognized tax benefits will decrease by approximately $15.0 million during the next twelve months primarily due to certain adjustments to our prior year returns and the expiration of certain statutes of limitations.