Note 13—Income taxes:

	Three months ended September 30,						Nine months ended September 30,
	2015			2016			2015			2016
	(In millions)
Expected tax expense (benefit), at U.S. federal statutory income tax rate of 35%	$	(8.0	)	$	4.0		$	(10.5	)	$	(9.3	)
Incremental net tax (benefit) on earnings and losses of non-U.S. and non-tax group companies		(4.6	)		4.9			(32.7	)		7.6
Non-U.S. tax rates		—			(1.0	)		(.6	)		(1.4	)
Valuation allowance		2.3			(.8	)		152.6			2.1
Adjustment to the reserve for uncertain tax positions, net		.5			.5			(2.4	)		1.1
Nondeductible expenses		1.3			.7			1.2			1.3
U.S.- Canada APA		—			(5.5	)		—			(5.5	)
Domestic production activities deduction		—			.2			(1.0	)		(.6	)
U.S. state income taxes and other, net		(1.0	)		(.4	)		(1.2	)		(1.1	)
Income tax expense (benefit)	$	(9.5	)	$	2.6		$	105.4		$	(5.8	)

Comprehensive provision for income taxes (benefit) allocable to:
Income tax expense (benefit)	$	(9.5	)	$	2.6		$	105.4		$	(5.8	)
Other comprehensive income (loss):
Marketable securities		(2.8	)		.8			(3.5	)		1.0
Currency translation		(4.6	)		1.8			(12.7	)		3.6
Interest rate swap		(2.6	)		.5			(2.6	)		(2.2	)
Pension plans		1.1			.8			2.6			2.5
OPEB plans		(.1	)		(.2	)		(.5	)		(.6	)
Total	$	(18.5	)	$	6.3		$	88.7		$	(1.5	)

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 expense 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 investments in LandWell and BMI.

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. 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 the third quarter of 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 the third quarter of 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 Kronos’ 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 changes to prior year taxable income of Kronos’ U.S. and Canadian subsidiaries. As a result of such agreed-upon changes, we recognized a $5.5 million current U.S. income tax benefit in the third quarter of 2016. In addition, Kronos’ Canadian subsidiary will incur a cash income tax payment of approximately CAD $3 million (USD $2.3 million) as a result of the U.S.-Canada APA, but such payment was fully offset by previously provided accruals (such USD $2.3 million has not been paid as of September 30, 2016, and is classified as part of income taxes payable at such date). 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 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.

Kronos has substantial net operating losses in Germany and Belgium, the benefit of which Kronos had previously recognized under the more-likely-than-not recognition criteria. In the second quarter of 2015, Kronos determined that such losses did not meet the more-likely-than-not recognition criteria, and as a result Kronos recognized a non-cash deferred income tax expense of $150.3 million in the second quarter of 2015 as a valuation allowance against Kronos’ net deferred income tax assets in such jurisdictions. Kronos recognized an additional $2.3 million non-cash deferred income tax asset valuation allowance during the third quarter of 2015 and recognized an aggregate $2.1 million non-cash deferred income tax asset valuation allowance in the first nine months of 2016 (mostly in the second quarter) as additional valuation allowance against additional losses in such jurisdictions.

Due to the second quarter 2015 loss at Kronos, 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 the maximum amount deferred taxes we are required to recognize with regards to our investment. Accordingly, our provision for income taxes includes a non-cash income tax benefit of $29.7 million for the first nine months of 2015 (primarily in the second quarter 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. We recognized a non-cash income tax of $9.1 million for the first nine 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 increase related to our equity in Kronos’ net income (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 non-tax group companies (in addition to the other items indicated above). A portion of such increase (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.

In 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 may decrease by approximately $10.7 million during the next twelve months primarily due to the expiration of certain statutes of limitations and certain adjustments to our prior year returns.