Note 12 – Income taxes:

	Three months ended						Nine months ended
	September 30,						September 30,
	2017			2018			2017			2018
	(In millions)
Expected tax expense (benefit), at U.S. federal statutory income tax rate of 35% in 2017 and 21% in 2018	$	8.5		$	(4.4	)	$	34.0		$	(12.1	)
Rate differences on equity in earnings of Kronos		(2.1	)		(1.9	)		(5.0	)		(4.3	)
Nontaxable income		(.1	)		-			(.3	)		(.2	)
U.S. state income taxes and other, net		.2			.2			.2			1.2

Income tax expense (benefit)	$	6.5		$	(6.1	)	$	28.9		$	(15.4	)

Comprehensive provision for income taxes (benefit) allocable to:
Net income (loss)	$	6.5		$	(6.1	)	$	28.9		$	(15.4	)
Other comprehensive income (loss):
Marketable securities		(2.8	)		-			(5.3	)		-
Currency translation		3.1			.3			5.7			(.6	)
Interest rate swap		.2			-			.2			-
Pension plans		.4			.3			1.1			.8
OPEB plans		(.1	)		(.1	)		(.1	)		(.1	)

Total	$	7.3		$	(5.6	)	$	30.5		$	(15.3	)

In accordance with GAAP, we recognize deferred income taxes on our undistributed equity in earnings (losses) of Kronos. Because we and Kronos are part of the same U.S. federal income tax group, any dividends we receive from Kronos are nontaxable to us. Accordingly, we do not recognize and we are not required to pay income taxes on dividends from Kronos. We received aggregate dividends from Kronos of $15.8 million in the first nine months of 2017 and $18.0 million in the first nine months of 2018. The amounts shown in the above table of our income tax rate reconciliation for rate differences on equity in earnings of Kronos represents the net tax (benefit) associated with such non-taxability of the dividends we receive from Kronos, as it relates to the amount of deferred income taxes we recognize on our undistributed equity in earnings (losses) of Kronos and 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.

As discussed in the 2017 Annual Report, on December 22, 2017, H.R.1, formally known as the “Tax Cuts and Jobs Act” (“2017 Tax Act”) was enacted into law. This new tax legislation among other changes, (i) reduced the U.S. Federal corporate income tax rate from 35% to 21% effective January 1, 2018; (ii) eliminated the domestic production activities deduction beginning in 2018; and (iii) allows for the expensing of certain capital expenditures. Following the enactment of the 2017 Tax Act, the Securities and Exchange Commission issued Staff Accounting Bulletin (SAB) 118 to provide guidance on the accounting and reporting impacts of the 2017 Tax Act. SAB 118 states that companies should account for changes related to the 2017 Tax Act in the period of enactment if all information is available and the accounting can be completed. In situations where companies do not have enough information to complete the accounting in the period of enactment, a company must either 1) record an estimated provisional amount if the impact of the change can be reasonably estimated; or 2) continue to apply the accounting guidance that was in effect immediately prior to the 2017 Tax Act if the impact of the change cannot be reasonably estimated. If estimated provisional amounts are recorded, SAB 118 provides a measurement period of no longer than one year during which companies should adjust those amounts as additional information becomes available in the reporting period within the measurement period in which such adjustment is determined.

Under GAAP, we are required to revalue our net deferred tax liability associated with our U.S. net taxable temporary differences in the period in which the new tax legislation is enacted based on deferred tax balances as of the enactment date, to reflect the effect of such reduction in the corporate income tax rate. Other than with respect to temporary differences related to our marketable securities, and certain year-end actuarial valuations associated with our defined benefit pension and OPEB plans, our temporary differences as of December 31, 2017 were not materially different from our temporary differences as of the enactment date, accordingly revaluation of our net taxable temporary differences was based on our net deferred tax liability as of December 31, 2017 (except for our temporary differences related to our marketable securities, and certain year-end actuarial valuations associated with our defined benefit pension and OPEB plans, for which such revaluation was based on the deferred income tax asset/liability as of enactment date). Such revaluation resulted in a non-cash deferred income tax benefit of $37.5 million recognized as of December 31, 2017 in continuing operations, reducing our net deferred income tax liability. The amounts recorded as of December 31, 2017 as a result of the 2017 Tax Act represent estimates based on information currently available. We did not make any additional measurement-period adjustments to the provisional amounts recorded for this item during the first six months of 2018, as we were still waiting on additional guidance that might impact the income tax effects of the new legislation recognized at December 31, 2017. During the third quarter of 2018, in conjunction with finalizing our federal income tax return, we were able to obtain, prepare and analyze the necessary information to complete the accounting under ASC 740 related to the revaluation of our net deferred tax liability associated with our U.S. net taxable temporary differences as of December 31, 2017, which resulted in the recognition of an immaterial adjustment to the provisional amount recognized at December 31, 2017. Accordingly, we have completed our analysis related to such revaluation as of September 30, 2018.

Income tax matters related to Kronos

Kronos has substantial net operating loss (NOL) carryforwards in Germany (the equivalent of $652 million for Kronos’ German corporate purposes and $.5 million for German trade tax purposes at December 31, 2017) and in Belgium (the equivalent of $50 million for Kronos’ Belgian corporate tax purposes at December 31, 2017), all of which have an indefinite carryforward period. As a result, Kronos has 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. As discussed in the 2017 Annual Report, commencing June 30, 2015, Kronos concluded that it was required to recognize a non-cash deferred income tax asset valuation allowance under the more-likely-than-not recognition criteria with respect to its German and Belgian net deferred income tax assets at such date. During the first six months of 2017, Kronos recognized an aggregate non-cash deferred 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 NOL during the period, including $7.7 million in the second quarter of 2017. As also discussed in the 2017 Annual Report, at June 30, 2017, Kronos concluded it had sufficient positive evidence under the more-likely-than-not recognition criteria to support reversal of the entire valuation allowance related to its German and Belgian operations. 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, of which $141.9 million related to Germany and $8.0 million related to Belgium) relates to Kronos’ change in judgment at that date 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 and is recognized throughout the year, including interim periods subsequent to the date of the change in judgment. Accordingly, Kronos’ income tax benefit in calendar 2017 includes an aggregate non-cash deferred income tax benefit of $186.7 million related to the reversal of the German and Belgian valuation allowance, comprised of $12.7 million recognized in the first half of 2017 (noted above) related to the utilization of a portion of both the German and Belgian NOLs during such period, $149.9 million related to the portion of the valuation allowance reversed as of June 30, 2017 and $24.1 million recognized in the second half of 2017 (including $7.8 million reversed in the third quarter) related to the utilization of a portion of both the German and Belgian NOLs during such period. Kronos’ deferred income tax asset valuation allowance increased $13.7 million in 2017 as a result of changes in currency exchange rates, which increase was recognized as part of other comprehensive income (loss).

Prior to the enactment of the 2017 Tax Act, the undistributed earnings of Kronos’ European subsidiaries were deemed to be permanently reinvested (Kronos had not made a similar determination with respect to the undistributed earnings of its Canadian subsidiary). Pursuant to the Transition Tax provisions imposing a one-time repatriation tax on post-1986 undistributed earnings, Kronos recognized a provisional current income tax expense of $76.2 million in the fourth quarter of 2017. The amounts recorded as of December 31, 2017 as a result of the 2017 Tax Act represent estimates based on information currently available. Kronos elected to pay such tax over an eight year period beginning in 2018, including approximately $6.1 million which was paid in April 2018 (for the 2017 tax year) and $4.6 million which was paid in the second and third quarters of 2018 (for the 2018 tax year). Kronos did not make any measurement-period adjustments to the provisional amounts recorded for this item during the first six months of 2018 because no new information became available during the period that required an adjustment. During the third quarter of 2018, in conjunction with finalizing Kronos’ federal income tax return and based on additional information that became available (including proposed regulations issued by the IRS in August 2018 with respect to the Transition Tax), Kronos recognized a provisional income tax benefit of $1.7 million which amount is recorded as a measurement-period adjustment, reducing the provisional income tax expense of $76.2 million recognized in the fourth quarter of 2017. As a result, at September 30, 2018, taking into account the prior Transition Tax installments payments of $10.7 million (noted above), the balance of Kronos’ unpaid Transition Tax aggregates $63.8 million, which will be paid in quarterly installments over the remainder of the eight year period. Of the $63.8 million, $58.1 million is recorded as a noncurrent payable to affiliate (income taxes payable to Valhi) and $5.7 million is included with Kronos’ current payable to affiliate (income taxes payable to Valhi) classified as a current liability. The issuance of final regulations and/or additional guidance with respect to the Transition Tax may impact the amount of the Transition Tax recognized in the fourth quarter of 2017, as adjusted in the third quarter of 2018. Kronos continues to gather information and is awaiting further guidance from the state jurisdictions in which Kronos operates with respect to the Transition Tax. Kronos will complete its accounting for this item within the prescribed measurement period ending December 22, 2018, pursuant to the guidance under SAB 118, and if Kronos determines an adjustment to the provisional amount recognized at December 31, 2017 is required, Kronos will recognize such adjustment in the reporting period within the SAB 118 measurement period in which such adjustment is determined.

Prior to the enactment of the 2017 Tax Act the undistributed earnings of Kronos’ European subsidiaries were deemed to be permanently reinvested (Kronos had not made a similar determination with respect to the undistributed earnings of its Canadian subsidiary). As a result of the implementation of a territorial tax system under the 2017 Tax Act, effective January 1, 2018, and the Transition Tax which in effect taxes the post-1986 undistributed earnings of Kronos’ non-U.S. subsidiaries accumulated up through December 31, 2017, Kronos determined effective December 31, 2017 that all of the post-1986 undistributed earnings of its European subsidiaries are not permanently reinvested. Accordingly, in the fourth quarter of 2017 Kronos recognized an aggregate provisional non-cash deferred income tax expense of $4.5 million based on its reasonable estimates of the U.S. state and non-U.S. income tax and withholding tax liability attributable to all of such previously-considered permanently reinvested undistributed earnings through December 31, 2017. The amounts recorded as of December 31, 2017 as a result of the 2017 Tax Act represent estimates based on information currently available. Kronos has not made any measurement-period adjustments to the provisional amounts recorded at December 31, 2017 for this item during the first nine months of 2018. However, Kronos recorded a provisional non-cash deferred income tax expense of $2.5 million for the estimated U.S. state and non-U.S. income tax and withholding tax liability attributable to the 2018 undistributed earnings of its non-U.S. subsidiaries in the first nine months of 2018, including withholding taxes related to the undistributed earnings of Kronos’s Canadian subsidiary. Kronos is continuing its review of certain other provisions under the 2017 Tax Act and waiting on further guidance, primarily from the state jurisdictions in which it operates, that may impact its determination of the aggregate temporary differences attributable to its investments in its non-U.S. subsidiaries. Kronos will complete its accounting for this item within the prescribed measurement period ending December 22, 2018, pursuant to the guidance under SAB 118, and if Kronos determines an adjustment to the provisional amount recognized at December 31, 2017 and September 30, 2018 are required, Kronos will recognize such adjustment in the reporting period within the SAB 118 measurement period in which such adjustment is determined.

Under U.S. GAAP, as it relates to the new GILTI tax rules, Kronos is allowed to make an accounting policy choice of either (1) treating taxes due on future U.S. inclusions in taxable income related to GILTI as a current-period expense when incurred (the “period cost method”) or (2) factoring such amounts into the measurement of our deferred taxes (the “deferred method”). Kronos’ selection of an accounting policy related to the GILTI tax provisions will depend, in part, on analyzing our global income to determine whether it expects to have future U.S. inclusions in taxable income related to GILTI and, if so, what the impact is expected to be. While Kronos’ future global operations depend on a number of different factors, Kronos does expect to have future U.S. inclusions in taxable income related to GILTI. As such, Kronos has performed an analysis of GILTI’s impact on its provision and determined the impact is not material. Because the impact is not material to its tax provision, Kronos has not recorded any adjustments related to potential GILTI tax in its financial statements in the first nine months of 2018. Further, Kronos has not made a policy decision regarding whether to record deferred taxes on GILTI or record GILTI tax as a current-period expense when incurred. Kronos will complete its policy election for this item within the prescribed measurement period ending December 22, 2018, pursuant to the guidance under SAB 118 and if Kronos determines such policy election impacts its provision, it will recognize an adjustment in the reporting period within the SAB 118 measurement period in which such adjustment is determined. Similarly, Kronos has evaluated the tax impact of BEAT on its tax provision in the first nine months of 2018 and determined that the tax law has no material impact on its tax provision as it has historically not entered into international payments between related parties that are unrelated to cost of goods sold.

None of Kronos U.S. and non-U.S. tax returns are currently under examination. As a result of prior audits in certain jurisdictions, which are now settled, 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 Kronos would agree to execute and finalize such agreements.

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During the third quarter of 2017, Kronos’ Canadian subsidiary executed and finalized an Advance Pricing Agreement with the Competent Authority for Canada (the “Canada-Germany APA”) effective for tax years 2005 - 2017. Pursuant to the terms of the Canada-Germany APA, the Canadian and German tax authorities agreed to certain prior year changes to taxable income of our Canadian and German subsidiaries. As a result of such agreed-upon changes, Kronos reversed a significant portion of its reserve for uncertain tax positions and recognized a non-cash income tax benefit of $8.1 million related to such reversal in the third quarter of 2017. In addition, Kronos recognized a $2.6 million non-cash income tax benefit related to an increase in its German NOLs and a $.6 million German cash tax refund related to the Canada-Germany APA in the third quarter of 2017.

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During the first quarter of 2018, Kronos’ German subsidiary executed and finalized the related Advance Pricing Agreement with the Competent Authority for Germany (the “Germany- Canada APA”) effective for tax years 2005 - 2017. In the first quarter of 2018, Kronos recognized a net $1.4 million non-cash income tax benefit related to an APA tax settlement payment between its German and Canadian subsidiaries.