AMENDED AND RESTATED TAX AGREEMENT Between VALHI, INC. and NL INDUSTRIES, INC.

Exhibit 10.40

AMENDED AND RESTATED

TAX AGREEMENT

Between

VALHI, INC.

and

NL INDUSTRIES, INC.

AMENDED AND RESTATED TAX AGREEMENT (the “Agreement”) dated as of December 1, 2012 by and among Valhi, Inc. (“VHI”), a Delaware corporation having its principal executive offices at Three Lincoln Centre, ▇▇▇▇ ▇▇▇ ▇▇▇▇▇▇▇, ▇▇▇▇▇ ▇▇▇▇, ▇▇▇▇▇▇, ▇▇▇▇▇ ▇▇▇▇▇, Contran Corporation (“Contran”), a Delaware corporation having its principal executive offices at Three Lincoln Centre, ▇▇▇▇ ▇▇▇ ▇▇▇▇▇▇▇, ▇▇▇▇▇ ▇▇▇▇, ▇▇▇▇▇▇, ▇▇ ▇▇▇▇▇ and NL Industries, Inc. (“NL”), a Delaware corporation having its principal executive offices at Three Lincoln Centre, ▇▇▇▇ ▇▇▇ ▇▇▇▇▇▇▇, ▇▇▇▇▇ ▇▇▇▇, ▇▇▇▇▇▇, ▇▇ ▇▇▇▇▇.

WHEREAS, VHI and NL file consolidated returns of federal income taxes and, subject to certain jurisdictional limitations, are subject to combined state and local tax reporting;

WHEREAS, this Agreement supercedes and amends and restates the Tax Agreement dated November 30, 2004 previously entered into between VHI, Contran and NL;

WHEREAS, VHI and NL wish to provide for the allocation of liabilities, and procedures to be followed, with respect to federal income taxes of NL and any subsidiaries of NL and with respect to certain combined state and local taxes on the terms of this Agreement.

NOW, THEREFORE, in consideration of the promises and agreements herein contained, the parties hereto agree as follows:

1. Definitions. As used in this Agreement, the following terms have the meanings set forth below:

(a) Code: The Internal Revenue Code of 1986, as amended, and with respect to any section thereof any successor provisions under such Code or any successor Code.

(b) Combined Foreign, State and Local Taxes: For a taxable period, and with respect to a specified group of entities, the amount of all Foreign, State and Local Taxes, for which liability is computed on the basis of a combined, unitary or consolidated return (whether at the initiative of the tax authority or of the taxpayer).

(c) Contran Corporation: A Delaware corporation that is the common parent of a group of corporations, which group of corporations includes the NL Group and VHI Group, electing to file a consolidated federal income tax return.

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(d) Federal Taxes: All federal income taxes, together with all interest and penalties with respect thereto.

(e) Foreign, State and Local Taxes: All foreign, state and local taxes, including franchise and similar taxes, together with all interest and penalties with respect thereto.

(f) VHI Group: VHI and each of its direct and indirect subsidiaries which would be a member of an affiliated group, within the meaning of section 1504(a) of the Code, and eligible to file a combined, unitary or consolidated return of which Contran was the common parent (the “Contran Tax Group”), as such VHI Group is constituted from time to time. For purposes of this Agreement (to the extent related to the determination of Combined Foreign, State and Local Taxes for the VHI Group), the term “VHI Group” shall include all direct and indirect subsidiaries of VHI with reference to which Combined Foreign, State and Local Taxes are determined.

(g) NL Group: NL and each of its direct or indirect subsidiaries which would be a member of an affiliated group, within the meaning of section 1504(a) of the Code, and eligible to file a combined, unitary or consolidated return of which NL was the common parent, as such NL Group is constituted from time to time. For purposes of this Agreement (to the extent related to the determination of Combined Foreign, State and Local Taxes for the NL Group) , the term “NL Group” shall include all direct and indirect subsidiaries of NL with reference to which Combined, Foreign, State and Local taxes are determined.

(h) NL Group Tax Liability: For a taxable period, the liability for Federal Taxes and Combined Foreign, State and Local taxes, as applicable, that the NL Group would have had if it were not a member of the VHI Group or Contran Tax Group during such taxable period (or during any taxable period prior thereto including prior periods when the NL Group was part of the consolidated federal income tax group of which NL Industries, Inc., a Delaware corporation, was the common parent (“NL Group”) ), and instead filed a separate consolidated or combined return, as applicable, for such taxable period); provided, however, that for purposes of determining such liability for a taxable period all tax elections shall be consistent with the tax elections made by Contran for such period. In making such tax elections it is understood Contran will make those tax elections which are beneficial to the Contran Tax Group on a consolidated basis. Nevertheless, Contran will use its best efforts in the case of those elections which affect the computation of the NL Group Tax Liability, to make elections in a reasonable manner so as to minimize the NL Group Tax Liability. For purposes of this Agreement, in determining the Combined Foreign, State and Local Taxes for the NL Group, such determination shall be made based on a separate Foreign, State and Local Tax Calculation as if the NL Group were a separate unitary filer with respect to states and other jurisdictions in which Contran is required to file on a unitary or combined basis.

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(i) Foreign, State and Local Tax Calculation: For each reporting period, the Tax Calculation will be based on the estimated taxable income of the NL Group for the taxable period that includes such reporting period, applied to current year tax rates and using the NL Group’s applicable apportionment factors and state, local or other applicable adjustments, in each case based on the applicable combined or unitary return most recently-filed as of each reporting period by the Contran Tax Group for each applicable tax jurisdiction (as modified for extraordinary, one-time event adjustments or tax law changes, if any, impacting the unitary calculation for the NL Group).

2. Contran as Agent. Contran shall be the sole agent for the NL Group in all matters relating to the NL Group Tax Liability. The NL Group shall not (a) terminate such agency or (b) without the consent of Contran, participate, or attempt to participate, in any matters related to the NL Group Tax Liability, including, but not limited to, preparation or filing of, or resolution of disputes, protests or audits with the Internal Revenue Service, state or local taxing authorities concerning, the Contran Tax Group’s consolidated returns of Federal Taxes, returns of Combined Foreign, State and Local Taxes or the NL Group Tax Liability with respect thereto for any taxable period beginning after January 1, 2001. The NL Group shall cooperate fully in providing Contran with all information and documents necessary or desirable to enable Contran to perform its obligations under this Section, including completion of Internal Revenue Service and state or local tax audits in connection with such NL Group Tax Liability and determination of the proper liability for such NL Group Tax Liability.

3. Liability for Taxes; Refunds.

(a) VHI, as the common parent of the NL Group, shall be responsible for, and shall pay to Contran or a taxing authority, as applicable, the consolidated tax liability for Federal Taxes and Combined Foreign, State and Local Taxes for the VHI Group and has the sole right to any refunds received from Contran or a taxing authority, as applicable, subject to the provisions of Sections 5 and 6 of this Agreement.

(b) Notwithstanding any other provision of this Agreement, NL and each subsidiary of NL which is a member of the NL Group shall be severally liable to VHI for the NL Group Tax Liability.

(c) NL shall indemnify VHI and hold it and the VHI Group other than the NL Group, harmless from and against any deficiency in the NL Group Tax Liability that may be due to VHI.

(d) VHI shall indemnify NL and hold it and the NL Group harmless from and against any Federal Taxes and Combined Foreign, State and Local Taxes attributable to the VHI Group or any other member of the Contran Tax Group, other than the NL Group, as such taxes are determined under this and other tax sharing agreements.

4. Tax Returns. Contran shall file on behalf of the NL Group any and all federal, foreign, state and local tax returns that are required as they pertain to the NL Group Tax Liability. The NL Group, at Contran’s’s request, shall join in any applicable consolidated returns of Federal Taxes and any returns of Combined Foreign, State and Local Taxes (for which returns have not been theretofore filed) and execute its consent, if such consent has not previously been

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executed, to each such filing on any form as may be prescribed for such consent if such consent is required. The decision of Contran’s Vice President and Tax Director (or any other officer so designated by Contran) with responsibility for tax matters shall, subject to the provisions of this Agreement, be binding in any dispute between Contran, VHI and the NL Group as to what tax position should be taken with respect to any item or transaction of the NL Group. The preceding sentence is limited to the tax positions that affect the NL Group Tax Liability and the combined VHI Group and Contran Tax Group. In addition, VHI and members of the VHI Group, including NL and members of the NL Group, shall provide each other with such cooperation, assistance and information as each of them may request of the other with respect to the filing of any tax return, amended return, claim for refund or other document with any taxing authority. NL shall be solely responsible for all taxes due for the NL Group with respect to tax returns filed by NL or a member of the NL Group that are required to be filed on a separate company basis, independent of Contran or VHI.

5. Payment of NL Group Tax Liability for Federal Taxes and Foreign, State and Local Taxes. On or before each date, as determined under section 6655 of the Code (with respect to Federal Taxes) and the applicable tax provisions with respect to any Foreign, State and Local Taxes due pursuant to this Agreement, for payment of an installment of estimated Federal Taxes or any Foreign, State and Local Taxes, NL shall pay to VHI an amount equal to the installment which the NL Group would have been required to pay as an estimated payment of Federal Taxes to the Internal Revenue Service or any Foreign, State and Local Taxes to the applicable taxing authority if it were filing a separate consolidated, combined or unitary return in respect of the NL Group Tax Liability. Any balance owed with respect to the NL Group Tax Liability for such taxable period shall be paid to VHI on or before the 15th day of the third month after the close of such taxable period. If it is not possible to determine the amount of such balance on or before such day, (a) a reasonable estimate thereof shall be paid on or before such day, (b) the amount of such balance shall be finally determined on or before the earlier of; (i) the 15th day of the ninth month after the close of such taxable period (or the applicable due date for the Contran foreign, state or local combined or unitary return) and (ii) the date on which the Contran Group consolidated tax return for such period is filed with the Internal Revenue Service or the applicable tax authority, and (c) any difference between the amount so determined and the estimated amount paid shall; (i) in the case of an underpayment, be promptly paid to VHI and (ii) in the case of an overpayment, be promptly refunded or applied against the estimated NL Group Tax Liability for the immediately following tax period, at the option of VHI. If the overpayment is not applied to the immediately following tax period, such overpayment shall be promptly refunded to the NL Group. As between the parties to this Agreement, the NL Group shall be solely responsible for the NL Group Tax Liability and shall have no responsibility for Federal Taxes of the VHI Group or the Contran Group other than payment of the NL Group Tax Liability in accordance with the terms of this Agreement. Notwithstanding the foregoing, VHI at its option may extend the payment due date for any of the payments referenced above.

6. Refunds for NL Group Losses and Credits for Federal Taxes. If the calculation with respect to the NL Group Tax Liability for Federal Taxes results in a net operating loss (“NOL”) for the current tax period that, in the absence of a Code Section 172(b)(3) election made by Contran, is carried back under Code Sections 172 and 1502 to a prior taxable period or periods of the NL Group with respect to which the NL Group previously made payments to VHI,

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then, in that event, VHI shall pay (or credit) NL an amount equal to the tax refund to which the NL Group would have been entitled had the NL Group filed a separate consolidated federal income tax return for such year (but not in excess of the net aggregate amount of the NL Group Tax Liability paid to VHI with respect to the preceding two taxable periods). If the calculation with respect to the NL Group Tax Liability results in an NOL for the current tax period, that subject to the Code Section 172(b)(3) election made by Contran, is not carried back under Code Sections 172 and 1502 to a prior taxable period or periods of the NL Group with respect to which NL made payments to VHI or is not carried back because the Contran Tax Group does not have a consolidated net operating loss for the current tax period, then, in that event such NOL shall be an NOL carryover to be used in computing the NL Group Tax Liability for future taxable periods, under the law applicable to NOL carryovers in general, as such law applies to the relevant taxable period. Payments made pursuant to this Section 6 shall be made on the date that Contran (or any successor common parent of a tax group to which the VHI Group is a member) files its consolidated federal income tax return for the taxable period involved. Principles similar to those discussed in this Section 6 shall apply in the case of the utilization of all NL Group loss and credit carrybacks and carryovers.

7. Refunds for NL Group Combined or Unitary Foreign, State and Local Losses and Credits . The foregoing principles contained in Section 6 shall apply in similar fashion to any consolidated, unitary or combined foreign, state or other local income tax returns, containing any member of the NL Group, which may be filed based on the NL Group Tax Liability for Foreign, State and Local Taxes.

8. Subsequent Adjustments. If any settlement with the Internal Revenue Service, foreign, state or local tax authority or court decision which has become final results in any adjustment to any item of income, deduction, loss or credit to the Contran Group in respect of any taxable period subject to this Agreement, which, in any such case, affects or relates to any member of the NL Group as constituted during such taxable period, the NL Tax Group Liability shall be redetermined to give effect to such adjustment as if it had been made as part of or reflected in the original computation of the NL Tax Group Liability and proper adjustment of amounts paid or owing hereunder in respect of such liability and allocation shall be promptly made in light thereof.

9. Amendments. This Agreement may be amended, modified, superseded or cancelled, and any of the terms, covenants, or conditions hereof may be waived, only by a written instrument specifically referring to this Agreement and executed by all parties (or, in the case of a waiver, by or on behalf of the party waiving compliance). The failure of any party at any time or times to require performance of any provision of this Agreement shall in no manner affect the right at a later time to enforce the same. No waiver by any party of any condition, or of any breach of any term or covenant, contained in this Agreement, in any one or more instances, shall be deemed to be or construed as a further or continuing waiver of any such condition or breach, or a waiver of any other condition or of any breach of any other term or covenant.

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10. Retention of Records. Contran shall retain all tax returns, tax reports, related workpapers and all schedules (along with all documents that pertain to any such tax returns, reports or workpapers) that relate to a taxable period in which the NL Group is included in a consolidated or combined tax return with VHI and Contran. Contran shall make such documents available to NL at NL’s request. Contran shall not dispose of such documents without the permission of NL.

11. Headings. The headings of this Agreement are for convenience of reference only, and shall not in any way affect the meaning or interpretation of this Agreement.

12. Governing Law. This Agreement shall be construed and enforced in accordance with the laws of the State of Delaware without regard to conflicts of laws provisions.

13. Counterparts. This Agreement may be executed in multiple counterparts, each of which shall be an original, but all of which shall constitute but one agreement.

14. Successors. This Agreement shall be binding upon and inure to the benefit of the parties hereto and their respective subsidiaries, and their respective successors and assigns.

15. Effective Date. This Agreement shall be effective as of December 1, 2012.

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IN WITNESS WHEREOF, the parties hereto have executed this Agreement on the date first above written.