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, 5430 LBJ Freeway, Suite
1700, Dallas, Texas 75240, Contran Corporation (“Contran”), a Delaware
corporation having its principal executive offices at Three Lincoln Centre, 5430
LBJ Freeway, Suite 1700, Dallas, TX 75240 and NL Industries, Inc. (“NL”), a
Delaware corporation having its principal executive offices at Three Lincoln
Centre, 5430 LBJ Freeway, Suite 1700, Dallas, TX 75240.

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.

 

VALHI, INC. By:       Bobby D. O’Brien   Vice President and Chief Financial
Officer CONTRAN CORPORATION By:       Gregory M. Swalwell   Vice President and
Controller NL INDUSTRIES, INC. By:       Kelly D. Luttmer   Vice President and
Tax Director