Results of Operations · Reg FD Disclosure

UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C.   20549 FORM 8-K CURRENT REPORT Pursuant to Section 13 OR 15(d) of The Securities Exchange Act of 1934 Date of Report (Date of earliest event reported) May 6, 2021 Valhi, Inc. (Exact name of registrant as specified in its charter) Delaware 1-5467 87-0110150 (State or other jurisdiction of incorporation) (Commission File Number) (IRS Employer Identification No.)             5430 LBJ Freeway , Suite 1700 , Dallas , Texas 75240-2620 (Address of principal executive offices) (Zip Code) Registrant’s telephone number, including area code ( 972 ) 233-1700       (Former name or former address, if changed since last report.) Check the appropriate box below if the Form 8-K filing is intended to simultaneously satisfy the filing obligation of the registrant under any of the following provisions (see General Instruction A.2): ☐ Written communications pursuant to Rule 425 under the Securities Act (17 CFR 230.425)     ☐ Soliciting material pursuant to Rule 14a-12 under the Exchange Act (17 CFR 240.14a-12)     ☐ Pre-commencement communications pursuant to Rule 14d-2(b) under the Exchange Act (17 CFR 240.14d-2(b))     ☐ Pre-commencement communications pursuant to Rule 13e-4(c) under the Exchange Act (17 CFR 240.13e-4(c)) Securities registered pursuant to Section 12(b) of the Act: Title of each class   Trading Symbol(s)   Name of each exchange on which registered Common stock   VHI   NYSE Indicate by check mark whether the registrant is an emerging growth company as defined in Rule 405 of the Securities Act of 1933 (17 CFR §230.405) or Rule 12b-2 of the Securities Exchange Act of 1934 (17 CFR §240.12b-2). Emerging growth company  ☐ If an emerging growth company, indicate by check mark if the registrant has elected not to use the extended transition period for complying with any new or revised financial accounting standards provided pursuant to Section 13(a) of the Exchange Act.   ☐ Item 2.02 Results of Operations and Financial Condition. Item 7.01 Regulation FD Disclosure. The registrant hereby furnishes the information set forth in its press release issued on May 6, 2021, a copy of which is attached hereto as Exhibit 99.1 and incorporated herein by reference. The information, including Exhibit 99.1, the registrant furnishes in this current report under these items 2.02 and 7.01 is not deemed “filed” for purposes of section 18 of the Securities Exchange Act of 1934, as amended, or otherwise subject to the liabilities of that section.  Registration statements or other documents filed with the U.S. Securities and Exchange Commission shall not incorporate this information by reference, except as otherwise expressly stated in such filing. Item 8.01   Other Events. The registrant is also filing this current report to revise and update the description of its capital stock.  Such description is set forth in Exhibit 99.2 to this current report and is incorporated herein by reference. Item 9.01 Financial Statements and Exhibits. (d) Exhibits               Item No.   Exhibit Index           99.1   Press release dated May 6, 2021 entitled “Valhi Reports First Quarter 2021 Results” and issued by the registrant .           99.2*   Description of the Registrant’s Capital Stock .           104   Cover Page Interactive Data File (embedded within the Inline XBRL document)         ________ * Intended to be deemed filed rather than furnished pursuant to General Instruction B.2 to Form 8-K. SIGNATURE Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned hereunto duly authorized.   Valhi, Inc.   (Registrant)               By:   /s/ James W. Brown   Date:  May 6, 2021 James W. Brown, Executive Vice President and   Chief Financial Officer