1 EXHIBIT 10.4 EXECUTION COPY FIRST AMENDMENT TO WARRANT AGREEMENT THIS FIRST AMENDMENT TO WARRANT AGREEMENT (this "Amendment") dated as of February 17, 2000 is between Brigham Exploration Company, a Delaware corporation ("Issuer") and Bank of Montreal, a Canadian bank (the "Warrant Holder" or "BMO"). RECITALS A. Brigham Oil & Gas, L.P., a Delaware limited partnership (the "Borrower"), BMO and Societe Generale Southwest Agency (the "Prior Lenders") previously entered into that certain Credit Agreement dated as of January 26, 1998, as amended by First Amendment to Credit Agreement dated as of August 20, 1998, Second Amendment to Credit Agreement dated as of March 26, 1999, Third Amendment to Credit Agreement dated as of July 19, 1999 and Fourth Amendment to Credit Agreement dated as of October 7, 1999 (such Credit Agreement as amended called the "Prior Credit Agreement"), pursuant to which the Prior Lenders agreed to make certain loans and extensions of credit to the Borrower as evidenced by those certain promissory notes in the aggregate principal amount of $75,000,000 (the "Prior Notes"). B. By Partial Assignment of Notes of even date herewith Shell Capital Inc. ("SCI") has acquired an interest in the Prior Notes and a like interest in all security for the payment of the Prior Notes and the performance of the Borrower's obligations under the Prior Credit Agreement; and C. The Prior Lenders and SCI (collectively, the "Lenders") have agreed to provide senior secured debt in the amount of up to $75,000,000 consisting of a rearrangement of the Prior Notes and advances to the Borrower, and the Borrower, BMO as Agent (the "Agent") and the Lenders are entering into that certain Amended and Restated Credit Agreement (the "Credit Agreement") of even date herewith which amends and restates in its entirety the Prior Credit Agreement and Prior Notes; and D. Issuer and BMO now desire to amend certain provisions of the Warrant Agreement dated as of July 19, 1999 between Issuer and BMO (the "Warrant Agreement") in recognition of the benefits Issuer will obtain under the Credit Agreement. NOW THEREFORE, in consideration of the mutual covenants and agreements herein contained, Issuer and BMO hereby agree that the Warrant Agreement shall be amended as follows: Section 1. Certain Definitions. As used in this Amendment, the terms "Agent", "Amendment", "Borrower", "Credit Agreement", "Issuer", "BMO", "SCI", "Lenders", "Prior Credit Agreement", "Prior Lenders," "Prior Notes", and "Warrant Agreement" shall have the meanings indicated above; and unless otherwise defined herein, all terms beginning with a capital letter which are defined in the Warrant Agreement shall have the same meanings herein as therein unless the context hereof otherwise requires. 2 Section 2. Amendments to Warrant Agreement. Section 2.1 The definition of Current Warrant Price in section 1. of the Warrant Agreement is hereby deleted in its entirety and the following is substituted therefor: "Current Warrant Price" shall mean, in respect of a share of Common Stock at any date herein specified, two dollars and two cents ($2.02) per share of Common Stock, subject to adjustment from time to time as provided in this Agreement." Section 2.2 Exhibit A to the Warrant Agreement (Form of Warrant Certificate) is amended as follows: (a) to change the reference "of two and 25/100 dollars ($2.25)" to "of two and 02/100 dollars ($2.02)"; (b) to add the following language after the date "July 19, 1999, to the next to the last paragraph of the Form of Warrant Certificate: "as amended by that certain First Amendment to Warrant Agreement dated as of February 17, 2000". Section 2.3 All references to the "Credit Agreement" in the Warrant Agreement shall henceforth refer to the Credit Agreement as defined in this Amendment, as such Credit Agreement is from time to time further amended, supplemented or restated. Section 2.4 The second sentence of Section 4.3(b) of the Warrant Agreement is hereby deleted in its entirety and the following is substituted therefor: "No adjustment of the number of shares of Common Stock for which a Warrant shall be exercised shall be made under Section 4.3(a) of this Agreement upon the issuance of any Additional Shares of Common Stock which are issued pursuant to the exercise of any warrants or other subscription or purchase rights or pursuant to the exercise of any conversion or exchange rights in any Convertible Securities (i) if any such adjustment shall previously have been made upon the issuance of such Convertible Securities (or upon the issuance of any such warrants or other rights) pursuant to Section 4.4 or Section 4.5 of this Agreement, (ii) if no adjustment was required pursuant to such sections upon the issuance of such Convertible Securities, warrants or other rights or (iii) in the event the issuance of such Convertible Securities, warrants or other rights predates or is of the same date as this Agreement, if no adjustment would have been required pursuant to such sections upon such issuance had this Agreement been in effect." Section 3. Representations and Warranties. Issuer hereby reaffirms that as of the effective date of this Amendment, the representations and warranties made by the Issuer in the Warrant Agreement will be true and correct as though made on and as of the date of this Amendment. 2 3 Section 4. Ratification. Issuer hereby expressly ratifies and affirms its obligations under the Warrant Agreement as amended by this Amendment and agrees that the Warrant Agreement as amended by this Amendment remains in full force and effect. Section 5. Issuance of Warrant Certificate. Contemporaneously with the execution of this Amendment, Issuer will deliver to BMO a Warrant Certificate reflecting the amendments described in Section 2.2 hereof. Section 6. Governing Law. This Amendment and the rights and obligations of the parties hereunder and under the Warrant Agreement shall be construed in accordance with and be governed by the laws of the State of Texas and the United States of America. Section 7. Descriptive Headings, Etc. The descriptive headings of the several Sections of this Amendment are inserted for convenience only and shall not be deemed to affect the meaning or construction of any of the provisions hereof. Section 8. Counterparts. This Amendment may be executed in any number of counterparts and by different parties on separate counterparts and all of such counterparts shall together constitute one and the same instrument. [SIGNATURES ON NEXT PAGE.] 3 4 IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed and delivered and effective as of the date first above written. BANK OF MONTREAL, as Warrant Holder By: ------------------------------------- Name: Thomas E. McGraw Title: Director BRIGHAM EXPLORATION COMPANY, As Issuer By: ------------------------------------- Name: Karen E. Lynch Title: Vice President S