CREDIT SUISSE FIRST BOSTON/
SC 13D, EX-99.1, 2001-01-10
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                                                                       EXHIBIT 1

                          SECURITIES PURCHASE AGREEMENT


         This SECURITIES PURCHASE AGREEMENT (this "Agreement"), is entered into
as of November 1, 2000, between Brigham Exploration Company, a Delaware
corporation (the "Company"), DLJ MB Funding III, Inc., a Delaware corporation
("MB"), and DLJ ESC II, LP, a Delaware limited partnership ("ESC") (collectively
referred to as "Investors").

         WHEREAS, the Company has authorized the sale and issuance of an
aggregate of up to one million, (1,000,000) shares of its Series A Preferred
Stock (the "Shares") and warrants to acquire six million, six hundred sixty-six
thousand, six hundred sixty-seven (6,666,667) shares of its Common Stock, (the
"Warrants"), in the form attached hereto as Exhibit A;

         Whereas, Investors desire to purchase the Shares and the Warrants on
the terms and conditions set forth herein; and

         Whereas, the Company desires to issue and sell the Shares and the
Warrants to Investors on the terms and conditions set forth herein;

         NOW, THEREFORE, in consideration of the premises and the mutual
covenants and agreements herein contained, and intending to be legally bound
hereby, the Company and Investors hereby agree as follows:

                                    ARTICLE I

                            TERMS OF THE TRANSACTION

         1.1 Authorization of Shares. On or prior to the Closing (as defined in
Section 2.1 below), the Company shall have authorized (a) the sale and issuance
to Investors of the Shares and the Warrants and (b) the issuance of such shares
of Common Stock to be issued upon exercise of the Warrants (the "Warrant
Shares"). The Shares shall have the rights, preferences, privileges and
restrictions set forth in the Certificate of Designations of the Company, in the
form attached hereto as Exhibit B (the "Certificate of Designations").

         1.2 Sale and Purchase. Subject to the terms and conditions hereof, at
the Closing the Company hereby agrees to issue and sell to MB and ESC, and MB
and ESC agree to purchase from the Company, respectively, 905,500 units (each a
"Unit") and 94,500 Units at a purchase price of Twenty Dollars ($20.00) per
Unit, with each such Unit consisting of (i) one Share and (ii) Warrant to
purchase 6.666667 Warrant Shares.

                                   ARTICLE II

                                     CLOSING

         2.1 Closing. The closing of the sale and purchase of the Shares and
Warrants under this Agreement (the "Closing") shall take place at the offices of
Vinson & Elkins L.L.P., 2300 First City Tower, 1001 Fannin, Houston, Texas
77002-6760, at 10:00 a.m., local time, on the date of this Agreement or at such
other time or place as the Company and Investors may mutually agree (the
"Closing Date"). All closing transactions at the Closing shall be deemed to have
occurred simultaneously.


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         2.2 Closing Deliveries. At the Closing, subject to the terms and
conditions hereof, the Company will deliver to each Investor, against payment of
the purchase price therefor by wire transfer made payable to the Company, a
certificate representing the applicable Shares and a Warrant representing the
applicable Warrants to purchase Warrant Shares.

                                   ARTICLE III

                  REPRESENTATIONS AND WARRANTIES OF THE COMPANY

         The Company represents and warrants to Investors, as of the date
hereof, that:

         3.1 Corporate Organization. The Company is a corporation duly
organized, validly existing, and in good standing under the laws of the State of
Delaware and has all requisite corporate power and authority in all material
respects to own, lease, and operate its properties and to carry on its business
as now being conducted. No actions or proceedings to dissolve the Company are
pending or, to the best knowledge of the Company, threatened. The Company is
duly qualified to do business as a foreign corporation and is in good standing
in each jurisdiction where such qualification is necessary, except where the
failure to so qualify or to be in good standing would not reasonably be expected
to have a Material Adverse Effect.

         3.2 Capitalization of the Company.

         (a) On the Closing Date, the authorized capital stock of the Company
will consist of 50,000,000 shares of Common Stock and 10,000,000 shares of
preferred stock, $.01 par value, 1,500,000 of which are designated as Series A
Preferred Stock. As of the date hereof, but prior to giving effect to the Enron
Transactions and the Financing Transaction (i) 17,028,175 shares of Common Stock
are outstanding and no shares of preferred stock are outstanding and (ii)
1,426,500 shares of Common Stock are reserved for issuance upon exercise of
outstanding employee, officer and director stock options and 8,212,476 shares of
Common Stock are reserved for issuance upon exercise of outstanding warrants or
conversion rights. All outstanding shares of capital stock of the Company have
been validly issued and are fully paid and nonassessable, and no shares of
capital stock of the Company are subject to, nor have any been issued in
violation of, preemptive or similar rights. On the Closing Date, the rights,
preferences, privileges and restrictions of the Shares will be as stated in the
Certificate of Designations.

         (b) Except as set forth above in subparagraph (a) of this Section 3.2,
there are outstanding (i) no shares of capital stock or other voting securities
of the Company; (ii) no securities of the Company convertible into or
exchangeable for shares of capital stock or other voting securities of the
Company; (iii) no options or other rights to acquire from the Company, and no
obligation of the Company to issue or sell, any shares of capital stock or other
voting securities of the Company or any securities of the Company convertible
into or exchangeable for such capital stock or voting securities; and (iv) no
equity equivalents, interests in the ownership or earnings, or other similar
rights of or with respect to the Company.

         (c) Neither the execution of this Agreement nor the performance of the
Company's obligations hereunder, nor the consummation of any other transaction
currently contemplated


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by the Company or any of its Subsidiaries, including the Financing Transaction
(as hereinafter defined) and the Enron Transaction (as hereinafter defined),
will trigger or cause any adjustment under any anti-dilution provisions or any
other similar provisions contained in any agreement as currently in effect that
have the effect of (i) causing a decrease in any exercise price or conversion
price in any security exercisable for or convertible into shares of Common Stock
(a "Common Stock Equivalent"), or (ii) causing an increase in the number of
shares of Common Stock that may be acquired upon conversion or exercise of a
Common Stock Equivalent.

         3.3 Authority Relative to This Agreement. The Company has full
corporate power and authority to execute, deliver, and perform this Agreement
and to execute, deliver, and where applicable, perform the Ancillary Documents
to which it is a party and to consummate the transactions contemplated hereby
and thereby. The execution, delivery and performance by the Company of this
Agreement and the execution, delivery, and where applicable, performance by it
of the Ancillary Documents to which it is a party, and the consummation by it of
the transactions contemplated hereby and thereby, have been (or prior to the
Closing will have been) duly authorized by all necessary corporate action of the
Company. This Agreement has been duly executed and delivered by the Company and
constitutes, and each Ancillary Document executed or to be executed by the
Company has been, or when executed will be, duly executed and delivered by the
Company and constitutes, or when executed and delivered will constitute, a valid
and legally binding obligation of the Company, enforceable against the Company
in accordance with its terms, except that such enforceability may be limited by
(i) applicable bankruptcy, insolvency, reorganization, moratorium, and similar
laws affecting creditors' rights generally and (ii) general equitable principles
(regardless of whether such enforceability is considered in a proceeding in
equity or at law).

         3.4 Noncontravention. The execution, delivery, and performance by the
Company of this Agreement and the execution, delivery, and where applicable, the
performance by it of Ancillary Documents to which it is a party and the
consummation by it of the transactions contemplated hereby and thereby do not
and will not (i) conflict with or result in a violation of any provision of the
Company's Certificate of Incorporation, as amended, or the Company's Bylaws, as
amended, or the charter, bylaws, partnership agreement or other governing
instruments of any Subsidiary, (ii) conflict with or result in a violation of
any provision of, or constitute (with or without the giving of notice or the
passage of time or both) a default under, or give rise (with or without the
giving of notice or the passage of time or both) to any loss of material
benefit, or of any right of termination, cancellation, or acceleration under,
any Material Agreement, (iii) result in the creation or imposition of any
Encumbrance upon the properties of the Company or any Subsidiary or (iv)
assuming compliance with the matters referred to in Section 3.5, violate any
Applicable Law binding upon the Company or any Subsidiary, except, in the case
of clauses (ii), (iii) and (iv) above, for any such conflicts, violations,
defaults, terminations, cancellations, accelerations, or Encumbrances which
would not, individually or in the aggregate, have a Material Adverse Effect on
the Company.

         3.5 Consents and Approvals. No consent, approval, order, or
authorization of, or declaration, filing, or registration with, any Governmental
Entity is required to be obtained or made by the Company or any Subsidiary in
connection with the execution, delivery, or performance by the Company of this
Agreement and the execution, delivery, and where applicable, performance of
Ancillary Documents to which it is a party or the consummation of the
transactions contemplated hereby and thereby, other than (i) compliance with any



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applicable requirements of the Securities Act; (ii) compliance with any
applicable requirements of the Exchange Act; (iii) compliance with any
applicable state securities laws; (iv) filing of the Certificate of Designations
with the Delaware Secretary of State; (v) compliance with any applicable
requirements of the HSR Act as a result of the exercise of any of the Warrants;
and (vi) such consents, approvals, orders, or authorizations which, if not
obtained, and such declarations, filings, or registrations which, if not made,
would not, individually or in the aggregate, have a Material Adverse Effect on
the Company. Except for such consents as are obtained before or
contemporaneously with consummation of the Closing, no consent or approval of
any person other than the Company, Investors or any Governmental Entity is
required to be obtained or made by the Company or any Subsidiary in connection
with the execution, delivery, or performance by the Company of this Agreement
and execution, delivery and, where applicable, performance of the Ancillary
Documents to which it is a party or the consummation of the transactions
contemplated hereby and thereby, other than such consents, approvals, orders, or
authorizations which, if not obtained, and such declarations, filings, or
registrations which, if not made, would not, individually or in the aggregate,
have a Material Adverse Effect on the Company.

         3.6 Authorization of Issuance; Reservation of Shares. When issued and
delivered pursuant to this Agreement and the Certificate of Designations against
payment therefor, the Shares and the Warrants will be validly issued, fully paid
and nonassessable. The Warrant Shares have been duly and validly reserved for
issuance. The issuances of the Shares and the Warrants are not subject to any
preemptive or similar rights.

         3.7 Financial Condition. The audited consolidated balance sheet of the
Company and its Subsidiaries as at December 31, 1999 and the related
consolidated statement of income, stockholders' equity and cash flow of the
Company and its Subsidiaries for the fiscal year ended on said date, with the
opinion thereon of Price Waterhouse heretofore furnished to the Investors and
the unaudited consolidated balance sheet of the Company and its Subsidiaries as
at June 30, 2000, and their related consolidated statements of income,
stockholders' equity and cash flow of the Company and its Subsidiaries for the
six-month period ended on such date hereto fore furnished to the Investors, are
complete and correct and fairly present the consolidated financial condition of
the Company and its Subsidiaries as at said dates and the results of its
operations for the fiscal year and the six-month period on said dates, all in
accordance with GAAP, as applied on a consistent basis (subject, in the case of
the interim financial statements, to normal year-end adjustments). Neither the
Company nor any Subsidiary has on the Closing Date any debt, trade payables,
contingent liabilities, liabilities for taxes, unusual forward or long-term
commitments or unrealized or anticipated losses from any unfavorable
commitments, except as referred to or reflected or provided for in the Financial
Statements or in Schedule 3.7 or except to the extent that the existence of any
of the foregoing would not have a Material Adverse Effect relative to the
Company. Since December 31, 1999, there has been no change or event having a
Material Adverse Effect relative to the Company, except as disclosed to the
Investors in writing. Since the date of the Financial Statements, neither the
business nor the properties of the Company's Subsidiaries, taken as a whole,
have been materially and adversely affected as a result of any fire, explosion,
earthquake, flood, drought, windstorm, accident, strike or other labor
disturbance, embargo, requisition or taking of property or cancellation of
contracts, permits or concessions by any Governmental Entity, riot, activities
of armed forces or acts of God or of any public enemy.


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         3.8 Litigation. Except as disclosed in Schedule 3.8 hereto, at the
Closing Date there is no litigation, legal, administrative or arbitral
proceeding, investigation or other action of any nature pending or, to the
knowledge of the Company, threatened against or affecting the Company or any
Subsidiary which both (a) involves the possibility of any judgment or liability
against the Company or any Subsidiary not fully covered by insurance (except for
normal deductibles), and (b) would be more likely than not to have a Material
Adverse Effect relative to the Company.

         3.9 ERISA. The Company and each ERISA Affiliate have complied in all
material respects with ERISA and, where applicable, the Code regarding each
Plan. Each Plan is, and has been, maintained in substantial compliance with
ERISA and, where applicable, the Code.

         No act, omission or transaction has occurred which could result in
imposition on the Company or any ERISA Affiliate (whether directly or
indirectly) of an amount of $100,000 or more as (i) either a civil penalty
assessed pursuant to section 502(c), (i) or (1) of ERISA or a tax imposed
pursuant to Chapter 43 of Subtitle D of the Code or (ii) breach of fiduciary
duty liability damages under section 409 of ERISA.

         No Plan (other than a defined contribution plan) or any trust created
under any such Plan has been terminated since September 2, 1974. No liability to
the PBGC in excess of $100,000 (other than for the payment of current premiums
which are not past due) by the Company or any ERISA Affiliate has been or is
expected by the Company or any ERISA Affiliate to be incurred with respect to
any Plan. No ERISA Event with respect to any Plan has occurred which could
reasonably be expected to result in liabilities of $100,000 or more.

         Full payment when due has been made of all amounts which the Company or
any ERISA Affiliate is required under the terms of each Plan or applicable law
to have paid as contributions to such Plan, and no accumulated funding
deficiency in an amount of $100,000 or more (as defined in section 302 of ERISA
and section 412 of the Code), whether or not waived, exists with respect to any
Plan.

         The actuarial present value of the benefit liabilities under each Plan
which is subject to Title IV of ERISA does not, as of the end of the Company's
most recently ended fiscal year, exceed the current value of the assets
(computed on a plan termination basis in accordance with Title IV of ERISA) of
such Plan allocable to such benefit liabilities by $100,000 or more. The term
"actuarial present value of the benefit liabilities" shall have the meaning
specified in section 4041 of ERISA.

         None of the Company or any ERISA Affiliate sponsors, maintains, or
contributes to an employee welfare benefit plan, as defined in section 3(1) of
ERISA, including, without limitation, any such plan maintained to provide
benefits to former employees of such entities, that may not be terminated by the
Company or any ERISA Affiliate in its sole discretion at any time without any
material liability.

         None of the Company or any ERISA Affiliate sponsors, maintains or
contributes to, or has at any time in the preceding six calendar years,
sponsored, maintained or contributed to, any Multiemployer Plan.

         None of the Company or any ERISA Affiliate is required to provide
security under section 401(a)(29) of the Code due to a Plan amendment that
results in an increase in current liability for the Plan.


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         3.10 Taxes. The Company has filed all United States Federal income tax
returns and all other tax returns which are required to be filed by it and has
paid all material taxes due pursuant to such returns or pursuant to any
assessment received by the Company, except for any taxes which are being
contested in good faith and by proper proceedings and against which adequate
reserves are being maintained. The charges, accruals and reserves on the books
of the Company in respect of taxes and other governmental charges are, in the
opinion of the Company, adequate. No tax lien has been filed and, to the
knowledge of the Company, no claim is being asserted with respect to any such
tax, fee or other charge, except for any taxes, fees or other charges which are
not material or which are being contested in good faith and by proper
proceedings and against which adequate reserves are being maintained.

         3.11 Titles, etc.

         (a) Subject to the matters set out in Schedule 3.11, each of the
Company and the Subsidiaries has good and defensible title, in all material
respects, to the material Oil and Gas Properties that are evaluated in the most
recently delivered reserve report, free and clear of all Liens, other than
Excepted Liens. Except for immaterial divergences, after giving full effect to
the Excepted Liens, the Company owns, in all material respects, the net
interests in production attributable to the Hydrocarbon Interests that are
evaluated in the most recently delivered reserve report, and the ownership of
such Hydrocarbon Interests shall not in any material respect obligate the
Company to bear the costs and expenses relating to the maintenance, development
and operations of each such Hydrocarbon Interest in an amount in excess of the
working interest of such Hydrocarbon Interest (without a corresponding increase
in net revenue interest). The Company does not believe, based upon information
in its possession, that its most recently delivered reserve report materially
overstates its oil and gas reserves, bearing in mind that reserves are evaluated
based upon estimates and assumptions with respect to which reasonable minds of
competent reserve engineers may differ.

         (b) All leases and agreements necessary for the conduct of the business
of the Company and the Subsidiaries are valid and subsisting, in full force and
effect and there exists no default or event or circumstance which with the
giving of notice or the passage of time or both would give rise to a default
under any such lease or leases, which would have a Material Adverse Effect on
the conduct of the business of the Company and the Subsidiaries.

         (c) The Oil and Gas Properties presently owned, leased or licensed by
the Company and the Subsidiaries, including, without limitation, all easements
and rights of way, include all properties necessary to permit the Company and
the Subsidiaries to conduct their business in all material respects in the same
manner as its business has been conducted prior to the Closing Date.

         (d) All of the properties of the Company and the Subsidiaries which are
reasonably necessary for the operation of their business are in good working
condition in all material respects and are maintained in accordance with prudent
business standards.

         3.12 No Material Misstatements. Taken as a whole, the written
information, statements, exhibits, certificates, documents and reports furnished
to Investors by the



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Company or any Subsidiary in connection with the negotiation of this Agreement
do not contain any material misstatement of fact or omit to state a material
fact or any fact necessary to make the statements contained therein not
materially misleading in the light of the circumstances in which made and with
respect to the Company or any Subsidiary. As of the Closing Date, there is no
fact peculiar to the Company or Subsidiary which has a Material Adverse Effect
relative to the Company or in the future is reasonably likely to have (so far as
the Company can now foresee) a Material Adverse Effect and which has not been
set forth in this Agreement or the other documents, certificates and statements
furnished to Investors by or on behalf of the Company or any Subsidiary prior
to, or on, the Closing Date in connection with the transactions contemplated
hereby.

         3.13 Investment Company Act. Neither the Company nor any Subsidiary is
an "investment company" or a company "controlled" by an "investment company,"
within the meaning of the Investment Company Act of 1940, as amended.

         3.14 Public Utility Holding Company Act. Neither the Company nor any
Subsidiary is a "holding company," or a "subsidiary company" of a "holding
company," or an "affiliate" of a "holding company" or of a "subsidiary company"
of a "holding company," or a "public utility" within the meaning of the Public
Utility Holding Company Act of 1935, as amended.

         3.15 Subsidiaries. Except as set forth on Schedule 3.15, the Company
has no Subsidiaries. Each Subsidiary is a corporation or limited partnership,
duly incorporated or organized, validly existing and in good standing under the
laws of its jurisdiction of incorporation or organization, if applicable, and
has all requisite corporate power and authority in all material respects to own,
lease, and operate its properties and to carry on its business as now being
conducted. Each Subsidiary is duly qualified to do business as a foreign
corporation or limited partnership, if applicable, and is in good standing in
each jurisdiction where such qualification is necessary, except where the
failure to so qualify or to be in good standing would not reasonably be expected
to have a Material Adverse Effect. There are outstanding (i) no securities of
any Subsidiary of the Company convertible into or exchangeable for shares of
capital stock or other voting securities of any Subsidiary of the Company and
(ii) no options or other rights to acquire from any Subsidiary of the Company,
and no obligation of any Subsidiary of the Company to issue or sell, any shares
of capital stock or other voting securities of any Subsidiary of the Company or
any securities of any Subsidiary of the Company convertible into or exchangeable
for such capital stock or voting securities.

         3.16 Defaults. Neither the Company nor any Subsidiary is in default nor
has any event or circumstance occurred which, but for the expiration of any
applicable grace period or the giving of notice, or both, would constitute a
default under any material agreement or instrument to which the Company is a
party or by which the Company is bound, which default would have a Material
Adverse Effect.

         3.17 Environmental Matters. Except for matters which are more likely
than not to not to have a Material Adverse Effect (or with respect to (c), (d)
and (e) below, where the failure to take such actions is more likely than not to
not have a Material Adverse Effect):

         (a) Neither any Oil and Gas Property of the Company or any of its
Subsidiaries nor the operations conducted thereon violate any order or
requirement of any court or Governmental Entity or any Environmental Laws;


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         (b) Without limitation of clause (a) above, no Oil and Gas Property of
the Company or any of its Subsidiaries nor the operations currently conducted
thereon or, to the best knowledge of the Company, by any prior owner or operator
of such property or operation, are in violation of or subject to any existing,
pending or threatened action, suit, investigation, inquiry or proceeding by or
before any court or Governmental Entity or to any remedial obligations under
Environmental Laws;

         (c) All notices, permits, licenses or similar authorizations, if any,
required to be obtained or filed by the Company or any of its Subsidiaries in
connection with the operation or use of any and all Property of the Company and
each of its Subsidiaries, including without limitation present, or to the best
of Company's knowledge, past treatment, storage, disposal or release of a
hazardous substance or solid waste into the environment, have been duly obtained
or filed, and the Company and each Subsidiary thereof are in compliance with the
terms and conditions of all such notices, permits, licenses and similar
authorizations;

         (d) All hazardous substances, solid waste, and oil and gas exploration
and production wastes, if any, generated at any and all Oil and Gas Property of
the Company and each of its Subsidiaries have in the past, during the tenure of
ownership of the Company and its Subsidiaries and to the best of the Company's
knowledge, prior thereto, been transported, treated and disposed of in
accordance with Environmental Laws and so as not to pose an imminent and
substantial endangerment to public health or welfare or the environment, and, to
the best knowledge of the Company, all such transport carriers and treatment and
disposal facilities have been and are operating in compliance with Environmental
Laws and so as not to pose an imminent and substantial endangerment to public
health or welfare or the environment, and are not the subject of any existing,
pending or threatened action, investigation or inquiry by any Governmental
Entity in connection with any Environmental Laws;

         (e) The Company has taken all steps reasonably necessary to determine
and has determined that no hazardous substances, solid waste, or oil and gas
exploration and production wastes, have been disposed of or otherwise released
and there has been no threatened release of any hazardous substances on or to
any Oil and Gas Property of the Company or any of its Subsidiaries except in
compliance with Environmental Laws and so as not to pose an imminent and
substantial endangerment to public health or welfare or the environment; and

         (f) To the extent applicable, all Oil and Gas Property of the Company
and each of its Subsidiaries currently satisfies all design, operation, and
equipment requirements imposed by the OPA or scheduled as of the Closing Date to
be imposed by OPA during the term of this Agreement, and the Company does not
have any reason to believe that such Oil and Gas Property, to the extent subject
to OPA, will not be able to maintain compliance with the OPA requirements during
the term of this Agreement; and

         (g) Neither the Company nor any of its Subsidiaries has any known
contingent liability in connection with any release or threatened release of any
oil, hazardous substance or solid waste into the environment.

         3.18 Compliance with the Law. Neither the Company nor any Subsidiary
has violated any Governmental Requirement or failed to obtain any license,
permit, franchise or other



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governmental authorization necessary for the ownership of any of its Oil and Gas
Properties or the conduct of its business, which violation or failure would have
(in the event such violation or failure were asserted by any Person through
appropriate action) a Material Adverse Effect. Except for such acts or failures
to act as would not have a Material Adverse Effect, the Oil and Gas Properties
(and properties unitized therewith) have been maintained, operated and developed
in a good and workmanlike manner and in conformity with all applicable laws and
all rules, regulations and orders of all duly constituted authorities having
jurisdiction and in conformity with the provisions of all leases, subleases or
other contracts comprising a part of the Hydrocarbon Interests and other
contracts and agreements forming a part of the Oil and Gas Properties;
specifically in this connection, but subject to the Material Adverse Effect
qualification set forth above, (i) after the Closing Date, no Oil and Gas
Property is subject to having allowable production reduced below the full and
regular allowable (including the maximum permissible tolerance) because of any
overproduction (whether or not the same was permissible at the time) prior to
the Closing Date and (ii) none of the wells comprising a part of the Oil and Gas
Properties (or properties unitized therewith) are deviated from the vertical
more than the maximum permitted by applicable laws, regulations, rules and
orders, and such wells are, in fact, bottomed under and are producing from, and
the well bores are wholly within, the Oil and Gas Properties (or in the case of
wells located on properties unitized therewith, such unitized properties).

         3.19 Insurance. Schedule 3.19 attached hereto contains an accurate and
complete description of all material policies of fire, liability, workmen's
compensation and other forms of insurance owned or held by the Company and each
Subsidiary as of the Closing Date. All such policies are in full force and
effect, all premiums with respect thereto covering all periods up to and
including the Closing Date have been paid, and no notice of cancellation or
termination has been received with respect to any such policy. Such policies are
sufficient for compliance with all requirements of law and of all agreements to
which the Company or any Subsidiary is a party; are valid, outstanding and
enforceable policies; provide adequate insurance coverage in at least such
amounts and against at least such risks (but including in any event public
liability) as are usually insured against in the same general area by companies
engaged in the same or a similar business for the assets and operations of the
Company and each Subsidiary; will remain in full force and effect through the
respective dates set forth in Schedule 3.19 with the payment of additional
premiums; and will not in any way be affected by, or terminate or lapse by
reason of, the transactions contemplated by this Agreement. Schedule 3.19
identifies all material risks, if any, which the Company, the Subsidiaries and
their respective Board of Directors or officers have designated as being self
insured. Neither the Company nor any Subsidiary has been refused any insurance
with respect to its assets or operations, nor has its coverage been limited
below usual and customary policy limits, by an insurance carrier to which it has
applied for any such insurance or with which it has carried insurance during the
last three years.

         3.20 Hedging Agreements. Schedule 3.20 sets forth, as of the Closing
Date, a true and complete list of all Hedging Agreements (including commodity
price swap agreements, forward agreements or contracts of sale which provide for
prepayment for deferred shipment or delivery of oil, gas or other commodities)
of the Company and each Subsidiary.

         3.21 Material Agreements. Set forth on Schedule 3.21 hereto is a
complete and correct list of all material agreements, leases, indentures,
purchase agreements, obligations in respect of letters of credit, guarantees,
joint venture agreements, and other instruments in



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effect or to be in effect as of the Closing Date (other than Hedging Agreements)
providing for, evidencing, securing or otherwise relating to any material
Debt of the Company or any Subsidiary, and all obligations of the Company or any
Subsidiary to issuers of surety or appeal bonds (excluding operator's bonds,
plugging and abandonment bonds, and similar surety obligations obtained in the
ordinary course of business) issued for account of the Company or any such
Subsidiary.

         3.22 Gas Imbalances. As of the Closing Date, except as set forth in the
most recent Reserve Report furnished to Investors, on a net basis there are no
gas imbalances, take or pay or other prepayments with respect to the Company's
or any Subsidiary's Hydrocarbon Interests which would require the Company or
such Subsidiary to deliver five percent (5%) or more of the monthly production
from the Company's and its Subsidiaries' Hydrocarbons produced on a monthly
basis from the Hydrocarbon Interests, at some future time without then or
thereafter receiving full payment therefor.

         3.23 Brokerage Fees. The Company has not retained any financial
advisor, broker, agent, or finder or paid or agreed to pay any financial
advisor, broker, agent, or finder on account of the sale by the Company and the
purchase by Investors of the Shares pursuant to this Agreement, except for CIBC
World Markets Corp. (or an Affiliate), and the Company hereby agrees to pay all
fees owing to CIBC World Markets Corp. on account of the consummation of such
transaction, which fees are not to exceed $1,200,000.

         3.24 SEC Filings. The Company has complied in all material respects
with its obligations to file with the Securities and Exchange Commission all
forms, reports, schedules, statements and other documents required to be filed
by it since May 9, 1997 under the Securities Act and the Exchange Act. All
forms, reports, schedules, statements, and other documents (including all
amendments thereto) filed by the Company with the Securities and Exchange
Commission since such date are herein collectively referred to as the "SEC
Filings". The SEC Filings, at the time filed, complied in all material respects
with all applicable requirements of federal securities laws. None of the SEC
Filings, including, without limitation, any financial statements or schedules
included therein, at the time filed or as same may have been amended, contained
any untrue statement of a material fact or omitted to state any material fact
required to be stated therein or necessary in order to make the statements
contained therein, in light of the circumstances under which they were made, not
misleading.

         3.25 Stockholder Approval. Neither the execution of this Agreement nor
the consummation of the transactions contemplated hereunder require the approval
of the stockholders of the Company under the applicable listing rules of the
Nasdaq Stock Market, Inc.


                                                                              10
<PAGE>   11

                                   ARTICLE IV

                   REPRESENTATIONS AND WARRANTIES OF INVESTORS

         Each Investor represents and warrants to the Company that:

         4.1 Organization. MB is a corporation duly organized, validly existing
and in good standing under the laws of the State of Delaware. ESC is a limited
partnership duly organized, validly existing and in good standing under the laws
of the State of Delaware. Each Investor has all requisite corporate power and
authority in all material respects to own, lease, and operate its properties and
to carry on its business as now being conducted. No actions or proceedings to
dissolve either Investor are pending or, to the best knowledge of any Investor,
threatened.

         4.2 Authority Relative to This Agreement. Each Investor has full
corporate or (if applicable) other power and authority to execute, deliver, and
perform this Agreement and execute, deliver and, where applicable, perform the
Ancillary Documents to which it is a party and to consummate the transactions
contemplated hereby and thereby. The execution, delivery, and performance by
each Investor of this Agreement and execution, delivery, and, where applicable,
performance of the Ancillary Documents to which it is a party, and the
consummation by it of the transactions contemplated hereby and thereby, have
been duly authorized by all necessary corporate (if applicable) action of such
Investor. This Agreement has been duly executed and delivered by each Investor
and constitutes, and each Ancillary Document executed or to be executed by each
Investor has been, or when executed will be, duly executed and delivered by such
Investor and constitutes, or when executed and delivered will constitute, a
valid and legally binding obligation of such Investor, enforceable against such
Investor in accordance with its terms, except that such enforceability may be
limited by (i) applicable bankruptcy, insolvency, reorganization, moratorium,
and similar laws affecting creditors' rights generally and (ii) general
equitable principles (regardless of whether such enforceability is considered in
a proceeding in equity or at law).

         4.3 Noncontravention. The execution, delivery, and performance by each
Investor of this Agreement and the execution, delivery and, where applicable,
performance of Ancillary Documents to which it is a party and the consummation
by it of the transactions contemplated hereby and thereby do not and will not
(i) conflict with or result in a violation of any provision of MB's Certificate
of Incorporation or Bylaws or ESC's Certificate of Limited Partnership or
partnership agreement, (ii) conflict with or result in a violation of any
provision of, or constitute (with or without the giving of notice or the passage
of time or both) a default under, or give rise (with or without the giving of
notice or the passage of time or both) to any right of termination,
cancellation, or acceleration under, any bond, debenture, note, mortgage,
indenture, lease, agreement or other instrument or obligation to which any
Investor is a party or by which Investor or any of its properties may be bound,
(iii) result in the creation or imposition of any Encumbrance upon the
properties of any Investor, or (iv) violate any Applicable Law binding upon any
Investor, except, in the case of clauses (ii), (iii) and (iv) above, for any
such conflicts, violations, defaults, terminations, cancellations,
accelerations, or Encumbrances which would not, individually or in the
aggregate, have a Material Adverse Effect on any Investor.

         4.4 Consents and Approvals. No consent, approval, order, or
authorization of, or declaration, filing, or registration with, any Governmental
Entity is required to be obtained or made by Investors in connection with the
execution, delivery, or performance by Investors of this Agreement. No consent
or approval of any person other than any Governmental Entity is required to be
obtained or made by any Investor in connection with the execution, delivery or
performance by Investors of this Agreement and the execution, delivery and,
where applicable, performance of the Ancillary Documents to which it is a party.


                                                                              11
<PAGE>   12

         4.5 Purchase for Investment. Each Investor understands that none of the
Shares, the Warrants or the Warrant Shares have been registered under the
Securities Act. Each Investor also understands that the Shares, the Warrants and
the Warrant Shares are being offered and sold pursuant to an exemption from
registration contained in the Securities Act based in part upon Investors'
representations contained in the Agreement. Each Investor hereby represents and
warrants as follows:

               (a) Investor Bears Economic Risk. Each Investor has substantial
experience in evaluating and investing in private placement transactions of
securities in companies similar to the Company so that it is capable of
evaluating the merits and risks of its investment in the Company and has the
capacity to protect its own interests. Without limiting the generality of the
foregoing, each Investor further represents that it has such knowledge regarding
the oil and gas industry and the business of the Company and the current
circumstances surrounding such industry and business that it is capable of
evaluating the merits and risks of the acquisition of the Shares, the Warrants
and the Warrant Shares. Each Investor must bear the economic risk of this
investment indefinitely unless the Shares, the Warrants or the Warrant Shares
are registered pursuant to the Securities Act, or an exemption from registration
is available. Each Investor understands that the Company has no present
intention of registering the Shares, the Warrants or the Warrant Shares. Each
Investor also understands that there is no assurance that any exemption from
registration under the Securities Act will be available and that, even if
available, such exemption may not allow an Investor to transfer all or any
portion of the Shares, Warrants or Warrant Shares under the circumstances, in
the amounts or at the times an Investor might propose.

               (b) Acquisition for Own Account. Each Investor is acquiring the
Shares, the Warrants and Warrant Shares for such Investor's own account for
investment only, and not with a view towards their distribution.

               (c) Investor Can Protect Its Interest. Each Investor represents
that by reason of its, or of its management's, business or financial experience,
such Investor has the capacity to protect its own interests in connection with
the transactions contemplated in this Agreement and the Ancillary Agreements.
Further, neither Investor is aware of no publication of any advertisement in
connection with the transactions contemplated in the Agreement.

               (d) Accredited Investor. Each Investor represents that it is an
accredited investor within the meaning of Regulation D under the Securities Act.

               (e) Company Information. Each Investor has had access to the
Company's SEC Filings and has had an opportunity to discuss the Company's
business, management and financial affairs with directors, officers and
management of the Company and has had the opportunity to review the Company's
operations and facilities. Each Investor has also had the opportunity to ask
questions of, and receive answers from, the Company and its management regarding
the terms and conditions of this investment. Each Investor hereby acknowledges
and affirms that it has completed its own independent investigation, analysis,
and evaluation of the Company and its subsidiaries, that it has made all such
reviews and inspections of the business, assets, results of operations,
condition (financial or otherwise), and prospects of the Company and its
subsidiaries as it has deemed necessary or appropriate, and that in making its
decision to enter into this Agreement and to consummate the transactions
contemplated hereby it has relied solely on its own independent investigation,
analysis, and evaluation of the Company and its subsidiaries, or that of its own
independent advisers in evaluating its investment in the Shares, Warrants and
Warrant Shares.

                                                                              12
<PAGE>   13

         (f) Rule 144. Each Investor acknowledges and agrees that the Shares and
the Warrants, and, if issued, the Warrant Shares, must be held indefinitely
unless they are subsequently registered under the Securities Act or an exemption
from such registration is available. Each Investor has been advised or is aware
of the provisions of Rule 144, which permits limited resale of shares purchased
in a private placement subject to the satisfaction of certain conditions,
including, among other things: the availability of certain current public
information about the Company, the resale occurring following the required
holding period under Rule 144 and the number of shares being sold during any
three-month period not exceeding specified limitations.

         (g) Transfer Restrictions. Each Investor acknowledges and agrees that
the Shares, the Warrants and the Warrant Shares are subject to restrictions on
transfer as set forth in Section 5.5, below, and further understands that the
Shares, the Warrants and the Warrant Shares will not have been registered
pursuant to the Securities Act or any applicable state securities laws, that the
Shares, the Warrants and the Warrant Shares will be characterized as "restricted
securities" under federal securities laws, and that under such laws and
applicable regulations the Shares, the Warrants and the Warrant Shares cannot be
sold or otherwise disposed of without registration under the Securities Act or
an exemption therefrom. In this connection, each Investor represents that it is
familiar with Rule 144 promulgated under the Securities Act, as currently in
effect, and understands the resale limitations imposed thereby and by the
Securities Act. Appropriate stop transfer instructions may be issued to the
transfer agent for securities of the Company (or a notation may be made in the
appropriate records of the Company) in connection with the Shares, the Warrants
or the Warrant Shares.

         (h) Confirmation. The acquisition of the Shares by an Investor at the
Closing shall constitute such Investor's confirmation of the foregoing
representations.

         4.6 No Other Shares. Except for such rights as may be conferred on an
Investor by this Agreement and the Ancillary Documents, Investors do not
beneficially own, directly or indirectly, any shares of capital stock or other
securities of the Company or any of its Subsidiaries.

         4.7 Financial Resources. Each Investor has the financial resources
available to it as are necessary to perform its obligations to acquire the
Shares pursuant to the terms of this Agreement.

         4.8 Brokerage Fees. No Investor has retained any financial advisor,
broker, agent, or finder or paid or agreed to pay any financial advisor, broker,
agent, or finder on account of the sale by the Company and the purchase by
Investors of the Shares pursuant to this Agreement.


                                                                              13
<PAGE>   14

                                    ARTICLE V

                              ADDITIONAL AGREEMENTS

         5.1 Reasonable Best Efforts.

         (a) Each party hereto agrees that it will use its reasonable best
efforts to take, or cause to be taken, all action and to do, or cause to be
done, all things reasonably necessary, proper, or advisable under Applicable
Laws to consummate the transactions contemplated by this Agreement, including,
without limitation, (i) cooperation in determining whether any consents,
approvals, orders, authorizations, waivers, declarations, filings, or
registrations of or with any Governmental Entity or third party are required in
connection with the consummation of the transactions contemplated hereby; (ii)
reasonable best efforts to obtain any such consents, approvals, orders,
authorizations, and waivers and to effect any such declarations, filings, and
registrations; (iii) reasonable best efforts to cause to be lifted or rescinded
any injunction or restraining order or other order adversely affecting the
ability of the parties to consummate the transactions contemplated hereby; (iv)
reasonable best efforts to defend, and cooperation in defending, all lawsuits or
other legal proceedings challenging this Agreement or the consummation of the
transactions contemplated hereby; and (v) the execution of any additional
instruments necessary to consummate the transactions contemplated hereby.

         (b) Without limiting the generality of Section 5.1(a), to the extent
required by the HSR Act, each of the parties hereto shall (i) file or cause to
be filed, as promptly as practicable but in no event later than five (5)
consecutive Business Days after the execution and delivery of this Agreement,
with the Federal Trade Commission and the United States Department of Justice,
all reports and other documents required to be filed by such party under the HSR
Act concerning the transactions contemplated hereby and (ii) promptly comply
with or cause to be complied with any requests by the Federal Trade Commission
or the United States Department of Justice for additional information concerning
such transactions, in each case so that the waiting period applicable to this
Agreement and the transactions contemplated hereby under the HSR Act shall
expire as soon as practicable after the execution and delivery of this
Agreement. Each party hereto agrees to request, and to cooperate with the other
party or parties in requesting, early termination of any applicable waiting
period under the HSR Act. Notwithstanding the foregoing, if any report or other
document is required to be filed by any Investor under the HSR Act solely as
result of the purchase and sale of the Shares or the Warrants (with no regard to
any other securities held by such Investor or its Affiliates), the Company shall
pay any and all fees and expenses, including filing fees and legal expenses,
incurred by such Investor in connection with the filing of such reports or other
documents and any other actions required to comply with the provisions of the
HSR Act.

         5.2 Press Releases. Except as may be required by Applicable Law or by
the rules of any national securities exchange or registered securities
association, prior to the Closing, neither Investors nor the Company shall issue
any press release with respect to this Agreement or the transactions
contemplated hereby without the prior consent of the other party (which consent
shall not be unreasonably withheld under the circumstances). Any such press
release required by Applicable Law or by the rules of any national securities
exchange or registered securities association shall only be made after
reasonable notice to the other party.

         5.3 Fees and Expenses. Except as otherwise expressly provided in this
Agreement, all fees and expenses, including fees and expenses of counsel,
financial advisors and accountants, incurred in connection with this Agreement
and the transactions contemplated hereby shall be paid by the party incurring
such fee or expense.


                                                                              14
<PAGE>   15

         5.4 Survival. The representations and warranties made herein shall
survive the Closing, regardless of any investigation made by or on behalf of any
party, until the second anniversary of the Closing Date; provided, however, the
representations and warranties contained in Sections 3.9, 3.10 and 3.18 shall
survive until the expiration of the applicable statute limitations relating to
the subject matters of such representations and warranties (the "Survival
Date".) All statements as to factual matters contained in any certificate or
other instrument delivered by or on behalf of the Company pursuant hereto in
connection with the transactions contemplated hereby shall be deemed to be
representations and warranties by the Company herein for purposes of this
Section 5.5. No action may be brought with respect to a breach of any
representation or warranty after the Survival Date unless, prior to such time,
the party seeking to bring such an action has notified the other parties of such
claim, specifying in reasonable detail the nature of the loss suffered.

         5.5 Transfer Restrictions.

         (a) Notwithstanding any provision contained in this Agreement to the
contrary, each Investor agrees that it will not, directly or indirectly, sell,
assign, transfer, pledge, encumber, or otherwise dispose of any of the Shares,
Warrants or Warrant Shares except:

                  (i) In compliance with Rule 144; provided, however, that the
         Investor shall provide the Company with copies of all filings made with
         the Securities and Exchange Commission with respect to sales of
         securities under Rule 144 and with such other information and documents
         as the Company shall reasonably require in order to assure full
         compliance with Rule 144; or

                  (ii) Pursuant to a no-action letter or other interpretive
         statement or release of the Securities and Exchange Commission to the
         effect that the proposed sale or other disposition may be effected
         without registration under the Securities Act; or

                  (iii) Pursuant to an applicable exemption (other than Rule
         144) under the Securities Act; provided, however, that the Investor
         shall have furnished the Company with an opinion of counsel, which
         opinion and counsel shall be reasonably acceptable to the Company, to
         the effect that such disposition does not require registration of such
         securities under the Securities Act; provided further, however, that no
         opinion of counsel shall be required in the case of a transfer to an
         affiliate (as defined in Rule 405 of the Securities Act) of Investor if
         such affiliate shall have furnished the Company with the
         representations contained in Section 4.5 of this Agreement and shall
         have agreed with the Company to be subject to the terms of this
         Agreement to the same extent as if an original holder of securities
         pursuant hereto.

                  (iv) Pursuant to an effective registration statement filed
         under the Securities Act.

          (b) It is agreed and understood by each Investor that the certificates
or instruments representing the Shares, Warrants and Warrant Shares shall each
be stamped or otherwise imprinted with a legend in substantially the following
form:

         "THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN
REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY APPLICABLE STATE
SECURITIES LAWS, AND MAY NOT BE SOLD OR TRANSFERRED IN THE ABSENCE OF SUCH
REGISTRATION OR AN EXEMPTION THEREFROM. SUCH


                                                                              15
<PAGE>   16

SECURITIES ARE SUBJECT TO THE RESTRICTIONS AND PRIVILEGES SPECIFIED IN A
SECURITIES PURCHASE AGREEMENT, DATED AS OF __________, 2000, BETWEEN BRIGHAM
EXPLORATION COMPANY AND THE INITIAL HOLDERS OF SECURITIES NAMED THEREIN, A COPY
OF WHICH IS ON FILE WITH THE SECRETARY OF BRIGHAM EXPLORATION COMPANY AND WILL
BE FURNISHED WITHOUT CHARGE TO THE HOLDER HEREOF UPON WRITTEN REQUEST, AND THE
HOLDER OF THIS CERTIFICATE AGREES TO BE BOUND THEREBY."

         5.6 Transaction Fee. The sum of Two Hundred Thousand Dollars
($200,000), plus all reasonable out-of-pocket expenses incurred by the
investors, including attorneys fees, shall be paid by the Company to Investors
on the Closing Date upon Closing; provided, however, that in no event shall the
Company be obligated to pay more than $235,000 pursuant to this Section 5.6.

         5.7 Special Meeting of Stockholders.

         (a) The Company shall take all action necessary in accordance with
applicable law and the Company's Certificate of Incorporation and Bylaws to duly
call, give notice of, convene, and hold a special meeting of its stockholders as
promptly as practicable after the date hereof to consider and vote upon the
matters described in the Stockholders Voting Agreement dated as of October 31,
2000 by and among the Company and certain of its stockholders (the "Stockholder
Approval"). The Company shall not mail or otherwise distribute the proxy
statement or information statement (or any related proxy materials or amendments
or supplements thereto, if any) relating to such special meeting to its
stockholders without consultation with Investors and their counsel, and such
proxy statement or information statement and such other items shall be in such
form as Investors and their counsel shall approve (such approval not to
unreasonably withheld.

         (b) The Company covenants and agrees that, prior to obtaining the
Stockholder Approval, it shall not take any action that would cause an
adjustment, pursuant to the terms of the Warrants, to the Exercise Price (as
defined in the Warrant Certificates evidencing the Warrants) of the Warrants but
for the requirements of Section 2(i) of such Warrant Certificates.

         5.8 Capitalization Certification. The Company shall provide,
immediately after the Closing, a schedule reflecting the capitalization of the
Company as of immediately after the transactions contemplated by this Agreement
and those contemplated in the Enron Transactions and the Financing Transaction,
including at least the information provided in the representation in Section 3.2
and indicating the number of fully-diluted shares of Common Stock, and certified
by the Chief Financial Officer of the Company (the "Certificate"). Until the
second anniversary of the Closing Date, the Company shall amend the Certificate
at any time after the Closing to reflect any changes to the Certificate (which
in all cases shall reflect the capitalization of the Company as of immediately
after the transactions contemplated by this Agreement and those contemplated in
the Enron Transactions and the Financing Transaction) if the Company learns that
the Certificate is incorrect or not complete in any respect. Notwithstanding any
provision contained in this Agreement, the Registration Rights Agreement and the
Warrant Certificate, if the number of fully-diluted shares of Common Stock as
reflected in the Certificate at any time is more than 32,531 shares in excess of
32,531,187 shares of

                                                                              16
<PAGE>   17

Common Stock, then the number of shares purchasable upon exercise of the Warrant
shall be increased to a number of shares equal to 20.49% of the fully-diluted
shares of Common Stock. Upon any such adjustment to the number of shares to be
acquired upon exercise of the Warrant, the holder of the Warrant shall deliver
to the Company the Warrant Certificate for cancellation and immediately
thereupon the Company shall issue a new Warrant Certificate reflecting the
adjusted number of shares purchasable thereunder. For purposes of this Section
5.8, the term "fully-diluted shares of Common Stock" means the sum of shares of
Common Stock outstanding, plus all shares of Common Stock issuable pursuant to
(i) the conversion or exchange of securities that are convertible into or
exchangeable for shares of Common Stock or the exercise of any option, warrant
or other right to acquire shares of Common Stock from the Company, (ii) the
conversion or exchange of any security that is convertible into or exchangeable
for any securities referenced in 5.8(i) or the exercise of any security that is
exercisable for any securities referenced in 5.8(i), and (iii) the exercise of
any rights under any agreement regarding equity equivalents, interests in the
ownership or earnings, or other similar rights of or with respect to the
Company.



                                   ARTICLE VI

                    CONDITIONS TO OBLIGATIONS OF THE COMPANY

         The obligations of the Company to consummate the transactions
contemplated by this Agreement shall be subject to the fulfillment on or prior
to the Closing Date of each of the following conditions:

         6.1 Representations and Warranties. All the representations and
warranties of Investors contained in this Agreement shall be true and correct in
all material respects, except as affected by transactions contemplated or
permitted by this Agreement.

         6.2 Covenants and Agreements. Investors shall have performed and
complied with in all material respects all covenants and agreements required by
this Agreement to be performed or complied with by them on or prior to the
Closing Date.

         6.3 HSR Act. All waiting periods (and any extensions thereof)
applicable to this Agreement and the transactions contemplated hereby under the
HSR Act shall have expired or been terminated.

         6.4 Legal Proceedings. No Proceeding shall, on the Closing Date, be
pending or threatened seeking to restrain, prohibit or obtain damages or other
relief in connection with this Agreement or the consummation of the transactions
contemplated hereby.

         6.5 Consents. All consents, approvals, orders, authorizations and
waivers of, and all declarations, filings and registrations with, third parties
(including Governmental Entities) required to be obtained or made by or on the
part of the parties hereto, or otherwise reasonably necessary for the
consummation of the transactions contemplated hereby, shall have been obtained
or made, and all thereof shall be in full force and effect at the time of
Closing.


                                                                              17

<PAGE>   18

         6.6 Enron Transactions. All conditions precedent to the closing of the
Enron Transactions (other than conditions with respect to the consummation,
simultaneously with such closing, of the transactions contemplated hereby) shall
have been satisfied or waived at or prior to the Closing, and such closing shall
have occurred prior to or be occurring simultaneously with the Closing. For
purposes of this Agreement, the "Enron Transactions" mean (i) the repurchase by
the Company from affiliates of Enron North America Corp. of an aggregate of
1,052,632 shares of the Company's Common Stock, warrants to purchase an
aggregate of 1,000,000 shares of the Company's common stock and (ii) the
repayment in full (and/or repurchase or cancellation) of the Company's Senior
Subordinated Secured Notes due 2003, for an aggregate repurchase/repayment price
of no more than $20,000,000 in cash, excluding fees and commissions.

         6.7 Financing. All conditions precedent to the closing of a Financing
Transaction (other than conditions with respect to the consummation,
simultaneously with such closing, of the transactions contemplated hereby) shall
have been satisfied or waived at or prior to the Closing, and such closing shall
have occurred prior to or be occurring simultaneously with the Closing. For
purposes of this Agreement, a "Financing Transaction" means the financing
arrangements described in the Subordinated Credit Agreement dated as of October
31, 2000 among Brigham Oil & Gas, L.P. and Shell Capital, Inc.

                                   ARTICLE VII

                     CONDITIONS TO OBLIGATIONS OF INVESTORS

         The obligations of Investors to consummate the transactions
contemplated by this Agreement shall be subject to the fulfillment on or prior
to the Closing Date of each of the following conditions:

         7.1 Representations and Warranties. All the representations and
warranties of the Company contained in this Agreement shall be true and correct
in all material respects, except as affected by transactions contemplated or
permitted by this Agreement (or the announcement thereof).

         7.2 Covenants and Agreements. The Company shall have performed and
complied with in all material respects all covenants and agreements required by
this Agreement to be performed or complied with by it on or prior to the Closing
Date.

         7.3 HSR Act. All waiting periods (and any extensions thereof)
applicable to this Agreement and the transactions contemplated hereby under the
HSR Act shall have expired or been terminated.

         7.4 Legal Proceedings. No Proceeding shall, on the Closing Date, be
pending or threatened seeking to restrain, prohibit or obtain damages or other
relief in connection with this Agreement or the consummation of the transactions
contemplated hereby.

         7.5 Legal Opinion. Thompson & Knight, L.L.P., counsel to the Company,
shall have delivered to the Investors a legal opinion satisfactory in form and
substance to the Investors.

         7.6 Consents. All consents, approvals, orders, authorizations and
waivers of, and all declarations, filings and registrations with, third parties
(including Governmental Entities)

                                                                              18
<PAGE>   19

required to be obtained or made by or on the part of the parties hereto, or
otherwise reasonably necessary for the consummation of the transactions
contemplated hereby, shall have been obtained or made, and all thereof shall be
in full force and effect at the time of Closing.

         7.7 Appointment of Director. On or before the Closing Date, Steven A.
Webster shall be appointed as a member of the Board of Directors of the Company.

         7.8 Enron Transactions. All conditions precedent to the closing of the
Enron Transactions (other than conditions with respect to the consummation,
simultaneously with such closing, of the transactions contemplated hereby) shall
have been satisfied at or prior to the Closing, and such closing shall have
occurred prior to or be occurring simultaneously with the Closing.

         7.9 Financing. All conditions precedent to the closing of a Financing
Transaction (other than conditions with respect to the consummation,
simultaneously with such closing, of the transactions contemplated hereby) shall
have been satisfied at or prior to the Closing, and such closing shall have
occurred prior to or be occurring simultaneously with the Closing.

         7.10 Closing Deliveries. Investors shall have received the
certificates, instruments and documents required to be delivered by the Company
by Section 2.2.

                                  ARTICLE VIII

                              BOARD REPRESENTATION

         The Company covenants to nominate one representative of the Investors
appointed by MB to serve as a member of the Board of Directors of the Company
(the "Board") for so long as the Investors or their Affiliates own at least 10%
of the Shares or at least 5% of the outstanding shares of Common Stock of the
Company. Notwithstanding the foregoing, should a representative of the Investors
not be elected to the Board at a meeting of the stockholders of the Company, the
Company shall provide such representative with notice of each meeting of the
Board and shall provide such representative with access to such meeting as an
observer.

                                   ARTICLE IX

                                    COVENANTS

         9.1 Affirmative Covenants. The Company covenants and agrees that, so
long as any of the Shares are outstanding:

                  (a) Financial Statements and Other Reports. The Company shall
         deliver, or shall cause to be delivered, to the Investors:

                           (i) Annual Financial Statements. As soon as available
                  and in any event within 90 days after the end of each fiscal
                  year of the Company and its consolidated Subsidiaries for such
                  fiscal year, and the related consolidated and unaudited
                  consolidating balance sheets of the Company and its
                  consolidated Subsidiaries as at the end of such fiscal year,
                  and setting forth in each case in comparative form the
                  corresponding figures for the preceding fiscal year, and
                  accompanied by the related opinion of independent public
                  accountants which


                                                                              19
<PAGE>   20

                  opinion shall state that said financial statements fairly
                  present the consolidated financial condition and results of
                  operations of the Company and its consolidated Subsidiaries as
                  at the end of, and for, such fiscal year and that such
                  financial statements have been prepared in accordance with
                  GAAP except for such changes in such principles with which the
                  independent public accountants shall have concurred.

                           (ii) Quarterly Financial Statements. As soon as
                  available and in any event within 60 days after the end of
                  each of the first three fiscal quarterly periods of each
                  fiscal year of the Company, consolidated statements of income,
                  stockholders' equity, changes in financial position and cash
                  flow of the Company and its consolidated Subsidiaries for such
                  period and for the period from the beginning of the respective
                  fiscal year to the end of such period, and the related
                  consolidated and consolidating balance sheets as at the end of
                  such period.

                           (iii) Monthly Financial Statements. As soon as
                  available and in any event within forty-five (45) days after
                  the end of each calendar month that is not also the end of one
                  of the Company's first three fiscal quarterly periods or of
                  the Company's fiscal year, consolidated statements of income
                  and changes in financial position of the Company and its
                  consolidated Subsidiaries for such period and for the period
                  from the beginning of the respective fiscal year to the end of
                  such period, and the related consolidated balance sheets as at
                  the end of such period and beginning statements setting forth
                  in each case in comparative form the corresponding figures for
                  the corresponding period in the preceding fiscal year.

                  (b) SEC Filings, Etc. Promptly, upon its becoming available,
         each financial statement, report, notice or proxy statement sent by the
         Company to stockholders generally.

                  (c) Engineering Reports. Not later than April 30 and October
         30 of each year, the Company shall furnish to the Investors a Reserve
         Report as of the preceding December 31 and June 30, respectively. The
         Reserve Report to be furnished in April of each year shall be prepared
         by certified independent petroleum engineers or other independent
         petroleum consultant(s) and the Reserve Reports to be furnished in
         October of each year shall be prepared by or under the supervision of
         the chief engineer or Vice President of Operations of the Company who
         shall certify such Reserve Report to have been prepared in accordance
         with the procedures used in the immediately preceding April Reserve
         Report. At Company's option, the Reserve Report to be furnished in
         October of each year may instead consist of a report from the
         independent petroleum engineers referred to above on any new wells and
         a roll-forward by Company on any wells previously reported in the
         Reserve Report described in the immediately preceding April.

                  (d) Exchange Act Reports. At all times (i) timely file all
         reports required to be filed by the Company under Section 13(d) or
         Section 15 of the Exchange Act and the rules and regulations
         thereunder, and (ii) if the Company is no longer subject to the


                                                                              20
<PAGE>   21

         requirements of the Exchange Act, provide holders of the Shares reports
         in substantially the same form and at the same times as would be
         required if the Company were subject to the Exchange Act.

                  (e) Nasdaq Listing. Maintain at all times a valid listing for
         the Common Stock on a national securities exchange or the National
         Market System or SmallCap Market of the Nasdaq Stock Market, Inc.

                  (f) Further Assurances. The Company at its expense will
         promptly execute and deliver to the Investors upon request all such
         other documents, agreements and instruments to comply with or
         accomplish the covenants and agreements of the Company in this
         Agreement or any other agreements and documents executed by and between
         the Company and the Investors.

         9.2 Negative Covenants. The Company covenants and agrees that, so long
as at least 10% of the Shares are outstanding, without the prior written consent
of the persons holding 75% of the then outstanding Shares:

                  (a) Dividends, Distributions and Redemptions. The Company will
         not declare or pay any dividend, purchase, redeem, or otherwise acquire
         for value any of its Parity Security or Junior Security now or
         hereafter outstanding, return any capital or make a distribution of its
         assets to its stockholders.

                  (b) Nature of Business. Neither the Company nor Brigham Oil &
         Gas, L.P. will allow any material change to be made in the character of
         its business as an independent oil and gas exploration and production
         company.

                  (c) Environmental Matters. Neither the Company nor any
         Subsidiary will knowingly cause or permit any of its Property to be in
         violation of, or knowingly do anything or permit anything to be done
         which will subject any such Property to any remedial obligations under
         any Environmental Laws, assuming disclosure to the applicable
         Governmental Authority of all relevant facts, conditions and
         circumstances, if any, pertaining to such Property where such
         violations or remedial obligations would have a Material Adverse
         Effect.

                  (d) Transactions with Affiliates. Neither the Company nor any
         Subsidiary will enter into any transaction, including, without
         limitation, any purchase, sale, lease or exchange of Property or the
         rendering of any service, with any Affiliate unless such transactions
         are otherwise not in violation of this Agreement, and are upon fair and
         reasonable terms no less favorable to it than it would obtain in a
         comparable arm's length transaction with a Person not an Affiliate.

                                    ARTICLE X

                              AMENDMENT AND WAIVER

         10.1 Amendment. This Agreement may not be amended except by an
instrument in writing signed by or on behalf of all the parties hereto.


                                                                              21
<PAGE>   22

         10.2 Waiver. No failure or delay by a party hereto in exercising any
right, power, or privilege hereunder shall operate as a waiver thereof nor shall
any single or partial exercise thereof preclude any other or further exercise
thereof or the exercise of any other right, power, or privilege. The provisions
of this Agreement may not be waived except by an instrument in writing signed by
or on behalf of the party against whom such waiver is sought to be enforced.

                                   ARTICLE XI
                                  MISCELLANEOUS

         11.1 Notices. All notices, requests, demands, and other communications
required or permitted to be given or made hereunder by any party hereto shall be
in writing and shall be deemed to have been duly given or made if (i) delivered
personally, (ii) sent by prepaid overnight courier service, or (iii) sent by
telecopy or facsimile transmission, answer back requested, to the parties at the
following addresses (or at such other addresses as shall be specified by the
parties by like notice):

         (a)      If to the Company:
                  Brigham Exploration Company
                  6300 Bridge Point Parkway
                  Building 2, Suite 500
                  Austin, TX 78730
                  Attention: Chief Financial Officer
                  Telefax:   512-427-3400

         with a copy to:

                  Thompson & Knight L.L.P.
                  1700 Pacific Avenue, Suite 3300
                  Dallas, Texas 75201
                  Attention: Joe Dannenmaier
                  Telefax:   214-969-1751

         (b)      If to either Investor, to such Investor at:

                  277 Park Avenue
                  New York, New York 10172
                  Attention: Michael Isikow
                  Telefax:   212-892-2689

         with a copy to:

                  Gardere Wynne Sewell, LLP
                  1000 Louisiana, Suite 3400
                  Houston, Texas 77002
                  Attention: N.L. Stevens III
                  Telefax:   713-276-5807


                                                                              22
<PAGE>   23

Such notices, requests, demands, and other communications shall be effective (i)
if delivered personally or sent by courier service, upon actual receipt by the
intended recipient, or (ii) if sent by telecopy or facsimile transmission, when
the answer back is received.

         11.2 Entire Agreement. This Agreement, together with the Schedules,
Exhibits, Annexes, and other writings referred to herein or delivered pursuant
hereto, constitutes the entire agreement between the parties hereto with respect
to the subject matter hereof and supersedes all prior agreements and
understandings, both written and oral, between the parties and their Affiliates
with respect to the subject matter hereof.

         11.3 Binding Effect; Assignment; No Third Party Benefit. This Agreement
shall be binding upon and inure to the benefit of the parties hereto and their
respective successors and permitted assigns. Except as otherwise expressly
provided in this Agreement, neither this Agreement nor any of the rights,
interests or obligations hereunder shall be assigned by any of the parties
hereto without the prior written consent of the other party. Nothing in this
Agreement, express or implied, is intended to or shall confer upon any person
other than the parties hereto, and their respective heirs, legal
representatives, successors, and permitted assigns, any rights, benefits or
remedies of any nature whatsoever under or by reason of this Agreement.

         11.4 Severability. If any provision of this Agreement is held to be
unenforceable, then this Agreement shall be considered divisible and such
provision shall be deemed inoperative to the extent it is deemed unenforceable,
and in all other respects this Agreement shall remain in full force and effect
to the maximum extent permitted by Applicable Law.

         11.5 Injunctive Relief. The parties hereto acknowledge and agree that
irreparable damage would occur in the event any of the provisions of this
Agreement were not performed in accordance with their specific terms or were
otherwise breached. It is accordingly agreed that the parties shall be entitled
to an injunction or injunctions to prevent breaches of the provisions of this
Agreement, and shall be entitled to enforce specifically the provisions of this
Agreement, in any court of the United States or any state thereof having
jurisdiction, in addition to any other remedy to which the parties may be
entitled under this Agreement or at law or in equity.

         11.6 Governing Law. THIS AGREEMENT SHALL BE GOVERNED BY AND CONSTRUED
AND ENFORCED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK, WITHOUT
REGARD TO THE PRINCIPLES OF CONFLICTS OF LAWS THEREOF.

         11.7 Jurisdiction. Except as otherwise expressly provided in this
Agreement, any suit, action or proceeding seeking to enforce any provision of,
or based on any matter arising out of or in connection with, this Agreement or
the transactions contemplated hereby may be brought in the United States
District Court for the Southern District of New York or any other New York State
court sitting in New York City, and each of the parties hereby consents to the
jurisdiction of such courts (and of the appropriate appellate courts therefrom)
in any such suit, action or proceeding and irrevocably waives, to the fullest
extent permitted by law, any objection which it may now or hereafter have to the
laying of the venue of any such suit, action or proceeding in



                                                                              23
<PAGE>   24

any such court or that any such suit, action or proceeding which is brought in
any such court has been brought in an inconvenient forum. Process in any such
suit, action or proceeding may be served on any party anywhere in the world,
whether within or without the jurisdiction of any such court. Without limiting
the foregoing, each party agrees that service of process on such party as
provided in Section 10.01 shall be deemed effective service of process on such
party.

         11.8 Counterparts. This Agreement may be executed by the parties hereto
in any number of counterparts, each of which shall be deemed an original, but
all of which shall constitute one and the same agreement. Each counterpart may
consist of a number of copies hereof each signed by less than all, but together
signed by all, the parties hereto.

                                   ARTICLE XII

                                   DEFINITIONS

         12.1 Certain Defined Terms. As used in this Agreement, each of the
following terms has the meaning given it in this Article:

                  "Affiliate" of any Person shall mean (i) any Person directly
         or indirectly controlled by, controlling or under common control with
         such first Person, (ii) any director or officer of such first Person or
         of any Person referred to in clause (i) above and (iii) if any Person
         in clause (i) above is an individual, any member of the immediate
         family (including parents, spouse and children) of such individual and
         any trust whose principal beneficiary is such individual or one or more
         members of such immediate family and any Person who is controlled by
         any such member or trust. For purposes of this definition, any Person
         which owns directly or indirectly 50% or more of the securities having
         ordinary voting power for the election of directors or other governing
         body of a corporation or 50% or more of the partnership or other
         ownership interests of any other Person (other than as a limited
         partner of such other Person) will be deemed to "control" (including,
         with its correlative meanings, "controlled by" and "under common
         control with") such corporation or other Person.

                  "Ancillary Documents" means each agreement, instrument, and
         document (other than this Agreement) executed or to be executed by the
         Company or any Investor in connection with the sale and purchase of the
         Shares and the other transactions contemplated by this Agreement.

                  "Applicable Law" means any statute, law, rule, or regulation
         or any judgment, order, writ, injunction, or decree of any Governmental
         Entity to which a specified person or property is subject.

                  "BOG" means Brigham Oil & Gas, L.P.

                  "Business Day" shall mean any day other than a Saturday, a
         Sunday, or a day on which banking institutions in Austin, Texas are
         authorized or obligated by law or executive order to close.


                                                                              24
<PAGE>   25

                  "Code" shall mean the Internal Revenue Code of 1986, as
         amended from time to time and any successor statute.

                  "Common Stock" means the common stock, par value of $.01 per
         share, of the Company, and such other class of securities as shall
         represent the common equity of the Company.

                  "Debt" shall mean, for any Person the sum of the following
         (without duplication): (i) all obligations of such Person for borrowed
         money or evidenced by bonds, debentures, notes or other similar
         instruments (including principal, interest, fees and charges); (ii) all
         obligations of such Person (whether contingent or otherwise) in respect
         of bankers acceptances, letters of credit, surety or other bonds and
         similar instruments; (iii) all obligations of such Person to pay the
         deferred purchase price of Property or services (other than for
         borrowed money) excluding Trade Payables; (iv) all obligations under
         leases which shall have been, or should have been, in accordance with
         GAAP, recorded as capital leases in respect of which such Person is
         liable (whether contingent or otherwise); (v) all obligations under
         leases (other than capital leases and oil and gas leases) which require
         such Person or its Affiliate to make payments exceeding $100,000 over
         the term of such lease, including payments at termination, which are
         substantially equal to at least eighty percent (80%) of the purchase
         price of the Property subject to such lease plus interest at an imputed
         market rate of interest; (vi) all Debt (as described in the other
         clauses of this definition) of others secured by a Lien on any asset of
         such Person, whether or not such Debt is assumed by such Person; (vii)
         all Debt (as described in the other clauses of this definition) of
         others guaranteed by such Person or in which such Person otherwise
         assures a creditor against loss of the Debt of others; (viii) all
         obligations or undertakings of such Person to maintain or cause to be
         maintained the financial position or covenants of others including
         without limitation agreements expressed as an agreement to purchase the
         Debt or Property of others or otherwise; (x) obligations to pay for
         goods or services whether or not such goods or services are actually
         received or utilized by such Person; (xi) any capital stock of such
         Person in which such Person has a mandatory obligation to redeem such
         stock; (xii) the undischarged balance of any production payment created
         by such Person or for the creation of which such Person directly or
         indirectly received payment; and (xiii) all obligations of such Person
         under Hedging Agreements.

                  "Encumbrances" means liens, charges, pledges, options,
         mortgages, deeds of trust, security interests, claims, restrictions
         (whether on voting, sale, transfer, disposition, or otherwise),
         easements, and other encumbrances of every type and description,
         whether imposed by law, agreement, understanding, or otherwise.

                  "Environmental Laws" shall mean any and all Governmental
         Requirements pertaining to the environment in effect in any and all
         jurisdictions in which the Company or any Subsidiary is conducting or
         at any time has conducted business, or where any Oil and Gas Property
         of the Company or any Subsidiary is located, including without
         limitation, the Oil Pollution Act of 1990 ("OPA"), the Clean Air Act,
         as amended, the Comprehensive Environmental, Response, Compensation,
         and Liability Act of 1980 ("CERCLA"), as amended, the Federal Water
         Pollution Control Act, as amended, the


                                                                              25
<PAGE>   26

         Occupational Safety and Health Act of 1970, as amended, the Resource
         Conservation and Recovery Act of 1976 ("RCRA"), as amended, the Safe
         Drinking Water ACT, as amended, the Toxic Substances Control Act, as
         amended, the Superfund Amendments and Reauthorization Act of 1986, as
         amended, the Hazardous Materials Transportation Act, as amended, and
         other environmental conservation or protection laws. As used in the
         provisions hereof relating to Environmental Laws, the term "oil" shall
         have the meaning specified in OPA, the terms "hazardous substance" and
         "release" (or "threatened release") have the meanings specified in
         CERCLA, and the terms "solid waste" and "disposal" (or "disposal") have
         the meanings specified in RCRA; provided that to the extent the laws of
         the state in which any Oil and Gas Property of the Company or any
         Subsidiary is located establish a meaning for "oil", "hazardous
         substance," "release," "solid waste" or "disposal" which is broader
         than that specified in either OPA, CERCLA or RCRA, such broader meaning
         shall apply.

                  "ERISA" shall mean the Employee Retirement Income Security Act
         of 1974, as amended from time to time and any successor statute.

                  "ERISA Affiliate" shall mean each trade or business (whether
         or not incorporated) which together with the Company or any Subsidiary
         of the Company would be deemed to be a "single employer" within the
         meaning of section 4001(b)(1) of ERISA or subsections (b), (c), (m) or
         (o) of section 414 of the Code.

                  "Excepted Liens" shall mean: (i) Liens for taxes, assessments
         or other governmental charges or levies not yet due or which are being
         contested in good faith by appropriate action and for which adequate
         reserves have been maintained in accordance with GAAP; (ii) Liens in
         connection with workmen's compensation, unemployment insurance or other
         social security, old age pension or public liability obligations not
         yet due or which are being contested in good faith by appropriate
         action and for which adequate reserves have been maintained in
         accordance with GAAP; (iii) operators', vendors', carriers',
         warehousemen's, repairmen's, mechanics', workmen's, materialmen's,
         construction or other like Liens arising by operation of law in the
         ordinary course of business or incident to the exploration,
         development, operation and maintenance of Oil and Gas Properties or
         customary landlord's liens, each of which is in respect of obligations
         that have not been outstanding more than 90 days or which are being
         contested in good faith by appropriate proceedings and for which
         adequate reserves have been maintained in accordance with GAAP; (iv)
         any Liens reserved in leases or farmout agreements for rent or
         royalties and for compliance with the terms of the farmout agreements
         or leases in the case of leasehold estates, to the extent that any such
         Lien referred to in this clause does not materially impair the use of
         the property covered by such Lien for the purposes for which such
         property is held or materially impair the value of such property
         subject thereto; (v) encumbrances (other than to secure the payment of
         borrowed money or the deferred purchase price of property or services),
         easements, restrictions, servitudes, permits, conditions, covenants,
         exceptions or reservations in any rights of way or other property for
         the purpose of roads, pipelines, transmission lines, transportation
         lines, distribution lines for the removal of gas, oil, coal or other
         minerals or timber, and other like purposes, or for the joint or common
         use of real estate, rights of way, facilities and equipment, and
         defects, irregularities, zoning restrictions and deficiencies in title
         of any rights of way or other property which in the aggregate do not
         materially impair the use of such rights of way or


                                                                              26
<PAGE>   27

         other property for the purposes of which such rights of way and other
         property are held or materially impair the value of such property
         subject thereto; (vi) deposits of cash or securities to secure the
         performance of bids, trade contracts, leases, statutory obligations and
         other obligations of a like nature incurred in the ordinary course of
         business; and (vii) Liens (including "Excepted Liens") permitted by or
         created pursuant to the Senior Credit Agreement and Liens permitted by
         or created pursuant to the Subordinated Credit Agreement.

                  "Exchange Act" means the Securities Exchange Act of 1934, as
         amended.

                  "Governmental Entity" means any court or tribunal in any
         jurisdiction (domestic or foreign) or any public, governmental, or
         regulatory body, agency, department, commission, board, bureau, or
         other authority or instrumentality (domestic or foreign).

                  "Governmental Requirement" shall mean any law, statute, code,
         ordinance, order, determination, rule, regulation, judgment, decree,
         injunction, franchise, permit, certificate, license, authorization or
         other directive or requirement (in the case of banking regulatory
         authorities whether or not having the force of law), including, without
         limitation, Environmental Laws, energy regulations and occupational,
         safety and health standards or controls, of any Governmental Entity.

                  "Hedging Agreements" shall mean any commodity, interest rate
         or currency swap, cap, floor, collar, forward agreement or other
         exchange or protection agreements or any option with respect to any
         such transaction.

                  "HSR Act" means the Hart-Scott-Rodino Antitrust Improvements
         Act of 1976, as amended.

                  "Hydrocarbon Interests" shall mean all rights, titles,
         interests and estates now or hereafter acquired in and to oil and gas
         leases, oil, gas and mineral leases, or other liquid or gaseous
         hydrocarbon leases, mineral fee interests, overriding royalty and
         royalty interests, net profit interests and production payment
         interests, including any reserved or residual interests of whatever
         nature.

                  "Hydrocarbons" shall mean oil, gas, casinghead gas, drip
         gasoline, natural gasoline, condensate, distillate, liquid
         hydrocarbons, gaseous hydrocarbons and all products refined or
         separated therefrom.

                  "Lien" shall mean any interest in property securing an
         obligation owed to, or a claim by, a person other than the owner of the
         property, whether such interest is based on the common law, statute or
         contract, and whether such obligation or claim is fixed or contingent,
         and including but not limited to (i) the lien or security interest
         arising from a mortgage, encumbrance, pledge, security agreement,
         conditional sale or trust receipt or a lease, consignment or bailment
         for security purposes or (ii) production payments and the like payable
         out of Oil and Gas Properties. The term "Lien" shall include


                                                                              27
<PAGE>   28


         reservations, exceptions, encroachments, easements, rights of way,
         covenants, conditions, restrictions, leases and other title exceptions
         and encumbrances affecting property. For the purposes of this
         Agreement, a Person shall be deemed to be the owner of any property
         which it has acquired or holds subject to a conditional sale agreement,
         or leases under a financing lease or other arrangement pursuant to
         which title to the Property has been retained by or vested in some
         other Person in a transaction intended to create a financing.

                  "Material Adverse Effect" means, relative to the Company or
         the Investors, as the case may be, any change, development, or effect
         (individually or in the aggregate) which is, or is reasonably likely to
         be, materially adverse (i) to the business, assets, results of
         operations, condition (financial or otherwise), or prospects of the
         Company and the Subsidiaries considered as a whole, or the Investors,
         as the case may be, or (ii) to the ability of the Company or the
         Investors, as the case may be, to perform on a timely basis any
         material obligation of the Company or the Investors, as the case may
         be, under this Agreement or any agreement, instrument, or document
         entered into or delivered in connection herewith.

                  "Material Agreement" means (a) any written agreement,
         contract, lease, commitment, understanding, instrument or obligation to
         which the Company or any Subsidiary is a party or by which the Company
         or any Subsidiary or any of their respective properties may be bound
         involving total value or consideration or liability in excess of
         $500,000, (b) any loan or credit agreement, bond, debenture, note,
         mortgage or indenture by which the Company or any Subsidiary or any of
         their respective properties may be bound, or (c) any agreement set
         forth as an exhibit to the Company's Form 10-K for the fiscal year
         ended December 31, 1999.

                  "Person" or "person" means any individual, corporation,
         partnership, joint venture, association, joint-stock company, trust,
         enterprise, unincorporated organization, or Governmental Entity.

                  "Oil and Gas Properties" shall mean Hydrocarbon Interests; the
         Properties now or hereafter pooled or unitized with Hydrocarbon
         Interests; all presently existing or future unitization, pooling
         agreements and declarations of pooled units and the units created
         thereby (including without limitation all units created under orders,
         regulations and rules of any Governmental Authority) which may affect
         all or any portion of the Hydrocarbon Interests; all operating
         agreements, contracts and other agreements which relate to any of the
         Hydrocarbon Interests or the production, sale, purchase, exchange or
         processing of Hydrocarbons from or attributable to such Hydrocarbon
         Interests; all Hydrocarbons in and under and which may be produced and
         saved or attributable to the Hydrocarbon Interests, including all oil
         in tanks, the lands covered thereby and all rents, issues, profits,
         proceeds, products, revenues and other incomes from or attributable to
         the Hydrocarbon Interests; all tenements, hereditaments, appurtenances
         and Properties in any manner appertaining, belonging, affixed or
         incidental to the Hydrocarbon Interests; and all Properties, rights,
         titles, interests and estates described or referred to above, including
         any and all Property, real or personal, now owned or hereinafter
         acquired and situated upon, used, held for use or useful in connection
         with the operating, working or development of any of such Hydrocarbon
         Interests or Property (excluding drilling rigs, automotive equipment or
         other personal property which may be on such premises for


                                                                              28
<PAGE>   29

         the purpose of drilling a well or for other similar temporary uses) and
         including any and all oil wells, gas wells, injection wells or other
         wells, buildings, structures, fuel separators, liquid extraction
         plants, plant compressors, pumps, pumping units, field gathering
         systems, tanks and tank batteries, fixtures, valves, fittings,
         machinery and parts, engines, boilers, meters, apparatus, appliances,
         tools, implements, cables, wires, towers, casing, tubing and rods,
         similar equipment, surface leases, rights-of-way, easements and
         servitudes together with all additions, substitutions, replacements,
         accessions and attachments to any and all of the foregoing.

                  "Plan" shall mean any employee pension benefit plan, as
         defined in Section 3(2) of ERISA, which (i) is currently or hereafter
         sponsored, maintained or contributed to by the Company, any Subsidiary
         or an ERISA Affiliate or (ii) was at any time during the preceding six
         calendar years sponsored, maintained or contributed to, by the Company,
         any Subsidiary or an ERISA Affiliate.

                  "Proceeding" means any action, suit or proceeding, whether
         civil, criminal, administrative, arbitrative or investigative, any
         appeal in such an action, suit or proceeding, and any inquiry or
         investigation that could lead to such an action, suit or proceeding.

                  "reasonable best efforts" means a party's best efforts in
         accordance with reasonable commercial practice and without the
         incurrence of unreasonable expense.

                  "Rule 144" means Rule 144 promulgated under the Securities
         Act.

                  "Securities Act" means the Securities Act of 1933, as amended.

                  "Senior Credit Agreement" means that certain Amended and
         Restated Credit Agreement dated as of February 17, 2000, by and between
         BOG, Bank of Montreal, as Agent, and the Lenders signatory thereto, as
         amended on October 31, 2000, together with the "Loan Documents"
         described therein.

                  "Subordinated Credit Agreement" means the Subordinated Credit
         Agreement dated as of October 31, 2000 by and between BOG, Shell
         Capital, Inc., as Agent, and the Lenders signatory thereto.

                  "Subsidiaries" means Brigham Oil & Gas, L.P.; Brigham, Inc.;
         Brigham Holdings I, LLC and Brigham Holdings II, LLC.


                                                                              29
<PAGE>   30

         IN WITNESS WHEREOF, the parties have executed this Agreement, or caused
this Agreement to be executed by their duly authorized representatives, all as
of the day and year first above written.

                                                 THE COMPANY:


                                                 BRIGHAM EXPLORATION COMPANY
Address:

                                                 By: /s/ Karen E. Lynch
                                                     Vice President


                                                 Investor:

                                                    DLJ MB FUNDING III, INC.

Address:

                                                 By: /s/ Ivy B. Dodes
                                                     Principal


                                                 DLJ ESC II, LP

                                                 By: DLJ LBO Plans Management
                                                     Corporation, its general
                                                     partner

Address:

                                                 By: /s/ Ivy B. Dodes
                                                     Principal








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