<PAGE>   1
                                                                    EXHIBIT 10.1

                       THIRD AMENDMENT TO CREDIT AGREEMENT

                  THIRD AMENDMENT TO CREDIT AGREEMENT, dated as of July 19, 1999
("this Amendment"), among Brigham Oil & Gas, L.P., a limited partnership formed
under the laws of the State of Delaware (the "Borrower"), the financial
institutions party to the Credit Agreement referred to below (each a "Lender"
and collectively the "Lenders") and Bank of Montreal, a Canadian bank, as agent
for Lenders under the Credit Agreement (in such capacity, the "Agent").

                                    RECITALS


                  WHEREAS, the Borrower, the Lenders and the Agent are parties
to that certain Credit Agreement, dated as of January 26, 1998, as amended by
that certain First Amendment to Credit Agreement, dated as of August 20, 1998
and that certain Second Amendment to Credit Agreement dated as of March 26, 1999
(as so amended, the "Credit Agreement"); and

                  WHEREAS, the Borrower has advised the Lenders and the Agent
that it desires to amend certain provisions of the Credit Agreement, and the
Borrower has requested that the Lenders and the Agent agree to various
amendments to certain provisions of the Credit Agreement; and

                  WHEREAS, the Lenders and the Agent have agreed to so amend
certain provisions of the Credit Agreement upon the terms and subject to the
conditions and limitations of this Amendment;

                  NOW, THEREFORE, in consideration of the premises, covenants
and agreements contained herein, the parties hereto hereby agrees as follows:

                  Section 1. Definitions. Capitalized terms used and not
otherwise defined herein are used with the meanings ascribed thereto in the
Credit Agreement. The following capitalized terms shall have the following
respective meanings when used herein:

                  A. "Lending Relationship" shall refer to the Credit Agreement
and the other Loan Documents, including, without limitation, this Amendment,
together with any and all negotiations, discussions, acts, omissions, renewals,
extensions, and other agreements or events related to the Credit Agreement and
such other Loan Documents, the parties' obligations thereunder and the
transactions contemplated thereby, including, without limitation, any such
negotiations, discussions, acts, omissions, renewals, extensions, other
agreements or events that (a) occurred prior to the date hereof, (b) may occur
on the date hereof, or (c) occurred prior to the execution of this Amendment and
the instruments and documents executed and delivered in connection herewith or
relating hereto.


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                  B. "New Mortgage" shall mean that certain Mortgage, Deed of
Trust, Assignment of Production, Security Agreement and Financing Statement
dated as of March 26, 1999 from Brigham Oil & Gas, L.P. to Thomas McGraw, as
Trustee, for the benefit of Bank of Montreal, as Agent.

                  C. "Released Claims" shall mean any and all claims (including
without limitation any liabilities, damages, demands and causes of action
arising therefrom), whether (a) at law or in equity, (b) on the alleged
commission of a tort, (c) on the alleged breach (or anticipatory breach or
repudiation) of any contract, duty, or warranty (whether oral or written,
express or implied), (d) on the alleged violation of any statute, tariff, or
regulation (whether promulgated by the United States, any state thereof, any
foreign state or country, or any other governmental agency or entity, wherever
located), or (e) on any other factual, legal or equitable theory, including,
without limitation, any claim for damages of any type or nature, for injunctive
or other relief, for attorneys' fees, interest or any other liability whatsoever
on any theory, including without limitation any loss, cost or damage in
connection with or based upon "lender liability", unfair dealing, duress,
coercion, control or undue influence, extortion or commercial bribery, breach of
an implied covenant or duty of good faith and fair dealing, material
misrepresentation or omission, overreaching, unconscionability, conflict of
interest, bad faith, malpractice, disparate bargaining position, detrimental
reliance, promissory estoppel, estoppel by deed, waiver, laches, or any other
equitable theory, equitable subordination, breach of fiduciary duty or any other
duty, or tortious inducement to commit such breach, tortious interference with
contract or prospective business relations, negligent performance of contractual
obligations, or other theories of negligence, negligent or intentional
infliction of emotional distress, slander, libel, other defamation, fraudulent
transfer, conversion, trespass to (or clouding the title of) property, usury,
violations of the Racketeer Influenced and Corrupt Organizations Act, deceptive
trade practices, conspiracy, or any theory of liability as partners or joint
venturers, that any Releasing Party may have as of the date hereof against any
Released Party with respect to the Lending Relationship.

                  D. "Released Party" shall mean each of the Agent, the Lenders
and their respective predecessors, successors, assigns, directors, officers,
partners, employees, agents, attorneys, principals and Affiliates and all other
Persons liable or who might be claimed to be liable on their behalf
(collectively, the "Released Parties").

                  E. "Releasing Party" shall mean each of the Borrower and the
Guarantors and their respective predecessors, successors, assigns, directors,
officers, partners, employees, agents, attorneys, principals, Affiliates and all
other Persons who might have a claim against any Released Party (collectively,
the "Releasing Parties").

                  F. "Warrant Agreements" shall mean collectively (i) that
certain Warrant Agreement between Brigham Exploration and Bank of Montreal and
(ii) that certain Warrant Agreement between Brigham Exploration and Societe
Generale, each to be entered into within thirty (30) days after the date hereof.


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                  Section 2. Amendments to Credit Agreement. The Credit
Agreement is amended hereby as follows:

                  A. Section 1.02 is amended hereby:

                           (i) by deleting the definition of the term "Aggregate
Maximum Credit Amounts" in its entirety and substituting the following therefor:

                           "`Aggregate Maximum Credit Amounts' at any time prior
                  to the initial Borrowing Base determination shall equal
                  $56,000,000, as the same may be reduced pursuant to Section
                  2.03(b) and Section 2.07(d), and thereafter shall equal the
                  sum of the Maximum Credit Amounts.";

                           (ii) by deleting the definition of the term "EBITDA"
in its entirety and substituting the following therefor:

                           "'EBITDA' shall mean, for any period, the sum of
         Consolidated Net Income for such period PLUS the following expenses or
         charges to the extent deducted from Consolidated Net Income in such
         period: interest, taxes, depreciation, depletion and amortization, and
         other non-cash charges, MINUS (i) all non-cash income added to
         Consolidated Net Income in such period and (ii) capitalized general and
         administrative charges for such period.";

                           (iii) by deleting the reference "June 1, 1999" in the
definition of the term "First Borrowing Base Determination Date" and
substituting therefor the reference "January 31, 2000";

                  B. Section 2.03 of the Credit Agreement is amended hereby by
deleting the text of subsection (a) in its entirety, and substituting the
following therefor:

                           "Prior to the initial Borrowing Base determination,
                  the Aggregate Commitments shall at all times be equal to the
                  Aggregate Maximum Credit Amounts, after which date the
                  Aggregate Commitments shall be equal to the lesser of (i) the
                  Aggregate Maximum Credit Amounts or (ii) the Borrowing Base as
                  determined from time to time.".

                  C. Section 2.07 of the Credit Agreement is amended hereby as
follows:

                           (i) by inserting the following reference before the
last sentence of subsection (d):

                  "Prior to the initial Borrowing Base determination, all
                  prepayments on the Loans other than prepayments made from the
                  proceeds of sale of any equity or equity derivative securities
                  shall reduce the Aggregate Maximum Credit Amounts."


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                           (ii) by inserting the following new subsection (e):

                  "(e) Prior to the initial determination of the Borrowing Base,
                  the Borrower shall make prepayments as set forth below:

                           (i) Upon the sale, transfer or other disposition of
any asset that would be included in the Borrowing Base, as determined by the
Agent in its discretion, the Borrower shall prepay the Loans in an amount equal
to 100% of the net cash proceeds of any such sale; and

                           (ii) Upon any sale, transfer or other disposition of
any asset that would not be included in the Borrowing Base, the Borrower shall
prepay the Loans in an amount equal to 66-2/3% of the net cash proceeds
exceeding $500,000 of any such sale."

                  D. Section 8.07 of the Credit Agreement is amended hereby by
deleting the reference "June 1, 1999 " in the first sentence of subsection (b)
and substituting therefor the reference "January 31, 2000";

                  E. Annex I of the Credit Agreement is amended hereby by
deleting Annex I in its entirety and substituting therefor Annex I attached
hereto as Exhibit A.

                  Section 3. Covenants. The Borrower or Brigham Exploration, as
the case may be, covenants and agrees that during the period from July 1, 1999
through and including January 31, 2000:

                  A. Brigham Exploration shall deliver weekly cash budgets
reasonably satisfactory to the Agent in the form provided under the Second
Amendment to Credit Agreement, and weekly cash flow statements reasonably
satisfactory to the Agent based on such form, with variance analysis to budget
(including accounts receivables and accounts payables reporting) not later than
the Friday following the week to which such budgets and statements relate.

                  B. The Borrower shall not use any amounts advanced by the
Lenders to spud any wells or conduct any other drilling operations (other than
routine workovers and recompletions normally expensed in accordance with past
practice) without the prior written consent of the Agent and the Lenders, and
shall not use any amounts advanced by the Lenders to acquire acreage, leases or
seismic data provided that, notwithstanding the foregoing, (i) the Borrower may
pay liabilities and/or obligations outstanding as of the date hereof, (ii) the
Borrower may incur up to $300,000, in the aggregate, in discretionary new
commitments during the period from the date hereof through and including January
31, 2000 to acquire leases and seismic data (or licenses thereto) if, and only
if, the Borrower shall grant the Agent, for the benefit of the Lenders, a
perfected Lien on its interest in any new leases acquired pursuant to this
proviso within thirty (30) days or, upon request by the Agent, within fifteen
(15) days, of any such acquisition under a form


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of mortgage substantially identical to that of the New Mortgage; and (iii) the
Borrower may use amounts advanced by the Lenders to spud, drill and complete
wells identified in Schedule I hereto and any other wells that have no dry hole
costs associated therewith.

                  C. The Borrower shall provide to the Agent from time to time
upon request by the Agent the certificate of a Responsible Officer of the
Borrower stating that, except as disclosed in a schedule thereto, the Borrower
has not received written notice that any mechanics' liens have been filed or
will be filed on the Mortgaged Properties; provided that mere receipt of an
invoice for services rendered shall not constitute written notice that a
mechanics' lien will be filed.

                  D. The Borrower shall provide the Agent and Lenders with an
internal engineering report by October 31, 1999.

                  E. The Borrower will not, and will not allow any of its
Subsidiaries to, (i) transfer any assets to Quest Resources LLC or (ii) make any
investments in or loans or advances to Quest Resources LLC.

                  Section 4. Conditions Precedent. This Amendment shall become
binding upon receipt by the Agent of the following documents and satisfaction of
the other conditions provided in this Section 4, each of which must be
satisfactory to the Agent in form and substance:

                  A. counterparts of this Amendment executed by the Borrower,
the Agent and the Lenders;

                  B. certificates of the Secretary or an Assistant Secretary of
the Borrower and each of the Guarantors setting forth for each of them (i) the
resolutions of its board of directors or managers (or if such Guarantor is a
partnership, resolutions of the general partner of such partnership), as
applicable, with respect to the authorization to execute and deliver this
Amendment and consummate the transactions contemplated hereby; (ii) the
Responsible Officer of such entity authorized to sign this Amendment, and (iii)
the signature of such authorized Responsible Officer of such entity;

                  C. a Fourth Amendment to Guaranty Agreement executed by
Brigham Exploration Company;

                  D. a Consent and Acknowledgement executed by each of the
Guarantors;

                  E. an opinion of in-house counsel of Borrower and Brigham
Exploration substantially in the form issued by counsel to Borrower in
connection with the Second Amendment;


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                  F. payment to the Agent for the ratable benefit of the Lenders
of all accrued and unpaid Interest outstanding on all Base Rate Loans under the
Credit Agreement and the Notes;

                  G. payment of the expenses of the Agent and the Lenders in
accordance with Section 8.B hereof; and

                  H. such other documents as Agent or its counsel may reasonably
request.

                  Section 5. Representations and Warranties.

                  A. Except as provided in subsection (iii) of this Section
5.A., the Borrower hereby reaffirms that, as of the date of this Amendment, the
representations and warranties made by the Borrower and Brigham Exploration in
the Credit Agreement are true and correct as though made on and as of the date
hereof, and further, the Borrower represents that,

                     (i) as of the date hereof, no Default or Material Adverse
Effect has occurred and is continuing except as previously disclosed to the
Agent in writing;

                     (ii) the execution, delivery and performance by the
Borrower or the Guarantors of this Amendment and the other Loan Documents and
all instruments and documents to be delivered by the Borrower or the Guarantors,
to the extent a party thereto, hereunder and thereunder and the creation of all
Liens provided for herein and therein: (a) are within the Borrower's or such
Guarantor's corporate power; (b) have been duly authorized by all necessary or
proper corporate action, including the consent of stockholders, members and/or
partners therein or thereof; (c) are not in contravention of any provision of
the Borrower's or such Guarantor's certificate of incorporation, bylaws or
similar organizational and/or governing documents; (d) will not violate (1) any
law or regulation or (2) any order or decree of any court or governmental
instrumentality; (e) will not conflict with or result in the breach or
termination of, constitute a default under or accelerate any performance
required by, any indenture, mortgage, deed of trust, lease, agreement or other
instrument to which the Borrower or any of the Guarantors is a party or by which
the Borrower or any of the Guarantors or any of their respective property is
bound; (f) will not result in the creation or imposition of any Lien upon any of
the property of the Borrower or the Guarantors other than those in favor of the
Agent pursuant to the terms of this Amendment and the other Loan Documents to be
delivered in connection herewith; and (g) do not require the consent or approval
of any governmental body, agency, authority or any other Person that has not
been duly obtained, made or complied with prior to the date hereof. At or prior
to the date hereof, each of this Amendment and the other Loan Documents to be
delivered in connection herewith shall have been duly executed and delivered for
the benefit of or on behalf of the Borrower or the Guarantors, in each case to
the extent a party thereto, and each shall then constitute a legal, valid and
binding obligation of the Borrower or such Guarantor, enforceable against it in
accordance with its terms; and


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                     (iii) notwithstanding the foregoing, the representations
and warranties contained in the last sentence of Section 7.10(a) of the Credit
Agreement (and not those contained in the first two sentences) are reaffirmed
with respect to the Mortgaged Property covered by or described in the New
Mortgage.

                  B. Each of the Borrower and the Guarantors further represents
and warrants, for itself only that he or it (i) is executing this Amendment
after consultation with counsel of his or its own choosing, (ii) has read and
understands the release granted by Section 6 hereof, (iii) desires to execute
this Amendment and (iv) has the requisite authority to enter into and be bound
by this Amendment, including the release granted by Section 6 hereof.

                  Section 6. Release.

                  A. Each of the Releasing Parties desires and intends fully to
compromise, release and settle any and all of the Released Claims; and each of
the Releasing Parties hereby covenants, warrants and represents unto each of the
Released Parties that such Releasing Party does hereby FOREVER RELEASE, ACQUIT,
WAIVE AND DISCHARGE each of the Released Parties of and from the Released Claims
and each of the Releasing Parties hereby declares the same FOREVER RELEASED,
ACQUITTED, WAIVED, SETTLED AND DISCHARGED. This release is effective without
regard to whether (i) such Released Claims are known or unknown, (ii) damages
arising out of such Released Claims have yet accrued, (iii) such Released Claims
arose collaterally, directly, derivatively, or otherwise between the parties
hereto or (iv) an ordinary person in the same or similar circumstances would or
would not, through the exercise of due care, have discovered such claims by the
date of this Amendment. In connection with the foregoing release:

                  B. Borrower and each of the Guarantors represents and warrants
that it has the full power and authority to perform the release granted in this
Section 6 and that it has not in any manner made any assignment of any Released
Claim to any third party.

                  C. The release granted in this Section 6 will be effective
upon execution of this Amendment by all of the parties hereto.

                  D. Each party executing this Amendment understands and agrees
that the release granted in this Section 6 is a full, final and complete release
of the Released Claims and that such release may be pleaded as an absolute and
final bar to any or all suits which may hereafter be filed or prosecuted by any
one or more of the Releasing Parties or anyone claiming by, through or under any
one or more of the Releasing Parties in respect of any of the matters released
hereby, and that no recovery on account of the Released Claims may hereafter be
had from any of the Released Parties; and that the consideration given for such
release is not an admission of liability or fault on the part of any of the
Released Parties (it being the express intent of the parties hereto to obtain
peace of mind and avoid the expense and uncertainty of potential litigation),
and that


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none of the Releasing Parties or those claiming by, through or under any of them
will ever claim that it is.

                  E. The parties hereto acknowledge that the release granted by
this Section 6 does not have any effect with respect to relationships between
the Borrower and each of the Guarantors and the Lenders and the Agent other than
in connection with the Lending Relationship.

                  Section 7. Events of Default and Remedies.

                  A. The occurrence of any one or more of the following events
(regardless of the reason therefor) shall constitute an "Event of Default"
hereunder:

                     (i) Brigham Exploration shall fail to deliver within 30
days after closing a Warrant Agreement in form and substance satisfactory to the
Lenders executed by Brigham Exploration in favor of each of Bank of Montreal and
Societe Generale;

                     (ii) Brigham Exploration shall fail to deliver within 30
days after closing a legal opinion of Brigham Exploration's in-house counsel in
form and substance satisfactory to the Agent with respect to the Warrant
Agreements, any Loan Documents executed by Brigham Holdings I, LLC or Brigham
Holdings II, LLC in connection with this Third Amendment and consummation of the
transactions contemplated by the Warrant Agreements and such other Loan
Documents;

                     (iii) the Borrower shall fail to deliver within 30 days
after closing a Consent and Acknowledgement executed by Brigham Holdings I, LLC
in favor of the Agent;

                     (iv) the Borrower shall fail to deliver within 30 days
after closing a Consent and Acknowledgement executed by Brigham Holdings II, LLC
in favor of the Agent; and

                     (v) the Borrower shall fail to deliver certificates of the
Secretary or an Assistant Secretary of Brigham Exploration, Brigham Holdings I,
LLC and Brigham Holdings II, LLC setting forth for each of them (i) the
resolutions of its board of directors or managers (or if such entity is a
partnership, resolutions of the general partner of such partnership), as
applicable, with respect to the authorization to execute and deliver the Warrant
Agreements and the Loan Documents to be executed in connection with this Third
Amendment and to consummate the transactions contemplated hereby and thereby, in
each case, to the extent a party thereto; (ii) the Responsible Officer of such
entity authorized to execute such documents, and (iii) the signature of such
authorized Responsible Officer of such entity.


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                  B. The occurrence and continuation of an Event of Default
hereunder shall constitute an Event of Default under the Credit Agreement as
amended hereby.

                  Section 8. Payment of Fees and Expenses; Form of Payment.

                  A. Brigham Exploration, as Guarantor of Borrower's obligations
to Lenders under the Loan Documents, agrees, in consideration of the Lenders'
agreement to enter into this Third Amendment, to issue to each Lender its
ratable share, based on its Percentage Share of the Aggregate Commitments, of
warrants to purchase 1,000,000 shares of the common stock of Brigham Exploration
exercisable in accordance with the terms and conditions of the Warrant
Agreements.

                  B. The Borrower agrees, whether or not the transactions
contemplated hereby are consummated, to pay all reasonable expenses of the Agent
and the Lenders (including, without limitation, all reasonable fees and
disbursements of counsel and other outside consultants for the Agent and/or the
Lenders) in connection with the negotiation, investigation, preparation,
execution and delivery of, recording and filing of, preservation of rights under
and enforcement of this Amendment and the other Loan Documents to be delivered
in connection herewith.

                  C. All payments to be made by the Borrower under this
Amendment shall be made in Dollars, in immediately available funds, to the Agent
at such account as the Agent shall specify by notice in accordance with Section
4.01 of the Credit Agreement.

                  Section 9. Limitations. The amendments set forth herein are
limited precisely as written and shall not be deemed to (a) be a consent to, or
waiver or modification of, any other term or condition of the Credit Agreement
or any of the other Loan Documents, or (b) prejudice any right or rights which
the Lenders or the Agent may now have or may have in the future under or in
connection with the Credit Agreement or any of the other Loan Documents. Except
as expressly supplemented, amended or modified hereby, the terms and provisions
of the Credit Agreement or any other Loan Documents are and shall remain in full
force and effect. In the event of a conflict between this Amendment and any of
the foregoing documents, the terms of this Amendment shall be controlling.

                  Section 10. Non-Reliance on Agent and Other Lenders. Each
Lender acknowledges and agrees that it has, independently and without reliance
on the Agent or any other Lender, and based on such documents and information as
it has deemed appropriate, made its own decision to enter into this Amendment,
and that it will, independently and without reliance upon the Agent or any other
Lender, and based on such documents and information as it shall deem appropriate
at the time, continue to make its own analysis and decisions in taking or not
taking action under this Amendment or the Credit Agreement. The Agent shall not
be required to keep itself informed as to the performance or observance by the
Borrower of this Amendment or any other Loan Document or any other document
referred to or provided for herein or therein or to


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inspect the properties or books of the Borrower. Except for notices, reports and
other documents and information expressly required to be furnished to the
Lenders by the Agent hereunder and under the Credit Agreement, the Agent shall
not have any duty or responsibility to provide any Lender with any credit or
other information concerning the affairs, financial condition or business of the
Borrower (or any of its Affiliates) which may come into the possession of the
Agent or any of its Affiliates. In this regard, each Lender acknowledges that
Weil, Gotshal & Manges LLP is acting in this transaction as special counsel to
the Agent only. Each Lender will consult with its own legal counsel to the
extent that it deems necessary in connection with this Amendment and the matters
contemplated herein.

                  Section 11. Governing Law. This Amendment and the rights and
obligations of the parties hereunder and under the Credit Agreement shall be
construed in accordance with and be governed by the laws of the State of Texas
and the United States of America.

                  Section 12. Descriptive Headings, etc. The descriptive
headings of the several Sections of this Amendment are inserted for convenience
only and shall not be deemed to affect the meaning or construction of any of the
provisions hereof.

                  Section 13. Counterparts. This Amendment may be executed in
any number of counterparts and by different parties on separate counterparts and
all of such counterparts shall together constitute one and the same instrument.


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                  IN WITNESS WHEREOF, the parties hereto have caused this
Amendment to be executed as of the date first written above.

            NOTICE PURSUANT TO TEX. BUS. & COMM. CODE SECTION 26.02

                  THIS AMENDMENT AND OTHER LOAN DOCUMENTS EXECUTED BY ANY OF THE
PARTIES BEFORE OR SUBSTANTIALLY CONTEMPORANEOUSLY WITH THE EXECUTION HEREOF
TOGETHER CONSTITUTE A WRITTEN LOAN AGREEMENT AND REPRESENT THE FINAL AGREEMENT
BETWEEN THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR,
CONTEMPORANEOUS OR SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES. THERE ARE NO
UNWRITTEN ORAL AGREEMENT BETWEEN THE PARTIES.

BORROWER:                                BRIGHAM OIL & GAS, L.P.

                                         By: Brigham, Inc., its General Partner



                                         By: /s/ CRAIG M. FLEMING
                                            ------------------------------------
                                         Name: Craig M. Fleming
                                              ----------------------------------
                                         Title: Vice President and CEO
                                               ---------------------------------


AGENT:                                   BANK OF MONTREAL



                                         By: /s/ THOMAS E. MCGRAW
                                            ------------------------------------
                                            Thomas E. McGraw
                                            Director


LENDER:                                  BANK OF MONTREAL


                                         By: /s/ THOMAS E. MCGRAW
                                            ------------------------------------
                                            Thomas E. McGraw
                                            Director


                                       S

<PAGE>   12




LENDER:                                  SOCIETE GENERALE, Southwest Agency


                                         By: /s/ MARK A. COX
                                            ------------------------------------
                                         Name:  Mark A. Cox
                                                --------------------------------
                                         Title: Director
                                                --------------------------------



                                       S
<PAGE>   13



                                                                       EXHIBIT A

                                     ANNEX I


<TABLE>
<CAPTION>
Name of Lender               Percentage Share           Maximum Credit Amount
--------------               ----------------           ---------------------
<S>                          <C>                        <C>
Bank of Montreal                 66.1538                     $43,000,000
Societe Generale                 33.8462                     $22,000,000
</TABLE>


                                   ANNEX I-I