<PAGE>   1

                                 EXHIBIT 10.31

                               FIRST AMENDMENT TO
                                CREDIT AGREEMENT


     THIS FIRST AMENDMENT TO CREDIT AGREEMENT (this "Amendment"), dated as of
December 20, 1996, is made by and among RALSTON RESORTS, INC., a Colorado
corporation (the "Borrower"), THE PERSONS IDENTIFIED AS A "LENDER" ON THE
SIGNATURE PAGES HERETO (the "Lenders") and NATIONSBANK, N.A., as agent for the
Lenders (in such capacity, the "Agent").

                              W I T N E S S E T H:

         WHEREAS, pursuant to the Credit Agreement, dated as of September 30,
1996 (the "Credit Agreement"), among the Borrower, the Lenders and the Agent,
the Lenders have made available a $140,000,000 bridge loan facility to the
Borrower; and

         WHEREAS, the parties hereto have agreed to enter into this Amendment
in order to evidence certain agreements of the parties with respect to the
Credit Agreement as set forth herein;

         NOW, THEREFORE, in consideration of the agreements herein contained,
the parties hereby agree as follows:


                                     PART I
                                  DEFINITIONS

     SUBPART 1.1.  Certain Definitions.  Unless otherwise defined herein or the
context otherwise requires, the following term used in this Amendment has the
following meaning:

      "Effective Date" is defined in Subpart 3.1.

     SUBPART 1.2.  Other Definitions.  Unless otherwise defined herein or the
context otherwise requires, terms used in this Agreement, including its preamble
and recitals, have the meanings provided in the Credit Agreement.


                                    PART II
                                CREDIT AGREEMENT

         Effective on (and subject to the occurrence of) the Effective Date,
the parties hereto hereby agree as follows with respect to the Credit
Agreement:




                                      1
<PAGE>   2

     SUBPART 2.1.  Amendments to Section 1.01.  The definition of "Applicable
Margin" set forth in Section 1.01 of the Credit Agreement is amended in its
entirety to read as follows:

          "Applicable Margin" shall mean, for purposes of calculating the
     applicable interest rate for any day for any Eurodollar Loan, 87.5 bps.

     SUBPART 2.2.  Amendment to Section 10.15.  Section 10.15 of the Credit
Agreement is amended in its entirety to read as follows:

          SECTION 10.15.  Incorporated Provisions.  The Borrower hereby agrees
     that (i) the representations and warranties contained in Article VI of the
     Ralcorp Credit Agreement (together with any defined terms set forth in
     Article I of the Ralcorp Credit Agreement utilized in such representations
     and warranties), as in effect as of December 20, 1996 (after giving effect
     to all amendments to the Ralcorp Credit Agreement occurring as of or before
     such date), but excluding those which expressly relate to an earlier date
     (the "Incorporated Representations and Warranties"), (ii) the covenants
     contained in Articles VII and VIII of the Ralcorp Credit Agreement
     (together with any defined terms set forth in Article I of the Ralcorp
     Credit Agreement utilized in such covenants), as in effect as December 20,
     1996 (after giving effect to all amendments to the Ralcorp Credit Agreement
     occurring as of or before such date) (the "Incorporated Covenants") and
     (iii) the events of default contained in Article IX of the Ralcorp Credit
     Agreement (together with any defined terms set forth in Article I of the
     Ralcorp Credit Agreement utilized in such events of default), as in effect
     as of December 20, 1996 (after giving effect to all amendments to the
     Ralcorp Credit Agreement occurring as of or before such date) (the 
     "Incorporated Events of Default"), are hereby incorporated by reference and
     shall be as binding on the Borrower as if set forth fully herein.  The
     incorporation of provisions by reference to the Ralcorp Credit Agreement
     pursuant to this Section 10.15 shall survive the termination of the Ralcorp
     Credit Agreement.  For purposes of the incorporation of provisions in the
     Ralcorp Credit Agreement pursuant to this Section 10.15, (A) all references
     in the Incorporated Representations and Warranties, the Incorporated
     Covenants and the Incorporated Events of Default to a "Lender" or the
     "Lenders" shall be deemed to refer to a Lender or the Lenders hereunder,
     (B) all references in the Incorporated Representations and Warranties, the
     Incorporated Covenants and the Incorporated Events of Default to the
     "Required Lenders" shall be deemed to refer to the Required Lenders
     hereunder, (C) all references in the Incorporated Representations and
     Warranties, the Incorporated Covenants and the Incorporated Events of
     Default to the "Agent" shall be deemed to refer to the Agent hereunder and
     (D) all references in the Incorporated Representations and Warranties, the
     Incorporated Covenants and the Incorporated Events of Default to the
     "Agreement" shall be deemed to refer to this Agreement.




                                      2
<PAGE>   3

                    PART III CONDITIONS TO EFFECTIVENESS

     SUBPART 3.1.  Effective Date.  The agreements of the parties set forth in
Part II of this Amendment shall be and become effective as of the date hereof
(the "Effective Date") when all of the conditions set forth in this Part III
shall have been satisfied.

                 SUBPART 3.1.1.  Execution of Counterparts of Amendment.  The
Agent shall have received counterparts of this Amendment, which collectively
shall have been duly executed on behalf of the Borrower, the Agent and each of
the Lenders.

                 SUBPART 3.1.2.  Representations and Warranties, Etc.

                          (a)     After giving effect to the amendments
contained herein, the representations and warranties contained in Article VI of
the Credit Agreement shall be true and correct in all material respects on and
as of the Effective Date (except for those which expressly relate to an earlier
date).

                          (b)     After giving effect to the amendments
contained herein, no Default or Event of Default shall exist under the Credit
Agreement on and as of the Effective Date.

                 SUBPART 3.1.3.  Other Documents.  The Agent shall have
received such other documentation as the Agent may reasonably request in
connection with the foregoing.


                                    PART IV
                                 MISCELLANEOUS

     SUBPART 4.1.  Cross-References.  References in this Amendment to any Part
or Subpart are, unless otherwise specified, to such Part or Subpart of this
Amendment.

     SUBPART 4.2.  Instrument Pursuant to Credit Agreement.  This Amendment is a
Credit Document executed pursuant to the Credit Agreement and shall (unless
otherwise expressly indicated therein) be construed, administered and applied in
accordance with the terms and provisions of the Credit Agreement.

     SUBPART 4.3.  References in Other Credit Documents.  At such time as this
Amendment shall become effective pursuant to the terms of Subpart 3.1, all
references in the Credit Documents to the Credit Agreement shall be deemed to
refer to the Credit Agreement as amended by this Amendment.

     SUBPART 4.4.  Survival.  Except as expressly modified and amended in this
Amendment, all of the terms and provisions and conditions of the Credit
Agreement shall remain unchanged.




                                      3
<PAGE>   4

     SUBPART 4.5.  Counterparts.  This Amendment may be executed by the parties
hereto in several counterparts, each of which shall be deemed to be an original
and all of which shall constitute together but one and the same agreement.

     SUBPART 4.6.  Entirety.  This Amendment, the Credit Agreement and the other
Credit Documents embody the entire agreement between the parties and supersede
all prior agreements and understandings, if any, relating to the subject matter
hereof and thereof.  The Credit Documents represent the final agreement between
the parties relating to such subject matter and may not be contradicted by
evidence of prior, contemporaneous or subsequent oral agreements of the parties.

     SUBPART 4.7.  Governing Law. THIS AMENDMENT SHALL BE DEEMED TO BE A
CONTRACT MADE UNDER AND GOVERNED BY THE INTERNAL LAWS OF THE STATE OF NORTH
CAROLINA WITHOUT GIVING EFFECT TO THE CONFLICT OF LAW PRINCIPLES THEREOF.

     SUBPART 4.8.  Successors and Assigns.  This Amendment shall be binding upon
and inure to the benefit of the parties hereto and their respective successors
and assigns.





         [The remainder of this page has been left blank intentionally]




                                      4
<PAGE>   5

Each of the parties hereto has caused a counterpart of this Amendment to be
duly executed and delivered as of the date first above written.

BORROWER:                               RALSTON RESORTS, INC.

                                        By:
                                        Name:
                                        Title:


LENDERS:                                NATIONSBANK, N.A., individually in its 
                                        capacity as a Lender and in its
                                        capacity as Agent

                                        By:
                                        Name:
                                        Title:


                                        BANK OF AMERICA, NATIONAL TRUST AND
                                        SAVINGS ASSOCIATION


                                        By:
                                        Name:
                                        Title:


                                        THE BANK OF NEW YORK

                                        By:
                                        Name:
                                        Title:


                                        THE BOATMEN'S NATIONAL BANK 
                                        OF ST. LOUIS

                                        By:
                                        Name:
                                        Title:


                             [Signatures Continue]




                                      5
<PAGE>   6

                                        THE FIRST NATIONAL BANK OF CHICAGO

                                        By:
                                        Name:
                                        Title:


                                        TORONTO-DOMINION (TEXAS), INC.

                                        By:
                                        Name:
                                        Title:


                                        WACHOVIA BANK OF GEORGIA, N.A.

                                        By:
                                        Name:
                                        Title:


                                        MERCANTILE BANK OF ST. LOUIS NATIONAL
                                        ASSOCIATION 

                                        By: 
                                        Name: 
                                        Title:


                                        CREDIT SUISSE

                                        By:
                                        Name:
                                        Title:

                                        By:
                                        Name:
                                        Title:




                                      6