<PAGE>

                                                                    EXHIBIT 4.24


                          FOURTH AMENDMENT AND CONSENT
                          ----------------------------

           FOURTH AMENDMENT AND CONSENT (this "Amendment"), dated as of January
22, 1997, among BIG V HOLDING CORP. ("Holdings"), BV HOLDINGS CORPORATION ("BV
Holdings"), BIG V SUPERMARKETS, INC. (the "Borrower"), the financial
institutions party to the Credit Agreement referred to below (the "Banks") and
BANKERS TRUST COMPANY, as Agent (the "Agent"). Unless otherwise defined herein,
all capitalized terms used herein shall have the respective meanings provided
such terms in the Credit Agreement referred to below.

                             W I T N E S S E T H :
                             - - - - - - - - - -

           WHEREAS, Holdings, BV Holdings, the Borrower, the Banks and the Agent
are parties to an Amended and Restated Credit Agreement, dated as of December
28, 1990, and amended and restated as of November 1, 1993, and further amended
and restated as of December 17, 1993 (as amended, modified or supplemented
through the date hereof, the "Credit Agreement"); and

           WHEREAS, subject to the terms and conditions set forth herein, the
parties hereto wish to amend and/or modify the Credit Agreement as provided
herein;

           NOW, THEREFORE, it is agreed:

           1. The table appearing in Section 7.10 of the Credit Agreement is
hereby amended by deleting the phrase "June 30, 1997" and the corresponding
amount "$40,000,000" set forth opposite such phrase, in each case appearing
therein and inserting the following text in lieu thereof:

           "March 31, 1997                             $38,000,000


           First day of fiscal quarter beginning
           closest to April 1, 1997 through and
           including the last day of the fiscal
           quarter ended closest to June 30, 1997      $39,000,000".
<PAGE>
 
           2. Notwithstanding anything to the contrary contained in the Credit
Agreement, for the purpose of calculating EBITDA under the Credit Agreement (i)
for any period of four consecutive fiscal quarters of the Borrower (taken as one
accounting period) which includes the Borrower's fiscal quarter ended on October
5, 1996, there shall be added to EBITDA for such period an amount equal to
$3,904,000, which amount equals the one-time charges (a portion of which were
one-time non-cash charges) incurred by the Borrower in its fiscal quarter ended
on October 5, 1996 and (ii) for any period of four consecutive fiscal quarters
of the Borrower (taken as one accounting period), there shall be subtracted from
EBITDA for such period any cash payments made by the Borrower on or after
December 28, 1996 through and including the last day of the fiscal quarter of
the Borrower ending closest to June 30, 1997 with respect to any of the non-cash
charges referred to in clause (i) of this Section 2.

           3. Notwithstanding anything to the contrary contained in Section
7.08(a) of the Credit Agreement, the Borrower shall not be permitted to make any
Capital Expenditures pursuant to such Section 7.08(a) during its fiscal year
ending closest to December 31, 1997 in excess of $7,000,000 unless such excess
Capital Expenditures are financed with Equipment Financing Loans and/or the sale
of equity of Holdings, the proceeds of which are permitted to be retained
pursuant to clause (i) of the second parenthetical of Section 3.02(e) of the
Credit Agreement, it being understood and agreed that (i) the Borrower may
initially make such excess Capital Expenditures prior to incurring such
Equipment Financing Loans or receipt of such equity proceeds so long as (x) the
Borrower has theretofore delivered to the Agent a commitment letter from a
lender or lenders agreeing to make such Equipment Financing Loans, which
commitment letter shall be in form and substance satisfactory to the Agent and
(y) such Equipment Financing Loans are in fact incurred by the Borrower within
90 days after the opening of the respective store constructed with such Capital
Expenditures (or, to the extent such Equipment Financing Loans are not incurred
by such 90th day, such excess Capital Expenditures are financed by such 90th day
with equity proceeds permitted to be retained by the Borrower as provided above)
and (ii) nothing contained in this Section 3 shall otherwise permit the Borrower
(x) to make any Capital Expenditures in excess of the amounts otherwise
permitted under the Credit Agreement or (y) to incur any Equipment Financing
Loans in excess of the amounts otherwise permitted under the Credit Agreement.

                                      -2-
<PAGE>
 
           4. In order to induce the Banks to enter into this Amendment,
Holdings, BV Holdings and the Borrower hereby represent and warrant that (x) no
Default or Event of Default exists on the Fourth Amendment Effective Date (as
defined below), both before and after giving effect to this Amendment and (y)
all of the representations and warranties contained in the Credit Documents
shall be true and correct in all respects on the Fourth Amendment Effective
Date, both before and after giving effect to this Amendment with the same effect
as though such representations and warranties had been made on and as of the
Fourth Amendment Effective Date (it being understood that any representation or
warranty made as of a specified date shall be true and correct in all material
respects as of such specific date).

           5. This Amendment is limited as specified and shall not constitute a
modification, acceptance or waiver of any other provision of the Credit
Agreement or any other Credit Document.

           6. This Amendment may be executed in any number of counterparts and
by the different parties hereto on separate counterparts, each of which
counterparts when executed and delivered shall be an original, but all of which
shall together constitute one and the same instrument. A complete set of
counterparts shall be lodged with the Borrower and the Agent.

           7. THIS AMENDMENT AND THE RIGHTS AND OBLIGATIONS OF THE PARTIES
HEREUNDER SHALL BE CONSTRUED IN ACCORDANCE WITH AND GOVERNED BY THE LAW OF THE
STATE OF NEW YORK.

           8. This Amendment shall become effective on the date (the "Fourth
Amendment Effective Date") when Holdings, BV Holdings, the Borrower and the
Required Banks shall have signed a counterpart hereof (whether the same or
different counterparts) and shall have delivered (including by way of
telecopier) the same to the Agent at its Notice Office.

           9. From and after the Fourth Amendment Effective Date, all references
in the Credit Agreement and each of the other Credit Documents to the Credit
Agreement shall be deemed to be references to the Credit Agreement after giving
effect to this Amendment.

                                      -3-
<PAGE>
 
           IN WITNESS WHEREOF, 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.

                                    BIG V HOLDING CORP.


                                    By /s/ James A. Toopes, Jr.
                                      ------------------------------
                                      Title:  Executive Vice President-Finance,
                                                Adm. and Corporate Development


                                    BV HOLDINGS CORPORATION


                                    By /s/ James A. Toopes, Jr.
                                      ------------------------------
                                      Title:  Executive Vice President-Finance,
                                                Adm. and Corporate Development


                                    BIG V SUPERMARKETS, INC.


                                    By /s/ James A. Toopes, Jr.
                                      ------------------------------
                                      Title:  Executive Vice President-Finance,
                                                Adm. and Corporate Development


                                    BANKERS TRUST COMPANY,
                                      Individually and as Agent


                                    By /s/ Dana Klein
                                      ------------------------------
                                      Title: Vice President


                                    BANQUE NATIONALE DE PARIS


                                    By [SIGNATURE APPEARS HERE]
                                      ------------------------------
                                      Title: Vice President


                                    By [SIGNATURE APPEARS HERE]
                                      ------------------------------
                                      Title: Vice President


                                    BANKERS TRUST (DELAWARE)


                                    By [SIGNATURE APPEARS HERE]
                                      ------------------------------
                                      Title: Vice President
<PAGE>
 
                                          DLJ CAPITAL FUNDING, INC.

                                          By
                                            -------------------------------
                                            Title:

                                          FIRST SOURCE FINANCIAL LLP.

                                          By: First Source Financial, Inc.
                                                  its Agent/Manager.

                                          By /s/ Gary L. Francis
                                            -------------------------------
                                            Title: Senior Vice President

                                          BANK POLSKA KASA OPIEKI S.A.

                                          By
                                            -------------------------------
                                            Title:

                                          HELLER FINANCIAL, INC.

                                          By
                                            -------------------------------
                                            Title:

                                          DLJ CAPITAL FUNDING, INC.

                                          By
                                            -------------------------------
                                            Title:

                                          FIRST SOURCE FINANCIAL LLP.

                                          By: First Source Financial, Inc.
                                                  its Agent/Manager.

                                          By
                                            -------------------------------
                                            Title:

                                          BANK POLSKA KASA OPIEKI S.A.

                                          By  /s/ William A. Shea
                                            -------------------------------
                                            Title: Vice President Senior
                                                   Lending Officer

                                          HELLER FINANCIAL, INC.

                                          By
                                            -------------------------------
                                            Title:

                                          DLJ CAPITAL FUNDING, INC.           
                                                                              
                                          By
                                            -------------------------------
                                            Title:
                                                                               
                                          FIRST SOURCE FINANCIAL LLP.         
                                                                               
                                          By: First Source Financial, Inc.     
                                                its Agent/Manager.
                                                    
                                          By                                   
                                            ------------------------------
                                            Title:                              
                                                                               
                                          BANK POLSKA KASA OPIEKI S.A.         
                                                                               
                                          By                                   
                                            ------------------------------
                                            Title:
                                                                               
                                          HELLER FINANCIAL, INC.               
                                                                               
                                          By /s/ Robert A Pierce               
                                            ------------------------------
                                            Title: Vice President