<PAGE>   1
 
                                                                    EXHIBIT 4.18
 
                                FOURTH AMENDMENT
 
     FOURTH AMENDMENT (this "Amendment"), dated as of April 6, 1998, among
American Pad & Paper Company ("Holdings"), WR Acquisition, Inc. ("WR
Acquisition"), American Pad & Paper Company of Delaware, Inc. (the "Borrower"),
the lending institutions party to the Credit Agreement referred to below (each a
"Bank" and, collectively, the "Banks"), Bank of Tokyo-Mitsubishi Trust Company,
Bank One Texas, N.A., The Bank of Nova Scotia and The First National Bank of
Boston, as Co-Agents (the "Co-Agents"), and Bankers Trust Company, as Agent (the
"Agent"). All capitalized terms used herein and not otherwise defined herein
shall have the respective meanings provided such terms in the Credit Agreement.
 
                                  WITNESSETH:
 
     WHEREAS, Holdings, WR Acquisition, the Borrower, the Banks, the Co-Agents
and the Agent are party to a Credit Agreement, dated as of July 8, 1996 (as
amended, modified and supplemented prior to the date hereof, the "Credit
Agreement"); and
 
     WHEREAS, the Borrower has requested that the Banks provide the amendment
provided for herein and the Banks have agreed to provide such amendment on the
terms and conditions set forth herein;
 
     NOW, THEREFORE, it is agreed:
 
          1. Section 8.10 of the Credit Agreement is hereby amended to read in
     its entirety as follows:
 
             8.10  Minimum Consolidated EBITDA. The Borrower will not permit
        Consolidated EBITDA (i) for the fiscal quarter ending March 31, 1998, to
        be less than $11,300,000, (ii) for the two fiscal quarters ending June
        30, 1998 (taken as one accounting period), to be less than $28,000,000,
        (iii) for the three fiscal quarters ending September 30, 1998 (taken as
        one accounting period), to be less than $48,000,000, (iv) for the fiscal
        year ending December 31, 1998, to be less than $72,000,000 and (v) for
        any Test Period ending on or after March 31, 1999, to be less than
        $75,000,000.
 
          2. In order to induce the Banks to enter into this Amendment, each of
     Holdings, WR Acquisition and the Borrower hereby represents and warrants
     that (i) no Default or Event of Default exists as of the Amendment
     Effective Date (as defined below) after giving effect to this Amendment and
     (ii) on the Amendment Effective Date, both before and after giving effect
     to this Amendment, all representations and warranties contained in the
     Credit Agreement and in the other Credit Documents are true and correct in
     all material respects.
 
          3. This Amendment shall become effective on the date (the "Amendment
     Effective Date") when the Required Banks, Holdings, WR Acquisition and the
     Borrower shall have signed a counterpart hereof (whether the same or
     different counterparts) and shall have delivered (including by way of
     facsimile transmission) the same to the Agent at its Notice Office;
 
          4. 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.
 
          5. 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.
 
     THIS AMENDMENT AND THE RIGHTS AND OBLIGATIONS OF THE PARTIES HEREUNDER
SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF
NEW YORK.
<PAGE>   2
 
                                    *  *  *
 
     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 hereof.
 
                                            AMERICAN PAD & PAPER COMPANY
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                            WR ACQUISITION, INC.
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                            AMERICAN PAD & PAPER COMPANY OF
                                            DELAWARE, INC.
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                            BANKERS TRUST COMPANY, individually
                                            and as Agent
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                        2
<PAGE>   3
 
                                            ABN AMRO BANK
 
                                            By:             /s/
 
                                                --------------------------------
                                              Name:
                                              Title:
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                            BANK LEUMI TRUST CO. OF NEW YORK
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                            THE BANK OF NEW YORK
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                            THE BANK OF NOVA SCOTIA
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                            BANK OF SCOTLAND
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                        3
<PAGE>   4
 
                                            BANK OF TOKYO-MITSUBISHI TRUST
                                            COMPANY
 
                                            By:           /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                            BANK ONE TEXAS
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                            BANQUE PARIBAS
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                            CHRISTIANIA BANK OG KREDITKASSE,
                                            NEW YORK BRANCH
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                        4
<PAGE>   5
 
                                            CIBC INC.
 
                                            By:             /s/
 
                                                --------------------------------
                                              Name:
                                              Title:
 
                                            BANKBOSTON, N.A.
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                            GUARANTY FEDERAL BANK, F.S.B.
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                            THE INDUSTRIAL BANK OF JAPAN,
                                            LIMITED
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                            THE LONG-TERM CREDIT BANK OF
                                            JAPAN, LIMITED, NEW YORK BRANCH
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                        5
<PAGE>   6
 
                                            SANWA BUSINESS CREDIT
                                            CORPORATION
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                            SOCIETE GENERALE
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
                                            LEHMAN COMMERCIAL PAPER, INC.
 
                                            By:            /s/
 
                                              ----------------------------------
                                              Name:
                                              Title:
 
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