<PAGE>   1
                                                                   EXHIBIT 10(V)

                              SEVENTH AMENDMENT TO
                                CREDIT AGREEMENT

         This Seventh Amendment to Credit Agreement, dated as of May 10, 1999
("Seventh Amendment"), is made by and between POLARIS INDUSTRIES INC., a
Minnesota corporation (the "Borrower"); U.S. BANK NATIONAL ASSOCIATION, formerly
known as FIRST BANK NATIONAL ASSOCIATION, BANK OF AMERICA NATIONAL TRUST AND
SAVINGS ASSOCIATION, formerly known as BANK OF AMERICA ILLINOIS and FIRST UNION
NATIONAL BANK, formerly known as FIRST UNION NATIONAL BANK OF NORTH CAROLINA
(collectively, the "Banks"); and U.S. BANK NATIONAL ASSOCIATION, as
administrative agent for the Banks (the "Administrative Agent").

         WHEREAS, the Borrower, the Banks and the Administrative Agent have
entered into that certain Credit Agreement dated as of May 8, 1995, as amended
by First Amendment to Credit Agreement dated as of November 15, 1995, Second
Amendment to Credit Agreement dated as of February 13, 1996, Third Amendment to
Credit Agreement dated as of September 30, 1996, Fourth Amendment to Credit
Agreement dated as of March 31, 1997, Fifth Amendment to Credit Agreement dated
as of August 24, 1998, and a Sixth Amendment to Credit Agreement dated as of
December 7, 1998 (as so amended, the "Credit Agreement").

         WHEREAS, the Borrower has requested the Banks and the Administrative
Agent to modify certain provisions of the Credit Agreement to extend the
revolving credit commitment ending date and to change certain other provisions
thereof, and the Banks and the Administrative Agent are willing to do so on the
terms and conditions set forth herein.

         NOW THEREFORE, in consideration of the premises and for good and
valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, the parties hereto covenant and agree to be bound as follows:

         Section 1. Capitalized Terms.  All capitalized terms used herein
and not otherwise defined herein shall have the meanings assigned to them in the
Credit Agreement.

         Section 2. Amendments.

                (a) The definitions of "Applicable Fee Percentage", "Applicable
Margin" and "Revolving Commitment Amount" in Section 1.1 of the Credit
Agreement are amended as follows:


<PAGE>   2


                  (i) In the definition of "Applicable Fee Percentage" the table
                  setting out the Applicable Fee Percentage for the various
                  levels of Daily Average Cash Flow Coverage Ratio is amended to
                  read as follows:

                  <TABLE>
                  <CAPTION>

                       Daily Average                               Applicable
                  Cash Flow Coverage Ratio                      Fee Percentage
                  ------------------------                      --------------
                  <S>                                           <C>
                  Greater than 2.0 to 1.0                              0.25%
                  Greater than 1.0 to 1.0, but                         0.185%
                         less than or equal to
                         2.0 to 1.0
                  Less than or equal to 1.0 to 1.0                     0.15%
                  </TABLE>

                  (ii) In the definition of "Applicable Margin" the table
                  setting out the Applicable Margin for the various levels of
                  Daily Average Cash Flow Coverage Ratio is amended to read as
                  follows:

                  <TABLE>
                  <CAPTION>
                       Daily Average                                 Applicable
                  Cash Flow Coverage Ratio                             Margin
                  ------------------------                             ------
                  <S>                                                <C>
                  Greater than 2.0 to 1.0                               1.0%
                  Greater than 1.0 to 1.0, but                          0.50%
                          less than or equal to
                          2.0 to 1.0
                  Greater than 0.55 to 1.0, but                         0.40%
                          less than or equal to
                          1.0 to 1.0
                  Less than or equal to 0.55 to 1.0                     0.30%

                  </TABLE>

                  (iii) The definition of "Revolving Commitment Amount" is
                  amended to read as follows: "Revolving Commitment Amount":
                  With respect to a Bank:

                  (a) during the period commencing May 6, 1999 and ending on and
         including March 30, 2000, the amount set opposite such Bank's name in
         the table immediately below or as specified in the most recent
         Assignment Agreement to which such Bank is a party, but as the same may
         be from time to time reduced pursuant to Section 2.14:


<TABLE>
<CAPTION>

----------------------------------------------------------- --------------------------------------------------------
Bank                                                        Revolving Commitment Amount Prior
----                                                        ---------------------------------
                                                            to March 31, 2000
                                                            -----------------
----------------------------------------------------------- --------------------------------------------------------
<S>                                                         <C>
U.S. Bank National Association                              $63,000,000
----------------------------------------------------------- --------------------------------------------------------
Bank of America                                             $56,000,000
----------------------------------------------------------- --------------------------------------------------------
</TABLE>



<PAGE>   3

<TABLE>
----------------------------------------------------------- --------------------------------------------------------
<S>                                                         <C>
First Union National Bank                                   $56,000,000
----------------------------------------------------------- --------------------------------------------------------
</TABLE>


                 (b) during the period beginning on March 31, 2000 and ending
         on the Revolving Commitment Ending Date, the amount set opposite such
         Bank's name in the table immediately below or as specified in the most
         recent Assignment Agreement to which such Bank is a party, but as the
         same may be from time to time reduced pursuant to Section 2.14:

<TABLE>
<CAPTION>

----------------------------------------------------------- --------------------------------------------------------
Bank                                                        Revolving Commitment Amount on and after
----                                                        ----------------------------------------
                                                            March 31, 2000 thru the Revolving
                                                            ---------------------------------
                                                            Commitment Ending Date
                                                            ----------------------

----------------------------------------------------------- ---------------------------------------------------------
<S>                                                         <C>
U.S. Bank National Association                              $54,000,000
----------------------------------------------------------- ---------------------------------------------------------
Bank of America                                             $48,000,000
----------------------------------------------------------- ---------------------------------------------------------
First Union National Bank                                   $48,000,000
----------------------------------------------------------- ---------------------------------------------------------
</TABLE>


                  (b)       Section 2.20 of the Credit Agreement is amended by
deleting therefrom the date "March 31, 2000" and inserting in its place the date
"March 31, 2002".

                  (c)       Section 6.12 of the Credit Agreement is amended in
its entirety to read as follows:

                  Section 6.12 Contingent Liabilities. The Borrower will not,
and will not permit any Subsidiary to, be or become liable on any Contingent
Obligations except: (i) Contingent Obligations existing on the date of this
Agreement and described on Exhibit 6.12-4; (ii) the Borrower's guarantee of up
to a percentage of Acceptance Partnership's Indebtedness under the Acceptance
Partnership Credit Agreement equal to PAI's percentage ownership of Acceptance
Partnership and the Borrower's guarantee of PAI's obligation to make additional
capital contributions to Acceptance Partnership, provided that the Borrower's
maximum liability under such guarantee does not exceed $250,000,000 (with
respect to loans) and $50,000,000 (with respect to capital contributions); (iii)
PAI's liability as general partner for up to a percentage of Acceptance
Partnership's Indebtedness under the Acceptance Partnership Credit Agreement
equal to PAI's percentage ownership of Acceptance Partnership, provided that
PAI's maximum liability with respect thereto does not exceed $250,000,000; (iv)
PAI's obligation to make additional capital contributions to Acceptance
Partnership, provided that the sum of such obligation, to the extent quantified
at any time, and all Investments in Acceptance Partnership then existing does
not exceed $50,000,000; (v) the guarantee by the Subsidiaries of the


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Borrower's obligations under interest rate protection agreements; and (vi) the
guarantee by the Subsidiaries of the Borrower's obligations under import letters
of credit issued by one or more of the Banks.

         Section 3. Conditions to Effectiveness of Seventh Amendment. The
Amendments contained in this Seventh Amendment shall not become effective until,
and shall become effective when, the Administrative Agent shall have received
each of the following, in sufficient number to distribute to each Bank:


                (a) The Agent shall have received, with a counterpart for each
         Bank, this Amendment, duly executed by the Borrower, the Banks and the
         Agent, and consented to by the Guarantors;

                (b) The Agent shall have received, with a counterpart for each
         Bank, a copy of resolutions adopted by the Borrower, authorizing the
         execution, delivery and performance of this Amendment by the Borrower,
         certified by the Borrower's secretary or assistant secretary;

                (c) The Agent shall have received, with a counterpart for each
         Bank, a copy of resolutions adopted by each Guarantor, authorizing the
         execution, delivery and performance of that Guarantor's consent to this
         Amendment, certified by that Guarantor's secretary or assistant
         secretary;

                (d) The Agent shall have received, with a counterpart for each
         Bank, a certificate signed by the secretary or assistant secretary of
         the Borrower certifying (i) as to the incumbency of the person or
         persons authorized to execute and deliver on behalf of the Borrower
         this Amendment, and (ii) that the articles or certificate of
         incorporation and bylaws of the Borrower have not been repealed,
         rescinded, amended or otherwise modified since copies of the same were
         delivered to the Banks on or about May 8, 1995, pursuant to Section 3.1
         of the Credit Agreement;

                (e) The Agent shall have received, with a counterpart for each
         Bank, a certificate signed by the secretary or assistant secretary of
         each Guarantor certifying (i) as to the incumbency of the person or
         persons authorized to execute and deliver on behalf of that Guarantor
         its consent to this Amendment, and (ii) that the articles or
         certificate of incorporation and bylaws of that Guarantor have not been
         repealed, rescinded, amended or otherwise modified since copies of the
         same were delivered to the Banks on or about (x) May 8, 1995, pursuant
         to Section 3.1 of the Credit Agreement, or (y) the date such Guarantor
         became a Guarantor, pursuant to Section 6.5 of the Credit Agreement;

                                      -4-

<PAGE>   5


                (f) The Agent shall have received, for the account of each
         Bank, a written opinion from Kaplan, Strangis & Kaplan, P.A. covering
         the matters set forth on Exhibit A attached hereto; and

                (g) The Agent shall have received, with a counterpart for each
         Bank, such other documents, instruments, approvals and, if requested by
         the Agent, certified duplicates of executed copies thereof, that the
         Agent may reasonably request.

         Section 4. Acknowledgment. The Borrower acknowledges and agrees that
its obligations to the Banks and the Administrative Agent under the Credit
Agreement, as amended hereby, and the Revolving Notes exist and are owing
without offset, defense or counterclaim assertable by the Borrower against the
Banks and the Administrative Agent.

         Section 5. Effect of Seventh Amendment; Representations and Warranties;
No Waiver. The Banks, the Administrative Agent and the Borrower agree that after
this Seventh Amendment becomes effective, the Credit Agreement, as hereby
amended, shall remain in full force and effect. The Borrower represents and
warrants that on and as of the date hereof and after giving effect to this
Seventh Amendment: (i) all of the representations and warranties contained in
the Credit Agreement are correct and complete in all material respects as of the
date hereof, as though made on and as of such date, except to the extent such
representations and warranties specifically relate to an earlier date, in which
case they were true and correct as of such earlier date; (ii) there will exist
no Default or Event of Default on such date except as waived herein; (iii) there
has been no change in any of the certificates or articles of incorporation,
bylaws or partnership agreements of the Borrower or any Guarantor since the
Closing Date or (if later) the date such Guarantor became a Guarantor; (iv) the
Borrower has the power and legal right and authority to enter into this Seventh
Amendment; (v) neither this Seventh Amendment, nor the agreements contained
herein or therein contravene or constitute a default under any agreement,
instrument or indenture to which the Borrower is a party or signatory or a
provision of the Borrower's articles of incorporation or, to the best of the
Borrower's knowledge, any other agreement or requirement of law; and (vi) no
consent, approval or authorization of or registration or declaration with any
Person, including but not limited to any governmental authority, is required in
connection with the execution and delivery by the Borrower of this Seventh
Amendment, or the performance of obligations of the Borrower herein or therein
described.

         Section 6. Incorporation of Credit Agreement and Other Loan Documents
by Reference; Ratification of Loan Documents. Except as expressly modified under
this Seventh Amendment, all of the terms, conditions, provisions, agreements,
requirements, promises, obligations, duties, covenants and representations of
the Borrower under the Credit Agreement, the Revolving Notes and any and all
other documents and agreements entered into with respect to the obligations
under the Credit Agreement are incorporated herein by reference and are hereby
ratified and affirmed in all respects by the Borrower. All references in the
Credit Agreement to "this Agreement," "herein," "hereof," and similar
references, and all references in

                                      -5-

<PAGE>   6


the other Loan Documents to the "Credit Agreement," shall be deemed to refer
to the Credit Agreement, as amended by this Seventh Amendment.

         Section 7. Merger and Integration, Superseding Effect. This Seventh
Amendment, from and after the date hereof, embodies the entire agreement and
understanding between the parties hereto with respect to the subject matter
hereof and supersedes and has merged into it all prior oral and written
agreements on the same subjects by and between the parties hereto with the
effect that this Seventh Amendment shall control.

         Section 8. Expenses. As provided in Section 9.2 of the Credit
Agreement, the Borrower agrees to pay all of the expenses, including reasonable
attorneys' fees and expenses, incurred by the Administrative Agent in connection
with this Seventh Amendment.

         Section 9. Counterparts. This Seventh Amendment may be executed in any
number of counterparts, and by the parties hereto in separate counterparts, each
of which when so executed and delivered shall be deemed an original but all such
counterparts together shall constitute but one and the same instrument.

         Section 10. Governing Law. THE VALIDITY, CONSTRUCTION AND
ENFORCEABILITY OF THIS SEVENTH AMENDMENT SHALL BE GOVERNED BY THE INTERNAL LAWS
OF THE STATE OF MINNESOTA, WITHOUT GIVING EFFECT TO CONFLICT OF LAWS PRINCIPLES
THEREOF.

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<PAGE>   7
         IN WITNESS WHEREOF, the parties hereto have caused this Seventh
Amendment to Credit Agreement to be executed as of the date and year first above
written.


                            POLARIS INDUSTRIES INC., a Minnesota
                            corporation


                            By          /s/ Michael Malone
                              ------------------------------------------
                                   Michael Malone
                                   Vice President


                            U.S. BANK NATIONAL ASSOCIATION,
                            as Administrative Agent and a Bank


                            By          /s/ David Shapiro
                              ------------------------------------------
                            Name            David Shapiro
                                ----------------------------------------
                            Title           Assistant Vice President
                                 ---------------------------------------

                            BANK OF AMERICA NATIONAL TRUST AND
                            SAVINGS ASSOCIATION, as a
                            Documentation Agent and a Bank


                            By          /s/ Gretchen Spoo
                              ------------------------------------------
                            Name            Gretchen Spoo
                                ----------------------------------------
                            Title           Vice President
                                 ---------------------------------------


                            FIRST UNION NATIONAL BANK, as a
                            Documentation Agent and a Bank


                            By          /s/ C. Jeffrey Seaton
                              ------------------------------------------
                            Name            C. Jeffrey Seaton
                                ----------------------------------------
                            Title           Senior Vice President
                                 ---------------------------------------


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