<PAGE>

                                                                    EXHIBIT 10.4

                                   GUARANTEE
                                   ---------

          This GUARANTEE ("Guarantee"), dated as of May 31, 2000, is made by
each of the undersigned Subsidiaries of MGM Grand, Inc. (each a "Guarantor" and
collectively, jointly and severally, as "Guarantors") in favor of The Chase
Manhattan Bank, as successor in interest to PNC Bank, National Association (the
"Trustee"), as Trustee for the benefit of the holders of Notes (as defined
below) authenticated and delivered by the Trustee and to the Trustee pursuant to
the Indenture referred to below, with reference to the following facts:

                                   RECITALS
                                   --------

          A.   MGM Grand, Inc., a Delaware corporation (the "Company") has
previously entered into an Indenture dated as of February 2, 1998, with the
Trustee and the Guarantors referred to therein (as amended, supplemented or
otherwise modified, the "Indenture") pursuant to which the Company issued its
6.95% Senior Collateralized Notes due 2005 (the "Notes").

          B.   Each of the undersigned has become a Restricted Subsidiary of the
Company and as such is required to guarantee the obligations of the Company
under the Indenture and the Notes.

          C.   Each Guarantor expects to realize direct and indirect benefits as
the result of the availability of the aforementioned credit facilities to the
Company, as the result of financial and business support which will be provided
to the Guarantors by the Company.

                                   AGREEMENT
                                   ---------

          NOW, THEREFORE, in consideration of good and valuable consideration,
the receipt and sufficiency of which is hereby acknowledged, each Guarantor
hereby jointly and severally represents, warrants, covenants, agrees and
guaranties as follows:

          1.   Definitions.  This Guarantee is one of the Guarantees referred to
               -----------
in the Indenture.  Terms defined in the Indenture and not otherwise defined in
this Guarantee shall have the meanings given those terms in the Indenture when
used herein and such definitions are incorporated herein as though set forth in
full.

          2.   Guarantee.
               ---------

          (a) Each of the Guarantors, jointly and severally, hereby
unconditionally guarantees, which guarantee shall be secured as provided in the
Collateral Documents, to each holder of a Note authenticated and delivered by
the Trustee and to the Trustee, irrespective of the validity and enforceability
of the Indenture, the Notes or the obligations of the Company under the
Indenture or the Notes, that:  (i) the principal of and interest on the Notes
will be paid in full when due, whether at the maturity or interest payment date,
by acceleration, call for redemption, upon a purchase offer or otherwise, and
interest on the overdue principal and interest, if any, of the Notes, if lawful,
and all other obligations of the Company to the holders or the Trustee under the
Indenture or the Notes will be promptly paid in full or performed, all in
accordance with the terms of the Indenture and the Notes; and (ii) in case of
any extension of time of payment or renewal of any securities or any of such
other obligations, they will be paid in full when due or performed in accordance
with the terms of the

                                      -1-
<PAGE>

extension or renewal, whether at maturity, by acceleration, call for redemption,
upon a purchase offer or otherwise (collectively, the "Guaranteed Obligations").
This Guarantee is a guarantee of payment and not of collection.

          Failing payment when due of any amount so guaranteed for whatever
reason, the Guarantors shall be jointly and severally obligated to pay the same
before failure to so pay becomes an Event of Default.

          (b) Each Guarantor agrees that (i) its obligations with regard to this
Guarantee shall be unconditional, irrespective of the validity, regularity or
enforceability of the Notes or the Indenture, any amendments to the Indenture,
the Notes or the Collateral Documents (other than Article 15 of the Indenture or
any Collateral Document to the extent such amendment is not executed and
delivered by such Guarantor and adversely affects, or increases the obligations
of, such Guarantor under Article 15 of the Indenture or such Collateral
Document), the absence of any action to enforce the same, any delays in
obtaining or realizing upon (or failures to obtain or realize upon) Collateral,
the recovery of any judgment against the Company, any action to enforce the same
or any other circumstances that might otherwise constitute a legal or equitable
discharge or defense of a guarantor and (ii) this Guarantee will not be
discharged except by complete performance of the obligations contained in the
Notes and the Indenture.  Each of the Guarantors hereby waives diligence,
presentment, demand of payment, filing of claims with a court in the event of
insolvency or bankruptcy of the Company, any right to require a proceeding first
against the Company or right to require the prior disposition of the assets of
the Company to meet its obligations, protest, notice and all demands whatsoever.
Without limiting the generality of the foregoing, each of the Guarantors hereby
waives, to the extent permitted under Nev. Rev. Stat. 40.495, any rights arising
out of Nev. Rev. Stat. 40.430.

          (c) If any holder or the Trustee is required by any court or otherwise
to return to either the Company or any Guarantor, or any custodian, trustee, or
similar official acting in relation to either the Company or any Guarantor, any
amount paid by either the Company or any of the Guarantors to the Trustee or
such holder, this Guarantee, to the extent theretofore discharged, shall be
reinstated in full force and effect.  Each of the Guarantors agrees that it will
not be entitled to any right of subrogation in relation to the holders in
respect of any obligations guaranteed hereby except as set forth in Section 6
hereof.

          (d) Each of the Guarantors agrees that (i) the maturity of the
obligations guaranteed hereby may be accelerated as provided in Section 5.2 of
the Indenture for the purposes of this Guarantee, notwithstanding any stay,
injunction or other prohibition preventing such acceleration as to the Company
of the obligations guaranteed hereby, and (ii) in the event of any declaration
of acceleration of those obligations as provided in Section 5.2 of the
Indenture, those obligations (whether or not due and payable) will forthwith
become due and payable by each of the Guarantors for the purpose of this
Guarantee.

          3.   Execution and Delivery of Guarantee.
               -----------------------------------

          To evidence its guarantee set forth in Section 2 of this Guarantee,
each of the Guarantors agrees that a notation of such guarantee substantially in
the form of the notation included in the Note annexed to the Indenture as
Exhibit A shall be endorsed on each Note authenticated and

                                      -2-
<PAGE>

delivered by the Trustee and that this Guarantee shall be executed on behalf of
such Guarantor by a duly authorized officer.

          Each of the Guarantors agrees that its guarantee set forth in Section
2 of this Guarantee shall remain in full force and effect and apply to all the
Notes notwithstanding any failure to endorse on each Note a notation of such
guarantee.

          If an Officer whose facsimile signature is on a Note no longer holds
that office at the time the Trustee authenticates the Note on which a guarantee
is endorsed, the guarantee shall be valid nevertheless.

          The delivery of any Note by the Trustee, after the authentication
thereof hereunder, shall constitute due delivery of this Guarantee on behalf of
the Guarantors.

          4.   Limitation of Guarantors' Liability.  Each Guarantor and by its
               -----------------------------------
acceptance hereof each holder hereby confirms that it is the intention of all
such parties that the guarantee by such Guarantor pursuant to this Guarantee not
constitute a fraudulent transfer or conveyance for purposes of any federal or
state law.  To effectuate the foregoing intention, the holders and each
Guarantor hereby irrevocably agree that the obligations of each such Guarantor
under this Guarantee shall be limited to the maximum amount as will, after
giving effect to all other contingent and fixed liabilities of such Guarantor
and after giving effect to any collections from or payments made by or on behalf
of any other Guarantor (as defined in the Indenture) in respect of the
obligations of such other Guarantor (as defined in the Indenture) under its
Guarantee (as defined in the Indenture) or pursuant to Section 5 of this
Guarantee, result in the obligations of such Guarantor under this Guarantee not
constituting a fraudulent conveyance or fraudulent transfer under federal or
state law.  This Section 4 is for the benefit of the creditors of each
Guarantor.

          5.   Contribution.   In order to provide for just and equitable
               ------------
contribution among the Guarantors, the Guarantors agree, inter se, that in the
                                                         --------
event any payment or distribution is made by any Guarantor (a "Funding
Guarantor") under this Guarantee, such Funding Guarantor shall be entitled to a
contribution from each other Guarantor in a pro rata amount based on the net
                                            --------
worth of each Guarantor (including the Funding Guarantor) for all payments,
damages and expenses incurred by that Funding Guarantor in discharging the
Company's obligations with respect to the Notes or any other Guarantor's
obligations with respect to this Guarantee.

          6.   Rights Under This Guarantee.
               ---------------------------

          No payment by any Guarantor pursuant to the provisions hereof to the
Trustee shall entitle such Guarantor to any payment out of any Collateral held
by the Trustee under the Indenture or any Collateral Documents.

          (a) Each of the Guarantors waives notice of the issuance, sale and
purchase of the Notes and notice from the Trustee or the holders from time to
time of any of the Notes of their acceptance and reliance on this Guarantee.

          (b) Notwithstanding any payment or payments made by the Guarantors by
reason of this Guarantee, the Guarantors shall not be subrogated to any rights
of the Trustee, the Collateral Agent or any holder against the Company until all
the Notes shall have been paid or deemed to have

                                      -3-
<PAGE>

been paid within the meaning of the Indenture. Any payment made by the
Guarantors by reason of this Guarantee shall be in all respects subordinated to
the full and complete payment or discharge under the Indenture of all
obligations guaranteed hereby, and no payment by the Guarantors by reason of
this Guarantee shall give rise to any claim of the Guarantors against the
Trustee or any holder of the Notes. Unless and until the Notes shall have been
paid or deemed to have been paid within the meaning of the Indenture, neither
the Guarantors nor any of them will assign or otherwise transfer any such claim
against the Company to any other person.

          (c) No set-off, counterclaim, reduction or diminution of any
obligation or any defense of any kind or nature (other than performance by the
Guarantors of their obligations hereunder) which any Guarantor may have or
assert against the Trustee or any holder of any Note shall be available
hereunder to such Guarantor against the Trustee.

          (d) Each Guarantor agrees to pay all costs, expenses and fees,
including all reasonable attorneys' fees, which may be incurred by the Trustee
in enforcing or attempting to enforce this Guarantee or protecting the rights of
the Trustee, the Collateral Agent or the holders of the Notes, if any, in
accordance with the Indenture.

          7.   Primary Obligations.   Each Guarantor agrees that it is directly
               -------------------
liable to each holder hereunder, that the obligations of each Guarantor
hereunder are independent of the obligations of the Company or any other
guarantor, and that a separate action may be brought against each Guarantor,
whether such action is brought against the Company or any other guarantor or
whether the Company or any other guarantor is joined in such action.  Each
Guarantor agrees that its liability hereunder shall be immediate and shall not
be contingent upon the exercise or enforcement by the Trustee or the holders of
the Notes of whatever remedies they may have against the Company or any other
guarantor, or the enforcement of any Lien or realization upon any Collateral the
Trustee may at any time possess.  Each Guarantor agrees that any release which
may be given by the Trustee or the holders of the Notes to the Company or any
other guarantor shall not release such Guarantor. Each Guarantor consents and
agrees that the Trustee shall be under no obligation to marshal any property or
assets of the Company or any other guarantor in favor of such Guarantor, or
against or in payment of any or all of the Guaranteed Obligations.

          8.   Waivers.
               -------

          (a) Each Guarantor hereby waives any right to receive, or any claim or
defense based on failure to receive:  (i) notice of the amount of the Guaranteed
Obligations; (ii) notice of any adverse change in the financial condition of the
Company or of any other fact that might increase such Guarantor's risk
hereunder; (iii) notice of a Default or Event of Default; and (iv) all other
notices (except if such notice is specifically required to be given to such
Guarantor under the Indenture, this Guaranty or any of the Collateral Documents
to which such Guarantor is a party) and demands to which such Guarantor might
otherwise be entitled.

          (b) Each Guarantor hereby waives the right by statute or otherwise to
require the Trustee or the holders to institute suit against the Company (or
against any other Person) or to exhaust any rights and remedies which the
Trustee or the holders have or may have against the Company (or against any
other Person).  In this regard, each Guarantor agrees that it is bound to the
payment of each and all of the Guaranteed Obligations, whether now existing or
hereafter arising, as fully as if such Guaranteed Obligations were directly
owing to the Trustee and the holders by such Guarantor.

                                      -4-
<PAGE>

Each Guarantor further waives any defense arising by reason of any disability or
other defense (other than the defense that the Guaranteed Obligations shall have
been fully and finally performed and indefeasibly paid) of the Company or by
reason of the cessation from any cause whatsoever of the liability of the
Company in respect thereof.

          (c) Each Guarantor hereby waives:  (i) any claim or defense directly
or indirectly arising from or caused by any election of remedies by the Trustee
or holders of the Notes, whether or not such election of remedies directly or
indirectly results in impairment or loss of rights or claims of such Guarantor
against the Company or other Persons; and (ii) any defenses based on suretyship
law or impairment of collateral.

          9.   Releases.   Each Guarantor consents and agrees that, without
               --------
notice to or by such Guarantor and without affecting or impairing the
obligations of such Guarantor hereunder, the Trustee may, by action or inaction,
compromise or settle, extend the period of duration or the time for the payment,
or discharge the performance of, or may refuse to, or otherwise not enforce, or
may, by action or inaction, release all or any one or more parties to, any one
or more of the terms and provisions of the Indenture or the Collateral Documents
or may grant other indulgences to the Company in respect thereof, or may, by
action or inaction, release or substitute any other guarantor, if any, of the
Guaranteed Obligations, or may enforce, exchange, release, or waive, by action
or inaction, any security for the Guaranteed Obligations or any other guaranty
of the Guaranteed Obligations, or any portion thereof.

          10.  No Election.   The Trustee shall have the right to seek recourse
               -----------
against each Guarantor to the fullest extent provided for herein and no election
by the Trustee to proceed in one form of action or proceeding, or against any
party, or on any obligation, shall constitute a waiver of Trustee's right to
proceed in any other form of action or proceeding, or against other parties
unless the Trustee has expressly waived such right in writing.

          11.  Financial Condition of the Company.   Each Guarantor represents
               ----------------------------------
and warrants to the Trustee and holders that it is currently informed of the
financial condition of the Company and of all other circumstances which a
diligent inquiry would reveal and which bear upon the risk of nonpayment of the
Guaranteed Obligations.  Each Guarantor further represents and warrants to the
Trustee and holders that it has read and understands the terms and conditions of
the Indenture, this Guaranty and the Collateral Documents.  Each Guarantor
hereby covenants that it will continue to keep itself informed of the Company's
financial condition, the financial condition of other guarantors, if any, and of
all other circumstances which bear upon the risk of nonpayment or nonperformance
of the Guaranteed Obligations.

          12.  Benefits of the Indenture.  The provisions of Article 15 of the
               -------------------------
Indenture applicable to Guarantors (as defined therein) shall be binding upon,
and shall inure to the benefit of, each Guarantor hereunder.

          13.  Governing Law.   This Guaranty shall be deemed to be a contract
               -------------
made and to be performed entirely in the State of Nevada, and for all purposes
shall be governed by and construed in accordance with the internal laws of said
State without regard to the conflicts of law rules of said State.

                                      -5-
<PAGE>

          14.  Non-Involvement of Kirk Kerkorian and Tracinda Corporation.  By
               ----------------------------------------------------------
accepting the benefits of this Guarantee, the Trustee and the holders of each
Note acknowledge that neither Kirk Kerkorian nor Tracinda Corporation,
individually or collectively, is a party to the Indenture, the Notes or any
Collateral Documents executed as of the date hereof.  In the event (i) there is
any alleged breach or default by any Guarantor under this Guarantee or any such
agreement, or (ii) any party hereto has any claim arising from or relating to
this Guarantee or any such agreement, the Trustee and the holders of the Notes,
nor any party claiming through them (to the extent permitted by applicable law),
shall commence any proceedings or otherwise seek to impose any liability
whatsoever against Mr. Kerkorian or Tracinda Corporation by reason of such
alleged breach, default or claim.

          IN WITNESS WHEREOF, each Guarantor has executed this Guarantee by its
duly authorized officer as of the date first written above.

                               MGM GRAND ADVERTISING, INC.,
                               a Nevada corporation

                               MGM GRAND ENTERTAINMENT, INC.,
                               a Nevada corporation

                               MGM GRAND DETROIT, LLC,
                               a Delaware limited liability company

                               1533 WOODWARD, INC.,
                               a Michigan corporation

                               BUSINESS DEVELOPMENT FUND, LLC,
                               a Delaware limited liability company

                               NEW PRMA LAS VEGAS, INC.,
                               a Nevada corporation

                               NEW YORK-NEW YORK HOTEL & CASINO, LLC, a
                               Nevada limited liability company

                               METROPOLITAN MARKETING, LLC,
                               a Nevada limited liability company

                               THE PRIMADONNA COMPANY, LLC,
                               a Nevada limited liability company

                               PRMA, LLC,
                               a Nevada limited liability company

                               PRMA LAND DEVELOPMENT COMPANY,
                               a Nevada corporation

                               PRMA-MS, INC.,
                               a Mississippi corporation

                               By: /s/ Scott Langsner
                                  ----------------------------------
                                  Scott Langsner,
                                  Secretary to each of the foregoing

                                      -6-
<PAGE>

                               MGMGMR ACQUISITION, INC.,
                               a Nevada corporation

                               MGM ACQUISITION CO. #1,
                               a Nevada corporation

                               MGM ACQUISITION CO. #2,
                               a Nevada corporation

                               MGM ACQUISITION CO. #3,
                               a Nevada corporation

                               MGM ACQUISITION CO. #4,
                               a Nevada corporation

                               MGM ACQUISITION CO. #5,
                               a Nevada corporation

                               MGM ACQUISITION CO. #6,
                               a Nevada corporation

                               MGM ACQUISITION CO. #7,
                               a Nevada corporation

                               MGM ACQUISITION CO. #8,
                               a Nevada corporation

                               MGM ACQUISITION CO. #9,
                               a Nevada corporation

                               MGM ACQUISITION CO. #10,
                               a Nevada corporation

                               MGM ACQUISITION CO. #11,
                               a Nevada corporation

                               MGM ACQUISITION CO. #12,
                               a Nevada corporation

                               MGM ACQUISITION CO. #13,
                               a Nevada corporation

                               MGM ACQUISITION CO. #14,
                               a Nevada corporation

                               By: /s/ Scott Langsner
                                  ----------------------------------
                                  Scott Langsner,
                                  Secretary to each of the foregoing

                                      -7-
<PAGE>

                               MGM ACQUISITION CO. #15,
                               a Nevada corporation

                               MGM ACQUISITION CO. #16,
                               a Nevada corporation

                               MGM ACQUISITION CO. #17,
                               a Nevada corporation

                               MGM ACQUISITION CO. #18,
                               a Nevada corporation

                               MGM ACQUISITION CO. #19,
                               a Nevada corporation

                               MGM ACQUISITION CO. #20,
                               a Nevada corporation

                               MGM ACQUISITION CO. #21,
                               a Nevada corporation

                               MGM ACQUISITION CO. #22,
                               a Nevada corporation

                               MGM ACQUISITION CO. #23,
                               a Nevada corporation

                               MGM ACQUISITION CO. #24,
                               a Nevada corporation

                               MGM ACQUISITION CO. #25,
                               a Nevada corporation

                               MGM ACQUISITION CO. #26,
                               a Nevada corporation

                               MGM ACQUISITION CO. #27,
                               a Nevada corporation

                               MGM ACQUISITION CO. #28,
                               a Nevada corporation

                               MGM ACQUISITION CO. #29,
                               a Nevada corporation

                               By: /s/ Scott Langsner
                                  ----------------------------------
                                  Scott Langsner,
                                  Secretary to each of the foregoing

                                      -8-
<PAGE>


                               MGM ACQUISITION CO. #30,
                               a Nevada corporation

                               MGM ACQUISITION CO. #31,
                               a Nevada corporation

                               MGM ACQUISITION CO. #32,
                               a Nevada corporation

                               MGM ACQUISITION CO. #33,
                               a Nevada corporation

                               MGM ACQUISITION CO. #34,
                               a Nevada corporation

                               MGM ACQUISITION CO. #35,
                               a Nevada corporation

                               MGM ACQUISITION CO. #36
                               a Nevada corporation

                               MGM ACQUISITION CO. #37,
                               a Nevada corporation

                               MGM ACQUISITION CO. #38,
                               a Nevada corporation

                               MGM ACQUISITION CO. #39,
                               a Nevada corporation

                               MGM ACQUISITION CO. #40,
                               a Nevada corporation

                               MGM ACQUISITION CO. #41,
                               a Nevada corporation

                               MGM ACQUISITION CO. #42,
                               a Nevada corporation

                               MGM ACQUISITION CO. #43,
                               a Nevada corporation


                               By: /s/ Scott Langsner
                                  ----------------------------------
                                  Scott Langsner,
                                  Secretary to each of the foregoing

                                      -9-
<PAGE>


                               MGM ACQUISITION CO. #44,
                               a Nevada corporation

                               MGM ACQUISITION CO. #45,
                               a Nevada corporation

                               MGM ACQUISITION CO. #46,
                               a Nevada corporation

                               MGM ACQUISITION CO. #47,
                               a Nevada corporation

                               MGM ACQUISITION CO. #48,
                               a Nevada corporation

                               MGM ACQUISITION CO. #49,
                               a Nevada corporation

                               MGM ACQUISITION CO. #50,
                               a Nevada corporation

                               MGM ACQUISITION CO. #51,
                               a Nevada corporation

                               MGM ACQUISITION CO. #52,
                               a Nevada corporation

                               MGM ACQUISITION CO. #53,
                               a Nevada corporation

                               MGM ACQUISITION CO. #54,
                               a Nevada corporation

                               MGM ACQUISITION CO. #55,
                               a Nevada corporation

                               MGM ACQUISITION CO. #56,
                               a Nevada corporation



                               By: /s/ Scott Langsner
                                  ----------------------------------
                                  Scott Langsner,
                                  Secretary to each of the foregoing


                                     -10-
<PAGE>

                               MGM ACQUISITION CO. #60,
                               a Nevada corporation



                               By: /s/ Scott Langsner
                                  ----------------------------------
                                  Scott Langsner,
                                  Secretary to each of the foregoing


                               Address for notices for each of the Guarantors:

                               c/o MGM Grand, Inc.
                               3799 Las Vegas Boulevard South
                               Las Vegas, Nevada 89109-4319

                                     -11-