<PAGE>   1
                                                                    EXHIBIT 10.7



THIS WARRANT AND THE SHARES OF COMMON STOCK OF INTERAMERICAS COMMUNICATIONS
CORPORATION TO BE ISSUED UPON ANY EXERCISE OF THUS WARRANT HAVE NOT BEEN
REGISTERED UNDER THE UNITED STATES SECURITIES ACT OF 1933 AS AMENDED (THE
"ACT"), OR ANY STATE SECURITIES LAWS AND MAY NOT BE OFFERED OR SOLD,
TRANSFERRED, PLEDGED, HYPOTHECATED OR OTHERWISE DISPOSED OF EXCEPT (I) PURSUANT
TO AN EFFECTIVE REGISTRATION STATEMENT UNDER THE ACT, (II) TO THE EXTENT
APPLICABLE, RULE 144 UNDER THE ACT (OR ANY SIMILAR RULE UNDER THE ACT RELATING
TO THE DISTRIBUTION OF SECURITIES) OR (III) IF AN EXEMPTION FROM REGISTRATION
UNDER THE ACT IS AVAILABLE,


                                    WARRANT

                               TO PURCHASE SHARES

                                       OF

                                  COMMON STOCK

                                       OF

                    INTERAMERICAS COMMUNICATIONS CORPORATION

                                FEBRUARY 3, 1997

      This certifies that for value received, KA Investments, LDC ("KAI") and
any subsequent transferee pursuant to the terms of the Agreement (as defined
below) of even date herewith and this Warrant (each a "Holder") is entitled to
purchase, subject to the provisions of this warrant, from InterAmericas
Communications Corporation, a Texas corporation (the "Issuer"), at any time or
from time to time on or after the date hereof and on or before February 2, 2002
(the "Expiration Date"), Forty Thousand (40,000) fully paid and nonassessable
shares of common stock, par value $,001 per share (the "Common Stock"), of the
Issuer at an exercise price of Five Dollars ($5,00) per share, subject to
adjustment pursuant to the terms hereunder (the "Exercise Price") (such shares
of Common Stock and other securities issued and issuable upon exercise of this
Warrant (the "Warrant Shares").

      Section 1,   Definitions Except as otherwise specified herein, terms 
defined herein shall have the meanings assigned to them in the Subscription 
Agreement of even date herewith by and between KAI and the Issuer (the 
"Agreement").

      Section 2,   Exercise of Warrant,

           (a)     Subject to the provisions hereof, this Warrant may be 
      exercised, in whole or in part, but not as to a fractional share, at any 
      time or from time to time on or after the date hereof and on or before the
      Expiration Date, by presentation and surrender hereof to the issuer at
      the address which in accordance with the provisions of Section 9 hereof
      is then effective for notices to the Issuer, with the Election to
      Purchase Form annexed hereto as SCHEDULE ONE, duly executed and 
      accompanied by payment to the Issuer as further set forth below in this 
      Section 2, for the account of the Issuer, of the Exercise Price for the 
      number of Warrant Shares specified in such form, If this Warrant should 
      be exercised in part only, the Issuer shall, upon surrender of this 
      Warrant, execute and deliver a new Warrant evidencing the rights of the 
      Holder hereof to purchase the balance of the Warrant Shares purchasable 
      hereunder, The Issuer shall maintain at its principal place of business 
      a register for the registration of this Warrant and registration of 
      transfer of this Warrant, The Exercise Price for the number of Warrant 
      Shares specified in the Election to Purchase Form shall be payable in 
      United States Dollars by certified or official bank 

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<PAGE>   2

      check payable to the order of the Issuer or by wire transfer of
      immediately available funds to an account specified by the Issuer for
      that purpose.

            (b) Certificates representing Warrant Shares shall bear the 
      following restrictive legend:

            "The shares represented by this certificate have not
            been registered under the Securities Act of 1933, as
            amended (the "Securities Act") or any state securities
            laws. They may not be offered or transferred by sale,
            assignment, pledge or otherwise unless (i) a
            registration statement for the securities under the
            Securities Act is in effect or (ii) the corporation
            has received an opinion of counsel, which opinion is
            satisfactory to the corporation, to the effect that
            such registration is not required under the Securities
            Act."

            (c) Notwithstanding any provisions herein to the contrary, if the
      Fair Market Value (hereinafter defined) of one share of Common Stock is
      greater than the Exercise Price (at the date of calculation as set forth
      below), in lieu of exercising this Warrant for cash, the Holder may elect
      to receive shares equal to the value (as determined below) of this
      Warrant (or the portion thereof being canceled) by surrender of this
      Warrant at the principal office of the Issuer together with the properly
      endorsed Notice of Exercise and notice of such election in which event
      the Issuer shall issue to the Holder a number of shares of Common Stock
      computed using the following formula:


       X  =  Y(A-B)
             ------
               A

Where        X  =    the number of shares of Common Stock to be issued to the 
                     Holder

             Y  =    the number of shares of Common Stock purchasable under 
                     the Warrant or, if only a portion of the Warrant is
                     being exercised, the portion of the Warrant being 
                     canceled (at the date of such calculation)

             A  =    the Fair Market Value of one share of the Issuer's Common
                     Stock (at the date of such calculation)

             B  =    Exercise Price (as adjusted at the date of such 
                     calculation)


      For purposes of the above calculation, Fair Market Value of one share of
Common Stock shall be the average closing bid price (as reported by The
Nasdaq SmallCap Market) of the Issuer's Common Stock for the five (5)
consecutive trading days ending on the trading day immediately preceding the
date of the Election to Purchase.

     Section 3. Reservation of Shares; Preservation of Rights of Holder.  The
Issuer hereby agrees that there shall be reserved for issuance and/or delivery
upon exercise of this Warrant, such number of Warrant Shares as shall be
required for issuance or delivery upon exercise of this Warrant. The Warrant
surrendered upon exercise shall be canceled by the Issuer. After the Expiration
Date, no shares of Common Stock shall be subject to reservation in respect of
this Warrant. The Issuer further agrees (i) that it will not, by amendment of
its Articles of Incorporation or through reorganization, consolidation, merger,
dissolution or sale of assets, or by any other voluntary act, avoid or seek to
avoid the observation or performance of any of the covenants, stipulations or
conditions to be observed or performed hereunder by the Issuer, (ii) promptly
to take such action as may be required of the Issuer to permit the Holder to
exercise this Warrant and the Issuer duly and effectively to issue shares of
its Common Stock or other securities as provided herein upon the exercise
hereof, and (iii) promptly to take all action required or provided herein to
protect the rights of the Holder granted hereunder against dilution. Without
limiting the



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(generality of the foregoing, should the Warrant Shares at any time
consist in whole or in part of shares of capital stock having a par value, the
Issuer agrees that before taking any action which would cause an adjustment of
the Exercise Price so that the same would be less than the then par value of
such Warrant Shares, the Issuer shall take any corporate action which may. in
the opinion of its counsel, be necessary in order that the Issuer may validly
and legally issue fully paid and nonassessable shares of such Common Stock at
the Exercise Price as so adjusted. The Issuer further agrees that it will not
establish a par value for its Common Stock while this Warrant is outstanding in
an amount greater than the Exercise Price.

     Section 4.   Exchange, Transfer, Assignment or Loss of Warrant.  Any
attempted transfer of this Warrant, the Warrant Shares or any new Warrant not
in accordance with this Section shall be null and void, and the Issuer shall
not in any way be required to give effect to such transfer. No transfer of this
Warrant shall be effective for any purpose hereunder until (i) written notice
of such transfer and of the name and address of the transferee has been
received by the Issuer, and (ii) the transferee shall first agree in a writing
deposited with the Secretary of the Issuer to be bound by all the provisions of
this Warrant and the Agreement. Upon surrender of this Warrant to the Issuer by
any transferee authorized under the provisions of this Section 4, the Issuer
shall, without charge, execute and deliver a new Warrant registered in the name
of such transferee at the address specified by such transferee, and this
Warrant shall promptly be canceled. The Issuer may deem and treat the
registered holder of any Warrant as the absolute owner thereof for all
purposes, and the Issuer shall not be affected by any notice to the contrary.
Any Warrant, if presented by an authorized transferee, may be exercised by such
transferee without prior delivery of a new Warrant issued in the name of the
transferee.

     Upon receipt by the Issuer of evidence reasonably satisfactory to it of
the loss, theft, destruction or mutilation of this Warrant, and (in the case of
loss, theft or destruction) of reasonably satisfactory indemnification, and
upon surrender and cancellation of this Warrant, if mutilated, the Issuer will
execute and deliver a new Warrant of like tenor and date. Any such new Warrant
executed and delivered shall constitute a separate contractual obligation on
the part of the Issuer, whether or not the Warrant so lost, stolen, destroyed
or mutilated shall be at any time enforceable by anyone.

     Section 5.   Rights of Holder.  Neither a Holder nor his transferee by 
devise or the laws of descent and distribution or otherwise shall be,
or have any rights or privileges of, a shareholder of the Issuer with respect to
any Warrant Shares, unless and until certificates representing such Warrant
Shares shall have been issued and delivered thereto.

     Section 6.   Adjustments in Exercise Price and Warrant Shares. The Exercise
Price and Warrant Shares shall be subject to adjustment from time to time as
provided in this Section 6.

             (a)  If the Issuer is recapitalized through the subdivision or
     combination of its outstanding shares of Common Stock into a larger or
     smaller number of shares, the number of shares of Common Stock for which
     this Warrant may be exercised shall be increased or reduced, as of the
     record date for such recapitalization, in the same proportion as the
     increase or decrease in the outstanding shares of Common Stock, and the
     Exercise Price shall be adjusted so that the aggregate amount payable for
     the purchase of all Warrant Shares issuable hereunder immediately after
     the record date for such recapitalization shall equal the aggregate
     amount so payable immediately before such record date.
     
             (b)  If the Issuer declares a dividend on Common Stock, or makes a
     distribution to holders of Common Stock, and such dividend or
     distribution is payable or made in Common Stock or securities convertible
     into or exchangeable for Common Stock, or rights to purchase Common Stock
     or securities convertible into or exchangeable for Common Stock, the
     number of shares of Common Stock for which this Warrant may be exercised
     shall be increased, as of the record date for determining which holders of
     Common Stock shall be entitled to receive such dividend or distribution,
     in proportion to the increase in the number of outstanding shares (and
     shares of


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     Common Stock issuable upon conversion of all such securities
     convertible into Common Stock) of Common Stock as a result of such
     dividend or distribution, and the Exercise Price shall be adjusted so that
     the aggregate amount payable for the purchase of all the Warrant Shares
     issuable hereunder immediately after the record date for such dividend or
     distribution shall equal the aggregate amount so payable immediately
     before such record date.

          (c) If the Issuer declares a dividend on Common Stock (other than a
     dividend covered by subsection (b) above), or distributes to holders of
     its Common Stock, other than as part of its dissolution or liquidation or
     the winding up of its affairs, any shares of its capital stock, any
     evidence of indebtedness or any cash or other of its assets (other than
     Common Stock or securities convertible into or exchangeable for Common
     Stock), the Holder shall receive notice of such event as set forth in
     Section 9 below.
     
          (d) In case of any consolidation of the Issuer with, or merger of
     the Issuer into, any other corporation (other than a consolidation or
     merger in which the Issuer is the surviving or resulting corporation and
     in which the stockholders of the Issuer immediately prior to the merger
     or consolidation hold more than 50% of the voting stock of the Issuer
     following the merger or consolidation), or in case of any sale or
     transfer of all or substantially all of the assets of the Issuer, or in
     the case of any statutory exchange of securities with another corporation
     (including any exchange effected in connection with a merger of a third
     corporation into the Issuer, except where the Issuer is the surviving
     entity and the stockholders of the Issuer immediately prior to the
     exchange hold more than 50% of the voting stock of the Issuer after the
     exchange), the corporation formed by such consolidation or the
     corporation resulting from such merger or the corporation which shall
     have acquired such assets or securities of the Issuer as the case may be
     shall execute and deliver to the Holder simultaneously therewith a new
     Warrant, satisfactory in form and substance to the Holder, together with
     such other documents as the Holder may reasonably request, entitling the
     Holder thereof to receive upon exercise of such Warrant the kind and
     amount of shares of stock and other securities and property receivable
     upon such consolidation, merger, sale, transfer, or exchange of
     securities, or upon the dissolution following such sale or other
     transfer, by a holder of the number of shares of Common Stock purchasable
     upon exercise of this Warrant immediately prior to such consolidation,
     merger, sale, transfer, or exchange. Such new Warrant shall contain the
     same basic other terms and conditions as this Warrant and shall provide
     for adjustments which, for events subsequent to the effective date of
     such written instrument shall be as nearly equivalent as may be
     practicable to the adjustments provided for in this Section 6. The above
     provisions of this paragraph (d) shall similarly apply to successive
     consolidations, mergers, exchanges, sales or other transfers covered
     hereby.
     
          (e) If the Issuer shall, at any time before the expiration of this
     Warrant, sell all or substantially all of its assets and distribute the
     proceeds thereof to the Issuer's shareholders, the Holder shall, upon
     exercise of this Warrant have the right to receive, in lieu of the shares
     of Common Stock of the Issuer that the Holder otherwise would have been
     entitled to receive the same kind and amount of assets as would have been
     issued, distributed or paid to the Holder upon any such distribution with
     respect to such shares of Common Stock of the Issuer had the Holder been
     the holder of record of such shares of Common Stock receivable upon
     exercise of this Warrant on the date for determining those entitled to
     receive any such distribution. If any such distribution results in any
     cash distribution in excess of the Exercise Price provided by this Warrant
     for the shares of Common Stock receivable upon exercise of this Warrant,
     the Holder may at the Holder's option exercise this Warrant without
     making payment of the Exercise Price and, in such case, the Issuer shall,
     upon distribution to the Holder, consider the Exercise Price to have been
     paid in full and, in making settlement to the Holder, shall obtain receipt
     of the Exercise Price by deducting an amount equal to the Exercise Price
     for the shares of Common Stock receivable upon exercise of this Warrant
     from the amount payable to the Holder.



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<PAGE>   5

           (f) If an event occurs which is similar in nature to the events
      described in this Section 6, but is not expressly covered hereby, the
      Board of Directors of the Issuer shall make or arrange for an equitable
      adjustment to the number of Warrant Shares and the Exercise Price.

           (g) The term Common Stock shall mean the Common Stock of the
      Issuer as the same exists at the Closing Date or as such stock may be
      constituted from time to time, except that for the purpose of this
      Section 6, the term Common Stock shall include any stock of any class
      of the Issuer which has no preference in respect of dividends or of
      amounts payable in the event of any voluntary or involuntary liquidation,
      dissolution or winding up of the Issuer and which is not subject to
      redemption by the Issuer.

           (h) Whenever the number of Warrant Shares or the Exercise Price
      shall be adjusted as required by the provisions of this Section 6, the
      Issuer forthwith shall file in the custody of its secretary or an
      assistant secretary at its principal office, and furnish to each Holder
      hereof a certificate prepared in accordance with paragraph (h) above,
      showing the adjusted number of Warrant Shares and the Exercise Price and
      setting forth in reasonable detail the circumstances requiring the
      adjustments.



                                      5


<PAGE>   6

          (i)   Notwithstanding any other provision, this Warrant shall be
     binding upon and inure to the benefit of any successors and assigns of
     the Issuer.
     
          (j)   No adjustment in the Exercise Price in accordance with the
     provisions of this Section 6 need be made if such adjustment would amount
     to a change in such Exercise Price of less than $.01; provided however,
     that the amount by which any adjustment is not made by reason of the
     provisions of this paragraph (k) shall be carried forward and taken into
     account at the time of any subsequent adjustment in the Exercise Price.
     
          (k)   If an adjustment is made under this Section 6 and the event to
     which the adjustment relates does not occur, then any adjustments in
     accordance with this Section 6 shall be readjusted to the Exercise Price
     and the number of Warrant Shares which would be in effect had the earlier
     adjustment not been made.

     Section 7. Taxes on Issue or Transfer of Common Stock and Warrant.  The
Issuer shall pay any and all documentary' stamp or similar issue or transfer
taxes payable in respect of the issue or delivery of shares of Common Stock or
other securities on the exercise of this Warrant. The Issuer shall not be
required to pay any tax which may, be payable in respect of any transfer of this
Warrant or in respect of any transfers involved in the issue or delivery of
shares or the exercise of this Warrant in a name other than that of the Holder
and the person requesting such transfer, issue or delivery shall be responsible
for the payment of any such tax (and the Issuer shall not be required to issue
or deliver said shares until such tax has been paid or provided for).

     Section 8. Notice of Adjustment. So long as this Warrant shall be
outstanding, (a) if the Issuer shall propose to pay any dividends or
make any distribution upon the Common Stock, or (b) if the Issuer shall offer
generally to the holders of Common Stock the right to subscribe to or purchase
any shares of any class of Common Stock or securities convertible into Common
Stock or any other similar rights or (c) if there shall be any proposed capital
reorganization of the Issuer in which the Issuer is not the surviving entity,
recapitalization of the capital stock of the Issuer, consolidation or merger of
the Issuer with or into another corporation, sale, lease or other transfer of
all or substantially all of the property and assets of the Issuer, or voluntary
or involuntary dissolution, liquidation or winding up of the Issuer, or (d) if
the Issuer shall give to its stockholders any notice, report or other
communication respecting any significant or special action or event, then in
such event, the Issuer shall give to the Holder, at least ten (10) days prior 
to the relevant date described below (or such shorter period as is reasonably
possible if thirty days is not reasonably possible), a notice containing a
description of the proposed action or event and stating the date or expected
date on which a record of the lssuer's stockholders is to be taken for any of
the foregoing purposes, and the date or expected date on which any such
dividend, distribution, subscription, reclassification, reorganization,
consolidation, combination, merger, conveyance, sale, lease or transfer,
dissolution, liquidation or winding up is to take place and the date or
expected date, if any is to be fixed, as of which the holders of Common Stock
of record shall be entitled to exchange their shares of Common Stock for
securities or other property deliverable upon such event.

     Section 9. Notice. Any notice to be given or to be served upon any party
in connection with the Warrant must be in writing and will be deemed to have
been given and received upon confirmed receipt, if sent by facsimile, or two
(2) days after it has been submitted for delivery by Federal Express or an
equivalent carrier, charges prepaid and addressed to the following addresses
with a confirmation of delivery:

     If to the Issuer, to:


             InterAmericas Communications Corporation
             1221 Brickell Avenue, Suite 900



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             Miami, Florida 33131
             Attn.:         Patricio E. Northland, Chief Executive Officer
             Telephone:     (305) 377-6790
             Facsimile:     (305) 377-6791

     With copy to:

             Andrew Hulsh, Esq.
             Baker & McKenzie
             Barnett Tower - Suite 1600
             701 Brickell Avenue
             Miami, Florida 33131-2827
             Telephone:     (305) 789-8900
             Facsimile:     (305) 789-8953

    If to the Holder, to:

             KA Investments, LDC
             Field Secretaries
             c/o Bank of Butterfield International Ltd.
             P.O. Box 705
             Butterfield House, Fort Street
             Grand Cayman, Cayman Island
             Attn.:         Irwin Dikau
             Telephone:     (809) 949-7055
             Facsimile:     (809) 949-7004

    With a copy to:

             Kenneth S. Witt, Esq.
             Freeborn & Peters
             950 17th Street, Suite 2600
             Denver, Colorado 80202
             Telephone:     (303) 628-4200
             Facsimile:     (303) 628-4240



     Any party may at any time by giving notice to the other party, designate
any other address in substitution of an address established pursuant to the
foregoing to which such notice will be given.

     Section 10. Choice of Law; Conflict of Law: Jurisdiction and Venue.
Except as otherwise expressly provided herein, the terms, conditions and
enforceability of the Warrant shall be governed by and interpreted under the
laws of the State of Illinois. Any claim, dispute or disagreement relating to
the terms and conditions of this Warrant, or arising from this Warrant or the
subject matter of this Warrant, may be brought only in the Circuit Courts of
Cook or DuPage Counties in the State of Illinois or in the United States 
District Court for the Northern District of Illinois, which shall have exclusive
jurisdiction thereof. The parties to the Warrant consent to such jurisdiction
and venue and hereby knowing and voluntarily waive all objections thereto on
the basis of lack of personal jurisdiction, venue or convenience.

                          [SIGNATURE PAGE FOLLOWS)





<PAGE>   8

DATED:  FEBRUARY 3, 1997

                                       INTERAMERICAS COMMUNICATIONS
                                       CORPORATION


                                       By:    /s/ Patricio E. Northland
                                             ----------------------------

                                       Name:  Patricio E. Northland
                                             ----------------------------

                                       Title:   Chairman & CEO
                                               --------------------------


ATTEST:

----------------------------
               , Secretary
<PAGE>   9

                                                                    SCHEDULE ONE


                            ELECTION TO PURCHASE

     The undersigned hereby irrevocably elects to exercise this Warrant and to
purchase _______ shares of InterAmericas Communications Corporation Common
Stock issuable upon the exercise of this Warrant and requests that
certificates for such shares be issued in the name of:


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                                   (Name)


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                                  (Address)


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              (United States Social Security or other taxpayer
                     identifying number, if applicable)


and, if different from above, be delivered to:



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                                   (Name)


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                                  (Address)

and if the number of Warrant Shares so purchased are not all of the Warrant
Shares issuable upon exercise of this Warrant that a Warrant to purchase the
balance of such Warrant Shares be registered in the name of, and delivered to,
the undersigned at the address stated below.



Date:
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Name of Registered Owner:
                          ----------------------------------------------------

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Address:
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Signature:
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