<PAGE>
                                                                   EXHIBIT 10.54
                                                                       EXHIBIT A

                                                                         No.____

                            EQUALNET HOLDING CORP.

                            Stock Purchase Warrant

     This Stock Purchase Warrant ("Warrant") is issued as of the 15th day of
April, 1998, by EqualNet Holding Corp., a Texas corporation ("EqualNet"), to
Michael L. Hlinak ("Hlinak") pursuant to that certain Severance Agreement dated
as of April 1, 1998 between EqualNet and Hlinak.

                                  WITNESSETH:
                                  -----------

     (a)  ISSUANCE OF WARRANT; TERM.

         (i) For and in consideration of the sum of $10.00 and other good and
valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, EqualNet hereby grants to Hlinak, subject to the provisions
hereinafter set forth, the right to purchase up to 90,000 shares of EqualNet's
common stock, par value $.01 per share ("Common Stock"). The shares of Common
Stock issuable upon exercise of this Warrant are hereinafter referred to as the
"Shares".

         (ii) This Warrant shall be exercisable at any time on or before the
fifth anniversary of the date hereof, provided that the shareholders of EqualNet
shall have ratified the issuance of this Warrant by the vote, in person or by
proxy, of the holders of a majority of the shares of EqualNet's capital stock
present, entitled to vote and voting at a duly called meeting of EqualNet
shareholders at which a quorum is present.

     (b) EXERCISE PRICE. The exercise price per share for which all or any of
the Shares may be purchased pursuant to the terms of this Warrant shall be $2.00
(hereinafter referred to as the "Exercise Price").

     (c)  EXERCISE.

          (i) This Warrant may be exercised by Hlinak for the purchase of any of
the Shares for which this Warrant is then exercisable pursuant to Section 1(b)
hereof in whole or in part, upon delivery of written notice of intent to
EqualNet at the following address: 1250 Wood Branch Park Drive, Houston, Texas
77079 or such other address as EqualNet shall designate in written notice to
Hlinak, together with this Warrant and payment (in the manner described in
Section 3(b) below) for the aggregate Exercise Price of the Shares so 
purchased. Upon exercise of this Warrant as aforesaid, EqualNet shall as
promptly as practicable execute and deliver to Hlinak a certificate or
certificates for the total number of whole Shares for which this Warrant is
being exercised in such names and denominations as are requested by Hlinak. If
this Warrant shall be exercised with respect to less than all of the Shares,
Hlinak shall be entitled to receive a new Warrant covering the number of Shares
in respect of which this Warrant shall not have been exercised, which new
Warrant shall in all other respects be identical to this Warrant.

                                      A-1
<PAGE>
 
         (ii) Payment for the Shares to be purchased upon exercise of this
Warrant may be made by the delivery of a certified or cashier's check payable to
EqualNet for the aggregate Exercise Price of the Shares to be purchased.

     (d) COVENANTS AND CONDITIONS. The above provisions are subject to the
following:

         (i) Neither this Warrant nor the Shares have been registered under the
Securities Act of 1933, as amended (the "Act"), or any state securities laws
("Blue Sky Laws"). This Warrant and the Shares have been acquired for investment
purposes and not with a view to distribution or resale and the Shares may not be
made subject to a security interest pledged, hypothecated, sold or otherwise
transferred without an effective registration statement therefor under the Act
and such applicable Blue Sky Laws or an opinion of counsel (which opinion and
counsel rendering same shall be reasonably acceptable to EqualNet) that
registration is not required under the Act and under any applicable Blue Sky
Laws. The certificates representing the Shares shall bear substantially the
following legend:

     THE SHARES OF STOCK REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN
     REGISTERED UNDER THE SECURITIES ACT OF 1933 (THE "ACT") OR ANY APPLICABLE
     STATE SECURITIES LAWS, BUT HAVE BEEN ACQUIRED FOR THE PRIVATE INVESTMENT OF
     THE HOLDER HEREOF AND MAY NOT BE OFFERED, SOLD OR TRANSFERRED UNTIL A
     REGISTRATION STATEMENT UNDER THE ACT OR SUCH APPLICABLE STATE SECURITIES
     LAWS SHALL HAVE BECOME EFFECTIVE WITH REGARD THERETO, OR IN THE OPINION OF
     COUNSEL REGISTRATION UNDER THE ACT OR SUCH APPLICABLE STATE SECURITIES LAWS
     IS NOT REQUIRED IN CONNECTION WITH SUCH PROPOSED OFFER, SALE OR TRANSFER.

Other legends as required by applicable federal and state laws may be placed on
such certificates. Hlinak and EqualNet agree to execute such documents and
instruments as counsel for EqualNet reasonably deems necessary to effect
compliance of the issuance of this Warrant and any Shares issued upon exercise
hereof with applicable federal and state securities laws.

         (ii) EqualNet covenants and agrees that all Shares which may be issued
upon exercise of this Warrant will, upon issuance and payment therefor, be
legally and validly issued and outstanding, fully paid and nonassessable.
EqualNet shall at all times, commencing on the date this Warrant shall become
exercisable, reserve and keep available for issuance upon the exercise of this
Warrant such number of authorized but unissued shares of Common Stock as will be
sufficient to permit the exercise in full of the Warrant.

         (iii)  This Warrant shall not be subject to voluntary or involuntary
alienation, assignment or transfer.

     (e) WARRANT HOLDER NOT STOCKHOLDER. This Warrant does not confer upon
Hlinak any right whatsoever as a stockholder of EqualNet.

     (f) ANTI-DILUTION. In case at any time or from time to time after the date
of this Warrant, all of the holders of Common Stock of EqualNet shall have
received or shall have become legally entitled to receive:

                                      A-2
<PAGE>
 
          (A) other or additional stock or other securities or property (other
     than cash) by way of a dividend or other distribution; or

          (B) other or additional (or less) stock or other securities or
     property (including cash) by way of stock-split, spin-off, split-up,
     reclassification, combination of shares or similar corporate rearrangement
     (but not including any cash dividends),

then and in each such case Hlinak, upon the exercise hereof as provided in
Section 3, shall be entitled to receive, in lieu of (or in addition to, as the
case may be) the Shares theretofore receivable upon the exercise of this
Warrant, the amount of stock and other securities and property (including cash
in the case referred to in clause (ii) above) which Hlinak would have held on
the date of such exercise if on the date of such conversion, dividend,
distribution, corporate rearrangement or such other event, as described in
clause (ii) above, Hlinak had been the holder of record of the number of Shares
receivable upon exercise of this Warrant and had thereafter, during the period
from the date thereof to and including the date of such exercise, obtained such
Shares and all other or additional (or less) stock and other securities and
property (including cash in the case referred to in clause (ii) above)
receivable by Hlinak as aforesaid during such period.

     (g) NOTICES. All notices, requests, offers, elections and other
communications under this Warrant shall be in writing and shall be deemed to
have been given at the time when deposited in the United States mail at a
general or branch post office, postage prepaid, registered or certified mail
(return receipt requested), and addressed to the respective parties at the
addresses stated below or to such other changed addresses as the parties may
have fixed by notice; provided, however, that any notice of change of address
shall be effective only upon receipt. Notices addressed as follows:

     If to EqualNet:    EqualNet Holding Corp.
                        1250 Wood Branch Park Drive
                        Houston, Texas 77079
                        Attention: General Counsel

     If to Hlinak:      Michael L. Hlinak
                        19910 Erika Way
                        Katy, Texas 77450
 

                                      A-3
<PAGE>
 
     IN WITNESS WHEREOF, EqualNet has caused this Stock Purchase Warrant to be
executed and delivered by its duly authorized officer as of the date first above
written.

                                                EQUALNET HOLDING CORP.

                                                By: ___________________

                                                Name: __________________

                                                Title: _________________

                                      A-4