
<PAGE>
 
                                  Exhibit 99.4

                                PURCHASE WARRANT

                   7,500 SHARES OF ACC CORP. $.015 PAR VALUE
                              CLASS A COMMON STOCK


        FOR VALUE RECEIVED, ACC Corp. , a Delaware corporation (the "Company"),
hereby grants to Peter H. Meyer (the "Holder"), the right, subject to the
further terms and conditions set forth herein, to purchase from the Company
7,500 whole, fully paid and nonassessable shares (the "Shares") of its $.015 par
value Class A Common Stock at a purchase price per Share of $18.75 (the
"Purchase Price").  This Warrant shall be fully exercisable on its date of
issuance and in all events shall expire and be of no further force or effect at
the earlier of the time when it has been exercised with respect to all Shares
which the Holder is entitled to purchase hereunder or 11:59 P.M., New York City
time, on October 31, 1999 (the "Expiration Date").  The number and character of
the Shares and the Purchase Price are subject to adjustment as hereinafter
provided.  As used herein, this "Warrant" means and includes this Warrant and
any Class A Common Stock purchase warrant of the Company hereafter issued in
substitution for or in replacement of this Warrant or to evidence to continuing
effect of any part of this Warrant after any partial exercise hereof:

        1.   EXERCISE.  This Warrant may be exercised in whole, or in part from
time to time, by the Holder by delivering this Warrant together with an executed
Subscription Agreement in the form annexed hereto as Exhibit A to the Company or
such person as the Company may have appointed as warrant agent, as its principal
office ( or at the office of the agency maintained for such purpose),
accompanied by payment by certified or bank check payable to the order of the
Company, in an aggregate amount equal to the per share Purchase Price as then
adjusted multiplied by the number of Shares as to which this Warrant is then
being exercised.  The Company or such agent shall cancel this Warrant on any
such exercise, and if such exercise is partial, shall issue and deliver to the
Holder a new Warrant upon the same terms as contained herein with respect to the
unexercised portion of this Warrant.  Anything in this Warrant to the contrary
notwithstanding, this Warrant may not be exercised after the Expiration Date and
may be exercised only with respect to whole Shares.

        The Company will, or will direct its transfer agent to, issue a
certificate or certificates for the number of fully paid and nonassessable
Shares as to which this Warrant is so exercised, and in lieu of any fractional
shares to which the Holder would otherwise be entitled, pay cash equal to such
fraction multiplied by the Purchase Price as then adjusted, as soon as
practicable after any exercise of this Warrant, and in any event within five
business days thereafter, at the Company's expense (including the payment by it
of any applicable issue taxes), in the name of, and deliver the same to, the
Holder (on payment by the Holder of any applicable transfer taxes).

        Notwithstanding the proceeding paragraph, any Shares as to which this
Warrant is exercised shall be deemed issued on and as of the date of such
exercise in accordance with
<PAGE>
 
the first paragraph of this Section and the Holder shall thereupon be deemed to
be the owner of record thereof.

        All shares issued pursuant to any exercise of this Warrant shall be
"restricted securities" within the meaning of the Securities Act of 1933, as
amended (the "Act") and the rules and regulations thereunder, and shall bear the
standard restrictive legend under the Act.  Upon any exercise of this Warrant,
the Holder shall also execute the form of representation letter attached as
Exhibit B hereto making the representations regarding the status of the Shares
contained therein.

        2.   ADJUSTMENTS.

        (a) STOCK DIVIDENDS, SPLITS, ETC.  The number of Shares that may be
purchased on exercise of this Warrant and the Purchase Price therefor shall be
proportionately increased or decreased, as the case may be, for any stock
dividend, stock split, combination, subdivision or other changes made with
respect to the Class A Common Stock of the Company at any time prior to the
Expiration Date.  An adjustment made pursuant to this paragraph shall, in the
case of a stock dividend or distribution, be made as of the record date therefor
and, in the case of subdivision or combination, be made as of the effective date
thereof.

        (b) REORGANIZATION, RECAPITALIZATION, CONSOLIDATION, MERGER OR SALE OF
ASSETS.  In the event of any reorganization or recapitalization of the Company
or in the event of the Company consolidates with or merges into another
corporation or transfers all or substantially all of its assets to another
entity, the Holder, at any time after the consummation of such event, upon the
exercise of this Warrant and payment of the Purchase Price as provided herein,
shall be entitled to receive the stock to which the Holder would have been
entitled on such consummation if the Holder had exercised this Warrant
immediately prior thereto.  In such case, the terms of this Warrant shall
survive the consummation of any such event and shall be applicable to the shares
of stock receivable on the exercise of this Warrant after such consummation.

        3.   NOTICES OF RECORD DATES, ETC.  The Company shall mail or cause to
be mailed to the Holder all notices specifying any record date for shareholders
of its Class A Common Stock with respect to any dividend, distribution or right,
or with respect to any shareholder meeting to be held at which a vote is to be
taken for the purpose of approving any reorganization, recapitalization,
reclassification, consolidation, merger, transfer, dissolution, liquidation or
winding up of the affairs of the Company.  The Company also shall provide to the
Holder all reports that it normally provides to its shareholders.

        4.   REPLACEMENT OF WARRANT.  On receipt of evidence reasonably
satisfactory to the Company of the loss, theft, destruction or mutilation of
this Warrant, and, in the case of any such loss, theft or destruction, on
delivery of a bond or other indemnity reasonably satisfactory to the Company,
or, in the case of any such mutilation, or surrender and cancellation of this
Warrant, the Company shall issue a new Warrant, of like tenor in lieu of such
lost, stolen, destroyed or mutilated Warrant.
<PAGE>
 
        5.   TRANSFERS.  The Holder represents by his acceptance hereof that the
Holder shall transfer or assign this Warrant only in accordance with all of the
requirements of the Act or an applicable exemption from registration thereunder.
The Company shall cause to be kept a register of the Holder of this Warrant (the
"Warrant Register").  In the event of any transfer permitted by this Section,
the Company shall or shall cause its agent to register the transfer or
assignment on its Warrant Register on surrender of this Warrant, duly endorsed,
or accompanied by a written instrument or instruments of transfer in form
reasonably satisfactory to the Company, duly executed by the Holder or by the
duly appointed legal representative or attorney-in-fact hereof.  On any such
registration of transfer, the Company shall issue a new Warrant or Warrants, of
like tenor, in lieu of the transferred or assigned Warrant.  Notwithstanding the
foregoing provisions of this Section, this Warrant may be surrendered to the
Company, together with a written request for exchange, and thereupon the Company
shall issue and exchange therefor one or more new Warrants, of like tenor as
requested by Holder, and the Company shall cancel this Warrant on such surrender
for exchange.  In no event, however, will the Company be required to effect any
registration of transfer, assignment or exchange that would result in the
issuance of a fraction of a share.  For purposes of this Warrant, the term
"Holder" shall refer to all persons who any time are listed in the Warrant
Register as holding a Warrant representing any portion of the rights hereunder.

        6.   RESERVATION OF SHARES.  The Company shall at all times reserve, for
the purpose of issuance on exercise of this Warrant, such number of its duly
authorized and unissued and/or treasury shares of Class A Common Stock or such
class or classes of capital stock or other securities as shall from time to time
be sufficient to comply with this Warrant.  If, at anytime, the authorized and
unissued and/or treasury shares of Class A Common Stock or such other class or
classes of capital stock or other securities are not sufficient for the exercise
of this Warrant, the Company shall take such corporate action as may in the
opinion of its counsel be necessary to increase its authorized and unissued
and/or treasury shares of Class A Common Stock or such other class or classes of
capital stock or other securities to such number as shall be sufficient for that
purpose.

        7.   SURVIVAL.  All agreements, covenants, representations and
warranties herein shall survive the execution and delivery of this Warrant and
any investigation at any time made by or on behalf of any party hereto and the
exercise, sale and purchase of this Warrant and the Class A Common Stock
issuable on exercise hereof.

        8.   SHAREHOLDER RIGHTS.  This Warrant shall not entitle the Holder, as
such, to any voting rights or other rights as a shareholder of the Company, or
to any other rights except the rights stated herein.

        9.   NOTES.  All demands, notices, consents and other communications to
be given hereunder shall be in writing and shall be deemed duly given when
delivered personally or three days after being mailed by certified first class
mail, postage prepaid, return receipt requested, properly addressed, if to the
Company at:  400 West Avenue, Rochester, New York 14611, or if to the Holder, at
its address set forth above.  The Company and the Holder may change their
respective addresses at any time or times by notice given hereunder to the
other.
<PAGE>
 
        10.  AMENDMENTS; WAIVERS; TERMINATIONS; GOVERNING LAW; HEADINGS.  This
Warrant and any term hereof may be changed, waived, discharged or terminated
only by an instrument in writing signed by the party against which enforcement
of such change waiver, discharge or termination is sought.  The corporation laws
of the State of Delaware shall govern all issues concerning the relative rights
of the Company and its shareholders.  All other questions concerning the
construction, validity, enforcement and interpretation of this Warrant shall be
governed by and construed and interpreted in accordance with the internal laws
of the State of New York, without giving effect to any choice of law or conflict
of law provision or rule of any jurisdiction.  The headings of the Warrant are
for convenience of reference only and are not part of this Warrant.


Dated:  October 30, 1995                         ACC CORP.
        ---------------------------

Witness:  /s/ Catherine St. George              By:  /s/ David K. Laniak
          -------------------------                  ----------------------

Secretary:  /s/ Francis Coleman                 Title:  CEO
            -----------------------                     -------------------
<PAGE>
 
                                   EXHIBIT A.


                                  SUBSCRIPTION


        (To be completed and signed only on an exercise of the Warrant.)


TO ACC CORP.:

        The undersigned, the Holder of the within Warrant, hereby irrevocably
elects to exercise the purchase right represented by such Warrant for, and to
purchase thereunder, _____ shares of the Class A Common Stock of ACC CORP. to
which such Holder is entitled thereunder, and herewith makes payment of $_______
therefor in cash or by certified or official bank check.  The undersigned hereby
requests that the Certificate(s) for such shares be issued in his name and
delivered to the following address:



        If the foregoing Subscription evidences an exercise of the within
Warrant to purchase fewer than all of the Shares to which the undersigned is
entitled under such Warrant, please issue a new warrant, of like tenor, for
remaining Shares in his name, and deliver the same to the same address as set
forth above.



Dated:  ________, 19  .


                                       (Name of Holder)



                                       ___________________________
                                       (Signature of Holder or
                                       Authorized Signatory)
<PAGE>
 
                                   EXHIBIT B

TO:     ACC CORP.
        400 West Avenue
        Rochester, New York  14611


Gentlemen:

        In connection with the issuance to me of ______ shares of the Class A
Common Stock (the "Shares") of ACC CORP. (the "Company"), I hereby represent to
the Company that all of the Shares are being acquired by the undersigned for my
own investment account and not with a view to, or for resale in connection with,
any distribution of the Shares nor with any intention of dividing my
participation with others.

        I understand that the Shares have not been registered under the
Securities Act of 1933, as amended, (the "Act") by reason of a specific
exemption under the provisions of the Act which depends upon my representations
contained in this letter and that you are relying on such representations as a
condition precedent to permitting the issuance of the Shares to me.  I also
understand that any sales made by me publicly under Rule 144 can only be made
after I have held the Shares for two years, and then only in limited quantities
and only under the terms and conditions of said Rule; and that any other public
resale of the Shares may require registration under the Act or compliance with
an exemption from the registration requirements of the Act.

        I agree that the Shares my not be transferred unless and until the
Company shall have been informed of the proposed transfer and:

        1.   A registration statement with respect to the Shares shall be
effective under the Act, and I shall have furnished satisfactory proof of
compliance with any other applicable law; or

        2.   I have obtained an opinion of counsel, in form and content
satisfactory to the Company and its counsel, that no violation of the Act or any
other applicable law will be involved in such transfer, and/or such other
documentation in connection therewith as counsel for the Company may in its
reasonable discretion require as a condition precedent in order to make a
determination that the transfer will involve no such violation.

        I agree that appropriate legends may be placed on any certificates
delivered to me representing the Shares in order to give notice of the transfer
restrictions set forth in this letter and that the Company may cause stop
transfer orders to be placed on my account.

        I further acknowledge and agree that neither the Company nor any of its
agents, officers or directors have made any representations concerning the
Company or its prospects and that I have based my decision to acquire the
Company's stock upon information furnished to me by persons other than the
Company, its officers, directors or agents.
<PAGE>
 
        In consideration of the transfer of the Shares to me, I hereby agree to
indemnify and hold harmless the Company, its officers, directors, employees and
agents, from and against any and all liability, losses, damages, expenses and
attorneys' fees which any of them may hereafter incur, suffer or be required to
pay by reason of the falsity of, or my failure to comply with, any
representations contained in this letter.


                                       Very truly yours,


                                       _________________________ 
                                       (Signature of Holder)
                                       (Date)
