<PAGE>   1
                                                                    EXHIBIT 10.7


THIS WARRANT AND THE SHARES OF COMMON STOCK PURCHASABLE HEREUNDER HAVE NOT BEEN
REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR UNDER THE SECURITIES
LAWS OF ANY STATE OR OTHER JURISDICTION AND MAY NOT BE SOLD, OFFERED FOR SALE OR
OTHERWISE TRANSFERRED UNLESS REGISTERED OR QUALIFIED UNDER SAID ACT AND
APPLICABLE STATE SECURITIES LAWS OR UNLESS THE COMPANY RECEIVES AN OPINION OF
COUNSEL IN REASONABLY ACCEPTABLE FORM AND SCOPE REASONABLY SATISFACTORY TO THE
COMPANY THAT REGISTRATION, QUALIFICATION OR OTHER SUCH ACTIONS ARE NOT REQUIRED
UNDER ANY SUCH LAWS. THE OFFERING OF THIS SECURITY HAS NOT BEEN REVIEWED OR
APPROVED BY ANY STATE'S SECURITIES ADMINISTRATOR. THIS WARRANT AND THE SHARES OF
COMMON STOCK PURCHASABLE HEREUNDER ARE ALSO SUBJECT TO A STOCKHOLDERS AGREEMENT,
AS AMENDED, DATED AS OF OCTOBER 16, 1996, BY AND AMONG THE COMPANY AND THE OTHER
PARTIES LISTED THEREIN, COPIES OF WHICH ARE ON FILE WITH THE COMPANY AND WILL BE
FURNISHED UPON WRITTEN REQUEST AND WITHOUT CHARGE.

                                                            Dated: April 1, 1998

                                     WARRANT

              To Purchase 2,553,182 Shares of Class C Common Stock

                        CAPSTAR BROADCASTING CORPORATION

                           EXPIRING FEBRUARY 20, 2007

         THIS IS TO CERTIFY THAT, for value received, R. Steven Hicks, or
registered assigns as a holder of this Warrant (the "Holder") is entitled to
purchase from the Company (as hereinafter defined) at any time or from time to
time prior to 5:00 p.m., Dallas, Texas time, February 20, 2007 at the place
where the Warrant Agency (as hereinafter defined) is located, at the Exercise
Price (as hereinafter defined) 2,042,546 shares of Class C common stock, par
value $.01 per share (the "Common Stock"), of the Company (the "A Warrant") and
at the Exercise Price 510,636 shares of the Common Stock (the "B Warrant", and,
collectively with the A Warrant, the "Warrant"), all subject to adjustment and
upon the terms and conditions as hereinafter provided; provided, however, that,
except as provided in Section 3.1, in no event may the B Warrant be exercised by
the Holder until the earlier to occur of June 30, 2001 or immediately preceding
the consummation of a Sale of the Company (as hereinafter defined); and provided
further, however, that the B Warrant shall terminate and not be exercisable
pursuant to the provisions of Section 3.1 or 3.2. The Holder shall designate at
the time of exercise whether the Holder is exercising an A Warrant or a B
Warrant and the number of shares of Common Stock to be purchased respectively
thereunder. This Warrant amends and restates, supersedes and replaces that
certain Warrant dated July 1, 1997, among the Company, the Initial Holder and
Capstar Broadcasting Partners, Inc.

         Certain terms used in this Warrant are defined in Article V.



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                                    ARTICLE I
                              EXERCISE OF WARRANTS

         1.1 Method of Exercise. To exercise this Warrant in whole or in part,
the Holder shall deliver to the Company, at the Warrant Agency, (a) this
Warrant, (b) a written notice, in substantially the form of the Subscription
Notice attached hereto as Annex A, of such Holder's election to exercise this
Warrant, which notice shall specify (i) whether the Holder is exercising an A
Warrant and/or a B Warrant, (ii) the number of shares of Common Stock to be
purchased under an A Warrant and/or a B Warrant, as applicable, (iii) the
denominations of the share certificate or certificates desired, and (iv) the
name or names in which such certificates are to the registered, (c) if the
Common Stock to be received upon the exercise of this Warrant has not been
registered under the Securities Act, a written certification in substantially
the form of the Certification attached hereto as Annex B, and (d) payment of the
Exercise Price with respect to such shares. Such payment may be made, at the
option of the Holder, by cash, money order, certified or bank cashier's check or
wire transfer.

         The Company shall, as promptly as practicable and in any event within
five Business Days thereafter, execute and deliver or cause to be executed and
delivered, in accordance with such notice, a certificate or certificates
representing the aggregate number of shares of Common Stock specified in said
notice. The share certificate or certificates so delivered shall be in such
denominations as may be specified in such notice or, if such notice shall not
specify denominations, shall be in the amount of the number of shares of Common
Stock for which the Warrant is being exercised, and shall be issued in the name
of the Holder or such other name or names as shall be designated in such notice.
Such certificate or certificates shall be deemed to have been issued, and such
Holder or any other Person so designated to be named therein shall be deemed for
all purposes to have become a holder of record of such shares, as of the date
the aforementioned notice is received by the Company. If this Warrant shall have
been exercised only in part, the Company shall, at the time of delivery of the
certificate or certificates, deliver to the Holder a new Warrant evidencing the
rights to purchase the remaining shares of Common Stock called for by this
Warrant, which new Warrant shall in all other respects be identical with this
Warrant, or, at the request of the Holder, appropriate notation may be made on
this Warrant which shall then be returned to the Holder. The Company shall pay
all expenses, taxes (if any) and other charges payable in connection with the
preparation, issuance and delivery of share certificates and a new Warrant,
except that, if share certificates or a new Warrant shall be registered in a
name or names other than the name of the Holder, funds sufficient to pay all
transfer taxes payable as a result of such transfer shall be paid by the Holder
at the time of delivering the aforementioned notice of exercise or promptly upon
receipt of a written request of the Company for payment.

         1.2 Shares To Be Fully Paid and Nonassessable. All shares of Common
Stock issued upon the exercise of this Warrant shall be validly issued, fully
paid and nonassessable and free from all preemptive rights of any stockholder,
and from all taxes.

         1.3 No Fractional Shares To Be Issued. The Company shall not be
required to issue fractions of shares of Common Stock upon exercise of this
Warrant. If any fraction of a share would, but for this Section, be issuable
upon any exercise of this Warrant, in lieu of such fractional share the Company
shall pay to the Holder, in cash, an amount equal to such fraction of the Fair
Market Value per share of Common Stock of the Company on the Business Day
immediately prior to the date of such exercise.

         1.4 Share Legend. Each certificate for shares of Common Stock issued
upon exercise of this Warrant, unless at the time of exercise such shares are
registered under the Securities Act, shall bear the following legend:


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         "This security has not been registered under the Securities Act of
         1933, as amended, or under the securities laws of any state or other
         jurisdiction and may not be sold, offered for sale or otherwise
         transferred unless registered or qualified under said Act and
         applicable state securities laws or unless the Company receives an
         opinion of counsel in reasonably acceptable form and scope reasonably
         satisfactory to the Company that registration, qualification or other
         such actions are not required under any such laws. The offering of this
         security has not been reviewed or approved by any state securities
         administrator.

         Any certificate issued at any time in exchange or substitution for any
certificate bearing such legend (except a new certificate issued upon completion
of a public distribution pursuant to a registration statement under the
Securities Act) shall also bear such legend unless, in the opinion of counsel
selected by the holder of such certificate and reasonably acceptable to the
Company, the securities represented thereby are no longer subject to
restrictions on resale under the Securities Act.

         1.5 Reservation; Authorization. The Company has reserved and will keep
available for issuance upon exercise of this Warrant the total number of shares
of Common Stock deliverable upon exercise of this Warrant from time to time
outstanding. The issuance of such shares has been duly and validly authorized
and, when issued and sold in accordance with this Warrant, such shares will be
duly and validly issued, fully paid and nonassessable.

                                   ARTICLE II

                       WARRANT AGENCY; TRANSFER, EXCHANGE
                           AND REPLACEMENT OF WARRANTS

         2.1 Warrant Agency. At any time after a public offering of Common Stock
registered under the Securities Act, the Company may promptly appoint and
thereafter maintain, at its own expense, an agency in New York, New York, which
agency may be the Company's then existing transfer agent (the "Warrant Agency"),
for certain purposes specified herein, and shall give prompt notice of such
appointment (and appointment of any successor Warrant Agency) to the Holder.
Until an independent Warrant Agency is so appointed, the Company shall perform
the obligations of the Warrant Agency provided herein at its address as
specified on the signature page hereto or such other address as the Company
shall specify by notice to the Holder.

         2.2 Ownership of Warrant. The Company may deem and treat the Person in
whose name this Warrant is registered as the Holder and owner hereof
(notwithstanding any notations of ownership or writing hereon made by any Person
other than the Warrant Agency) for all purposes and shall not be affected by any
notice to the contrary, until presentation of this Warrant for registration of
transfer as provided in this Article II.

         2.3 Transfer of Warrant. The Company agrees to maintain at the Warrant
Agency books for the registration of transfers of the Warrants, and transfer of
this Warrant and all rights hereunder shall be registered, in whole or in part,
on such books, upon surrender of this Warrant at the Warrant Agency, together
with a written assignment of this Warrant duly executed by the Holder or his
duly authorized agent or attorney, with (unless the Holder is the original
Holder or another institutional investor) signatures guaranteed by a bank or
trust company or a broker or dealer registered with the NASD, and funds
sufficient to pay any transfer taxes payable upon such transfer. Upon surrender
the Company shall execute and deliver a new Warrant or Warrants in the name of
the assignee or assignees and in the denominations specified in the instrument
of


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<PAGE>   4



assignment, and this Warrant shall promptly be canceled. The Warrant Agency
shall not be required to register any transfers if the Holder fails to furnish
to the Company, after a request therefor, an opinion of counsel (who may be an
employee of such Holder) reasonably satisfactory to the Company that such
transfer is exempt from the registration requirements of the Securities Act and
applicable blue sky laws.

         2.4 Division of Warrant. This Warrant may be divided upon surrender
hereof to the Warrant Agency, together with a written notice specifying the
names and denominations in which the new Warrants are to be issued, signed by
the Holder. Subject to compliance with Section 2.3 as to any transfer which may
be involved in the division, the Company shall execute and deliver new Warrants
in exchange for the Warrant or Warrants to be divided in accordance with such
notice.

         2.5 Loss, Theft, Destruction or Mutilation of Warrants. Upon receipt of
evidence 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, upon receipt of indemnity or security reasonably satisfactory to
the Company, or, in the case of any such mutilation, upon surrender and
cancellation of such Warrant, the Company will make and deliver, in lieu of such
lost, stolen, destroyed or mutilated Warrant, a new Warrant of like tenor and
representing the right to purchase the same aggregate number of shares of Common
Stock as provided for in such lost, stolen, destroyed or mutilated Warrant.

         2.6 Expenses of Delivery of Warrants. The Company shall pay all
expenses, taxes (other than transfer taxes) and other charges payable in
connection with the preparation, issuance and delivery of this Warrant and the
Common Stock issuable hereunder.

                                   ARTICLE III

                                 CERTAIN RIGHTS

         3.1 Termination of Employment.

             (a) Upon the termination of the Initial Holder's employment with 
the Company or any Related Entity due to the Initial Holder's death, the B
Warrant shall become exercisable on the Date of Termination, and the Holder
(or, in the case of the Initial Holder, the Holder's estate or any person who
acquired the right to exercise the B Warrant by bequest or inheritance or
otherwise by reason of the Holder's death) may, until the earlier to occur of
5:00 p.m., Dallas, Texas time, on May 31, 2003 or the first anniversary of the
Date of Termination, exercise the B Warrant with respect to all or any part of
the shares of Common Stock purchasable under the B Warrant; provided, however,
that in no event will the Holder (or, in the case of the Initial Holder, the
Holder's estate or any person who acquired the right to exercise the B Warrant
by bequest or inheritance or otherwise by reason of the Holder's death) have
less than 90 days after the Date of Termination to exercise the B Warrant.

             (b) Upon the termination of the Initial Holder's employment with 
the Company or any Related Entity due to the Initial Holder's Disability, the B
Warrant shall become exercisable on the Date of Termination, and the Holder
(or, in the case of the Initial Holder, the Holder's legal representatives)
may, until the earlier to occur of 5:00 p.m., Dallas, Texas time, on May 31,
2003 or the first anniversary of the Date of Termination, exercise the B
Warrant with respect to all or any part of the shares of Common Stock
purchasable under the B Warrant; provided, however, that in no event will the
Holder (or, in the case of the Initial Holder, the Holder's legal
representatives) have less than 90 days after the Date of Termination to
exercise the B Warrant.


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             (c) Upon the termination of the Initial Holder's employment with 
the Company or any Related Entity due to the Initial Holder's termination of
employment for Cause or the Initial Holder's resignation for other than Good
Reason, the Holder shall forfeit all of the Holder's rights under the B
Warrant, except as to those shares of Common Stock already purchased under the
B Warrant, and the B Warrant shall automatically, and without notice, terminate
and become null and void at 5:00 p.m., Dallas, Texas time, on the Date of
Termination.

             (d) Upon the termination of the Initial Holder's employment with 
the Company or any Related Entity due to the Initial Holder's termination of
employment without Cause or the Initial Holder's resignation for Good Reason
and, in either case, without a Board Determination, the B Warrant shall become
exercisable on the Date of Termination, and the Holder may, until the earlier
to occur of 5:00 p.m., Dallas, Texas time, on May 31, 2003 or the 90th day
after the Date of Termination, exercise the B Warrant with respect to all or
any part of the shares of Common Stock purchasable under the B Warrant;
provided, however, that in no event will the Holder have less than 90 days
after the Date of Termination to exercise the B Warrant.

             (e) Upon the termination of the Initial Holder's employment with 
the Company or any Related Entity due to the Initial Holder's termination of
employment without Cause or the Initial Holder's resignation for Good Reason
and, in either case, with a Board Determination, if the B Warrant has become
exercisable on or before the Date of Termination, then the Holder may, until
the earlier to occur of 5:00 p.m., Dallas, Texas time, on May 31, 2003 or the
30th day after the Date of Termination, exercise the B Warrant with respect to
all or any part of the shares of Common Stock purchasable under the B Warrant;
provided, however, that in no event will the Holder have less than 30 days
after the Date of Termination to exercise the B Warrant. If the B Warrant has
not become exercisable on or before the Date of Termination, the B Warrant
shall automatically, and without notice, terminate and become null and void at
5:00 p.m., Dallas, Texas time, on the Date of Termination.

             (f) If, pursuant to Section 3.2, the B Warrant shall terminate
earlier than provided for in this Section 3.1, then the provisions of Section
3.2 shall prevail.

         3.2 Termination of B Warrant. Notwithstanding any provision of this
Warrant to the contrary, the B Warrant shall expire and no longer be exercisable
upon either (a) the consummation of a Sale of the Company or (b) the
consummation of a Capital Reorganization in which (i) the stockholders of the
Company receive only cash consideration for each share of common stock of the
Company held by such stockholder that is less (when added to any cash
consideration attributable to any prior Capital Reorganization) than the
Qualifying Cash Consideration, (ii) a majority of directors of the purchaser or
surviving entity in such Capital Reorganization consists of persons who are not
Continuing Directors, and (iii) such purchaser or surviving entity is not a
member of the HMC Group. The Company shall give the Holder reasonable prior
notice of the consummation of a Capital Reorganization. Appropriate per share
adjustments shall be made to take into account, on a comparable per share basis,
any cash consideration attributable to any prior Capital Reorganization.

         3.3 Stockholders Agreement. This Warrant and the Common Stock issuable
upon exercise of this Warrant is subject to a Stockholders Agreement, dated as
of October 16, 1996, as amended, by and among the Company and the other parties
listed therein (the "Stockholders Agreement"). The Company shall keep a copy of
the Stockholders Agreement, and any amendments thereto, at the Warrant Agency
and shall furnish copies thereof to the Holder upon request.


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<PAGE>   6



         3.4 Notice of Fair Market Value. Upon each determination of Fair Market
Value hereunder (other than a determination relating solely to setting the value
of fractional shares), the Company shall promptly give notice thereof to the
Holder.

                                   ARTICLE IV

                             ANTIDILUTION PROVISIONS

         4.1 Adjustments Generally. The Exercise Price and the number of shares
of Common Stock (or other securities or property) issuable upon exercise of this
Warrant shall be subject to adjustment from time to time upon the occurrence of
certain events, as provided in this Article IV.

         4.2 Common Stock Reorganization. If the Company shall after the date of
issuance of this Warrant subdivide its outstanding shares of Common Stock into a
greater number of shares or consolidate its outstanding shares of Common Stock
into a smaller number of shares (any such event being called a "Common Stock
Reorganization"), then (a) the Exercise Price shall be adjusted, effective
immediately after the record date at which the holders of shares of Common Stock
are determined for purposes of such Common Stock Reorganization, to a price
determined by multiplying the Exercise Price in effect immediately prior to such
record date by a fraction, the numerator of which shall be the number of shares
of Common Stock outstanding on such record date before giving effect to such
Common Stock Reorganization and the denominator of which shall be the number of
shares of Common Stock outstanding after giving effect to such Common Stock
Reorganization, and (b) the number of shares of Common Stock subject to purchase
upon exercise of the A Warrant and the B Warrant shall each be adjusted,
effective at such time, to a number determined by multiplying the number of
shares of Common Stock subject to purchase immediately before such Common Stock
Reorganization by a fraction, the numerator of which shall be the number of
shares outstanding after giving effect to such Common Stock Reorganization and
the denominator of which shall be the number of shares of Common Stock
outstanding immediately before such Common Stock Reorganization.

         4.3 Capital Reorganization. If after the date of issuance of this
Warrant there shall be any consolidation or merger to which the Company is a
party (whether or not the Company is the surviving entity), other than a
consolidation or a merger in which the Company is a continuing corporation and
which does not result in any reclassification of, or change (other than a Common
Stock Reorganization or a change in par value), in, outstanding shares of Common
Stock, or any sale, assignment, lease, exchange, conveyance or other transfer
(in one transaction or series of related transactions) of the property of the
Company as an entirety or substantially as an entirety or all or substantially
all of the outstanding equity securities of the Company to any person or group
of related persons for the purposes of Section 13(d) of the Exchange Act (any
such event being called a "Capital Reorganization"), then, effective upon the
effective date of such Capital Reorganization, the Holder shall have the right
to purchase, upon exercise of this Warrant, the kind and amount of shares of
stock and other securities and property (including cash) which the Holder would
have owned or have been entitled to receive after such Capital Reorganization if
this Warrant had been exercised immediately prior to such Capital
Reorganization. As a condition to effecting any Capital Reorganization, the
Company or the successor or surviving corporation, as the case may be, shall
execute and deliver to the Holder an agreement as to the Holder's rights in
accordance with this Section 4.3, providing for subsequent adjustments as nearly
equivalent as may be practicable to the adjustments provided for in this Article
IV. The provisions of this Section 4.3 shall similarly apply to successive
Capital Reorganizations.



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<PAGE>   7



          4.4 Certain Other Events. If any event occurs after the date of
issuance of this Warrant as to which the foregoing provisions of this Article
IV are not strictly applicable or, if strictly applicable, would not, in the
good faith judgment of the Board of Directors of the Company (the "Board"),
fairly protect the purchase rights of the Holder in accordance with the
essential intent and principles of such provisions, then the Board shall make
such adjustments in the application of such provisions, in accordance with such
essential intent and principles, as shall be reasonably necessary, in the good
faith opinion of the Board, to protect such purchase rights as aforesaid.

          4.5 Adjustment Rules. (a) Any adjustments pursuant to this Article IV
shall be made successively whenever an event referred to herein shall occur.

                  (b) If the Company shall set a record date to determine the
holders of shares of Common Stock for purposes of a Common Stock Reorganization
or Capital Reorganization, and shall legally abandon such action prior to
effecting such action, then no adjustment shall be made pursuant to this Article
IV in respect of such action.

                  (c) No adjustment in the amount of shares purchasable upon
exercise of this Warrant or in the Exercise Price shall be made hereunder unless
such adjustment increases or decreases such amount or price by one percent or
more, but any such lesser adjustment shall be carried forward and shall be made
at the time and together with the next subsequent adjustment which together with
any adjustments so carried forward shall serve to adjust such amount or price by
one percent or more.

                  (d) No adjustment in the Exercise Price shall be made
hereunder if such adjustment would reduce the exercise price to an amount below
par value of the Common Stock, which par value shall initially be $.01 per share
of Common Stock.

         4.6 Notice of Adjustment. The Company shall give the Holder reasonable
notice of the record date or effective date, as the case may be, of any action
which requires or might require an adjustment or readjustment pursuant to this
Article IV. Such notice shall describe such event in reasonable detail and
specify the record date or effective date, as the case may be, and, if
determinable, the required adjustment and the computation thereof. If the
required adjustment is not determinable at the time of such notice, the Company
shall give reasonable notice to the Holder of such adjustment and computation
promptly after such adjustment becomes determinable.

                                    ARTICLE V

                                   DEFINITIONS

         The following terms, as used in this Warrant, have the following
respective meanings:

         "Affiliate", means, with respect to any Person, any Person who,
directly or indirectly, controls, is controlled by or is under common control
with that Person.

         "Board Determination" shall have the meaning set forth in Section 3(b)
of the Employment Agreement.

         "Business Day" shall mean (a) if any class of common stock of the
Company is listed or admitted to trading on a national securities exchange, a
day on which the principal national securities exchange on which such class of
common stock of the Company is listed or admitted to trading is open for
business or 

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(b) if no class of common stock of the Company is so listed or admitted to
trading, a day on which the New York Stock Exchange is open for business.

          "Capital Reorganization" shall have the meaning set forth in Section
4.3.

          "Cause" shall have the meaning set fort in Section 3(b) of the
Employment Agreement.

         "Class A Common Stock" means the Class A Common Stock, par value $.01
per share, of the Company, and any capital stock into which such Class A Common
Stock thereafter may be changed.

         "Closing Price" with respect to any security on any day means (a) if
such security is listed or admitted for trading on a national securities
exchange, the reported last sales price regular way or, if no such reported sale
occurs on such day, the average of the closing bid and asked prices regular way
on such day, in each case as reported in the principal consolidated transaction
reporting system with respect to securities listed on the principal national
securities exchange on which such class of security is listed or admitted to
trading, or (b) if such security is not listed or admitted to trading on any
national securities exchange, the last quoted sales price, or, if not so quoted,
the average of the high bid and low asked prices in the over-the-counter market
on such day as reported by NASDAQ or any comparable system then in use or, if
not so reported, as reported by any New York Stock Exchange member firm
reasonably selected by the Company for such purpose.

         "Common Stock" shall have the meaning set forth in the first paragraph
of this Warrant.

          "Common Stock Reorganization" shall have the meaning set forth in
Section 4.2.

         "Company" shall mean Capstar Broadcasting Corporation, a Delaware
corporation, or any entity which is the continuing corporation of a
consolidation or merger to which the Company is a party or to which the Company
sells or conveys the property of the Company as an entirety or substantially as
an entirety.

         "Continuing Director" means, as of the date of determination, any
person who (i) was a member of the Board immediately prior to the date of
determination or (ii) is a designee or member of the HMC Group.

         "Date of Termination" shall have the meaning set forth in Section 3(e)
of the Employment Agreement.

         "Disability" shall have the meaning set forth in Section 3(a) of the
Employment Agreement.

         "Employment Agreement" means that certain Executive Employment
Agreement dated as of February 14, 1997, as amended, by and between the Company
and the Initial Holder, a copy of which is attached as Annex C hereto.

         "Exchange Act" means the Securities Exchange Act of 1934, as amended,
and any similar or successor federal statute, and the rules and regulations of
the Securities and Exchange Commission (or its successor) thereunder, all as the
same shall be in effect at the time.

         "Exercise Price" means a per share price of $1.54.



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<PAGE>   9


         "Fair Market Value" means the fair market value of the business or
property in question, as determined in good faith by the Board, provided,
however, that the Fair Market Value of any security for which a Closing Price is
available shall be the Market Price of such security.

         "Good Reason" shall have the meaning set forth in Section 3(c) of the
Employment Agreement.

         "Holder" shall have the meaning set forth in the first paragraph of
this Warrant. The term Holders shall refer to all Holders of Warrants.

         "HMC Group" means HMTF and its Affiliates and its and their respective
officers, directors, and employees (and members of their respective families
(other than R. Steven Hicks) and trusts for the primary benefit of such family
members).

         "HMTF" means Hicks, Muse, Tate & Furst Incorporated.

         "Initial Holder" means R. Steven Hicks.

         "IPO Offering Price" means the initial public offering price per share
of Class A Common Stock in a Qualified IPO, prior to deducting any underwriters'
discounts and commissions from such offering price.

         "Market Price", with respect to any security on any day means the
average of the daily Closing Prices of a share or unit of such security for the
20 consecutive Business Days ending on the most recent Business Day for which a
Closing Price is available; provided, however, that in the event that, in the
case of common stock of the Company, the Market Price is determined during a
period following the announcement by the Company of any subdivision, combination
or reclassification of common stock of the Company or the record date for such
subdivision, combination or reclassification, then, and in each such case, the
Market Price shall be appropriately adjusted to reflect the current market price
per share equivalent of common stock of the Company.

         "NASD" means The National Association of Securities Dealers, Inc.

         "NASDAQ" means The National Association of Securities Dealers, Inc.
Automated Quotation System.

         "Person" or "person" means any individual, corporation, partnership,
joint venture, association, joint-stock company, trust, unincorporated
organization or government or other agency or political subdivision thereof.

         "Qualified IPO" means a firm commitment underwritten public offering of
Class A Common Stock for cash pursuant to a registration statement under the
Securities Act where the aggregate proceeds to the Company prior to deducting
any underwriters' discounts and commissions from such offering and any similar
prior public offerings exceed $200 million.

         "Qualifying Cash Consideration" means cash consideration for each share
of common stock of the Company received pursuant to a Capital Reorganization
that equals or exceeds the lesser of (i) $6.00 per share or (ii) the greater of
(A) a per share amount equal to $1.40 compounded at an annual rate of 30% for
the period from April 3, 1998 to the end of the calendar month immediately
preceding the consummation of such Capital Reorganization or (B) a per share
amount equal to the IPO Offering Price compounded at an annual rate of 20% for
the period from the date on which a Qualified IPO is consummated to the end of


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<PAGE>   10

the calendar month immediately preceding the consummation of such Capital
Reorganization. Upon the completion of a Common Stock Reorganization, each of
the per share amounts set forth in the foregoing sentence shall be adjusted,
effective immediately after the record date at which the holders of shares of
Common Stock are determined for purposes of such Common Stock Reorganization, to
a dollar amount determined by multiplying such amount in effect immediately
prior to such record date by a fraction, the numerator of which shall be the
number of shares of Common Stock outstanding on such record date before giving
effect to such Common Stock Reorganization and the denominator of which shall be
the number of shares of Common Stock outstanding after giving effect to such
Common Stock Reorganization.

         "Related Entity" means any direct or indirect subsidiary of the Company
now existing or hereafter formed or acquired, any entity that directly or
indirectly owns the outstanding capital stock of the Company, and any entity
that issues equity securities to or at the direction of the Holder upon exercise
of this Warrant.

         "Sale of the Company" means a Capital Reorganization in which (i) the
stockholders of the Company receive cash consideration for each share of common
stock of the Company held by such stockholder that (when added to any cash
consideration attributable to any prior Capital Reorganization) equals or
exceeds the Qualifying Cash Consideration, (ii) a majority of directors of the
purchaser or surviving entity in such Capital Reorganization consists of persons
who are not Continuing Directors, and (iii) such purchaser or surviving entity
is not a member of the HMC Group. Appropriate per share adjustments shall be
made to take into account, on a comparable per share basis, any cash
consideration attributable to any prior Capital Reorganization.

         "Securities Act,, shall mean the Securities Act of 1933, as amended,
and any similar or successor federal statute, and the rules and regulations of
the Securities and Exchange Commission (or its successor) thereunder, all as the
same shall be in effect at the time.

         "Stockholders Agreement" shall have the meaning set forth in Section
3.2.

         "Warrant Agency" shall have the meaning set forth in Section 2.1.

         "Warrant" shall have the meaning set forth in the first paragraph of
this Warrant. The term Warrants shall refer to the Warrants resulting in any
subdivision of this Warrant.

                                   ARTICLE VI
                                  MISCELLANEOUS

         6.1 Notices. All notices, requests, consents and other communications
provided for herein shall be in writing and shall be effective upon delivery in
person, faxed or telecopied, or mailed by certified or registered mail, return
receipt requested, postage pre-paid, to the addresses specified on the signature
pages hereto or, in any case, at such other address or addresses as shall have
been furnished in writing to the Company (in the case of a Holder) or to the
Holder (in the case of the Company) in accordance with the provisions of this
paragraph.

         6.2 Waivers; Amendments. No failure or delay of the Holder in
exercising any power or right hereunder shall operate as a waiver thereof, nor
shall any single or partial exercise of any such right or power, or any
abandonment or discontinuance of steps to enforce such a right or power,
preclude any other or further exercise thereof or the exercise of any other
right or power. The rights and remedies of the Holder are cumulative and not
exclusive of any rights or remedies which it would otherwise have. The
provisions of this Warrant may be amended, modified or waived with (and only
with) the written consent of the 



                                      10

<PAGE>   11

Company and Holders who collectively hold Warrants to purchase a majority of the
Common Stock subject to purchase upon exercise of such Warrants at the time
outstanding.

         Any such amendment, modification or waiver effected pursuant to this
Section shall be binding upon the Holders, upon each future Holder thereof and
upon the Company. In the event of any such amendment, modification or waiver the
Company shall give prompt notice thereof to all Holders and, if appropriate,
notation thereof shall be made on all Warrants thereafter surrendered for
registration of transfer or exchange.

         No notice or demand on the Company in any case shall entitle the
Company to any other or further notice or demand in similar or other
circumstances.

         6.3      Governing Law.  This Warrant shall be construed in accordance 
with and governed by the laws of the State of Delaware.

         6.4 Severability. In case any one or more of the provisions contained
in this Warrant shall be invalid, illegal or unenforceable in any respect, the
validity, legality or enforceability of the remaining provisions contained
herein and therein shall not in any way be affected or impaired thereby. The
parties shall endeavor in good faith negotiations to replace the invalid,
illegal or unenforceable provisions with valid provisions the economic effect of
which comes as close as possible to that of the invalid, illegal or
unenforceable provisions.

         6.5 Section Headings. The sections headings used herein are for
convenience of reference only, are not part of this Warrant and are not to
affect the construction of or be taken into consideration in interpreting this
Warrant.

         6.6      No Rights as Stockholder.  This Warrant shall not entitle the 
Holder to any rights as a stockholder of the Company.

         6.7 Employment Agreement. In the event of any conflict or inconsistency
between the terms and conditions of this Warrant and the terms and conditions of
the Employment Agreement, the terms and conditions of this Warrant shall be
controlling.

                  [Remainder of page intentionally left blank]




                                       11

<PAGE>   12



         IN WITNESS WHEREOF, the Company has caused this Warrant to be executed
in its corporate name by one of its officers thereunto duly authorized,
effective as of the day and year first above written.

                                               CAPSTAR BROADCASTING CORPORATION



                                                By: /s/ WILLIAM S. BANOWSKY, JR.
                                                   -----------------------------
                                                   William S. Banowsky, Jr.
                                                   Executive Vice President


                                                Address:    600 Congress Avenue
                                                            Suite 1400
                                                            Austin, Texas 78701



ACCEPTED AND AGREED TO:



Name: /s/ R. STEVEN HICKS
     -------------------------------------
Name:       R. Steven Hicks 
Address:    600 Congress Avenue
            Suite 1400
            Austin, Texas 78701









<PAGE>   13



                                     ANNEX A

                               SUBSCRIPTION NOTICE

                    (To be executed upon exercise of Warrant)

         TO CAPSTAR BROADCASTING CORPORATION

         The undersigned hereby irrevocably elects to exercise the attached
Warrant and to purchase thereunder, in exercise of the [ ] A Warrant for _____
shares of Common Stock and/or [ ] B Warrant for _________ shares of Common Stock
in payment of an Exercise Price in an amount equal to $__________.

         Please issue a certificate or certificates for such shares of Common
Stock in the following name or names and denominations:



         If said number of shares shall not be all the shares issuable upon
exercise of the attached Warrant, a new Warrant is to be issued in the name of
the undersigned for the balance remaining of such shares less any fraction of a
share paid in cash.



Dated: ___________________, ______



                                     -------------------------------------------
                                     Note: The above signature should correspond
                                           exactly with the name on the face of
                                           the attached Warrant or with the name
                                           of the assignee appearing in the 
                                           assignment form below.





<PAGE>   14



                                     ANNEX B

                                  CERTIFICATION

         The undersigned hereby certifies to Capstar Broadcasting Corporation
that he, she or it is:


                  a.    an "accredited investor" as that term is defined in
                        Regulation D promulgated pursuant to the Securities
                        Act or any successor regulation, as such provisions
                        may be in effect on the date hereof, and is an
                        "accredited investor" pursuant to Section of such
                        provision; and

                  b.    is knowledgeable, sophisticated and experienced in 
                        business and financial matters and in securities similar
                        to the Common Stock; is aware of the limitation on the
                        transfer of the Common Stock imposed by applicable
                        securities laws and any limitations on transfer imposed
                        by contracts with the Company or others; and has had
                        access to, or been furnished with, all information about
                        the Common Stock and the Company deemed necessary to
                        conclude that he, she or it has the ability to bear the
                        economic risk of the investment in the Common Stock and
                        to afford the complete loss of such investment.

         IN WITNESS WHEREOF, the undersigned has executed this CERTIFICATION
this _____ day of ________________, _____.

For Individuals:                                    For Entities:



---------------------------------                   ----------------------------
Signature                                           Printed Name of Entity


                                                    By:
---------------------------------                      -------------------------
Printed Name                                           Name:
                                                            --------------------
                                                       Title:
                                                             -------------------




<PAGE>   15


                                     ANNEX C

                              EMPLOYMENT AGREEMENT