<PAGE>   1
                                                                   EXHIBIT 10.12




THIS WARRANT AND THE SHARES OF COMMON STOCK PURCHASABLE HEREUNDER HAVE NOT BEEN
REGISTERED UNDER THE SECURITIES ACT OF 1933 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, DATED
AS OF NOVEMBER 26, 1996, AS AMENDED, 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 1,500,000 Shares of Class A Common Stock

                        CAPSTAR BROADCASTING CORPORATION

                             EXPIRING MAY 31, 2003

         THIS IS TO CERTIFY THAT, for value received, William S. Banowsky, Jr.,
or registered assigns as a holder (the "Holder") of this Warrant (the
"Warrant") is entitled to purchase from the Company (as hereinafter defined) at
the place where the Warrant Agency (as hereinafter defined) is located, at the
Exercise Price (as hereinafter defined), 1,500,000 shares (the "Warrant
Shares") of Class A Common Stock, par value $.01 per share (the "Common
Stock"), of the Company, subject to adjustment and upon the terms and
conditions as hereinafter provided.

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

                                   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) the number of shares of Common Stock to
be purchased under the Warrant, (ii) the denominations of the share certificate
or certificates desired, and (iii) 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
<PAGE>   2
(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:

         "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.
<PAGE>   3
         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 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





                                       3
<PAGE>   4
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     Exercise.

                 (a)      Except as otherwise provided in Sections 3.2 and 3.3,
the Warrant Shares shall become "Vested Warrant Shares" with respect to 20% of
the Warrant Shares on the first anniversary of the date of this Warrant, and
1/60th of the Warrant Shares shall vest and become Vested Warrant Shares on the
last day of each calendar month thereafter, so that all of the Warrant Shares
shall be vested and become Vested Warrant Shares 60 months after the date of
this Warrant.

                 (b)      Except as otherwise provided in Sections 3.2 and 3.3,
this Warrant shall become exercisable to acquire Vested Warrant Shares at any
time or from time to time after the date on which the average Fair Market Value
of the Common Stock, calculated on a daily basis (when added to  any cash
consideration attributable to any prior Capital Reorganization), equals or
exceeds $6.00 per share (the "Exercisability Value") for a period of 180
consecutive days (excluding non-Business Days for purposes of calculating the
average Fair Market Value during such 180-day period) during the period from
(and including) April 1, 1998 through (and including) May 31, 2003.  Upon the
completion of a Common Stock Reorganization, the Exercisability Value 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 the Exercisability
Value 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.

                 (c)      Notwithstanding clauses (a) and (b), the Warrant
Shares shall become Vested Warrant Shares, and this Warrant shall become
exercisable, immediately preceding the consummation of a Sale of the Company.





                                       4
<PAGE>   5
                 (d)      Except as otherwise provided in Section 3.2, the
unexercised portion of this Warrant, if any, will automatically, and without
notice, terminate and become null and void at 5:00 p.m., Dallas, Texas time, on
the later to occur of May 31, 2003 or the 90th day after this Warrant becomes
exercisable.

         3.2     Termination of Employment.  Notwithstanding Section 3.1:

                 (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 Warrant Shares shall become Vested Warrant Shares on the Date of
Termination.  If this Warrant has become exercisable on or before the Date of
Termination, then the Holder (or, in the case of the Initial Holder, the
Holder's estate or any person who acquired the right to exercise this 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 this Warrant with
respect to all or any part of the Vested Warrant Shares; 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 this 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 this Warrant.  If
this Warrant has not become exercisable on or before the Date of Termination,
then (i) this Warrant shall remain in full force and effect until May 31, 2003
and (ii) if this Warrant becomes exercisable on or before May 31, 2003, then
the Holder (or, in the case of the Initial Holder, the Holder's estate or any
person who acquired the right to exercise this 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 on which this Warrant becomes exercisable, exercise
this Warrant with respect to all or any part of the Vested Warrant Shares;
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 this Warrant by bequest or inheritance or otherwise by reason of the
Holder's death) have less than 90 days to exercise this 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 Warrant Shares shall become Vested Warrant Shares on the Date
of Termination.  If this Warrant has become exercisable on or before the Date
of Termination, then 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 this Warrant with respect to all or any part of the
Vested Warrant Shares; 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 this Warrant.  If
this Warrant has not become exercisable on or before the Date of Termination,
then (i) this Warrant shall remain in full force and effect until May 31, 2003
and (ii) if this Warrant becomes exercisable on or before May 31, 2003, then
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 on which this
Warrant becomes exercisable, exercise this Warrant with respect to all or any
part of the Vested Warrant Shares; 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 to exercise this Warrant.

                 (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





                                       5
<PAGE>   6
Holder's resignation for other than Good Reason, the Holder shall forfeit all
of the Holder's rights under this Warrant, except as to those Warrant Shares
already purchased, and this 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 Warrant
Shares shall become Vested Warrant Shares on the Date of Termination.  If this
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 90th day after the Date of Termination, exercise this Warrant
with respect to all or any part of the Vested Warrant Shares; provided,
however, that in no event will the Holder have less than 90 days after the Date
of Termination to exercise this Warrant.  If this Warrant has not become
exercisable on or before the Date of Termination, then (i) this Warrant shall
remain in full force and effect until May 31, 2003 and (ii) if this Warrant
becomes exercisable on or before May 31, 2003, then 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 on which this Warrant becomes exercisable, exercise this
Warrant with respect to all or any part of the Vested Warrant Shares; provided,
however, that in no event will the Holder have less than 90 days to exercise
this 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, no additional
Warrant Shares shall vest after the Date of Termination.  If this 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 this Warrant with respect
to all or any part of the Vested Warrant Shares; provided, however, that in no
event will the Holder have less than 30 days after the Date of Termination to
exercise this Warrant.  If this Warrant has not become exercisable on or before
the Date of Termination, then (i) this Warrant shall remain in full force and
effect until May 31, 2003, and (ii) if this Warrant becomes exercisable on or
before May 31, 2003, 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 on
which this Warrant becomes exercisable, exercise this Warrant with respect to
all or any part of the Vested Warrant Shares; provided, however, that in no
event will the Holder have less than 30 days to exercise this Warrant.

                 (f)      If, pursuant to Section 3.3, this Warrant shall
terminate earlier than provided for in this Section 3.2, then the provisions of
Section 3.3 shall prevail.

         3.3     Termination of Warrant.  Notwithstanding any provision of this
Warrant to the contrary, this 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





                                       6
<PAGE>   7
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.

         3.4     Stockholders Agreement.  This Warrant and the Common Stock
issuable upon exercise of this Warrant is subject to a Stockholders Agreement
dated as of November 26, 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.

         3.5     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 this Warrant shall 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





                                       7
<PAGE>   8
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.

         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.

                                            





                                       8
<PAGE>   9
                                  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 (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.

         "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.





                                       9
<PAGE>   10
         "Employment Agreement" means that certain Executive Employment
Agreement dated as of July 1, 1997, as amended, by and between the Company and
the Initial Holder and for certain limited purposes, Capstar Broadcasting
Partners, Inc., 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.

         "Exercisability Value" shall have the meaning set forth in Section
3.1(b).

         "Exercise Price" means a per share price of $1.40.

         "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 William S. Banowsky, Jr.

         "IPO Offering Price" means the initial public offering price per share
of 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 for purposes of determining
Fair Market Value as used in Section 3.1(b), "Market Price" means the daily
Closing Price of a share of Common Stock on the date of determination; provided
further, however, that in the event that, in the case of Common Stock, the
Market Price is determined following the announcement by the Company of any
subdivision, combination or reclassification of Common Stock 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.

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





                                       10
<PAGE>   11
         "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 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) the Exercisability
Value or (ii) the greater of (A) the Exercise Price 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 the calendar month immediately preceding the consummation of such
Capital 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 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
3.4.

         "Vested Warrant Shares" shall have the meaning set forth in Section
3.1 (a).

         "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.





                                       11
<PAGE>   12
         "Warrant Shares" shall have the meaning set forth in the first
paragraph 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 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.





                                       12
<PAGE>   13
         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]





                                       13
<PAGE>   14
         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/ PAUL D. STONE                
                                             -----------------------------------
                                          Name:   Paul D. Stone                 
                                               ---------------------------------
                                                  Executive Vice President
                                               ---------------------------------

                                          Address:  600 Congress Avenue
                                                    Suite 1400
                                                    Austin, Texas  78701



ACCEPTED AND AGREED TO:

 /s/ WILLIAM S. BANOWSKY
--------------------------------------
Name:     William S. Banowsky, Jr.
Address:  600 Congress Avenue
          Suite 1400
          Austin, Texas  78701



<PAGE>   15
                                    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 _________ 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>   16
                                    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>   17
                                    ANNEX C

                              EMPLOYMENT AGREEMENT