
<PAGE>   1
                                                                    EXHIBIT 4.32

                           CERTIFICATE OF DESIGNATION
                                       OF
               $3.00 CONVERTIBLE EXCHANGEABLE PREFERRED STOCK OF
                          EVERGREEN MEDIA CORPORATION

                       Pursuant to Section 151(g) of the
                General Corporation Law of the State of Delaware


         Evergreen Media Corporation, a Delaware corporation (hereinafter
called, the "Company"), pursuant to Section 151 of the General Corporation Law
of the State of Delaware does hereby make this Certificate of Designation and
does hereby state and certify that pursuant to the authority expressly vested
in the Board of Directors of the Company (the "Board") by the Certificate of
Incorporation, a duly authorized and constituted Committee of the Board duly
adopted the following resolution:

         RESOLVED, that pursuant to Article Four of the Certificate of
Incorporation (which authorizes 6,000,000 shares of preferred stock, $.01 par
value), the Committee as authorized by the Board hereby fixes the designation,
powers and preferences, and the relative participating, optional and other
special rights, and the qualifications, limitations and restrictions thereof,
of a series of Convertible Exchangeable Preferred Stock.

         RESOLVED, that each share of the Convertible Exchangeable Preferred
Stock shall rank equally in all respects and shall be subject to the following
provisions:

           1.  Number of Shares; Designation.  A total of 6,000,000 shares of
Preferred Stock, par value $.01 per share, of the Company are hereby designated
as $3.00 Convertible Exchangeable Preferred Stock (the "CONVERTIBLE PREFERRED
STOCK").  The number of authorized shares of Convertible Preferred Stock may be
decreased, at any time and from time to time, by resolution of the Board of
Directors of the Company; provided, however, that no decrease shall reduce the
authorized number of shares of the Convertible Preferred Stock  to a number
less than the number of shares outstanding.

          2.   Rank.  The Convertible Preferred Stock shall, with respect to
payment of dividends, redemption payments and rights upon liquidation,
dissolution or winding up of the affairs of the Company (x) rank senior and
prior to (a) all classes of Common Stock, par value $.01 per share, of the
Company (the "COMMON STOCK") and (b) any other class or series of capital stock
of the Company that by its terms ranks junior to the Convertible Preferred
Stock as to payment of dividends, redemption payments and rights upon
liquidation, dissolution or winding up of the affairs of the Company, (y) rank
on a parity with all Parity Dividend Shares (as defined in Section 3 (a)) and
all
<PAGE>   2
Parity Liquidation Shares (as defined in Section 5(b)) and (z) rank junior to
all Senior Dividend Shares (as defined in Section 3(c)), all Senior Liquidation
Shares (as defined in Section 5(b)) and to any class or series of capital stock
(other than Common Stock) of the Company, whether currently issued or issued in
the future, that does not by its terms expressly provide that it ranks on a
parity with or junior to the Convertible Preferred Stock as to dividends and
rights upon liquidation, dissolution or winding-up of the Company (which shall
include, for purposes of the foregoing, any entity with which the Company may
be merged or consolidated or to which all or substantially all the assets of
the Company may be transferred or which transfers all or substantially all of
its assets to the Company).

          3.   Dividends. (a) The cash dividend rate per annum on shares of the
Convertible Preferred Stock shall be $3.00 per share of Convertible Preferred
Stock.  Dividends on shares of Convertible Preferred Stock shall be fully
cumulative, accruing, without interest (or sum of money in lieu of interest),
from the most recent date to which dividends have been paid or, if none have
been paid, from June 16, 1997 and shall be payable quarterly in arrears, when,
as and if declared by the Board of Directors out of funds legally available for
the payment of dividends on March 15, June 15, September 15 and December 15 of
each year (each, a "DIVIDEND PAYMENT DATE") commencing September 15, 1997,
except that if any Dividend Payment Date is not a business day then the
Dividend Payment Date shall be on the first immediately succeeding business day
(as used herein, the term "business day" shall mean any day except a Saturday,
Sunday or day on which banking institutions are legally authorized to close in
the City of New York).  Each dividend shall be paid to the holders of record of
shares of the Convertible Preferred Stock as they appear on the stock register
of the Company at the close of business on the March 1, June 1, September 1,
and December 1 immediately preceding the relevant Dividend Payment Date (each,
a "DIVIDEND PAYMENT RECORD DATE"). Dividends payable for each quarterly
dividend period shall be computed by dividing the annual dividend by four.
Dividends payable for any partial dividend period shall be computed on the
basis of a 360-day year of twelve 30-day months.  Dividends on account of
arrears for any past dividend periods may be declared and paid at any time,
without reference to any regular Dividend Payment Date, to holders of record on
such date not more than 60 days nor fewer than 10 days preceding the date on
which dividends in arrears will be paid, as may be fixed by the Board of
Directors of the Company.  No interest shall be payable with respect to any
dividend payment that may be in arrears.  Holders of shares of the Convertible
Preferred Stock shall be entitled to receive dividends in preference to and in
priority over dividends upon the Common Shares (as defined in Section 12) and
any other series or class of the Company's capital stock that ranks junior as
to dividends to the Convertible Preferred Stock ("JUNIOR DIVIDEND SHARES") and
shall be on a parity as to dividends with any series or class of the Company's
capital stock that does not rank senior or junior as to dividends to the
Convertible Preferred Stock ("PARITY DIVIDEND





                                       2
<PAGE>   3
SHARES").  The holders of shares of the Convertible Preferred Stock shall not
be entitled to any dividends other than the cash dividends provided for in this
Section 3.

         (b)      No dividends, other than dividends payable solely in Common
Shares, Junior Dividend Shares, or warrants or other rights to acquire such
Common Shares or Junior Dividend Shares, shall be paid or declared and set
apart for payment on, and no purchase, redemption or other acquisitions shall
be made by the Company of, any Common Shares or Junior Dividend Shares unless
and until all accrued and unpaid dividends on the Convertible Preferred Stock,
including the full dividend for the then-current quarterly dividend period,
shall have been paid or declared and set apart for payment without interest.

         (c)     If at any time the Company issues any class or series of
capital stock ranking senior and prior to the Convertible Preferred Stock with
respect to the payment of dividends ("SENIOR DIVIDEND SHARES") and fails to pay
or declare and set apart for payment all accrued and unpaid dividends on such
Senior Dividend Shares, then (except to the extent allowed by the terms of the
Senior Dividend Shares) no dividend shall be paid or declared and set apart for
payment on the Convertible Preferred Stock unless and until all accrued and
unpaid dividends with respect to the Senior Dividend Shares, including the full
dividends for the then-current dividend period, shall have been paid or
declared and set apart for payment, without interest.  Except as provided in
Section 3(d) below, no dividends shall be paid or declared and set apart for
payment on any Parity Dividend Shares for any period unless the Company has
paid or declared and set apart for payment, or contemporaneously pays or
declares and sets apart for payment, on the Convertible Preferred Stock all
accrued and unpaid dividends for all dividend payment periods terminating on or
prior to the date of payment of such dividends.  Except as provided in Section
3(d) below, no dividends shall be paid or declared and set apart for payment on
the Convertible Preferred Stock for any period unless the Company has paid or
declared and set apart for payment, or contemporaneously pays or declares and
sets apart for payment, on any Parity Dividend Shares all accrued and unpaid
dividends for all dividend payment periods terminating on or prior to the date
of payment of such dividends.

         (d)     If at any time the Company has failed to pay accrued dividends
on any shares of the Convertible Preferred Stock on any Dividend Payment Date
or on any Parity Dividend Shares on a stated payment date, as the case may be,
the Company shall not:

                          (i)   purchase any shares of the Convertible
                 Preferred Stock or Parity Dividend Shares (except for a
                 consideration payable in Common Shares or Junior Dividend
                 Shares) or redeem fewer than all of the shares of the
                 Convertible Preferred Stock and Parity





                                       3
<PAGE>   4
                 Dividend Shares then outstanding except for the repurchase or
                 redemption made pro rata with respect to all shares of the
                 Convertible Preferred Stock and Parity Dividend Shares then
                 outstanding so that the amounts repurchased or redeemed shall
                 in all cases bear to each other the same ratio that, at the
                 time of the repurchase or redemption, the required redemption
                 payments on the shares of the Convertible Preferred Stock and
                 the other Parity Dividend Shares then outstanding,
                 respectively, bear to each other; or

                         (ii)   permit any corporation or other entity directly
                 or indirectly controlled by the Company to purchase any Common
                 Shares, Junior Dividend Shares, shares of the Convertible
                 Preferred Stock or Parity Dividend Shares, except to the same
                 extent that the Company could purchase such shares.

                 Unless and until all dividends accrued but unpaid in respect
of prior dividend payment periods on shares of the Convertible Preferred Stock
and any Parity Dividend Shares at the time outstanding have been paid in full
or a sum sufficient for such payment is declared and set apart, as provided in
the preceding paragraph, all dividends accrued upon shares of the Convertible
Preferred Stock or Parity Dividend Shares shall be declared pro rata with
respect to all shares of the Convertible Preferred Stock and Parity Dividend
Shares then outstanding, so that the amounts of any dividends declared on
shares of the Convertible Preferred Stock and on the Parity Dividend Shares
shall in all cases bear to each other the same ratio that, at the time of the
declaration, all accrued but unpaid dividends in respect of prior dividend
payment periods on shares of the Convertible Preferred Stock and the other
Parity Dividend Shares, respectively, bear to each other.





                                       4
<PAGE>   5
          4.   Optional Redemptions for Cash. (a) Shares of the Convertible
Preferred Stock shall not be redeemable prior to June 16, 1999. Thereafter,
subject to the restrictions in Section 3 above, shares of the Convertible
Preferred Stock may be redeemed by the Company, in whole or in part, at the
option of the Company at the following redemption prices (expressed as
percentages of the liquidation preference thereof) per share if redeemed during
the 12-month period beginning June 15 in the year indicated below (June 16, in
the case of 1999):


<TABLE>
<CAPTION>
--------------------------------------------------------------------------------
 YEAR         PERCENTAGE                           YEAR               PERCENTAGE
--------------------------------------------------------------------------------
 <S>            <C>                                <C>
 1999  . . . .  104.8%                             2003  . . . . . . .  102.4%
                                                                              
 2000  . . . .  104.2%                             2004  . . . . . . .  101.8%
                                                                              
 2001  . . . .  103.6%                             2005  . . . . . . .  101.2%
                                                                              
 2002  . . . .  103.0%                             2006  . . . . . . .  100.6%
                                      
                                                   2007 and thereafter  100.0%
                                                                          
</TABLE>

plus, in each case, an amount equal to the dividends accrued and unpaid
thereon, whether or not declared, to the redemption date ("OPTIONAL REDEMPTION
PRICE").

         Notwithstanding the foregoing, the Company may not redeem any shares
of Convertible Preferred Stock on or prior to June 15, 2000, unless the last
reported Sale Price (as defined in Section 6(c)) of the Company's Class A
Common Stock, par value $.01 per share (the "CLASS A COMMON STOCK"), in its
principal trading market for any 20 trading days within a period of 30
consecutive trading days ending not more than 15 days prior to the date of the
notice of redemption is at least 150% of the Conversion Price (as defined in
Section 6(a)) then in effect.

         (b)     Not less than 15 nor more than 60 days (such date as fixed by
the Board of Directors of the Company referred to herein as the "REDEMPTION
RECORD DATE") prior to the date fixed for any redemption of shares of the
Convertible Preferred Stock pursuant to this Section 4, a notice specifying the
time and place of the redemption and the number of shares of Convertible
Preferred Stock to be redeemed shall be given by first class mail, postage
prepaid, to the holders of record on the Redemption Record Date of the shares
of the Convertible Preferred Stock to be redeemed at their respective addresses
as the same shall appear on the books of the Company, calling upon each holder
of record to surrender to the Company on the redemption date at the





                                       5
<PAGE>   6
place designated in the notice such holder's certificate or certificates
representing the number of shares specified in the notice of redemption.
Neither failure to mail such notice, nor any defect therein or in the mailing
thereof, to any particular holder shall affect the sufficiency of the notice or
the validity of the proceedings for redemption with respect to the other
holders. Any notice mailed in the manner herein provided shall be conclusively
presumed to have been duly given whether or not the holder receives the notice.
On or after the redemption date, each holder of shares of Convertible Preferred
Stock to be redeemed shall present and surrender such holder's certificate or
certificates for such shares to the Company at the place designated in the
redemption notice and thereupon the Optional Redemption Price of the shares
shall be paid to or on the order of the person whose name appears on such
certificate or certificates as the owner thereof, and each surrendered
certificate shall be canceled. In case fewer than all the shares represented by
any such certificate are redeemed, a new certificate shall be issued
representing the unredeemed shares.

         (c)     If a notice of redemption has been given pursuant to this
Section 4 and if, on or before the redemption date, the funds necessary for
such redemption (including all dividends on the shares of Convertible Preferred
Stock to be redeemed that will accrue to but not including the redemption date)
shall have been set aside by the Company, separate and apart from its other
funds, in trust for the pro rata benefit of the holders of the shares so called
for redemption, then, notwithstanding that any certificates for such shares
have not been surrendered for cancellation, on the redemption date dividends
shall cease to accrue on the shares of the Convertible Preferred Stock to be
redeemed, and at the close of business on the date on which such funds have
been segregated and set aside by the Company as provided in this Section 4(c),
the holders of such shares shall cease to be stockholders with respect to those
shares, shall have no interest in or claims against the Company by virtue
thereof and shall have no voting or other rights with respect thereto, except
the conversion rights provided in Section 6 below and the right to receive the
moneys payable upon such redemption, without interest thereon, upon surrender
(and endorsement, if required by the Company) of their certificates, and the
shares evidenced thereby shall no longer be outstanding.  Subject to applicable
escheat laws, any moneys so set aside by the Company and unclaimed at the end
of two years from the redemption date shall revert to the general funds of the
Company, after which reversion the holders of such shares so called for
redemption shall look only to the general funds of the Company for the payment
of the Optional Redemption Price, without interest.  Any interest accrued on
funds so deposited shall belong to the Company and be paid thereto from time to
time.

         (d)     If a notice of redemption has been given pursuant to this
Section 4 and any holder of shares of Convertible Preferred Stock shall, prior
to the close of business on the redemption date, give written notice to the
Company pursuant to Section 6 below of the conversion of any or all of the
shares to be redeemed held by the holder (accompanied by a certificate or
certificates for such shares, duly endorsed or assigned





                                       6
<PAGE>   7
to the Company, and any necessary transfer tax payment, as required by Section
6 below), then such redemption shall not become effective as to such shares to
be converted and such conversion shall become effective as provided in Section
6 below, whereupon any funds deposited by the Company for the redemption of
such shares shall (subject to any right of the holder of such shares to receive
the dividend payable thereon as provided in Section 6 below) immediately upon
such conversion be returned to the Company or, if then held in trust by the
Company, shall automatically and without further corporate action or notice be
discharged from the trust.

         (e)     In every case of redemption of fewer than all of the
outstanding shares of the Convertible Preferred Stock pursuant to this Section
4, the shares to be redeemed shall be selected pro rata or by lot or in such
other manner as the Board of Directors of the Company may determine, as may be
prescribed by resolution of the Board of Directors of the Company, provided
that only whole shares of Convertible Preferred Stock shall be selected for
redemption.  In the event that any quarterly dividends payable on the
Convertible Preferred Stock are in arrears, the Company may not redeem less
than all of the outstanding shares of Convertible Preferred Stock until such
dividends in arrears have been paid in full.

          5.   Liquidation.  (a) The liquidation value of shares of Convertible
Preferred Stock, in case of the voluntary or involuntary liquidation,
dissolution or winding-up of the Company, shall be $50.00 per share, plus an
amount equal to the dividends accrued and unpaid thereon, whether or not
declared, to the payment date (the "LIQUIDATION VALUE").

         (b)     In the event of any voluntary or involuntary liquidation,
dissolution or winding-up of the Company, the holders of shares of Convertible
Preferred Stock (i) shall not be entitled to receive the Liquidation Value of
the shares held by them until payment in full or provision has been made for
the payment of all claims of creditors of the Company and the liquidation
preference of any class or series of capital stock ranking senior to the
Convertible Preferred Stock with respect to redemption rights and rights upon
liquidation, dissolution or winding-up of the affairs of the Company ("SENIOR
LIQUIDATION SHARES") shall have been paid in full and (ii) shall be entitled to
receive the Liquidation Value of such shares held by them in preference to and
in priority over any distributions upon the Common Shares and any other series
or class of the Company's capital stock that ranks junior to the Convertible
Preferred Stock as to redemption rights and rights upon liquidation,
dissolution or winding-up of the affairs of the Company ("JUNIOR LIQUIDATION
SHARES").  Upon payment in full of the Liquidation Value to which the holders
of shares of the Convertible Preferred Stock are entitled, the holders of
shares of the Convertible Preferred Stock will not be entitled to any further
participation in any distribution of assets by the Company.  Subject to clause
(i) above, if the assets of the Company are not sufficient to pay in full the
Liquidation Value payable to the holders of shares of the Convertible Preferred





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<PAGE>   8
Stock and the liquidation preference payable to the holders of any series or
class of the Company's capital stock, outstanding on the date hereof or
hereafter issued, that ranks on a parity with the Convertible Preferred Stock
as to redemption rights and rights upon liquidation, dissolution or winding-up
of the affairs of the Company ("PARITY LIQUIDATION SHARES"), the holders of all
such shares shall share ratably in accordance with the respective preferential
amounts payable on such shares in any distribution.

         (c)     Neither a consolidation or merger of the Company with or into
any other entity, nor a merger of any other entity with or into the Company,
nor a sale or transfer of all or any part of the Company's assets for cash,
securities or other property shall be considered a liquidation, dissolution or
winding-up of the Company within the meaning of this Section 5.

          6.   Conversion.  (a)  Holders of shares of Convertible Preferred
Stock will have the right, exercisable at any time, except in the case of
shares of Convertible Preferred Stock called for redemption (as described in
Section 4(d) above), to convert shares of Convertible Preferred Stock into
shares of Class A Common Stock at the conversion price of $50.00 per share of
Class A Common Stock, subject to adjustment as described below in Section 6(f)
(the "CONVERSION PRICE").  The number of shares of Class A Common Stock into
which a share of the Convertible Preferred Stock shall be convertible
(calculated as to each conversion to the nearest 1/100th of a share) shall be
determined by dividing $50.00 by the Conversion Price then in effect.  In the
case of shares of the Convertible Preferred Stock called for redemption,
conversion rights will expire at the close of business on the redemption date.
Certificates representing shares of the Convertible Preferred Stock surrendered
for conversion during the period between the close of business on any Dividend
Payment Record Date and the opening of business on any corresponding Dividend
Payment Date must be accompanied by payment of an amount equal to the dividend
payable on such shares on such Dividend Payment Date.  No such payment will be
required to accompany shares of the Convertible Preferred Stock called for
redemption and surrendered during the period between the close of business on
any Dividend Payment Record Date and the opening of business on any
corresponding Dividend Payment Date (it being the case that, except as may be
otherwise provided herein, any shares so redeemed shall not be entitled to
receive the dividend payable by the Company on such Dividend Payment Date).
Notwithstanding the foregoing, a holder of shares of the Convertible Preferred
Stock on a Dividend Payment Record Date who (or whose transferee) tenders any
such shares for conversion into shares of Class A Common Stock on the relevant
Dividend Payment Date shall be entitled to receive the dividend payable by the
Company on such shares of Convertible Preferred Stock on such Dividend Payment
Date, and the converting holder need not include payment of the amount of such
dividend upon surrender of shares of Convertible Preferred Stock for
conversion.  Except as provided in the immediately preceding sentence, no
payment or allowance for accrued dividends on the shares of Convertible
Preferred Stock is to be made on conversion.





                                       8
<PAGE>   9
         (b)     Any holder of shares of Convertible Preferred Stock electing
to convert the shares or any portion thereof in accordance with Section 6(a)
above shall deliver the certificates therefor and the dividend payment referred
to in Section 6(a) above, if applicable, to the principal office of any
transfer agent for the Class A Common Stock, with a form of conversion notice
fully completed and duly executed and, if required by Section 6(a) above,
accompanied by payment of an amount equal to the dividend payable on such
shares on the applicable Dividend Payment Date.  The conversion right with
respect to any shares of Convertible Preferred Stock shall be deemed to have
been exercised on the date upon which the certificates therefor and the
dividend payment referred to in Section 6(a) above, if applicable, with the
conversion notice duly executed (and the payment required by Section 6(d), if
applicable), shall have been so delivered and the person or persons entitled to
receive the Class A Common Stock issuable upon conversion shall be treated for
all purposes as the record holder or holders of such Class A Common Stock upon
that date.

         (c)     No fractional shares of Class A Common Stock or scrip
representing fractional shares shall be issued upon conversion of shares of
Convertible Preferred Stock.  If more than one share of Convertible Preferred
Stock shall be surrendered for conversion at one time by the same record
holder, the number of full shares of Class A Common Stock issuable upon
conversion thereof shall be computed on the basis of the aggregate number of
shares of Convertible Preferred Stock so surrendered.  Instead of any
fractional shares of Class A Common Stock otherwise issuable upon conversion of
any shares of Convertible Preferred Stock, the Company shall pay a cash
adjustment in respect of such fraction in an amount equal to the same fraction
of Sale Price (as defined below) of the Class A Common Stock at the close of
business on the day of conversion.  In the absence of a Sale Price, the Board
of Directors shall in good faith determine the current market price on such
basis as it considers appropriate and such current market price shall be used
to calculate the cash adjustment.  As used herein, "SALE PRICE" means the last
sale price of the Class A Common Stock (or if no sale price is reported, the
average of the high and low bid prices) as reported by the the principal
national or regional stock exchange on which the Class A Common Stock is listed
or, if the Class A Common Stock is not listed on a national or regional stock
exchange, as reported by the Nasdaq National Market or if the Class A Common
Stock is not approved for quotation and trading on the Nasdaq National Market
as reported by the National Quotation Bureau Incorporated.

         (d)     If a holder converts shares of Convertible Preferred Stock,
the Company shall pay any documentary, stamp or similar issue or transfer tax
due on the issue of Class A Common Stock upon the conversion or due upon the
issuance of a new certificate or certificates for any shares of Convertible
Preferred Stock not converted.  The holder, however, shall pay any such tax
that is due because any such





                                       9
<PAGE>   10
shares of the Class A Common Stock or of the Convertible Preferred Stock are
issued in a name other than the name of the holder.

         (e)     The Company shall reserve out of its authorized but unissued
Class A Common Stock or its Class A Common Stock held in treasury enough shares
of Class A Common Stock to permit the conversion of all of the then-outstanding
shares of Convertible Preferred Stock.  For the purposes of this Section 6(e),
the full number of shares of Class A Common Stock then issuable upon the
conversion of all then-outstanding shares of Convertible Preferred Stock shall
be computed as if at the time of computation all outstanding shares of
Convertible Preferred Stock were held by a single holder.  The Company shall
from time to time, in accordance with the laws of the State of Delaware and its
Certificate of Incorporation, increase the authorized amount of its Class A
Common Stock if at any time the authorized amount of its Class A Common Stock
remaining unissued shall not be sufficient to permit the conversion of all
shares of Convertible Preferred Stock at the time outstanding.  If any shares
of Class A Common Stock required to be reserved for issuance upon conversion of
shares of Convertible Preferred Stock hereunder require registration with or
approval of any governmental authority under any federal or state law before
the shares may be issued upon conversion, the Company will in good faith and as
expeditiously as possible endeavor to cause the shares to be so registered or
approved.  All shares of Class A Common Stock issued upon conversion of the
shares of Convertible Preferred Stock shall be validly issued, fully paid and
nonassessable.

         (f)     The Conversion Price shall be subject to adjustment as
follows:

                          (i)   In case the Company shall (A) pay a dividend on
                 any class of its capital stock in shares of its Common Stock
                 of any class, (B) subdivide its outstanding shares of Class A
                 Common Stock into a greater number of shares or (C) combine
                 its outstanding shares of Class A Common Stock into a smaller
                 number of shares, the Conversion Price in effect immediately
                 prior thereto shall be adjusted retroactively as provided
                 below so that the Conversion Price thereafter shall be
                 determined by multiplying the Conversion Price at which the
                 shares of Convertible Preferred Stock were theretofore
                 convertible by a fraction, the denominator of which  shall be
                 the number of shares of Class A Common Stock outstanding
                 immediately following such action and the numerator of which
                 shall be the number of shares of Class A Common Stock
                 outstanding immediately prior thereto.  Such adjustment shall
                 be made whenever any event listed above shall occur and shall
                 become effective retroactively immediately after the record
                 date in the case of a dividend and immediately after the
                 effective date in the case of a subdivision or combination.





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<PAGE>   11
                         (ii)   In case the Company shall issue rights or
                 warrants to all holders of its Class A Common Stock entitling
                 them (for a period expiring within 45 days after the record
                 date for determining stockholders entitled to receive such
                 rights or warrants) to subscribe for or purchase shares of its
                 Common Stock of any class at a price per share less than the
                 current market price per share of Class A Common Stock (as
                 determined in accordance with the provisions of Section
                 6(f)(iv) below) on the record date therefor (the "CURRENT
                 MARKET PRICE"), or in case the Company shall issue to all
                 holders of its Class A Common Stock other securities
                 convertible into or exchangeable for shares of its Common
                 Stock of any class for a consideration per share of Common
                 Stock deliverable upon conversion or exchange thereof less
                 than the Current Market Price, then the Conversion Price in
                 effect immediately prior thereto shall be adjusted as provided
                 below so that the Conversion Price therefor shall be equal to
                 the price determined by multiplying (A) the Conversion Price
                 at which shares of Convertible Preferred Stock were
                 theretofore convertible by (B) a fraction, the denominator of
                 which shall be the sum of (1) the number of shares of Common
                 Stock of all classes outstanding on the date of issuance of
                 the convertible or exchangeable securities, rights or warrants
                 and (2) the number of additional shares of Common Stock
                 offered for subscription or purchase, or issuable upon such
                 conversion or exchange, and the numerator of which shall be
                 the sum of (1) the number of shares of Common Stock of all
                 classes outstanding on the date of issuance of such
                 convertible or exchangeable securities, rights or warrants and
                 (2) the number of additional shares of Common Stock of all
                 classes which the aggregate offering price of the number of
                 shares of Common Stock so offered would purchase at the
                 Current Market Price per share of Class A Common Stock (as
                 determined in accordance with the provisions of Section
                 6(f)(iv) below).  Such adjustment shall be made whenever such
                 convertible or exchangeable securities, rights or warrants are
                 issued, and shall become effective immediately after the
                 record date for the determination of stockholders entitled to
                 receive such securities.  However, upon the expiration of any
                 right or warrant to purchase Common Stock, the issuance of
                 which resulted in an adjustment in the Conversion Price
                 pursuant to this Section 6(f)(ii), if any such right or
                 warrant shall expire and shall not have been exercised, the
                 Conversion Price shall be recomputed immediately upon such
                 expiration and effective immediately upon such expiration
                 shall be increased to the price it would have been (but
                 reflecting any other adjustments to the Conversion Price made
                 pursuant to the provisions of this Section 6(f) after the
                 issuance of such rights or warrants) had the





                                       11
<PAGE>   12
                 adjustment of the Conversion Price made upon the issuance of
                 such rights or warrants been made on the basis of offering for
                 subscription or purchase only that number of shares of Common
                 Stock actually purchased upon the exercise of such rights or
                 warrants.  No further adjustment shall be made upon exercise
                 of any right, warrant, convertible security or exchangeable
                 security if any adjustment shall have been made upon issuance
                 of such security.

                        (iii)   In case the Company shall pay a dividend to all
                 holders of its Class A Common Stock (including any dividend
                 paid in connection with a consolidation or merger in which the
                 Company is the continuing company) of any shares of capital
                 stock of the Company or its subsidiaries (other than its
                 Common Stock of any class) or evidences of its indebtedness or
                 assets (excluding cash dividends payable solely in cash that
                 may from time to time be fixed by the Board of Directors, or
                 dividends or distributions in connection with the liquidation,
                 dissolution or winding up of the Company) or rights or
                 warrants to subscribe for or purchase any of its securities or
                 those of its subsidiaries or securities convertible or
                 exchangeable for Common Stock (excluding those securities
                 referred to in Section 6(f)(ii) above), then in each such case
                 the Conversion Price in effect immediately prior thereto shall
                 be adjusted as provided below so that the Conversion Price
                 thereafter shall be equal to the price determined by
                 multiplying (A) the Conversion Price in effect on the record
                 date mentioned below by (B) a fraction, the numerator of which
                 shall be the Current Market Price per share of Class A Common
                 Stock on the record date mentioned below less the then fair
                 market value (as determined by the Board of Directors, whose
                 good faith determination shall be conclusive) as of such
                 record date of the assets, evidences of indebtedness or
                 securities so paid with respect to one share of Class A Common
                 Stock, and the denominator of which shall be the Current
                 Market Price per share of Class A Common Stock on such record
                 date; provided, however, that in the event the then fair
                 market value (as so determined) so paid with respect to one
                 share of Class A Common Stock is equal to or greater than the
                 Current Market Price per share of Class A Common Stock on the
                 record date mentioned above, in lieu of the foregoing
                 adjustment, adequate provision shall be made so that each
                 holder of shares of the Convertible Preferred Stock shall have
                 the right to receive the amount and kind of assets, evidences
                 of indebtedness, or securities such holder would have received
                 had such holder converted each such share of Convertible
                 Preferred Stock immediately prior to the record date for such
                 dividend. Such adjustment shall be made whenever any such
                 payment is made, and shall become





                                       12
<PAGE>   13
                 effective retroactively immediately after the record date for
                 the determination of stockholders entitled to receive the
                 payment.

                         (iv)   For the purpose of any computation under
                 Sections 6(f)(ii) and 6(f)(iii) above, the Current Market
                 Price per share of Class A Common Stock at any date shall be
                 deemed to be the average Sale Price for the 30 consecutive
                 trading days commencing 45 trading days before the day in
                 question.

                          (v)   No adjustment in the Conversion Price shall be
                 required unless the adjustment would require an increase or
                 decrease of at least 1% in the Conversion Price then in
                 effect; provided, however, that any adjustments that by reason
                 of this Section 6(f)(v) are not required to be made shall be
                 carried forward and taken into account in any subsequent
                 adjustment.  All calculations under this Section 6(f) shall be
                 made to the nearest cent or to the nearest 1/100th of a share,
                 as the case may be.

                         (vi)   In the event that, at any time as a result of
                 an adjustment made pursuant to Section 6(f)(i) or 6(f)(iii)
                 above, the holder of any share of Convertible Preferred Stock
                 thereafter surrendered for conversion shall become entitled to
                 receive any shares of the Company other than shares of the
                 Class A Common Stock, thereafter the number of such other
                 shares so receivable upon conversion of any share of
                 Convertible Preferred Stock shall be subject to adjustment
                 from time to time in a manner and on terms as nearly
                 equivalent as practicable to the provisions with respect to
                 the Class A Common Stock contained in Section 6(f)(i) through
                 6(f)(v) above, and the other provisions of this Section 6 with
                 respect to the Class A Common Stock shall apply on like terms
                 to any such other shares.

                        (vii)   Whenever the Conversion Price is adjusted, as
                 herein provided, the Company shall promptly file with the
                 transfer agent for the Convertible Preferred Stock a
                 certificate of an officer of the Company setting forth the
                 Conversion Price after the adjustment and setting forth a
                 brief statement of the facts requiring such adjustment and a
                 computation thereof.  The certificate shall be conclusive
                 evidence of the correctness of the adjustment.  The Company
                 shall promptly cause a notice of the adjusted Conversion Price
                 to be mailed to each registered holder of shares of
                 Convertible Preferred Stock.

                       (viii)   In the case of any reclassification of the
                 Class A Common Stock, any consolidation of the Company with,
                 or merger of the





                                       13
<PAGE>   14
                 Company into, any other entity, any merger of another entity
                 into the Company (other than a merger that does not result in
                 any reclassification, conversion, exchange or cancellation of
                 outstanding shares of Class A Common Stock of the Company),
                 any sale or transfer of all or substantially all of the assets
                 of the Company or any compulsory share exchange pursuant to
                 which share exchange the Class A Common Stock is converted
                 into other securities, cash or other property, then lawful
                 provision shall be made as part of the terms of such
                 transaction whereby the holder of each share of Convertible
                 Preferred Stock then outstanding shall have the right
                 thereafter, during the period such share of Convertible
                 Preferred Stock  shall be convertible, to convert such share
                 only into the kind and amount of securities, cash and other
                 property receivable upon the reclassification, consolidation,
                 merger, sale, transfer or share exchange by a holder of the
                 number of shares of Class A Common Stock of the Company into
                 which a share of Convertible Preferred Stock would have been
                 convertible immediately prior to the reclassification,
                 consolidation, merger, sale, transfer or share exchange.  The
                 Company, the person formed by the consolidation or resulting
                 from the merger or which acquires such assets or which
                 acquires the Company's shares, as the case may be, shall make
                 provisions in its certificate or articles of incorporation or
                 other constituent document to establish such rights.  The
                 certificate or articles of incorporation or other constituent
                 document shall provide for adjustments, which, for events
                 subsequent to the effective date of the certificate or
                 articles of incorporation or other constituent document, shall
                 be as nearly equivalent as may be practicable to the
                 adjustments provided for in this Section 6.  The provisions of
                 this Section 6(f)(viii) shall similarly apply to successive
                 reclassifications, consolidations, mergers, sales, transfers
                 or share exchanges.

                 (g)   The Company from time to time may reduce the Conversion
         Price by any amount for any period of time if (i) the period is at
         least 20 days, (ii) the Board has made a determination that such
         reduction would be in the best interests of the Company, which
         determination shall be conclusive and (iii)  the reduction is
         irrevocable during the period.  Whenever the Conversion Price is so
         reduced, the Company shall mail to holders of record of the
         Convertible Preferred Stock a notice of the reduction at least 15 days
         before the date the reduced Conversion Price takes effect, stating the
         reduced Conversion Price and the period it will be in effect.  A
         voluntary reduction of the Conversion Price does not change or adjust
         the Conversion Price otherwise in effect for purposes of paragraph
         6(f) above.





                                       14
<PAGE>   15
          7.   Status of Shares.  All shares of the Convertible Preferred Stock
that are at any time redeemed pursuant to Section 4 above or converted pursuant
to Section 6 above, or exchanged pursuant to Section 10 below, and all shares
of the Convertible Preferred Stock that are otherwise reacquired by the Company
and subsequently canceled by the Board of Directors of the Company shall have
the status of authorized but unissued shares of Preferred Stock, without
designation as to series, subject to reissuance by the Board of Directors of
the Company as shares of any one or more other series.

          8.   Voting Rights.  Except as set forth below or otherwise required
by law, holders of shares of the Convertible Preferred Stock shall have no
voting rights.  In connection with any right to vote, each holder of shares of
Convertible Preferred Stock will have one vote for each share held except that
shares held by the Company or any entity controlled by the Company shall have
no voting rights.

                 (a)   Dividend Defaults.

                          (i)   Whenever, at any time or times, dividends
                 payable on the shares of Convertible Preferred Stock at the
                 time outstanding shall be in arrears in an aggregate amount
                 equal to at least six quarterly dividend payments (whether or
                 not consecutive), the holders of shares of Convertible
                 Preferred Stock shall have the right, voting separately as a
                 class with holders of Parity Dividend Shares to the extent
                 such Parity Dividend Shares have such voting rights (the
                 shares of Convertible Preferred Stock and any such other
                 Parity Dividend Shares, collectively for purposes of this
                 Section 8, the "DEFAULTED PREFERRED STOCK"), to elect two
                 directors of the Company at the Company's next annual meeting
                 of stockholders and at each subsequent annual meeting of
                 stockholders; provided, however, that if such voting rights
                 shall become vested more than 90 days or less than 20 days
                 before the date prescribed for the annual meeting of
                 stockholders the holders of the shares of Defaulted Preferred
                 Stock shall be entitled to exercise their voting rights at a
                 special meeting of the holders of shares of Defaulted
                 Preferred Stock as set forth in Section 8(a)(ii) hereof.  At
                 elections for such directors, each holder of shares of
                 Convertible Preferred Stock shall be entitled to one vote for
                 each share held (the holders of any Parity Preferred Stock
                 being entitled to such number of votes, if any, for each share
                 of stock held as may be granted to them).  Upon the vesting of
                 such voting rights, the maximum authorized number of members
                 of the Board of Directors of the Company shall automatically
                 be increased by two and the two vacancies so created shall be
                 filled by





                                       15
<PAGE>   16
                 vote of the holders of outstanding Defaulted Preferred Stock
                 as herein set forth.  The right of holders of Defaulted
                 Preferred Stock, voting separately as a class without regard
                 to series, to elect members of the Board of Directors of the
                 Company as aforesaid shall continue until such time as all
                 dividends accumulated on Defaulted Preferred Stock shall have
                 been paid in full or declared and set aside for payment in
                 full, at which time such right immediately shall terminate
                 subject to revesting in the event of each and every subsequent
                 default of the character above mentioned.

                         (ii)   At any time when such voting right shall have
                 vested in the holders of shares of Defaulted Preferred Stock
                 entitled to vote thereon, and if such right shall not already
                 have been initially exercised, an officer of the Company
                 shall, upon the written request of holders of record of 10% of
                 the voting power represented by the shares of such Defaulted
                 Preferred Stock then outstanding, addressed to the Secretary
                 of the Company, call a special meeting of holders of shares of
                 such Defaulted Preferred Stock.  Such meeting shall be held at
                 the earliest practicable date upon the notice required for
                 annual meetings of stockholders at the place for holding
                 annual meetings of stockholders of the Company or, if none, at
                 a place designated by the Secretary of the Company.  If such
                 meeting shall not be called by the proper officers of the
                 Company within 30 days after the personal service of such
                 written request upon the Secretary of the Company, or within
                 30 days after mailing the same within the United States, by
                 registered mail, addressed to the Secretary of the Company at
                 its principal office (such mailing to be evidenced by the
                 registry receipt issued by the postal authorities), then the
                 holders of record of 10% of the voting power represented by
                 the shares of Defaulted Preferred Stock then outstanding may
                 designate in writing any person to call such meeting at the
                 expense of the Company, and such meeting may be called by such
                 person so designated upon the notice required for annual
                 meetings of stockholders and shall be held at the same place
                 as is elsewhere provided in this Section.  Any holder of
                 shares of Defaulted Preferred Stock then outstanding that
                 would be entitled to vote at such meeting shall have access to
                 the stock books of the Company for the purpose of causing a
                 meeting of stockholders to be called pursuant to the
                 provisions of this Section.  Notwithstanding the provisions of
                 this Section, however, no such special meeting shall be called
                 or held during a period within 45 days immediately preceding
                 the date fixed for the next annual meeting of stockholders.





                                       16
<PAGE>   17
                        (iii)   So long as any shares of Convertible Preferred
                 Stock are outstanding, the By-laws of the Company shall
                 contain no provisions that would restrict the exercise, by the
                 holders of Defaulted Preferred Stock, of the right to elect
                 directors under the circumstances provided in Section 8(a)(i)
                 above.

                         (iv)   Directors elected pursuant to Section 8(a)(i)
                 shall serve until the earlier of (A) the next annual meeting
                 of the stockholders of the Company and the election (by the
                 holders of Defaulted Preferred Stock) and qualification of
                 their respective successors or (B) the date upon which all
                 dividends accumulated  on the Defaulted Preferred Stock shall
                 have been paid in full or declared and set apart for payment.
                 If, prior to the end of the term of any director elected as
                 aforesaid, a vacancy in the office of that director shall
                 occur during the continuation of a default in dividends on the
                 shares of the Convertible Preferred Stock or such Parity
                 Dividend Shares by reason of death, resignation or disability,
                 the vacancy shall be filled for the unexpired term by the
                 appointment by the remaining director elected as aforesaid of
                 a new director for the unexpired term of the former director.

                 (b)   Miscellaneous.  Without the affirmative vote or consent
         of the holders of at least 66 2/3% of the outstanding shares of the
         Convertible Preferred Stock and outstanding Parity Dividend Shares,
         voting as a single class (or, if less than all shares of the
         Convertible Preferred Stock or Parity Dividend Shares then outstanding
         would be adversely affected thereby, without the affirmative vote of
         the holders of at least 66 2/3% of the outstanding shares of each
         series so affected, voting as a separate class), the Company may not:

                          (i)   amend, alter or repeal (by merger or otherwise)
                 any provision of the Company's Certificate of Incorporation or
                 this Certificate or the By-laws of the Company so as to
                 adversely affect the relative rights, preferences,
                 qualifications, limitations or restrictions of the shares of
                 the Convertible Preferred Stock; or

                         (ii)   effect any reclassification of the shares of
                 the Convertible Preferred Stock.

         The above notwithstanding, the Company's Certificate of Incorporation
may be amended (i) to increase or decrease the number of authorized shares of
Preferred Stock (but not below the number of shares thereof then outstanding)
by the affirmative vote of the holders of a majority of the stock of the
Company entitled to vote thereon or (ii) to authorize any other class or series
of capital stock of the Company, regardless





                                       17
<PAGE>   18
of the relative rights, preferences, qualifications, limitations or
restrictions thereof, including an amendment to increase the authorized number
of shares of Common Stock or Preferred Stock of the Company without the vote of
the holders of shares of the Convertible Preferred Stock.

          9.   Change of Control.  If there occurs a Change in Control (as
defined below) with respect to the Company, then shares of the Convertible
Preferred Stock may be converted (the "SPECIAL CONVERSION RIGHTS"), at the
option of the holder thereof, in whole or in part,  at any time from the date
of such Change in Control until the expiration of 45 days after the date of the
Conversion Notice (as defined below) (the "EXPIRATION DATE"), into the number
of shares of Class A Common Stock determined by dividing (i) the Optional
Redemption Price for the Convertible Preferred Stock in effect on the date of
the Change in Control by (ii) the Special Conversion Price.  The "SPECIAL
CONVERSION PRICE" is the greater of (i) the average of the Sale Prices per
share of the Class A Common Stock for the last five trading days before the
Change in Control and (ii)  66 2/3% of the Sale Price (adjusted for any stock
splits or combinations) of the Class A Common Stock on June 10, 1997.  If the
Change in Control occurs prior to June 16, 1999, the Optional Redemption Price
then in effect shall, solely for purposes of the Special Conversion Rights, be
deemed to be the Optional Redemption Price applicable on June 16, 1999.  The
Special Conversion Rights will exist upon the occurrence of any Change in
Control whether or not the transaction relating thereto is approved by the
Board of Directors of the Company and may not be waived by the Board of
Directors.

         The Company may, at its option, out of funds legally available
therefor, elect to pay the holders of the Convertible Preferred Stock
exercising their Special Conversion Rights (the "CONVERTING HOLDERS") an amount
in cash equal to 101% of the liquidation preference of the Convertible
Preferred Stock, plus any accrued and unpaid dividends (the "CONVERTING HOLDERS
PAYMENT").

         Any holder of shares of Convertible Preferred Stock electing to
exercise the Special Conversion Rights in accordance with this Section 9 shall,
not later than the close of business on the fifth day prior to the Expiration
Date, deliver the certificates therefor and the dividend payment referred to in
Section 6(a), if applicable, to the principal office of any transfer agent for
the Class A Common Stock, with a form of conversion notice fully completed and
duly executed and the payment, if any, required by Section 6(d).  Unless the
Company elects to pay the Converting Holders the Converting Holders Payment,
the Special Conversion Right with respect to any shares of Convertible
Preferred Stock shall be deemed to have been exercised on the Expiration Date
so long as the certificates therefor and the dividend payment referred to in
Section 6(a), if applicable, with the notice of exercise of the Special
Conversion Rights duly executed (and the payment required by Section 6(d), if
applicable), shall have been so delivered and the person or persons entitled to
receive the Class A





                                       18
<PAGE>   19
Common Stock issuable upon conversion shall be treated for all purposes as the
record holder or holders of such Class A Common Stock on the Expiration Date.

         Within five days after the occurrence of a Change in Control, the
Company shall give notice of the occurrence of the Change in Control and of the
Special Conversion Rights set forth herein in accordance with the procedures
set forth below to each holder of a share of the Convertible Preferred Stock
(the "CONVERSION NOTICE").

         Each Conversion Notice shall state:

                 (1)   that a Change in Control has occurred (and shall specify
         the date of occurrence), the circumstances and relevant facts
         regarding such Change in Control and that the holder's Special
         Conversion Rights may be exercised in accordance with this Section;

                 (2)   the Expiration Date of the Special Conversion Rights;

                 (3)   that a holder of a share of the Convertible Preferred
         Stock to exercise the Special Conversion Rights must deliver on or
         before the fifth day prior to the Expiration Date of the Special
         Conversion Rights written notice to the Company of the holder's
         exercise of such option, together with the certificate evidencing such
         holder's shares with respect to which the option is being exercised,
         duly endorsed for transfer and the dividend payment, if any, required
         by Section 6(a) hereof and the payment required by Section 6(d), if
         applicable;

                 (4)   the applicable Special Conversion Price and the
         Conversion Price;

                 (5)   a description of the procedure which a holder must
         follow to exercise its Special Conversion Rights;

                 (6)   that holders of shares of the Convertible Preferred
         Stock electing to have such shares converted will be required to
         surrender the certificates evidencing such shares for delivery of
         shares of Class A Common Stock;

                 (7)   that any shares of Convertible Preferred Stock not
         tendered for conversion will continue to accrue dividends and that
         holders whose shares of Convertible Preferred Stock are converted only
         in part will be issued a new certificate representing the unconverted
         shares of Convertible Preferred Stock; and





                                       19
<PAGE>   20
                 (8)   that the Company may, at its option, elect to pay all
         Converting Holders the Converting Holders Payment and if the Company
         elects to pay the Converting Holders Payment, all Converting Holders
         shall receive the Converting Holders Payment in lieu of shares of
         Class A Common Stock.

         The Conversion Notice shall be given by first class mail, postage
paid, to the holders of record of the shares of the Convertible Preferred Stock
at their respective addresses as the same shall appear on the books of the
Company.

         No failure of the Company to give the foregoing Conversion Notice
shall limit any holder's right to exercise its Special Conversion Rights.

         Exercise of the Special Conversion Rights by the holder of a share of
Convertible Preferred Stock will be irrevocable.  The Company shall not enter
into any consolidation, merger or sale of assets, unless in connection
therewith, the holders of Convertible Preferred Stock exercising their Special
Conversion Rights will be entitled to receive the same consideration as
received for the number of shares of Class A Comnmon Stock into which their
shares of Convertible Preferred Stock would have been converted pursuant to the
Special Conversion Rights.  The Special Conversion Rights are in addition to
the regular conversion rights that apply to the Convertible Preferred Stock.

         The Company will comply with any securities laws and regulations, to
the extent such laws and regulations are applicable to the conversion of the
Convertible Preferred Stock in connection with exercise of the Special
Conversion Rights by the holders of the Convertible Preferred Stock.

         If the Company elects to pay the Converting Holders the Converting
Holders Payment, then on  the Expiration Date (other than as may be required by
law), payment (in cash) of the Converting Holders Payment shall be made to the
Converting Holders.

         "Chancellor Merger Agreement" means the Agreement and Plan of Merger
dated February 19, 1997 among the Company, Chancellor Broadcasting Company, a
Delaware corporation, and Chancellor Radio Broadcasting Company, a Delaware
corporation, as the same may be amended or amended and restated  from time to
time.

         "Change in Control" means the occurrence of one or more of the
following events: (i) any sale, lease, exchange or other transfer (in one
transaction or a series of related transactions) of all or substantially all of
the assets of the Company to any Person (as defined below) or group of related
Persons for





                                       20
<PAGE>   21
purposes of Section 13(d) of the Securities Exchange Act of 1934, as amended (a
"Group"), other than to the Permitted Holders (as defined below); or (ii) a
majority of the Board shall consist of Persons who are not Continuing Directors
(as defined below); or (iii) the acquisition by any Person or Group (other than
the Permitted Holders) of the power, directly or indirectly, to vote or direct
the voting of securities having more than 50% of the ordinary voting power for
the election of directors of the Company.

         "Continuing Director" means, as of the date of determination, any
Person who (i) was a member of the Board on June 10, 1997 or who becomes a
director upon consummation of the merger contemplated by the Chancellor Merger
Agreement, (ii) was nominated for election or elected to the with the
affirmative vote of a majority of the Continuing Directors who were members of
the Board at the time of such nomination or election, or (iii) is a
representative of a Permitted Holder.

         "Permitted Holders" means (i) if the merger contemplated by the
Chancellor Merger Agreement is not consummated, Scott K. Ginsburg and (ii) if
the merger contemplated by the Chancellor Merger Agreement is consummated, from
and after the effective date thereof, Scott K. Ginsburg, Hicks, Muse, Tate and
Furst, Incorporated or any of its affiliates, officers and directors, or Steven
Dinetz.

         "Person" means an individual, partnership, corporation, limited
liability company, unincorporated organization, trust or joint venture, or a
governmental agency or political subdivision thereof.

         10.   Exchange Provisions.   (a) Shares of Convertible Preferred Stock
will be exchangeable at the option of the Company, out of funds legally
available therefor, in whole but not in part, on any March 15, June 15,
September 15 or December 15 commencing September 15, 2000 (a "DEBENTURE EXHANGE
DATE"), through the issuance of the Company's 6% Convertible Subordinated
Debentures due 2012 (the "EXCHANGE DEBENTURES") in redemption of and in
exchange for shares of Convertible Preferred Stock, in the manner provided in
this Section 10.  The Exchange Debentures will be subject to the terms and
conditions of an indenture (the "INDENTURE") between the Company and The Bank
of New York, as Trustee in substantially the form attached hereto as Exhibit A.

         (b)     Holders of the Convertible Preferred Stock will be entitled to
receive Exchange Debentures at the rate of $50.00 principal amount of Exchange
Debentures for each share of Convertible Preferred Stock.  Such exchange may be
made only if, at the time of the exchange there shall be no dividend arrearage
(including the dividend payable on the date of exchange) on the shares of the





                                       21
<PAGE>   22
Convertible Preferred Stock and no Event of Default (as defined in the
Indenture) under the Indenture shall have occurred and be continuing.  Exchange
Debentures will only be issued in denominations of $1,000 or any multiple
thereof and holders of the Convertible Preferred Stock holding less than such a
multiple will receive in cash the liquidation preference of Convertible
Preferred Stock not so exchanged.

         (c)     The Company will mail notice of its intention to redeem
through such an exchange to each holder of record of the Convertible Preferred
Stock not less than 60 days before the Debenture Exchange Date.  Such notice
shall be given by first class mail, postage prepaid, to the holders of record
of shares of the Convertible Preferred Stock at their respective addresses as
the same shall appear on the books of the Company, specifying the Debenture
Exchange Date and the place where certificates for shares of the Convertible
Preferred Stock are to be surrendered for Exchange Debentures and stating that
dividends on shares of the Convertible Preferred Stock will cease to accrue on
the Debenture Exchange Date, but neither failure to mail such notice, nor any
defect therein or in the mailing thereof, to any particular holder shall affect
the sufficiency of the notice or the validity of the proceedings for redemption
and exchange with respect to the other holders.  Any notice which was mailed in
the manner herein provided shall be conclusively presumed to have been duly
given whether or not the holder receives the notice.  If the notice of exchange
has been given pursuant to this Section 10(c) then (unless the Company defaults
in issuing Exchange Debentures in redemption of and in exchange for the
Convertible Preferred Stock or fails to pay or set aside accrued and unpaid
dividends on the Convertible Preferred Stock as set forth in Section 10 (d)
hereof and notwithstanding that any certificates for shares of the Convertible
Preferred Stock have not been surrendered for exchange) on the Debenture
Exchange Date the holders of the Convertible Preferred Stock will cease to the
stockholders with respect to such shares and will have no interests in or
claims against the Company by virtue thereof (except the right to receive
Exchange Debentures in exchange therefor and accrued and unpaid dividends
thereon to the Debenture Exchange Date) and will have no voting, conversion or
other rights with respect to such shares, and the shares of Convertible
Preferred Stock will no longer be outstanding.

         Upon the surrender (and endorsement, if required by the Company) in
accordance with such notice of the certificates for shares of the Convertible
Preferred Stock, such certificates shall be exchanged for Exchange Debentures
and such accrued and unpaid dividends in accordance with this Section 10(c).
Notwithstanding the foregoing, if notice of redemption and exchange has been
given pursuant ot this Section 10(c) and any holder of shares of the
Convertible Preferred Stock shall, prior to the close of business on the fifth
day preceding the Debenture Exchange





                                       22
<PAGE>   23
Date, given written notice to the Company pursuant to Section 6 hereof of the
conversion into Class A Common Stock of any or all of the shares to be redeemed
and exchanged held by such holder (accompanied by a certificate or certificates
for such shares, duly endorsed or assigned to the Company, and any necessary
transfer tax payment, as required by Section 6 hereof), then such redemption
and exchange shall not become effective as provided in Section 6 hereof and any
funds which have been deposited by the Company, or on its behalf, with a paying
agent or segregated and held in trust by the Company for the redemption and
exchange of such shares shall (subject to any right of the holder of such
shares to receive the dividend payable thereon as provided in Section 6 hereof)
immediately upon such conversion be returned to the Company or, if then held in
trust by the Company, shall be discharged from such trust.

         (d)     No shares of Convertible Preferred Stock may be exchanged for
Exchange Debentures unless the Company has paid or set aside for the benefit of
the holders of the Convertible Preferred Stock all accrued and unpaid dividends
on the Convertible Preferred Stock to the Debenture Exchange Date.

         11.   Mandatory Redemption.  The shares of the Convertible Preferred
Stock are not subject to mandatory redemption or sinking fund requirements.

         12.   Certain Definitions.  As used in this Certificate, the following
terms shall have the following respective meanings:

         "COMMON SHARES" shall mean any stock of the Company which has no
preference in respect of dividends or of amounts payable in the event of any
voluntary or involuntary liquidation, dissolution or winding-up of the Company
and which is not subject to redemption by the Company.  Unless the context
otherwise specifies or requires, all references in this certificate to "COMMON
SHARES" include the Common Stock.





                                       23
<PAGE>   24

         IN WITNESS WHEREOF, the Company has caused this Certificate to be duly
executed on its behalf of its undersigned duly authorized officer this 13th day
of June 1997.



EVERGREEN MEDIA CORPORATION



By:
   ----------------------------------
   Name:  Matthew E. Devine
   Title: Senior Vice President and 
          Chief Financial Officer





                                       24
