<PAGE>
                                                                    EXHIBIT 10.4

THIS WARRANT AND THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED
UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR UNDER THE SECURITIES OR BLUE
SKY LAWS OF ANY STATE AND MAY NOT BE SOLD, OR OTHERWISE TRANSFERRED, IN THE
ABSENCE OF SUCH REGISTRATION OR AN EXEMPTION THEREFROM UNDER SUCH ACT AND UNDER
ANY SUCH APPLICABLE STATE LAWS, OR IN VIOLATION OF THE PROVISIONS OF THIS
WARRANT.

<TABLE>
<S>                                                   <C>
Number of Shares of Class A Common Stock: 100,000     Date of Issuance: March 31, 2003
</TABLE>


                                     WARRANT

                        TO PURCHASE CLASS A COMMON STOCK

                                       OF

                        SPANISH BROADCASTING SYSTEM, INC.

                            VOID AFTER MARCH 31, 2006

         THIS IS TO CERTIFY THAT, for value received, International Church of
the FourSquare Gospel (the "Holder") is entitled, subject to the terms and
conditions set forth herein, to purchase from Spanish Broadcasting System, Inc.
(the "Company") 100,000 shares of the Company's Class A Common Stock, par value
$0.0001 per share (the "Class A Common Stock"). The number, character and
Exercise Price (defined below) of such shares of Class A Common Stock are
subject to adjustment as provided herein. The term "Warrant" as used herein
shall include this Warrant and any warrants delivered in substitution,
replacement or exchange therefor as provided herein.

         This Warrant is issued pursuant to that certain Amendment No. 1 dated
as of February 8, 2002 to Time Brokerage Agreement dated as of March 13, 2001,
by and between Holder, as Licensee, and the Company, as Broker.


         1.       TERM OF WARRANT. Subject to the terms and conditions set forth
herein, this Warrant shall be exercisable, in whole only and not in part,
during the term commencing on the date hereof and ending at 5:00 p.m.,
prevailing local time in New York, New York, on March 31, 2006, and shall be
void thereafter.

         2.       EXERCISE PRICE. The price at which this Warrant may be
exercised shall be $6.14 per share of Class A Common Stock, as adjusted from
time to time pursuant to Section 9 hereof (the "Exercise Price").


                                       1
<PAGE>
         3.       EXERCISE OF WARRANT.

                  (a)      The purchase right represented by this Warrant shall
be exercisable by the Holder, in whole only and not in part, at any time during
the term hereof upon (i) the surrender of this Warrant and the delivery of a
duly completed and executed Notice of Exercise (in the form of Exhibit A
attached hereto) at the principal office of the Company (listed as the
Company's address in Section 14 herein) or such other office or agency as the
Company may designate by notice pursuant to Section 14 herein, and (ii) payment
of the aggregate Exercise Price equal to the number of shares of Class A Common
Stock being purchased upon exercise of this Warrant multiplied by the Exercise
Price (the "Aggregate Exercise Price") in cash, by certified or official bank
check payable to the order of the Company, or by wire transfer to an account in
a bank designated for such purpose by the Company.

                  (b)      This Warrant shall be deemed to have been exercised
immediately prior to the close of business on the date of its surrender for
exercise and payment as provided above, and the person entitled to receive the
shares of Class A Common Stock issuable upon such exercise shall be treated for
all purposes as the holder of record of such shares as of the close of business
on such date. As promptly as practicable on or after such date, the Company
shall issue and deliver to the person entitled to receive the same, a
certificate for the number of shares of Class A Common Stock issuable upon such
exercise. If such certificate shall be registered in a name other than the name
of the Holder, then funds sufficient to pay all stock transfer taxes which
shall be payable upon the issuance of such certificate shall be paid by the
Holder at the time of exercise of this Warrant and the Company shall not be
required to issue or deliver any certificate until such tax or other charge has
been paid by the Holder.

                  (c)      Notwithstanding any provisions herein to the
contrary, if the Current Market Price (defined below) of one share of Class A
Common Stock is greater than the Exercise Price on the date of calculation, the
Holder shall have the right, at its election, in lieu of delivering the
Aggregate Exercise Price in cash, to instruct the Company in the Notice of
Exercise to retain, in payment of the Aggregate Exercise Price, the number of
shares of Class A Common Stock equal to the quotient of the Aggregate Exercise
Price divided by the Current Market Price. Upon exercise, the Holder shall then
receive the number of shares of Class A Common Stock computed using the
following formula:

                         X = Y(A-B)
                             ------
                             A

Where     X=       the number of shares of Class A Common Stock to be issued by
                   the Company to the Holder;

          Y=       the number of shares of Class A Common Stock purchasable
                   under the Warrant;

          A=       the Current Market Price of one share of the
                   Company's Class A Common Stock; and


                                       2
<PAGE>

          B=       the Exercise Price.

The "Current Market Price" shall mean the closing price per share of the Class A
Common Stock on the day immediately preceding the day as of which the Current
Market Price is being determined. The closing price shall be the last reported
sale price on the principal national securities exchange on which the shares are
listed or admitted to trading, or if the shares are not so listed or admitted to
trading, the last reported sale price as officially quoted on The Nasdaq Stock
Market or through a similar organization if The Nasdaq Stock Market is no longer
reporting such information. If shares of the Class A Common Stock are not listed
or admitted to trading on any exchange or quoted through The Nasdaq Stock Market
or any similar organization, the Current Market Price shall be determined in
good faith by the Company's Board of Directors.

         4.       NO FRACTIONAL SHARES OR SCRIP. No fractional shares or scrip
representing fractional shares shall be issued upon the exercise of this
Warrant. In lieu of any fractional share to which the Holder would otherwise be
entitled, the Company shall make a cash payment equal to the Current Market
Price of one share of Class A Common Stock multiplied by such fraction.

         5.       REPLACEMENT OF WARRANT. On receipt of evidence reasonably
satisfactory to the Company of the loss, theft, destruction or mutilation of
this Warrant and, in the case of loss, theft or destruction, on delivery of an
indemnity agreement reasonably satisfactory in form and substance to the Company
or, in the case of mutilation, on surrender and cancellation of this Warrant,
the Company shall execute and deliver, in lieu of this Warrant, a new warrant of
like tenor and equal amount.

         6.       NO RIGHTS AS STOCKHOLDER. This Warrant shall not entitle the
Holder to any rights as a stockholder of the Company.

         7.       WARRANT REGISTER. The Company shall maintain a register (the
"Warrant Register") containing the name and address of the Holder. The Company
may treat the Holder as shown on the Warrant Register as the absolute owner of
this Warrant for all purposes and shall not be affected by any notice to the
contrary.

         8.       RESERVATION OF STOCK. The Company covenants that during the
term that this Warrant is exercisable, the Company shall reserve from its
authorized and unissued Class A Common Stock a sufficient number of shares to
provide for the issuance of Class A Common Stock upon the exercise hereof.

         9.       ADJUSTMENTS. The Exercise Price and the number and type of
shares purchasable hereunder are subject to adjustment from time to time as
follows:

                  9.1      STOCK SPLIT, SUBDIVISION OR COMBINATION OF SHARES. If
         during the period that this Warrant remains outstanding and unexpired,
         the Company shall split or subdivide the securities as to which
         purchase rights exist under this Warrant into a different number of
         securities of the same class, the Exercise Price for such securities
         shall be proportionately


                                       3
<PAGE>

         decreased, and the number of shares of such securities for which this
         Warrant may be exercised shall be proportionately increased. If during
         the period that this Warrant remains outstanding and unexpired, the
         Company shall combine the securities as to which purchase rights exist
         under this Warrant into a different number of securities of the same
         class, the Exercise Price for such securities shall be proportionately
         increased and the number of shares of such securities for which this
         Warrant may be exercised shall be proportionately decreased.

                  9.2      ADJUSTMENTS FOR DIVIDENDS IN STOCK OR OTHER
         SECURITIES. If during the period that this Warrant remains outstanding
         and unexpired, the Company shall take a record of the holders of Class
         A Common Stock for the purpose of entitling them to receive a dividend,
         without payment therefor, payable in additional stock or other
         securities of the Company, then this Warrant shall represent the right
         to acquire, in addition to the number of shares of Class A Common Stock
         receivable upon exercise of this Warrant, the amount of such additional
         stock or other securities of the Company that the Holder would have
         received if the Holder had exercised this Warrant in full to purchase
         shares of Class A Common Stock and had been the record holder of such
         shares on the date that the Company took a record of the holders of
         Class A Common Stock for the purpose of entitling them to receive such
         dividend.

                  9.3      MERGER, SALE OF ASSETS, REORGANIZATION,
         RECLASSIFICATION. If during the period that this Warrant remains
         outstanding and unexpired, there shall be (i) a merger or consolidation
         of the Company with or into another corporation in which the Company is
         not the surviving entity and by which the shares of the Company's
         capital stock outstanding immediately prior to the merger are converted
         by virtue of the merger into other property, whether in the form of
         securities, cash, or otherwise, (ii) a sale or transfer of all or
         substantially all of the Company's properties and assets to any other
         person, or (iii) a capital reorganization or reclassification of the
         Class A Common Stock (other than a combination or subdivision of shares
         otherwise provided for herein), then, lawful provision shall be made so
         that, upon the basis and the terms and in the manner provided in this
         Warrant, the Holder, upon the exercise hereof at any time after the
         consummation of such event, shall be entitled to purchase, in lieu of
         the shares of Class A Common Stock for which this Warrant could have
         been exercised immediately prior to such consummation, the stock or
         other securities, cash or property which the Holder would have been
         entitled to receive upon such consummation if the Holder had exercised
         this Warrant for such shares of Class A Common Stock immediately prior
         thereto, subject to adjustment as nearly equivalent as possible to the
         adjustments provided for in this Section 9. If the per share
         consideration payable to the Holder in connection with any such event
         is in a form other than cash or marketable securities, then the value
         of such consideration shall be determined in good faith by the
         Company's Board of Directors. In all events, appropriate adjustment (as
         determined in good faith by the Company's Board of Directors) shall be
         made in the application of the provisions of this Warrant such that the
         Holder's rights and interest in this Warrant shall be applicable after
         such event, to the greatest extent possible, in relation to any shares
         or other property deliverable after that event upon exercise of this
         Warrant.


                                       4

<PAGE>

         10.      CERTIFICATES OF ADJUSTMENTS; NOTICES.

                  (a)      Whenever the Exercise Price or number or type of
         shares purchasable hereunder shall be adjusted or readjusted pursuant
         to Section 9 herein, the Company shall issue a certificate signed by
         its Chief Financial Officer setting forth, in reasonable detail, the
         event requiring the adjustment or readjustment, the amount of the
         adjustment or readjustment, the method by which such adjustment or
         readjustment was calculated, the Exercise Price and number of shares
         purchasable hereunder after giving effect to such adjustment or
         readjustment and the amount, if any, of other property to be received
         upon exercise of this Warrant after giving effect to such adjustment or
         readjustment. The Company shall deliver a copy of such certificate to
         the Holder in accordance with Section 14 herein.

                  (b)      In the event:

                           (i)      that the Company shall take a record of the
         holders of its Class A Common Stock (or other stock or securities at
         the time receivable upon the exercise of this Warrant) for the purpose
         of entitling them to receive any dividend in stock or other securities;
         or

                           (ii)     of any capital reorganization of the
         Company, any reclassification of the capital stock of the Company, any
         consolidation or merger of the Company with or into another
         corporation, or any conveyance of all or substantially all of the
         assets of the Company to another person; or

                           (iii)    of any voluntary dissolution, liquidation or
         winding-up of the Company,

then, and in each such case, the Company shall mail or cause to be mailed to the
Holder a notice specifying, as the case may be, (A) the date on which a record
is to be taken for the purpose of such dividend, and stating the amount and
character of such dividend, or (B) the date on which such reorganization,
reclassification, consolidation, merger, conveyance, dissolution, liquidation or
winding-up is to take place, and the date, if any is to be fixed, as of which
the holders of record of Class A Common Stock (or such other stock or securities
at the time receivable upon the exercise of this Warrant), shall be entitled to
exchange their shares of Class A Common Stock (or such other stock or securities
at the time receivable upon exercise of this Warrant), for securities or other
property deliverable upon such reorganization, reclassification, consolidation,
merger, conveyance, dissolution, liquidation or winding-up. Such notice shall be
mailed at least 15 days prior to the date therein specified for the occurrence
of any of the foregoing events.

         (c)      All notices pursuant to this Section 9 shall be given in the
manner set forth in Section 14 herein.


                                       5
<PAGE>

         11.      RESTRICTIVE LEGEND ON STOCK CERTIFICATE. A certificate for
shares issued upon exercise of this Warrant, unless at the time of exercise such
shares are registered under the Securities Act, shall bear a legend in
substantially the following form:

                  THE SHARES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN
                  REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR
                  UNDER THE SECURITIES OR BLUE SKY LAWS OF ANY STATE AND ARE
                  SUBJECT TO THE CONDITIONS SPECIFIED IN A CERTAIN WARRANT DATED
                  MARCH 31, 2003, BY AND BETWEEN SPANISH BROADCASTING SYSTEM,
                  INC. AND INTERNATIONAL CHURCH OF THE FOURSQUARE GOSPEL, COPIES
                  OF WHICH WARRANT ARE AVAILABLE FOR INSPECTION AT THE PRINCIPAL
                  OFFICE OF SPANISH BROADCASTING SYSTEM, INC. THE SHARES
                  REPRESENTED BY THIS CERTIFICATE MAY NOT BE SOLD, OR OTHERWISE
                  TRANSFERRED, IN THE ABSENCE OF SUCH REGISTRATION OR AN
                  EXEMPTION THEREFROM UNDER SUCH ACT AND UNDER ANY SUCH
                  APPLICABLE STATE LAWS, OR IN VIOLATION OF THE PROVISIONS OF
                  THE WARRANT. THE HOLDER OF THIS CERTIFICATE, BY ACCEPTANCE OF
                  THIS CERTIFICATE, AGREES TO BE BOUND BY THE PROVISIONS OF SUCH
                  WARRANT.

         12.      NO TRANSFER. This Warrant may not be transferred in whole or
in part.

         13.      AMENDMENTS. This Warrant may not be modified or amended
without the written consent of the Company and the Holder.

         14.      GOVERNING LAW. This Warrant shall be governed by and construed
in accordance with the laws of the State of Delaware.

         15.      NOTICES. All notices and other communications required or
permitted hereunder shall be in writing and shall be deemed to have been given
if (i) personally delivered by hand or by messenger, (ii) mailed by registered
or certified mail, postage prepaid and return receipt requested or (iii) sent by
a nationally recognized overnight courier service for next morning delivery. Any
such notice shall be deemed to have been received on the date of personal
delivery; on the fourth day after deposit in the U.S. mail if mailed by
registered or certified mail; and on the day after delivery to a nationally
recognized overnight courier service. Notices shall be addressed as follows (or
to such other address as a party requests by written notice):

         If to Holder, to:          International Church of the FourSquare
                                    Gospel 1910 W. Sunset Boulevard


                                      6
<PAGE>
                                    Los Angeles, CA 90026-0176
                                    Attention: Brent R. Morgan

         with a copy (which shall not constitute notice) to:

                                    Farrand Cooper, P.C.
                                    235 Montgomery Street, Suite 905
                                    San Francisco, CA 94104
                                    Attention: Stephen R. Farrand, Esq.

         If to the Company, to:

                                    Spanish Broadcasting System, Inc.
                                    2601 South Bayshore Drive, PH II
                                    Coconut Grove, Florida 33133
                                    Attention: Joseph A. Garcia

         with a copy (which shall not constitute notice) to:

                                    Kaye Scholer LLP
                                    425 Park Avenue
                                    New York, New York 10022-3598
                                    Attention: William E. Wallace, Jr., Esq.


         16.      SEVERABILITY. If any provision of this Warrant is held to be
prohibited by or invalid under applicable law, then such provision shall be
ineffective to the extent of such prohibition or invalidity, without
invalidating the remainder of such provision or the remaining provisions of this
Warrant.

         17.      HEADINGS. The headings used in this Warrant are for the
convenience of reference only and shall not, for any purpose, be deemed a part
of this Warrant.


                                       7
<PAGE>

         IN WITNESS WHEREOF, the Company has caused this Warrant to be duly
executed as of March 31, 2003 by its duly authorized officer and its corporate
seal to be impressed hereon and attested by its Secretary.

                                SPANISH BROADCASTING SYSTEM, INC.


                                By: /s/ Raul Alarcon, Jr.
                                   ------------------------------------------
                                    Name:  Raul Alarcon, Jr.
                                    Title: Chairman of the Board of Directors,
                                           Chief Executive Officer and President


Attest:

By: /s/ Joseph A. Garcia
   ---------------------------------------------------
      Name:  Joseph A. Garcia
      Title: Executive Vice President,
             Chief Financial Officer and Secretary


                                       8
<PAGE>
                                                                       EXHIBIT A


                               NOTICE OF EXERCISE


         The undersigned registered owner of the attached Warrant irrevocably
exercises the attached Warrant in full for the purchase of 100,000 shares of
Class A Common Stock of SPANISH BROADCASTING SYSTEM, INC. and herewith makes
payment therefor, all at the price and on the terms and conditions specified in
the attached Warrant, and requests that a certificate for the shares of Class A
Common Stock hereby purchased (and any securities or other property issuable
upon such exercise) be issued in the name of the undersigned and delivered to
the undersigned at the address below.

         In exercising the attached Warrant, the undersigned hereby confirms and
acknowledges that the shares of Class A Common Stock to be issued are being
acquired solely for the account of the undersigned and not as a nominee for any
other party, and for investment, and that the undersigned shall not offer, sell
or otherwise dispose of any such shares of Class A Common Stock except under
circumstances that will not result in a violation of the Securities Act of 1933,
as amended, or any state securities laws.


Dated:
      ----------------------------

                                     Signature:
                                               -----------------------------
                                               Registered Owner

                                               -----------------------------
                                               Print Name

                                               -----------------------------

                                               -----------------------------
                                               Address


                                       9