
<PAGE>   1
 
                                                                    EXHIBIT 12.1
 
                          EVERGREEN MEDIA CORPORATION
 
         COMPUTATION OF RATIO OF EARNINGS TO COMBINED FIXED CHARGES AND
                           PREFERRED STOCK DIVIDENDS
                                 (IN THOUSANDS)
 
<TABLE>
<CAPTION>
                                                                                                                           PRO
                                                                                                                          FORMA
                                                                                  ACTUAL      ACTUAL      PRO FORMA     COMBINED
                                                                                  QUARTER     QUARTER      COMBINED      QUARTER
                                          YEAR ENDED DECEMBER 31,                  ENDED       ENDED      YEAR ENDED      ENDED
                             -------------------------------------------------   MARCH 31,   MARCH 31,   DECEMBER 31,   MARCH 31,
                              1992       1993      1994      1995       1996       1996        1997          1996         1997
                             -------   --------   -------   -------   --------   ---------   ---------   ------------   ---------
<S>                          <C>       <C>        <C>       <C>       <C>        <C>         <C>         <C>            <C>
Earnings:
Income (loss) before income
  taxes....................  $(4,989)  $(20,749)  $    39   $(5,658)  $(19,090)  $(17,196)    $(7,320)    $(206,274)    $(59,358)
Fixed charges..............   11,030     15,086    15,252    20,854     40,461      9,515       8,889       224,092       56,126
Less: Dividends on
  preferred stock of
  subsidiary...............       --         --        --        --         --         --          --       (59,077)     (14,829)
                             -------   --------   -------   -------   --------   --------     -------     ---------     --------
Earnings as adjusted (A)...    6,041     (5,663)   15,291    15,196     21,371     (7,681)      1,569       (41,259)     (18,061)
                             =======   ========   =======   =======   ========   ========     =======     =========     ========
Fixed Charges:
  Interest expense.........   10,112     13,878    13,809    19,199     37,527      8,973       8,053       159,912       39,978
  Amortization of deferred
    financing costs........      398        728       712       631      1,113        158         295         1,113          279
  Dividends on preferred
    stock of
    subsidiary(1)..........       --         --        --        --         --         --          --        59,077       14,829
  Rents under leases
    representative of an
    interest factor(2).....      520        480       731     1,024      1,821        384         541         3,990        1,040
                             -------   --------   -------   -------   --------   --------     -------     ---------     --------
Fixed charges as
  adjusted.................   11,030     15,086    15,252    20,854     40,461      9,515       8,889       224,092       56,126
Preferred stock
  dividends(1).............    1,140      7,317     7,431     7,431      5,877      1,858          --        39,492        9,874
                             -------   --------   -------   -------   --------   --------     -------     ---------     --------
Total fixed charges and
  preferred stock dividends
  (B)......................   12,170     22,403    22,683    28,285     46,338     11,373       8,889       263,584       66,000
                             =======   ========   =======   =======   ========   ========     =======     =========     ========
Deficiency of earnings to
  combined fixed charges
  and preferred stock
  dividends (B) minus
  (A)......................  $ 6,129   $ 28,066   $ 7,392   $13,089   $ 24,967   $ 19,054     $ 7,320     $ 304,843     $ 84,061
</TABLE>
 
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(1) Represents pretax earnings required to cover preferred stock dividends.
 
(2) Management of Evergreen Media Corporation believes approximately one-third
    of rental and lease expense is representative of the interest component of
    rent expense.
