<PAGE>   1
                                                                    Exhibit 11.1

                     HORIZON MENTAL HEALTH MANAGEMENT, INC.

                       COMPUTATIONS OF EARNINGS PER SHARE
   
<TABLE>
<CAPTION>
Year Ended August 31,
In Thousands, Except per Share Amounts                         1994            1995              1996
                                                             -------          --------          -------
<S>                                                          <C>              <C>               <C>
SIMPLE

    Net income                                               $ 1,476          $  3,946          $ 5,564
    Average outstanding shares (2)                             3,123             4,142            5,393
                                                             -------          --------          -------
    Simple net income per share                              $  0.47          $   0.95          $  1.03
                                                             =======          ========          =======

PRIMARY

    Net income                                               $ 1,476          $  3,946          $ 5,564
    Average outstanding shares (2)                             3,123             4,142            5,393
    Common stock equivalents assuming                        
      exercise of stock options (2)                            1,061             1,021            1,132
                                                             -------          --------          -------
                                                             
Shares for primary                                             4,184             5,163            6,525
                                                             =======           =======          =======
                                                             
Primary net income per share (1)                             $  0.35           $  0.76          $  0.85
                                                             =======           =======          ========
                                                             
FULLY DILUTED                                                
                                                             
    Net income                                               $ 1,476           $ 3,946          $ 5,564
    Average outstanding shares (2)                             3,123             4,142            5,393
    Common stock equivalents assuming                        
      exercise of stock options (2)                            1,061             1,033            1,153
                                                             -------           -------          -------
                                                             
Shares for fully diluted                                       4,184             5,175            6,546
                                                             =======           =======          ========
                                                                                         
Fully diluted net income per share (1)                       $  0.35           $  0.76          $  0.85
                                                             =======           =======          =======
</TABLE>                                                     


(1) The calculations for primary and fully diluted net income per share are
    submitted in accordance with Regulation S-K Item 601(b)(11).

(2) The Board of Directors of the Company approved a three-for-two stock split
    effected in the form of a 50% stock dividend, pursuant to which one
    additional share of Common Stock of the Company was issued on January 31,
    1997 for every two shares of Common Stock held by stockholders of record at
    close of business on January 22, 1997.  Upon effecting the stock
    split/dividend, the stock options and their related exercise prices were
    adjusted proportionately.  Such stock split/dividend has been retroactively
    reflected herein in conjunction with the filing of this 10K-A.