<PAGE>   1


                                                                      EXHIBIT 11

                                CLECO CORPORATION
                   COMPUTATION OF NET INCOME PER COMMON SHARE
                    FOR THE THREE MONTHS ENDED SEPTEMBER 30,
                                   (Unaudited)

                                                     (In thousands, except share
                                                        and per share amounts)
<TABLE>
<CAPTION>

                                                      1998                1997
                                                 --------------      --------------
<S>                                              <C>                 <C>           
BASIC

Net income applicable to common stock            $       22,320      $       22,360
                                                 ==============      ==============
Weighted average number of shares of common
  stock outstanding during the period                22,484,269          22,460,931
                                                 ==============      ==============
Basic net income per common share                $         0.99      $         1.00
                                                 ==============      ==============
DILUTED

Net income applicable to common stock            $       22,320      $       22,360

Adjustments to net income related to
  Employee Stock Ownership Plan (ESOP)
   under the "if-converted" method:
  Add loss of deduction from net income
   for actual dividends paid on convertible
   preferred stock, net of tax                              359                 364
  Deduct additional cash contribution
    required which is equal to dividends
    on preferred stock less dividends
    paid at the common dividend rate, net
    of tax                                                  (15)                (25)
  Add tax benefit associated with dividends
    paid on allocated common shares                          91                  77
                                                 --------------      --------------
Adjusted income applicable to common stock       $       22,755      $       22,776
                                                 ==============      ==============

Weighted average number of shares of common
    stock outstanding during the period              22,484,269          22,460,931

Number of equivalent common shares
    attributable to ESOP                              1,377,265           1,396,778

Common stock under stock option grants                    4,963               6,768
                                                 --------------      --------------
  Average shares                                     23,866,497          23,864,477
                                                 ==============      ==============

Diluted net income per common share              $         0.95      $         0.95
                                                 ==============      ==============
</TABLE>


<PAGE>   2


                                CLECO CORPORATION
                   COMPUTATION OF NET INCOME PER COMMON SHARE
                     FOR THE NINE MONTHS ENDED SEPTEMBER 30,
                                   (Unaudited)

<TABLE>
<CAPTION>

                                                         (In thousands, except share
                                                            and per share amounts)

                                                               1998           1997
                                                           ------------   ------------
<S>                                                        <C>            <C>         
BASIC

Net income applicable to common stock                      $     43,280   $     40,106
                                                           ============   ============
Weighted average number of shares of common
  stock outstanding during the period                        22,478,499     22,459,128
                                                           ============   ============

Basic net income per common share                          $       1.93   $       1.79
                                                           ============   ============

DILUTED

Net income applicable to common stock                      $     43,280   $     40,106

Adjustments to net income related to Employee
 Stock Ownership Plan (ESOP) under the
  "if-converted" method:
 Add loss of deduction from net income for actual
  dividends paid on convertible preferred stock,
  net of tax                                                      1,077          1,092
 Deduct additional cash contribution
  required which is equal to dividends
  on preferred stock less dividends
  paid at the common dividend rate, net
  of tax                                                            (54)           (82)
 Add tax benefit associated with dividends
   paid on allocated common shares                                  262            217
                                                           ------------   ------------
Adjusted income applicable to common stock                 $     44,565   $     41,333
                                                           ============   ============
Weighted average number of shares of common
    stock outstanding during the period                      22,478,499     22,459,128

Number of equivalent common shares
    attributable to ESOP                                      1,381,675      1,398,141

Common stock under stock option grants                            6,085          6,912
                                                           ------------   ------------

 Average shares                                              23,866,259     23,864,181
                                                           ============   ============
Diluted net income per common share                        $       1.87   $       1.73
                                                           ============   ============
</TABLE>