<PAGE>   1

                                                                      EXHIBIT 11

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


<TABLE>
<CAPTION>
                                                                                    (In thousands, except share and
                                                                                           per share amounts)
                                                                                        1999              1998
                                                                                    ------------      ------------
<S>                                                                                 <C>               <C>
BASIC

Net income applicable to common stock                                               $     25,152      $     22,320
                                                                                    ============      ============

Weighted average number of shares of common stock outstanding
    during the period                                                                 22,505,272        22,484,269
                                                                                    ============      ============

Basic net income per common share                                                   $       1.12      $       0.99
                                                                                    ============      ============

DILUTED

Net income applicable to common stock                                               $     25,152      $     22,320

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                                348               359
    Deduct additional cash contribution required which is equal to
        dividends on preferred stock less dividends paid at the
        common dividend rate, net of tax                                                      (7)              (15)
    Add tax benefit associated with dividends paid on allocated
        common shares                                                                         99                91
                                                                                    ------------      ------------
Adjusted income applicable to common stock                                          $     25,592      $     22,755
                                                                                    ============      ============

Weighted average number of shares of common stock outstanding
    during the period                                                                 22,505,272        22,484,269

Number of equivalent common shares attributable to ESOP                                1,336,864         1,377,265

Common stock under stock option grants                                                        --             4,963
                                                                                    ------------      ------------

    Average shares                                                                    23,842,136        23,866,497
                                                                                    ============      ============
Diluted net income per common share                                                 $       1.07      $       0.95
                                                                                    ============      ============
</TABLE>
<PAGE>   2


                                                                    EXHIBIT 11

                                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)
                                                                                        1999              1998
                                                                                    ------------      ------------
<S>                                                                                 <C>               <C>
BASIC

Net income applicable to common stock                                               $     46,886      $     43,280
                                                                                    ============      ============

Weighted average number of shares of common stock outstanding
    during the period                                                                 22,511,688        22,478,499
                                                                                    ============      ============

Basic net income per common share                                                   $       2.08      $       1.93
                                                                                    ============      ============

DILUTED

Net income applicable to common stock                                               $     46,886      $     43,280

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                              1,055             1,077
    Deduct additional cash contribution required which is equal to
        dividends on preferred stock less dividends paid at the
        common dividend rate, net of tax                                                     (21)              (54)
    Add tax benefit associated with dividends paid on allocated
        common shares                                                                        283               262
                                                                                    ------------      ------------
Adjusted income applicable to common stock                                          $     48,203      $     44,565
                                                                                    ============      ============

Weighted average number of shares of common stock outstanding
    during the period                                                                 22,511,688        22,478,499

Number of equivalent common shares attributable to ESOP                                1,350,147         1,381,675

Common stock under stock option grants                                                       146             6,085
                                                                                    ------------      ------------

    Average shares                                                                    23,861,981        23,866,259
                                                                                    ============      ============
Diluted net income per common share                                                 $       2.02      $       1.87
                                                                                    ============      ============
</TABLE>