<PAGE>
 
                                                                    EXHIBIT 11.1
                                                                    ------------

                       TERRA NOVA (BERMUDA) HOLDINGS LTD.
                                AND SUBSIDIARIES

                COMPUTATION OF PRIMARY EARNINGS PER COMMON SHARE

                          AND COMMON SHARE EQUIVALENTS

<TABLE>
<CAPTION>
                                                                                  NINE MONTHS                    NINE MONTHS
                                                                              ENDED SEPTEMBER 30,            ENDED SEPTEMBER 30, 
                                                                                     1997                            1996
                                                                              -------------------            -------------------
<S>                                                                              <C>                               <C> 
Earnings per common share and common share equivalents              
-- Primary      
      Weighted average common shares outstanding                                 25,874,208                         22,342,562
      Weighted average common shares outstanding
            (under as if converted method)                                               --                                --
      Average stock options and warrants outstanding
            (net of repurchased shares under the treasury
             stock method)                                                          196,747                            371,062
      Other dilutive securities assumed to be outstanding
             under regulatory rules (net of repurchased shares
             under the treasury stock method)                                            --                                 --
                                                                                ------------                       -----------
      Weighted average common shares and common
             share equivalents outstanding                                        26,070,955                        22,713,624
                                                                                 ===========                       ===========
      Net income                                                                 $53,656,854                       $48,475,445
                                                                                 ===========                       ===========
      Primary earnings per common share
             and common share equivalent                                               $2.06                             $2.13
                                                                                 ===========                       ===========
</TABLE> 

                                      19

<PAGE>
 
                                                                    EXHIBIT 11.1
                                                                    ------------

                       TERRA NOVA (BERMUDA) HOLDINGS LTD.
                                AND SUBSIDIARIES

                COMPUTATION OF PRIMARY EARNINGS PER COMMON SHARE

                          AND COMMON SHARE EQUIVALENTS

<TABLE> 
<CAPTION> 
                                                                             THREE MONTHS                  THREE MONTHS
                                                                          ENDED SEPTEMBER 30            ENDED SEPTEMBER 30,
                                                                                1997                          1996

<S>                                                                       <C>                            <C> 
Earnings per common share and common share equivalents
-- Primary
        Weighted average common shares outstanding                          25,901,389                      25,823,308
        Weighted average common shares outstanding
              (under as if converted method)                                        --                              --
        Average stock options and warrants outstanding
              (net of repurchased shares under the treasury             
               stock method)                                                  (102,458)                        383,782
        Other dilutive securities assumed to be outstanding
               under regulatory rules (net of repurchased shares
               under the treasury stock method)                                     --                              --
                                                                           -----------                     ----------- 
        Weighted average common shares and common
               share equivalents outstanding                                25,798,931                      26,207,090  
                                                                           -----------                     ----------- 
        Net income                                                         $19,009,853                     $14,449,621
                                                                           ===========                     ===========
        Primary earnings per common share
           and common share equivalent                                           $0.74                           $0.55
                                                                           ===========                     =========== 
</TABLE> 

                                      20

<PAGE>
 
                                                                    EXHIBIT 11.1
                                                                    ------------

                       TERRA NOVA (BERMUDA) HOLDINGS LTD.
                                AND SUBSIDIARIES

             COMPUTATION OF FULLY DILUTED EARNINGS PER COMMON SHARE

                          AND COMMON SHARE EQUIVALENTS

<TABLE> 
<CAPTION> 
                                                                           NINE MONTHS                 NINE MONTHS
                                                                       ENDED SEPTEMBER 30,         ENDED SEPTEMBER 30,
                                                                             1997                         1996
<S>                                                                        <C>                            <C> 
Earnings per common share and common share equivalents
-- Fully Diluted
        Weighted average common shares outstanding                          25,874,208                    21,663,276
        Weighted average common shares outstanding
            (under as if converted method)                                          --                     1,148,916
        Average stock options and warrants outstanding
            (net of repurchased shares under the treasury
             stock method)                                                     229,641                       391,994
        Other dilutive securities assumed to be outstanding
            under regulatory rules (net of repurchased shares
            under the treasury stock method)                                         --                           --
                                                                            -----------                  -----------
        Weighted average common shares and common
            share equivalents outstanding                                    26,103,849                   23,204,186
                                                                            ===========                  ===========
        Net income                                                          $53,656,854                  $49,064,445
                                                                            ===========                  ===========
        Fully diluted earnings per common share
             and common share equivalent                                          $2.06                        $2.11
                                                                            ===========                  ===========
</TABLE> 
 
                                      21

<PAGE>
 
                                                                    EXHIBIT 11.1
                                                                    ------------

                      TERRA NOVA (BERMUDA) HOLDINGS LTD.
                               AND SUBSIDIARIES

            COMPUTATION OF FULLY DILUTED EARNINGS PER COMMON SHARE

                         AND COMMON SHARE EQUIVALENTS

<TABLE> 
<CAPTION> 
                                                               THREE MONTHS            THREE MONTHS    
                                                            ENDED SEPTEMBER 30,     ENDED SEPTEMBER 30, 
                                                                   1997                    1996       
                                                            -------------------     -------------------  
<S>                                                         <C>                    <C> 
Earnings per common share and common share  equivalents
--Fully Diluted
      Weighted average common shares outstanding              25,898,286               25,823,308
      Weighted average common shares outstanding                     
        (under as if converted method)                                --                       --
      Average stock options and warrants outstanding
        (net of repurchased shares under the treasury
        stock method)                                            (72,362)                 398,779
      Other dilutive securities assumed to be outstanding
        under regulatory rules (net of repurchased shares
        under the treasury stock method)                              --                       --
                                                              ----------              -----------       
      Weighted average common shares and common share
        equivalents outstanding                               25,825,924               26,222,087
                                                             ===========              ===========
      Net income                                             $19,009,853              $14,449,621
                                                             ===========              ===========       
      Fully diluted earnings per common share and
        common share equivalent                                    $0.74                    $0.55
                                                             ===========              ===========  
</TABLE> 


                                      22