<PAGE>   1
                                                                      EXHIBIT 11


             FRESENIUS MEDICAL CARE HOLDINGS, INC. AND SUBSIDIARIES
        WEIGHTED AVERAGE NUMBER OF SHARES AND EARNINGS USED IN PER SHARE
                                   COMPUTATION
                        (DOLLARS AND SHARES IN THOUSANDS)

<TABLE>
<CAPTION>
                                                           THREE MONTHS ENDED
                                                                MARCH 31,
                                                          ---------------------
                                                            1999         1998
                                                          ---------     -------
<S>                                                       <C>           <C>
The weighted average number of shares of
                                                          ---------     -------
  Common Stock were as follows ......................        90,000      90,000
                                                          =========     =======
</TABLE>

Income used in the computation of earnings per share were as follows:

<TABLE>
<CAPTION>
                                                           THREE MONTHS ENDED
                                                                MARCH 31,
                                                          ---------------------
CONTINUED OPERATIONS                                        1999         1998
                                                          ---------     -------
<S>                                                       <C>           <C>    
Net Earnings ........................................     $  17,627     $ 9,846

Dividends paid on preferred stocks ..................          (130)       (130)
                                                          ---------     -------

                                                          ---------     -------
Income used in per share computation of earnings ....     $  17,497     $ 9,716
                                                          =========     =======

Basic and fully dilutive earnings per share .........     $    0.19     $  0.11
                                                          =========     =======
</TABLE>


<TABLE>
<CAPTION>
                                                           THREE MONTHS ENDED
                                                               MARCH 31,
                                                          ---------------------
DISCONTINUED OPERATIONS                                     1999         1998
                                                          ---------     -------
<S>                                                       <C>           <C>     
Net Earnings ........................................     $      --     $(4,429)

Dividends paid on preferred stocks ..................            --          --
                                                          ---------     -------

                                                          ---------     -------
Loss used in per share computation of earnings ......     $      --     $(4,429)
                                                          =========     =======

Basic and fully dilutive earnings per share .........     $      --     $ (0.05)
                                                          =========     =======
</TABLE>

<TABLE>
<CAPTION>
                                                           THREE MONTHS ENDED
                                                                MARCH 31,
                                                          --------------------
                                                            1999        1998
                                                          --------     -------
<S>                                                       <C>          <C>
Cumulative effect of accounting change ..............     $     --     $(4,890)

Dividends paid on preferred stocks ..................           --          --
                                                          --------     -------

                                                          --------     -------
Loss used in per share computation of earnings ......     $     --     $(4,890)
                                                          ========     =======

Basic and fully dilutive earnings per share .........     $     --     $ (0.05)
                                                          ========     =======
</TABLE>

<TABLE>
<CAPTION>
                                                           THREE MONTHS ENDED
                                                                MARCH 31,
                                                          ---------------------
CONSOLIDATED                                                1999         1998
                                                          ---------     -------
<S>                                                       <C>           <C>    
Net Earnings ........................................     $  17,627     $   527

Dividends paid on preferred stocks ..................          (130)       (130)
                                                          ---------     -------

                                                          ---------     -------
Income used in per share computation of earnings ....     $  17,497     $   397
                                                          =========     =======

Basic and fully dilutive earnings per share .........     $    0.19     $  0.01
                                                          =========     =======
</TABLE>