BANCROFT CONVERTIBLE FUND INC
N-30D, 1996-07-01
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<PAGE>   1
BANCROFT CONVERTIBLE FUND, INC.

TO OUR SHAREHOLDERS:

      BANCROFT CONVERTIBLE FUND, INC. went public twenty-five years ago this
spring. Ronald E. Dinsmore and Bancroft G. ("Gary") Davis founded the Fund in
April 1971. It is the oldest domestic closed-end convertible fund. Throughout
the 1970's Ron and Gary managed the Fund through some very interesting markets
including the 1973-1974 bear market and the oil crises of 1974 and 1979. Gary
Davis died in 1981 but the Fund he helped found moved forward. Tom Dinsmore was
hired in 1983 to assist Ron manage the Fund during the 1980's through two great
bull markets separated by the crash of '87. More recently, in 1994, Jane
Dinsmore O'Keeffe was hired. She came with a background in portfolio management
going back to 1980 that included time working with George Soros and five years
as portfolio manager at Fiduciary Trust Co.

      Since Jane's hiring, Ron Dinsmore changed his function with the Fund from
Portfolio Manager to Chief Portfolio Strategist. Today, Tom Dinsmore and Jane
O'Keeffe are the portfolio managers of the Fund. Transitions are sometimes rocky
but this one has gone well. Indeed, the Bancroft Fund has maintained a four star
overall rating from Morningstar* and was recently given a fifth star for its
3-year performance in their April 26, 1996 report. While this measures past
performance and does not guarantee future performance, we hope to build on it
for the future.

      We estimate that the Fund's net asset value (NAV) rose 4.90%, 23.88%,
92.96% and 164.50% for the three-month, one-year, five-year and ten-year periods
ended March 31, 1996 (assuming all dividends reinvested at NAV). The value of
the Fund's shares appreciated 0.66%, 19.94%, 96.75% and 149.80%** for those
three-month, one-year, five-year and ten-year periods (assuming all dividends
reinvested at actual reinvestment price). As quoted in Barron's, Lipper
Analytical Services reported that the average open-end convertible fund's NAV+
rose 4.71%, 20.52%, 89.61% and 145.01% for those same periods (also assuming all
dividends reinvested).

      At its June meeting, the Board of Directors announced that a special
meeting of shareholders will be held on September 25, 1996 for shareholders of
record August 1, 1996. The purpose of the meeting will be to consider reapproval
of the management contract with Davis/Dinsmore Management Company. Further
details will be made available in the proxy materials that will be sent to you.

      At its April meeting the Board of Directors declared a 28 cents per share
dividend payable on June 24, 1996 to shareholders of record June 10, 1996.




/s/ Ronald E. Dinsmore
Chairman of the Board




/s/ Thomas H. Dinsmore
President


June 12, 1996





**  Morningstar is an independent statistical service that rates mutual funds.

**  Assumes full exercise of rights issued in 1988.

 +  Average NAV of the forty-one open-end convertible funds followed by Lipper
    Analytical Services, Inc., an independent statistical service.
<PAGE>   2
BANCROFT CONVERTIBLE FUND, INC.
INVESTMENTS       APRIL 30, 1996

<TABLE>
<CAPTION>
   PRINCIPAL
    AMOUNT                                                                                                               VALUE
   OR SHARES                                                                                                            (NOTE A)
   ---------                                                                                                           -----------
<S>                  <C>                                                                                               <C>
                     ADVERTISING--5.2%
 $ 1,025,000         Interpublic Group Cos., Inc. 3 3/4% 2002 Euro. cv. sub. deb.....................................  $ 1,071,125
     650,000         Interpublic Group Cos., Inc. 3 3/4% 2002 cv. sub. deb. *........................................      677,625
   1,475,000         Omnicom Group, Inc. 4 1/2% 2000 cv. sub. deb. *.................................................    2,352,625
                                                                                                                       -----------
                                                                                                                         4,101,375
                                                                                                                       -----------
                     AEROSPACE--4.0%
   2,000,000         Morgan Stanley Group, Inc. 0% 2000 medium-term exchangeable notes...............................    1,945,000
                     (exch. for Boeing Company common stock)
   1,134,000         Orbital Sciences Corp. 6 3/4% 2003 cv. sub. deb.................................................    1,202,040
                                                                                                                       -----------
                                                                                                                         3,147,040
                                                                                                                       -----------
                     AUTOMOTIVE--2.7%
      15,000  shs    Ford Motor Co. depositary shares (representing $4.20 cum. cv. A pfd.)...........................    1,747,500
      25,100  shs    MascoTech Industries, Inc. 6% cv. pfd...........................................................      348,263
                                                                                                                       -----------
                                                                                                                         2,095,763
                                                                                                                       -----------
                     BANKING--13.4%
      37,736  shs    Barnett Banks, Inc. common stock................................................................    2,391,519
      32,500  shs    Boatmens Bancshares, Inc. depositary shares (representing 7% cum. cv. A pfd.)...................    1,105,000
      15,375  shs    Chase Manhattan Corp. common stock..............................................................    1,060,875
      25,000  shs    First Commerce Corp. 7 1/4% cum. cv. pfd........................................................      987,500
      45,530  shs    National City Corp. common stock................................................................    1,678,919
      15,000  shs    ONBANCorp, Inc. 6 3/4% cv. B pfd................................................................      397,500
      15,000  shs    Washington Mutual Savings Bank $6.00 cv. perpetual D pfd........................................    1,680,000
      15,000         Jefferson-Pilot Corp. 7 1/4% 2000 FCENS #.......................................................    1,215,000
                                                                                                                       -----------
                                                                                                                        10,516,313
                                                                                                                       -----------
                     CAPITAL GOODS--6.4%
       5,000  shs    Greenfield Capital Trust 6% cv. pfd. * (conv. into Greenfield Industries, Inc. common stock)....      273,750
      70,000  shs    Westinghouse Electric Corp. depositary shares (representing $1.30 cv. C pfd.)...................    1,242,500
   1,067,000         Cooper Industries, Inc. 7.05% 2015 cv. sub. deb.................................................    1,141,690
   2,250,000         General Signal Corp. 5 3/4% 2002 cv. sub. notes.................................................    2,385,000
                                                                                                                       -----------
                                                                                                                         5,042,940
                                                                                                                       -----------
                     COMMUNICATIONS--3.6%
         354  shs    MFS Communications Co., Inc. common stock.......................................................       12,279
      15,000  shs    MFS Communications Co., Inc. depositary shares (representing 8% cum. cv. A pfd.)................      885,000
   1,200,000         Comcast Cellular Corp. 0% 2000 senior participating zero coupon redeemable series A notes.......      882,000
      25,000         Sprint Corp. 8 1/4% 2000 FCENS # (exch. for Southern New Eng. Telecom. Corp. common stock)......    1,059,375
                                                                                                                       -----------
                                                                                                                         2,838,654
                                                                                                                       -----------
                     DATA-PROCESSING SERVICES--7.2%
      21,117  shs    General Motors Corp. (GME) common stock.........................................................    1,190,471
       7,500  shs    Wang Laboratories, Inc. depositary shares (representing 6 1/2% cum. cv. B pfd.) *...............      409,688
      35,000         American Express Company 6 1/4% 1996 FCENS # (exch. for First Data Corp. common stock)..........    2,183,125
   1,000,000         First Financial Management Corp. 5% 1999 cv. sub. deb...........................................    1,825,000
                                                                                                                       -----------
                                                                                                                         5,608,284
                                                                                                                       -----------
                     ENERGY--6.6%
      41,000  shs    Chieftain International Funding Corp. 7 1/4% cv. red. pfd.......................................    1,091,625
         500  shs    MCN Corp. 8 3/4% Preferred Redeemable Increased Dividend Equity Securities......................       13,188
      25,000  shs    Unocal Corp. $3.50 cv. pfd. *...................................................................    1,381,250
      12,500  shs    Sun Company, Inc. depositary shares (representing $1.80 cum. cv. A pfd.)........................      387,500
     375,000         AES Corp. 6 1/2% 2002 cv. deb...................................................................      397,500
     500,000         Pennzoil Company 4 3/4% 2003 exch. sr. deb. (exch. for Chevron Corp. common stock)..............      532,500
   1,000,000         Pennzoil Company 6 1/2% 2003 exch. sr. deb. (exch. for Chevron Corp. common stock)..............    1,390,000
                                                                                                                       -----------
                                                                                                                         5,193,563
                                                                                                                       -----------
                     ENTERTAINMENT--5.4%
      40,000  shs    Cablevision Systems Corp. depositary shares (representing 8 1/2% cum. cv. exch. pfd.)...........    1,035,000
      50,000  shs    Triathlon Broadcasting Co. depositary shares (representing 9% mandatory cv. pfd.)...............      537,500
     975,000         Comcast Corp. 3 3/8% 2005 cv. sub. deb..........................................................      887,250
   1,000,000         Imax Corp. 5 3/4% 2003 cv. sub. notes *.........................................................    1,005,000
     600,000         International CableTel, Inc. 7 1/4% 2005 cv. sub. notes *.......................................      741,000
                                                                                                                       -----------
                                                                                                                         4,205,750
                                                                                                                       -----------
                     ENVIRONMENTAL SERVICES--1.0%
     750,000         Sanifill, Inc. 5% 2006 cv. sub. deb.............................................................      813,750
                                                                                                                       -----------

                     FINANCIAL & INSURANCE--11.5%
      30,000  shs    American General Delaware, LLC 6% cv. A MIPS +..................................................    1,545,000
      23,536  shs    Old Republic International Corp. common stock...................................................      776,688
      33,410  shs    Pioneer Financial Services, Inc. common stock...................................................      513,679
     750,000         American Travellers Corp. 6 1/2% 2005 cv. sub. deb..............................................    1,100,625
   1,300,000         Chubb Capital Corp. 6% 1998 Euro. cv. sub. deb..................................................    1,475,500
   1,025,000         First Central Financial Corp. 9% 2000 cv. sub. deb..............................................    1,035,250
   1,000,000         Pioneer Financial Services, Inc. 6 1/2% 2003 cv. sub. notes.....................................      995,000
      55,000         Pioneer Financial Services, Inc. 8% 2000 cv. sub. deb...........................................       70,950
      55,000         US West, Inc. 7 5/8% 1998 FCENS # (exch. for Enhance Financial Services Group,
                       Inc. common stock)............................................................................    1,491,875
                                                                                                                       -----------
                                                                                                                         9,004,567
                                                                                                                       -----------
</TABLE>
<PAGE>   3
<TABLE>
<CAPTION>

   PRINCIPAL
    AMOUNT                                                                                                     VALUE
   OR SHARES                                                                                                  (NOTE A)
   ---------                                                                                                 -----------
<S>                 <C>                                                                                      <C>
                    FOODS--1.4%
  $1,000,000        Grand Metropolitan Public Limited Co. 6 1/2% 2000 cv. sub. deb. *......................  $ 1,100,000
                                                                                                             -----------

                    HEALTH CARE & DRUGS--8.5%
     500,000        Ciba Geigy Corp. 6 1/4% 2016 exch. sub. deb. * (exch. for ALZA Corp. common stock).....      516,250
   1,250,000        Medco Containment Service, Inc. 6% 2001 cv. sub. deb...................................    2,537,500
   1,200,000        Morgan Stanley Group, Inc. 0% 2000 medium-term exchangeable notes......................      964,500
                    (exch. for ADR's representing SmithKline Beecham plc common stock)
     500,000        Quintiles Transnational Corp. 4 1/4% 2000 cv. sub. deb. *..............................      542,500
   2,500,000        Roche Holdings, Inc. 0% 2010 liquid yield option notes *...............................    1,093,750
     500,000        Sandoz Capital BVI Ltd. 2% 2002 cv. sub. notes *.......................................      537,500
     500,000        TheraTx, Inc. 8% 2002 cv. sub. notes *.................................................      477,500
                                                                                                             -----------
                                                                                                               6,669,500
                                                                                                             -----------
                    HOTEL SERVICES--0.9%
     250,000        HFS, Inc. 4 3/4% 2003 cv. senior notes.................................................      260,625
     875,000        Marriott International, Inc. 0% 2011 liquid yield option notes.........................      461,563
                                                                                                             -----------
                                                                                                                 722,188
                                                                                                             -----------
                    OFFICE EQUIPMENT--0.9%
       7,500  shs   Alco Standard Corp. depositary shares (representing 6 1/2% cv. BB pfd.)................      742,500
                                                                                                             -----------

                    PAPER & PAPER PRODUCTS--1.2%
      20,000  shs   International Paper Capital Trust Company 5 1/4% cv. pfd. *............................      930,000
                                                                                                             -----------

                    RETAIL--0.8%
      10,000  shs   AnnTaylor Finance Trust 8 1/2% cv. trust originated pfd. * (conv. into Ann Taylor
                            Stores Corp. common stock).....................................................      502,500
     400,000        Tops Appliance City, Inc. 6 1/2% 2003 cv. sub. deb.                                          152,000
                                                                                                             -----------
                                                                                                                 654,500
                                                                                                             -----------
                    TECHNOLOGY--10.1%
   1,100,000        Conner Peripherals, Inc. 6 1/2% 2002 cv. sub. deb......................................    1,254,000
   1,000,000        Conner Peripherals, Inc. 6 3/4% 2001 cv. sub. deb......................................    1,070,000
     750,000        Emerson Radio Corp. 8 1/2% 2002 sr. cv. sub. deb. *....................................      626,250
     600,000        Motorola, Inc. 0% 2013 liquid yield option notes.......................................      452,250
     300,000        Texas Instruments, Inc. 2 3/4% 2002 Euro. cv. sub. deb.................................      410,250
     475,000        Thermo Electron Corp. 5% 2001 cv. sub. deb. *..........................................      945,844
     925,000        Thermo Electron Corp. 4 1/4% 2003 cv. sub. deb. *......................................    1,142,375
     200,000        Thermo Optek Corp. 5% 2000 cv. sub. deb. *.............................................      224,000
     125,000        Thermo Quest Corp. 5% 2000 cv. sub. deb. *.............................................      140,000
     250,000        Thermo Terratech, Inc. 4 5/8% 2003 cv. sub. deb. *.....................................      262,188
     500,000        3Com Corp. 10 1/4% 2001 cv. sub. notes *...............................................      771,250
     600,000        VLSI Technology, Inc. 8 1/4% 2005 cv. sub. notes.......................................      573,000
                                                                                                             -----------
                                                                                                               7,871,407
                                                                                                             -----------
                    TRANSPORTATION--4.0%
      12,658  shs   AMR Corp. common stock.................................................................    1,129,727
       5,000  shs   Delta Air Lines, Inc. depositary shares (representing $3.50 cum. cv. C pfd.)...........      316,875
   1,075,000        Delta Air Lines, Inc. 3.23% 2003 cv. sub. notes........................................    1,103,219
     500,000        Mercury Air Group, Inc. 7 3/4% 2006 cv. sub. deb.......................................      572,500
                                                                                                             -----------
                                                                                                               3,122,321
                                                                                                             -----------
                    U.S. TREASURY NOTES--1.2%
     952,000        4 1/4% 5/15/96.........................................................................      952,000
      25,000        6 5/8% 3/31/97 **......................................................................       25,219
                                                                                                             -----------
                                                                                                                 977,219
                                                                                                             -----------

                    CORPORATE SHORT-TERM NOTES--2.7%
   1,500,000        General Electric Capital Services, Inc. 5.20% 5/2/96...................................    1,499,567
     350,000        Sears Roebuck Acceptance Corp. 5.05% 5/2/96............................................      349,853
     240,000        Sears Roebuck Acceptance Corp. 5.29% 5/23/96...........................................      239,154
                                                                                                             -----------
                                                                                                               2,088,574
                                                                                                             -----------

TOTAL BONDS AND NOTES--62.6%...............................................................................  $49,043,833
TOTAL PREFERRED STOCKS--22.4%..............................................................................   17,559,639
TOTAL COMMON STOCKS--11.2%.................................................................................    8,754,157
TOTAL CORPORATE SHORT-TERM NOTES--2.7%.....................................................................    2,088,574
                                                                                                             -----------
TOTAL INVESTMENTS--98.9%...................................................................................   77,446,203
OTHER ASSETS AND LIABILITIES, NET--1.1%....................................................................      863,105
                                                                                                             -----------
TOTAL NET ASSETS--100.0%...................................................................................  $78,309,308
                                                                                                             -----------
</TABLE>


 *  Rule 144A security, may be sold only to qualified institutional buyers.
 #  Forced Conversion Exchangeable Notes.
 +  Monthly Income Preferred Securities.
**  Collateral for a letter of credit.

The cost of investments for federal income tax purposes is $66,079,748 resulting
in gross unrealized appreciation and depreciation of $12,394,017 and $1,027,562,
respectively, or net unrealized appreciation of $11,366,455 on a tax cost basis.

                 See accompanying notes to financial statements.
<PAGE>   4
BANCROFT CONVERTIBLE FUND, INC.
STATEMENT OF OPERATIONS (UNAUDITED)

<TABLE>
<CAPTION>
                                                                       SIX MONTHS ENDED 
                                                                        APRIL 30, 1996
                                                                       -----------------
        <S>                                                            <C>       
        INVESTMENT INCOME (NOTE A):
          Interest...................................................      $1,255,005
          Dividends..................................................         737,807
                                                                           ----------
            Total Income.............................................       1,992,812
                                                                           ----------
        EXPENSES (NOTE B)
          Management fee.............................................         276,293
          Custodian..................................................          13,742
          Transfer agent.............................................          27,876
          Professional fees..........................................          33,096
          Reports to Shareholders....................................          47,646
          Directors' fees............................................          16,550
          Treasurer's office.........................................          12,500
          Listing fee................................................           7,500
          Other......................................................          25,411
                                                                           ----------
            Total Expenses...........................................         460,614
        
                                                                           ----------
        NET INVESTMENT INCOME........................................       1,532,198
                                                                           ----------
        REALIZED AND UNREALIZED GAIN ON INVESTMENTS:
          Net realized gain from investment transactions.............       2,633,427
          Net increase in unrealized appreciation of investments.....       4,444,776
                                                                           ----------
          Net gain on investments....................................       7,078,203
                                                                           ----------
        NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS.........      $8,610,401
                                                                           ==========
        </TABLE>

                 See accompanying notes to financial statements.

================================================================================

MAJOR PORTFOLIO CHANGES     FEBRUARY 1 TO APRIL 30, 1996

<TABLE>
<CAPTION>
                                                                                       SHARES OR PRINCIPAL AMOUNT
                                                                                  ------------------------------------
                                                                                                              HELD AT
                                                                                  ADDITIONS   REDUCTIONS      4-30-96
                                                                                  ---------   ----------     ---------
<S>                                                                               <C>         <C>            <C>
AMR Corp. common stock                                                               12,658                     12,658
Bindley Western Industries, Inc. 61/2% 2002 cv. sub. deb.                                      1,475,000            --
Boatmens Bancshares, Inc. depositary shares (representing 7% cum cv. A pfd.)         15,000                     32,500
Browning-Ferris Industries, Inc. 71/4% 1998 notes                                                 25,000            --
Conner Peripherals, Inc. 61/2% 2002 cv. sub. deb.                                 1,100,000                  1,100,000
Conner Peripherals, Inc. 63/4% 2001 cv. sub. deb.                                   750,000      250,000     1,000,000
General Signal Corp. 53/4% 2002 cv. sub. notes                                      500,000                  2,250,000
Imax Corp. 53/4% 2003 cv. sub. notes *                                            1,000,000                  1,000,000
Old Republic International Corp. common stock                                        35,000                     23,536
Pioneer Financial Services, Inc. 61/2% 2003 cv. sub. notes                        1,000,000                  1,000,000
Sanifill, Inc. 5% 2006 cv. sub. deb.                                                750,000                    750,000
Seagate Technology, Inc. 63/4% 2012 cv. sub. deb.                                              1,295,000            --
Starbucks Corp. 41/4% 2002 cv. sub. deb.                                                         500,000            --
Thermo Electron Corp. 41/4% 2003 cv. sub. deb. *                                    800,000                    925,000
Thermo Electron Corp. 5% 2001 cv. sub. deb. *                                                    500,000       475,000
United Technologies Corp. 0% 1997 pharmaceutical exch. notes                                     500,000            --
</TABLE>

* Rule 144A security.

<PAGE>   5
STATEMENT OF ASSETS AND LIABILITIES

<TABLE>
<CAPTION>
                                                                          APRIL 30, 1996
                                                                          --------------
<S>                                                                       <C>        
ASSETS:
  Investments at value (cost $66,079,748) (Note A).....................    $77,446,203
  Cash.................................................................        478,567
  Receivable for securities sold.......................................      1,068,594
  Dividends and interest receivable....................................        485,740
  Other assets.........................................................         16,335
                                                                           -----------
  Total assets.........................................................     79,495,439
                                                                           -----------
LIABILITIES:
  Payable for securities purchased.....................................      1,173,907
  Accrued expenses.....................................................         12,224
                                                                           -----------
  Total liabilities....................................................      1,186,131
                                                                           -----------
NET ASSETS                                                                 $78,309,308
                                                                           ===========
NET ASSETS CONSIST OF:
  Accumulated undistributed net investment income......................    $   706,102
  Accumulated net realized gain from investment transactions...........      2,617,989
  Unrealized appreciation on investments...............................     11,366,455
  Capital shares (Note D)..............................................         29,503
  Additional paid-in capital...........................................     63,589,259
                                                                           -----------
NET ASSETS.............................................................    $78,309,308
                                                                           ===========
  Net asset value per share ($78,309,308 / 2,950,343
     outstanding shares)...............................................    $     26.54
                                                                           ===========
</TABLE>

                 See accompanying notes to financial statements.

================================================================================


STATEMENT OF CHANGES IN NET ASSETS

<TABLE>
<CAPTION>
                                                                SIX MONTHS ENDED     YEAR ENDED
                                                                 APRIL 30, 1996   OCTOBER 31, 1995
                                                                ----------------  ----------------
<S>                                                               <C>               <C>         
Increase in net assets from operations:                                            
    Net investment income....................................     $  1,532,198      $  3,285,250
    Net realized gain from investment transactions...........        2,633,427         1,869,444
    Net increase in unrealized appreciation of investments...        4,444,776         5,012,325
                                                                  ------------      ------------
      Net increase in net assets resulting from operations...        8,610,401        10,167,109
Dividends paid from net investment income....................       (1,599,546)       (3,350,427)
Distribution from net realized gain on investments...........       (1,871,807)       (1,497,574)
Capital share transactions (Note D)..........................        1,745,224         1,554,561
                                                                  ------------      ------------
    Increase in net assets...................................        6,884,272         6,873,579
Net assets at beginning of period............................       71,425,036        64,551,457
                                                                  ------------      ------------
Net assets at end of period (including undistributed net                           
  investment income of $706,102 and $779,084, respectively)..     $ 78,309,308      $ 71,425,036
                                                                  ============      ============
</TABLE>
                                                                       
                 See accompanying notes to financial statements.      
<PAGE>   6
BANCROFT CONVERTIBLE FUND, INC.

FINANCIAL HIGHLIGHTS

Selected data for a share of common stock outstanding

<TABLE>
<CAPTION>
                                              SIX MONTHS
                                                ENDED                           YEARS ENDED OCTOBER 31,
                                           ---------------     -------------------------------------------------------
PER SHARE OPERATING PERFORMANCE            APRIL 30, 1996+      1995        1994        1993        1992         1991
- -------------------------------            ---------------     ------      ------      ------      ------       ------

<S>                                        <C>                 <C>         <C>         <C>         <C>          <C>   
Net asset value, beginning of period            $24.84         $23.11      $25.00      $22.75      $21.02       $17.86
                                                ------         ------      ------      ------      ------       ------
Net investment income                              .52           1.14        1.20        1.26        1.35         1.34
Net realized and unrealized gain (loss)           2.39           2.30       (1.18)       3.07        1.70         3.28
                                                ------         ------      ------      ------      ------       ------
Total from investment operations                  2.91           3.44         .02        4.33        3.05         4.62
Dividends paid from net
investment income                                 (.56)         (1.17)      (1.24)      (1.24)      (1.32)       (1.46)
Distributions from realized gains                 (.65)          (.54)       (.67)       (.84)         --           --
                                                ------         ------      ------      ------      ------       ------
Net asset value, end of period                   26.54          24.84       23.11       25.00       22.75        21.02
                                                ======         ======      ======      ======      ======       ======
Market value, end of period                      22.63          22.25       20.13       23.00       20.63        18.63
Total investment return:
Based on market value                             6.99%         20.17%      (4.88)%     22.90%      18.35%       33.90%
Based on net asset value**                       11.93%         15.79%        .18%      20.12%      14.87%       26.64%

Ratios/Supplemental Data:

Net assets, end of period (000's)               78,309         71,425      64,551      67,829      59,436       54,915
Ratio of expenses to average net assets            1.2%#          1.2%        1.2%        1.2%        1.2%         1.3%*
Ratio of net investment income to
average net assets                                 4.1%#          4.9%        5.2%        5.4%        6.1%         6.7%
Portfolio turnover rate                             27%            43%         39%        102%         71%          39%
Average commission rate paid                    $0.072
</TABLE>

 +  Unaudited.
 *  Includes $23,038 ($.01 per share) legal expenses for shareholder proposals.
**  Assumes valuation of the Fund's shares, and reinvestment of dividends, at
    net asset values.
 #  Annualized.

                 See accompanying notes to financial statements.

- --------------------------------------------------------------------------------
     Shareholders voted as follows at the Annual Meeting of Stockholders held on
February 15, 1996:

1. All nominated directors were elected.

<TABLE>
<CAPTION>
                                             Votes for           Votes withheld
                                             ---------           --------------
<S>                                          <C>                      <C>   
         Ronald E. Dinsmore                  1,564,446                40,666
         Thomas H. Dinsmore                  1,562,590                45,522
         Donald M. Halsted, Jr.              1,563,946                41,166
</TABLE>

2. Fundamental investment policy changes were approved regarding:

<TABLE>
<CAPTION>
                                                               For            Against         Abstain
                                                               ---            -------         -------
<S>                                                         <C>                <C>             <C>   
         a. Qualitative requirements for investment.        1,447,805          71,213          69,243
         b. History of operations requirement.              1,439,524          78,847          69,890
         c. Issuer diversification.                         1,392,351         118,055          77,855
         d. Illiquid and restricted securities.             1,362,309         142,530          83,422
         e. Lending of portfolio securities.                1,341,290         162,211          84,760
         f. Puts and calls.                                 1,355,685         162,032          70,544
</TABLE>

3. The selection of Coopers & Lybrand L.L.P. as independent accountants was 
ratified with 1,546,455 votes for, 14,081 against and 44,576 abstaining.
- --------------------------------------------------------------------------------

     Pursuant to Section 23 of the Investment Company Act of 1940, notice is
hereby given that the Fund may in the future purchase shares of Bancroft
Convertible Fund, Inc. Common Stock from time to time, at such times, and in
such amounts, as may be deemed advantageous to the Fund. Nothing herein shall be
considered a commitment to purchase such shares.
<PAGE>   7
NOTES TO FINANCIAL STATEMENTS

(A) The Fund is registered under the Investment Company Act of 1940, as amended,
as a diversified, closed-end management investment company. The following is a
summary of significant accounting policies consistently followed by the Fund in
the preparation of its financial statements:

1. Security Valuation

Investments in securities traded on a national securities exchange are valued at
market using the last reported sales price. Securities traded in the
over-the-counter market and listed securities for which no sales were reported
are valued at the mean between closing reported bid and asked prices. Where no
closing prices are available, value is determined by management, with the
approval of the Board of Directors.

2. Securities Transactions and Related Investment Income

Investment transactions are accounted for on the trade date. Realized gain or
loss on securities is determined based upon identified cost. Dividend income is
recorded on the ex-dividend date and interest income is recorded on the accrual
basis. For the six months ended April 30, 1996, interest of $5,025 was earned on
cash balances held by the custodian of the Fund's assets.

3. Federal Taxes

It is the policy of the Fund to distribute substantially all of its taxable
income within the prescribed time and to otherwise comply with the provisions of
the Internal Revenue Code applicable to regulated investment companies.
Therefore, no provisions for federal income or excise taxes are believed
necessary.

4. Dividends and Distributions to Shareholders

The liability for dividends and distributions payable is recorded on the
ex-dividend date.

(B) The management fee is paid to Davis/Dinsmore Management Company, investment
adviser. The contract provides for payment of a monthly advisory fee, computed
at an annual rate of 3/4 of 1% of the first $100,000,000 and 1/2 of 1% of the
excess over $100,000,000 of the Fund's net asset value in such month. The annual
fee is subject to reduction to the extent that the ordinary expenses of the Fund
(excluding taxes and interest) exceed 1.5% of the first $100,000,000 and 1% of
the excess over $100,000,000 of the average of the monthly net asset values of
the Fund for the year.

The adviser's organization furnishes investment advice, office equipment and
facilities, and pays the salaries of all executive officers of the Fund, except
that the costs associated with personnel and certain non-personnel expenses of
the office of the Treasurer, up to a maximum of $50,000 a year, are reimbursed
by the Fund. Such reimbursements amounted to $12,500 for the six months ended
April 30, 1996. The officers of the Fund are also directors, officers or
employees of the investment adviser, and are compensated by the investment
adviser.

(C) Purchases and sales of investments aggregated $20,746,811 and $19,249,436,
respectively, for the six months ended April 30, 1996, exclusive of short-term
notes.

(D) At April 30, 1996, 2,950,343 shares of $.01 par value capital stock were
outstanding (9,000,000 shares authorized). During the six months ended April 30,
1996, 75,036 shares were issued in connection with reinvestment of dividends
from net investment income and capital gains, resulting in an increase in
paid-in capital of $1,744,475.

(E) A distribution of $.28 per share from net investment income was declared
April 18, 1996 to shareholders of record at the close of business June 10, 1996,
payable June 24, 1996.
<PAGE>   8
================================================================================

DIRECTORS

GORDON F. AHALT

WILLIAM A. BENTON

ELIZABETH C. BOGAN

RONALD E. DINSMORE

THOMAS H. DINSMORE, C.F.A.

DONALD M. HALSTED, JR.

GEORGE R. LIEBERMAN

JANE D. O'KEEFFE


DIRECTOR EMERITUS

DUNCAN O. MCKEE

================================================================================

OFFICERS

RONALD E. DINSMORE            Chairman of the Board

THOMAS H. DINSMORE            President

JANE D. O'KEEFFE              Executive Vice President

SIGMUND LEVINE                Senior Vice President
                                 and Secretary

H. TUCKER LAKE                Vice President, Trading

GARY I. LEVINE                Treasurer and Assistant
                                 Secretary


                     STOCKHOLDER SERVICES AND TRANSFER AGENT
                  Chemical Mellon Shareholder Services, L.L.C.
                                  P.O. Box 590
                            Ridgefield Park, NJ 07660
                                 1-800/526-0801

                  Printed on [RECYCLED SYMBOL] recycled paper.

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                                     (LOGO)



================================================================================


                                      1996
                                   SEMI-ANNUAL
                                     REPORT
                                 APRIL 30, 1996




                                     (LOGO)




                                65 MADISON AVENUE
                            MORRISTOWN, NJ 07960-7308
                                 (201) 631-1177


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