BANCROFT CONVERTIBLE FUND INC
N-30D, 1998-07-01
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<PAGE>   1

BANCROFT CONVERTIBLE FUND, INC.


TO OUR SHAREHOLDERS:

     The first quarter of calendar 1998 saw a continuation of the strong bull
market that propelled the Standard and Poor's 500 stock index from a low of 104
in August of 1982 to over 1100. This market move has been matched in post-WWII
American history only by the 1949 to 1968 rise from 14 to 109. For the last two
months, however, the stock market has trended sideways to down at a time when
long-term interest rates have fallen from over 6% on the 30 year treasury bond
to 5.61%. Because of this decline in interest rates, we do not currently fear
the coming of a bear market. All previous post-war bear markets in U.S. stocks
began only after a significant rise in interest rates.

     Questions about when this bull market will end are prompted by volatility
in other economies, especially in Japan and Southeast Asia. Within the U.S.
market, companies with a large exposure to Asia as a market may see future
earnings growth decline as Asia slips into a recession. Companies that buy from
Asia may see earnings expectations grow as lower costs of production may allow
an expansion of margins. Companies that sell to Europe may also see earnings
grow as Europe finally appears to be coming out of its long malaise and is
likely moving towards more prosperous times.

     It appears to us that the economic growth of the U.S. and of Europe will
help keep Asia's economy out of a truly disastrous prolonged depression. Many
Asian nations will still have to go through the process of restructuring their
economies, as the "industrial policy" model of economic growth has proven
faulty. The governmental bureaucracies and mega corporations that ran their
economies have not been flexible enough to accommodate change and until more
entrepreneurial organizations gain sufficient foothold, many Asian economies
will have very bumpy rides. We expect them to succeed, but it will take time and
it may reduce growth in the global economy by enough to affect our markets. We
will be watching carefully.

     Lipper Analytical Services, Inc. has determined that the Fund's net asset
value (NAV) rose 9.44%, 31.75%, 106.72% and 244.75% for the three-month,
twelve-month, five-year and ten-year periods ended March 31, 1998.* We have
determined that the value of the Fund's shares rose 18.88%, 49.87%, 137.65% and
293.04%+ for those same three-month, one-year, five-year and ten-year periods
(assuming all dividends reinvested at actual reinvestment price). The average
closed-end convertible fund's NAV rose 7.51%, 24.66%, 89.72% and 250.16%@ and
the average open-end convertible fund's NAV rose 7.47%, 25.58%, 83.08% and
221.41% for those same periods.**

     Morningstar++ has rated Bancroft Convertible Fund, Inc. at four-star
overall (above average). Interested shareholders may contact us for a copy of
this report.

     In January Bancroft enhanced its service to shareholders by providing net
asset value on a daily basis. We report the daily value every evening to Lipper
Analytical and we publish it on our website (www.bcvecf.com). We are hopeful
that this will reduce uncertainty among potential shareholders and promote the
visibility of the Fund.

     At its May meeting, the Board of Directors declared a dividend of
twenty-three cents per share payable from net investment income. The dividend is
payable June 30, 1998 to shareholders of record on June 16, 1998.

/s/ Thomas K. Dinsmore

Chairman of the Board
June 17, 1998


*  Lipper Analytical Services Inc. is an independent statistical rating service.

+  Assumes participation in rights offering in 1988.

@  From Lipper Analytical Services, Inc., Lipper Closed-End Fund Performance
   Analysis Service dated March 31, 1998 with dividends reinvested, for the nine
   closed-end convertible funds followed by Lipper Analytical (eight for 5 years
   and seven for 10 years).

** As quoted in Barrons, this consists of the fifty-seven open-end convertible
   funds followed by Lipper Analytical Services, Inc. with dividends reinvested.

++ Morningstar is a mutual fund analysis and statistical reporting service that
   reports on and rates most mutual funds.
<PAGE>   2
BANCROFT CONVERTIBLE FUND, INC.


INVESTMENTS             APRIL 30, 1998
<TABLE>
<CAPTION>
                                                                              PRINCIPAL
                                                                               AMOUNT
                                                                              OR SHARES             VALUE
                                                                               -------            --------
<S>                                                                          <C>                <C>
ADVERTISING -- 2.0%
Interpublic Group Cos., Inc. 1.80% 2004 cv. sub. deb.* (Aa) ..........      $1,000,000          $   956,250
Omnicom Group, Inc. 2 1/4% 2013 cv. sub. deb.* (A-) ..................       1,000,000            1,135,000
                                                                                                -----------
                                                                                                  2,091,250
                                                                                                -----------
AEROSPACE -- 4.6%
Coltec Capital Trust 5 1/4% cv. pfd.* (B2) ............................         15,000 shs          795,000
Morgan Stanley Dean Witter Discover & Co. 0% 2000 
medium-term exch. notes (A1)
(exch. for Boeing Company common stock) ...............................       1,500,000           1,708,125
Orbital Sciences Corp. 5% 2002 cv. sub. notes* (NR) ...................         350,000             603,313
Simula, Inc. 8% 2004 sr. cv. sub. notes (NR) ..........................         750,000             855,000
SPACEHAB, Inc. 8% 2007 cv. sub. notes* (NR) ...........................         705,000             757,875
                                                                                                -----------
                                                                                                  4,719,313
                                                                                                -----------
BANKING -- 7.4%
National Australia Bank Ltd. 7 7/8% exch. capital units (A1) ..........          40,000 shs       1,177,500
National City Corp. common stock ......................................          13,400 shs         927,950
BankAtlantic Bancorp 5 5/8% 2007 cv. sub. deb. (NR) ...................       1,855,000           2,221,363
First State Bancorp 7 1/2% 2017 cv. sub. deb. (NR) ....................         500,000             702,500
Jefferson-Pilot Corp. 7 1/4% 2000 ACES# (A1)
(exch. for NationsBank Corp. common stock) ............................          20,000           2,577,500
                                                                                                -----------
                                                                                                  7,606,813
                                                                                                -----------
BUILDING & REAL ESTATE -- 0.8%
The Rouse Company 5 3/4% 2002 euro. cv. sub. deb. (Baa2) ..............         750,000             805,500
                                                                                                -----------
CAPITAL GOODS -- 7.0%
Ingersoll-Rand Co. 6 3/4% FELINE PRIDES# (A3) .........................          39,500 shs         960,344
CS First Boston, Inc. 2 1/4% 2003 sr. medium-term exch. notes* (Aa3)
(exch. for General Electric Corp. common stock) .......................       1,700,000           1,700,000
CS First Boston, Inc. 2 5/8% 2003 sr. medium-term exch. notes* (Aa)
(exch. for Minnesota Mining and Manufacturing common stock) ...........       1,250,000           1,260,938
Robbins & Myers, Inc. 6 1/2% 2003 cv. sub. notes (NR) .................       1,710,000           2,223,000
U.S. Filter Corp. 4 1/2% 2001 cv. sub. notes (B1) .....................         950,000           1,008,781
                                                                                                -----------
                                                                                                  7,153,063
                                                                                                -----------
COMMUNICATIONS -- 0.1%
WorldCom, Inc. GA depositary shares (representing 8% cum. cv. A pfd.) (B1)       10,000 shs       1,475,625
Bell Atlantic Financial 5 3/4% 2003 cv. sub. deb.* (A+)
(exch. for cash equiv. of Telephone New Zealand common stock) .........       3,000,000           3,120,000
NatWest Markets 0% 2003 exch. trust securities*+ (AA2)
(exch. for Lucent Technologies, Inc. common stock) ....................       2,000,000           3,882,500
Premiere Technologies, Inc. 5 3/4% 2004 cv. sub. notes* (NR) ..........         500,000             593,125
Telefonica De Espana 2% 2002 gtd. exch. deb.* (NR) ....................       1,000,000           1,360,000
                                                                                                -----------
                                                                                                 10,431,250
                                                                                                -----------
CONSUMER GOODS -- 1.0%
Newell Financial Trust I 5 1/4% trust cv. pfd.* (A-)
(conv. into Newell Co. common stock) ..................................           17500 shs         998,594
                                                                                                -----------
DATA-PROCESSING SERVICES -- 3.3%
Affiliated Computer Services, Inc 4% 2005 cv. sub. notes* (Ba2) .......         500,000             517,500
American Express Credit Corp. 1 1/8% 2003 cash exch. notes (A+) .......       1,100,000           1,098,625
Data Processing Resources Corp. 5 1/4% 2005 cv. sub. notes* (NR) ......         250,000             255,000
National Data Corp. 5% 2003 cv. sub. notes (NR) .......................       1,500,000           1,542,188
                                                                                                -----------
                                                                                                  3,413,313
                                                                                                -----------
ENERGY -- 10.0%
AES Trust I $2.6875 term cv. securities, series A (exch. for AES 
Corp. common stock) (Ba1) .............................................          40,000 shs       3,275,000
MCN Energy Group, Inc. 8% FELINE PRIDES# (Ba2) ........................          10,000 shs         590,000
Unocal Capital Trust 6 1/4% trust cv. pfd. (Ba1) ......................          12,500 shs         721,094
Diamond Offshore Drilling, Inc. 3 3/4% 2007 cv. sub. notes (Baa2) .....         750,000           1,021,875
Parker Drilling Co. 5 1/2% 2004 cv. sub. notes (B3) ...................       1,200,000           1,198,500
Pennzoil Company 4 3/4% 2003 exch. sr. deb.  (Baa2)
(exch. for Chevron Corp. common stock) ................................       1,800,000           2,533,500
Swiss Life Financial Ltd. 2% 2005 GEMMS* (NR)
(exch. for Royal Dutch Petroleum common stock) ........................       1,000,000           1,000,000
                                                                                                -----------
                                                                                                 10,339,969
                                                                                                -----------
</TABLE>
<PAGE>   3
<TABLE>
<CAPTION>
                                                                              PRINCIPAL
                                                                               AMOUNT
                                                                              OR SHARES             VALUE
                                                                               -------         -----------


<S>                                                                          <C>               <C>   
ENTERTAINMENT -- 11.8%
Chancellor Media Corp. 6% cv. exch. pfd.* (B) .........................           5,000 shs    $    491,250
Chancellor Media Corp. 7% cv. pfd. (Caa) ..............................          10,000 shs       1,348,125
Hollinger International, Inc. depositary shares (representing 
9 3/4% cv. B pfd.) (B2) ...............................................          40,000 shs         532,500
Houston Industries, Inc. 7% 2000 ACES pfd.# (Baa1)
(exch. for Time Warner, Inc. common stock) ............................          30,000 shs       2,083,125
News Corporation Exchange Trust 5% cv. trust originated pfd.* (Ba2)
(exch. for British Sky Broadcasting Group plc American Depositary Shares)        10,000 shs         878,125
SFX Broadcasting, Inc. 6 1/2% cum. cv. exch. D pfd.* (Caa) ............           4,000 shs         474,750
Triathlon Broadcasting Co. depositary shares (representing 9% 
mandatory cv. pfd.) (NR) ..............................................          50,000 shs         543,750
Clear Channel Communications, Inc. 2 5/8% 2003 sr. cv. notes ..........      $1,500,000           1,497,188
Credit Suisse 3% 2001 equity linked certificates# (Aa)
(exch. for the cash equivalent of Walt Disney Co. common stock) .......       1,000,000           1,610,000
Imax Corp. 5 3/4% 2003 cv. sub. notes* (B3) ...........................       1,000,000           1,387,500
International CableTel, Inc. 7% 2008 cv. sub. notes* (Caa)
(conv. into NTL, Inc. common stock) ...................................         750,000             901,875
International CableTel, Inc. 7% 2008 cv. sub. notes (Caa)
(conv. into NTL, Inc. common stock) ...................................         350,000             420,875
                                                                                                -----------
                                                                                                 12,169,063
                                                                                                -----------
FINANCIAL & INSURANCE -- 7.4%
American General Delaware, L.L.C. 6% cv. A MIPS (A1) ..................          20,000 shs       1,665,000
Frontier Financing Trust 6 1/4% cv. trust originated pfd.* (Baa3) .....          25,000 shs       1,621,875
(conv. into Frontier Insurance Group, Inc. common stock)
American International Group 2 1/4% 2004 cv. notes (AAA) ..............         500,000             582,500
First Central Financial Corp. 9% 2000 cv. sub. deb.@ (NR) .............         851,000                 --
Penn Treaty American Corp. 6 1/4% 2003 cv. sub. notes* (BB+) ..........       1,375,000           1,672,344
US West, Inc. 7 5/8% 1998 DECS# (A2)
(exch. for Enhance Financial Services Group, Inc. common stock) .......          35,000           2,051,875
                                                                                                -----------
                                                                                                  7,593,594
                                                                                                -----------
FOODS -- 2.9%
Apple South Financing I 7% cv. A pfd. (conv. into Apple 
South, Inc. common stock)* (NR) .......................................          15,000 shs         921,094
Suiza Capital Trust II 5 1/2% cv. pfd (conv. into Suiza Foods Corp. 
common stock)* (B2) ...................................................           5,000 shs         247,500
Ralston Purina Co. 7% 2000 SAILS# (A1)
(exch. for Interstate Bakeries Corp. common stock) ....................          30,000           1,820,625
                                                                                                -----------
                                                                                                  2,989,219
                                                                                                -----------
HEALTH CARE & DRUGS -- 10.0%
American Retirement Corp. 5 3/4% 2002 cv. sub. deb. (NR) ..............         500,000             527,500
Assisted Living Concepts, Inc. 5 5/8% 2003 cv. sub. deb. (NR)* ........         250,000             238,750
Assisted Living Concepts, Inc. 6% 2002 cv. sub. deb. (NR) .............         500,000             536,875
Atria Communities, Inc. 5% 2002 cv. sub. notes* (NR) ..................         750,000             741,563
HealthSouth Corp. 3 1/4% 2003 cv. sub. notes* (Ba2) ...................       1,000,000           1,039,375
Morgan Stanley Dean Witter Discover & Co. 0% 2001 medium-term 
exchangeable notes (A1) (exch. for ADR's representing SmithKline 
Beecham plc common stock) .............................................       1,200,000           1,910,250
Republic National Bank of NY 1 7/8% 2002 sr. exch. notes (Aa1)
(exch. for the cash equivalent of Merck & Co., Inc. common stock) .....       2,000,000           2,065,000
Roche Holdings, Inc. 0% 2010 LYON* (Aa2) ..............................       2,500,000           1,412,500
Sandoz Capital BVI Ltd. 2% 2002 cv. sub. notes* (AAA)
(cv. into Novartis AG common stock) ...................................         500,000             786,250
Swiss Life Financial Ltd. 2% 2003 GEMMS* (NR)
(exch. for Glaxo Wellcome PLC common stock) ...........................       1,000,000           1,035,000
                                                                                                -----------
                                                                                                 10,293,063
                                                                                                -----------
HOTEL SERVICES -- 3.0%
Host Marriott Financial Trust 6 3/4% cv. quarterly income pfd. (NR) ...          10,000 shs         570,000
Royal Caribbean Cruises Ltd. $3.625 cv. A pfd. (Ba2) ..................           7,500 shs         824,063
Hilton Hotels Corp. 5% 2006 cv. sub. notes (Baa2) .....................       1,500,000           1,663,125
                                                                                                -----------
                                                                                                  3,057,188
                                                                                                -----------
MANUFACTURED HOUSING -- 2.3%
Fleetwood Capital Trust 6% cv. trust pfd.* (NR)
(conv. into Fleetwood Enterprises, Inc. common stock) .................          40,000 shs       2,325,000
                                                                                                -----------
</TABLE>
<PAGE>   4
BANCROFT CONVERTIBLE FUND, INC.


<TABLE>
<CAPTION>
                                                                              PRINCIPAL
                                                                               AMOUNT
                                                                              OR SHARES             VALUE
                                                                               -------            --------
<S>                                                                         <C>                  <C>
OFFICE EQUIPMENT -- 0.9%
Xerox Credit 2 7/8% 2002 medium-term notes (A1) .......................     $   750,000          $  915,000
                                                                                                 ----------
PARKING SERVICES -- 0.6%                                                                         
Central Parking Financial Trust 5 1/4% trust cv. pfd.* (NR)
(conv. into Central Parking Corp. common stock) .......................          25,000 shs         648,438
                                                                                                 ----------
RETAIL -- 5.1%
Costco Companies, Inc. 0% 2017 cv. sub. notes* (A1) ...................       1,000,000             690,625
Costco Companies, Inc. 0% 2017 cv. sub. notes (A1) ....................         500,000             345,313
Home Depot, Inc. 3 1/4% 2001 cv. sub. notes (A1) ......................       2,000,000           3,111,250
Rite Aid Corp. 5 1/4% 2002 cv. sub. notes* (Baa1) .....................       1,000,000           1,130,000
                                                                                                 ----------
                                                                                                  5,277,188
                                                                                                 ----------
TECHNOLOGY -- 6.8%
Arbor Software Corp. 4 1/2% 2005 cv. sub. notes* (NR) .................         125,000             133,906
The Bear Stearns Companies, Inc. 6 3/4% 2000 medium-term notes* (Aa2)
(exch. for Seagate Technology, Inc. common stock) .....................           7,500             540,300
Hewlett-Packard Co., Inc. 0% 2017 liquid yield option notes* (NR) .....       3,500,000           1,929,375
Morgan Stanley Dean Witter Discover & Co. 6% 1998 DECS# (A1)
(exch. for Cisco Systems, Inc. common stock) ..........................           7,500             753,750
Morgan Stanley Dean Witter Discover & Co. 0% 2001
 technology exch. note trust certificates* (A1) (exch. for 
technology basket common stocks++) ....................................       1,000,000           1,222,500
Thermo Electron Corp. 4 1/4% 2003 cv. sub. deb.* (Ba2) ................       1,000,000           1,149,375
VLSI Technology, Inc. 8 1/4% 2005 cv. sub. notes (B) ..................       1,250,000           1,231,250
                                                                                                 ----------
                                                                                                  6,960,456
                                                                                                 ----------
U.S. TREASURY NOTES -- 0.0%
6 1/4% 3/31/99** ......................................................          25,000              25,164
                                                                                                 ----------
CORPORATE SHORT-TERM NOTES -- 5.0%
American Express Credit Corp. 5.51% 5/1/98 (P1) .......................       5,100,000           5,097,658
                                                                                                 ----------
TOTAL CONVERTIBLE BONDS AND NOTES -- 71.6% ............................                        $ 73,716,731
TOTAL CONVERTIBLE PREFERRED STOCKS -- 24.5% ...........................                          25,167,752
TOTAL COMMON STOCKS -- 0.9% ...........................................                             927,950
TOTAL CORPORATE SHORT-TERM NOTES -- 5.0% ..............................                           5,097,658
                                                                                                 ----------
TOTAL INVESTMENTS -- 102.0% ...........................................                         104,910,091
OTHER ASSETS AND LIABILITIES, NET -- (2.0)% ...........................                          (2,016,326)
                                                                                                 ----------
TOTAL NET ASSETS -- 100.0% ............................................                        $102,893,765
                                                                                                  =========
</TABLE>




* Rule 144A security, may be sold only to qualified institutional buyers 
# See Note A(5) 
+ Guaranteed by National Westminster Bank PLC 
@ Value reflects fair value determination made by the Board of Directors of the 
  Company as a result of FCC financial difficulties 
++ Ticker symbols: CSCO, EDS, HWP, INTC, MSFT & ORCL
** Collateral for a letter of credit

ACES      Automatically convertible equity securities
ADR       American Depository Receipts
DECS      Debt exchangeable for common stock
FELINES   Family of equity-linked income securities
GEMMS     Guaranteed exchangeable monetisation of multiple shares
LYON      Liquid yield option note
MIPS      Monthly income preferred securities
PRIDES    Preferred redeemable increased dividend equity securities
SAILS     Stock appreciation income-linked securities
STRYPES   Structured yield product exchangeable for stock

Ratings in parentheses by Moody's Investors Service, Inc. or Standard & Poor's,
a division of McGraw-Hill Companies, Inc.

The cost of investments for federal income tax purposes is $86,644,896 resulting
in gross unrealized appreciation and depreciation of $19,913,062 and $1,647,867,
respectively, or net unrealized appreciation of $18,265,195 on a tax cost basis.



                 See accompanying notes to financial statements
<PAGE>   5
STATEMENT OF ASSETS AND LIABILITIES (unaudited)


<TABLE>
<CAPTION>
                                                                                              APRIL 30, 1998
                                                                                               ------------
<S>                                                                                           <C> 
ASSETS:
 Investments at value (cost $86,644,896) (Note A) ...................................          $104,910,091
 Cash ...............................................................................                29,803
 Receivable for securities sold .....................................................             1,712,829
 Dividends and interest receivable ..................................................               527,762
 Other assets .......................................................................                37,417
                                                                                               ------------
  Total assets ......................................................................           107,217,902
                                                                                               ------------

LIABILITIES:
 Payable for securities purchased ...................................................             4,273,199
 Accrued management fee (Note B) ....................................................                13,694
 Accrued expenses ...................................................................                37,244
                                                                                               ------------
 Total liabilities ..................................................................             4,324,137
                                                                                               ------------
NET ASSETS ..........................................................................          $102,893,765
                                                                                               ============
NET ASSETS CONSIST OF:
 Accumulated undistributed net investment income ....................................          $    628,823
 Accumulated net realized gain from investment transactions .........................             7,908,363
 Unrealized appreciation on investments .............................................            18,265,195
 Capital shares (Note C) ............................................................                34,753
 Additional paid-in capital .........................................................            76,056,631
                                                                                               ------------
NET ASSETS ..........................................................................          $102,893,765
                                                                                               ============
Net asset value per share ($102,893,765 / 3,475,291 outstanding shares) .............          $      29.61
                                                                                               ============
</TABLE>



                 See accompanying notes to financial statements
<PAGE>   6
BANCROFT CONVERTIBLE FUND, INC.



<TABLE>
<S>                                                                                            <C>  
STATEMENT OF OPERATIONS
Six Months Ended April 30, 1998 (unaudited)
INVESTMENT INCOME (Note A):
 Interest............................................................................          $  1,350,950
 Dividends...........................................................................               662,325
                                                                                                -----------
  Total Income.......................................................................             2,013,275
                                                                                                -----------
EXPENSES (Note B):
 Management fee.......................................................................               370,973
 Custodian...........................................................................                11,146
 Transfer agent......................................................................                19,775
 Professional fees...................................................................                25,673
 Reports to Shareholders.............................................................                38,695
 Directors' fees.....................................................................                35,050
 Treasurer's office..................................................................                12,500
 Listing fee.........................................................................                 8,000
 Other...............................................................................                46,938
                                                                                                -----------
  Total Expenses.....................................................................               568,750
                                                                                                -----------
NET INVESTMENT INCOME................................................................             1,444,525
                                                                                                ===========
REALIZED AND UNREALIZED GAIN ON INVESTMENTS:
 Net realized gain from investment transactions.............. .......................             7,908,363
                                                                                                -----------
 Net change in unrealized appreciation of investments....... ........................             2,271,520
                                                                                                -----------
 Net gain on investments................................... .........................            10,179,883
                                                                                                -----------
 NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS................................           $11,624,408
                                                                                                ===========
</TABLE>



                 See accompanying notes to financial statements
<PAGE>   7
STATEMENT OF CHANGES IN NET ASSETS

<TABLE>
<CAPTION>
                                                                            SIX MONTHS ENDED    YEAR ENDED
                                                                             APRIL 30, 1998  OCTOBER 31, 1997
                                                                              ------------      -----------

<S>                                                                          <C>               <C>  
Increase in net assets from operations:
 Net investment income ....................................................  $   1,444,525     $  2,955,432
 Net realized gain from investment transactions ...........................      7,908,363       11,286,484
 Net unrealized appreciation of investments ...............................      2,271,520        3,620,296
                                                                              ------------      -----------
  Net increase in net assets resulting from operations ....................     11,624,408       17,862,212

Dividends to shareholders from:
 Net investment income ....................................................     (1,383,226)      (2,898,260)
 Net realized gain on investments .........................................    (11,271,015)      (6,815,292)
                                                                              ------------      -----------
  Total dividends..........................................................    (12,654,241)      (9,713,552)
                                                                              ------------      -----------
Capital share transactions (Note C) .......................................      7,736,438        4,736,186
                                                                              ------------      -----------
 Increase in net assets ...................................................      6,706,605       12,884,846

Net assets at beginning of period .........................................     96,187,160       83,302,314
                                                                              ------------      -----------

Net assets at end of period (including undistributed net
investment income of $645,208 and $581,173, respectively) .................   $102,893,765      $96,187,160
                                                                              ============      ===========
</TABLE>



                 See accompanying notes to financial statements
<PAGE>   8
BANCROFT CONVERTIBLE FUND, INC.



FINANCIAL HIGHLIGHTS
Selected data for a share of common stock outstanding

                                             
<TABLE>
<CAPTION>
                                              SIX MONTHS                           YEARS ENDED OCTOBER 31,
                                                 ENDED          ----------------------------------------------------------
PER SHARE OPERATING PERFORMANCE:            APRIL 30, 1998+     1997         1996          1995         1994         1993  
- -------------------------------             --------------     -----         -----         -----        -----        -----
                                                                                                                   
<S>                                              <C>           <C>           <C>          <C>          <C>           <C>   
Net asset value, beginning of period..........   $30.48        $28.23        $24.84       $23.11       $25.00        $22.75
                                                 ------        ------        ------       ------       ------        ------
Net investment income.........................      .42           .94           .96         1.14         1.20          1.26
Net realized and unrealized gain (loss).......     2.70          4.55          4.19         2.30        (1.18)         3.07
                                                 ------        ------        ------       ------       ------        ------
 Total from investment operations.............     3.12          5.49          5.15         3.44          .02          4.33
Dividends paid from net investment income.....     (.42)         (.93)        (1.11)       (1.17)       (1.24)        (1.24)
Distributions from realized gains.............    (3.57)        (2.31)         (.65)        (.54)        (.67)         (.84)
                                                 ------        ------        ------       ------       ------        ------
Net asset value, end of period................   $29.61        $30.48        $28.23       $24.84       $23.11        $25.00
                                                  =====         =====        =====          ====         ====         =====
Market value, end of period...................    28.81         26.81         23.88        22.25        20.13         23.00
Total Investment Return:                                                                                           
 Based on market value........................    25.08%        28.19%        15.65%       20.17%      (4.88)%        22.90%
 Based on net asset value*....................    11.75%        21.18%        21.55%       15.79%         .18%        20.12%
Ratios/Supplemental Data:                                                                                          
Net assets, end of period (000's).............  102,894        96,187        96,187       71,425       64,551        67,829
Ratio of expenses to average net assets.......      1.2%**        1.2%          1.2%         1.2%         1.2%          1.2%
Ratio of net investment income to average                                                                          
 net assets...................................      3.0%**        3.3%          3.9%         4.9%         5.2%          5.4%
Portfolio turnover rate.......................       34%           71%           70%          43%          39%          102%
Average commission rate paid..................    $0.06         $0.06         $0.07                                
</TABLE>

+   Unaudited   
*   Assumes valuation of the Fund's shares, and reinvestment of dividends, at 
    net asset values                  
**  Annualized



                 See accompanying notes to financial statements
<PAGE>   9
MAJOR PORTFOLIO CHANGES February 1 to April 30, 1998
<TABLE>
<CAPTION>
                                                                                  SHARES OR PRINCIPAL AMOUNT    
                                                                           ---------------------------------------
                                                                                                          HELD AT
                                                                           ADDITIONS      REDUCTIONS       4-30-98
                                                                           --------         --------     ---------
<S>                                                                       <C>             <C>            <C>               
American Bankers Insurance Group $3.125 cv. B pfd......................                        7,500            --
American Express Credit Corp. 1-1/8% 2003 cash exch. notes.............   1,100,000                      1,100,000
Avatar Holdings, Inc. 7% 2005 cv. sub. notes...........................                      750,000            --
BankAtlantic Bancorp 5-5/8% 2007 cv. sub. deb..........................     750,000                      1,855,000
BankAtlantic Bancorp 6-3/4% 2006 cv. sub. deb..........................                      625,000            --
Bell Atlantic Financial Services 5-3/4% 2003 cv. sub. deb. 144A........   3,000,000                      3,000,000
Central Parking Financial Trust 5-1/4% trust cv. pfd. 144A ............      25,000                         25,000
Ciba Geigy Corp. 6-1/4% 2016 exch. sub. deb. 144A......................                    1,850,000            --
Clear Channel Communications, Inc. 2-5/8% 2003 sr. cv. notes...........   1,500,000                      1,500,000
Coltec Capital Trust 5-1/4% cv. pfd. 144A..............................      15,000                         15,000
Credit Suisse First Boston Corp. 2-5/8% 2003                                                             
 sr. medium term exch. notes 144A......................................   1,250,000                      1,250,000
Credit Suisse First Boston Corp. 2-1/4% 2003                                                             
 sr. medium term exch. notes 144A......................................   1,700,000                      1,700,000
Credit Suisse First Boston Corp. 3-1/2% 2001                                                             
 sr. medium term exch. notes 144A......................................                    1,000,000            --
Devon Financing Trust 6-1/2% trust cv. pfd. 144A ......................                       10,000            --
Enserch Corp. 6-3/8% 2002 euro. cv. sub. deb...........................                    1,500,000            --
First Data Corp. common stock..........................................                       45,966            --
Fleetwood Capital Trust 6% cv. trust pfd. 144A.........................      40,000                         40,000
Genesco, Inc. 5-1/2% 2005 cv. sub. notes 144A..........................   1,000,000        1,000,000            --
Halter Marine Group, Inc. 4-1/2% 2004 cv. sub. notes 144A..............                      625,000            --
HealthSouth Corp. 3-1/4% 2003 cv. sub. notes 144A......................   1,000,000                      1,000,000
Host Marriott Financial Trust 6-3/4% cv. quarterly income pfd. 144A ...      10,000                         10,000
Houston Industries, Inc. 7% 2000 ACES..................................       8,000                         30,000
Ingersoll-Rand Co. 6-3/4% FELINE PRIDES................................      39,500                         39,500
International CableTel, Inc. 7-1/4% 2005 cv. sub. notes 144A...........                      600,000            --
Microsoft Corp. 2-3/4% cv. exch. A pfd.................................                        5,000            --
Nabors Industries, Inc. 5% 2006 cv. sub. notes.........................                      550,000            --
Roche Holdings, Inc. 0% 2010 LYON 144A.................................                    1,000,000     2,500,000
Swiss Life Financial Ltd. 2% 2003 GEMMS 144A...........................   1,000,000                      1,000,000
Swiss Life Financial Ltd. 2% 2005 GEMMS 144A...........................   1,000,000                      1,000,000
Thermo Instrument Systems 4-1/2% 2003 cv. sub. deb. 144A...............                      375,000            --
U.S. Filter Corp. 4-1/2% 2001 cv. sub. notes...........................     950,000                        950,000
Union Bank Of Switzerland Finance N.V. 2-1/2% 2001 euro. cv. deb.......                      500,000            --
Washington Mutual Savings Bank common stock............................                        7,800            --
</TABLE>

- -----------------------  

ACES      Automatically convertible equity securities                       
FELINES   Family of equity-linked income securities                      
GEMMS     Guaranteed exchangeable monetisation of multiple shares          
LYON      Liquid yield option note                                          
PRIDES    Preferred redeemable increased dividend equity securities     
<PAGE>   10
NOTES TO FINANCIAL STATEMENTS

(A) Bancroft Convertible Fund, Inc. (the Fund) is registered under the
Investment Company Act of 1940 as a diversified, closed-end management
investment company. The preparation of financial statements in conformity with
generally accepted accounting principles requires management to make estimates
and assumptions that affect the reported amounts of assets and liabilities at
the date of the financial statements, and the reported amounts of revenue and
expenses during the reporting period. Actual results could differ from those
estimates. 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

Security transactions are accounted for on the trade date (date the order to buy
or sell is executed) with gain or loss on the sale of securities being
determined based upon identified cost. Dividend income is recorded on the
ex-dividend date and interest income is recorded on the accrual basis. Interest
of $6,800 was earned on cash balances held by the custodian of the Fund's assets
during the six months ended April 30, 1998.

3. Federal Income 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 provision for federal income or excise taxes is believed
necessary.

4. Dividends and Distributions to Shareholders

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


5. Market Risk

It is the Fund's policy to invest the majority of its assets in convertible
securities. Although convertible securities do derive part of their value from
that of the securities into which they are convertible, they are not considered
derivative financial instruments. However, certain of the Fund's investments
include features which render them more sensitive to price changes in their
underlying security. Thus they expose the Fund to greater downside risk than
traditional convertible securities, but still less than that of the underlying
common stock. The market value of those securities was $12,447,219 at April 30,
1998, representing 12.1% of net assets.

(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 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 $25,000 a year are reimbursed by the Fund. Such
reimbursements amounted to $12,500 for the six months ended April 30, 1998. The
officers of the Fund are also directors, officers or employees of the investment
adviser, and are compensated by the investment adviser.

(C) At April 30, 1998 there were 3,475,291 shares of $.01 par value common stock
outstanding (9,000,000 shares authorized). During the six months ended April 30,
1998, 319,028 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 $7,736,436.
<PAGE>   11
(D) Purchases and sales of investments, exclusive of corporate short-term notes,
aggregated $31,174,324 and $33,309,239, respectively, for the six months ended
April 30, 1998.

(E) A distribution of $.23 per share from net investment income was declared on
May 18, 1998, payable June 30, 1998 to shareholders of record at the close of
business June 16, 1998.

(F) The Year 2000 Issue

Like other investment companies and financial and business organizations around
the world, the Fund could be adversely affected if the computer systems used by
the Adviser and other service providers do not properly process and calculate
date-related information and data from and after January 1, 2000. The Adviser
has reviewed its in-house systems and found them to be Year 2000 compliant.
Assurances have been obtained from all outside service providers that they
either are now compliant or will be by 1998 year-end and that they will begin
testing any replacement systems in 1999. The Fund does not expect to incur any
significant costs in order to address the Year 2000 issue.

Results of the 1998 Annual Shareholders Meeting

The results of the shareholder vote at the Annual Meeting of Shareholders held
on February 23, 1998, were:

1. All directors nominated by management were elected for terms expiring in
   2001.

<TABLE>
<CAPTION>
                                          Votes for       Votes withheld
                                          ---------        ------------
<S>                                      <C>                 <C>
          Gordon F. Ahalt                 2,433,556           52,203
          Jane D. O'Keeffe                2,446,470           39,289
          Nicolas W. Platt                2,426,215           59,544

</TABLE>

2. The selection of Coopers & Lybrand as independent accountants was ratified
   with 2,436,449 shares voted for, 17,019 shares voted against, and 32,291
   abstained.

3. The proposal to eliminate the fundamental investment policy of the Company
   that prohibits investments in other investment companies passed, as 1,721,943
   shares voted for, 137,495 shares voted against, 78,366 shares abstained and
   547,955 shares were broker non-votes.

- -------------------------------------------------------------------------------
Important Factors Regarding Forward-Looking Statements

Information contained within the letter to Shareholders constitutes
forward-looking statements within the meaning of the Private Securities
Litigation Reform Act of 1995. Although the Company believes its expectations
are based on reasonable assumptions, the Company's actual results could differ
materially from its expectations. Factors which could cause actual results to
differ from expectations include, among others, the effect of the global economy
on domestic and foreign markets, changes to foreign and domestic markets in
general or changes to the market for convertible securities.

- -------------------------------------------------------------------------------
Pursuant to Section 23 of the Investment Company Act of 1940, notice is hereby
given that the Company may in the future purchase shares of its Common Stock
from time to time whenever it may be deemed advantageous to the Company. Nothing
herein shall be considered a commitment to purchase such shares.
<PAGE>   12
DIRECTORS
GORDON F. AHALT
WILLIAM A. BENTON
ELIZABETH C. BOGAN
THOMAS H. DINSMORE, C.F.A.
DONALD M. HALSTED, JR.
GEORGE R. LIEBERMAN
DUNCAN O. MCKEE
JANE D. O'KEEFFE
NICOLAS W. PLATT


OFFICERS


THOMAS H. DINSMORE            Chairman of the Board

JANE D. O'KEEFFE              President

SIGMUND LEVINE                Senior Vice President
                              and Secretary

H. TUCKER LAKE                Vice President, Trading

GERMAINE M. ORTIZ             Assistant Vice President

GARY I. LEVINE                Treasurer and Assistant
                              Secretary

MERCEDES A. PIERRE            Assistant Treasurer


                     STOCKHOLDER SERVICES AND TRANSFER AGENT
                  Chemical Mellon Shareholder Services, L.L.C.
                                  P.O. Box 590
                            Ridgefield Park, NJ 07660
                                 1-800/851-9677

                   Printed on [RECYCLE LOGO] recycled paper.






                                     (LOGO)




                                      1998
                                   SEMI-ANNUAL
                                     REPORT
                                 APRIL 30, 1998




                                     (LOGO)




                                65 MADISON AVENUE
                            MORRISTOWN, NJ 07960-7308
                                 (973) 631-1177
                                 www.bcvecf.com
                             email: [email protected]






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