VALUE LINE CONVERTIBLE FUND INC
N-30D, 1997-01-02
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<PAGE>
- --------------------------------------------------------------------------------
 
<TABLE>
<S>                    <C>
INVESTMENT ADVISER     Value Line, Inc.
                       220 East 42nd Street
                       New York, NY 10017-5891
 
DISTRIBUTOR            Value Line Securities, Inc.
                       220 East 42nd Street
                       New York, NY 10017-5891
 
CUSTODIAN BANK         State Street Bank and Trust
                       Co.
                       225 Franklin Street
                       Boston, MA 02110
 
SHAREHOLDER            State Street Bank and Trust
SERVICING AGENT        Co.
                       c/o NFDS
                       P.O. Box 419729
                       Kansas City, MO 64141-6729
 
INDEPENDENT            Price Waterhouse LLP
ACCOUNTANTS            1177 Avenue of the Americas
                       New York, NY 10036
 
LEGAL COUNSEL          Peter D. Lowenstein, Esq.
                       Two Greenwich Plaza, Suite
                       100
                       Greenwich, CT 06830
 
DIRECTORS              Jean Bernhard Buttner
                       John W. Chandler
                       Leo R. Futia
                       Charles E. Reed
                       Paul Craig Roberts
                       Nancy-Beth Sheerr
 
OFFICERS               Jean Bernhard Buttner
                       CHAIRMAN AND PRESIDENT
                       John Risner
                       VICE PRESIDENT
                       David T. Henigson
                       VICE PRESIDENT and
                       SECRETARY/TREASURER
                       Jack M. Houston
                       ASSISTANT SECRETARY/TREASURER
                       Stephen La Rosa
                       ASSISTANT SECRETARY/TREASURER
</TABLE>
 
         THE FINANCIAL STATEMENTS INCLUDED HEREIN HAVE BEEN TAKEN FROM THE
         RECORDS OF THE FUND WITHOUT EXAMINATION BY THE INDEPENDENT ACCOUNTANTS
         AND, ACCORDINGLY, THEY DO NOT EXPRESS AN OPINION THEREON.
 
         THIS UNAUDITED REPORT IS ISSUED FOR INFORMATION OF SHAREHOLDERS. IT IS
         NOT AUTHORIZED FOR DISTRIBUTION TO PROSPECTIVE INVESTORS UNLESS
         PRECEDED OR ACCOMPANIED BY A CURRENTLY EFFECTIVE PROSPECTUS OF THE FUND
         (OBTAINABLE FROM THE DISTRIBUTOR).
 
                                                                       VLF610208
 
                      ------------------------------------
 
                              SEMI-ANNUAL  REPORT
                      ------------------------------------
                                OCTOBER 31, 1996
                    ----------------------------------------
 
                                   VALUE LINE
                                  CONVERTIBLE
                                   FUND, INC.
 
                                     [LOGO]
<PAGE>
VALUE LINE CONVERTIBLE FUND, INC.
 
                                                   To Our Value Line Convertible
- -------------------------------------------
 
DEAR SHAREHOLDER:
 
We are pleased to report that the performance of the Value Line Convertible
Fund, Inc. for the six months ending October 31, 1996 remained strong. The
Fund's total return over this period was 5.7%, which ranked in the top quartile
of the 42 convertible funds tracked by Lipper Analytical Services.
 
The stock market has continued its strong upward move, albeit with a definite
tiering effect between blue chip stocks and smaller, more volatile issues. This
tiering is easily seen by comparing the 8.27% increase in the Dow Jones
Industrial Average with the 2.6% advance in the Nasdaq Composite Index over the
six months ended October 31, 1996. When we last wrote to you in June of this
year, we noted that interest rates had risen sharply throughout the first six
months of 1996. That rise has been reversed. The yield on the U.S. Treasury
10-year note peaked at just over 7% in early July, and has fallen steadily since
then to where it is now just over 6%.
 
At this writing your fund has over 20% of its assets in cash, with the balance
in convertible bonds and preferred stocks. There are no common stocks held at
this time. In making investment decisions, your Fund continues to rely on the
Value Line Timeliness Ranking System, introduced in 1965. We are also using the
new Performance Ranking System, which was developed for the 'Expanded Edition'
of The Value Line Investment Survey. The stock ranks provided by these systems
are incorporated into the Value Line Convertible Ranking System, which
identifies attractively priced convertibles that can be exchanged for favorably
ranked stocks.
 
As we look into 1997, we expect to remain defensive through at least the early
part of the year. In addition to our fundamental analysis of the underlying
business, this involves focusing on the current yield and downside protection a
security offers. In the convertible sector, the key to executing this strategy
is obtaining this downside protection at the smallest possible cost in upside
participation.
 
We thank you for your interest in The Value Line Convertible Fund, and look
forward to serving your investment needs in the future.
 
                Yours truly,
 
                                                          [SIGNATURE]
 
                CHAIRMAN and PRESIDENT
 
December 9, 1996
 
- --------------------------------------------------------------------------------
 
2
<PAGE>
                                               VALUE LINE CONVERTIBLE FUND, INC.
 
Fund Shareholders
- -------------------------------------------
 
ECONOMIC OBSERVATIONS
 
The domestic economy is now expanding at a decidedly slower pace than had been
the case several months earlier. Real, inflation-adjusted GDP, for example,
which increased by better than 3% in the first half of 1996, as the housing,
auto, retail, and industrial markets all pushed forward briskly, was rising by
perhaps 2%, or so, as 1996 drew to a close. Moreover, current indications point
to more of the same in the new year, with growth probably averaging 1.7%-2.0%.
 
The case for slow, but sustained growth, is a compelling one. The present easing
in activity is largely the result of two factors, the first being the jump in
long-term interest rates early in 1996 (which made the financing of certain
purchases more costly) and the second being the ongoing runup in household debt.
Our sense, for now, however, is that neither event is sufficient to bring the
uptrend to a close. Long-term interest rates, for one thing, have recently
turned lower (as the earlier inflation fears, which led to the rise in rates in
the first place, have subsided). Second, several areas of the country, notably
the East and the West Coasts, are now strengthening selectively. Finally,
inventory levels remain low, and this should obviate the need to clear goods off
the shelves before factory production can again ramp up.
 
The slower growth pace is likely to keep inflation below 3%, on average, over
the next year. The combination of a modest level of business activity and
persistent moderate inflation should also keep the Federal Reserve Board from
pursuing overly restrictive monetary policies. Interest rates, meanwhile, will
probably remain fairly stable over the next year or so. The one potential fly in
the ointment is a likely deceleration in corporate profit growth as the economy
slows a bit further in 1997.
 
PERFORMANCE DATA:*
 
<TABLE>
<CAPTION>
                                        GROWTH OF
                  AVERAGE              AN ASSUMED
                  ANNUAL               INVESTMENT
               TOTAL RETURN            OF $10,000
           ---------------------  ---------------------
<S>        <C>                    <C>
 1 Year
 ended
 9/30/96...        20.17%                $12,017
 5 Years
 ended
 9/30/96...        13.39%                $18,742
10 Years
 ended
 9/30/96...        10.47%                $27,075
</TABLE>
 
*  THE PERFORMANCE DATA QUOTED REPRESENT PAST PERFORMANCE AND ARE NO GUARANTEE
   OF FUTURE PERFORMANCE. THE AVERAGE ANNUAL TOTAL RETURN AND GROWTH OF AN
   ASSUMED INVESTMENT OF $10,000 INCLUDE DIVIDENDS REINVESTED AND CAPITAL GAINS
   DISTRIBUTIONS ACCEPTED IN SHARES. THE INVESTMENT RETURN AND PRINCIPAL VALUE
   OF AN INVESTMENT WILL FLUCTUATE SO THAT AN INVESTMENT, WHEN REDEEMED, MAY BE
   WORTH MORE OR LESS THAN ITS ORIGINAL COST. THE AVERAGE ANNUAL TOTAL RETURNS
   AT OCTOBER 31, 1996, FOR THE ONE-YEAR, FIVE-YEAR, AND 10-YEAR PERIODS WERE
   24.58%, 13.15%, AND 10.29%.
 
- --------------------------------------------------------------------------------
 
                                                                               3
<PAGE>
VALUE LINE CONVERTIBLE FUND, INC.
 
Schedule of Investments (unaudited)
- -------------------------------------------
 
<TABLE>
<CAPTION>
 PRINCIPAL
  AMOUNT                                                                                            VALUE
<C>          <S>                                                                                 <C>
- ------------------------------------------------------------------------------------------------------------
CONVERTIBLE CORPORATE BONDS & NOTES (58.4%)
             AIR TRANSPORT (2.9%)
$ 1,000,000  Airborne Freight Corp. 6 3/4%, 8/15/01............................................  $   987,500
  1,000,000  Alaska Air Group, Inc. 6 1/2%, 6/15/05............................................    1,132,500
                                                                                                 -----------
                                                                                                   2,120,000
 
             AUTO PARTS-ORIGINAL EQUIPMENT (2.0%)
  1,380,000  Arvin Industries, Inc. 7 1/2%, 9/30/14............................................    1,449,000
 
             BANK-FOREIGN (1.5%)
  1,000,000  MBL International Finance (Bermuda) Trust, Exchangeable Notes, 3%, 11/30/02.......    1,091,250
 
             BROADCASTING/CABLE TV (1.0%)
    750,000  Scandinavian Broadcasting System S.A. 7 1/4%, 8/1/05..............................      756,563
 
             BUILDING & CONSTRUCTION (1.4%)
  1,500,000  Empresas ICA Sociedad Controladora de C.V. 5%, 3/15/04............................    1,005,000
 
             CEMENT & AGGREGATES (1.1%)
    750,000  Medusa Corp. 6%, 11/15/03.........................................................      819,375
 
             COMPUTER & PERIPHERALS (3.3%)
    250,000  Conner Peripherals, Inc. 6 3/4%, 3/1/01...........................................      282,187
    500,000  SCI Systems, Inc. 5%, 5/1/06......................................................      607,500
    500,000  Storage Technology Corp. 8%, 5/31/15..............................................      613,750
  1,000,000  Synoptics Communications, Inc. 5 1/4%, 5/15/03....................................      881,250
                                                                                                 -----------
                                                                                                   2,384,687
 
             COMPUTER SOFTWARE & SERVICES (2.2%)
  2,000,000  Automatic Data Processing, Inc. zero coupon, 2/20/12..............................    1,106,500
    500,000  Comverse Technology, Inc. 5 3/4%, 10/1/06*........................................      495,625
                                                                                                 -----------
                                                                                                   1,602,125
 
             DIVERSIFIED COMPANIES (0.3%)
    250,000  Thermo Instrument Systems, Inc. 4 1/2%, 10/15/03..................................      246,875
 
             DRUG (3.6%)
  1,250,000  ALZA Corp. 5%, 5/1/06.............................................................    1,203,125
  1,500,000  NABI Inc. 6 1/2%, 2/1/03..........................................................    1,433,124
                                                                                                 -----------
                                                                                                   2,636,249
 
             ELECTRICAL EQUIPMENT (1.2%)
    500,000  Broadband Technologies, Inc. 5%, 5/15/01*.........................................      395,000
</TABLE>
 
- --------------------------------------------------------------------------------
 
4
<PAGE>
                                               VALUE LINE CONVERTIBLE FUND, INC.
 
                                                                OCTOBER 31, 1996
- -------------------------------------------
<TABLE>
<CAPTION>
 PRINCIPAL
  AMOUNT                                                                                            VALUE
- ------------------------------------------------------------------------------------------------------------
<C>          <S>                                                                                 <C>
$   550,000  Broadband Technologies, Inc. 5%, 5/15/01..........................................  $   434,500
                                                                                                 -----------
                                                                                                     829,500
 
             FOREIGN ELECTRONICS/ENTERTAINMENT (1.4%)
  1,000,000  Imax Corp. 5 3/4%, 4/1/03*........................................................      982,500
 
             GOLD/SILVER MINING (1.2%)
  1,000,000  Asanti Goldfields Ltd. 5 1/2%, 3/15/03............................................      881,250
 
             HOMEBUILDING (0.7%)
    500,000  Continental Homes Holdings Corp. 6 7/8%, 3/15/02..................................      490,000
 
             HOTEL/GAMING (2.0%)
    500,000  HFS Incorporated 4 3/4%, 3/1/03...................................................      641,875
    500,000  Hilton Hotels Corp. 5%, 5/15/06...................................................      555,000
    500,000  Marriott International, Inc. zero coupon, 3/25/11.................................      285,000
                                                                                                 -----------
                                                                                                   1,481,875
 
             INSURANCE-DIVERSIFIED (1.6%)
  3,000,000  Mutual Risk Management, Ltd. zero coupon, 10/30/15................................    1,188,750
 
             INSURANCE-LIFE (1.6%)
  1,000,000  Equitable Companies, Inc. 6 1/8%, 12/15/24........................................    1,127,500
 
             INSURANCE-PROPERTY/CASUALTY (0.8%)
  1,000,000  Fremont General Corp. zero coupon, 10/12/13.......................................      580,000
 
             MACHINERY (0.7%)
    500,000  Robbins & Meyers, Inc. 6 1/2%, 9/1/03.............................................      532,500
 
             MEDICAL SERVICES (3.2%)
    750,000  Healthsource, Inc. 5%, 3/1/03.....................................................      596,250
  1,000,000  NovaCare Inc. 5 1/2%, 1/15/00.....................................................      896,250
    500,000  RoTech Medical Corp. 5 1/4%, 6/1/03...............................................      422,500
    400,000  Tenet Healthcare Corp. 6%, 12/1/05................................................      410,500
                                                                                                 -----------
                                                                                                   2,325,500
 
             MEDICAL SUPPLIES (1.9%)
  1,000,000  McKesson Corp. 4 1/2%, 3/1/04.....................................................      915,000
    500,000  UroMed Corp. 6%, 10/15/03*........................................................      488,750
                                                                                                 -----------
                                                                                                   1,403,750
 
             METALS & MINING (2.0%)
  1,365,000  INCO Ltd. 7 3/4%, 3/15/16.........................................................    1,433,250
</TABLE>
 
- --------------------------------------------------------------------------------
 
                                                                               5
<PAGE>
VALUE LINE CONVERTIBLE FUND, INC.
 
SCHEDULE OF INVESTMENTS (UNAUDITED)
- -------------------------------------------
<TABLE>
<CAPTION>
 PRINCIPAL
  AMOUNT                                                                                            VALUE
- ------------------------------------------------------------------------------------------------------------
<C>          <S>                                                                                 <C>
             NATURAL GAS-DIVERSIFIED (1.3%)
$   300,000  Kelley Oil & Gas Partners, Ltd. 8 1/2%, 4/1/00....................................  $   285,000
    712,000  Kelley Oil & Gas Partners, Ltd. 7 7/8%, 12/15/99..................................      660,380
                                                                                                 -----------
                                                                                                     945,380
 
             OILFIELD SERVICES/EQUIPMENT (3.2%)
  1,000,000  Baker Hughes, Inc. zero coupon, 5/5/08............................................      743,750
    500,000  Key Energy Group Inc. 7%, 7/1/03*.................................................      660,000
    500,000  Nabors Industries, Inc. 5%, 5/15/06...............................................      567,500
    250,000  Pride Petroleum Services, Inc. 6 1/4%, 2/15/06....................................      388,750
                                                                                                 -----------
                                                                                                   2,360,000
 
             PAPER & FOREST PRODUCTS (0.6%)
    500,000  Sappi BVI Finance Ltd. 7 1/2%, 8/1/02.............................................      465,625
 
             PETROLEUM-INTEGRATED (1.3%)
  1,000,000  USX-Marathon Group 7%, 6/15/17....................................................      966,250
 
             R.E.I.T. (2.6%)
    500,000  Camden Property Trust 7.33%, 4/1/01...............................................      568,125
  1,000,000  Developers Diversified Realty Co. 7%, 8/15/99.....................................    1,040,000
    300,000  LTC Properties, Inc. 7 3/4%, 1/1/02...............................................      310,500
                                                                                                 -----------
                                                                                                   1,918,625
 
             RESTAURANT (0.6%)
    500,000  TPI Enterprises, Inc. 8 1/4%, 7/15/02.............................................      455,000
 
             RETAIL-SPECIAL LINES (2.2%)
    250,000  Sports Authority Inc. 5 1/4%, 9/15/01*............................................      248,750
  1,250,000  Waban, Inc. 6 1/2%, 7/1/02........................................................    1,373,438
                                                                                                 -----------
                                                                                                   1,622,188
 
             RETAIL BUILDING SUPPLY (1.4%)
  1,000,000  Home Depot, Inc. 3 1/4%, 10/1/01..................................................    1,002,500
 
             RETAIL STORE (2.0%)
  1,000,000  Price Co. 6 3/4%, 3/1/01..........................................................    1,051,250
    350,000  Saks Holdings, Inc. 5 1/2%, 9/15/06...............................................      368,375
                                                                                                 -----------
                                                                                                   1,419,625
 
             SEMICONDUCTOR (1.6%)
  1,000,000  Analog Devices, Inc. 3 1/2%, 12/1/00..............................................    1,170,000
</TABLE>
 
- --------------------------------------------------------------------------------
 
6
<PAGE>
                                               VALUE LINE CONVERTIBLE FUND, INC.
 
                                                                OCTOBER 31, 1996
- -------------------------------------------
<TABLE>
<CAPTION>
 PRINCIPAL
  AMOUNT                                                                                            VALUE
- ------------------------------------------------------------------------------------------------------------
<C>          <S>                                                                                 <C>
             TELECOMMUNICATION SERVICES (3.0%)
$ 1,000,000  International Cabletel Inc. 7%, 6/15/08...........................................  $   885,000
  2,000,000  United States Cellular Corp., zero coupon 6/15/15.................................      667,500
  1,000,000  Winstar Communications, Inc. 14%, 10/15/05*.......................................      627,500
                                                                                                 -----------
                                                                                                   2,180,000
 
             OTHER (1.0%)
    750,000  Republic of Italy-Istituto Nazional delle Assicurazioni Sp.A. 5%, 6/28/01.........      751,875
                                                                                                 -----------
 
             TOTAL CONVERTIBLE CORPORATE BONDS & NOTES (COST $42,225,220)......................  $42,624,567
                                                                                                 -----------
</TABLE>
 
- --------------------------------------------------------------------------------
 
                                                                               7
<PAGE>
VALUE LINE CONVERTIBLE FUND, INC.
 
SCHEDULE OF INVESTMENTS (UNAUDITED)
- -------------------------------------------
 
<TABLE>
<CAPTION>
  SHARES                                                                                             VALUE
<C>          <S>                                                                                  <C>
- -------------------------------------------------------------------------------------------------------------
CONVERTIBLE PREFERRED STOCKS (13.9%)
             BANK (0.4%)
     5,000   Banco Commercial Portugues SA 8% Pfd. Series "A"...................................  $   254,375
 
             CEMENT & AGGREGRATES (1.7%)
    25,400   Southdown Inc., $2.875 Series "D"..................................................    1,270,000
 
             COPPER (0.1%)
     3,000   Freeport-McMoran Copper & Gold Inc. $1.75 Pfd......................................       90,000
 
             FOREIGN TELECOMMUNICATIONS (0.8%)
    10,000   Philippine Long Distance Telephone Co. $3.50, Depositary Shares....................      565,000
 
             HOTEL/GAMING (0.7%)
    20,000   FelCor Suite Hotels Inc., $1.95 Series "A".........................................      522,500
 
             INSURANCE-DIVERSIFIED (1.7%)
    22,000   American Bankers Insurance Group, Inc. $3.125 Series "B"...........................    1,262,250
 
             NATURAL GAS-DISTRIBUTION (1.2%)
    25,000   Western Gas Resources Inc. $2.625 Pfd. "A".........................................      881,250
 
             NATURAL GAS-DIVERSIFIED (0.9%)
    27,000   Kelley Oil & Gas Corp. $2.625 exchangeable Pfd.....................................      648,000
 
             PETROLEUM-INTEGRATED (2.6%)
    30,000   Occidental Petroleum Corp. $3.00 Pfd...............................................    1,927,500
 
             R.E.I.T. (0.7%)
    20,000   Security Capital Pacific Trust Series "A" $1.75 Pfd................................      537,500
 
             TELECOMMUNICATION EQUIPMENT (0.7%)
    20,000   General Datacomm Industries, Inc. 9% exchangeable Pfd.*............................      482,500
 
             TELECOMMUNICATION SERVICES (2.4%)
    20,000   MFS Communications Inc. 8% Depositary Shares.......................................    1,735,000
                                                                                                  -----------
 
             TOTAL CONVERTIBLE PREFERRED STOCKS (COST $8,813,363)...............................   10,175,875
                                                                                                  -----------
 
             TOTAL INVESTMENT SECURITIES (72.3%) (COST $51,038,583).............................   52,800,442
                                                                                                  -----------
</TABLE>
 
- --------------------------------------------------------------------------------
 
8
<PAGE>
VALUE LINE CONVERTIBLE FUND, INC.
 
SCHEDULE OF INVESTMENTS (UNAUDITED)                             OCTOBER 31, 1996
- -------------------------------------------
 
<TABLE>
<CAPTION>
 PRINCIPAL
  AMOUNT                                                                                            VALUE
<C>          <S>                                                                                 <C>
- ------------------------------------------------------------------------------------------------------------
SHORT-TERM INVESTMENTS (28.6%)
 
             U.S. GOVERNMENT AGENCY OBLIGATIONS (13.7%)
$10,000,000  Federal Home Loan Bank 5.18%, discount note, 11/21/96.............................  $ 9,971,222
 
             REPURCHASE AGREEMENT (14.9%) (INCLUDING ACCRUED INTEREST)
 10,900,000  Collateralized by $10,670,000 U.S. Treasury Note 6 1/2% due 5/31/01, with a value
               of $11,124,978 (With State Street Bank & Trust & Co. 5.6%, dated 10/31/96, due
               11/1/96, delivery value $10,901,696)............................................   10,901,696
                                                                                                 -----------
 
             TOTAL SHORT-TERM INVESTMENTS (COST $20,872,918)...................................   20,872,918
                                                                                                 -----------
 
EXCESS OF LIABILITIES OVER CASH AND RECEIVABLES (-0.9%)........................................     (637,132)
                                                                                                 -----------
 
NET ASSETS (100.0%)............................................................................  $73,036,228
                                                                                                 -----------
 
NET ASSET VALUE, OFFERING AND REDEMPTION PRICE PER OUTSTANDING SHARE ($73,036,228  DIVIDED BY
5,003,423 SHARES OUTSTANDING)..................................................................  $     14.60
                                                                                                 -----------
</TABLE>
 
*  PURSUANT TO RULE 144A UNDER THE SECURITIES ACT OF 1933, THIS SECURITY CAN
   ONLY BE SOLD TO QUALIFIED INSTITUTIONAL INVESTORS.
 
SEE NOTES TO FINANCIAL STATEMENTS.
 
- --------------------------------------------------------------------------------
 
                                                                               9
<PAGE>
VALUE LINE CONVERTIBLE FUND, INC.
 
STATEMENT OF ASSETS AND LIABILITIES
                                      STATEMENT OF OPERATIONS
AT OCTOBER 31, 1996 (UNAUDITED)
                                      FOR THE SIX MONTHS ENDED OCTOBER 31, 1996
(UNAUDITED)
- ------------------------------------------------------------------------
<TABLE>
<S>                                     <C>
ASSETS:
Investment securities, at value
  (Cost--$51,038,583).................  $ 52,800,442
Short-term investments
  (Cost--$20,872,918).................    20,872,918
Cash..................................        20,656
Receivable for capital shares sold....     2,537,775
Interest and dividends receivable.....       610,412
Receivable for securities sold........        42,768
                                        ------------
 
    TOTAL ASSETS......................    76,884,971
                                        ------------
 
LIABILITIES:
Payable for securities purchased......     3,624,667
Payable for capital shares
  repurchased.........................       130,429
Accrued expenses:
  Advisory fee........................        45,837
  Other...............................        47,810
                                        ------------
 
    TOTAL LIABILITIES.................     3,848,743
                                        ------------
NET ASSETS............................  $ 73,036,228
                                        ------------
NET ASSETS CONSIST OF:
Capital stock, at $1.00 par value
  (authorized 50,000,000, outstanding
  5,003,423 shares)...................  $  5,003,423
Additional paid-in capital............    57,691,013
Undistributed investment
  income--net.........................       296,161
Accumulated net realized gain on
  investments.........................     8,283,772
Unrealized net appreciation of
  investments.........................     1,761,859
                                        ------------
    NET ASSETS........................  $ 73,036,228
                                        ------------
 
NET ASSET VALUE, OFFERING AND
  REDEMPTION PRICE PER OUTSTANDING
  SHARE ($73,036,228 5,003,423 SHARES
  OUTSTANDING)........................  $      14.60
                                        ------------
</TABLE>
 
<TABLE>
<S>                                       <C>
INVESTMENT INCOME:
Interest................................  $1,647,955
Dividends (Net of foreign withholding
  tax of $6,985)........................     279,250
                                          ----------
    TOTAL INCOME........................   1,927,205
                                          ----------
 
EXPENSES:
Advisory fee............................     262,612
Auditing and legal fees.................      21,419
Transfer agent..........................      19,176
Registration and filing fees............      13,813
Printing and stationery.................       9,756
Custodian fees..........................       7,872
Directors' fees and expenses............       6,812
Postage.................................       5,590
Insurance, dues and other...............       3,804
Telephone...............................       2,995
                                          ----------
    TOTAL EXPENSES BEFORE OFFSET........     353,849
    Less: Expense Offset................      (3,880)
                                          ----------
    TOTAL EXPENSES......................     349,969
                                          ----------
 
INVESTMENT INCOME--NET..................   1,577,236
                                          ----------
 
REALIZED AND UNREALIZED GAIN ON
  INVESTMENTS--NET:
  Realized Gain--Net....................   7,322,872
  Change in Unrealized Appreciation.....  (5,291,571)
                                          ----------
NET REALIZED GAIN AND CHANGE IN
  UNREALIZED APPRECIATION ON
  INVESTMENTS...........................   2,031,301
                                          ----------
NET INCREASE IN NET ASSETS FROM
  OPERATIONS............................  $3,608,537
                                          ----------
</TABLE>
 
SEE NOTES TO FINANCIAL STATEMENTS.
 
- --------------------------------------------------------------------------------
 
10
<PAGE>
                                               VALUE LINE CONVERTIBLE FUND, INC.
 
STATEMENT OF CHANGES IN NET ASSETS
FOR THE SIX MONTHS ENDED OCTOBER 31, 1996 (UNAUDITED) AND FOR THE YEAR ENDED
APRIL 30, 1996
- ------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                                           SIX MONTHS ENDED
                                                                           OCTOBER 31, 1996   YEAR ENDED APRIL
                                                                             (UNAUDITED)          30, 1996
<S>                                                                        <C>                <C>
                                                                           -----------------------------------
OPERATIONS:
  Investment income--net.................................................     $  1,577,236       $  2,958,285
  Realized gain on investments--net......................................        7,322,872          4,046,566
  Change in unrealized appreciation......................................       (5,291,571)         6,409,849
                                                                           -----------------------------------
  Net increase in net assets from operations.............................        3,608,537         13,414,700
                                                                           -----------------------------------
 
DISTRIBUTIONS TO SHAREHOLDERS:
  Investment income--net.................................................       (1,462,962)        (3,024,424)
  Realized gains on investments..........................................        --                 --
                                                                           -----------------------------------
  Total distributions....................................................       (1,462,962)        (3,024,424)
                                                                           -----------------------------------
 
CAPITAL SHARE TRANSACTIONS:
  Net proceeds from sale of shares.......................................       56,049,941         52,653,026
  Net proceeds from reinvestment of distributions to shareholders........        1,224,610          2,474,940
  Cost of shares repurchased.............................................      (59,004,012)       (43,421,496)
                                                                           -----------------------------------
  (Decrease) Increase from capital share transactions....................       (1,729,461)        11,706,470
                                                                           -----------------------------------
TOTAL INCREASE...........................................................          416,114         22,096,746
 
NET ASSETS:
  Beginning of period....................................................       72,620,114         50,523,368
                                                                           -----------------------------------
  End of period..........................................................     $ 73,036,228       $ 72,620,114
                                                                           -----------------------------------
 
UNDISTRIBUTED INVESTMENT INCOME--NET,
  AT END OF PERIOD.......................................................     $    296,161       $    181,887
                                                                           -----------------------------------
</TABLE>
 
SEE NOTES TO FINANCIAL STATEMENTS.
 
- --------------------------------------------------------------------------------
 
                                                                              11
<PAGE>
                                               VALUE LINE CONVERTIBLE FUND, INC.
 
NOTES TO FINANCIAL STATEMENTS (UNAUDITED)
- -------------------------------------------
 
1.SIGNIFICANT ACCOUNTING POLICIES
 
Value Line Convertible Fund, Inc. (the "Fund") is registered under the
Investment Company Act of 1940, as amended, as a diversified, open-end
management investment company whose investment objective is to seek high current
income together with capital appreciation. The Fund seeks to accomplish its
objective by investing primarily in convertible securities.
 
The following significant accounting policies are in conformity with generally
accepted accounting principles for investment companies. Such policies are
consistently followed by the Fund in the preparation of its financial
statements. Generally accepted accounting principles may require management to
make estimates and assumptions that affect the reported amounts and disclosures
in the financial statements. Actual results may differ from those estimates.
 
(A) SECURITY VALUATION. The Fund's securities are valued by an independent
pricing service approved by the Fund's Board of Directors. Securities for which
quotations are not available from the pricing service are valued at the mean
between the latest available and representative asked and bid prices provided by
dealers in such securities. Securities for which market quotations are not
readily available or which are not readily marketable, and all other assets of
the Fund, are valued at fair value as the Board of Directors may determine in
good faith. Short-term investments that mature in less than 60 days are valued
at amortized cost if their original maturity was 60 days or less, or by
amortizing their value on the 61st day prior to maturity, if their original term
exceeds 60 days.
 
(B) REPURCHASE AGREEMENTS. In connection with transactions in repurchase
agreements, the Fund's custodian takes possession of the underlying collateral
securities, the value of which exceeds the principal amount of the repurchase
transaction, including accrued interest. To the extent that any repurchase
transaction exceeds one business day, the value of the collateral is
marked-to-market on a daily basis to ensure the adequacy of the collateral. In
the event of default of the obligation to repurchase, the Fund has the right to
liquidate the collateral and apply the proceeds in satisfaction of the
obligation. Under certain circumstances, in the event of default or bankruptcy
by the other party to the agreement, realization and/or retention of the
collateral or proceeds may be subject to legal proceedings.
 
(C) FEDERAL INCOME TAXES. It is the Fund's policy to comply with the
requirements of the Internal Revenue Code of 1986, as amended, applicable to
regulated investment companies and to distribute all of its taxable income to
its shareholders. Therefore, no federal income tax or excise tax provision is
required.
 
(D) SECURITY TRANSACTIONS AND DISTRIBUTIONS. Security transactions are accounted
for on the date the securities are purchased or sold. Interest income is accrued
as earned. Realized gains and losses on sales of securities are calculated for
financial accounting and federal income tax purposes on the identified-cost
basis. Dividend income and distributions to shareholders are recorded on the ex-
dividend date.
 
Distributions are determined in accordance with income tax regulations, which
may differ from generally accepted accounting principles.
 
(E) AMORTIZATION. Discounts on debt securities are amortized to interest income
over the life of the security with a corresponding increase to the security's
cost basis; premiums on debt securities are not amortized.
 
- --------------------------------------------------------------------------------
 
12
<PAGE>
                                               VALUE LINE CONVERTIBLE FUND, INC.
 
                                                                OCTOBER 31, 1996
- -------------------------------------------
 
2.CAPITAL SHARE TRANSACTIONS
 
Transactions in capital stock were as follows:
 
<TABLE>
<CAPTION>
                          SIX MONTHS
                          ENDED OCT.      YEAR ENDED
                           31, 1996        APRIL 30,
                          (UNAUDITED)        1996
<S>                      <C>             <C>
                         -----------------------------
Shares sold............     3,960,079       3,953,152
Shares issued to
  shareholders in
  reinvestment of
  dividends............        86,263         194,152
                         -----------------------------
                            4,046,342       4,147,304
Shares repurchased.....    (4,192,712)     (3,281,081)
                         -----------------------------
Net (decrease)
  increase.............      (146,370)        866,223
                         -----------------------------
</TABLE>
 
3.PURCHASES AND SALES OF SECURITIES
 
Purchases and sales of investment securities, excluding short-term securities,
were as follows:
 
<TABLE>
<CAPTION>
                                   SIX MONTHS
                                  ENDED OCTOBER
                                    31, 1996
                                   (UNAUDITED)
<S>                               <C>
                                  -------------
PURCHASES:
Investment Securities             $ 40,635,919
                                  -------------
SALES OR REDEMPTIONS:
Investment Securities             $ 55,446,797
                                  -------------
</TABLE>
 
At October 31, 1996, the aggregate cost of investment securities and short-term
securities for Federal income tax purposes is $71,911,501. The aggregate
appreciation and depreciation of investments at October 31, 1996, based on a
comparison of investment values and their costs for Federal income tax purposes
was $2,770,361 and $1,008,502 respectively, resulting in a net appreciation of
$1,761,859.
 
4.INVESTMENT ADVISORY CONTRACT, MANAGEMENT FEES, AND
  TRANSACTIONS WITH AFFILIATES
 
An advisory fee of $262,612 was paid or payable to Value Line, Inc. (the
Adviser), for the six months ended October 31, 1996. This was computed at the
rate of 3/4 of 1% of average daily net assets during the period and paid
monthly. The Adviser provides research, investment programs, supervision of the
investment portfolio and pays costs of certain administrative services, office
space, equipment and compensation of administrative, bookkeeping, and clerical
personnel necessary for managing the affairs of the Fund. The Adviser also
provides persons, satisfactory to the Fund's Board of Directors, to act as
officers and employees of the Fund and pays their salaries and wages. The Fund
bears all other costs and expenses.
 
A fee of $2,880 for printing services was paid to the Advisor for the six months
ended October 31, 1996.
 
Certain officers and directors of the Adviser and its subsidiary, Value Line
Securities, Inc. (the Fund's distributor and a registered broker/dealer), are
also officers and a director of the Fund.
 
The Adviser and/or affiliated companies owned 518,895 shares of the Fund's
capital stock, representing 10.4% of the outstanding shares at October 31, 1996.
 
- --------------------------------------------------------------------------------
 
                                                                              13
<PAGE>
VALUE LINE CONVERTIBLE FUND, INC.
 
FINANCIAL HIGHLIGHTS
- -------------------------------------------
SELECTED DATA FOR A SHARE OF CAPITAL STOCK OUTSTANDING THROUGHOUT EACH PERIOD:
 
<TABLE>
<CAPTION>
                                         SIX MONTHS
                                         ENDED OCT.                           YEARS ENDED APRIL 30,
                                          31, 1996     -------------------------------------------------------------------
                                        (UNAUDITED)       1996          1995          1994          1993          1992
<S>                                     <C>            <C>           <C>           <C>           <C>           <C>
                                        ----------------------------------------------------------------------------------
 
NET ASSET VALUE, BEGINNING OF
  PERIOD..............................     $14.10         $11.79        $12.26        $13.80        $12.24        $11.07
                                        ----------------------------------------------------------------------------------
   INCOME (LOSS) FROM INVESTMENT
   OPERATIONS:
      Net investment income...........        .32            .66           .74           .71           .62           .65
      Net gains or losses on
        securities
        (both realized and
        unrealized)...................        .48           2.33          (.02)          .11          1.54          1.13
                                        ----------------------------------------------------------------------------------
      Total from investment
      operations......................        .80           2.99           .72           .82          2.16          1.78
                                        ----------------------------------------------------------------------------------
 
   LESS DISTRIBUTIONS:
      Dividends from investment
         income--net..................       (.30)          (.68)         (.76)         (.69)         (.60)         (.61)
      Distributions from capital
         gains........................         --             --          (.43)        (1.67)           --            --
                                        ----------------------------------------------------------------------------------
      Total distributions.............       (.30)          (.68)        (1.19)        (2.36)         (.60)         (.61)
                                        ----------------------------------------------------------------------------------
NET ASSET VALUE, END OF PERIOD........    $ 14.60        $ 14.10       $ 11.79       $ 12.26       $ 13.80       $ 12.24
                                        ----------------------------------------------------------------------------------
Total return..........................       5.71%+        26.07%         6.53%         5.50%        18.16%        16.42%
                                        ----------------------------------------------------------------------------------
 
RATIOS/SUPPLEMENTAL DATA:
Net assets, end of period (in
  thousands)..........................    $73,036        $72,620       $50,523       $49,823       $43,936       $37,177
Ratio of expenses to average net
  assets                                     1.00%*         1.08%         1.08%         1.07%         1.10%         1.14%
Ratio of net investment income
  to average net assets...............       4.48%*         5.14%         6.13%         5.32%         4.80%         5.45%
Portfolio turnover rate...............         79%+          129%           87%          142%          146%          140%
</TABLE>
 
+  NOT ANNUALIZED
 
*  ANNUALIZED.
 
SEE NOTES TO FINANCIAL STATEMENTS.
 
- --------------------------------------------------------------------------------
 
14
<PAGE>
                 (This page has been left blank intentionally.)
 
- --------------------------------------------------------------------------------
 
                                                                              15
<PAGE>
VALUE LINE CONVERTIBLE FUND, INC.
 
                         The Value Line Family of Funds
- -------------------------------------------
 
1950--THE VALUE LINE FUND seeks long-term growth of capital along with modest
current income by investing substantially all of its assets in common stocks or
securities convertible into common stock.
 
1952--THE VALUE LINE INCOME FUND'S primary investment objective is income, as
high and dependable as is consistent with reasonable growth. Capital growth to
increase total return is a secondary objective.
 
1956--THE VALUE LINE SPECIAL SITUATIONS FUND seeks to obtain long-term growth of
capital by investing not less than 80% of its assets in "special situations". No
consideration is given to achieving current income.
 
1972--VALUE LINE LEVERAGED GROWTH INVESTORS' sole investment objective is to
realize capital growth by investing substantially all of its assets in common
stocks. The Fund may borrow up to 50% of its net assets to increase its
purchasing power.
 
1979--THE VALUE LINE CASH FUND, a money market fund, seeks high current income
consistent with preservation of capital and liquidity.
 
1981--VALUE LINE U.S. GOVERNMENT SECURITIES FUND seeks maximum income without
undue risk to principal. Under normal conditions, at least 80% of the value to
its assets will be invested in issues of the U.S. Government and its agencies
and instrumentalities.
 
1983--VALUE LINE CENTURION FUND* seeks long-term growth of capital as its sole
objective by investing primarily in stocks ranked 1 or 2 by Value Line for
year-ahead relative performance.
 
1984--THE VALUE LINE TAX EXEMPT FUND seeks to provide investors with maximum
income exempt from federal income taxes while avoiding undue risk to principal.
The Fund offers investors a choice of two portfolios: a Money Market Portfolio
and a High-Yield Portfolio.
1985--VALUE LINE CONVERTIBLE FUND seeks high current income together with
capital appreciation primarily from convertible securities ranked 1 or 2 for
year-ahead performance by the Value Line Convertible Ranking System.
 
1986--VALUE LINE AGGRESSIVE INCOME TRUST seeks to maximize current income by
investing in high-yielding, lower-rated, fixed-income corporate securities.
 
1987--VALUE LINE NEW YORK TAX EXEMPT TRUST seeks to provide New York taxpayers
with maximum income exempt from New York State, New York City and federal
individual income taxes while avoiding undue risk to principal.
 
1987--VALUE LINE STRATEGIC ASSET MANAGEMENT TRUST* invests in stocks, bonds and
cash equivalents according to computer trend models developed by Value Line. The
objective is to professionally manage the optimal allocation of these
investments at all times.
 
1992--VALUE LINE INTERMEDIATE BOND FUND seeks high current income consistent
with low volatility of principal by investing in a diversified portfolio of
investment-debt securities with a dollar-weighted average portfolio maturity of
between three and ten years.
 
1993--VALUE LINE SMALL-CAP GROWTH FUND invests primarily in common stocks or
securities convertible into common stock, with its primary objective being
long-term growth of capital.
 
1993--VALUE LINE ASSET ALLOCATION FUND seeks high total investment return,
consistent with reasonable risk. The Fund invests in stocks, bonds and money
market instruments utilizing quantitative modeling to determine the correct
asset mix.
 
1995--VALUE LINE U.S. MULTINATIONAL COMPANY FUND'S investment objective is
maximum total return. It invests primarily in securities of U.S. companies that
have significant sales from international operations.
 
* ONLY AVAILABLE THROUGH THE PURCHASE OF GUARDIAN INVESTOR, A TAX DEFERRED
  VARIABLE ANNUITY, OR VALUEPLUS, A VARIABLE LIFE INSURANCE POLICY.
 
FOR MORE COMPLETE INFORMATION ABOUT ANY OF THE VALUE LINE FUNDS, INCLUDING
CHARGES AND EXPENSES, SEND FOR A PROSPECTUS FROM VALUE LINE SECURITIES, INC.,
220 EAST 42ND STREET, NEW YORK, NEW YORK 10017-5891 OR CALL 1-800-223-0818, 24
HOURS A DAY, 7 DAYS A WEEK. READ THE PROSPECTUS CAREFULLY BEFORE YOU INVEST OR
SEND MONEY.
 
- --------------------------------------------------------------------------------
 
16


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