VALUE LINE CONVERTIBLE FUND INC
N-30D, 1996-07-02
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INVESTMENT ADVISER Value Line, Inc.                   -----------------------
                   220 East 42nd Street                    ANNUAL REPORT
                   New York, NY 10017-5891            -----------------------
                                                           APRIL 30, 1996
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 Co.
SERVICING AGENT    c/o NFDS                                VALUE LINE
                   P.O. Box 419729                         CONVERTIBLE
                   Kansas City, MO 64141-6729              FUND, INC.

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

OFFICERS           Jean Bernhard Buttner
                   CHAIRMAN and PRESIDENT
                   John Risner
                   VICE PRESIDENT
                   Richard Cunniffe
                   VICE PRESIDENT
                   David T. Henigson
                   VICE PRESIDENT and 
                   SECRETARY/TREASURER
                   Jack M. Houston
                   ASSISTANT SECRETARY/TREASURER           [LOGO]
                   Stephen La Rosa
                   ASSISTANT SECRETARY/TREASURER

THIS REPORT IS ISSUED FOR THE 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).

                                          VLF046896


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VALUE LINE CONVERTIBLE FUND, INC.



                                                               TO OUR VALUE LINE
- --------------------------------------------------------------------------------



To Our Shareholders:

We are pleased to report that the performance of the Value Line Convertible 
Fund, Inc. (the "Fund") for the 12 months ending April 30, 1996, was excellent.
The Fund's total return was 26.07%.

The bull market in both stocks and bonds throughout 1995 gave way in 1996 to a
bull market solely in stocks.  Yields on the 10-year U.S. Treasury note have
risen from 5.6% in January to over 6.60% currently.  This rise translates into a
total return of -6.00%, year-to-date.  By contrast, your Fund was up 11.57%,
year-to-date.  This compares favorably with the 13.15% and 6.88% returns posted
by the NASDAQ Composite and the S&P 500, respectively, over the same time
period.

At this writing your Fund has 10% of its assets in cash, with the balance
predominantly in convertible bonds and preferred stocks.  There are currently
two common-stock positions (General Motors Class E and AMR Corp.), both of which
resulted from forced conversion of long-term convertible holdings.  Both of
these stocks are ranked favorably by The Value Line Investment Survey;
therefore, they will be held until the Fund needs to raise cash or their
Timeliness-TM- Ranks fall.

In making investment decisions, your Fund continues to rely on the Value Line
Timeliness-TM- 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.

For the balance of 1996, we will be taking a defensive stance towards the equity
market.  This will include both selling those convertibles whose prices have
risen to a point that they are essentially common-stock equivalents and
purchasing convertibles with greater downside protection.  The advantage of this
approach under current market conditions is that it allows investors to shed
some equity-market risk yet maintain reasonable participation in further price
rises if our conservative approach proves to be unwarranted.

We thank you for your interest in the Value Line Convertible Fund, and we look
forward to serving your investment needs in the future.

                                       Sincerely,



                                       /s/  Jean Bernhard Buttner
                                       Jean Bernhard Buttner
                                       CHAIRMAN and PRESIDENT

June 14, 1996


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2

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                                               VALUE LINE CONVERTIBLE FUND, INC.



CONVERTIBLE FUND SHAREHOLDERS



ECONOMIC OBSERVATIONS

The economic expansion is heating up once again.  True, there's no all-out boom
under way, nor does one figure to evolve over the next few quarters.  Indeed,
it's likely that the economy will start to slow down later this year, under
pressure from high consumer-debt levels and rising long-term borrowing costs. 
But for now, at least, the government and private-sector reports coming out show
sufficient strength to virtually assure that growth in the second and third
quarters of this year will exceed the 0.5% and 2.3% rates of expansion logged,
respectively, in last year's final three months and the opening quarter of 1996.

The current pickup in business activity is producing some unwelcome side
effects, however, namely inflationary pressures--dormant for so long--that are
starting to selectively resurface.  This can be observed in the higher prices
now being paid for manufactured goods, in the emergence of some wage pressures,
and in the somewhat elevated pricing levels of certain commodities.  Thus, while
inflation is still being fairly well contained on an overall basis, the
disquieting trends cited above will have to be watched.

The Federal Reserve Board will be among those monitoring the situation closely. 
In particular, the central bank is likely to focus on upcoming job-growth
figures, on retail-sales trends, and on producer- and consumer-price reports to
determine whether the selective inflationary pressures being seen become more
widespread.  Should that happen, the Fed would likely start to push interest
rates higher, in an effort to cool down the expansion--and ultimately inflation.
One obvious casualty of slower growth could be corporate profits.

[GRAPH]

                                From 5/1/86 to 4/30/96
+  THE STANDARD & POOR'S 500 INDEX IS AN UNMANAGED INDEX THAT IS REPRESENTATIVE
OF THE LARGER-CAPITALIZATION STOCKS TRADED IN THE UNITED STATES. THE
PRESENTATION INCLUDES REINVESTED DIVIDENDS. 

PERFORMANCE DATA:*

                                                        Growth of
                                         Average        an Assumed
                                          Annual        Investment
                                       Total Return     of $10,000
                                       ------------     ----------

  1 Year ended 3/31/96 . . . . . .       26.33%          $ 12,633
  5 Years ended 3/31/96. . . . . .       14.21%            19,434
  10 Years ended 3/31/96 . . . . .        9.79%            25,454

* 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
APRIL 30, 1996, FOR THE ONE-YEAR, FIVE-YEAR, AND 10-YEAR PERIODS WERE 26.07%,
14.28%, AND 9.89%.

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                                                                               3

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VALUE LINE CONVERTIBLE FUND, INC.



SCHEDULE OF INVESTMENTS
- --------------------------------------------------------------------------------
Shares or
Principal Amount                                                        Value 
- --------------------------------------------------------------------------------

COMMON STOCKS (4.8%)

              AIR TRANSPORT (1.0%)
    7,700    +AMR Corp.. . . . . . . . . . . . . . . . . . .     $     687,225

              COMPUTER SOFTWARE 
              & SERVICES (3.8%)
   49,273     General Motors Corp. Class "E" . . . . . . .           2,777,765
                                                                   -----------

              TOTAL COMMON STOCKS 
              (Cost $2,667,213). . . . . . . . . . . . . . .         3,464,990
                                                                   -----------

CONVERTIBLE CORPORATE
BONDS & NOTES (65.6%)

              AIR TRANSPORT (3.4%)
$1,000,000    Air Express International Corp. 
               6%, 1/15/03 . . . . . . . . . . . . . . . . .         1,231,250
   100,000    Airborne Freight Corp. 6 3/4%, 
               8/15/01 . . . . . . . . . . . . . . . . . . .            99,875
 1,000,000   *Continental Airlines, Inc. 6 3/4%, 
               4/15/06 . . . . . . . . . . . . . . . . . . .         1,110,000
                                                                   -----------
                                                                     2,441,125

              BANK-FOREIGN (1.6%)
 1,000,000    MBL International Finance 
               (Bermuda) Trust, Exchangeable 
               Notes, 3%, 11/30/02 . . . . . . . . . . . . .         1,168,750

              BANK-MIDWEST (1.8%)
 1,000,000    Fifth Third Bancorp 4 1/4%, 
               1/15/98 . . . . . . . . . . . . . . . . . . .         1,302,500

              BROADCASTING/CABLE 
              TV (1.1%)
   750,000    Scandinavian Broadcasting 
               System S.A. 7 1/4%, 8/1/05. . . . . . . . . .           777,187

              BUILDING & 
              CONSTRUCTION (1.3%)
 1,500,000    Empresas ICA Sociedad Controladora 
               de C.V. 5%, 3/15/04 . . . . . . . . . . . . .           971,250


Principal
Amount                                                                  Value 
- --------------------------------------------------------------------------------

              COMPUTER AND 
              PERIPHERALS (1.3%)
$  250,000    Conner Peripherals, Inc. 
               6 3/4%, 3/1/01. . . . . . . . . . . . . . . .     $     267,500
   500,000    Conner Peripherals, Inc. 
               6 1/2%, 3/1/02. . . . . . . . . . . . . . .             567,500
   100,000    Unisys Corp. 8 1/4%, 3/15/06 . . . . . . . .             110,875
                                                                   -----------
                                                                       945,875

              COMPUTER SOFTWARE 
              & SERVICES (7.0%)
 4,500,000    Automatic Data Processing, Inc. 
               zero coupon, 2/20/12. . . . . . . . . . . . .         2,278,125
   500,000   *Safeguard Scientifics, Inc. 6%,
               2/1/06. . . . . . . . . . . . . . . . . . . .           615,625
 2,500,000    Softkey International, Inc. 5 1/2%, 
               11/1/00 . . . . . . . . . . . . . . . . . . .         2,162,500
                                                                   -----------
                                                                     5,056,250

              DIVERSIFIED 
              COMPANIES (2.3%)
   860,000    Thermo Electron Corp. 5%, 
               4/15/01 . . . . . . . . . . . . . . . . . . .         1,707,100

              DRUG (3.7%)
 1,250,000    ALZA Corp. 5%, 5/1/06  . . . . . . . . . . . .         1,253,125
   300,000   *NABI 6 1/2%, 2/1/03  . . . . . . . . . . . . .           333,000
 1,000,000   *Quintiles Transnational Corp. 
               4 1/4%, 5/31/00 (a) . . . . . . . . . . . . .         1,085,000
                                                                   -----------
                                                                     2,671,125
              ELECTRONICS (5.1%)
   500,000   *Richey Electronics, Inc. 7%, 
               3/1/06. . . . . . . . . . . . . . . . . . . .           512,500
 1,750,000   *SCI Systems, Inc. 5%, 5/1/06 . . . . . . . . .         1,925,000
 1,490,000    Park Electrochemical Corp. 
               5 1/2%, 3/1/06 . . . . . . . . . . . . . . .         1,296,300
                                                                   -----------
                                                                     3,733,800


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4

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                                               VALUE LINE CONVERTIBLE FUND, INC.



                                                                  APRIL 30, 1996
- --------------------------------------------------------------------------------
Principal
Amount                                                                  Value 
- --------------------------------------------------------------------------------

ENVIRONMENTAL (3.0%)
$1,000,000    Molten Metal Technology, Inc.
               5 1/2%, 5/1/06. . . . . . . . . . . . . . . .     $   1,022,500
   500,000    Sanifill, Inc. 5%, 3/1/06. . . . . . . . . . .           540,625
   500,000   *United States Filter Corp. 6%, 
               9/15/05 . . . . . . . . . . . . . . . . . . .           638,750
                                                                   -----------
                                                                     2,201,875

              FINANCIAL SERVICES (2.3%)
   500,000   *Aames Financial Corp. 5 1/2%, 
               3/15/06 . . . . . . . . . . . . . . . . . . .           592,500
   500,000   *Cityscape Financial Corp. 6%, 
               5/1/06. . . . . . . . . . . . . . . . . . . .           502,500
   600,000    Pioneer Financial Services, Inc. 
               6 1/2%, 1/1/03. . . . . . . . . . . . . . . .           597,750
                                                                   -----------
                                                                     1,692,750

              FOREIGN ELECTRONICS/
              ENTERTAINMENT (3.8%)
 2,750,000   *Imax Corp. 5 3/4%, 4/1/03. . . . . . . . . . .         2,772,344

              GOLD/SILVER MINING (1.4%)
 1,000,000    Ashanti Goldfields Ltd. 5 1/2%, 
               3/15/03 . . . . . . . . . . . . . . . . . . .           995,000

              HOMEBUILDING (0.8%)
   500,000    Continental Homes Holdings Corp. 
               6 7/8%, 11/1/02 . . . . . . . . . . . . . . .           563,750

              HOTEL/GAMING (0.4%)
   500,000   *Marriott International, Inc. zero 
               coupon, 3/25/11 . . . . . . . . . . . . . . .           264,063

              INDUSTRIAL 
              SERVICES (1.9%)
   500,000    Career Horizons, Inc. 7%, 11/1/02. . . . . . .         1,062,500
   250,000    Mercury Air Group, Inc. 7 3/4%, 
               2/1/06. . . . . . . . . . . . . . . . . . . .           284,375
                                                                   -----------
                                                                     1,346,875
              MACHINERY (0.8%)
   500,000    Raymond Corp. 6 1/2%, 12/15/03 . . . . . . . .           583,125


Principal
Amount                                                                  Value 
- --------------------------------------------------------------------------------

              MEDICAL SERVICES (6.1%)
$  500,000   *ARV Assisted Living, Inc. 
               6 3/4%, 4/1/06  . . . . . . . . . . . . . . .     $     538,750
   750,000   *Healthsource, Inc. 5%, 3/1/03. . . . . . . . .           729,375
   500,000   *PHP Healthcare Corp. 6 1/2%,
               12/15/02. . . . . . . . . . . . . . . . . . .           645,000
   500,000    PhyCor, Inc. 4 1/2%, 2/15/03 . . . . . . . . .           521,875
   400,000    Tenet Healthcare Corp. 6%, 
               12/1/05 . . . . . . . . . . . . . . . . . . .           432,000
 1,000,000   *U.S. Diagnostic Laboratories, 
               Inc. 9%, 3/31/03. . . . . . . . . . . . . . .         1,050,000
   500,000   *Veterinary Centers of America, Inc. 
               5 1/4%, 5/1/06. . . . . . . . . . . . . . . .           512,500
                                                                   -----------
                                                                     4,429,500

              MEDICAL SUPPLIES (0.7%)
   500,000    AMSCO International, Inc. 6 1/2%,
               10/15/02. . . . . . . . . . . . . . . . . . .           488,750

              OILFIELD SERVICES/
              EQUIPMENT (0.5%)
   250,000    Pride Petroleum Services, Inc. 
               6 1/4%, 2/15/06 . . . . . . . . . . . . . . .           373,125

              PAPER & FOREST 
              PRODUCTS (0.7%)
   500,000    Sappi BVI Finance Ltd. 7 1/2%, 
               8/1/02. . . . . . . . . . . . . . . . . . . .           476,250

              PETROLEUM-
              INTEGRATED (1.3%)
 1,000,000    USX-Marathon Group 7%, 
               6/15/17 . . . . . . . . . . . . . . . . . . .           956,250

              PRECISION 
              INSTRUMENTS (1.3%)
   500,000    Thermo Instrument Systems, Inc.
               3 3/4%, 9/15/00 . . . . . . . . . . . . . . .           967,500


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                                                                               5

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VALUE LINE CONVERTIBLE FUND, INC.



SCHEDULE OF INVESTMENTS
- --------------------------------------------------------------------------------
Principal
Amount                                                                  Value 
- --------------------------------------------------------------------------------
              R.E.I.T. (1.1%)
$  500,000    Camden Property Trust 7.33%, 
               4/1/01. . . . . . . . . . . . . . . . . . . .     $     491,875
   300,000    LTC Properties Inc. 7 3/4%, 
               1/1/02. . . . . . . . . . . . . . . . . . . .           294,375
                                                                   -----------
                                                                       786,250

              RESTAURANT (0.6%)
   500,000    TPI Enterprises Inc. 8 1/4%, 
               7/15/02 . . . . . . . . . . . . . . . . . . .           438,125

              RETAIL-SPECIAL LINES (4.1%)
 1,000,000    Baby Superstore Inc. 4 7/8%, 
               10/1/00 . . . . . . . . . . . . . . . . . . .         1,016,250
   500,000    Pier 1 Imports, Inc. 6 7/8%, 
               4/1/02. . . . . . . . . . . . . . . . . . . .           597,500
 1,250,000    Waban, Inc. 6 1/2%, 7/1/02 . . . . . . . . . .         1,356,250
                                                                   -----------
                                                                     2,970,000

              RETAIL STORE (0.8%)
   500,000    Federated Department Stores, Inc. 
               5%, 10/1/03 . . . . . . . . . . . . . . . . .           566,250

              SECURITIES 
              BROKERAGE (2.5%)
 1,200,000    Waterhouse Investor Services, Inc. 
               6%, 12/15/03. . . . . . . . . . . . . . . . .         1,855,500

              SEMICONDUCTOR (2.4%)
 1,000,000    Analog Devices, Inc. 3 1/2%, 
              12/1/00. . . . . . . . . . . . . . . . . . . .         1,135,000
   500,000   *Applied Magnetics Corp. 7%, 
               3/15/06 . . . . . . . . . . . . . . . . . . .           637,500
                                                                   -----------
                                                                     1,772,500

              TELECOMMUNICATION
              SERVICES (0.5%)
   925,000    United States Cellular Corp., 
               zero coupon, 6/15/15. . . . . . . . . . . . .           328,375
                                                                   -----------

              TOTAL CONVERTIBLE 
              CORPORATE BONDS & 
              NOTES (Cost $42,780,828) . . . . . . . . . . .        47,603,119
                                                                   -----------

Shares                                                                  Value 
- --------------------------------------------------------------------------------

CONVERTIBLE PREFERRED STOCKS (18.9%)

              AIR TRANSPORT (2.4%)
   10,000     Delta Air Lines, Inc. Series "C"
               $3.50 Pfd.. . . . . . . . . . . . . . . . . .     $     633,750
   20,000    *Trans World Airlines, Inc. 8%
               Pfd. Exchangeable . . . . . . . . . . . . . .         1,090,000
                                                                 -------------
                                                                     1,723,750

              COMPUTER SOFTWARE &
              SERVICES (0.3%)
    4,000    *Wang Laboratories, Inc. 6 1/2% 
               Series "B" Depositary Shares. . . . . . . . .           218,000

              COPPER (0.1%)
    3,000     Freeport-McMoran Copper & 
               Gold, Inc. $1.75 Pfd. . . . . . . . . . . . .            96,375

              FINANCIAL SERVICES (0.6%)
    5,000     Travelers Group, Inc. Series "B"
               5.50% Pfd.. . . . . . . . . . . . . . . . . .           422,500

              FOREIGN-
              TELECOMMUNICATIONS (2.4%)
   35,000     Philippine Long Distance Telephone 
               Co. $3.50 Sponsored Depositary 
               Shares. . . . . . . . . . . . . . . . . . . .         1,767,500

              HOTEL/GAMING (0.4%)
    5,000     Station Casinos, Inc. $3.50 Pfd. . . . . . . .           266,875

              INSURANCE-
              DIVERSIFIED (1.0%)
   10,000     Penncorp Financial Group, Inc.
               $3.375 Pfd. . . . . . . . . . . . . . . . . .           745,000

              INSURANCE-LIFE (2.4%)
   30,000     Conseco, Inc. Series "D"
               $3.25 Pfd.. . . . . . . . . . . . . . . . . .         1,725,000


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6

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                                               VALUE LINE CONVERTIBLE FUND, INC.



                                                                  APRIL 30, 1996
- --------------------------------------------------------------------------------
Shares                                                                  Value 
- --------------------------------------------------------------------------------

              INSURANCE-PROPERTY/
              CASUALTY (0.8%)
   10,000     Integon Corp. 3.875% Pfd.. . . . . . . . . . .     $     571,250

              PAPER & FOREST PRODUCTS 
              (2.3%)
   36,000     James River Corp. of Virginia 
               Series "K"  Exchangeable 
               $3.375 Pfd. . . . . . . . . . . . . . . . . .         1,683,000

              PETROLEUM-
              INTEGRATED (2.7%)
   30,000     Occidental Petroleum Corp. 
               $3.00 Pfd.. . . . . . . . . . . . . . . . . .         1,942,500

              PETROLEUM-
              PRODUCING (1.1%)
   20,000    *Lomak Petroleum, Inc. 8 1/8% 
               Exchangeable Pfd. . . . . . . . . . . . . . .           780,000

              R.E.I.T. (0.7%)
   20,000     Security Capital Pacific Trust 
               Series "A" $1.75 Pfd. . . . . . . . . . . . .           512,500

              RETAIL-SPECIAL LINES (0.9%)
   12,000     TJX Companies, Inc. Series "C"
               $3.125 Pfd. . . . . . . . . . . . . . . . . .           705,000

              TELECOMMUNICATION 
              SERVICES (0.8%)
   10,000     MFS Communications, Inc. 8% 
               Depositary Shares . . . . . . . . . . . . . .           590,000
                                                                   -----------


              TOTAL CONVERTIBLE 
              PREFERRED STOCKS
              (Cost $12,239,438) . . . . . . . . . . . . . .        13,749,250
                                                                   -----------

Principal
Amount                                                                  Value 
- --------------------------------------------------------------------------------

              WARRANTS (0.7%)

   15,000    +Bank of New York Co., Inc., 
               expires 11/29/98. . . . . . . . . . . . . . .     $     538,125

              TOTAL WARRANTS 
              (Cost $614,575). . . . . . . . . . . . . . . .           538,125
                                                                   -----------

              TOTAL INVESTMENT 
              SECURITIES (90.0%)
              (Cost $58,302,054) . . . . . . . . . . . . . .        65,355,484
                                                                   -----------


              REPURCHASE AGREEMENT (10.5%)
              (including accrued interest)

$7,600,000    Collateralized by $7,825,000 
              U.S. Treasury Bills, due 7/5/96, 
              with a value of $7,753,701
              (with First Chicago Capital 
              Markets, Inc. 5.30%, dated 
              4/30/96, due 5/1/96, delivery 
              value $7,601,119). . . . . . . . . . . . . . .         7,601,119

EXCESS OF LIABILITIES OVER CASH 
AND RECEIVABLES (-0.5%). . . . . . . . . . . . . . . . . . .          (336,489)
                                                                   -----------

NET ASSETS (100.0%). . . . . . . . . . . . . . . . . . . . .     $  72,620,114
                                                                   -----------
                                                                   -----------

NET ASSET VALUE, OFFERING
AND REDEMPTION PRICE PER 
OUTSTANDING SHARE ($72,620,114  
DIVIDED BY 5,149,793 shares outstanding) . . . . . . . . . .     $       14.10
                                                                   -----------
                                                                   -----------


* PURSUANT TO RULE 144A UNDER THE SECURITIES ACT OF 1933, THIS SECURITY CAN ONLY
BE SOLD TO QUALIFIED INSTITUTIONAL INVESTORS.

+ NON-INCOME PRODUCING

(A) WHEN-ISSUED SECURITY

SEE NOTES TO FINANCIAL STATEMENTS


- --------------------------------------------------------------------------------
                                                                               7

<PAGE>

VALUE LINE CONVERTIBLE FUND, INC.



STATEMENT OF ASSETS
AND LIABILITIES AT APRIL 30, 1996
- --------------------------------------------------------------------------------

ASSETS:

Investment securities, at value
  (Cost--$58,302,054). . . . . . . . . . . . . . . . .  $  65,355,484
Repurchase agreement
  (Cost--$7,601,119) . . . . . . . . . . . . . . . . .      7,601,119
Cash . . . . . . . . . . . . . . . . . . . . . . . . .         29,579
Receivable for securities sold . . . . . . . . . . . .      4,667,579
Interest and dividends receivable. . . . . . . . . . .        489,608
Receivable for capital shares sold . . . . . . . . . .         58,593
                                                           ----------

  TOTAL ASSETS . . . . . . . . . . . . . . . . . . . .     78,201,962
                                                           ----------


LIABILITIES:

Payable for securities purchased . . . . . . . . . . .      4,500,000
Payable for capital shares repurchased . . . . . . . .      1,000,000
Accrued expenses:
  Advisory fee . . . . . . . . . . . . . . . . . . . .         43,567
  Other. . . . . . . . . . . . . . . . . . . . . . . .         38,281
                                                           ----------

  TOTAL LIABILITIES. . . . . . . . . . . . . . . . . .      5,581,848
                                                           ----------

NET ASSETS . . . . . . . . . . . . . . . . . . . . . .  $  72,620,114
                                                           ----------
                                                           ----------

NET ASSETS CONSIST OF:

Capital stock, at $1.00 par value
  (authorized 50,000,000, outstanding
  5,149,793 shares). . . . . . . . . . . . . . . . . .  $   5,149,793
Additional paid-in capital . . . . . . . . . . . . . .     59,274,104
Undistributed investment income--net . . . . . . . . .        181,887
Accumulated net realized gain on
  investments. . . . . . . . . . . . . . . . . . . . .        960,900
Unrealized net appreciation 
  of investments . . . . . . . . . . . . . . . . . . .      7,053,430
                                                           ----------

    NET ASSETS . . . . . . . . . . . . . . . . . . . .  $  72,620,114
                                                           ----------
                                                           ----------

    NET ASSET VALUE, OFFERING AND 
      REDEMPTION PRICE PER
      OUTSTANDING SHARE ($72,620,114 DIVIDED BY
      5,149,793 SHARES OUTSTANDING). . . . . . . . . .  $       14.10
                                                           ----------
                                                           ----------

STATEMENT OF OPERATIONS 
FOR THE YEAR ENDED APRIL 30, 1996
- --------------------------------------------------------------------------------


INVESTMENT INCOME:

Interest . . . . . . . . . . . . . . . . . . . . . . .  $   2,882,864
Dividends  . . . . . . . . . . . . . . . . . . . . . .        690,671
                                                           ----------
  Total Income . . . . . . . . . . . . . . . . . . . .      3,573,535
                                                           ----------
                                                           ----------

EXPENSES:
Advisory fee . . . . . . . . . . . . . . . . . . . . .        428,535
Auditing and legal fees. . . . . . . . . . . . . . . .         43,570
Transfer agent . . . . . . . . . . . . . . . . . . . .         38,300
Registration and filing fees . . . . . . . . . . . . .         29,683
Printing and stationery. . . . . . . . . . . . . . . .         23,887
Custodian fees . . . . . . . . . . . . . . . . . . . .         20,376
Directors' fees and expenses . . . . . . . . . . . . .         11,745
Postage  . . . . . . . . . . . . . . . . . . . . . . .          9,476
Telephone  . . . . . . . . . . . . . . . . . . . . . .          8,574
Insurance, dues and other. . . . . . . . . . . . . . .          7,789
                                                           ----------
  Total Expenses Before Offset . . . . . . . . . . . .        621,935
  Less: Expense Offset . . . . . . . . . . . . . . . .         (6,685)
                                                           ----------
  Net Expenses . . . . . . . . . . . . . . . . . . . .        615,250
                                                           ----------
INVESTMENT INCOME--NET . . . . . . . . . . . . . . . .      2,958,285
                                                           ----------


REALIZED AND UNREALIZED GAIN ON
  INVESTMENTS--NET:
      Realized Gain--Net . . . . . . . . . . . . . . .      4,046,566

      Change in Unrealized 
        Appreciation . . . . . . . . . . . . . . . . .      6,409,849
                                                           ----------

NET REALIZED GAIN AND CHANGE IN 
  UNREALIZED APPRECIATION ON
  INVESTMENTS. . . . . . . . . . . . . . . . . . . . .     10,456,415
                                                           ----------

NET INCREASE IN NET ASSETS FROM
  OPERATIONS . . . . . . . . . . . . . . . . . . . . .  $  13,414,700
                                                           ----------
                                                           ----------



SEE NOTES TO FINANCIAL STATEMENTS


- --------------------------------------------------------------------------------
8

<PAGE>

                                               VALUE LINE CONVERTIBLE FUND, INC.



STATEMENT OF CHANGES IN NET ASSETS 
FOR THE YEARS ENDED APRIL 30, 1996, AND 1995
APRIL 30, 1996
- --------------------------------------------------------------------------------

 

<TABLE>
<CAPTION>

                                                                                                   1996                   1995   
                                                                                          ------------------------------------------

<S>                                                                                       <C>                        <C>
OPERATIONS:
  Investment income--net . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       $   2,958,285          $   2,939,994
  Realized gain (loss) on investments--net . . . . . . . . . . . . . . . . . . . . . .           4,046,566             (3,085,606)
  Change in unrealized appreciation  . . . . . . . . . . . . . . . . . . . . . . . . .           6,409,849              3,169,098
                                                                                              --------------------------------------
  Net increase in net assets from operations . . . . . . . . . . . . . . . . . . . . .          13,414,700              3,023,486
                                                                                              --------------------------------------

DISTRIBUTIONS TO SHAREHOLDERS:
  Investment income--net . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          (3,024,424)            (3,046,333)
  Realized gains on investments--net . . . . . . . . . . . . . . . . . . . . . . . . .              -                  (1,656,367)
                                                                                              --------------------------------------
  Net decrease in net assets from distributions. . . . . . . . . . . . . . . . . . . .          (3,024,424)            (4,702,700)
                                                                                              --------------------------------------

CAPITAL SHARE TRANSACTIONS:
  Net proceeds from sale of shares . . . . . . . . . . . . . . . . . . . . . . . . . .          52,653,026              9,276,461
  Net proceeds from reinvestment of distributions to shareholders. . . . . . . . . . .           2,474,940              3,984,512
  Cost of shares repurchased . . . . . . . . . . . . . . . . . . . . . . . . . . . . .         (43,421,496)           (10,881,849)
                                                                                              --------------------------------------
  Net increase in net assets from capital share transactions . . . . . . . . . . . . .          11,706,470              2,379,124
                                                                                              --------------------------------------

TOTAL INCREASE IN NET ASSETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          22,096,746                699,910

NET ASSETS:
  Beginning of year. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .          50,523,368             49,823,458
                                                                                              --------------------------------------
  End of year. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       $  72,620,114          $  50,523,368
                                                                                              --------------------------------------
                                                                                              --------------------------------------

UNDISTRIBUTED INVESTMENT INCOME--NET, AT END OF YEAR . . . . . . . . . . . . . . . . .       $     181,887          $     248,026
                                                                                              --------------------------------------
                                                                                              --------------------------------------

</TABLE>




SEE NOTES TO FINANCIAL STATEMENTS


- --------------------------------------------------------------------------------
                                                                               9

<PAGE>

VALUE LINE CONVERTIBLE FUND, INC.



NOTES TO FINANCIAL STATEMENTS
- --------------------------------------------------------------------------------

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 that 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
amoritzing 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.



- --------------------------------------------------------------------------------
10

<PAGE>

                                               VALUE LINE CONVERTIBLE FUND, INC.



                                                                  APRIL 30, 1996
- --------------------------------------------------------------------------------

2.  CAPITAL SHARE TRANSACTIONS
Transactions in capital stock were as follows:

                                                 YEAR           YEAR   
                                                 ENDED          ENDED  
                                               APRIL 30,      APRIL 30,
                                                 1996           1995   
                                                -------------------------
Shares sold. . . . . . . . . . . . . . .       3,953,152        793,187
Shares issued in reinvestment 
  of dividends and distributions . . . .         194,152        351,729
                                                -------------------------
                                               4,147,304      1,144,916

Shares repurchased . . . . . . . . . . .      (3,281,081)      (924,107)
                                                -------------------------
Net increase . . . . . . . . . . . . . .         866,223        220,809
                                                -------------------------
                                                -------------------------

3.  PURCHASES AND SALES OF SECURITIES
Purchases and sales of investment securities, excluding repurchase agreements,
were as follows:
                                                           YEAR ENDED  
                                                         APRIL 30, 1996
                                                       ----------------
PURCHASES:
Investment securities. . . . . . . . . . . . . . .          $77,319,221
                                                       ----------------
                                                       ----------------

SALES OR REDEMPTIONS:
Investment securities. . . . . . . . . . . . . . .          $61,425,189
                                                       ----------------
                                                       ----------------

At April 30, 1996, the aggregate cost of investment securities and repurchase
agreement for Federal income-tax purposes was $65,903,173. The aggregate
appreciation and depreciation of investments at April 30, 1996, based on a
comparison of investment values and their costs for Federal income-tax purposes,
was $7,885,736 and $832,306, respectively, resulting in a net appreciation of
$7,053,430.

For federal income-tax purposes, the Fund fully utilized its capital loss
carryover of approximately $1,277,569 to partially  offset gains realized during
the year ended April 30, 1996.

4. INVESTMENT ADVISORY CONTRACT, MANAGEMENT FEES, AND TRANSACTIONS WITH
   AFFILIATES

An advisory fee of $428,535 was paid or payable to Value Line, Inc. (the
Adviser) for the year ended April 30, 1996.  This was computed at the rate of
3/4 of 1% of average daily net assets during the year and paid monthly. The
Adviser provides research, investment programs, and supervision of the
investment portfolio and pays costs of 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.  If the aggregate expenses of the Fund,
other than taxes, interest, brokerage commissions, and extraordinary expenses,
exceed the expense limitation imposed by any state in which the Fund's shares
are sold, the advisory fee will be reduced by the amount of such excess, or the
amount of such excess will be refunded. No  reimbursement was required for the
year ended April 30, 1996.

A fee of $5,760 for printing services was paid to the Adviser for the year ended
April 30, 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 1,016,568 shares of the Fund's 
capital stock, representing 20% of the outstanding shares at April 30, 1996.

- --------------------------------------------------------------------------------
                                                                              11

<PAGE>

VALUE LINE CONVERTIBLE FUND, INC.



FINANCIAL HIGHLIGHTS
- --------------------------------------------------------------------------------


SELECTED DATA FOR A SHARE OF CAPITAL STOCK OUTSTANDING THROUGHOUT EACH YEAR:

 

<TABLE>
<CAPTION>

                                                                                      YEARS ENDED APRIL 30,
                                                                1996             1995          1994          1993          1992 
                                                            ----------------------------------------------------------------------

<S>                                                         <C>                  <C>           <C>           <C>           <C>
NET ASSET VALUE, BEGINNING OF YEAR . . . . . . . . . .         $11.79           $12.26        $13.80        $12.24        $11.07
INCOME (LOSS) FROM INVESTMENT OPERATIONS:
Net investment income. . . . . . . . . . . . . . . . .            .66              .74           .71           .62           .65
Net gains or losses on securities 
(both realized and unrealized) . . . . . . . . . . . .           2.33            ( .02)          .11          1.54          1.13
                                                            ----------------------------------------------------------------------

Total from investment operations . . . . . . . . . . .           2.99              .72           .82          2.16          1.78
                                                            ----------------------------------------------------------------------

LESS DISTRIBUTIONS:
Dividends from investment income--net. . . . . . . . .          ( .68)           ( .76)         (.69)        ( .60)        ( .61)
Distributions from capital gains . . . . . . . . . . .            --             ( .43)        (1.67)          --            -- 
                                                            ----------------------------------------------------------------------
Total distributions. . . . . . . . . . . . . . . . . .           (.68)           (1.19)        (2.36)        ( .60)        ( .61)
                                                            ----------------------------------------------------------------------

NET ASSET VALUE, END OF YEAR . . . . . . . . . . . . .         $14.10           $11.79        $12.26        $13.80        $12.24
                                                            ----------------------------------------------------------------------
                                                            ----------------------------------------------------------------------

TOTAL RETURN . . . . . . . . . . . . . . . . . . . . .          26.07%            6.53%         5.50%        18.16%        16.42%
                                                            ----------------------------------------------------------------------
                                                            ----------------------------------------------------------------------

RATIOS/SUPPLEMENTAL DATA:

Net assets, end of year (in thousands) . . . . . . . .        $72,620          $50,523       $49,823       $43,936       $37,177
Ratio of expenses to average net assets. . . . . . . .           1.07%(1)         1.08%         1.07%         1.10%         1.14%
Ratio of net investment income to
 average net assets. . . . . . . . . . . . . . . . . .           5.14%            6.13%         5.32%         4.80%         5.45%
Portfolio turnover rate. . . . . . . . . . . . . . . .            129%              87%          142%          146%          140%

</TABLE>
 


(1) NET OF CUSTODY-CASH CREDITS. HAD THE FUND NOT RECEIVED THESE CUSTODY
CREDITS, THE RATIO OF OPERATING EXPENSES TO AVERAGE NET ASSETS WOULD HAVE BEEN
1.08%.



SEE NOTES TO FINANCIAL STATEMENTS
- --------------------------------------------------------------------------------
12

<PAGE>

                                               VALUE LINE CONVERTIBLE FUND, INC.



REPORT OF INDEPENDENT ACCOUNTANTS
- --------------------------------------------------------------------------------



TO THE SHAREHOLDERS AND BOARD OF DIRECTORS 
OF VALUE LINE CONVERTIBLE FUND, INC.

In our opinion, the accompanying statement of assets and liabilities, including
the schedule of investments, and the related statements of operations and of
changes in net assets and the financial highlights present fairly, in all
material respects, the financial position of Value Line Convertible Fund, Inc.
(the "Fund") at April 30, 1996, the results of its operations for the year then
ended, the changes in its net assets for each of the two years in the period
then ended and the financial highlights for each of the five years in the period
then ended, in conformity with generally accepted accounting principles. These
financial statements and financial highlights (hereafter referred to as
"financial statements") are the responsibility of the Fund's management; our
responsibility is to express an opinion on these financial statements based on
our audits. We conducted our audits of these financial statements in accordance
with generally accepted auditing standards which require that we plan and
perform the audit to obtain reasonable assurance about whether the financial
statements are free of material misstatement. An audit includes examining, on a
test basis, evidence supporting the amounts and disclosures in the financial
statements, assessing the accounting principles used and significant estimates
made by management, and evaluating the overall financial statement presentation.
We believe that our audits, which included confirmation of securities at April
30, 1996 by correspondence with the custodian and brokers and the application of
alternative auditing procedures where confirmations from brokers were not
received, provide a reasonable basis for the opinion expressed above. 



PRICE WATERHOUSE  LLP
1177 Avenue of the Americas
New York, New York 10036
June 14, 1996



                   FEDERAL TAX STATUS OF DISTRIBUTIONS (UNAUDITED)
        FOR CORPORATE TAXPAYERS 17% OF THE ORDINARY INCOME DISTRIBUTIONS PAID
          DURING THE CALENDAR YEAR 1995 QUALIFY FOR THE CORPORATE DIVIDENDS
                                 RECEIVED DEDUCTIONS.



- --------------------------------------------------------------------------------
                                                                              13

<PAGE>

VALUE LINE CONVERTIBLE FUND, INC.




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



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- --------------------------------------------------------------------------------
14

<PAGE>

                                               VALUE LINE CONVERTIBLE FUND, INC.




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



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- --------------------------------------------------------------------------------
                                                                              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 of
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 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
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 primarily in a diversified
portfolio of investment-grade debt securities.

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 THE 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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