VALUE LINE CONVERTIBLE FUND INC
485BPOS, 1998-08-20
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<PAGE>
   
    AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON AUGUST 20, 1998
    
 
                                                                FILE NO. 2-96484
 
                                                               FILE NO. 811-4258
- --------------------------------------------------------------------------------
- --------------------------------------------------------------------------------
 
                       SECURITIES AND EXCHANGE COMMISSION
 
                              WASHINGTON, DC 20549
                                 --------------
 
                                   FORM N-1A
 
                             REGISTRATION STATEMENT
                                     UNDER
                           THE SECURITIES ACT OF 1933                        /X/
                                 --------------
 
                          Pre-Effective Amendment No.                        / /
 
   
                        Post-Effective Amendment No. 15                      /X/
    
 
                                      and
 
                        REGISTRATION STATEMENT UNDER THE
                         INVESTMENT COMPANY ACT OF 1940                      /X/
   
                                Amendment No. 15                             /X/
    
                                 -------------
 
                       VALUE LINE CONVERTIBLE FUND, INC.
 
               (Exact Name of Registrant as Specified in Charter)
 
                              220 East 42nd Street
 
                            New York, New York          10017-5891
                   (ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)    (ZIP CODE)
 
       Registrant's Telephone Number, including Area Code: (212) 907-1500
 
                               David T. Henigson
                                Value Line, Inc.
                              220 East 42nd Street
                         New York, New York 10017-5891
                    (NAME AND ADDRESS OF AGENT FOR SERVICE)
 
                                    Copy to:
                           Peter D. Lowenstein, Esq.
                         Two Greenwich Plaza, Suite 100
                              Greenwich, CT 06830
 
                                 --------------
 
   
        It is proposed that this filing will become effective (check
        appropriate box)
    
 
   
        / / immediately upon filing pursuant to paragraph (b)
    
 
   
        / / 60 days after filing pursuant to paragraph (a)(1)
    
 
   
        / / 75 days after filing pursuant to paragraph (a)(2)
    
 
   
        /X/ on September 1, 1998 pursuant to paragraph (b)
    
 
   
        / / on (date) pursuant to paragraph (a)(1)
    
 
   
        / / on (date) pursuant to paragraph (a)(2) of rule 485
    
 
   
        If appropriate, check the following box:
    
 
   
        / / This post-effective amendment designates a new effective
            date for a previously filed post-effective amendment.
    
 
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<PAGE>
                        VALUE LINE CONVERTIBLE FUND, INC
                                   FORM N-1A
                             CROSS REFERENCE SHEET
                           (AS REQUIRED BY RULE 495)
 
<TABLE>
<CAPTION>
N-1A ITEM NO.                                                                            LOCATION
- ----------------                                                          ---------------------------------------
<S>               <C>                                                     <C>
PART A (PROSPECTUS)
    Item  1.      Cover Page............................................  Cover Page
    Item  2.      Synopsis..............................................  Not Applicable
    Item  3.      Condensed Financial Information.......................  Summary of Fund Expenses; Financial
                                                                            Highlights
    Item  4.      General Description of Registrant.....................  Cover Page; Investment Objective and
                                                                            Policies; Investment Restrictions;
                                                                            Additional Information
    Item  5.      Management of the Fund................................  Summary of Fund Expenses; Management of
                                                                            the Fund; Additional Information
    Item  6.      Capital Stock and Other Securities....................  Dividends, Distributions and Taxes;
                                                                            Additional Information
    Item  7.      Purchase of Securities Being Offered..................  How to Buy Shares; Calculation of Net
                                                                            Asset Value; Investor Services
    Item  8.      Redemption or Repurchase..............................  How to Redeem Shares
    Item  9.      Pending Legal Proceedings.............................  Not Applicable
 
PART B (STATEMENT OF ADDITIONAL INFORMATION)
    Item 10.      Cover Page............................................  Cover Page
    Item 11.      Table of Contents.....................................  Table of Contents
    Item 12.      General Information and History.......................  Additional Information (Part A)
    Item 13.      Investment Objectives and Policies....................  Investment Objective and Policies;
                                                                            Investment Restrictions
    Item 14.      Management of the Fund................................  Directors and Officers
    Item 15.      Control Persons and Principal Holders of Securities...  Management of the Fund (Part A);
                                                                            Directors and Officers
    Item 16.      Investment Advisory and Other Services................  Management of the Fund (Part A); The
                                                                            Adviser
    Item 17.      Brokerage Allocation..................................  Management of the Fund (Part A);
                                                                            Brokerage Arrangements
    Item 18.      Capital Stock and Other Securities....................  Additional Information (Part A)
    Item 19.      Purchase, Redemption and Pricing of Securities Being
                    Offered.............................................  How to Buy Shares; Suspension of
                                                                            Redemptions; Calculation of Net Asset
                                                                            Value (Part A)
    Item 20.      Tax Status............................................  Taxes
    Item 21.      Underwriters..........................................  Not Applicable
    Item 22.      Calculation of Performance Data.......................  Performance Information (Part A);
                                                                            Performance Data
    Item 23.      Financial Statements..................................  Financial Statements
</TABLE>
 
PART C
 
    Information required to be included in Part C is set forth under the
appropriate Item, so numbered, in Part C to this Registration Statement.
<PAGE>
 
   
<TABLE>
<S>                                                                 <C>
VALUE LINE                                                                PROSPECTUS
CONVERTIBLE FUND, INC.                                                 September 1, 1998
</TABLE>
    
 
   
  220 East 42nd Street, New York, New York 10017-5891
  1-800-223-0818 or 1-800-243-2729
  www.valueline.com
    
 
               Value Line Convertible Fund, Inc. (the "Fund") is
               a no-load 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 Fund's investment adviser is Value Line, Inc.
               (the "Adviser").
 
               Shares of the Fund are offered at net asset value.
               There are no sales charges or redemption fees.
 
   
    This Prospectus sets forth concise information about the Fund that a
    prospective investor ought to know before investing. This Prospectus
    should be retained for future reference. Additional information about
    the Fund is contained in a Statement of Additional Information, dated
    September 1, 1998, which may be obtained at no charge by writing or
    telephoning the Fund at the address or telephone numbers listed above.
    The Statement, which is incorporated into this Prospectus by reference,
    has been filed with the Securities and Exchange Commission and is
    available along with other related materials on the Commission's
    Internet Web site at http://www.sec.gov.
    
 
                                  DISTRIBUTOR
                          Value Line Securities, Inc.
                              220 East 42nd Street
                         New York, New York 10017-5891
 
  THESE SECURITIES HAVE NOT BEEN APPROVED OR DISAPPROVED BY THE SECURITIES AND
  EXCHANGE COMMISSION OR ANY STATE SECURITIES COMMISSION NOR HAS THE
  COMMISSION OR ANY STATE SECURITIES COMMISSION PASSED UPON THE ACCURACY OR
  ADEQUACY OF THIS PROSPECTUS. ANY REPRESENTATION TO THE CONTRARY IS A
  CRIMINAL OFFENSE.
<PAGE>
                            SUMMARY OF FUND EXPENSES
 
   
<TABLE>
<S>                                                                                <C>
SHAREHOLDER TRANSACTION EXPENSES
 
  Sales Load on Purchases........................................................       None
 
  Sales Load on Reinvested Dividends.............................................       None
 
  Deferred Sales Load............................................................       None
 
  Redemption Fees................................................................       None
 
  Exchange Fee...................................................................       None
 
ANNUAL FUND OPERATING EXPENSES (AS A PERCENTAGE OF AVERAGE NET ASSETS)
 
  Management Fees................................................................      0.75%
 
  12b-1 Fees.....................................................................       None
 
  Other Expenses.................................................................      0.23%
 
  Total Fund Operating Expenses..................................................      0.98%
</TABLE>
    
 
   
<TABLE>
<CAPTION>
EXAMPLE                                                    1 YEAR       3 YEARS      5 YEARS     10 YEARS
                                                         -----------  -----------  -----------  -----------
 
<S>                                                      <C>          <C>          <C>          <C>
You would pay the following expenses on a $1,000
  investment, assuming (1) 5% annual return and (2)
  redemption at the end of each time period:...........   $      10    $      31    $      54    $     120
</TABLE>
    
 
   
    The foregoing is based upon the expenses for the year ended April 30, 1998,
and is designed to assist investors in understanding the various costs and
expenses that an investor in the Fund will bear directly or indirectly. This
example should not be considered a representation of past or future expenses.
ACTUAL EXPENSES IN THE FUTURE MAY BE GREATER OR LESS THAN THOSE SHOWN.
    
 
FINANCIAL HIGHLIGHTS
  (SELECTED DATA FOR A SHARE OF CAPITAL STOCK OUTSTANDING THROUGHOUT EACH
  PERIOD)
 
   
    The following information on selected per share data and ratios with respect
to each of the five years in the period ended April 30, 1998, and the related
financial statements, have been audited by PricewaterhouseCoopers LLP,
independent accountants, whose unqualified report thereon appears in the Fund's
Annual Report to Shareholders which is incorporated by reference in the
Statement of Additional Information. This information should be read in
conjunction with the financial statements and notes thereto which also appear in
the Fund's Annual Report to Shareholders available from the Fund without charge.
    
 
                                       2
<PAGE>
   
<TABLE>
<CAPTION>
                                                                         YEARS ENDED APRIL 30,
                                             -----------------------------------------------------------------------------
                                                 1998         1997         1996         1995         1994         1993
                                             ------------  -----------  -----------  -----------  -----------  -----------
<S>                                          <C>           <C>          <C>          <C>          <C>          <C>
Net asset value, beginning of year.........      $13.07        $14.10       $11.79       $12.26       $13.80       $12.24
                                             ------------  -----------  -----------  -----------  -----------  -----------
 INCOME (LOSS) FROM INVESTMENT OPERATIONS:
    Net investment income..................         .65          .70          .66          .74          .71          .62
    Net gains or losses on securities (both
     realized and unrealized)..............         2.50         .50          2.33         (.02 )       .11          1.54
                                             ------------  -----------  -----------  -----------  -----------  -----------
      Total from investment operations.....         3.15         1.20         2.99         .72          .82          2.16
                                             ------------  -----------  -----------  -----------  -----------  -----------
 LESS DISTRIBUTIONS:
    Dividends from net investment income...         (.67 )       (.65 )       (.68 )       (.76 )       (.69 )       (.60 )
    Distributions from capital gains.......         (.75 )      (1.58 )         --         (.43 )      (1.67 )         --
                                             ------------  -----------  -----------  -----------  -----------  -----------
      Total distributions..................        (1.42 )      (2.23 )       (.68 )      (1.19 )      (2.36 )       (.60 )
                                             ------------  -----------  -----------  -----------  -----------  -----------
Net asset value, end of year...............       $14.80       $13.07       $14.10       $11.79       $12.26       $13.80
                                             ------------  -----------  -----------  -----------  -----------  -----------
                                             ------------  -----------  -----------  -----------  -----------  -----------
Total return...............................        25.04 %       8.80 %      26.07 %       6.53 %       5.50 %      18.16 %
RATIOS/SUPPLEMENTAL DATA:
Net assets, end of year (in thousands).....       $97,679      $68,684      $72,620      $50,523      $49,823      $43,936
Ratio of expenses to average net assets....         .98  %(1)       1.01 %(1)       1.08 %       1.08 %       1.07 %       1.10 %
Ratio of net investment income to average
  net assets...............................         4.63 %       4.94 %       5.14 %       6.13 %       5.32 %       4.80 %
Portfolio turnover rate....................          111 %        164 %        129 %         87 %        142 %        146%
 
<CAPTION>
 
                                                1992         1991         1990         1989
                                             -----------  -----------  -----------  -----------
<S>                                          <C>          <C>          <C>          <C>
Net asset value, beginning of year.........      $11.07       $10.90       $11.45       $10.28
                                             -----------  -----------  -----------  -----------
 INCOME (LOSS) FROM INVESTMENT OPERATIONS:
    Net investment income..................        .65          .62          .69          .69
    Net gains or losses on securities (both
     realized and unrealized)..............        1.13         .38          (.62 )       1.06
                                             -----------  -----------  -----------  -----------
      Total from investment operations.....        1.78         1.00         .07          1.75
                                             -----------  -----------  -----------  -----------
 LESS DISTRIBUTIONS:
    Dividends from net investment income...        (.61 )       (.83 )       (.62 )       (.58 )
    Distributions from capital gains.......          --           --           --           --
                                             -----------  -----------  -----------  -----------
      Total distributions..................        (.61 )       (.83 )       (.62 )       (.58 )
                                             -----------  -----------  -----------  -----------
Net asset value, end of year...............      $12.24       $11.07       $10.90       $11.45
                                             -----------  -----------  -----------  -----------
                                             -----------  -----------  -----------  -----------
Total return...............................       16.42 %       9.98 %       0.51 %      17.68 %
RATIOS/SUPPLEMENTAL DATA:
Net assets, end of year (in thousands).....      $37,177      $36,553      $44,818      $62,074
Ratio of expenses to average net assets....        1.14 %       1.19 %       1.05 %       1.03 %
Ratio of net investment income to average
  net assets...............................        5.45 %       5.50 %       5.81 %       6.32 %
Portfolio turnover rate....................         140 %        216 %        105 %        112 %
</TABLE>
    
 
- ---------------
   
(1) Before offset of custody credits.
    
 
INVESTMENT OBJECTIVE AND POLICIES
 
    The investment objective of the Fund is to seek high current income together
with capital appreciation. The Fund's investment objective cannot be changed
without shareholder approval. There can be no assurance that such objective will
be achieved as there are risks in all investments.
 
BASIC INVESTMENT STRATEGY
 
    In seeking its investment objective, under normal market conditions the Fund
will invest at least 70% of the value of its net assets in "convertible
securities"--that is, bonds, debentures, corporate notes, preferred stocks or
other securities which are convertible into common stock. The balance may be
invested in non-convertible debt or equity securities, warrants, U.S. government
securities, repurchase agreements or other money market instruments. Securities
received upon conversion or exercise of warrants and securities remaining upon
the breakup of units or detachments of warrants may also be retained in the
Fund's portfolio to permit orderly disposition or for federal income tax
purposes. The Fund is not required to sell securities for the purpose of
assuring that 70% of its assets are invested in convertible securities. When the
Fund's Adviser deems it advisable because of unusual economic or market
conditions, part or all of the Fund's assets may be temporarily held in cash,
cash equivalents or invested in U.S. government securities or in other
high-quality debt securities. The Fund may also lend its portfolio securities,
write covered call options, make short sales, and enter into repurchase
agreements.
 
    In selecting securities for purchase or sale, the Adviser relies on the
Value Line Ranking System for convertible securities which has evolved over many
years of research. The return provided by a convertible security depends largely
on the performance of the common stock for which it can be exchanged.
 
                                       3
<PAGE>
   
Thus, the Value Line Ranking System's evaluation of the convertible begins with
its ranking of the underlying common stock, using the Value Line Timeliness-TM-
Ranking System or the Value Line Performance-TM- Ranking System. The Value Line
Timeliness Ranking System, which has been used in substantially its present form
since 1965, is based upon historical prices and reported earnings, recent
earnings and price momentum and the degree to which the latest reported earnings
deviate from estimated earnings, among other factors. The Timeliness Rankings
are published weekly in the Standard Edition of The Value Line Investment Survey
for approximately 1,700 stocks. On a scale of 1 (highest) to 5 (lowest), the
Timeliness Rankings compare the Adviser's estimate of the probable market
performance of each Standard Edition stock during the coming twelve months
relative to all 1,700 stocks under review in the Standard Edition. The Value
Line Performance Ranking System for common stocks was introduced in 1995. It is
a variation of the Value Line Small-Capitalization Ranking System, which has
been employed in managing pension client assets since 1981, and in managing the
Value Line Small-Cap Growth Fund, Inc. since 1993. The Performance Ranking
System evaluates the approximately 1,800 stocks in the Expanded Edition of The
Value Line Investment Survey. This stock selection system relies on factors
similar to those found in the Value Line Timeliness Ranking System except that
it does not rely on earnings estimates. The Performance Ranks use a scale of 1
(highest) to 5 (lowest) to compare the Adviser's estimate of the probable market
performance of each Expanded Edition stock during the coming twelve months
relative to all 1,800 stocks under review in the Expanded Edition. The rank for
the common stock is then combined with the Adviser's evaluation of the
convertible. Using a statistical evaluation model, a rank is assigned to the
approximately 400 convertibles and more than 25 warrants in The Value Line
Convertibles Survey issued by companies that are ranked in The Value Line
Investment Survey. An additional 230 convertibles and 95 warrants are evaluated
but not ranked because the underlying stocks are not ranked by The Value Line
Investment Survey. The Value Line Convertible Ranking System, which has been
published in essentially its present form since 1973, makes a comparison of the
historic price relationship of the convertible to its underlying stock (or to
other issues of a similar nature) making adjustments for any changes in
conditions that have occurred, to estimate the degree to which the convertible
may be underpriced or overpriced. Convertibles issued by companies that are
ranked by The Value Line Investment Survey are then ranked on a scale of 1
(highest) to 5 (lowest) based on the total return (from income or dividends plus
appreciation) the Adviser estimates it will provide relative to its risk during
the coming year. The Value Line Convertible Rankings are published four times a
month in The Value Line Convertibles Survey.
    
 
   
    The Value Line Rankings do not eliminate market risk, but the Adviser
believes that they provide objective standards for determining whether the
market is undervaluing or overvaluing a particular security. Under normal
conditions, the Fund will confine its purchases to convertible securities ranked
1 or 2; those convertible securities that fall in rank below 2 will be sold as
soon as practical, although those ranked 1 or 2 may also be sold if the Adviser
deems a sale advisable. The number of convertible securities ranked 1 and 2 will
change from week to week. As of July 22, 1998, there were 72 convertible
securities ranked 1 and 128 ranked 2, not all of which will be purchased by the
Fund. Reliance on the Rankings is no assurance that the Fund will perform more
favorably than the market in general over any particular period.
    
 
    PORTFOLIO TURNOVER.  The Fund's annual portfolio turnover rate may exceed
100%. A portfolio turnover rate of 100% would occur if all of the Fund's
portfolio were replaced in a period of one year. To the extent that the Fund
engages in short-term trading in attempting to achieve its objective, it may
 
                                       4
<PAGE>
increase portfolio turnover and incur larger brokerage commissions and other
expenses than might otherwise be the case. The Fund's portfolio turnover rate
for recent fiscal years is set forth under "Financial Highlights", see page 3.
 
MISCELLANEOUS INVESTMENT PRACTICES
 
    LENDING PORTFOLIO SECURITIES.  The Fund may lend its portfolio securities to
broker-dealers or institutional investors if as a result thereof the aggregate
value of all securities loaned does not exceed 33 1/3% of the total assets of
the Fund. The loans will be made in conformity with applicable regulatory
policies and will be 100% collateralized by cash, cash equivalents or U.S.
Treasury bills on a daily basis in an amount equal to the market value of the
securities loaned and interest earned. The Fund will retain the right to call,
upon notice, the loaned securities and intends to call loaned voting securities
in anticipation of any important or material matter to be voted on by
stockholders. While there may be delays in recovery or even loss of rights in
the collateral should the borrower fail financially, the loans will be made only
to firms deemed by the Adviser to be of good standing and will not be made
unless, in the judgment of the Adviser, the consideration which can be earned
from such loans justifies the risk. The Fund may pay reasonable custodian and
administrative fees in connection with the loans.
 
   
    COVERED CALL OPTIONS.  The Fund may write covered call options on portfolio
securities held in its portfolio ("covered options") in an attempt to earn
additional income on its portfolio or to partially offset an expected decline in
the price of a security. When the Fund writes a covered call option, it gives
the purchaser of the option the right to buy the underlying common stock at the
price specified in the option (the "exercise price") at any time during the
option period. If the option expires unexercised, the Fund will realize income
to the extent of the amount received for the option (the "premium"). If the
option is exercised, a decision over which the Fund has no control, the Fund
must sell the underlying security to the option holder at the exercise price. By
writing a covered option, the Fund foregoes, in exchange for the premium less
the commission ("net premium"), the opportunity to profit during the option
period from an increase in the market value of the underlying security above the
exercise price. The Fund will not write call options in an aggregate amount
greater than 25% of its net assets and will only write call options which are
traded on a national securities exchange.
    
 
    The Fund will purchase call options only to close out a position. When an
option is written on securities in the Fund's portfolio and it appears that the
purchaser of that option is likely to exercise the option and purchase the
underlying security, it may be considered appropriate to avoid liquidating the
Fund's position, or the Fund may wish to extinguish a call option sold by it so
as to be free to sell the underlying security. In such instances the Fund may
purchase a call option on the same security with the same exercise price and
expiration date which had been previously written. Such a purchase would have
the effect of closing out the option which the Fund has written. The Fund
realizes a gain if the amount paid to purchase the call option is less than the
premium received for writing a similar option and a loss if the amount paid to
purchase a call option is greater than the premium received for writing a
similar option. If the underlying security has substantially risen in value, it
may be difficult or expensive to purchase the call option for the closing
transaction.
 
    SHORT SALES.  The Fund may from time to time make short sales of securities
in order to protect a profit or to attempt to minimize a loss with respect to
convertible securities. The Fund will only make a
 
                                       5
<PAGE>
short sale of a security if it owns other securities convertible into an
equivalent amount of such securities. No more than 10% of the value of the
Fund's net assets taken at market may at any one time be held as collateral for
such sales.
 
    REPURCHASE AGREEMENTS.  The Fund may invest temporary cash balances in
repurchase agreements. A repurchase agreement involves a sale of securities to
the Fund, with the concurrent agreement of the seller (a member bank of the
Federal Reserve System or a securities dealer which the Adviser believes to be
financially sound) to repurchase the securities at the same price plus an amount
equal to an agreed-upon interest rate, within a specified time, usually less
than one week, but, on occasion, at a later time. The Fund will make payment for
such securities only upon physical delivery or evidence of book-entry transfer
to the account of the custodian or a bank acting as agent for the Fund.
Repurchase agreements may also be viewed as loans made by the Fund which are
collateralized by the securities subject to repurchase. The value of the
underlying securities will be at least equal at all times to the total amount of
the repurchase obligation, including the interest factor. In the event of a
bankruptcy or other default of a seller of a repurchase agreement, the Fund
could experience both delays in liquidating the underlying security and losses,
including (a) possible decline in the value of the underlying security during
the period while the Fund seeks to enforce its rights thereto; (b) possible
subnormal levels of income and lack of access to income during this period; and
(c) expenses of enforcing its rights. The Fund has a fundamental policy that it
will not enter into repurchase agreements which will not mature within seven
days if any such investment, together with all other assets held by the Fund
which are not readily marketable, amounts to more than 10% of its total assets.
The Board of Directors monitors the creditworthiness of parties dealing with the
Fund in repurchase agreements and loans of portfolio securities.
 
    RESTRICTED SECURITIES.  On occasion, the Fund may purchase securities which
would have to be registered under the Securities Act of 1933 if they were to be
publicly distributed. However, it will not do so if the value of such securities
and other securities which are not readily marketable (including repurchase
agreements maturing in more than seven days) would exceed 10% of the market
value of its total assets. It is management's policy to permit the occasional
acquisition of such restricted securities only if (except in the case of
short-term, non-convertible debt securities) there is an agreement by the issuer
to register such securities, ordinarily at the issuer's expense, when requested
to do so by the Fund. The acquisition in limited amounts of restricted
securities is believed to be helpful toward the attainment of the Fund's
investment objective without unduly restricting its liquidity or freedom in the
management of its portfolio. However, because restricted securities may only be
sold privately or in an offering registered under the Securities Act of 1933, or
pursuant to an exemption from such registration, substantial time may be
required to sell such securities, and there is greater than usual risk of price
decline prior to sale.
 
    In addition, the Fund may purchase certain restricted securities ("Rule 144A
securities") for which there is a secondary market of qualified institutional
buyers, as contemplated by Rule 144A under the Securities Act of 1933. Rule 144A
provides an exemption from the registration requirements of the Securities Act
for the resale of certain restricted securities to qualified institutional
buyers.
 
    The Adviser, under the supervision of the Board of Directors, will consider
whether securities purchased under Rule 144A are liquid or illiquid for purposes
of the Fund's limitation on investment in securities which are not readily
marketable or are illiquid. Among the factors to be considered are the frequency
of trades and quotes, the number of dealers and potential purchasers, dealer
undertakings to make a market and the nature of the security and the time needed
to dispose of it.
 
                                       6
<PAGE>
    To the extent that the liquid Rule 144A securities that the Fund holds
become illiquid, due to lack of sufficient qualified institutional buyers or
market or other conditions, the percentage of the Fund's assets invested in
illiquid assets would increase. The Adviser, under the supervision of the Board
of Directors, will monitor the Fund's investments in Rule 144A securities and
will consider appropriate measures to enable the Fund to maintain sufficient
liquidity for operating purposes and to meet redemption requests.
 
    FOREIGN SECURITIES.  The Fund may purchase U.S. dollar denominated
securities of foreign issuers which are publicly traded in the United States.
Foreign securities involve additional risks and may be affected by the strength
of foreign currencies relative to the U.S. dollar, or by political or economic
developments in foreign countries. Foreign companies may not be subject to
accounting standards or government supervision comparable to U.S. companies, and
there may be less public information about their operations. These risks are
typically greater for investments in less-developed countries whose governments
and financial markets may be more susceptible to adverse political and economic
developments. The Adviser considers these factors in making investments for the
Fund. There is no limitation on the amount of the Fund's assets that may be
invested in these types of foreign securities.
 
   
RISK FACTORS
    
 
   
    Investors should be aware of the following:
    
 
   
    - There are risks in all investments, including any stock investment, and in
      all mutual funds. The Fund's net asset value will fluctuate to reflect the
      investment performance of the securities held by the Fund.
    
 
   
    - The value a shareholder receives upon redemption may be greater or less
      than the value of such shares when acquired.
    
 
   
    - Short-selling and the use of investment techniques, such as investing in
      repurchase agreements, lending portfolio securities, purchasing restricted
      securities and purchasing foreign securities, involves greater risk than
      does an investment in a fund that does not engage in these activities.
    
 
INVESTMENT RESTRICTIONS
 
    The Fund has adopted a number of investment restrictions which may not be
changed without shareholder approval. These are set forth in the Statement of
Additional Information and provide, among other things, that the Fund may not:
 
        (a) borrow in excess of 10% of the value of its assets and then only as
    a temporary measure;
 
        (b) purchase securities (other than U.S. government securities) if the
    purchase would cause the Fund, at the time, to have more than 5% of the
    value of its total assets invested in the securities of any one issuer or to
    own more than 10% of the outstanding voting securities of any one issuer; or
 
        (c) invest 25% or more of the value of the Fund's assets in securities
    of issuers in one particular industry.
 
MANAGEMENT OF THE FUND
 
   
    The management and affairs of the Fund are supervised by the Fund's Board of
Directors. The Fund's officers conduct and supervise the daily business
operations of the Fund. The Fund's investment decisions are made by an
investment committee of employees of the Adviser.
    
 
                                       7
<PAGE>
   
    THE ADVISER.  The Adviser was organized in 1982 and is the successor to
substantially all of the operations of Arnold Bernhard & Co., Inc. ("AB&Co.").
The Adviser was formed as part of a reorganization of AB&Co., a sole
proprietorship formed in 1931 which became a New York corporation in 1946.
AB&Co. currently owns approximately 81% of the outstanding shares of the
Adviser's common stock. Jean Bernhard Buttner, Chairman, President and Chief
Executive Officer of the Adviser, owns all of the voting stock of AB&Co.
Substantially all of the non-voting stock is owned by or for the benefit of
members of the Buttner family. The Adviser currently acts as investment adviser
to the other Value Line funds and furnishes investment advisory services to
private and institutional accounts with combined assets in excess of $5 billion.
Value Line Securities, Inc., the Fund's distributor, is a subsidiary of the
Adviser. Another subsidiary of the Adviser publishes The Value Line Investment
Survey and other publications. The Adviser manages the Fund's investments,
provides various administrative services and supervises the Fund's daily
business affairs, subject to the authority of the Board of Directors. The
Adviser is paid an advisory fee at an annual rate of 3/4 of 1% of the Fund's
average daily net assets during the year (a fee which is higher than that paid
by many other investment companies, although comparable with investment
companies with investment policies similar to those of the Fund). For more
information about the Fund's management fees and expenses, see the "Summary of
Fund Expenses" on page 2.
    
 
   
    BROKERAGE.  The Fund may pay a portion of its total brokerage commissions to
Value Line Securities, Inc., a subsidiary of the Adviser, which clears
transactions for the Fund through unaffiliated broker-dealers.
    
 
CALCULATION OF NET ASSET VALUE
 
   
    The net asset value of the Fund's shares for purposes of both purchases and
redemptions is determined once daily as of the scheduled close of trading of the
New York Stock Exchange (generally 4:00 p.m., New York time) on each day that
the New York Stock Exchange is open for trading except on days on which no
orders to purchase, sell or redeem Fund shares have been received. The holidays
on which the New York Stock Exchange is closed currently are: New Year's Day,
Martin Luther King, Jr. Day, Presidents' Day, Good Friday, Memorial Day,
Independence Day, Labor Day, Thanksgiving Day and Christmas Day. The net asset
value per share is determined by dividing the total value of the investments and
other assets of the Fund, less any liabilities, by the total outstanding shares.
    
 
   
    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, and all other assets of the Fund, are valued
at fair value as the Board of Directors or persons acting at their direction may
determine in good faith. Short-term instruments with maturities of 60 days or
less at the date of purchase are valued at amortized cost, which approximates
market.
    
 
HOW TO BUY SHARES
 
    PURCHASE BY CHECK.  To buy shares, send a check made payable to "NFDS-Agent"
and a completed and signed application form to Value Line Funds, c/o National
Financial Data Services, Inc., P.O. Box 419729, Kansas City, MO 64141-6729.
Third party checks will not be accepted for either initial or subsequent
investments. For assistance in completing the application, call Value Line
Securities at 1-800-223-0818 during New York business hours. Upon receipt of the
completed purchase application and a check, National Financial Data Services,
Inc. ("NFDS"), the Fund's shareholder servicing agent,
 
                                       8
<PAGE>
   
will buy full and fractional shares (to three decimal places) at the net asset
value next computed after the funds are received and will confirm the investment
to the investor. Subsequent investments may be made by attaching a check to the
confirmation's "next payment" stub, by telephone or by federal funds wire.
Investors may also buy shares through broker-dealers other than Value Line
Securities. Such broker-dealers may charge investors a reasonable service fee.
Neither Value Line Securities nor the Fund receives any part of such fees when
charged (and which can be avoided by investing in the Fund directly). If an
order to purchase shares is cancelled due to nonpayment or because the
investor's check does not clear, the purchaser will be responsible for any loss
incurred by the Fund or Value Line Securities by reason of such cancellation. If
the purchaser is a shareholder, Value Line Securities reserves the right to
redeem sufficient shares from the shareholder's account to protect the Fund
against loss. Minimum orders are $1,000 for an initial purchase and $250 for
each subsequent purchase. The Fund reserves the right to waive the initial and
subsequent investment minimums at any time and may refuse any order for the
purchase of shares.
    
 
    WIRE PURCHASE--$1,000 MINIMUM.  An investor should call 1-800-243-2729 to
obtain an account number. After receiving an account number, instruct your
commercial bank to wire transfer "federal funds" via the Federal Reserve System
as follows:
 
    State Street Bank and Trust Company, Boston, MA.
 
    ABA #011000028
 
    Attn: DDA #99049868
    Value Line Convertible Fund, Inc.
    A/C #________________________
    Shareholder's name and account information
    Tax ID #________________________
 
NOTE:  A COMPLETED AND SIGNED APPLICATION MUST BE MAILED IMMEDIATELY AND
RECEIVED BY NFDS BEFORE IT CAN HONOR ANY WITHDRAWAL OR EXCHANGE TRANSACTIONS.
 
    After your account has been opened you may wire additional investments in
the same manner.
 
    For an initial investment made by federal funds wire purchase, the wire must
include a valid social security number or tax identification number. Investors
purchasing shares in this manner will then have 30 days after purchase to
provide the certification and signed account application. All payments should be
made in U.S. dollar and, to avoid fees and delays, should be drawn on only U.S.
banks.
 
   
    SUBSEQUENT TELEPHONE PURCHASES--$250 MINIMUM.  Upon completion of the
telephone purchase authorization section of the account application,
shareholders who own Fund shares with a current value of $500 or more may also
purchase additional shares in amounts of $250 or more up to twice the value of
their shares by calling 1-800-243-2729 between 9:00 a.m. and 4:00 p.m. New York
time. Such orders will be priced at the closing net asset value on the day
received and payment will be due within three business days. If payment is not
received within the required time or a purchaser's check does not clear, the
order is subject to cancellation and the purchaser will be responsible for any
loss incurred by the Fund or Value Line Securities. Shares may not be purchased
by telephone for a qualified retirement plan. The Fund will employ reasonable
procedures to confirm that instructions communicated by telephone are genuine.
These procedures include requiring some form of personal identification prior to
acting upon instructions received by telephone. The Fund will not be liable for
following instructions communicated by telephone that it reasonably believes to
be genuine.
    
 
                                       9
<PAGE>
   
DIVIDENDS, DISTRIBUTIONS AND TAXES
    
 
   
    The Fund intends to distribute net investment income quarterly and any net
realized capital gains at least annually. Income dividends and capital gains
distributions are automatically reinvested in additional shares of the Fund
unless the shareholder has requested otherwise.
    
 
   
    The following discussion is intended for general information only. A
prospective investor should consult with his or her own tax advisor as to the
tax consequences of an investment in the Fund.
    
 
   
    The Fund intends to qualify annually and elect to be treated as a regulated
investment company under the Internal Revenue Code of 1986, as amended (the
"Code"). To qualify, the Fund must meet certain income, distribution and
diversification requirements. In any year in which the Fund qualifies as a
regulated investment company and timely distributes all of its taxable income,
the Fund generally will not pay any U.S. federal income or excise tax.
    
 
   
    Dividends paid out of the Fund's investment company taxable income
(including dividends, interest and net short-term capital gains) will be taxable
to U.S. shareholders as ordinary income. Because a portion of the Fund's income
will consist of dividends paid by U.S. corporations, a portion of the dividends
paid by the Fund will be eligible for the corporate dividends-received
deduction. Distributions of net capital gains (the excess of net long-term
capital gains over net short-term capital losses), if any, designated as capital
gain dividends may be taxable to individuals and certain other shareholders at
the maximum federal 20% or 28% capital gains rates (depending upon the Fund's
holding period for the assets giving rise to the capital gains), regardless of
how long the shareholder has held the Fund's shares. Dividends are taxable to
shareholders in the same manner whether received in cash or reinvested in
additional Fund shares.
    
 
   
    A distribution will be treated as paid on December 31 of a calendar year if
it is declared by the Fund in October, November or December with a record date
within such period and paid by the Fund during January of the following calendar
year. Such distributions will be taxable to shareholders in the calendar year in
which the distributions are declared, rather than the calendar year in which the
distributions are received. Each year the Fund will notify shareholders of the
tax status of dividends and distributions paid or declared with respect to the
Fund.
    
 
   
    Upon the sale or other disposition of shares of the Fund, including an
exchange of shares in the Fund for shares of another Value Line fund, a
shareholder may realize a capital gain or loss for federal income tax purposes.
Capital gains may be taxable to individuals and certain other shareholders at
the maximum federal 20% or 28% capital gains rate (depending upon the
shareholder's holding period for the shares).
    
 
   
    The Fund may be required to withhold U.S. federal income tax at the rate of
31% of all taxable distributions payable to certain shareholders who fail to
provide the Fund with their correct taxpayer identification number or to make
required certifications, or who have been notified by the Internal Revenue
Service that they are subject to backup withholding. Backup withholding is not
an additional tax. Any amounts withheld may be credited against the
shareholder's U.S. federal income tax liability. The Fund reserves the right to
close, by redemption, accounts for which the holder fails to provide a valid
social security or taxpayer identification number when required to do so.
    
 
                                       10
<PAGE>
   
    Further information relating to U.S. income tax matters is contained in the
Statement of Additional Information. Prospective investors should consult their
own tax advisors with regard to the federal tax consequences of the purchase,
ownership, or disposition of Fund shares, as well as the tax consequences
arising under the laws of any state, foreign country or other taxing
jurisdiction.
    
 
PERFORMANCE INFORMATION
 
    The Fund may from time to time include information regarding its total
return performance or yield in advertisements or in information furnished to
existing or prospective shareholders. When information regarding total return is
furnished, it will be based upon changes in the Fund's net asset value and will
assume the reinvestment of all capital gains distributions and income dividends.
It will take into account nonrecurring charges, if any, which the Fund may incur
but will not take into account income taxes due on Fund distributions.
 
   
    The table below illustrates the total return performance of the Fund for the
periods indicated by showing the value of a hypothetical $1,000 investment made
at the beginning of each period. The information contained in the table has been
computed by applying the Fund's average annual total return to the hypothetical
$1,000 investment. The table assumes reinvestment of all capital gains
distributions and income dividends, but does not take into account income taxes
due on Fund distributions or dividends. Investors should note that the
investment results of the Fund will fluctuate over time, and any presentation of
the Fund's current yield, total return or distribution rate for any period
should not be considered as a representation of what an investment may earn or
what an investor's total return, yield or distribution rate may be in any future
period.
    
 
   
<TABLE>
<CAPTION>
                                                                                AVERAGE ANNUAL
                                                                                 TOTAL RETURN
                                                                               -----------------
<S>                                                                 <C>        <C>
For the year ended April 30, 1998.................................  $   1,250         25.04%
For the 5 years ended April 30, 1998..............................  $   1,929         14.03%
For the 10 years ended April 30, 1998.............................  $   3,449         13.18%
</TABLE>
    
 
    When information regarding "yield" is furnished it will refer to the net
investment income per share generated by an investment in the Fund over a
thirty-day period. This income will then be annualized by assuming that the
amount of income generated by the investment during that thirty-day period is
generated each 30 days over one year and assuming that the income is reinvested
every six months.
 
   
    Comparative performance information may be used from time to time in
advertising the Fund's shares, including data from Lipper Analytical Services,
Inc. and other industry or financial publications such as KIPLINGER'S PERSONAL
FINANCE, MONEY MAGAZINE, FINANCIAL WORLD, MORNINGSTAR, PERSONAL INVESTORS,
FORBES, FORTUNE, BUSINESS WEEK, WALL STREET JOURNAL, INVESTOR'S BUSINESS DAILY,
DONOGHUE and BARRON'S. The Fund may compare its performance to that of other
mutual funds with similar investment objectives and to stock or other relevant
indices. From time to time, articles about the Fund regarding its performance or
ranking may appear in national publications. Some of these publications may
publish their own rankings or performance reviews of mutual funds, including the
Fund. Reference to or reprints of such articles may be used in the Fund's
promotional literature.
    
 
HOW TO REDEEM SHARES
 
    Shares of the Fund may be redeemed at any time at their current net asset
value next determined after NFDS receives a request in proper form. ALL REQUESTS
FOR REDEMPTION SHOULD BE SENT TO NFDS,
 
                                       11
<PAGE>
P.O. BOX 419729, KANSAS CITY, MO 64141-6729. The value of shares of the Fund on
redemption may be more or less than the shareholder's cost, depending upon the
market value of the Fund's assets at the time. A shareholder with certificates
for shares must surrender the certificate properly endorsed with signature
guaranteed. A signature guarantee may be executed by any "eligible" guarantor.
Eligible guarantors include domestic banks, savings associations, credit unions,
member firms of a national securities exchange, and participants in the New York
Stock Exchange Medallion Signature Program, the Securities Transfer Agents
Medallion Program ("STAMP") and the Stock Exchanges Medallion Program. A
guaranty from a Notary Public is not an acceptable source. The signature on any
request for redemption of shares not represented by certificates, or on any
stock power in lieu thereof, must be similarly guaranteed. In each case the
signature or signatures must correspond to the names in which the account is
registered. Additional documentation may be required when shares are registered
in the name of a corporation, agent or fiduciary. For further information, you
should contact NFDS.
 
   
    The Fund does not impose a redemption charge but shares redeemed through
brokers or dealers may be subject to a service charge by such firms. A check for
the redemption proceeds will be mailed within seven days following receipt of
all required documents. However, payment may be postponed under unusual
circumstances such as when normal trading is not taking place on the New York
Stock Exchange. In addition, shares purchased by check may not be redeemed until
the check has cleared which may take up to 15 calendar days from the purchase
date.
    
 
    If the Board of Directors determines that it is in the best interests of the
Fund, the Fund has the right to redeem, upon prior written notice, at net asset
value, all shareholder accounts which, due to redemptions, fall below $500 in
net asset value. In such event, an investor will have 30 days to increase the
shares in his account to the minimum level.
 
    BY TELEPHONE OR WIRE.  You may redeem shares by telephone or wire
instructions to NFDS by so indicating on the initial application. Payment will
normally be transmitted on the business day following receipt of your
instructions to the bank account at the member bank of the Federal Reserve
System you have designated on your initial purchase application. The Fund
employs reasonable procedures to confirm that instructions communicated by
telephone are genuine. These procedures include requiring some form of personal
identification prior to acting upon instructions received by telephone. The Fund
will not be liable for following instructions communicated by telephone that it
reasonably believes to be genuine. Any loss will be borne by the investor. Heavy
wire traffic may delay the arrival of a wire until after public hours at your
bank. Telephone or wire redemptions must be in amounts of $1,000 or more and
your instructions must include your name and account number. The number to call
before the close of business on the New York Stock Exchange is 1-800-243-2729.
Procedures for redeeming Fund shares by telephone may be modified or terminated
without notice at any time by the Fund.
 
    BY CHECK.  You may elect this method of redemption by so indicating on the
initial application and you will be provided a supply of checks by NFDS. These
checks may be made payable to the order of any person in any amount of $500 or
more. When your check is presented for payment, the Fund will redeem a
sufficient number of full and fractional shares in your account to cover the
amount of the check. Checks will be returned unpaid if there are insufficient
shares to meet the withdrawal amount. Potential fluctuations in the net asset
value of the Fund's shares should be considered in determining the amount of the
check.
 
                                       12
<PAGE>
    This method of redemption requires that your shares must remain in an open
account and that no share certificates are issued and outstanding. You cannot
close your account through the issuance of a check because the exact balance at
the time your check clears will not be known when you write the check.
 
    If you use this privilege you will be required to sign a signature card
which will subject you to State Street Bank and Trust Company's rules and
regulations governing checking accounts. The authorization form which you must
sign also contains a provision relieving the bank, NFDS, the Fund, Value Line
Securities and the Adviser from liability for loss, if any, which you may
sustain arising out of a non-genuine instruction pursuant to this redemption
feature. Any additional documentation required to assure a genuine redemption
must be maintained on file with NFDS in such a current status as NFDS may deem
necessary. A new form properly signed and with the signature guaranteed as
described above must be received and accepted by NFDS before authorized
redemption instructions already on file with NFDS can be changed.
 
    An additional supply of checks will be furnished upon request. There
presently is no charge to the shareholder for these checks or their clearance.
However, the Fund and NFDS reserve the right to make reasonable charges and to
terminate or modify any or all of the services in connection with this privilege
at any time and without prior notice. NFDS will impose a $5 fee for stopping
payment of a check upon your request or if NFDS cannot honor the check due to
insufficient or uncollected funds or other valid reasons.
 
    IMPORTANT: Shares purchased by check may not be redeemed until the Fund is
reasonably assured of the final collection of such check, currently determined
to be up to 15 days.
 
INVESTOR SERVICES
 
    VALU-MATIC.-REGISTERED TRADEMARK-  The Fund offers a free service to its
shareholders, Valu-Matic-Registered Trademark-, through which monthly
investments of $25 or more may be made automatically into the shareholder's Fund
account. The shareholder authorizes the Fund to debit the shareholder's bank
account monthly for the purchase of Fund shares on or about the 3rd or 18th of
each month. Further information regarding this service can be obtained from
Value Line Securities by calling 1-800-223-0818.
 
    EXCHANGE OF SHARES.  Shares of the Fund may be exchanged for shares of the
other Value Line funds in any identically registered account on the basis of the
respective net asset values next computed after receipt of the exchange order.
No telephone exchanges can be made for less than $1,000. In the event shares of
the Fund are being exchanged for shares of The Value Line Cash Fund, Inc. or The
Value Line Tax Exempt Fund--Money Market Portfolio and the shares (including
shares in accounts under the control of one investment adviser) have a value in
excess of $500,000, then at the discretion of the Adviser the shares to be
purchased will be purchased at the closing price on the third business day
following the redemption of the shares being exchanged to allow the Fund to
utilize normal securities settlement procedures in transferring the proceeds of
the redemption.
 
    The exchange privilege may be exercised only if the shares to be acquired
may be sold in the investor's State. Prospectuses for the other Value Line funds
may be obtained from Value Line Securities by calling 1-800-223-0818. Each such
exchange involves a redemption and a purchase for tax purposes. Broker-dealers
are not prohibited from charging a commission for handling the exchange of Fund
shares. To avoid paying such a commission send the request in proper form to
NFDS. The Fund reserves
 
                                       13
<PAGE>
the right to terminate the exchange privilege of any account making more than
eight exchanges a year. (An exchange out of The Value Line Cash Fund, Inc. or
The Value Line Tax Exempt Fund--Money Market Portfolio is not counted for this
purpose.) The exchange privilege may be modified or terminated at any time, and
any of the Value Line funds may discontinue offering its shares generally, or in
any particular state, without prior notice. To make an exchange, call
1-800-243-2729. Although it has not been a problem in the past, shareholders
should be aware that a telephone exchange may be difficult during periods of
major economic or market changes.
 
    SYSTEMATIC CASH WITHDRAWAL PLAN.  A shareholder who has invested a minimum
of $5,000 in the Fund, or whose shares have attained that value, may request a
transfer of his shares to a Value Line Systematic Cash Withdrawal Account which
NFDS will maintain in his name on the Fund's books. Under the Systematic Cash
Withdrawal Plan (the "Plan") the shareholder will request that NFDS, acting as
his agent, redeem monthly or quarterly a sufficient number of shares to provide
for payment to him, or someone he designates, of any specified dollar amount
(minimum $25). All certificated shares must be placed on deposit under the Plan
and dividends and capital gains distributions, if any, are automatically
reinvested at net asset value. The Plan will automatically terminate when all
shares in the account have been redeemed. The shareholder may at any time
terminate the Plan, change the amount of the regular payment, or request
liquidation of the balance of his account on written notice to NFDS. The Fund
may terminate the Plan at any time on written notice to the shareholder.
 
   
    QUALIFIED RETIREMENT PLANS.  Shares of the Fund may be purchased for various
types of retirement plans. For more complete information, contact Value Line
Securities at 1-800-223-0818 during New York business hours.
    
 
ADDITIONAL INFORMATION
 
    The Fund is an open-end, diversified management investment company
incorporated in Maryland in March, 1985. The Fund has 50,000,000 authorized
shares of common stock, $1 par value. Each share has one vote, with fractional
shares voting proportionately. Shares have no preemptive rights, are freely
transferable, are entitled to dividends as declared by the Directors, and, if
the Fund were liquidated, would receive the net assets of the Fund.
 
   
    INQUIRIES.  All inquiries regarding the Fund should be directed to the Fund
at the telephone numbers or address set forth on the cover page of this
Prospectus. Shareholder inquiries regarding their accounts and account balances
should be directed to NFDS, Inc., servicing agent for State Street Bank and
Trust Company, the Fund's transfer agent, at 1-800-243-2729. Shareholders should
note that they may be required to pay a fee for special requests such as
historical transcripts for an account. The Fund's Info-Line (1-800-243-2739)
provides the latest account information 24 hours a day, every day, and is
available to shareholders with push-button phones. The Fund's Annual Report
contains a discussion of the Fund's performance and will be made available upon
request and without charge.
    
 
   
    SHAREHOLDER MEETINGS.  The Fund does not intend to hold routine annual
meetings of shareholders. However, special meetings of shareholders will be held
as required by law for purposes such as changing fundamental policies or
approving an advisory agreement.
    
 
   
    YEAR 2000.  Like other mutual funds, the Fund could be adversely affected if
the computer systems used by the Adviser and other service providers do not
properly process and calculate date-related information and data from and after
January 1, 2000. This is commonly known as the "Year 2000
    
 
                                       14
<PAGE>
   
Problem." The Adviser is taking steps that it believes are reasonably designed
to address the Year 2000 Problem with respect to the computer systems that it
uses and to obtain satisfactory assurances that comparable steps are being taken
by the Fund's other major service providers. At this time, however, there can be
no assurance that these steps will be sufficient to avoid any adverse impact to
the Fund.
    
 
   
    The Year 2000 Problem is expected to impact corporations, which may include
issuers of portfolio securities held by the Fund, to varying degrees based upon
various factors, including, but not limited to, the corporation's industry
sector and degree of technological sophistication. The Fund is unable to predict
what impact, if any, the Year 2000 Problem will have on issuers of the portfolio
securities held by the Fund.
    
 
                                       15
<PAGE>
                         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 net 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, low-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.
 
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 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 INVESTORS, 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 E. 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
<PAGE>
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
 
SHAREHOLDER SERVICING AGENT
State Street Bank and Trust Company
c/o NFDS
P.O. Box 419729
Kansas City, MO 64141-6729
 
CUSTODIAN & TRANSFER AGENT
State Street Bank and Trust Company
225 Franklin Street
Boston, MA 02110
 
   
INDEPENDENT ACCOUNTANTS
PricewaterhouseCoopers LLP
1177 Avenue of the Americas
New York, NY 10036
    
 
LEGAL COUNSEL
Peter D. Lowenstein, Esq.
Two Greenwich Plaza, Suite 100
Greenwich, CT 06830
 
                                   ----------
 
                               TABLE OF CONTENTS
 
   
<TABLE>
<CAPTION>
                                                    PAGE
                                                    -----
<S>                                              <C>
Summary of Fund Expenses.......................           2
Financial Highlights...........................           2
Investment Objective and Policies..............           3
Risk Factors...................................           7
Investment Restrictions........................           7
Management of the Fund.........................           7
Calculation of Net Asset Value.................           8
How to Buy Shares..............................           8
Dividends, Distributions and Taxes.............          10
Performance Information........................          11
How to Redeem Shares...........................          11
Investor Services..............................          13
Additional Information.........................          14
</TABLE>
    
 
- -------------------------------------------
                                   PROSPECTUS
- -------------------
 
   
                               SEPTEMBER 1, 1998
    
 
                                   VALUE LINE
                                  CONVERTIBLE
                                   FUND, INC.
 
                                 (800) 223-0818
 
                                     [LOGO]
<PAGE>
                       VALUE LINE CONVERTIBLE FUND, INC.
 
              220 East 42nd Street, New York, New York 10017-5891
                        1-800-223-0818 or 1-800-243-2729
                               www.valueline.com
 
- --------------------------------------------------------------------------------
 
                      STATEMENT OF ADDITIONAL INFORMATION
                               SEPTEMBER 1, 1998
 
- --------------------------------------------------------------------------------
 
    This Statement of Additional Information is not a prospectus and must be
read in conjunction with the Prospectus of Value Line Convertible Fund, Inc.
dated September 1, 1998, a copy of which may be obtained without charge by
writing or telephoning the Fund. The Fund's investment adviser is Value Line,
Inc. (the "Adviser").
                                 --------------
 
                               TABLE OF CONTENTS
 
<TABLE>
<CAPTION>
                                                                                              PAGE
                                                                                            ---------
<S>                                                                                         <C>
Investment Objective and Policies.........................................................       B-1
 
Investment Restrictions...................................................................       B-2
 
Directors and Officers....................................................................       B-4
 
The Adviser...............................................................................       B-5
 
Brokerage Arrangements....................................................................       B-6
 
How to Buy Shares.........................................................................       B-7
 
Suspension of Redemptions.................................................................       B-8
 
Taxes.....................................................................................       B-8
 
Performance Data..........................................................................       B-10
 
Additional Information....................................................................       B-12
 
Financial Statements......................................................................       B-12
</TABLE>
 
                                 --------------
 
                       INVESTMENT OBJECTIVE AND POLICIES
    (SEE ALSO "INVESTMENT OBJECTIVE AND POLICIES" IN THE FUND'S PROSPECTUS)
 
GENERAL
 
    Value Line Convertible Fund, Inc. (the "Fund") is a no-load, diversified,
open-end management investment company. Its investment objective is to seek high
current income together with capital appreciation. To attain its primary
investment objective, the Fund has a fundamental policy that under normal
conditions at least 70% of the value of its net assets will be invested in
convertible securities.
 
                                      B-1
<PAGE>
    The Fund will not concentrate its investments in any particular industry but
reserves the right to invest up to 25% of its total assets (taken at market
value) in any one industry. The Fund does not invest for the purposes of
management or control of companies whose securities the Fund owns. The Fund
intends to limit its annual portfolio turnover so that realized short-term gains
on securities held for less than three months do not exceed 30% of the Fund's
gross income so that the Fund will meet one of the tests for qualification as a
regulated investment company under the Internal Revenue Code.
 
    The policies set forth in the Fund's Prospectus and above in the preceding
paragraphs and the policies set forth below under "Investment Restrictions" are,
unless otherwise indicated, fundamental policies of the Fund and may not be
changed without the affirmative vote of a majority of the outstanding voting
securities of the Fund. As used in this Statement of Additional Information and
in the Prospectus, a "majority of the outstanding voting securities of the Fund"
means the lesser of (1) the holders of more than 50% of the outstanding shares
of capital stock of the Fund or (2) 67% of the shares present if more than 50%
of the shares are present at a meeting in person or by proxy.
 
                            INVESTMENT RESTRICTIONS
 
    The Fund may not:
 
        (1) Engage in short sales, except to the extent that it owns other
    securities convertible into an equivalent amount of such securities. Such
    transactions may only occur for the purpose of protecting a profit or in
    attempting to minimize a loss with respect to convertible securities. No
    more than 10% of the value of the Fund's net assets taken at market may at
    any one time be held as collateral for such sales.
 
        (2) Purchase or sell any put or call options or any combination thereof,
    except that the Fund may write and sell covered call option contracts on
    securities owned by the Fund. The Fund may also purchase call options for
    the purpose of terminating its outstanding obligations with respect to
    securities upon which covered call option contracts have been written (i.e.,
    "closing purchase transactions").
 
        (3) Borrow money in excess of 10% of the value of its assets and then
    only as a temporary measure to meet unusually heavy redemption requests or
    for other extraordinary or emergency purposes. Securities will not be
    purchased while borrowings are outstanding. No assets of the Fund may be
    pledged, mortgaged or otherwise encumbered, transferred or assigned to
    secure a debt.
 
        (4) Engage in the underwriting of securities, except to the extent that
    the Fund may be deemed an underwriter as to restricted securities under the
    Securities Act of 1933 in selling portfolio securities.
 
        (5) Invest in real estate, mortgages or illiquid securities of real
    estate investment trusts although the Fund may purchase securities of
    issuers which engage in real estate operations.
 
        (6) Invest in commodities or commodity contracts.
 
        (7) Lend money except in connection with the purchase of debt
    obligations or by investment in repurchase agreements, provided that
    repurchase agreements maturing in more than seven days, when taken together
    with other illiquid investments including restricted securities, do not
    exceed 10% of the Fund's assets. The Fund may lend its portfolio securities
    to broker-dealers and institutional investors if as a result thereof the
    aggregate value of all securities loaned does not exceed 33 1/3% of the
    total assets of the Fund.
 
                                      B-2
<PAGE>
        (8) Invest more than 5% of the value of its total assets in the
    securities of any one issuer or purchase more than 10% of the outstanding
    voting securities, or any other class of securities, of any one issuer. For
    purposes of this restriction, all outstanding debt securities of an issuer
    are considered as one class, and all preferred stock of an issuer is
    considered as one class. This restriction does not apply to obligations
    issued or guaranteed by the United States Government, its agencies or
    instrumentalities.
 
        (9) Purchase securities of other investment companies.
 
        (10) Invest 25% or more of its assets in securities of issuers in any
    one industry.
 
        (11) Invest more than 5% of its total assets in securities of issuers
    having a record, together with predecessors, of less than three years of
    continuous operation. The restriction does not apply to any obligation
    issued or guaranteed by the U.S. government, its agencies or
    instrumentalities.
 
        (12) Purchase or retain the securities of any issuer if, to the
    knowledge of the Fund, those officers and directors of the Fund and of the
    Adviser, who each owns more than 0.5% of the outstanding securities of such
    issuer, together own more than 5% of such securities.
 
        (13) Issue senior securities except evidences of indebtedness permitted
    by restriction No. 3 above.
 
        (14) Purchase securities for the purpose of exercising control over
    another company.
 
        (15) Purchase securities on margin or participate on a joint or a joint
    and several basis in any trading account in securities.
 
        (16) Purchase oil, gas or other mineral type development programs or
    leases, except that the Fund may invest in the securities of companies which
    invest in or sponsor such programs.
 
        (17) Invest more than 2% of the value of its total assets in warrants
    (valued at the lower of cost or market), except that warrants attached to
    other securities are not subject to these limitations.
 
    If a percentage restriction is adhered to at the time of investment, a later
change in percentage resulting from changes in values or assets will not be
considered a violation of the restriction. For purposes of industry
classifications, the Fund follows the industry classifications in The Value Line
Investment Survey.
 
                                      B-3
<PAGE>
                             DIRECTORS AND OFFICERS
 
<TABLE>
<CAPTION>
NAME, ADDRESS AND AGE               POSITION WITH FUND          PRINCIPAL OCCUPATION DURING PAST 5 YEARS
- ----------------------------------  ---------------------  ---------------------------------------------------
<S>                                 <C>                    <C>
*Jean Bernhard Buttner              Chairman of the Board  Chairman, President and Chief Executive Officer of
 Age 63                             of Directors and       the Adviser and Value Line Publishing, Inc.
                                    President              Chairman and President of the Value Line Funds and
                                                           Value Line Securities, Inc. (the "Distributor").
 John W. Chandler                   Director               Consultant, Academic Search Consultation Service,
 2801 New Mexico                                           Inc.; Trustee Emeritus and Chairman (1993-1994) of
   Ave., N.W.                                              Duke University; President Emeritus, Williams
 Washington, DC 20007                                      College.
 Age 74
*Leo R. Futia                       Director               Retired Chairman and Chief Executive Officer of The
 201 Park Avenue South                                     Guardian Life Insurance Company of America and
 New York, NY 10003                                        Director since 1970. Director (Trustee) of The
 Age 79                                                    Guardian Insurance & Annuity Company, Inc.,
                                                           Guardian Investor Services Corporation and the
                                                           Guardian-sponsored mutual funds.
 David H. Porter                    Director               President of Skidmore College; Director of
 813 North Broadway                                        Adirondack Trust Company.
 Saratoga Springs, NY 12866
 Age 62
 Paul Craig Roberts                 Director               Chairman, Institute for Political Economy;
 505 S. Fairfax Street                                     Director, A. Schulman Inc. (plastics).
 Alexandria, VA 22320
 Age 59
 Nancy-Beth Sheerr                  Director               Chairman, Radcliffe College Board of Trustees.
 1409 Beaumont Drive
 Gladwyne, PA 19035
 Age 49
 Bruce Alston                       Vice President         Portfolio Manager with the Adviser since 1997;
 Age 52                                                    Portfolio Manager with Dreyfus Management, Inc.
                                                           1994-1996, and Prudential Capital Markets Group,
                                                           1981-1994.
 Anthony Cichocki                   Vice President         Executive Editor, The Value Line Options and
 Age 37                                                    Convertibles Surveys since February 1998; prior
                                                           thereto, Vice President of Convertible Research at
                                                           NatWest Markets.
 David T. Henigson                  Vice President,        Vice President, Director and Compliance Officer of
 Age 41                             Secretary and          the Adviser. Director and Vice President of the
                                    Treasurer              Distributor.
</TABLE>
 
- --------------
* "Interested" director as defined in the Investment Company Act of 1940 (the
"1940 Act").
 
    Unless otherwise indicated, the address for each of the above is 220 East
42nd Street, New York, NY.
 
                                      B-4
<PAGE>
    Directors and certain officers of the Fund are also directors/trustees and
officers of other investment companies for which the Adviser acts as investment
adviser. The following table sets forth information regarding compensation of
Directors by the Fund and by the Fund and the eleven other Value Line Funds of
which each of the Directors is a director or trustee for the fiscal year ended
April 30, 1998. Directors who are officers or employees of the Adviser do not
receive any compensation from the Fund or any of the Value Line Funds.
 
                               COMPENSATION TABLE
                        FISCAL YEAR ENDED APRIL 30, 1998
 
<TABLE>
<CAPTION>
                                                                                                                TOTAL
                                                                         PENSION OR           ESTIMATED      COMPENSATION
                                                                         RETIREMENT            ANNUAL         FROM FUND
                                                      AGGREGATE           BENEFITS            BENEFITS         AND FUND
                                                    COMPENSATION       ACCRUED AS PART          UPON           COMPLEX
NAME OF PERSON                                        FROM FUND       OF FUND EXPENSES       RETIREMENT       (12 FUNDS)
- -------------------------------------------------  ---------------  ---------------------  ---------------  --------------
<S>                                                <C>              <C>                    <C>              <C>
Jean B. Buttner                                       $     -0-                 N/A                 N/A       $      -0-
John W. Chandler                                          2,968                 N/A                 N/A           35,620
Leo R. Futia                                              2,968                 N/A                 N/A           35,620
David H. Porter                                           1,335                 N/A                 N/A           16,018
Paul Craig Roberts                                        2,968                 N/A                 N/A           35,620
Nancy-Beth Sheerr                                         2,968                 N/A                 N/A           35,620
</TABLE>
 
    As of April 30, 1998, no person owned of record or, to the knowledge of the
Fund, owned beneficially, 5% or more of the outstanding stock of the Fund other
than Charles Schwab & Co., Inc., 101 Montgomery Street, San Francisco, CA 94104,
which owned 689,929 shares or 10.5% of the outstanding shares of the Fund,
National Financial Services Co., 200 Liberty Street, New York, NY 10281, which
owned 390,759 shares (5.9%) and Donaldson Lufkin Jenrette Securities Corp, POB
2052, Jersey City, NJ 07303, which owned 339,243 shares (5.1%). In addition, the
Adviser and affiliated companies owned 205,171 shares (3.1%) and officers and
directors of the Fund as a group owned 80,178 shares (1.2%).
 
                                  THE ADVISER
          (SEE ALSO "MANAGEMENT OF THE FUND" IN THE FUND'S PROSPECTUS)
 
    The Fund's investment adviser is Value Line, Inc. (the "Adviser"). The
investment advisory agreement between the Fund and the Adviser dated August 10,
1988 provides for an advisory fee payable monthly at an annual rate of 3/4 of 1%
of the Fund's average daily net assets during the year. During the fiscal years
ended April 30, 1996, 1997 and 1998, the Fund paid or accrued to the Adviser
advisory fees of $428,535, $517,810 and $638,379, respectively.
 
    The investment advisory agreement provides that the Adviser shall render
investment advisory and other services to the Fund including, at its expense,
all administrative services, office space and the services of all officers and
employees of the Fund. The Fund pays all other expenses incurred in its
organization and operation which are not assumed by the Adviser including taxes,
interest, brokerage commissions, insurance premiums, fees and expenses of the
custodian and shareholder servicing agent, legal and accounting fees, fees and
expenses in connection with qualification under federal and state securities
laws and costs of shareholder reports and proxy materials. The Fund has agreed
that it will use the words "Value Line" in its name only so long as Value Line,
Inc. serves as investment adviser of the Fund. The agreement will terminate upon
its assignment.
 
                                      B-5
<PAGE>
    The Adviser acts as investment adviser to 14 other investment companies
constituting The Value Line Family of Funds, and furnishes investment counseling
services to private and institutional accounts with combined assets in excess of
$5 billion.
 
    Certain of the Adviser's clients may have investment objectives similar to
the Fund and certain investments may be appropriate for the Fund and for other
clients advised by the Adviser. From time to time, a particular security may be
bought or sold for only one client or in different amounts and at different
times for more than one but less than all such clients. In addition, a
particular security may be bought for one or more clients when one or more other
clients are selling such security, or purchases or sales of the same security
may be made for two or more clients on the same day. In such event, such
transactions will be averaged as to price and allocated as to amount in
accordance with the daily purchase or sale orders actually placed for each
client. In some cases, this procedure could have a detrimental effect on the
price or amount of the securities purchased or sold by the Fund. In other cases,
however, it is believed that the ability of the Fund to participate, to the
extent permitted by law, in volume transactions will produce better results for
the Fund.
 
    The Adviser and/or its affiliates, officers, directors and employees may
from time to time own securities which are also held in the portfolio of the
Fund. The Adviser has imposed rules upon itself and such persons requiring
monthly reports of security transactions for their respective accounts and
restricting trading in various types of securities in order to avoid possible
conflicts of interest. The Adviser may from time to time, directly or through
affiliates, enter into agreements to furnish for compensation special research
or financial services to companies, including services in connection with
acquisitions, mergers or financings. In the event that such agreements are in
effect with respect to issuers of securities held in the portfolio of the Fund,
specific reference to such agreements will be made in the "Schedule of
Investments" in shareholder reports of the Fund. As of the date of this
Statement of Additional Information, no such agreements exist.
 
                             BROKERAGE ARRANGEMENTS
          (SEE ALSO "MANAGEMENT OF THE FUND" IN THE FUND'S PROSPECTUS)
 
    Orders for the purchase and sale of portfolio securities are placed with
brokers and dealers who, in the judgment of the Adviser, are able to execute
them as expeditiously as possible and at the best obtainable price. Purchases
and sales of securities which are not listed or traded on a securities exchange
will ordinarily be executed with primary market makers acting as principal,
except when it is determined that better prices and executions may otherwise be
obtained. The Adviser is also authorized to place purchase or sale orders with
brokers or dealers who may charge a commission in excess of that charged by
other brokers or dealers if the amount of the commission charged is reasonable
in relation to the value of the brokerage and research services provided. Such
allocation will be in such amounts and in such proportions as the Adviser may
determine. Orders may also be placed with brokers or dealers who sell shares of
the Fund or other funds for which the Adviser acts as investment adviser, but
this fact, or the volume of such sales, is not a consideration in their
selection. During fiscal 1996, 1997 and 1998, the Fund paid brokerage
commissions of $24,792, $33,824 and $22,709, respectively.
 
    The Board of Directors has adopted procedures incorporating the standards of
Rule 17e-1 under the 1940 Act which requires that commissions paid to Value Line
Securities, Inc. or any other "affiliated person" be "reasonable and fair"
compared to the commissions paid to other brokers in connection with comparable
transactions. The procedures require that the Adviser furnish reports to the
Directors with
 
                                      B-6
<PAGE>
respect to the payment of commissions to affiliated brokers and maintain records
with respect thereto. During the fiscal year ended April 30, 1998, all of the
Fund's brokerage commissions were paid to brokers or dealers solely for their
services in obtaining best prices and executions. The information and services
furnished to the Adviser include the furnishing of research reports and
statistical compilations and computations and the providing of current
quotations for securities. These services and information were furnished to the
Adviser at no cost to it; no such services or information were furnished
directly to the Fund, but certain of these services might have relieved the Fund
of expenses which it would otherwise have had to pay. Such information and
services are considered by the Adviser, and brokerage commissions are allocated
in accordance with its assessment of such information and services, but only in
a manner consistent with the placing of purchase and sale orders with brokers
and/or dealers, which, in the judgment of the Adviser, are able to execute such
orders as expeditiously as possible and at the best obtainable price. The Fund
is advised that the receipt of such information and services has not reduced in
any determinable amount the overall expenses of the Adviser.
 
                               HOW TO BUY SHARES
      (SEE ALSO "CALCULATION OF NET ASSET VALUE", "HOW TO BUY SHARES" AND
                 "INVESTOR SERVICES" IN THE FUND'S PROSPECTUS)
 
    Shares of the Fund are purchased at net asset value next calculated after
receipt of a purchase order. Minimum orders are $1,000 for an initial purchase
and $250 for each subsequent purchase. The Fund reserves the right to reduce or
waive the minimum purchase requirements in certain cases such as pursuant to
payroll deduction plans, etc., where subsequent and continuing purchases are
contemplated.
 
    The Fund has entered into a distribution agreement with Value Line
Securities, Inc. (the "Distributor"), a wholly-owned subsidiary of the Adviser,
pursuant to which the Distributor acts as principal underwriter and distributor
of the Fund for the sale and distribution of its shares. The Distributor
receives no compensation for its services under the Agreement. The Distributor
also serves as distributor to the other Value Line funds.
 
    The Fund has authorized one or more brokers to accept on its behalf purchase
and redemption orders and such brokers are authorized to designate other
intermediaries to accept purchase and redemption orders on the Fund's behalf.
The Fund will be deemed to have received a purchase or redemption order when an
authorized broker or its authorized designee accepts the order, in which event
customer orders will be priced at the Fund's net asset value next computed after
they are accepted by the authorized broker or the broker's authorized designee.
 
    AUTOMATIC PURCHASES.  The Fund offers a free service to its shareholders,
Valu-Matic, through which monthly investments of $25 or more may be made
automatically into the shareholder's Fund account. The required form to enroll
in this program is available upon request from the Distributor.
 
    QUALIFIED RETIREMENT PLANS.  Shares of the Fund may be purchased as the
investment medium for various retirement plans. Upon request, the Distributor
will provide information regarding eligibility and permissible contributions.
Because a retirement plan is designed to provide benefits in future years, it is
important that the investment objectives of the Fund be consistent with the
participant's retirement objectives. Premature withdrawals from a retirement
plan may result in adverse tax consequences.
 
                                      B-7
<PAGE>
                           SUSPENSION OF REDEMPTIONS
 
    The right of redemption may be suspended, or the date of payment postponed
beyond the normal seven-day period by the Fund's Board of Directors under the
following conditions authorized by the 1940 Act: (1) For any period (a) during
which the New York Stock Exchange is closed, other than customary weekend and
holiday closing, or (b) during which trading on the New York Stock Exchange is
restricted; (2) For any period during which an emergency exists as a result of
which (a) disposal by the Fund of securities owned by it is not reasonably
practical, or (b) it is not reasonably practical for the Fund to determine the
fair value of its net assets; (3) For such other periods as the Securities and
Exchange Commission may by order permit for the protection of the Fund's
shareholders.
 
    The Fund will ordinarily pay in cash all redemptions by any shareholder of
record. However, the Fund has reserved the right under the 1940 Act to make
payment in whole or in part in securities of the Fund, if the Directors
determine that such action is in the best interests of the other shareholders.
Under such circumstances, the Fund will, nevertheless, pay to each shareholder
of record in cash all redemptions by such shareholder, during any 90-day period,
up to the lesser of $250,000 or 1% of the Fund's net assets. Securities
delivered in payment of redemptions are valued at the same value assigned to
them in computing the net asset value per share. Shareholders receiving such
securities may incur brokerage costs on their sales.
 
                                     TAXES
      (SEE "DIVIDENDS, DISTRIBUTIONS AND TAXES" IN THE FUND'S PROSPECTUS)
 
    Set forth below is a discussion of certain U.S. federal income tax issues
concerning the Fund and the purchase, ownership and disposition of Fund shares.
This discussion does not purport to be complete or to deal with all aspects of
federal income taxation that may be relevant to shareholders in light of their
particular circumstances, nor to certain types of shareholders subject to
special treatment under the federal income tax laws. This discussion is based
upon present provisions of the Internal Revenue Code of 1986, as amended (the
"Code"), the regulations promulgated thereunder and judicial and administrative
ruling authorities, all of which are subject to change, which change may be
retroactive. Prospective investors should consult their own tax advisors with
regard to the federal tax consequences of the purchase, ownership, or
disposition of Fund shares, as well as the tax consequences arising under the
laws of any state, foreign country, or other taxing jurisdiction.
 
    FUND STATUS.  The Fund intends to qualify and elect to be treated each year
as a regulated investment company under Subchapter M of the Code. Accordingly,
the Fund generally must, among other things, (i) derive in each taxable year at
least 90% of its gross income from dividends, interest, payments from certain
securities loans, and gains from the sale of stock, securities or foreign
currencies or other income (such as gains from options, futures or forward
contracts) from investing in stock, securities or currencies; and (ii) hold as
of the close of each quarter, at least 50% of its assets in certain investment
assets, such as cash, U.S. Government securities, securities of other regulated
investment companies and other securities, with such other securities limited as
to any issuer to not more than 5% of the value of the Fund's total assets and
10% of the outstanding voting securities of such issuer, and hold not more than
25% of the value of the Fund's assets in the securities of any issuer (other
than U.S. Government securities or securities of other regulated investment
companies).
 
    FUND DISTRIBUTIONS.  As a regulated investment company, the Fund generally
will not be subject to U.S. federal income tax on income and gains that it
distributes to shareholders, if at least 90% of the
 
                                      B-8
<PAGE>
Fund's investment company income -- dividends, interest and net short-term
capital gains in excess of net long-term capital losses -- for the taxable year
is distributed. The Fund intends to distribute substantially all of its
investment company income and net capital gains to shareholders for federal
income tax purposes although such distributions will be automatically reinvested
in additional shares of the Fund unless the shareholder has requested otherwise.
 
    Amounts not timely distributed by the Fund are subject to a nondeductible 4%
excise tax at the Fund level. To avoid the tax, the Fund must distribute during
a calendar year at least 98% of its ordinary income, 98% of its capital gains in
excess of capital losses for the one year period ended October 31 of such year,
and all ordinary income and capital gains for previous years that were not
distributed in earlier years. The Fund will satisfy the annual distribution
requirement if it distributes the required amount on or before December 31 of
such year or if the distribution is declared in October, November or December of
such year with a record date within such period and paid by the Fund during
January of the following calendar year. Such distributions will be taxable to
shareholders in the calendar year in which the distributions are declared,
rather than the calendar year in which the distributions are received. The Fund
anticipates that it will make sufficient timely distributions to avoid
imposition of the excise tax.
 
    Options, futures contracts and short sales entered into by the Fund will be
subject to special tax rules. These rules may accelerate income to the Fund,
defer Fund losses, cause adjustments in the holding periods of Fund securities,
convert capital gain into ordinary income and convert short-term capital losses
into long-term capital losses. As a result, these rules could affect the amount,
timing and character of Fund distributions.
 
    Distributions of investment company taxable income are taxable to a U.S.
shareholder as ordinary income, whether paid in cash or reinvested. Dividends
paid to a corporate shareholder may qualify for the dividends-received
deduction, to the extent such dividends are attributable to dividends received
from a U.S. corporation. It is expected that dividends from U.S. corporations
will constitute most of the Fund's gross income and that a substantial portion
of the dividends paid by the Fund will qualify for the dividends-received
deduction for corporate shareholders of the Fund. Upon request, the Fund will
advise Fund shareholders of the amount of dividends which qualify for the
dividends-received deduction.
 
    Distributions of net capital gains (the excess of net long-term capital
gains over net short-term capital losses), if any, designated as capital gain
dividends may be taxable to individuals and certain other shareholders at the
maximum federal 20% or 28% capital gains rates (depending upon the Fund's
holding period for the assets giving rise to the capital gains), regardless of
how long the shareholder has held the Fund's shares. The maximum 20% capital
gains rate generally applies to gains from the sale of assets held for more than
18 months; the maximum 28% capital gains rate generally applies to gains from
the sale of assets held for more than one year but not more than 18 months.
Capital gain from the sale of assets held for one year or less will generally be
taxed as ordinary income.
 
    Investors purchasing Fund shares prior to a distribution should be aware of
the tax consequences of purchasing such Fund shares. The purchase price paid for
such shares may reflect the amount of the forthcoming distribution. Although
distributions from the Fund shortly after the purchase of Fund shares may be
viewed in substance as a return of capital, nevertheless, such a distribution
will be attributed to the dividend or capital gain income of the Fund and,
therefore, be taxable to the shareholder.
 
    REDEMPTION, SALE OR EXCHANGE OF FUND SHARES.  Upon a redemption or sale of
shares of the Fund, a shareholder may realize a gain or loss for federal income
tax purposes depending upon his or her basis in the shares. A gain or loss will
be treated as capital gain or loss if the shares are capital assets in the
 
                                      B-9
<PAGE>
shareholder's hands. Capital gains may be taxable to individuals and certain
other shareholders at the maximum federal 20% or 28% capital gains rate
(depending upon the shareholder's holding period for the shares). Any loss
realized on a redemption or sale of Fund shares will be disallowed to the extent
the Fund shares disposed of are replaced (including through reinvestment of
dividends) within a period of 61 days beginning 30 days before and ending 30
days after the Fund shares are disposed of. In such a case, the basis of the
Fund shares acquired will be adjusted to reflect the disallowed loss. If a
shareholder held Fund shares for six months or less and during that period
received a distribution taxable to the shareholder as long-term capital gain,
any loss realized on the sale of such Fund shares during such six-month period
would be a long-term loss to the extent of such distribution.
 
    An exchange of shares in the Fund for shares of another Value Line fund will
be treated as a taxable sale of the exchanged Fund shares. Accordingly, a
shareholder may recognize a gain or loss for federal income tax purposes
depending upon his or her basis in the Fund shares exchanged. A gain or loss
will be treated as capital gain or loss if the shares are capital assets in the
shareholder's hands. Capital gains may be taxable to individuals and certain
other shareholders at the maximum federal 20% or 28% capital gains rate
(depending upon the shareholder's holding period for the shares). The
shareholder will have a tax basis in the newly-acquired Fund shares equal to the
amount invested and will begin a new holding period for federal income tax
purposes.
 
    If a shareholder exchanges shares in the Fund for shares in another Value
Line fund pursuant to a reinvestment right, the sales charge incurred in the
purchase of the Fund shares exchanged may not be added to tax basis in
determining gain or loss for federal income tax purposes. Instead, the sales
charge for the exchanged Fund shares shall be added to basis for purposes of
determining gain or loss on the disposition of the newly-acquired Fund shares,
if such newly-acquired Fund shares are not disposed of in a similar exchange
transaction.
 
    REPORTING AND BACKUP WITHHOLDING.  The Fund will be required to report to
the Internal Revenue Service ("IRS") all distributions and gross proceeds from
the redemption of the Fund's shares, except in the case of certain exempt
shareholders. The Fund may be required to withhold U.S. federal income tax at
the rate of 31% of all taxable distributions and redemption proceeds payable to
shareholders who fail to provide the Fund with their correct taxpayer
identification number or to make certain certifications, or who have been
notified by the IRS that they are subject to backup withholding. Corporate
shareholders and certain other shareholders specified in the Code generally are
exempt from such backup withholding. Backup withholding is not an additional
tax. Any amounts withheld may be credited against the shareholder's U.S. federal
income tax. If the backup withholding provisions are applicable to a
shareholder, distributions and gross proceeds payable to such shareholder will
be reduced by the amounts required to be withheld, regardless of whether such
distributions are paid or reinvested.
 
                                PERFORMANCE DATA
 
    From time to time, the Fund may state its total return in advertisements and
investor communications. Total return may be stated for any relevant period as
specified in the advertisement or communication. Any statements of total return
or other performance data on the Fund will be accompanied by information on the
Fund's average annual total return over the most recent four calendar quarters
and the period from the Fund's inception of operations. The Fund may also
advertise aggregate total return information for different periods of time.
 
                                      B-10
<PAGE>
    The Fund's average annual total return is determined by reference to a
hypothetical $1,000 investment that includes capital appreciation and
depreciation for the stated period, according to the following formula:
 
                                P(1+T)(n) = ERV
 
<TABLE>
<S>       <C>   <C>  <C>
Where:    P     =    a hypothetical initial purchase order of
                     $1,000
          T     =    average annual total return
          n     =    number of years
          ERV   =    ending redeemable value of the
                     hypothetical $1,000 purchase at the end
                     of the period.
</TABLE>
 
    Aggregate total return is calculated in a similar manner, except that the
results are not annualized. Each calculation assumes that all dividends and
distributions are reinvested at net asset value on the reinvestment dates during
the period.
 
    As stated in the Prospectus, the Fund may also quote its current yield in
advertisements and investor communications.
 
    The yield computation is determined by dividing the net investment income
per share earned during the period by the maximum offering price per share on
the last day of the period and annualizing the resulting figure, according to
the following formula:
 
                                               6
                                       a - b
                          Yield = 2[(------- +1) - 1]
                                        cd
 
<TABLE>
<S>       <C>  <C>  <C>
Where:    a    =    dividends and interest earned
                    during the period (calculated
                    as required by the Securities
                    and Exchange Commission);
          b    =    expenses accrued for the
                    period (net of
                    reimbursements);
          c    =    the average daily number of
                    shares outstanding during the
                    period that were entitled to
                    receive dividends;
          d    =    the maximum offering price per
                    share on the last day of the
                    period.
</TABLE>
 
    The above formula will be used in calculating quotations of yield, based on
specified 30-day periods identified in advertising by the Fund.
 
    The Fund may also, from time to time, include a reference to its current
quarterly or annual distribution rate in investor communications and sales
literature preceded or accompanied by a Prospectus, reflecting the amounts
actually distributed to shareholders which could include capital gains and other
items of income not reflected in the Fund's yield, as well as interest and
dividend income received by the Fund and distributed to shareholders (which is
reflected in the Fund's yield).
 
    All calculations of the Fund's distribution rate are based on the
distributions per share which are declared, but not necessarily paid, during the
fiscal year. The distribution rate is determined by dividing the distributions
declared during the period by the maximum offering price per share on the last
day of the period and annualizing the resulting figure. In calculating its
distribution rate, the Fund has used the same assumptions that apply to its
calculation of yield. The distribution rate does not reflect capital
appreciation or depreciation in the price of the Fund's shares and should not be
considered to be a complete indicator of the return to the investor on his
investment.
 
                                      B-11
<PAGE>
    The Fund's current yield, distribution rate and total return may be compared
to relevant indices, including U.S. domestic and international taxable bond
indices and data from Lipper Analytical Services, Inc., or Standard & Poor's
Indices. From time to time, evaluations of the Fund's performance by independent
sources may also be used in advertisements and in information furnished to
present or prospective investors in the Fund.
 
                             ADDITIONAL INFORMATION
 
EXPERTS
 
    The financial statements of the Fund and the financial highlights included
in the Fund's Annual Report to Shareholders and incorporated by reference in
this Statement of Additional Information have been so incorporated by reference
in reliance on the report of PricewaterhouseCoopers LLP, independent
accountants, given on the authority of said firm as experts in auditing and
accounting.
 
CUSTODIAN
 
    The Fund employs State Street Bank and Trust Company, Boston, MA as
custodian for the Fund. The custodian's responsibilities include safeguarding
and controlling the Fund's cash and securities, handling the receipt and
delivery of securities and collecting interest and dividends on the Fund's
investments. The custodian does not determine the investment policies of the
Fund or decide which securities the Fund will buy or sell.
 
                              FINANCIAL STATEMENTS
 
    The Fund's financial statements for the year ended April 30, 1998, including
the financial highlights for each of the five fiscal years in the period ended
April 30, 1998, appearing in the 1998 Annual Report to Shareholders and the
report thereon of PricewaterhouseCoopers LLP, independent accountants, appearing
therein, are incorporated by reference in this Statement of Additional
Information.
 
    The Fund's 1998 Annual Report to Shareholders is enclosed with this
Statement of Additional Information.
 
                                      B-12
<PAGE>
   
                                     PART C
                               OTHER INFORMATION
    
 
ITEM 24.  FINANCIAL STATEMENTS AND EXHIBITS.
 
   
    a.  Financial Statements
       Included in Part A of this Registration Statement:
         Financial Information
           Financial Highlights for each of the ten years in the period ended
           April 30, 1998.
    
 
   
    Included in Part B of this Registration Statement:*
         Schedule of Investments at April 30, 1998
        Statement of Assets and Liabilities at April 30, 1998
        Statement of Operations for the year ended April 30, 1998
        Statements of Changes in Net Assets for the years ended April 30, 1998
          and April 30, 1997
        Financial Highlights for each of the five years in the period ended
       April 30, 1998
        Notes to Financial Statements
        Report of Independent Accountants
    
 
    Statements, schedules and historical information other than those listed
       above have been omitted since they are either not applicable or are not
       required.
 
- ---------
 
   
     *  Incorporated by reference from the Annual Report to Shareholders for the
        year ended April 30, 1998.
    
 
    b.  Exhibits
       16.  Calculation of Performance Data--Exhibit 1
 
ITEM 25.  PERSONS CONTROLLED BY OR UNDER COMMON CONTROL WITH REGISTRANT.
 
          None
 
ITEM 26.  NUMBER OF HOLDERS OF SECURITIES.
 
   
    As of April 30, 1998, there were 3,407 record holders of the Registrant's
Capital Stock ($1.00 par value).
    
 
ITEM 27.  INDEMNIFICATION.
 
   
    Incorporated by reference from Post-Effective Amendment No. 3 (filed on
August 24, 1987).
    
 
                                      C-1
<PAGE>
ITEM 28.  BUSINESS OR OTHER CONNECTIONS OF INVESTMENT ADVISER.
 
    Value Line, Inc., Registrant's investment adviser, acts as investment
adviser for a number of individuals, trusts, corporations and institutions, in
addition to the registered investment companies in the Value Line Family of
Funds listed in Item 29.
 
   
<TABLE>
<CAPTION>
                                        POSITION WITH
            NAME                         THE ADVISER                              OTHER EMPLOYMENT
- ----------------------------  ----------------------------------  ------------------------------------------------
 
<S>                           <C>                                 <C>
Jean Bernhard Buttner         Chairman of the Board,              Chairman of the Board and Chief Executive
                              President, and Chief Executive      Officer of Arnold Bernhard & Co., Inc., 220 East
                              Officer                             42nd Street, New York, NY 10017; Chairman of the
                                                                  Value Line Funds and the Distributor
Samuel Eisenstadt             Senior Vice President and Director
 
David T. Henigson             Vice President, Treasurer and       Vice President and a Director of Arnold Bernhard
                              Director                            & Co., Inc. and the Distributor
 
Howard A. Brecher             Vice President, Secretary and       Vice President, Secretary, Treasurer and a
                              Director                            Director of Arnold Bernhard & Co., Inc.
 
Harold Bernard, Jr.           Director                            Retired Administrative Law Judge
 
William S. Kanaga             Director                            Retired Chairman of Arthur Young (now Ernst &
                                                                  Young)
 
W. Scott Thomas               Director                            Partner, Brobeck, Phleger & Harrison, attorneys,
                                                                  One Market Plaza, San Francisco, CA 94105
 
Linda S. Wilson               Director                            President, Radcliffe College, 10 Garden Street,
                                                                  Cambridge, MA 02138
</TABLE>
    
 
                                      C-2
<PAGE>
ITEM 29.  PRINCIPAL UNDERWRITER.
 
   
    (a) Value Line Securities, Inc., acts as principal underwriter for the
       following Value Line funds, including the Registrant: The Value Line
       Fund, Inc.; The Value Line Income Fund, Inc.; The Value Line Special
       Situations Fund, Inc.; Value Line Leveraged Growth Investors, Inc.; The
       Value Line Cash Fund, Inc.; Value Line U.S. Government Securities Fund,
       Inc.; Value Line Centurion Fund, Inc.; The Value Line Tax Exempt Fund,
       Inc.; Value Line Convertible Fund, Inc.; Value Line Aggressive Income
       Trust; Value Line New York Tax Exempt Trust; Value Line Strategic Asset
       Management Trust; Value Line Small-Cap Growth Fund, Inc.; Value Line
       Asset Allocation Fund, Inc.; Value Line U.S. Multinational Company Fund,
       Inc.
    
 
    (b)
 
<TABLE>
<CAPTION>
                                    (2)
                               POSITION AND                 (3)
           (1)                    OFFICES               POSITION AND
    NAME AND PRINCIPAL        WITH VALUE LINE           OFFICES WITH
     BUSINESS ADDRESS        SECURITIES, INC.            REGISTRANT
- --------------------------  -------------------  --------------------------
 
<S>                         <C>                  <C>
Jean Bernhard Buttner       Chairman of the      Chairman of the Board
                            Board
 
David T. Henigson           Vice President,      Vice President, Secretary
                            Secretary,           and Treasurer
                            Treasurer and
                            Director
 
Stephen LaRosa              Asst. Vice           Asst. Treasurer,
                            President            Asst. Secretary
</TABLE>
 
        The business address of each of the officers and directors is 220 East
        42nd Street, New York, NY 10017-5891.
 
    (c) Not applicable.
 
                                      C-3
<PAGE>
ITEM 30.  LOCATION OF ACCOUNTS AND RECORDS.
 
    Value Line, Inc.
 
    220 East 42nd Street
 
    New York, NY 10017
 
    For records pursuant to:
 
    Rule 31a-1(b)(4),(5),(6),(7),(10),(11)
 
    Rule 31a-1(f)
 
    State Street Bank and Trust Company
 
    c/o NFDS
 
    P.O. Box 419729
 
    Kansas City, MO 64141
 
    For records pursuant to Rule 31a-1(b)(2)(iv)
 
    State Street Bank and Trust Company
 
    225 Franklin Street
 
    Boston, MA 02110
 
    For all other records
 
ITEM 31.  MANAGEMENT SERVICES.
 
    None.
 
ITEM 32.  UNDERTAKINGS.
 
    Registrant undertakes to furnish each person to whom a prospectus is
delivered with a copy of the Registrant's latest annual report to shareholders,
upon request and without charge.
 
                                 --------------
 
                       CONSENT OF INDEPENDENT ACCOUNTANTS
 
   
We hereby consent to the incorporation by reference in the Prospectus and
Statement of Additional Information constituting parts of this Post-Effective
Amendment No. 15 to the registration statement on Form N-1A (the "Registration
Statement") of our report dated June 19, 1998, relating to the financial
statements and financial highlights appearing in the April 30, 1998 Annual
Report to Shareholders of Value Line Convertible Fund, Inc., which are also
incorporated by reference into the Registration Statement. We also consent to
the references to us under the heading "Financial Highlights" in the Prospectus
and under the headings "Additional Information" and "Financial Statements" in
the Statement of Additional Information.
    
 
   
PricewaterhouseCoopers LLP
    
 
   
1177 Avenue of the Americas
New York, New York
August 18, 1998
    
 
                                      C-4
<PAGE>
                                   SIGNATURES
 
   
    Pursuant to the requirements of the Securities Act of 1933 and the
Investment Company Act of 1940, the Registrant certifies that it meets all of
the requirements for effectiveness of the Registration Statement pursuant to
Rule 485(b) under the Securities Act of 1933 and has duly caused this Amendment
to its Registration Statement to be signed on its behalf by the undersigned,
thereunto duly authorized, in the City of New York, and State of New York, on
the 18th day of August, 1998.
    
 
                                      VALUE LINE CONVERTIBLE FUND, INC.
 
                                       By:         /s/ DAVID T. HENIGSON
                                      ..........................................
 
                                                    DAVID T. HENIGSON
                                                     VICE PRESIDENT
 
    Pursuant to the requirements of the Securities Act of 1933, this Amendment
has been signed below by the following persons in the capacities and on the
dates indicated.
 
   
<TABLE>
<CAPTION>
                      SIGNATURES                                        TITLE                         DATE
- ------------------------------------------------------  -------------------------------------  -------------------
 
<C>                                                     <S>                                    <C>
                                                        Chairman of the                          August 18, 1998
                   *JEAN B. BUTTNER                       Board of Directors; President;
                  (JEAN B. BUTTNER)                       Principal Executive Officer
 
                  *JOHN W. CHANDLER                     Director                                 August 18, 1998
                  (JOHN W. CHANDLER)
 
                    *LEO R. FUTIA                       Director                                 August 18, 1998
                    (LEO R. FUTIA)
 
                   *DAVID H. PORTER                     Director                                 August 18, 1998
                  (DAVID H. PORTER)
 
                 *PAUL CRAIG ROBERTS                    Director                                 August 18, 1998
                 (PAUL CRAIG ROBERTS)
 
                  *NANCY-BETH SHEERR                    Director                                 August 18, 1998
                 (NANCY-BETH SHEERR)
 
                      /s/ DAVID T. HENIGSON             Treasurer; Principal Financial and       August 18, 1998
 .....................................................    Accounting Officer
                 (DAVID T. HENIGSON)
</TABLE>
    
 
* By       /s/ DAVID T. HENIGSON
 .....................................
 
           (DAVID T. HENIGSON,
          ATTORNEY-IN-FACT)
 
                                      C-5

<PAGE>

                         VALUE LINE CONVERTIBLE FUND, INC.

                 SCHEDULE FOR COMPUTATION OF PERFORMANCE QUOTATION
                                    EXHIBIT 16

<TABLE>
<CAPTION>

Year(s) Ended 4/30/98:         1 year            5 years           10 years
                            --------------    -------------      ------------
<S>                         <C>               <C>                <C>

Initial Investment:                1,000             1,000             1,000
Balance at End of Period:          1,250             1,928             3,449
Change:                              250               928             2,449

Percentage Change:                25.04%            92.76%           244.94%

Average Annual Total Return:      25.04%            14.03%            13.18%

</TABLE>


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