VALUE LINE CONVERTIBLE FUND INC
N-30D, 1999-12-29
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================================================================================

                               ------------------
                               SEMI-ANNUAL REPORT
                               ------------------
                                October 31, 1999
                               ------------------


                                   Value Line
                                   Convertible
                                   Fund, Inc.






                                     [LOGO]
                               ------------------
                                   VALUE LINE
                                     No-Load
                                     Mutual
                                      Funds



<PAGE>

Value Line Convertible Fund, Inc.


                                                               To Our Value Line
- --------------------------------------------------------------------------------

To Our Shareholders:

I am pleased to report that The Value Line  Convertible Fund returned 10.26% for
the six months ended October 31, 1999. The fund's performance exceeded by a wide
margin  the  results of its  competitors.  As shown  below,  your Fund more than
tripled the Lipper  Convertible  Peer Group Average (a collection of convertible
funds) and the unmanaged Value Line Convertible  Index, a proxy for the domestic
convertible market with over 600 convertible securities.

                                           6 Mos.
                                          10/31/99
                                          --------
o Value Line Convertible Fund............   10.26%
o Lipper Convertible Peer Group Avg......    2.86%
o Value Line Convertible Index ..........    2.99%
o S&P 500................................    2.74%
o Russell 2000...........................   -0.25%
o Lehman Brothers Gov/Corp...............   -0.55%
o Lehman High Yield Bond.................   -3.60%

Since our last report,  the financial  markets have  weathered two interest rate
hikes  by  the  Federal  Reserve  Board.  Interest  rates,  represented  by  the
thirty-year  Treasury  bond,  trended  higher  from  5.53% to 6.16%  and  prices
consequently  fell,  resulting in slightly  negative  returns for bonds.  On the
other hand,  equities were mixed,  with the S&P 500 index eking out a small gain
of 2.74% while the Russell 500 index slipped 0.25% for the period.

Your Fund benefited  from a market weight  (previously  underweight)  in the top
performing telecommunications and technology sectors. Additionally,  several new
issues were purchased at favorable  prices  relative to the general  market.  As
these issues returned to fair value, returns were enhanced.

The outlook for the markets is mixed.  We approach  the  relatively  high equity
valuations  with caution,  while we anticipate  good economic  growth,  moderate
earnings  growth and muted  inflation.  This will take the pressure off interest
rates,  allowing them to drop below 6% next year on the 30-year  Treasury  bond.
Gently declining  interest rates will support higher equity prices well into the
next  millennium  and,  therefore,   excellent   risk-adjusted   performance  by
convertible  securities.  We believe that a sound investment  policy includes an
allocation to convertible securities to spread risk and enhance overall results.

Our strategy is to maintain  our focus on  convertible  securities  and to lower
risk by continuing to focus on the more liquid, larger capitalization and higher
quality  convertibles.  The number of  positions  held by your Fund will  likely
increase, as we seek to increase  diversification and reduce the significance of
any one  position  in the  portfolio.  Our  discipline  continues  to  emphasize
convertibles  that offer  favorable  leverage.  Favorable  leverage is a balance
between  potential  securities  with solid  fundamentals  and a high rank in the
Value Line Convertible Survey.

As always,  your  confidence in Value Line is appreciated and we look forward to
serving your future investment needs.

                                                       Sincerely,


                                                       /s/ Jean Bernhard Buttner
                                                       Jean Bernhard Buttner
                                                       Chairman and President

December 3, 1999

- --------------------------------------------------------------------------------
2


<PAGE>

                                               Value Line Convertible Fund, Inc.

Convertible Fund Shareholders
- --------------------------------------------------------------------------------

Economic Observations

The  American  economy  continues  to perform  well as we approach the new year.
Evidence of this healthy  level of business  activity can be found in the strong
pace of manufacturing, the healthy rate at which new jobs are being created, and
the generally solid  performance by the consumer  sector.  Overall,  we estimate
that GDP growth,  which probably  averaged,  or even  exceeded,  4% in the final
quarter of 1999, will come in at  still-respectable  3%, or so, in 2000. Indeed,
the long-lived expansion, which will soon enter its tenth year, could well start
a second decade in 2001.

Inflationary  pressures,  meanwhile,  continue  to be held at bay, in spite of a
tightening labor market,  with strong  increases in productivity  being at least
partially  responsible  for  this  pricing  stability.  Nevertheless,  a  slight
increase in pricing pressures does seem possible over the next several quarters.
The  Federal  Reserve,  taking note of this  possibly  somewhat  higher  expense
structure,  is likely to  maintain  a neutral  to at most  modestly  restrictive
monetary stance in the months ahead.

Performance Data:*

                                 Average    Growth of
                                 Annual     an Assumed
                                  Total     Investment
                                 Return     of $10,000
                                 ------     ----------
 1 year ended 9/30/99.........   16.43%      $11,643
 5 years ended 9/30/99........   12.65%       18,140
10 years ended 9/30/99........   10.65%       27,509


*    The performance data quoted represent past performance and are no guarantee
     of future  performance.  The average  annual  total return and growth of an
     assumed  investment of $10,000  include  dividends  reinvested  and capital
     gains distributions accepted in shares. The investment return and principal
     value of an investment will fluctuate so that an investment, when redeemed,
     may be worth more or less than its original  cost. The average annual total
     returns at October 31, 1999 for the one-year, five-year and 10-year periods
     were 21.84%, 14.01%, and 11.80%, respectively.

- --------------------------------------------------------------------------------
                                                                               3

<PAGE>

Value Line Convertible Fund, Inc.

Schedule of Investments (unaudited)

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

   Principal
    Amount                                                    Value
- --------------------------------------------------------------------------------
CONVERTIBLE CORPORATE BONDS & NOTES (46.8%)

                 AEROSPACE/DEFENSE
                   (0.4%)
     $ 500,000   Kellstrom Industries, Inc.
                    5 1/2%, 6/15/03.................       $ 328,750

                 AUTO PARTS--ORIGINAL
                   EQUIPMENT (1.2%)
     1,000,000   Magna International Inc.
                    4 7/8%, 2/15/05.................         887,500

                 COMPUTER &
                   PERIPHERALS (1.9%)
     1,000,000   VERITAS Software Corp.
                    1.856%, 8/13/06.................       1,387,500

                 COMPUTER SOFTWARE
                   & SERVICES (3.9%)
       500,000   Affiliated Computer
                    Services Inc. 4%,
                    3/15/05.........................         543,125
     1,000,000   Citrix Systems Inc.
                    Zero Coupon, Series 144A,
                    3/22/19* .......................         508,750
       250,000   Comverse Technology, Inc.
                    4 1/2%, 7/1/05..................         664,063
       500,000   Siebel Systems, Inc. Series
                    144A, 51/2%, 9/15/06*...........         663,750
       500,000   USinternetworking, Inc.
                    Series 144A,
                    7%, 11/1/04*....................         513,125
                                                          ----------
                                                           2,892,813

                 DRUG (2.0%)
     1,000,000   Athena Neurosciences Inc.
                    4 3/4%, 11/15/04................         978,750
       500,000   Inhale Therapeutic
                    Systems, Inc. Series 144A,
                    6 3/4%, 10/13/06* ..............         508,125
                                                          ----------
                                                           1,486,875

                 ELECTRONICS (3.4%)
     $ 500,000   Safeguard Scientifics, Inc.
                    Series 144A, 5%,
                    6/15/06*........................         638,125
       500,000   Sanmina Corp. 4 1/4%,
                    Series 144A, 5/1/04*............         602,500
     2,000,000   Solectron Corp. Zero
                    Coupon, 1/27/19*................       1,262,500
                                                          ----------
                                                           2,503,125

                 ENTERTAINMENT (3.2%)
     1,000,000   Clear Channel
                    Communications, Inc.
                    2 5/8%, 4/1/03..................       1,411,250
     1,000,000   Merrill Lynch & Co., Inc.
                    0.25%, 5/10/06
                    (exchangeable into
                    Time Warner Inc.)...............         971,250
                                                          ----------
                                                           2,382,500

                 FOREIGN
                   TELECOMMUNICATIONS
                   (2.1%)
       500,000   Global Telesystems Group, Inc.
                    5 3/4%, 7/1/10..................         523,125
     1,000,000   Telefonos de Mexico S.A.
                    4 1/4%, 6/15/04.................       1,047,500
                                                          ----------
                                                           1,570,625

                 INSURANCE (PROPERTY/  CASUALTY) (3.3%)
     1,000,000   Berkshire Hathaway Inc.
                    1%, 12/2/01.....................       2,436,250

                 INTERNET (3.0%)
       500,000   DoubleClick Inc. Series 144A,
                    4 3/4%, 3/15/06*................         917,500
       600,000   MindSpring Enterprises, Inc.
                    5%, 4/15/06.....................         581,250
       500,000   VerticalNet, Inc. Series 144A,
                    5 1/4%, 9/27/04*................         757,500
                                                          ----------

                                                           2,256,250

- --------------------------------------------------------------------------------
4

<PAGE>

                                               Value Line Convertible Fund, Inc.

                                                                October 31, 1999

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

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

                 MEDICAL SERVICES (1.7%)
    $1,000,000   Affymetrix, Inc. Series 144A,
                    5%, 10/1/06*....................       $ 960,000
       500,000   WellPoint Health
                    Networks Inc.
                    Zero Coupon, 7/2/19 ............         291,250
                                                          ----------
                                                           1,251,250

                 OILFIELD SERVICES/
                   EQUIPMENT (1.4%)
     1,000,000   Diamond Offshore Drilling
                    Inc. 3 3/4%, 2/15/07............       1,027,500

                 PETROLEUM--
                   INTEGRATED (1.3%)
     1,000,000   Texaco Capital Inc.
                    3 1/2%, 8/5/04..................         990,000

                 R.E.I.T. (1.2%)
     1,000,000   Healthcare Realty Trust, Inc.
                    6.55%, 3/14/02..................         915,000

                 RETAIL--
                   SPECIAL LINES (0.8%)
     1,000,000   AnnTaylor Stores Corp.
                    Series 144A, .55%,
                    6/18/19*........................         583,750

                 RETAIL STORE (1.3%)
     1,000,000   Costco Companies, Inc.
                    Zero Coupon, 8/19/17............         951,250

                 SEMICONDUCTOR (3.9%)
       500,000   Conexant Systems, Inc.
                    4 1/4%, 5/1/06..................       1,045,625
       500,000   Lattice Semiconductor Corp.
                    Series 144A, 43/4%,
                    11/1/06* .......................         541,875
       500,000   Level One Communications,
                    Inc. 4%, 9/1/04.................       1.285,625
                                                          ----------
                                                           2,873,125

                 TELECOMMUNICATION
                   SERVICES (10.8%)
    $1,500,000   American Tower Corp.
                    Series 144A, 2 1/4%,
                    10/15/09*.......................       1,010,625
     2,000,000   Bell Atlantic Financial
                    Services Inc. Series 144A,
                    4 1/4%, 9/15/05*................       2,110,000
       700,000   Comcast Corp. 2%, 10/15/29
                    (exchangeable into Sprint
                    Corp.--PCS Group)...............         579,250
       200,000   CoreComm Limited Series
                    144A, 6%, 10/1/06*..............         223,750
     1,000,000   Gilat Satellite
                    Networks Ltd. 6 1/2%,
                    6/3/04..........................       1,303,750
       500,000   ITC Deltacom, Inc.
                    Series 144A,
                    4 1/2%, 5/15/06*................         548,750
     1,000,000   Level 3 Communications,
                    Inc. 6%, 9/15/09................       1,228,750
       500,000   Nextel Communications, Inc.
                    Series 144A, 43/4%,
                    7/1/07*.........................         966,875
                                                          ----------
                                                           7,971,750
                                                          ----------

                 TOTAL CONVERTIBLE
                 CORPORATE BONDS
                 & NOTES
                 (Cost $29,840,648) ................     $34,695,813
                                                         -----------

- --------------------------------------------------------------------------------
                                                                               5

<PAGE>

Value Line Convertible Fund, Inc.

Schedule of Investments (unaudited)

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

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

CONVERTIBLE PREFERRED STOCKS (20.7%)

                 BANK (3.3%)
        10,000   BCP International Bank Ltd.
                    $4.00 exchangeable
                    Series "A"......................      $1,040,000
        50,000   National Australia Bank,
                    Ltd. Cap Units 7 7/8%,
                    exchangeable Pfd. ..............       1,409,375
                                                          ----------
                                                           2,449,375

                 CABLE TV (1.1%)
         5,000   Adelphia Communications
                    Corp.  5 1/2%,
                    Series "D" Pfd. ................         856,562

                 COMPUTER SOFTWARE
                   & SERVICES (0.3%)
         5,000   Verio Inc. 6 3/4%,
                    Series 144A Pfd.*...............         237,500

                 ELECTRIC UTILITY--
                   CENTRAL (0.7%)
        10,000   AES Corporation (The)
                    Trust III  63/4%, Pfd. .........         504,375

                 ELECTRIC UTILITY--
                   WEST (0.7%)
        10,000   Calpine Corp. Capital Trust
                    53/4%, Pfd......................         540,625

                 ENTERTAINMENT (2.6%)
         4,000   EMMIS Communications
                    Corp.  6 1/4%,
                    Series "A" Pfd. ................         224,000
        10,000   Entercom Communications
                    Corp. Capital Trust
                    6 1/4%, Pfd. ...................         646,250
        15,000   Reliant Energy, Inc.
                    Variable Rate
                    Pfd. (exchangeable into
                    Time Warner Inc.)...............       1,053,750
                                                          ----------
                                                           1,924,000

                 INTERNET (1.1%)
        20,000   PSINet Inc. 6 3/4%,
                    Series "C" Pfd..................         795,000

                 PACKAGING &
                   CONTAINER (2.2%)
       30,000    Sealed Air Corp.
                    $2.00 exchangeable
                    Series "A" .....................       1,620,000

                 PETROLEUM--
                   PRODUCING (1.0%)
        20,000   Apache Corp. 6 1/2%,
                    Series "C" Pfd..................         716,000

                 RAILROAD (0.9%)
        14,500   Union Pacific Capital
                    Trust 6 1/4%, Pfd...............         701,438

                 TELECOMMUNICATION
                   SERVICES (6.8%)

        10,000   Broadwing Inc.
                    6 3/4%, Pfd.....................         420,625
        10,000   Global Crossing Ltd. 6 3/8%,
                    Series 144A Pfd.*...............       1,000,000
        10,000   ICG Communications, Inc.
                    6 3/4%, Pfd.....................         426,250
         3,000   McLeodUSA, Inc.
                    6 3/4%, Series "A" Pfd..........       1,237,125
        10,000   MediaOne Group, Inc.
                    6 1/4%, Pfd.....................       1,040,000
        20,000   MediaOne Group, Inc.
                    7%, Pfd.........................         912,500
                                                          ----------
                                                           5,036,500
                                                          ----------

                 TOTAL CONVERTIBLE
                 PREFERRED STOCKS
                 (Cost $13,955,455) ................     $15,381,375
                                                         -----------


- --------------------------------------------------------------------------------
6

<PAGE>

                                               Value Line Convertible Fund, Inc.

                                                                October 31, 1999

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

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

COMMON STOCKS (4.2%)

                 COMPUTER &
                   PERIPHERALS (2.0%)
        10,000   Cisco Systems, Inc.**..............      $  740,000
        10,000   EMC Corp.**........................         730,000
                                                          ----------
                                                           1,470,000

                 RETAIL BUILDING
                   SUPPLY (1.0%)
        10,000   Home Depot, Inc. (The).............         755,000

                 TELECOMMUNICATION
                   SERVICES (1.2%)
        10,000   MCI WorldCom, Inc.**...............         858,125
                                                          ----------

                 TOTAL COMMON
                 STOCKS
                 (Cost $1,579,379) .................       3,083,125
                                                          ----------


                 TOTAL INVESTMENT
                 SECURITIES (71.7%)
                 (Cost $45,375,482) ................      53,160,313
                                                          ----------


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

REPURCHASE AGREEMENTS (29.0%)
(including accrued interest)

   $5,400,000    Collateralized by $4,299,000
                    U.S. Treasury Bonds 8 3/4%,
                    due 5/15/20, with a value
                    of $5,533,708 (with Warburg
                    Dillon Read LLC, 5.22%,
                    dated 10/29/99, due 11/1/99,
                    delivery value
                    $5,402,349).....................      $5,402,349

    $5,400,000   Collateralized by $5,520,000
                    U.S. Treasury Notes 5%,
                    due 2/28/01, with a value
                    of $5,513,235 (with State
                    Street Bank & Trust
                    Company 5.18%, dated
                    10/29/99, due 11/1/99,
                    delivery value
                    $5,402,331) ....................      $5,402,331

     5,400,000   Collateralized by $4,780,000
                    U.S. Treasury Bonds 9 1/8%,
                    due 5/15/09, with a value
                    of $5,526,146 (with Morgan
                    Stanley & Co., Incorporated,
                    5.16%, dated 10/29/99,
                    due 11/1/99, delivery value
                    $5,402,322) ....................       5,402,322

     5,300,000   Collateralized by $5,356,000
                    U.S. Treasury Notes 5 5/8%,
                    due 12/31/02, with a value
                    of $5,411,544 (with Banc
                    One Capital Markets, Inc.,
                    5.18%, dated 10/29/99,
                    due 11/1/99, delivery
                    value $5,302,288) ..............       5,302,288
                                                          ----------

                 Total Repurchase Agreements
                 (Cost $21,509,290) ................      21,509,290
                                                          ----------


EXCESS OF LIABILITIES
OVER CASH AND
RECEIVABLES (-0.7%) ................................        (541,335)
                                                          ----------

NET ASSETS (100.0%) ................................     $74,128,268
                                                         ===========


NET ASSET VALUE, OFFERING
AND REDEMPTION PRICE PER
OUTSTANDING SHARE
($74,128,268 / 5,343,744
shares outstanding) ................................          $13.87
                                                         ===========

*    Pursuant to Rule 144A under the  Securities  Act of 1933,  this
     security can only be sold to qualified institutional investors.

**   Non-income producing.

See Notes to Financial Statements.

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

<PAGE>

Value Line Convertible Fund, Inc.

Statement of Assets and Liabilities
at October 31, 1999 (unaudited)
================================================================================

Assets:
Investment securities, at value
  (Cost--$45,375,482) .....................................          $53,160,313
Repurchase agreements
  (Cost--$21,509,290) .....................................           21,509,290
Cash ......................................................               56,703
Receivable for securities sold ............................            4,506,915
Receivable for capital shares sold ........................              394,685
Interest and dividends receivable .........................              269,003
                                                                     -----------
    Total Assets ..........................................           79,896,909
                                                                     -----------
Liabilities:
Payable for securities purchased ..........................            5,586,070
Payable for capital shares repurchased ....................               71,874
Accrued expenses:
  Advisory fee ............................................               66,795
  Other ...................................................               43,902
                                                                     -----------
    Total Liabilities .....................................            5,768,641
                                                                     -----------
Net Assets ................................................          $74,128,268
                                                                     ===========
Net assets consist of:
Capital stock, at $1.00 par value
  (authorized 50,000,000,
  outstanding 5,343,744 shares) ...........................          $ 5,343,744
Additional paid-in capital ................................           60,564,856
Undistributed net investment income .......................              168,933
Undistributed net realized gain
  on investments ..........................................              265,904
Net unrealized appreciation of
  investments .............................................            7,784,831
                                                                     -----------
Net Assets ................................................          $74,128,268
                                                                     ===========

Net Asset Value, Offering and
  Redemption Price per
  Outstanding Share
  ($74,128,268 / 5,343,744
  shares outstanding) .....................................          $     13.87
                                                                     ===========


Statement of Operations
for the six months ended October 31, 1999 (unaudited)
================================================================================

Investment Income:
Interest ................................................           $   983,003
Dividends ...............................................               370,238
                                                                    -----------
    Total Income ........................................             1,353,241
                                                                    -----------
Expenses:
Advisory fee ............................................               256,183
Auditing and legal fees .................................                21,160
Transfer agent ..........................................                21,160
Registration and filing fees ............................                11,960
Printing and stationery .................................                11,040
Custodian fees ..........................................                10,280
Postage .................................................                10,120
Directors' fees and expenses ............................                 8,280
Telephone ...............................................                 4,600
Insurance, dues and other ...............................                 2,173
                                                                    -----------
    Total Expenses before
      custody credits ...................................               356,956
    Less: custody credits ...............................                (2,552)
                                                                    -----------
    Net Expenses ........................................               354,404
                                                                    -----------
Net Investment Income ...................................               998,837
                                                                    -----------
Net Realized and Unrealized Gain
  (Loss) on Investments:
    Net Realized Gain ...................................             6,434,339
    Change in Net Unrealized
      Appreciation ......................................              (350,073)
                                                                    -----------
Net Realized Gain and Change in
  Net Unrealized Appreciation
  on Investments ........................................             6,084,266
                                                                    -----------
Net Increase in Net Assets
  from Operations .......................................           $ 7,083,103
                                                                    ===========

See Notes to Financial Statements.
- --------------------------------------------------------------------------------
8

<PAGE>
                                               Value Line Convertible Fund, Inc.

<TABLE>
Statement of Changes in Net Assets
for the six months ended October 31, 1999 (unaudited) and for the year ended April 30, 1999
====================================================================================================
<CAPTION>
                                                               Six Months Ended    Year Ended
                                                               October 31, 1999     April 30,
                                                                 (unaudited)          1999
                                                               -------------------------------
<S>                                                             <C>              <C>
Operations:
  Net investment income .....................................   $     998,837    $   3,168,591
  Net realized gain (loss) on investments ...................       6,434,339       (6,168,354)
  Change in net unrealized appreciation .....................        (350,073)        (952,017)
                                                                ------------------------------
  Net increase (decrease) in net assets from operations .....       7,083,103       (3,951,780)
                                                                ------------------------------

Distributions to Shareholders:
  Net investment income .....................................        (974,040)      (3,431,409)
  Net realized gain from investment transactions ............            --         (3,713,370)
                                                                ------------------------------
  Total distributions .......................................        (974,040)      (7,144,779)
                                                                ------------------------------

Capital Share Transactions:
  Proceeds from sale of shares ..............................     135,732,486      176,887,275
  Proceeds from reinvestment of distributions to shareholders         809,274        5,916,259
  Cost of shares repurchased ................................    (137,799,827)    (200,108,922)
                                                                ------------------------------
  Net decrease from capital share transactions ..............      (1,258,067)     (17,305,388)
                                                                ------------------------------
Total Increase (Decrease) in Net Assets .....................       4,850,996      (28,401,947)

Net Assets:
  Beginning of period .......................................      69,277,272       97,679,219
                                                                ------------------------------
  End of period .............................................   $  74,128,268    $  69,277,272
                                                                ==============================
Undistributed net investment income, at end of period .......   $     168,933    $     144,136
                                                                ==============================
</TABLE>



See Notes to Financial Statements.
- --------------------------------------------------------------------------------
                                                                               9

<PAGE>

Value Line Convertible Fund, Inc.

Notes to Financial Statements (unaudited)
- --------------------------------------------------------------------------------

1.   Significant Accounting Policies

Value  Line  Convertible  Fund,  Inc.  (the  "Fund")  is  registered  under  the
Investment  Company  Act  of  1940,  as  amended,  as  a  diversified,  open-end
management investment company whose investment objective is to seek high current
income  together with capital  appreciation.  The Fund seeks to  accomplish  its
objective by investing primarily in convertible securities.

The following  significant  accounting policies are in conformity with generally
accepted  accounting  principles  for  investment  companies.  Such policies are
consistently   followed  by  the  Fund  in  the  preparation  of  its  financial
statements.  Generally accepted accounting  principles may require management to
make estimates and assumptions  that affect the reported amounts and disclosures
in the financial statements. Actual results may differ from those estimates.

(A)  Security  Valuation.  The Fund's  securities  are valued by an  independent
pricing service approved by the Fund's Board of Directors.  Securities for which
quotations  are not  available  from the pricing  service are valued at the mean
between the latest available and representative asked and bid prices provided by
dealers in such  securities.  Securities  for which  market  quotations  are not
readily  available or which are not readily  marketable  and all other assets of
the Fund,  are valued at fair value as the Board of Directors  may  determine in
good faith.  Short-term  investments that mature in less than 60 days are valued
at  amortized  cost if  their  original  maturity  was 60 days  or  less,  or by
amoritzing their value on the 61st day prior to maturity, if their original term
exceeds 60 days.

(B)  Repurchase  Agreements.  In  connection  with  transactions  in  repurchase
agreements,  the Fund's custodian takes possession of the underlying  collateral
securities,  the value of which exceeds the principal  amount of the  repurchase
transaction,  including  accrued  interest.  To the extent  that any  repurchase
transaction   exceeds  one  business  day,  the  value  of  the   collateral  is
marked-to-market  on a daily basis to ensure the adequacy of the collateral.  In
the event of default of the obligation to repurchase,  the Fund has the right to
liquidate  the  collateral  and  apply  the  proceeds  in  satisfaction  of  the
obligation.  Under certain circumstances,  in the event of default or bankruptcy
by the  other  party  to the  agreement,  realization  and/or  retention  of the
collateral or proceeds may be subject to legal proceedings.

(C)  Federal  Income  Taxes.  It  is  the  Fund's  policy  to  comply  with  the
requirements  of the Internal  Revenue Code of 1986,  as amended,  applicable to
regulated  investment  companies and to distribute  all of its taxable income to
its  shareholders.  Therefore,  no federal income tax or excise tax provision is
required.

(D) Security Transactions and Distributions. Security transactions are accounted
for on the date the securities are purchased or sold. Interest income is accrued
as earned.  Realized  gains and losses on sales of securities are calculated for
financial  accounting  and federal  income tax purposes on the  identified  cost
basis.  Dividend income and  distributions  to shareholders  are recorded on the
ex-dividend date. The amount of dividends and distributions  from net investment
income and net realized  capital gains are determined in accordance with federal
income tax  regulations,  which may differ from  generally  accepted  accounting
principles.  These  "book/tax"  differences are either  considered  temporary or
permanent in nature.  Permanent  differences are reclassified within the capital
accounts based on their federal tax basis  treatment.  Temporary  differences do
not require reclassification.

(E) Amortization.  Discounts on debt securities are amortized to interest income
over the life of the security with a  corresponding  increase to the  security's
cost basis; premiums on debt securities are not amortized.

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

<PAGE>

                                               Value Line Convertible Fund, Inc.

                                                                October 31, 1999
- --------------------------------------------------------------------------------

2.   Capital Share Transactions.

Transactions in capital stock were as follows:

                                                  Six Months
                                                    Ended               Year
                                                  October 31,           Ended
                                                     1999             April 30,
                                                  (unaudited)           1999
                                                  -----------------------------

Shares sold ..............................        10,391,188         13,575,401
Shares issued to shareholders
  in reinvestment
  of dividends ...........................            62,718            477,763
                                                  -----------------------------
                                                  10,453,906         14,053,164
Shares repurchased .......................        10,534,572         15,226,596
                                                  -----------------------------
Net decrease .............................           (80,666)        (1,173,432)
                                                  =============================

3.   Purchases and Sales of Securities

Purchases and sales of investment  securities,  excluding short-term securities,
were as follows:

                                                               Six Months
                                                                 Ended
                                                           October 31, 1999
                                                              (unaudited)
                                                            --------------
PURCHASES:
  Investment Securities ................................      $34,290,811
                                                              ===========

SALES OR REDEMPTIONS:
  Investment Securities ................................      $50,780,290
                                                              ===========

At October 31, 1999, the aggregate cost of investment  securities and repurchase
agreements  for federal  income tax  purposes  was  $66,884,772.  The  aggregate
appreciation  and  depreciation  of investments at October 31, 1999,  based on a
comparison of investment values and their costs for federal income tax purposes,
was $8,903,533 and $1,118,702  respectively,  resulting in a net depreciation of
$7,784,831.

For federal  income tax purposes  the Fund had a net capital  loss  carryover at
April 30, 1999 of  $2,832,872  which will expire in the year 2007. To the extent
future  capital  gains are  offset  by such  capital  losses,  the Fund does not
anticipate distributing any such gains to its shareholders.

4.   Investment  Advisory  Contract,  Management  Fees,  and  Transactions  with
     Affiliates

An  advisory  fee of  $256,183  was paid or payable  to Value  Line,  Inc.  (the
Adviser),  for the six months ended  October 31, 1999.  This was computed at the
rate of 3/4 of 1% of  average  daily  net  assets  during  the  period  and paid
monthly. The Adviser provides research, investment programs,  supervision of the
investment  portfolio and pays costs of administrative  services,  office space,
equipment  and  compensation  of  administrative,   bookkeeping,   and  clerical
personnel  necessary  for  managing  the affairs of the Fund.  The Adviser  also
provides  persons,  satisfactory  to the Fund's  Board of  Directors,  to act as
officers and employees of the Fund and pays their  salaries and wages.  The Fund
bears all other costs and expenses.

Certain  officers and  directors of the Adviser and its  subsidiary,  Value Line
Securities,  Inc. (the Fund's distributor and a registered  broker/dealer),  are
also officers and a director of the Fund.

The Advisor  and/or  affiliated  companies  owned  210,406  shares of the Fund's
capital stock, representing 3.9% of the outstanding shares at October 31, 1999.

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

<PAGE>

Value Line Convertible Fund, Inc.

                          Other Information (unaudited)
================================================================================

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  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.


- --------------------------------------------------------------------------------
12

<PAGE>

                                               Value Line Convertible Fund, Inc.

Financial Highlights
================================================================================

Selected data for a share of capital stock outstanding throughout each period:

<TABLE>
<CAPTION>
                                  Six Months Ended                           Years Ended April 30,
                                    Oct. 31, 1999     ------------------------------------------------------------------
                                     (unaudited)         1999            1998          1997            1996        1995
                                  ----------------    ------------------------------------------------------------------
<S>                                    <C>             <C>             <C>            <C>            <C>         <C>
Net asset value, beginning
  of period ........................   $ 12.77         $ 14.80         $ 13.07        $ 14.10        $ 11.79     $ 12.26
                                       ---------------------------------------------------------------------------------

  Income (loss) from investment
    operations:
  Net investment income ............       .20             .57             .65            .70            .66         .74
  Net gains or losses on securities
    (both realized and unrealized) .      1.09           (1.33)           2.50            .50           2.33        (.02)
                                       ---------------------------------------------------------------------------------
    Total from investment operations      1.29            (.76)           3.15           1.20           2.99         .72
                                       ---------------------------------------------------------------------------------

  Less distributions:
    Dividends from net
      investment income ............      (.19)           (.60)           (.67)          (.65)          (.68)       (.76)
    Distributions from realized
      capital gains ................      --              (.67)           (.75)         (1.58)          --          (.43)
                                       ---------------------------------------------------------------------------------
    Total distributions ............      (.19)          (1.27)          (1.42)         (2.23)          (.68)      (1.19)
                                       ---------------------------------------------------------------------------------
Net asset value, end of period .....   $ 13.87         $ 12.77         $ 14.80        $ 13.07        $ 14.10     $ 11.79
                                       =================================================================================
Total return .......................     10.26%+        -4.64%           25.04%          8.80%         26.07%       6.53%
                                       =================================================================================

Ratios/Supplemental Data:
Net assets, end of period
  (in thousands) ...................   $74,128         $69,277         $97,679        $68,684        $72,620     $50,523
Ratio of expenses to
  average net assets ...............      1.05%*(1)       1.00%*(1)        .98%(1)       1.01%(1)       1.08%       1.08%
Ratio of net investment income
  to average net assets ............      2.93%*          3.98%*          4.63%          4.94%          5.14%       6.13%
Portfolio turnover rate ............        61%+           123%            111%           164%           129%         87%
</TABLE>

(1)  Before custody credits.

+    Not annualized.

*    Annualized.



See Notes to Financial Statements.
- --------------------------------------------------------------------------------
13

<PAGE>

Value Line Convertible Fund, Inc.

                         The Value Line Family of Funds
================================================================================

1950--The Value Line Fund seeks long-term growth of capital. Current income is a
secondary objective.

1952--Value  Line  Income and Growth  Fund's  primary  investment  objective  is
income,  as high and dependable as is consistent with reasonable  risk.  Capital
growth to increase total return is a secondary objective.

1956--The Value Line Special  Situations Fund seeks long-term growth of capital.
No consideration is given to current income in the choice of investments.

1972--Value  Line Leveraged  Growth  Investors' sole investment  objective is to
realize capital growth.

1979--The  Value Line Cash Fund, a money market fund,  seeks to secure as high a
level  of  current  income  as is  consistent  with  maintaining  liquidity  and
preserving capital.

1981--Value  Line U.S.  Government  Securities Fund seeks maximum income without
undue risk to capital. Under normal conditions, at least 80% of the value of its
net assets will be  invested  in  securities  issued or  guaranteed  by the U.S.
Government and its agencies and instrumentalities.

1983--Value Line Centurion Fund* seeks long-term growth of capital.

1984--The Value Line Tax Exempt Fund seeks to provide investors with the maximum
income exempt from federal  income taxes while avoiding undue risk to principal.
The Fund offers investors a choice of two portfolios: The Money Market Portfolio
and The National Bond 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.

1987--Value  Line New York Tax Exempt Trust seeks to provide New York  taxpayers
with the maximum  income  exempt from New York State,  New York City and federal
income taxes while avoiding undue risk to principal.

1987--Value Line Strategic Asset Management Trust* seeks to achieve a high total
investment return consistent with reasonable risk.

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  Investor,  a tax deferred
     variable annuity, or ValuePlus, a variable life insurance policy.

For more  complete  information  about any of the Value  Line  Funds,  including
charges and expenses,  send for a prospectus from Value Line  Securities,  Inc.,
220 East 42nd Street, New York, New York 10017-5891 or call  1-800-223-0818,  24
hours  a day,  7  days a  week,  or  visit  us at  www.valueline.com.  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

CUSTODIAN BANK        State Street Bank and Trust Co.
                      225 Franklin Street
                      Boston, MA 02110

SHAREHOLDER           State Street Bank and Trust Co.
SERVICING AGENT       c/o NFDS
                      P.O. Box 219729
                      Kansas City, MO 64121-9729

INDEPENDENT           PricewaterhouseCoopers LLP
ACCOUNTANTS           1177 Avenue of the Americas
                      New York, NY 10036

LEGAL COUNSEL         Peter D. Lowenstein, Esq.
                      Two Greenwich Plaza, Suite 100
                      Greenwich, CT 06830

DIRECTORS             Jean Bernhard Buttner
                      John W. Chandler
                      David H. Porter
                      Paul Craig Roberts
                      Nancy-Beth Sheerr

OFFICERS              Jean Bernhard Buttner
                      Chairman and President
                      Bruce H. Alston
                      Vice President
                      Nathan N. J. Grant
                      Vice President
                      David T. Henigson
                      Vice President and
                      Secretary/Treasurer
                      Jack M. Houston
                      Assistant Secretary/Treasurer
                      Stephen La Rosa
                      Assistant Secretary/Treasurer


The financial statements included herein have been taken from the records of the
Fund without examination by the independent  accountants and, accordingly,  they
do not  express  an  opinion  thereon.

This  unaudited  report is issued for  information  of  shareholders.  It is not
authorized  for  distribution  to  prospective   investors  unless  preceded  or
accompanied by a currently effective prospectus of the Fund (obtainable from the
Distributor).


                                                                         #501786



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