VALUE LINE CONVERTIBLE FUND INC
N-30D, 1998-12-18
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================================================================================

                               ------------------
                               SEMI-ANNUAL REPORT
                               ------------------
                                October 31, 1998
                               ------------------


                                   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:

The Value Line  Convertible  Fund's net asset value declined 6.17% in the twelve
months  ended  October  31,  1998.  On balance,  the fund fared  better than the
unmanaged Value Line Convertible  Index (-6.60%) -- the most complete  indicator
of performance of the domestic convertible market.

Since our last report,  the U.S.  financial  markets have been subject to global
economic turmoil,  the effects of trading activities by several hedge funds, and
the slowing of corporate  earnings  growth.  As investors lost confidence in the
troubled foreign  markets,  a flight to quality ensued that saw US Treasury bond
yields  decline to an all-time low of 4.69% on October 5, before  settling in at
just above 5% on October 31,  1998.  Stocks,  meanwhile,  plummeted,  especially
small caps,  while credit risk premiums more than doubled,  with high-yield bond
rates jumping by an unprecedented  4.00%. The convertible  market suffered under
the dual pressures  applied from small stock  underperformance  and from growing
credit risks.

                                                                  Total Return
                                                                     12 Mos
                                                                    10/31/98
                                                                    --------
Value Line Convertible Fund ................................         -6.17%
Value Line Convertible Index* ..............................         -6.60%
S&P 500* ...................................................         21.99%
Russell 2000* ..............................................        -11.84%
Lehman Brothers High Yield Bond* ...........................         -0.50%
US Treasury 30 Year Bonds* .................................         19.62%

*    unmanaged

Interest rate cuts  domestically  and abroad,  together  with banking  reform in
Japan  and a more  stable  political  situation  at  home  soothed  the  markets
sufficiently to enable the convertible  market to begin a recovery in October of
1998. The convertible market is still undervalued on a technical and fundamental
basis not  withstanding  the  rebound  and we expect the  convertible  market to
continue to improve during the months ahead.

Our strategy is to stay focused on high-quality  convertible  securities,  which
lowers  risk by  emphasizing  liquid,  larger-capitalization  and higher  credit
quality issues with sound fundamentals and favorable Value Line Timeliness Ranks
on their  common  stock.  We then select  those bonds that also rank high in the
Value Line Convertible Survey.

We appreciate your confidence in Value Line, and hope we can continue to serve.


                                           Sincerely,
                                  
                                  
                                           /s/ JEAN BERNHARD BUTTNER

                                           Jean Bernhard Buttner
                                           Chairman and President

December 7, 1998

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

<PAGE>

                                               Value Line Convertible Fund, Inc.


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

Economic Observations

Steady growth and low inflation continue to be two of the dominant themes in the
domestic  economy  as 1998  rapidly  draws to a close.  This is  underscored  by
reports that show relative stability in retailing, housing, personal income, and
employment.  Such trends suggest that GDP growth,  which has generally moderated
over the past six-months,  will average 2%, or perhaps a shade more,  during the
next two to four quarters.  At the same time, inflation remains quiescent,  with
producer and consumer  price  increases  still modest overall and key industrial
sectors finding it difficult to implement price increases.

At this  point,  though,  we do not  believe  that this  modest pace of economic
activity is the opening act in a serious domestic business  downturn.  Our sense
is that the global  crisis still  afflicting  Asia,  Russia,  and parts of Latin
America  will  gradually  recede  over  the  next 12 to 18  months  and that the
continuing subdued level of inflation in this country will encourage the Federal
Reserve Board to pursue a stable or looser monetary policy over the next several
quarters.

Performance Data:*
                                                       Average        Growth of
                                                       Annual        an Assumed
                                                        Total        Investment
                                                       Return        of $10,000
                                                       ------        ----------
 1 year ended 9/30/98 .......................           -8.07%        $ 9,193
 5 years ended 9/30/98 ......................            8.62%         15,118
10 years ended 9/30/98 ......................           10.63%         27,469


*    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, 1998 for the one-year, five-year and 10-year periods
     were -6.17%, 8.86%, and 10.56%, respectively.

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

<PAGE>

Value Line Convertible Fund, Inc.


Schedule of Investments (unaudited)
- --------------------------------------------------------------------------------

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

CONVERTIBLE CORPORATE BONDS & NOTES (46.6%)

               ADVERTISING (1.0%)
$1,000,000     Getty Images, Inc.
                  4 3/4%, 6/1/03*..................................    $ 746,250

               AEROSPACE/DEFENSE
                 (1.1%)
 1,000,000     Kellstrom Industries, Inc.
                  5 1/2%, 6/15/03..................................      877,500

               AIR TRANSPORT (0.3%)
   600,000     World Airways, Inc.
                   8%, 8/26/04.....................................      273,750

               COAL/ALTERNATE
                 ENERGY (1.3%)
 1,000,000     AES Corp.
                  4 1/2%, 8/15/05..................................      982,500

               COMPUTER SOFTWARE
                 & SERVICES (5.3%)
   350,000     Aspen Technology, Inc.
                  5 1/4%, 6/15/05*.................................      176,312
 1,500,000     Comverse Technology, Inc.
                  4 1/2%, 7/1/05*..................................    1,340,625
 1,000,000     Learning Company, Inc.
                  (The) 5 1/2%, 11/1/00............................      948,750
 1,330,000     MacNeal-Schwendler Corp.
                  7 7/8%, 8/18/04..................................    1,243,550
 1,000,000     Network Associates, Inc.
                   zero coupon, 2/13/18............................      421,250
                                                                      ----------
                                                                       4,130,487

               DIVERSIFIED
                 COMPANIES (1.8%)
 1,000,000     Berkshire Hathaway Inc.
                   1%, 12/2/01.....................................    1,405,000

               DRUG (4.2%)
 1,000,000     ALZA Corp. zero coupon,
                   7/14/14.........................................      636,250
 2,000,000     Dura Pharmaceuticals, Inc.
                  3 1/2%, 7/15/02..................................    1,417,500
 1,000,000     Genzyme Corporation
                  5 1/4%, 6/1/05*..................................    1,236,250
                                                                      ----------
                                                                       3,290,000

               ENTERTAINMENT
                 (2.9%)
 1,500,000     Clear Channel
                   Communications, Inc.
                  2 5/8%, 4/1/03...................................    1,413,750
 2,000,000     Jacor Communications, Inc.
                   zero coupon, 2/9/18.............................      836,500
                                                                      ----------
                                                                       2,250,250

               ENVIRONMENTAL
                 (2.3%)
 2,000,000     United States Filter Corp.
                  4 1/2%, 12/15/01.................................    1,842,500

               FINANCIAL
                 SERVICES (4.8%)
 3,000,000     Bell Atlantic Financial
                   Services, Inc.
                  4 1/4%, 9/15/05*.................................    2,940,000
 1,000,000     Loews Corp.
                  3 1/8%, 9/15/07..................................      822,500
                                                                      ----------
                                                                       3,762,500

               INDUSTRIAL
                 SERVICES (1.1%)
 1,000,000     Data Processing Resources
                   Corporation
                  5 1/4%, 4/1/05...................................      883,750

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

<PAGE>

                                               Value Line Convertible Fund, Inc.


                                                                October 31, 1998
- --------------------------------------------------------------------------------

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

               INSURANCE--
                 PROPERTY/
                 CASUALTY (3.8%)
$3,000,000     Fremont General Corp.
                   zero coupon, 10/12/13...........................  $ 2,988,750

               MEDICAL SERVICES
                 (1.4%)
 1,000,000     Omnicare, Inc.
                   5%, 12/1/07.....................................    1,077,500

               OFFICE EQUIPMENT &
                 SUPPLIES (1.9%)
 1,000,000     Corporate Express, Inc.
                  4 1/2%, 7/1/00...................................      885,000
 2,000,000     Danka Business Systems
                   PLC 63/4%, 4/1/02...............................      587,500
                                                                      ----------
                                                                       1,472,500

               OILFIELD SERVICES/
                 EQUIPMENT (1.4%)
 1,000,000     Nabors Industries, Inc.
                   5%, 5/15/06.....................................    1,107,500

               PAPER & FOREST
                 PRODUCTS (1.5%)
 1,500,000     Mail-Well, Inc.
                   5%, 11/1/02.....................................    1,179,375

               PETROLEUM--
                 INTEGRATED (1.3%)
 1,000,000     Texaco Capital Inc.
                  3 1/2%, 8/5/04...................................    1,025,000

               PUBLISHING (1.2%)
 1,000,000     World Color Press, Inc.
                   6%, 10/1/07.....................................      961,250

               R.E.I.T. (1.2%)
 1,000,000     Healthcare Realty
                   Trust, Inc.
                   6.55%, 3/14/02..................................      932,500

               RETAIL BUILDING
                 SUPPLY (2.4%)
 1,000,000     Home Depot, Inc. (The)
                   3.25%, 10/1/01..................................    1,903,750

               RETAIL STORE (1.8%)
 2,000,000     Costco Companies, Inc.
                   zero coupon, 8/19/17............................    1,392,500

               TELECOMMUNICATION
                 SERVICES (1.5%)
 3,000,000     U.S. Cellular Corp.
                   zero coupon, 6/15/15............................    1,181,250

               THRIFT (0.2%)
   200,000     Bay View Capital Corp.
                  9 1/8%, 8/15/07..................................      180,000

               TOBACCO (0.9%)
 1,000,000     Standard Commercial Corp.
                  7 1/4%, 3/31/07..................................      695,000
                                                                      ----------

               TOTAL CONVERTIBLE
               CORPORATE BONDS
               & NOTES
               (Cost $39,397,534) .................................   36,541,362
                                                                      ----------


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

<PAGE>

Value Line Convertible Fund, Inc.


Schedule of Investments (unaudited)
- --------------------------------------------------------------------------------

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

CONVERTIBLE PREFERRED STOCKS (23.8%)

               BANK (3.8%)
    10,000     BCP International Bank Ltd.
                   $4.00, exchangeable
                   Series "A"......................................  $ 1,170,000
    16,000     Matewan Bancshares, Inc.
                   7.50%, Series "A"...............................      480,000
    50,000     National Australia Bank,
                   Ltd. Cap Units 7 7/8%,
                   exchangeable Pfd................................    1,321,875
                                                                      ----------
                                                                       2,971,875

               CEMENT &
                 AGGREGATES (1.6%)
    35,300     TXI Capital Trust I
                  5 1/2%, Pfd......................................    1,222,263

               COMPUTER SOFTWARE
                 & SERVICES (1.4%)
    20,000     L & H Capital Trust I
                  4 3/4%, Pfd......................................      715,000
    15,000     Tribune Company
                  6 1/4%, exchangeable
                   Notes Series "TLC"..............................      371,250
                                                                      ----------
                                                                       1,086,250

               ENTERTAINMENT
                 (1.9%)
    20,000     Chancellor Media Corp.
                   $3.00, Pfd......................................    1,517,500

               FOOD PROCESSING
                 (1.3%)
    20,000     Ralston-Ralston Purina
                   Group 7%, Stock
                   Appreciation Income
                   Linked Securities...............................      991,250

               MEDICAL SUPPLIES
                 (2.5%)
    10,000     McKesson Corporation
                   Financing Trust
                   5%, Pfd.........................................    1,052,500
    20,000     Owens & Minor, Inc. Trust 1
                  5 3/8%, Pfd......................................      940,000
                                                                      ----------
                                                                       1,992,500

               PACKAGING &
                 CONTAINER (2.5%)
    30,000     Owens-Illinois, Inc.
                  4 3/4%, Pfd......................................    1,203,750
    20,000     Sealed Air Corp.
                   $2.00 exchangeable
                   Series "A"......................................      797,500
                                                                      ----------
                                                                       2,001,250

               R.E.I.T. (1.8%)
    20,000     Camden Property Trust
                   $2.25, Series "A"...............................      495,000
    15,000     Glenborough Realty Trust,
                   Inc. 7 3/4%, Series "A".........................      287,812
    25,000     U.S. Restaurant Properties,
                   Inc. 7.72%, Series "A"..........................      590,625
                                                                      ----------
                                                                       1,373,437

               RAILROAD (0.8%)
    14,500     Union Pacific Capital Trust
                  6 1/4%, Pfd......................................      670,625

               STEEL (1.1%)
    20,000     USX Capital Trust I
                  6 3/4%, Pfd......................................      860,000

               TELECOMMUNICATIONS
                 EQUIPMENT (0.5%)
    20,000     Omnipoint Corp. 7%,
                   Series "144A"*..................................      392,500


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

<PAGE>

                                               Value Line Convertible Fund, Inc.


                                                                October 31, 1998
- --------------------------------------------------------------------------------

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

               TELECOMMUNICATION
                 SERVICES (4.6%)
    10,000     AirTouch Communications,
                  Inc. 4 1/4%, Series "C"........................  $   800,625
    20,000     ICG Communications, Inc.
                  6 3/4%, Pfd....................................    1,012,500
    20,000     IXC Communications, Inc.
                  6 3/4%, Pfd.
                   Series "144A"*................................      728,750
    10,000     MediaOne Group, Inc.
                  6 1/4%, Premium Income
                   Exchange Securities...........................      538,750
    10,000     Salomon Smith Barney
                   Holdings, Inc. 6 1/4%,
                   exchangeable Notes
                   Series "CSN"..................................      493,750
                                                                   -----------
                                                                     3,574,375
                                                                   -----------

               TOTAL CONVERTIBLE
               PREFERRED STOCKS
               (Cost $20,235,260) ...............................   18,653,825
                                                                   -----------

COMMON STOCKS (4.9%)

               TELECOMMUNICATION
                 SERVICES (4.9%)
    68,854     MCI WorldCom, Inc.................................    3,804,184
                                                                   -----------

               TOTAL COMMON
               STOCKS
               (Cost $1,192,580) ................................    3,804,184
                                                                   -----------

               TOTAL INVESTMENT
               SECURITIES (75.3%)
               (Cost $60,825,374) ...............................   58,999,371
                                                                   -----------


REPURCHASE AGREEMENTS (24.9%)
(including accrued interest)
$11,200,000  Collateralized by $11,185,000
               U.S. Treasury Notes 5 7/8%,
               due 8/31/99, with a value
               of $11,424,989 (with
               First Chicago Capital
               Markets, Inc., 5.27%,
               dated 10/30/98,
               due 11/2/98, delivery
               value $11,204,919)..............................    $11,203,279

  8,300,000  Collateralized by $5,760,000
                U.S. Treasury Bonds 12%,
                due 5/15/05, with a value
                of $8,478,548 (with
                Morgan Stanley & Co.,
                Incorporated, 5.33%,
                dated 10/30/98,
                due 11/2/98, delivery
                value $8,303,687)..............................      8,302,458
                                                                   -----------
                                                                    19,505,737
                                                                   -----------

EXCESS OF LIABILITIES
OVER CASH AND
RECEIVABLES (-0.2%) ...........................................       (107,721)
                                                                   -----------

NET ASSETS (100.0%) ...........................................    $78,397,387
                                                                   ===========

NET ASSET VALUE, OFFERING
AND REDEMPTION PRICE PER
OUTSTANDING SHARE
($78,397,387 / 6,284,254
shares outstanding) ...........................................    $     12.48
                                                                   ===========


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


See Notes to Financial Statements.
- --------------------------------------------------------------------------------
                                                                               7
<PAGE>

Value Line Convertible Fund, Inc.


Statement of Assets and Liabilities
at October 31, 1998 (unaudited)
- --------------------------------------------------------------------------------
Assets:
Investment securities, at value
  (Cost--$60,825,374)...........................................  $58,999,371
Repurchase agreements
  (Cost--$19,505,737)...........................................   19,505,737
Cash ...........................................................       44,245
Interest and dividends receivable ..............................      479,868
Receivable for capital shares sold .............................      331,540
                                                                  -----------
    Total Assets ...............................................   79,360,761
                                                                  -----------
Liabilities:
Payable for securities purchased................................      836,500
Payable for capital shares
  repurchased ..................................................       39,096
Accrued expenses:
  Advisory fee .................................................       46,488
  Other ........................................................       41,290
                                                                  -----------
    Total Liabilities ..........................................      963,374
                                                                  -----------
Net Assets .....................................................  $78,397,387
                                                                  ===========
Net assets consist of:
Capital stock, at $1.00 par value
  (authorized 50,000,000,
  outstanding 6,284,254 shares).................................  $ 6,284,254
Additional paid-in capital .....................................   72,624,582
Undistributed net investment income ............................      434,137
Accumulated net realized gain
  on investments................................................      880,417
Net unrealized depreciation of
  investments ..................................................   (1,826,003)
                                                                  -----------
Net Assets .....................................................  $78,397,387
                                                                  ===========
Net Asset Value, Offering and
  Redemption Price per
  Outstanding Share
  ($78,397,387 / 6,284,254
  shares outstanding) ..........................................  $     12.48
                                                                  ===========


Statement of Operations
for the six months ended October 31, 1998 (unaudited)
- --------------------------------------------------------------------------------

Investment Income:
Interest .......................................................  $ 1,569,912
Dividends ......................................................      753,545
                                                                  -----------
    Total Income ...............................................    2,323,457
                                                                  -----------
Expenses:
Advisory fee ...................................................      318,273
Transfer agent .................................................       22,190
Auditing and legal fees ........................................       19,378
Registration and filing fees ...................................       11,983
Custodian fees .................................................       11,348
Printing and stationery ........................................        9,599
Postage ........................................................        9,138
Directors' fees and expenses ...................................        7,862
Telephone ......................................................        4,324
Insurance, dues and other ......................................        3,055
                                                                  -----------
    Total Expenses Before
      Custody Credits ..........................................      417,150
    Less: Custody Credits ......................................       (2,311)
                                                                  -----------
    Net Expenses ...............................................      414,839
                                                                  -----------
Net Investment Income ..........................................    1,908,618
                                                                  -----------
Net Realized and Unrealized Loss
  on Investments:
    Net Realized Loss ..........................................   (2,832,872)
    Change in Net Unrealized
      Appreciation (Depreciation) ..............................  (10,912,924)
                                                                  -----------
Net Realized Loss and Change in
  Net Unrealized Appreciation
  (Depreciation) on Investments ................................  (13,745,796)
                                                                  -----------
Net Decrease in Net Assets
  from Operations .............................................. $(11,837,178)
                                                                  ============ 

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

<PAGE>
                                               Value Line Convertible Fund, Inc.


Statement  of Changes in Net Assets for the six months  ended  October  31, 1998
(unaudited) and for the year ended April 30, 1998
- --------------------------------------------------------------------------------
<TABLE>
<CAPTION>
                                                              Six Months Ended    Year Ended
                                                              October 31, 1998     April 30,
                                                                 (unaudited)         1998
                                                              ------------------------------
<S>                                                             <C>             <C>         
Operations:
  Net investment income .....................................   $  1,908,618    $  3,933,911
  Net realized (loss) gain on investments ...................     (2,832,872)      6,520,865
  Change in net unrealized (depreciation) appreciation ......    (10,912,924)      7,785,510
                                                                ----------------------------
  Net (decrease) increase in net assets from operations .....    (11,837,178)     18,240,286
                                                                ----------------------------

Distributions to Shareholders:
  Net investment income .....................................     (1,881,435)     (3,967,522)
  Net realized gain from investment transactions ............           --        (4,337,642)
                                                                ----------------------------
Total distributions .........................................     (1,881,435)     (8,305,164)
                                                                ----------------------------

Capital Share Transactions:
  Proceeds from sale of shares ..............................     88,971,110      85,988,521
  Proceeds from reinvestment of distributions to shareholders      1,500,932       6,626,383
  Cost of shares repurchased ................................    (96,035,261)    (73,554,612)
                                                                ----------------------------
  (Decrease) Increase from capital share transactions .......     (5,563,219)     19,060,292
                                                                ----------------------------
Total (Decrease) Increase ...................................    (19,281,832)     28,995,414

Net Assets:
  Beginning of period .......................................     97,679,219      68,683,805
                                                                ----------------------------
  End of period .............................................   $ 78,397,387    $ 97,679,219
                                                                ============================
Undistributed Net Investment Income, at end of period .......   $    434,137    $    406,954
                                                                ============================
</TABLE>

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

<PAGE>
Value Line Convertible Fund, Inc.


Notes to Financial Statements (unaudited)                       October 31, 1998
- --------------------------------------------------------------------------------

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.  To the extent these  differences  are permanent in nature,
such amounts 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.


Notes to Financial Statements (unaudited)                       October 31, 1998
- --------------------------------------------------------------------------------


2.   Capital Share Transactions. 

     Transactions in capital stock were as follows:

                                                  Six Months
                                                     Ended              Year
                                                  October 31,          Ended
                                                     1998             April 30,
                                                  (unaudited)           1998
                                                 -------------------------------
                            
Shares sold ...............................         6,695,644          5,969,380
Shares issued to shareholders
  in reinvestment
  of dividends ............................           112,446            475,431
                                                 -------------------------------
                                                    6,808,090          6,444,811
Shares repurchased ........................         7,121,678          5,102,466
                                                 -------------------------------
                            
Net (decrease) increase ...................          (313,588)         1,342,345
                                                 ===============================


3.   Purchases and Sales of Securities

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

                                                                   Six Months
                                                                      Ended
                                                                October 31, 1998
                                                                   (unaudited)
                                                                 --------------
                               
PURCHASES:
  Investment Securities ................................           $39,270,053
                                                                   ===========

SALES OR REDEMPTIONS:
  Investment Securities ................................           $43,674,013
                                                                   ===========

At October 31, 1998, the aggregate cost of investment  securities and repurchase
agreements  for federal  income tax  purposes  was  $80,331,111.  The  aggregate
appreciation  and  depreciation  of investments at October 31, 1998,  based on a
comparison of investment values and their costs for federal income tax purposes,
was $5,679,247 and $7,505,250  respectively,  resulting in a net depreciation of
$1,826,003.

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

An  advisory  fee of  $318,273  was paid or payable  to Value  Line,  Inc.  (the
Adviser),  for the six months ended  October 31, 1998.  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  209,974  shares of the Fund's
capital stock,  representing  3.3% of the outstanding  shares and an officer and
Directors owned 82,055 shares representing 1.3% at October 31, 1998.


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


<PAGE>


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, 1998     ------------------------------------------------------------------------
                                         (unaudited)        1998             1997             1996          1995          1994
                                         ----------       ------------------------------------------------------------------------
<S>                                    <C>                <C>             <C>               <C>            <C>           <C>
Net asset value, beginning
  of period ........................   $    14.80         $  13.07        $   14.10        $   11.79     $    12.26     $   13.80
                                       -------------------------------------------------------------------------------------------
  Income (loss) from investment                                                                                             
    operations:                                                                                                             
  Net investment income ............          .32              .65              .70              .66            .74           .71
  Net gains or losses on                                                                                                    
     securities (both realized                                                                                              
     and unrealized)................        (2.33)            2.50              .50             2.33           (.02)          .11
                                       -------------------------------------------------------------------------------------------
    Total from investment operations        (2.01)            3.15             1.20             2.99            .72           .82
                                       -------------------------------------------------------------------------------------------
  Less distributions:                                                                                                       
    Dividends from net                                                                                                      
      investment income ............         (.31)            (.67)            (.65)            (.68)          (.76)         (.69)
    Distributions from realized                                                                                             
      capital gains ................         --               (.75)           (1.58)            --             (.43)        (1.67)
                                       -------------------------------------------------------------------------------------------
    Total distributions ............         (.31)           (1.42)           (2.23)            (.68)         (1.19)        (2.36)
                                       -------------------------------------------------------------------------------------------
                                                                                                                            
Net asset value, end of period .....   $    12.48         $  14.80        $   13.07        $   14.10     $    11.79     $   12.26
                                       ===========================================================================================
Total return .......................       -13.70%+          25.04%            8.80%           26.07%          6.53%         5.50%
                                       ===========================================================================================
Ratios/Supplemental Data:                                                                                                   
Net assets, end of period                                                                                                   
  (in thousands) ...................   $   78,397         $ 97,679        $  68,684        $  72,620     $   50,523     $  49,823
Ratio of expenses to                                                                                                        
  average net assets ...............          .97%*(1)         .98%(1)         1.01%(1)         1.08%          1.08%         1.07%
Ratio of net investment income                                                                                              
  to average net assets ............         4.42%*           4.63%            4.94%            5.14%          6.13%         5.32%
Portfolio turnover rate ............           56%+            111%             164%             129%            87%          142%
</TABLE>                                                                      
                                                                              

(1)  Before custody credits.

+    Not annualized.

*    Annualized.


See Notes to Financial Statements.
- --------------------------------------------------------------------------------
12

<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 419729
                      Kansas City, MO 64141-6729

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
                      Leo R. Futia
                      David H. Porter
                      Paul Craig Roberts
                      Nancy-Beth Sheerr

OFFICERS              Jean Bernhard Buttner
                      Chairman and President
                      Bruce H. Alston
                      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).


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