VALUE LINE CONVERTIBLE FUND INC
N-30D, 1999-06-28
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================================================================================

                                 --------------
                                  ANNUAL REPORT
                                 --------------
                                 April 30, 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:

It is with  pleasure that we report the  following  results of your  convertible
fund for the fiscal year ended April 30, 1999. The Value Line Convertible Index,
which is a proxy for the convertible market because it represents the collective
performance of over 600  convertible  securities,  had a return of -7.60%.  Your
Fund's performance of -4.64% clearly outperformed this unmanaged index by 2.96%.
Please  note that the index  incurs no  expenses  as do all mutual  funds.  Your
fund's  average  expense ratio of 1.00%  compares  favorably to the  convertible
industry average expense of 1.54%.

                                                         FYE 4/30/99
                                                          ---------
Value Line Convertible Index...........................    -7.60%
Value Line Convertible Fund............................    -4.64%
Lipper Convertible Peer Group Average..................     1.56%
S&P 500...............................................     21.82%
Russell 2000...........................................    -9.25%
Lehman Brothers Gov/Corp..............................      6.28%

Since our last report,  as of October 31, 1998, the financial  markets rebounded
from the effects of a global financial crisis. The Dow Jones Stock Index rallied
from a low of 8,592 on October 30 to 10,789 on April 30, for a gain of more than
twenty-five percent.  Prices of Treasury bonds, however, fell precipitously over
the same period with yields  jumping from 5.16% to 5.66%,  a rise of one-half of
one percentage  point. In fact,  recently rates have further  increased,  rising
slightly above 6%.

Your fund's  performance fell short of its peer group, as several  highly-ranked
convertible issues (namely,  Rite Aid, Network Associates and McKesson) reported
negative  earnings  surprises in 1999,  causing the  securities'  prices to drop
35%-45% in value.  This  reduced  performance  by over 3.00% and was the primary
reason the Fund's performance lagged its peers.

Other  contributing  factors to these  lackluster  results  included:  (i) heavy
equity exposure by competitors -- the average  convertible  fund held 15% of its
assets in common stocks, compared to less than 5% on average for your fund; (ii)
the hedged positions carried by some funds, that your fund does not carry; (iii)
the relative  under  performance  of  traditional  convertibles  (that we favor)
compared  to  the  more  volative  equity-alternative   convertibles;  (iv)  the
continued  under  performance of mid and small cap securities and (v) the recent
rotation  from growth  securities  (that Value Line  favors) to the value group,
ranked lower by Value Line.

Periodic bouts of market turbulence are rarely a pleasant experience. Occasional
fluctuations  in  performance  are  the  price  investors  usually  pay to  reap
long-term financial rewards. We believe that over the long run it is sensible to
balance  the  overall  level of risk in an  investment  portfolio  with a mix of
stocks & bonds,  including  convertibles,  to achieve the appropriate  degree of
risk.

Value Line will continue to strive to deliver competitive returns in convertible
securities  by  seeking  those  securities  that offer a  favorable  risk/return
profile and attractive fundamentals.

We thank you for your  confidence  in the Fund and look  forward to serving your
future investment needs.


                                             Sincerely,

                                             /s/ Jean Bernhard Buttner

                                             Jean Bernhard Buttner
                                             Chairman and President
June 25, 1999

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

<PAGE>


                                               Value Line Convertible Fund, Inc.

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

Economic Observations

For now, at least, our economy continues to move ahead at a brisk pace. Evidence
of this ongoing  strength can be found in the first  quarter's  4.1% increase in
gross  domestic  product,  as  well  as in  reports  showing  further  gains  in
manufacturing  and retailing.  In fact, the only area of major concern currently
is our widening  international  trade deficit,  as faltering  business  overseas
continues  to limit  demand for  American  exports.  Even with this bleak  trade
situation,  though,  it appears unlikely that economic growth will fall short of
3% in the second quarter or 2%-3% in the second half.

Inflation  reports  take on  increasing  significance  in this  setting.  That's
because  the  persistence  of solid  levels of economic  growth,  along with the
recent  increases in energy  prices,  has the  potential  to  introduce  pricing
pressures  for the  first  time in  years.  For now,  such  fears  have not been
realized to any sustainable degree.  Indeed, many corporations  continue to have
limited  pricing  power.  Even so, with the economy still moving ahead  solidly,
with oil and gas prices at a much  higher  level than  earlier in the year,  and
with the labor  markets still  tightening,  it is realistic to expect at least a
moderately higher rate of inflation in the coming months.

At this  juncture,  though,  we do not see a  compelling  reason for the Federal
Reserve to push interest rates materially higher. We note, however,  that as the
economic situation starts to improve globally, the temptation for the Fed--which
has already  signaled that it is now more likely to raise interest rates than to
lower them in the weeks  ahead--to  push up  interest  rates at least  modestly,
would increase.

Performance Data:*
                                             Average       Value of
                                             Annual       an Assumed
                                              Total       Investment
                                             Return       of $10,000
                                             ------        --------
 1 year ended 3/31/99..................       -5.18%       $ 9,483
 5 years ended 3/31/99.................       11.26%        17,046
10 years ended 3/31/99.................       11.18%        28,846


*    The performance data quoted represent past performance and are no guarantee
     of future  performance.  The average  annual  total return and growth of an
     assumed  investment of $10,000  include  dividends  reinvested  and capital
     gains distributions accepted in shares. The investment return and principal
     value of an investment will fluctuate so that an investment, when redeemed,
     may be worth more or less than its original  cost. The average annual total
     returns at April 30, 1999 for the one-year,  five-year and 10-year  periods
     were -4.64%, 11.74%, and 10.83%, respectively.

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

<PAGE>

Value Line Convertible Fund, Inc.

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

         Comparison of a change in value of a $10,000 investment in the
            Value Line Convertible Fund, Inc. and the S&P 500 Index+

 [THE FOLLOWING TABLE WAS REPRESENTED BY A LINE CHART IN THE PRINTED MATERIAL.]


                                          Value Line
                 S&P 500 Index       Convertible Fund, Inc.
                 -------------       ----------------------
4/89               10,000.00              10,000.00
10/89              11,199.69              10,099.57
4/90               11,062.62              10,051.38
10/90              10,358.08               9,136.25
4/91               13,005.99              11,054.61
10/91              13,828.27              12,278.38
4/92               14,833.43              12,869.44
10/92              15,201.12              13,642.47
4/93               16,200.47              15,206.55
10/93              17,464.00              16,548.88
4/94               17,063.24              16,043.61
10/94              18,139.84              15,997.58
4/95               20,035.22              17,091.79
10/95              22,921.08              18,283.77
4/96               26,072.75              21,547.41
10/96              28,427.41              22,777.27
4/97               32,619.76              23,442.37
10/97              37,554.04              26,960.21
4/98               45,990.37              29,312.47
10/98              45,807.92              25,296.42
4/99               56,024.22              27,952.52


                             From 5/1/89 to 4/30/99

+    The   Standard  &  Poor's  500  Index  is  an   unmanaged   index  that  is
     representative  of the  larger-capitalization  stocks  traded in the United
     States. The presentation includes reinvested dividends.

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

<PAGE>

                                               Value Line Convertible Fund, Inc.


Schedule of Investments                                           April 30, 1999
- --------------------------------------------------------------------------------

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

CONVERTIBLE CORPORATE BONDS & NOTES (56.7%)
                 AEROSPACE/
                   DEFENSE (1.2%)
    $1,000,000   Kellstrom Industries, Inc.
                    5 1/2%, 6/15/03.................       $ 830,000

                 AUTO PARTS (ORIGINAL
                   EQUIPMENT) (1.5%)
     1,000,000   Magna International Inc.
                    4 7/8%, 2/15/05.................       1,020,000

                 COMPUTER SOFTWARE
                   & SERVICES (6.5%)
     1,000,000   Affiliated Computer
                    Services Inc.
                    4%, 3/15/05.....................       1,107,500
     2,000,000   Citrix Systems Inc.
                    Zero Coupon
                    Series 144A, 3/22/19*...........         755,000
     1,000,000   Comverse Technology, Inc.
                    4 1/2%, 7/1/05..................       1,641,250
     1,000,000   Softkey International Inc.
                    5 1/2%, 11/1/00.................         977,500
                                                          ----------
                                                           4,481,250

                 DIVERSIFIED
                   COMPANIES (3.2%)
     1,000,000   Berkshire Hathaway Inc.
                    1%, 12/2/01.....................       2,195,000

                 DRUG (3.2%)
     1,000,000 Athena Neurosciences Inc.
                    4 3/4%, 11/15/04................       1,046,250
     1,000,000   Genzyme Corporation
                    5 1/4%, 6/1/05..................       1,168,750
                                                         -----------
                                                           2,215,000

                 DRUGSTORE (1.4%)
     1,000,000 Rite Aid Corp.
                    5 1/4%, 9/15/02.................       1,010,000

                 ELECTRONICS (3.6%)
    $1,000,000   Sanmina Corp. 4 1/4%,
                    Series 144A, 5/1/04*............       1,027,500
     3,000,000   Solectron Corp.
                    Zero Coupon,
                    Series 144A, 1/27/19*...........       1,466,250
                                                         -----------
                                                           2,493,750

                 ENTERTAINMENT (5.8%)
     1,500,000   Clear Channel
                    Communications, Inc.
                    2 5/8%, 4/1/03..................       1,897,500
     2,000,000   Jacor Communications, Inc.
                    Zero Coupon, 2/9/18.............       1,107,500
     1,000,000   Merrill Lynch & Co., Inc.
                    0.25%, 5/10/06
                    (exchangable into Time
                    Warner Inc.)....................       1,000,000
                                                          ----------
                                                           4,005,000

                 ENVIRONMENTAL (1.4%)
     1,000,000   United States Filter Corp.
                    4 1/2%, 12/15/01................         988,750

                 INTERNET (6.4%)
     1,000,000 Amazon.com, Inc.
                    Series 144A,
                    4 3/4%, 2/1/09*.................       1,278,750
       500,000   At Home Corp. Series 144A,
                    .5246%, 12/28/18*...............         492,500
       500,000   CNET, Inc. Series 144A,
                    5%, 3/1/06*.....................         910,625
       500,000   DoubleClick Inc.
                    Series 144A,
                    4 3/4%, 3/15/06*................         886,875
       600,000   MindSpring Enterprises, Inc.
                    5%, 4/15/06.....................         638,250
       250,000   SportsLine USA Inc.
                    Series 144A,
                    5%, 4/1/06*.....................         211,250
                                                          ----------
                                                           4,418,250

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

<PAGE>

                                               Value Line Convertible Fund, Inc.
Schedule of Investments
- --------------------------------------------------------------------------------

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

                 MEDICAL  SERVICES (1.8%)
   $1,000,000    Sunrise  Assisted Living,  Inc.
                    5 1/2%, 6/15/02.................     $ 1,221,250

                 MEDICAL SUPPLIES (1.5%)
    1,000,000    Centocor Inc.
                    4 3/4%, 2/15/05.................       1,063,750

                 OFFICE EQUIPMENT
                   & SUPPLIES (2.4%)
     2,000,000   Office Depot Inc.
                    Zero Coupon, 11/1/08............       1,667,500

                 OILFIELD SERVICES/
                   EQUIPMENT (1.5%)
     1,000,000   Diamond Offshore
                    Drilling Inc.
                    3 3/4%, 2/15/07.................       1,075,000

                 PETROLEUM--
                   INTEGRATED (1.5%)
     1,000,000   Texaco Capital Inc.
                    3 1/2%, 8/5/04..................       1,040,000

                 PUBLISHING (1.4%)
     1,000,000   World Color Press, Inc.
                    6%, 10/1/07.....................         962,500

                 R.E.I.T. (1.3%)
     1,000,000   Healthcare Realty Trust,
                    Inc. 6.55%, 3/14/02.............         905,000

                 RETAIL BUILDING
                   SUPPLY (3.6%)
    $1,000,000   Home Depot, Inc. (The)
                    3 1/4%, 10/1/01.................     $ 2,523,750

                 RETAIL STORE (1.4%)
     1,000,000   Costco Companies, Inc.
                    zero coupon, 8/19/17............         962,500

                 TELECOMMUNICATIONS
                   EQUIPMENT (2.9%)
     1,000,000   Level One Communications,
                    Inc. 4%, 9/1/04.................       2,001,250

                 TELECOMMUNICATION
                   SERVICES (3.2%)
     2,000,000   Bell Atlantic Financial
                    Services Inc. Series 144A,
                    4 1/4%, 9/15/05*................       2,207,500
                                                         -----------

                 TOTAL CONVERTIBLE CORPORATE BONDS
                 & NOTES
                 (Cost $35,723,087) ................     $39,287,000
                                                         -----------

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

<PAGE>

                                               Value Line Convertible Fund, Inc.

                                                                  April 30, 1999
- --------------------------------------------------------------------------------

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

CONVERTIBLE PREFERRED STOCKS (28.9%)
                 BANK (5.9%)
        10,000 BCP International Bank Ltd.
                    $4.00, exchangeable
                    Series "A"......................     $ 1,050,000
        16,000   Matewan Bancshares, Inc.
                    7.50%, Series "A"...............         502,000
        75,000   National Australia Bank,
                    Ltd. Cap Units 7 7/8%,
                    exchangeable Pfd................       2,554,687
                                                          ----------
                                                           4,106,687

                 CABLE TV (0.7%)
         2,500   Adelphi Communications
                    Corp. 5 1/2%,
                    Series "D" Pfd. ................         510,625

                 CEMENT &
                   AGGREGATES (1.8%)
        35,300   TXI Capital Trust I
                    5 1/2%, Pfd.....................       1,261,975

                 COMPUTER SOFTWARE
                   & SERVICES (0.4%)
         9,200   Tribune Co. 61/4%
                    exchangeable Notes..............         262,200

                 ENTERTAINMENT (3.1%)
        20,000 Chancellor Media Corp.
                    $3.00, exchangeable Pfd.........       2,140,000

                 FOOD PROCESSING
                   (1.3%)
        20,000   Ralston Purina Co.
                    7%, Pfd.........................         930,000

                 MEDICAL SUPPLIES
                   (0.8%)
        10,000   McKesson Corporation
                    Financing Trust
                    5%, Pfd.........................         532,500

                 PACKAGING &
                   CONTAINER (2.6%)
        30,000   Sealed Air Corp.
                    $2.00 exchangeable
                    Series "A"......................     $ 1,762,500

                 RAILROAD (1.1%)
        14,500   Union Pacific Capital
                    Trust 6 1/4%, Pfd...............         784,813

                 RETAIL--SPECIAL
                   LINES (1.7%)
        10,000   AnnTaylor Financial Trust
                    8 1/2%, Pfd.....................       1,203,750

                 TELECOMMUNICATION
                   SERVICES (9.5%)
        10,000   AirTouch Communications,
                    Inc. 4 1/4%, Series "C".........       1,300,000
        25,000   Comcast Corp. 3.35%
                    exchangeable Pfd................       1,890,625
        20,000   ICG Communications, Inc.
                    6 3/4%, Pfd.....................       1,072,500
        20,000   IXC Communications, Inc.
                    6 3/4%, Pfd.*...................         792,500
        10,000   MediaOne Group, Inc.
                    6 1/4%, Pfd.....................         801,250
        10,000   Salomon Smith Barney
                    Holdings, Inc. 6 1/4%,
                    exchangeable Notes
                    Series "CSN"....................         700,000
                                                          ----------
                                                           6,556,875
                                                          ----------
                 TOTAL CONVERTIBLE
                 PREFERRED STOCKS
                 (Cost $17,462,109) ................      20,051,925
                                                          ----------
- --------------------------------------------------------------------------------
                                                                               7

<PAGE>

Value Line Convertible Fund, Inc.

Schedule of Investments                                           April 30, 1999
- --------------------------------------------------------------------------------


       Shares                                                  Value
- --------------------------------------------------------------------------------
COMMON STOCKS (6.1%)
                 COMPUTER &
                   PERIPHERALS (1.6%)
         5,000   Cisco Systems, Inc.**..............       $ 570,313
         5,000   EMC Corp.**........................         544,687
                                                         -----------
                                                           1,115,000

                 INTERNET (1.0%)
         5,000   America Online, Inc.**.............         713,750

                 TELECOMMUNICATION
                   SERVICES (3.5%)
        28,854   MCI WorldCom, Inc.**...............       2,371,438
                                                         -----------

                 TOTAL COMMON
                 STOCKS
                 (Cost $2,219,013) .................       4,200,188
                                                         -----------

                 TOTAL INVESTMENT
                 SECURITIES (91.7%)
                 (Cost $55,404,209) ................      63,539,113
                                                         -----------

REPURCHASE AGREEMENTS (15.0%)
(including accrued interest)
    $5,200,000   Collateralized by $4,948,000
                    U.S. Treasury Notes 6 1/2%,
                    due 10/15/06, with a value
                    of $5,304,449 (with Banc
                    One Capital Markets, Inc.,
                    4.84%, dated 4/30/99, due
                    5/3/99, delivery value
                    $5,202,097).....................     $ 5,200,699

     5,200,000   Collateralized by $4,965,000
                    U.S. Treasury Bonds
                    7 5/8%, due 2/15/07, with
                    a value of $5,324,774
                    (with Morgan Stanley &
                    Co., Incorporated,
                    4.84%, dated 4/30/99,
                    due 5/3/99,
                    delivery value
                    $5,202,097).....................       5,200,699
                                                         -----------
                                                          10,401,398
                                                         -----------

EXCESS OF LIABILITIES OVER
CASH AND RECEIVABLES (-6.7%)........................      (4,663,239)
                                                         -----------

NET ASSETS (100.0%) ................................     $69,277,272
                                                         ===========

NET ASSET VALUE, OFFERING
AND REDEMPTION PRICE, PER
OUTSTANDING SHARE
($69,277,272 / 5,424,410
shares outstanding).................................         $ 12.77
                                                         ===========

*    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.

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

<PAGE>

                                               Value Line Convertible Fund, Inc.

Statement of Assets and Liabilities
at April 30, 1999
- --------------------------------------------------------------------------------

Assets:
Investment securities, at value
  (Cost--$55,404,209)............................     $63,539,113
Repurchase agreements
  (Cost--$10,401,398)............................      10,401,398
Cash ...........................................          686,764
Receivable for securities sold .................        2,199,861
Interest and dividends receivable ..............          326,103
Receivable for capital shares sold .............            6,955
                                                       ----------
    Total Assets ...............................       77,160,194
                                                       ----------
Liabilities:
Payable for securities
  purchased.....................................        7,782,319
Payable for capital shares
  repurchased ..................................           11,475
Accrued expenses:
  Advisory fee .................................           44,419
  Other ........................................           44,709
                                                       ----------
    Total Liabilities ..........................        7,882,922
                                                       ----------
Net Assets .....................................      $69,277,272
                                                       ==========
Net assets consist of:
Capital stock, at $1.00 par value
  (authorized 50,000,000,
  outstanding 5,424,410 shares).................      $ 5,424,410
Additional paid-in capital .....................       61,742,257
Undistributed net investment income ............          144,055
Accumulated net realized loss
  on investments................................       (6,168,354)
Net unrealized appreciation
  of investments ...............................        8,134,904
                                                       ----------
Net Assets .....................................      $69,277,272
                                                       ==========
Net Asset Value, Offering and
  Redemption Price, per
  Outstanding Share
  ($69,277,272 / 5,424,410
  shares outstanding) ..........................          $ 12.77
                                                       ==========


Statement of Operations
for the year ended April 30, 1999
- --------------------------------------------------------------------------------

Investment Income:
Interest .......................................       $ 2,621,176
Dividends ......................................         1,339,016
                                                      ------------
    Total Income ...............................         3,960,192
                                                      ------------
Expenses:
Advisory fee ...................................           592,362
Auditing and legal fees ........................            44,977
Transfer agent .................................            42,383
Registration and filing fees ...................            24,685
Custodian fees .................................            22,324
Printing and stationery ........................            21,289
Postage ........................................            19,061
Directors' fees and expenses ...................            15,811
Telephone ......................................             8,690
Insurance, dues and other ......................             5,818
                                                      ------------
    Total Expenses Before
      Custody Credits ..........................           797,400
    Less: custody credits ......................            (5,799)
                                                      ------------
    Net Expenses ...............................           791,601
                                                      ------------
Net Investment Income ..........................         3,168,591
                                                      ------------
Net Realized and Unrealized
  Loss on Investments:
    Net Realized Loss ..........................        (6,168,354)
    Change in Net Unrealized
      Appreciation..............................          (952,017)
                                                      ------------
Net Realized Loss and Change
  in Net Unrealized Appreciation
  (Depreciation) on Investments ................        (7,120,371)
                                                      ------------
Net Decrease in Net Assets
  from Operations ..............................      $ (3,951,780)
                                                      ============

See Notes to Financial Statements.

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

<PAGE>

Value Line Convertible Fund, Inc.


Statement of Changes in Net Assets
for the years ended April 30, 1999 and 1998
- --------------------------------------------------------------------------------

<TABLE>
<CAPTION>
                                                                  Year Ended       Year Ended
                                                                April 30, 1999   April 30, 1998
                                                               --------------------------------
<S>                                                             <C>              <C>
Operations:
  Net investment income .....................................   $   3,168,591    $   3,933,911
  Net realized (loss) gain on investments ...................      (6,168,354)       6,520,865
  Change in net unrealized (depreciation) appreciation ......        (952,017)       7,785,510
                                                                ------------------------------
  Net (decrease) increase in net assets from operations .....      (3,951,780)      18,240,286
                                                                ------------------------------

Distributions to Shareholders:
  Net investment income .....................................      (3,431,409)      (3,967,522)
  Net realized gain from investment transactions ............      (3,713,370)      (4,337,642)
                                                                ------------------------------
  Total distributions .......................................      (7,144,779)      (8,305,164)
                                                                ------------------------------

Capital Share Transactions:
  Proceeds from sale of shares ..............................     176,887,275       85,988,521
  Proceeds from reinvestment of distributions to shareholders       5,916,259        6,626,383
  Cost of shares repurchased ................................    (200,108,922)     (73,554,612)
                                                                ------------------------------
  Net (decrease) increase from capital share transactions ...     (17,305,388)      19,060,292
                                                                ------------------------------

Total (Decrease) Increase in Net Assets .....................     (28,401,947)      28,995,414

Net Assets:
  Beginning of year .........................................      97,679,219       68,683,805
                                                                ------------------------------
  End of year ...............................................   $  69,277,272    $  97,679,219
                                                                ------------------------------
Undistributed net investment income at end of year ..........   $     144,136    $     406,954
                                                                ==============================
</TABLE>

See Notes to Financial Statements.

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

<PAGE>

                                               Value Line Convertible Fund, Inc.

Notes to Financial Statements                                     April 30, 1999
- --------------------------------------------------------------------------------

1. Significant Accounting Policies

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

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

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

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

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

(D) Security Transactions and Distributions. Security transactions are accounted
for on the date the securities are purchased or sold. Interest income is accrued
as earned.  Realized  gains and losses on sales of securities are calculated for
financial  accounting  and federal  income tax purposes on the  identified  cost
basis.  Dividend income and  distributions  to shareholders  are recorded on the
ex-dividend date. 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.


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

<PAGE>

Value Line Convertible Fund, Inc.

Notes to Financial Statements                                     April 30, 1999
- --------------------------------------------------------------------------------


2. Capital Share Transactions Transactions in capital stock were as follows:

                                           Year Ended     Year Ended
                                            April 30,      April 30,
                                              1999           1998
                                            -------------------------

Shares sold ...........................     13,575,401      5,969,380
Shares issued to shareholders
  in reinvestment  of
  dividends and distributions..........        477,763        475,431
                                            -------------------------
                                            14,053,164      6,444,811
Shares repurchased ....................     15,226,596      5,102,467
                                            -------------------------
Net (decrease) increase ...............     (1,173,432)     1,342,344
                                            =========================

3. Purchases and Sales of Securities

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

                                                       Year Ended
                                                     April 30, 1999
                                                     --------------
PURCHASES:
  Investment Securities ..........................     $83,276,990
                                                       ===========
SALES OR REDEMPTIONS:
  Investment Securities ..........................     $89,960,969
                                                       ===========
At April 30, 1999,  the aggregate  cost of investment  securities and repurchase
agreements  for federal  income tax  purposes  was  $66,219,057.  The  aggregate
appreciation  and  depreciation  of  investments  at April 30, 1999,  based on a
comparison of investment values and their costs for federal income tax purposes,
was $10,172,678 and $2,451,224 respectively,  resulting in a net depreciation of
$7,721,454.

During the year ended April 30, 1999,  as  permitted  under  federal  income tax
regulations,  the Fund has  elected  to defer  $2,922,032  of  Post-October  net
capital losses to the next taxable year.

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 $592,362 was paid or payable to Value Line,  Inc.
(the Adviser),  for the year ended April 30, 1999. This was computed at the rate
of 3/4 of 1% of average daily net assets  during the year and paid monthly.  The
Adviser provides research,  investment  programs,  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 Adviser  and/or  affiliated  companies  owned  226,754  shares of the Fund's
capital stock, representing 4.2% of the outstanding shares at April 30, 1999.


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

<PAGE>

                                               Value Line Convertible Fund, Inc.

Financial Highlights
- --------------------------------------------------------------------------------

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

<TABLE>
<CAPTION>
                                                                             Years Ended April 30,
                                                    ------------------------------------------------------------------------------
                                                        1999             1998               1997              1996          1995
                                                    ------------------------------------------------------------------------------
<S>                                                <C>               <C>               <C>               <C>            <C>
Net asset value, beginning of  year ............   $    14.80        $    13.07        $    14.10        $    11.79     $    12.26
                                                    ------------------------------------------------------------------------------
  Income (loss) from
    investment operations:
    Net investment income ......................          .57               .65               .70               .66            .74
    Net gains or losses on securities
      (both realized and unrealized) ...........        (1.33)             2.50               .50              2.33           (.02)
                                                    ------------------------------------------------------------------------------
    Total from investment operations ...........         (.76)             3.15              1.20              2.99            .72
                                                    ------------------------------------------------------------------------------
  Less distributions:
    Dividends from net investment
      income ...................................         (.60)             (.67)             (.65)             (.68)          (.76)
    Distributions from
      realized capital gains ...................         (.67)             (.75)            (1.58)             --             (.43)
                                                    ------------------------------------------------------------------------------
    Total distributions ........................        (1.27)            (1.42)            (2.23)             (.68)         (1.19)
                                                    ------------------------------------------------------------------------------
Net asset value, end of year ...................   $    12.77        $    14.80        $    13.07        $    14.10     $    11.79
                                                    ==============================================================================
Total return ...................................       -4.64%             25.04%             8.80%            26.07%          6.53%
                                                    ==============================================================================
Ratios/Supplemental Data:
Net assets, end of year (in thousands) .........   $   69,277        $   97,679        $   68,684        $   72,620     $   50,523
Ratio of expenses to average net assets ........         1.00%(1)           .98%(1)          1.01%(1)          1.08%          1.08%
Ratio of net investment income
  to average net assets ........................         3.98%             4.63%             4.94%             5.14%          6.13%
Portfolio turnover rate ........................          123%              111%              164%              129%            87%
</TABLE>

(1)  Before  offset of custody  credits.  The ratio of  expenses  to average net
     assets would not have changed net of custody credits.



See Notes to Financial Statements.

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

                                                                              13

<PAGE>

Value Line Convertible Fund, Inc.

Report of Independent Accountants
- --------------------------------------------------------------------------------

To the Board of Directors and Shareholders
of Value Line Convertible Fund, Inc.

In our opinion, the accompanying statement of assets and liabilities,  including
the schedule of  investments,  and the related  statements of operations  and of
changes  in net assets  and the  financial  highlights  present  fairly,  in all
material  respects,  the financial position of Value Line Convertible Fund, Inc.
(the "Fund") at April 30, 1999,  the results of its operations for the year then
ended,  the  changes  in its net  assets for each of the two years in the period
then ended and the financial highlights for each of the five years in the period
then ended, in conformity with generally accepted accounting  principles.  These
financial  statements  and  financial  highlights   (hereafter  referred  to  as
"financial  statements") are the  responsibility of the Fund's  management;  our
responsibility  is to express an opinion on these financial  statements based on
our audits. We conducted our audits of these financial  statements in accordance
with  generally  accepted  auditing  standards  which  require  that we plan and
perform the audit to obtain  reasonable  assurance  about  whether the financial
statements are free of material misstatement.  An audit includes examining, on a
test basis,  evidence  supporting  the amounts and  disclosures in the financial
statements,  assessing the accounting  principles used and significant estimates
made by management, and evaluating the overall financial statement presentation.
We believe that our audits,  which included  confirmation of securities at April
30, 1999 by correspondence with the custodian and brokers,  provide a reasonable
basis for the opinion expressed above.

PricewaterhouseCoopers  LLP
1177 Avenue of the Americas
New York, New York 10036
June 18, 1999

                          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.


- --------------------------------------------------------------------------------
                 Federal Tax Status of Distributions (unaudited)
For corporate taxpayers 23.91% of the ordinary income  distributions paid during
the calendar year 1998 qualify for the corporate dividends received  deductions.
- --------------------------------------------------------------------------------



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

<PAGE>

                                               Value Line Convertible Fund, Inc.

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



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- --------------------------------------------------------------------------------
                                                                              15


<PAGE>


                         The Value Line Family of Funds

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

1952--The  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 High-Yield Portfolio.

1985--Value  Line  Convertible  Fund seeks high  current  income  together  with
capital  appreciation  primarily from convertible  securities  ranked 1 or 2 for
year-ahead performance by the Value Line Convertible Ranking System.

1986--Value Line Aggressive Income Trust seeks to maximize current income.

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 achive 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 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
                              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

This 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).

                                                                          507457



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