VALUE LINE CONVERTIBLE FUND INC
N-30D, 1998-06-26
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================================================================================

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

It is with pleasure  that we report the  following  results of your Fund for the
fiscal year ended April 30, 1998. The total return of the Fund (25.04%) exceeded
its peer group average and was, as would be expected, between the stock and bond
market performances, as shown below. Your Fund's expense ratio of 0.98% compares
favorably to the convertible industry average of 1.54%, and moreover,  your Fund
does not charge a sales load.

                                                               FYE
                                                             4/30/98
- ---------------------------------------------------------------------
o Value Line Convertible Fund                                 25.04%
o Lipper Convertible Peer
    Group Average                                             24.79%
o S&P 500                                                     41.07%
o Lehman Brothers Gov/Corp                                    11.91%

Since our last report,  the financial markets have continued to be rocked by the
situation in Asia. The difficulties in that part of the world, and the potential
economic  ramifications  in the U.S., have led to an  extraordinary  increase in
volatility in our financial markets.  The convertible market, as well as others,
was also  besieged with heavy new security  issuance and more marginal  issuers.
However,  the  large  appetite  for  convertible   securities  of  many  of  our
competitors  has caused most of these issues to perform well.  Furthermore,  the
strength in the equity  markets has caused many of our  competitors  to increase
reliance on stocks to bolster performance.

Our strategy is to maintain our focus on convertible securities because of their
lower risk and  potential  for  excellent  returns.  We continue to select those
issues with sound  fundamentals and higher Value Line Timeliness  Rankings.  Our
discipline emphasizes  traditional  convertible  securities that offer favorable
leverage.  Favorable  leverage is essentially a balance between potential equity
appreciation and protection from stock market declines. Ideally, your fund might
achieve 70% of the bull market return, but only 35% of a bear market correction.

We use the Value Line Ranking System for  Convertibles to identify  attractively
priced  convertibles.  We expect to continue  systematically  taking  profits in
convertibles  that have become equity  surrogates,  and to reinvest the proceeds
from such sales in attractively  leveraged convertibles to hedge against adverse
market volatility. The Fund is well diversified with approximately 60 issues.

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

                                         Sincerely,

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

June 8, 1998


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

<PAGE>


                                               Value Line Convertible Fund ,Inc.

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

Economic Observations

The business  expansion  continues to proceed at a healthy  clip, as we make our
way through the second quarter of the year.  True, the uptrend is unlikely to be
as uniformly strong in the current period and during the second half of the year
as it was in the opening quarter, when growth exceeded 4%. But, with most of the
key consumer and industrial  indicators still in relatively good shape, and with
inflation  continuing  to be under  control,  growth could still average a solid
2.5%,  or so, over the balance of the year.  What's  more,  we would expect both
producer (or wholesale) and consumer prices to evidence little upward pressure.

The wild card in this  forecast,  of course,  remains  the  Pacific  Rim,  which
continues  to face the  daunting  task of turning  itself  around  economically.
Obviously,  the problems  afflicting that part of the globe will lead to gradual
reductions  in demand for goods and  services  produced  in the  United  States.
Nonetheless,  assuming that the affected  nations take  corrective  actions in a
timely fashion,  so that the situation  eventually  starts to stabilize,  little
more than minor dislocations should be apparent here. At this juncture,  we feel
that the current long business expansion can go on for several more years.

Performance Data:*

                                                     Average         Growth of 
                                                     Annual          an Assumed 
                                                      Total          Investment 
                                                     Return          of $10,000 
                                                     ------          -----------
 1 year ended 3/31/98..........................       26.53%           $12,653 
 5 years ended 3/31/98.........................       13.93%            19,196 
10 years ended 3/31/98.........................       13.53%            35,558 

*    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, 1998 for the one-year,  five-year and 10-year  periods
     were 25.04%, 14.03%, and 13.18%, respectively.


- --------------------------------------------------------------------------------
                                                                               3
<PAGE>


Value Line Convertible Fund ,Inc.

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

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

  [THE FOLLOWING TABLE WAS REPRESENTED AS A LINE CHART INTHE PRINTED MATERIAL]

                Value Line Convertible Fund             S&P 500
                 ---------------------------             -------
4/89                        $12,282                      $11,767
4/90                        $13,575                      $11,828
4/91                        $15,973                      $13,008
4/92                        $18,214                      $15,144
4/93                        $19,896                      $17,894
4/94                        $20,955                      $18,879
4/95                        $24,615                      $20,112
4/96                        $32,052                      $25,356
4/97                        $40,103                      $27,586
4/98                        $56,576                      $34,493
                                                     
- --------------------------------------------------------------------------------

                             From 5/1/88 to 4/30/98

+    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, 1998
- --------------------------------------------------------------------------------

Principal
 Amount                                                                 Value
- --------------------------------------------------------------------------------
CONVERTIBLE CORPORATE BONDS & NOTES (50.5%)

               AIR TRANSPORT (1.0%)
$1,200,000     World Airways, Inc.
                   8%, 8/26/04*.................................       $ 930,000

               BANK (2.1%)
 1,500,000     First State Bancorporation
                   7 1/2%, 4/30/17..............................       2,073,750

               CABLE TV (2.2%)
 2,370,000     Tele-Communications
                   International, Inc.
                   4 1/2%, 2/15/06 .............................       2,130,038

               COMPUTER &
                 PERIPHERALS (1.9%)
 1,000,000     Adaptec, Inc.
                   4 3/4%, 2/1/04...............................         855,000
 1,000,000     Quantum Corp.
                   7%, 8/1/04...................................         992,500
                                                                      ----------
                                                                       1,847,500

               COMPUTER SOFTWARE
                 & SERVICES (2.1%)
 2,000,000     MacNeal-Schwendler Corp.
                   7 7/8%, 8/18/04..............................       2,065,000
               DIVERSIFIED
                 COMPANIES (0.5%)
   500,000     Thermo Instrument
                   Systems Inc.
                   4%, 1/15/05..................................         513,125

               DRUG (2.9%)
$3,000,000     ALZA Corp. zero coupon,
                   7/14/14......................................     $ 1,923,750
 1,000,000     Dura Pharmaceuticals, Inc.
                   3 1/2%, 7/15/02..............................         862,500
                                                                      ----------
                                                                       2,786,250

               ENTERTAINMENT (1.5%)
 1,500,000     Clear Channel
                   Communications, Inc.
                   2 5/8%, 4/1/03...............................       1,494,375

               ENVIRONMENTAL
                 (2.2%)
 2,000,000     United States Filter Corp.
                   4 1/2%, 12/15/01.............................       2,107,500

               FINANCIAL SERVICES
                 (0.5%)
   500,000     Loews Corp.
                   3 1/8%, 9/15/07..............................         502,500

               HOTEL/GAMING (1.0%)
 1,000,000     CapStar Hotel Co.
                   4 3/4%, 10/15/04.............................         941,250

               HOUSEHOLD
                 PRODUCTS (0.8%)
 2,500,000     Sunbeam Corp.
                   zero coupon, 3/25/18*........................         781,250

               INSURANCE--
                 PROPERTY
                 CASUALTY (3.3%)
 3,000,000     Fremont General Corp.
                   zero coupon, 10/12/13........................       3,236,250


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

<PAGE>


Value Line Convertible Fund ,Inc.

Schedule of Investments                                           April 30, 1998
- --------------------------------------------------------------------------------

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

               MEDICAL SERVICES
                 (3.5%)
$1,000,000     NovaCare, Inc.
                   5 1/2%, 1/15/00..............................      $  946,250
 1,000,000     Omnicare, Inc.
                   5%, 12/1/07*.................................       1,106,250
 1,000,000     PhyCor, Inc.
                   4 1/2%, 2/15/03..............................         901,250
   600,000     PhyMatrix Corp.
                   6 3/4%, 6/15/03..............................         490,500
                                                                      ----------
                                                                       3,444,250

               NATURAL GAS--
                 DISTRIBUTION (1.0%)
 1,000,000     NorAm Energy Corp.
                   6%, 3/15/12..................................         942,500

               OFFICE EQUIPMENT
                 & SUPPLIES (3.1%)
 1,000,000     Corporate Express, Inc.
                   4 1/2%, 7/1/00...............................         908,750
 1,000,000     Danka Business
                   Systems PLC
                   6 3/4%, 4/1/02...............................         978,750
 1,000,000     U.S. Office Products Co.
                   5 1/2%, 2/1/01...............................       1,107,500
                                                                      ----------
                                                                       2,995,000
               OILFIELD SERVICES
                 /EQUIPMENT (4.8%)
 3,000,000     Key Energy Group, Inc.
                   5%, 9/15/04*.................................       2,490,000
 2,250,000     Parker Drilling Co.
                   5 1/2%, 8/1/04...............................       2,247,187
                                                                      ----------
                                                                       4,737,187

               PETROLEUM--
                 INTEGRATED (1.1%)
$1,000,000     Texaco Capital Inc.
                   3.50%, 8/5/04................................     $ 1,037,500

               PUBLISHING (2.1%)
 2,000,000     World Color Press, Inc.
                   6%, 10/1/07..................................       2,092,500

               R.E.I.T. (2.2%)
 1,000,000     Capstone Capital Corp.
                   6.55%, 3/14/02...............................         990,000
 1,000,000     Developers Diversified
                   Realty Corp.
                   7%, 8/15/99..................................       1,207,500
                                                                      ----------
                                                                       2,197,500

               RETAIL--SPECIAL
                 LINES (2.3%)
   500,000     Inacom Corp.
                   4 1/2%, 11/1/04..............................         536,875
   500,000     Men's Wearhouse, Inc. (The)
                   5 1/4%, 3/1/03...............................         659,375
 1,000,000     Michaels Stores, Inc.
                   6 3/4%, 1/15/03..............................       1,010,000
                                                                      ----------
                                                                       2,206,250
               TELECOMMUNICATION
                 SERVICES (2.2%)
 1,000,000     SmarTalk Teleservices, Inc.
                   5 3/4%, 9/15/04*.............................       1,011,250
 3,000,000     U.S. Cellular Corp.
                   zero coupon, 6/15/15.........................       1,143,750
                                                                      ----------
                                                                       2,155,000


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

<PAGE>


                                               Value Line Convertible Fund ,Inc.

Schedule of Investments                                           April 30, 1998
- --------------------------------------------------------------------------------

Principal Amount
  or Shares                                                              Value
- --------------------------------------------------------------------------------
               THRIFT (2.6%)
 1,000,000     BankAtlantic Bancorp, Inc.
                   6 3/4%, 7/1/06...............................      $2,040,000
   500,000     BayView Capital Corp.
                   9 1/8%, 8/15/07..............................         515,000
                                                                      ----------
                                                                       2,555,000

               TOBACCO (0.9%)
$1,000,000     Standard Commercial Corp.
                   7 1/4%, 3/31/07..............................         897,500

               OTHER (2.7%)
   500,000     Assisted Living Concepts, Inc.
                   6%, 11/1/02..................................         522,500
 1,250,000     Republic of Italy-Istituto
                   Nazionale delle
                   Assicurazioni Sp.A,
                   5%, 6/28/01 .................................       2,150,000
                                                                      ----------
                                                                       2,672,500
                                                                      ----------

               TOTAL CONVERTIBLE
               CORPORATE BONDS
               & NOTES
               (Cost $46,527,240)  .............................      49,341,475
                                                                      ----------

CONVERTIBLE PREFERRED STOCKS (28.2%)
                          BANK (6.0%)
    20,000     BCP International Bank Ltd.
                   $4.00 exchangeable
                   Series "A" .....................................    2,600,000
    16,000     Matewan Bancshares, Inc.
                   7.50% Series "A"................................      472,000
    70,000     National Australia
                   Bank, Ltd. Cap Units 77/8%
                   exchangeable Pfd. ..............................    2,060,625
     8,900     Union Planters Corp.
                   $2.00 Series "E"................................      671,950
                                                                      ----------
                                                                       5,804,575
                
    Shares                                                               Value
- --------------------------------------------------------------------------------
               ELECTRONICS (2.1%)
    40,000     Pioneer-Standard
                   Electronics, Inc.
                   6 3/4%, Series "144A"* .........................    2,085,000

               ENTERTAINMENT (2.0%)
    20,000     Chancellor Media Corp.
                   $3.00 Series "144A"*............................    1,955,000

               HOTEL/GAMING (0.6%)
    20,000     FelCor Suite Hotels Inc.
                   $1.95 Series "A" ...............................      572,500

               INSURANCE--
                 DIVERSIFIED (1.2%)
    20,000     PennCorp Financial
                   Group, Inc. $3.375 Pfd..........................    1,205,000

               MANUFACTURED HOUSING/
                 RECREATIONAL
                 VEHICLE (1.2%)
    20,000     Fleetwood Capital Trust
                   6%, Series "144A"*..............................    1,175,000

               NATURAL GAS--
                 DIVERSIFIED (1.5%)
    10,000     Williams Companies, Inc.
                   (The) $3.50 Pfd.................................    1,466,250

               R.E.I.T. (3.6%)
    40,000     Camden Property Trust
                   $2.25, Series "A"...............................    1,105,000
    10,000     Dynex Capital Inc.
                   9.73% Series "C"................................      307,500
    15,000     Glenborough Realty Trust, Inc.
                   7 3/4%, Series "A"..............................      382,500
    40,000     Thornburg Mortgage
                   Asset Corp.
                   9.68%, Series "A" ..............................    1,047,500
    25,000     U.S. Restaurant
                   Properties, Inc.,
                   7.72%, Series "A" ..............................      681,250
                                                                      ----------
                                                                       3,523,750

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

<PAGE>


Value Line Convertible Fund ,Inc.

Schedule of Investments                                           April 30, 1998
- --------------------------------------------------------------------------------
                
    Shares                                                               Value
- --------------------------------------------------------------------------------
               RAILROAD (0.8%)
    14,500     Union Pacific Capital Trust
                   6 1/4%, Series "144A"* .........................  $   790,250

               STEEL (2.1%)
    40,000     USX Capital Trust I,
                   6 3/4% Pfd......................................    2,042,500

               TELECOMMUNICATION
                 SERVICES (7.1%)
    10,000     AirTouch Communications, Inc.
                   4 1/4%, Series "C"..............................      768,125
    20,000     ICG Communications, Inc.
                   6 3/4%, Series "144A"* .........................    1,507,500
    20,000     IXC Communications, Inc.
                   6 3/4%, Pfd.
                   Series "144A"*.................................      995,000
    10,000     Salomon Smith Barney
                   Holdings, Inc. 61/4%,
                   exchangeable Notes
                   Series "CSN" ...................................      686,250
    20,000     WorldCom Inc. 8%,
                   Depositary shares (1)...........................    2,963,750
                                                                      ----------
                                                                       6,920,625

               TOTAL CONVERTIBLE
               PREFERRED STOCKS
               (Cost $21,267,764) .................................   27,540,450
                                                                      ----------

               TOTAL INVESTMENT
               SECURITIES (78.7%)
               (Cost $67,795,004) .................................   76,881,925
                                                                      ----------

Principal
 Amount                                                                 Value
- --------------------------------------------------------------------------------
REPURCHASE AGREEMENTS (18.4%)
               (including accrued interest)

$18,000,000    Collateralized by $17,605,000
               U.S. Treasury Note 63/8%,
               due 5/15/00 with a value
               of $18,367,225 (with
               Morgan Stanley Dean Witter
               Discover & Co.,
               Inc. 5.50%,
               dated 4/30/98, due
               5/1/98, delivery value
               $18,002,750)....................................      $18,002,750

CASH AND RECEIVABLES
LESS LIABILITIES (2.9%) .......................................        2,794,544
                                                                     -----------
NET ASSETS (100.0%) ...........................................      $97,679,219
                                                                     -----------
NET ASSET VALUE, OFFERING
AND REDEMPTION PRICE PER
OUTSTANDING SHARE
($97,679,219 / 6,597,842
shares outstanding) ...........................................          $ 14.80
                                                                     ===========

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

(1)  Represents 1/100th of a share of Conv. Pfd.

See Notes to Financial Statements

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

<PAGE>


                                               Value Line Convertible Fund ,Inc.


Statement of Assets and Liabilities
at April 30, 1998
================================================================================

Assets:
Investment securities, at value
  (Cost--$67,795,004) .....................................          $76,881,925
Repurchase agreement
  (Cost--$18,002,750) .....................................           18,002,750
Cash ......................................................              684,938
Receivable for capital shares sold ........................            1,719,997
Interest and dividends receivable .........................              527,804
                                                                     -----------
    Total Assets ..........................................           97,817,414
                                                                     -----------
Liabilities:
Payable for capital shares
  repurchased .............................................               30,678
Accrued expenses:
  Advisory fee ............................................               60,481
  Other ...................................................               47,036
                                                                     -----------
    Total Liabilities .....................................              138,195
                                                                     -----------
Net Assets ................................................          $97,679,219
                                                                     ===========
Net assets consist of:
Capital stock, at $1.00 par value
  (authorized 50,000,000,
  outstanding 6,597,842 shares) ...........................          $ 6,597,842
Additional paid-in capital ................................           77,874,213
Undistributed net investment income .......................              406,954
Accumulated net realized gain
  on investments ..........................................            3,713,289
Net unrealized appreciation of
  investments .............................................            9,086,921
                                                                     -----------
Net Assets ................................................          $97,679,219
                                                                     ===========
Net Asset Value, Offering and
  Redemption Price per
  Outstanding Share
  ($97,679,219 / 6,597,842
  shares outstanding) .....................................          $     14.80
                                                                     ===========

Statement of Operations
for the year ended April 30, 1998
- --------------------------------------------------------------------------------

Investment Income:
Interest ...............................................           $  3,531,278
Dividends (Net of foreign
  withholding tax of $15,583) ..........................              1,225,033
                                                                   ------------
    Total Income .......................................              4,756,311
                                                                   ------------
Expenses:
Advisory fee ...........................................                638,379
Transfer agent fee .....................................                 40,990
Auditing and legal fees ................................                 35,041
Registration and filing fees ...........................                 29,954
Custodian fees .........................................                 23,256
Printing and stationery ................................                 20,009
Directors' fees and expenses ...........................                 15,228
Postage ................................................                 10,339
Insurance and other ....................................                 16,432
                                                                   ------------
    Total Expenses Before
      Custody Credits ..................................                829,628
    Less: Custody Credits ..............................                 (7,228)
                                                                   ------------
    Total Expenses .....................................                822,400
                                                                   ------------
Net Investment Income ..................................              3,933,911
                                                                   ------------
Net Realized and Unrealized
  Gain (Loss) on Investments:
    Net Realized Gain ..................................              6,520,865
    Change in Net Unrealized
      Appreciation .....................................              7,785,510
                                                                   ------------
Net Realized Gain and Change
  in Net Unrealized Appreciation
  on Investments .......................................             14,306,375
                                                                   ------------
Net Increase in Net Assets
  from Operations ......................................           $ 18,240,286
                                                                   ============

See Notes to Financial Statements.
- --------------------------------------------------------------------------------
                                                                               9
<PAGE>


Value Line Convertible Fund ,Inc.

Statement of Changes in Net Assets
for the years ended April 30, 1998 and 1997
- --------------------------------------------------------------------------------
<TABLE>
<CAPTION>
                                                                     Year Ended         Year Ended
                                                                    April 30, 1998    April 30, 1997
                                                                    ---------------------------------
<S>                                                                 <C>              <C>          
Operations:
  Net investment income .........................................   $   3,933,911    $   3,416,967
  Net realized gain on investments ..............................       6,520,865        7,919,219
  Change in net unrealized appreciation .........................       7,785,510       (5,752,019)
                                                                    ------------------------------
  Net increase in net assets from operations ....................      18,240,286        5,584,167
                                                                    ------------------------------

Distributions to Shareholders:
  Net investment income .........................................      (3,967,522)      (3,158,289)
  Realized gains ................................................      (4,337,642)      (7,350,053)
                                                                    ------------------------------
  Total distributions ...........................................      (8,305,164)     (10,508,342)
                                                                    ------------------------------

Capital Share Transactions:
  Net proceeds from sale of shares ..............................      85,988,521       95,369,317
  Net proceeds from reinvestment of distributions to shareholders       6,626,383        8,470,140
  Cost of shares repurchased ....................................     (73,554,612)    (102,851,591)
                                                                       ---------------------------
  Increase from capital share transactions ......................      19,060,292          987,866
                                                                    ------------------------------

Total Increase (Decrease) .......................................      28,995,414       (3,936,309)

Net Assets:
  Beginning of year .............................................      68,683,805       72,620,114
                                                                    ------------------------------
  End of year ...................................................   $  97,679,219    $  68,683,805
                                                                    ------------------------------

Undistributed Net Investment Income, at end of year .............   $     406,954    $     440,565
                                                                    ==============================
</TABLE>


See Notes to Financial Statements.


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

<PAGE>

                                               Value Line Convertible Fund ,Inc.

Notes to Financial Statements                                     April 30, 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.


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

<PAGE>


                                               Value Line Convertible Fund ,Inc.

Notes to Financial Statements                                     April 30, 1998
- --------------------------------------------------------------------------------

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

                                                       Year Ended     Year Ended
                                                        April 30,      April 30,
                                                          1998            1997
                                                       -------------------------
Shares sold ....................................       5,969,380       6,848,012
Shares issued to shareholders
  in reinvestment
  of dividends .................................         475,431         640,516
                                                       -------------------------
                                                       6,444,811       7,488,528

Shares repurchased .............................       5,102,466       7,382,823
                                                       -------------------------
Net increase ...................................       1,342,345         105,705
                                                       =========================

3.   Purchases and Sales of Securities

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


                                                                    Year Ended
                                                                  April 30, 1998
                                                                  --------------
PURCHASES:
  Investment Securities ................................           $98,897,602
                                                                   ===========

SALES OR REDEMPTIONS:
  Investment Securities ................................           $79,168,635
                                                                   ===========

At April 30, 1998,  the aggregate  cost of investment  securities and repurchase
agreements  for federal  income tax  purposes  was  $85,797,754.  The  aggregate
appreciation  and  depreciation  of  investments  at April 30, 1998,  based on a
comparison of investment values and their costs for federal income tax purposes,
was $11,484,868 and $2,397,947 respectively,  resulting in a net appreciation of
$9,086,921.

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

An  advisory  fee of  $638,379  was paid or payable  to Value  Line,  Inc.  (the
Adviser),  for the year ended April 30,  1998.  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 Advisor  and/or  affiliated  companies  owned  205,171  shares of the Fund's
capital stock,  representing  3.1% of the outstanding  shares and an officer and
Director owned 80,178 shares representing 1.2% at April 30, 1998.



- --------------------------------------------------------------------------------
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,
                                                      -----------------------------------------------------------------------------
                                                            1998              1997              1996           1995           1994
                                                      -----------------------------------------------------------------------------
<S>                                                   <C>               <C>               <C>            <C>            <C>       
Net asset value, beginning of year ................   $    13.07        $    14.10        $    11.79     $    12.26     $    13.80
                                                      -----------------------------------------------------------------------------
  Income (loss) from
    investment operations:
    Net investment income .........................          .65               .70               .66            .74            .71
    Net gains or losses on securities
      (both realized and unrealized) ..............         2.50               .50              2.33           (.02)           .11
                                                      -----------------------------------------------------------------------------
    Total from investment operations ..............         3.15              1.20              2.99            .72            .82
                                                      -----------------------------------------------------------------------------
  Less distributions:
    Dividends from net investment
      income ......................................         (.67)             (.65)             (.68)          (.76)          (.69)
    Distributions from
      realized capital gains ......................         (.75)            (1.58)             --             (.43)         (1.67)
                                                      -----------------------------------------------------------------------------
    Total distributions ...........................        (1.42)            (2.23)             (.68)         (1.19)         (2.36)
                                                      -----------------------------------------------------------------------------
Net asset value, end of year ......................   $    14.80        $    13.07        $    14.10     $    11.79     $    12.26
                                                      =============================================================================
Total return ......................................        25.04%             8.80%            26.07%          6.53%          5.50%
                                                      =============================================================================

Ratios/Supplemental Data:

Net assets, end of year (in thousands) ............   $   97,679        $   68,684        $   72,620     $   50,523     $   49,823
Ratio of expenses to average net assets ...........          .98%(1)          1.01%(1)          1.08%          1.08%          1.07%
Ratio of net investment income
  to average net assets ...........................         4.63%             4.94%             5.14%          6.13%          5.32%
Portfolio turnover rate ...........................          111%              164%              129%            87%           142%
</TABLE>

(1)  Before 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, 1998,  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   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,  1998 by  correspondence  with  the
custodian  and  brokers,  provide a reasonable  basis for the opinion  expressed
above.

PRICE WATERHOUSE LLP
1177 Avenue of the Americas
New York, NY 10036

June 19, 1998



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

                 Federal Tax Status of Distributions (unaudited)
              For corporate taxpayers 11.33% of the ordinary income
            distributions paid during the calendar year 1997 qualify
                for the corporate dividends received deductions.

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

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

<PAGE>


                                               Value Line Convertible Fund ,Inc.

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







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- --------------------------------------------------------------------------------
                                                                              15
<PAGE>


Value Line Convertible Fund ,Inc.


                         The Value Line Family of Funds
- --------------------------------------------------------------------------------

1950--The  Value Line Fund seeks  long-term  growth of capital along with modest
current income by investing  substantially all of its assets in common stocks or
securities convertible into common stock.

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

1956--The Value Line Special Situations Fund seeks to obtain long-term growth of
capital by investing not less than 80% of its assets in "special situations". No
consideration is given to achieving current income.

1972--Value  Line Leveraged  Growth  Investors' sole investment  objective is to
realize  capital growth by investing  substantially  all of its assets in common
stocks.  The  Fund  may  borrow  up to 50% of its net  assets  to  increase  its
purchasing power.

1979--The  Value Line Cash Fund, a money market fund,  seeks high current income
consistent with preservation of capital and liquidity.

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

1983--Value  Line Centurion Fund* seeks long-term  growth of capital as its sole
objective  by  investing  primarily  in stocks  ranked 1 or 2 by Value  Line for
year-ahead relative performance.

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

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

1986--Value  Line  Aggressive  Income Trust seeks to maximize  current income by
investing in high-yielding, lower-rated, fixed-income corporate securities.

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

1987--Value Line Strategic Asset Management Trust* invests in stocks,  bonds and
cash equivalents according to computer trend models developed by Value Line. The
objective  is  to  professionally   manage  the  optimal   allocation  of  these
investments at all times.

1993--Value  Line  Small-Cap  Growth Fund invests  primarily in common stocks or
securities  convertible  into common  stock,  with its primary  objective  being
long-term growth of capital.

1993--Value  Line Asset  Allocation  Fund seeks  high total  investment  return,
consistent  with  reasonable  risk. The Fund invests in stocks,  bonds and money
market instruments utilizing quantitative modeling to determine the asset mix.

1995--Value  Line U.S.  Multinational  Company  Fund's  investment  objective is
maximum total return. It invests primarily in securities of U.S.  companies that
have significant sales from international operations.

*    Only available through the purchase of Guardian  Investor,  a tax deferred,
     variable annuity, or Value Plus, 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           Price Waterhouse LLP
ACCOUNTANTS           1177 Avenue of the Americas
                      New York, NY 10036

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

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

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


                                                                       VLF805010



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