VALUE LINE CONVERTIBLE FUND INC
N-30D, 1997-06-30
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<PAGE>
- --------------------------------------------------------------------------------
 
<TABLE>
<S>                    <C>
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
SERVICING AGENT        Co.
                       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
                       Charles E. Reed
                       Paul Craig Roberts
                       Nancy-Beth Sheerr
 
OFFICERS               Jean Bernhard Buttner
                       CHAIRMAN AND PRESIDENT
                       Christopher Bischof
                       VICE PRESIDENT
                       Richard Cunniffe
                       VICE PRESIDENT
                       David T. Henigson
                       VICE PRESIDENT and
                       SECRETARY/TREASURER
                       Jack M. Houston
                       ASSISTANT SECRETARY/TREASURER
                       Stephen La Rosa
                       ASSISTANT SECRETARY/TREASURER
</TABLE>
 
         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 TRUST (OBTAINABLE FROM THE DISTRIBUTOR).
 
                                                                       VLF704040
 
                      ------------------------------------
 
                                 ANNUAL  REPORT
                      ------------------------------------
                                 APRIL 30, 1997
                    ----------------------------------------
 
                                   VALUE LINE
                                  CONVERTIBLE
                                   FUND, INC.
 
                                     [LOGO]
<PAGE>
VALUE LINE CONVERTIBLE FUND, INC.
 
                                                               TO OUR VALUE LINE
- -------------------------------------------
 
TO OUR SHAREHOLDERS:
 
We are pleased to report that the total return for the Value Line Convertible
Fund, Inc. (the "Fund") for the 12 months ended April 30, 1997 was 8.80%.
 
The stock market continued to move ahead during the Fund's latest fiscal year,
however, blue chip stocks easily outperformed smaller issues. The disparity
between the two market segments is most evident when comparing the 28.5%
increase in the Dow Jones Industrial Average with the 5.4% increase in the
NASDAQ Composite Index over the same period. When we last wrote to you in
December, we expressed our concerns about the uneven showing of the equity
markets as well as the volatility of interest rates. Thus, we stated our
intention to remain defensive through the end of the fiscal year, which we did.
Such a strategy involves focusing on the current yield and the downside
protection a security offers. In the convertible sector, the best execution of
this approach is to obtain the maximum downside protection at the smallest
possible cost of upside participation.
 
In making investment decisions, your Fund relies on the Value Line Timeliness
Ranking System, introduced in 1965. We have also begun to use the new
Performance Ranking System, which was developed for the "Expanded Edition" of
the Value Line Investment Survey. The stock ranks provided by these systems are
incorporated in the Value Line Convertible Ranking System, which identifies
attractively priced convertibles that can be exchanged for favorably ranked
stocks. Nevertheless, strength in the prices of many equities has made finding
attractively priced convertibles more difficult. At this writing, your Fund has
over 30% of its assets in cash, with the balance in convertible bonds and
preferred stocks. There are no common stocks in the Fund as of the date of this
letter.
 
For now, we intend to keep our defensive posture toward the equity markets.
Since your Fund seeks income and appreciation, we will sell those convertibles
whose prices have risen sufficiently to turn them into common-stock equivalents
and purchase convertibles with greater downside protection. In our view, this
approach will allow investors to shed some equity-market risk while maintaining
reasonable participation in further price rises if our stance proves to be
overly conservative.
 
We thank you for your interest in the Value Line Convertible Fund, and we look
forward to serving your investment needs in the future.
 
                Sincerely,
 
                                                          [SIGNATURE]
 
                Jean Bernhard Buttner
                CHAIRMAN AND PRESIDENT
 
May 29, 1997
 
- --------------------------------------------------------------------------------
 
2
<PAGE>
                                               VALUE LINE CONVERTIBLE FUND, INC.
 
CONVERTIBLE FUND SHAREHOLDERS
- -------------------------------------------
 
ECONOMIC OBSERVATIONS
 
The current economic expansion is now in its seventh year. Although this does
not yet qualify as the longest peacetime period of growth in our nation's
history (both the 1960s and the 1980s experienced somewhat longer upcycles), it
is still quite noteworthy, especially since there are as yet few signs that this
lengthy run of uninterrupted prosperity is about to draw to a close. In fact,
recent reports show that there is still a good deal of strength around, with
high doses of consumer confidence, continuing solid job growth, and healthy
levels of retail, housing, and manufacturing activity pointing to relatively
good levels of economic growth over the next few quarters.
 
Inflation, meanwhile, continues to be reasonably subdued. This healthy pricing
trend, which is remarkable given the longevity of the business expansion, is,
moreover, unlikely to change dramatically in the months ahead. Underscoring our
optimism in this area is the recent hammering out of a presumably workable
budget accord (which should reduce the government's need to borrow to finance
the deficit) and the fact that there is still a lack of serious shortages on
either the labor or the raw materials fronts. On this latter score, though, we
do note that the recent pickup in wage pressures could, if unchecked, pose a
threat later in the year or in 1998.
 
Interest rates, meantime, reflecting the likely moderate pace of upcoming
economic growth and the fairly subdued pricing structure, are unlikely to
increase all that much over the next year. Nevertheless, we caution that recent
remarks by Federal Reserve Chairman Alan Greenspan, in which he indicated that
the central bank has, in the past, occasionally raised rates before higher
inflation actually took hold, and the one-quarter of a percentage point increase
in short-term interest rates that was tacked on in March, would seem to suggest
that the Fed will not be shy about tightening the credit reins further, if it
sees the need. An additional upward move in rates, if sufficiently pronounced,
would not be good news for either the stock or the bond markets, or, ultimately,
for the U.S. economy.
 
PERFORMANCE DATA:*
 
<TABLE>
<CAPTION>
                                               GROWTH OF
                                 AVERAGE      AN ASSUMED
                              ANNUAL TOTAL    INVESTMENT
                                 RETURN       OF $10,000
                              -------------  -------------
<S>                           <C>            <C>
 1 year ended 3/31/97.......       10.58%      $  11,058
 5 years ended 3/31/97......       12.31%      $  17,868
10 years ended 3/31/97......        9.43%      $  24,622
</TABLE>
 
*  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, 1997 FOR THE ONE-YEAR, FIVE-YEAR AND 10-YEAR PERIODS WERE 8.80%,
   12.74%, AND 9.78%.
 
- --------------------------------------------------------------------------------
 
                                                                               3
<PAGE>
VALUE LINE CONVERTIBLE FUND, INC.
 
CONVERTIBLE FUND SHAREHOLDERS
- -------------------------------------------
 
EDGAR REPRESENTATION OF DATA POINTS USED IN PRINTED GRAPHIC
 
<TABLE>
<CAPTION>
COMPARISON OF A CHANGE IN VALUE OF A $10,000 INVESTMENT IN
                           THE
  VALUE LINE CONVERTIBLE FUND AND THE S&P 500 INDEX (+)
                                                            VALUE LINE CONVERTIBLE  S&P 500 INDEX
<S>                                                         <C>                     <C>
4/88                                                                       9213.59         9366.82
4/89                                                                      10842.21        11500.41
4/90                                                                       10897.9        12701.11
4/91                                                                      11985.61         14932.3
4/92                                                                      13953.26        17030.39
4/93                                                                      16487.22        18500.46
4/94                                                                      17394.77        19590.46
4/95                                                                      18531.24        23002.61
4/96                                                                      23362.11        29934.36
4/97                                                                      25416.65        37451.04
</TABLE>
 
                             From 5/1/87 to 4/30/97
 
+  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, 1997
- -------------------------------------------
 
<TABLE>
<CAPTION>
 PRINCIPAL
  AMOUNT                                                                                            VALUE
<C>          <S>                                                                                 <C>
- ------------------------------------------------------------------------------------------------------------
CONVERTIBLE CORPORATE BONDS & NOTES (42.8%)
             BANK (2.2%)
$ 1,500,000  First State Bancorporation 7 1/2%, 4/30/17........................................  $ 1,537,500
 
             COMPUTER & PERIPHERALS (2.0%)
  1,000,000  SCI Systems, Inc. 5%, 5/1/06*.....................................................    1,370,000
 
             DIVERSIFIED COMPANIES (1.9%)
    750,000  Berkshire Hathaway Inc. 1%, 12/2/01...............................................      733,125
    500,000  GenCorp, Inc. 8%, 8/1/02..........................................................      597,500
                                                                                                 -----------
                                                                                                   1,330,625
 
             DRUG (1.9%)
  3,000,000  ALZA Corp., zero coupon, 7/14/14..................................................    1,305,000
 
             ELECTRICAL EQUIPMENT (2.1%)
  1,275,000  MagneTek Inc., 8%, 9/15/01........................................................    1,416,843
 
             ENVIRONMENTAL (1.8%)
  1,250,000  United States Filter Corp. 4 1/2%, 12/15/01.......................................    1,228,125
 
             HOTEL/GAMING (1.2%)
    500,000  Marriott International, Inc. zero coupon, 3/25/11*................................      284,375
  1,000,000  Marriott International, Inc. zero coupon, 3/25/11.................................      568,750
                                                                                                 -----------
                                                                                                     853,125
 
             INSURANCE-DIVERSIFIED (1.9%)
  3,000,000  Mutual Risk Management Ltd. zero coupon, 10/30/15*................................    1,305,000
 
             INSURANCE-LIFE (1.7%)
    500,000  Penn Treaty American Corp. 6 1/4%, 12/1/03*.......................................      571,250
    500,000  Penn Treaty American Corp. 6 1/4%, 12/1/03........................................      571,250
                                                                                                 -----------
                                                                                                   1,142,500
 
             INSURANCE-PROPERTY/CASUALTY (1.6%)
  2,000,000  Fremont General Corp. zero coupon, 10/12/13.......................................    1,075,000
 
             MACHINERY (0.9%)
    500,000  Robbins & Meyers, Inc. 6 1/2%, 9/1/03.............................................      590,000
</TABLE>
 
- --------------------------------------------------------------------------------
 
                                                                               5
<PAGE>
VALUE LINE CONVERTIBLE FUND, INC.
 
SCHEDULE OF INVESTMENTS
- -------------------------------------------
<TABLE>
<CAPTION>
 PRINCIPAL
  AMOUNT                                                                                            VALUE
- ------------------------------------------------------------------------------------------------------------
<C>          <S>                                                                                 <C>
             MEDICAL SERVICES (2.7%)
$ 1,000,000  NovaCare, Inc. 5 1/2%, 1/15/00....................................................  $   907,500
  1,000,000  PhyCor, Inc. 4 1/2%, 2/15/03......................................................      940,000
                                                                                                 -----------
                                                                                                   1,847,500
 
             METALS & MINING-DIVERSIFIED (2.1%)
  1,365,000  INCO Ltd. 7 3/4%, 3/15/16.........................................................    1,431,544
 
             NATURAL GAS-DIVERSIFIED (1.4%)
  1,000,000  Enserch Corp. 6 3/8%, 4/1/02......................................................      986,250
 
             OILFIELD SERVICES/EQUIPMENT (3.0%)
  1,750,000  Baker Hughes, Inc. zero coupon, 5/5/08............................................    1,319,063
    500,000  Key Energy Group, Inc. 7 1/2%, 7/1/03*............................................      729,375
                                                                                                 -----------
                                                                                                   2,048,438
 
             R.E.I.T. (3.7%)
    500,000  Camden Property Trust 7.33%, 4/1/01...............................................      565,625
  1,000,000  Capstone Capital Corp. 6.55%, 3/14/02.............................................      913,750
  1,000,000  Developers Diversified Realty Co. 7%, 8/15/99.....................................    1,073,750
                                                                                                 -----------
                                                                                                   2,553,125
 
             RETAIL-SPECIAL LINES (0.6%)
    500,000  Michaels Stores, Inc. 6 3/4%, 1/15/03.............................................      425,000
 
             RETAIL STORE (2.8%)
  2,000,000  Costco Wholesale Corp. 5 3/4%, 5/15/02............................................    1,960,000
 
             TELECOMMUNICATION SERVICES (5.5%)
  2,750,000  Comcast Cellular Corp. zero coupon, 3/5/00........................................    2,028,125
  1,000,000  Midcom Communications, Inc. 8 1/4%, 8/15/03*......................................      847,500
  1,500,000  Winstar Communications, Inc. zero coupon, 10/15/05* (zero coupon until 10/15/00,
               14% thereafter).................................................................      900,000
                                                                                                 -----------
                                                                                                   3,775,625
 
             OTHER (1.8%)
  1,250,000  Republic of Italy-Istituto Nazional delle Assicurazioni Sp.A, 5%, 6/28/01.........    1,225,000
                                                                                                 -----------
 
             TOTAL CONVERTIBLE CORPORATE BONDS & NOTES (COST $28,806,408)......................   29,406,200
                                                                                                 -----------
</TABLE>
 
- --------------------------------------------------------------------------------
 
6
<PAGE>
                                               VALUE LINE CONVERTIBLE FUND, INC.
 
                                                                  APRIL 30, 1997
- -------------------------------------------
 
<TABLE>
<CAPTION>
  SHARES                                                                                            VALUE
<C>          <S>                                                                                 <C>
- ------------------------------------------------------------------------------------------------------------
CONVERTIBLE PREFERRED STOCKS (18.7%)
             BANK (3.6%)
     20,000  BCP International Ltd. $4.00 exchangeable series "A" Pfd..........................  $ 1,145,000
     50,000  National Australia Bank, Ltd. Cap units exchangeable Pfd.+........................    1,325,000
                                                                                                 -----------
                                                                                                   2,470,000
 
             CEMENT & AGGREGRATES (1.9%)
     22,000  Southdown, Inc., $2.875 Series "D"................................................    1,325,500
 
             COAL/ALTERNATE ENERGY (0.2%)
      3,000  AES Trust I, 5 3/8%, Series "A"...................................................      163,875
 
             ENTERTAINMENT (1.0%)
     15,000  SFX Broadcasting, Inc. 6 1/2%, exchangeable Series "D" Pfd........................      663,750
 
             FINANCIAL SERVICES (0.5%)
     10,000  Dynex Capital, Inc. 9.73% Series "C" Pfd..........................................      305,000
 
             FOREIGN TELECOMMUNICATIONS (1.5%)
     20,000  Philippine Long Distance Telephone Co. $3.50 Global Depositary Shares(1)..........    1,050,000
 
             HOTEL/GAMING (0.8%)
     20,000  FelCor Suite Hotels, Inc., $1.95 Series "A".......................................      570,000
 
             NATURAL GAS-DIVERSIFIED (0.9%)
     27,000  Kelly Oil & Gas Corp. $2.625 exchangeable Pfd.....................................      607,500
 
             PAPER & FOREST PRODUCTS (1.4%)
     20,000  James River Corp. of Virginia Series "K" exchangeable $3.375 Pfd..................      987,500
 
             R.E.I.T. (2.1%)
     30,000  Criimi Mae, Inc. 10 7/8%, Series "B"..............................................    1,061,250
     14,000  Excel Realty Trust, Inc. $2.125 Series "A" Pfd....................................      357,000
                                                                                                 -----------
                                                                                                   1,418,250
 
             RETAIL STORE (0.8%)
     10,000  K-Mart Financing, Inc. 7 3/4%, Pfd................................................      576,250
 
             TELECOMMUNICATION EQUIPMENT (0.1%)
      1,100  General Datacomm Industries, Inc. 9% exchangeable Pfd.*...........................       21,450
 
             TELECOMMUNICATION SERVICES (2.4%)
     20,000  WorldCom, Inc. 8%, Depository Shares(2)...........................................    1,670,000
</TABLE>
 
- --------------------------------------------------------------------------------
 
                                                                               7
<PAGE>
VALUE LINE CONVERTIBLE FUND, INC.
 
SCHEDULE OF INVESTMENTS                                           APRIL 30, 1997
- -------------------------------------------
 
<TABLE>
<CAPTION>
 SHARES OR
 PRINCIPAL
  AMOUNT                                                                                            VALUE
<C>          <S>                                                                                 <C>
- ------------------------------------------------------------------------------------------------------------
             OTHER (1.5%)
     10,000  IXC Communications, Inc. 7 1/4%, Jr Pfd.*.........................................  $   975,000
                                                                                                 -----------
 
             TOTAL CONVERTIBLE PREFERRED STOCKS (COST $12,102,456).............................   12,804,075
                                                                                                 -----------
 
             TOTAL INVESTMENT SECURITIES (61.5%) (COST $40,908,864)............................   42,210,275
                                                                                                 -----------
 
REPURCHASE AGREEMENTS (34.9%) (including accrued interest)
 
$12,000,000  Collateralized by $11,150,000 U.S. Treasury Note 8 1/2%, due 11/15/00, with a
               value of $12,257,088 (With Morgan Stanley & Co., Inc., 5.30%, dated 4/30/97, due
               5/1/97, delivery value $12,001,766).............................................   12,001,766
 12,000,000  Collateralized by $12,210,000 U.S. Treasury Note 6%, due 9/30/98, with a value of
               $12,243,340 (With First Chicago Capital Markets, Inc., 5.33%, dated 4/30/97 due
               5/1/97, delivery value $12,001,777).............................................   12,001,777
                                                                                                 -----------
 
             TOTAL REPURCHASE AGREEMENTS (COST $24,003,543)....................................   24,003,543
                                                                                                 -----------
 
CASH AND RECEIVABLES OVER LIABILITIES (3.6%)...................................................    2,469,987
                                                                                                 -----------
 
NET ASSETS (100.0%)............................................................................  $68,683,805
                                                                                                 -----------
                                                                                                 -----------
 
NET ASSET VALUE, OFFERING AND REDEMPTION PRICE PER OUTSTANDING SHARE ($68,683,805  DIVIDED BY
5,255,497 SHARES OUTSTANDING)..................................................................  $     13.07
                                                                                                 -----------
                                                                                                 -----------
</TABLE>
 
*  PURSUANT TO RULE 144A UNDER THE SECURITIES ACT OF 1933, THIS SECURITY CAN
   ONLY BE SOLD TO QUALIFIED INSTITUTIONAL INVESTORS.
 
+  NON INCOME PRODUCING
 
R.E.I.T. -- REAL ESTATE INVESTMENT TRUST
 
(1)REPRESENTS 1 SHARE OF SERIES III CONV PFD.
 
(2)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, 1997
- ------------------------------------------------------------------------
 
<TABLE>
<S>                                                                  <C>
ASSETS:
Investment securities, at value
  (Cost--$40,908,864)..............................................  $42,210,275
Repurchase agreements
  (Cost--$24,003,543)..............................................   24,003,543
Cash...............................................................       15,935
Receivable for securities sold.....................................    9,054,904
Interest and dividends receivable..................................      366,705
Receivable for capital shares sold.................................       68,061
                                                                     -----------
 
    TOTAL ASSETS...................................................   75,719,423
                                                                     -----------
 
LIABILITIES:
Payable for securities purchased...................................    6,168,678
Payable for capital shares repurchased.............................      783,059
Accrued expenses:
  Advisory fee.....................................................       41,746
  Other............................................................       42,135
                                                                     -----------
    TOTAL LIABILITIES..............................................    7,035,618
                                                                     -----------
 
NET ASSETS.........................................................  $68,683,805
                                                                     -----------
                                                                     -----------
NET ASSETS CONSIST OF:
Capital stock, at $1.00 par value (authorized 50,000,000,
  outstanding 5,255,497 shares)....................................  $ 5,255,497
Additional paid-in capital.........................................   60,156,266
Undistributed investment income--net...............................      440,565
Accumulated net realized gain on investments.......................    1,530,066
Unrealized net appreciation of investments.........................    1,301,411
                                                                     -----------
    NET ASSETS.....................................................  $68,683,805
                                                                     -----------
                                                                     -----------
NET ASSET VALUE, OFFERING AND REDEMPTION PRICE PER OUTSTANDING
  SHARE ($68,683,805  DIVIDED BY 5,255,497 SHARES OUTSTANDING).....  $     13.07
                                                                     -----------
                                                                     -----------
</TABLE>
 
STATEMENT OF OPERATIONS
FOR THE YEAR ENDED APRIL 30, 1997
- ----------------------------------
 
<TABLE>
<S>                                                                  <C>
INVESTMENT INCOME:
Interest...........................................................  $ 3,457,570
Dividends
   (Net of foreign withholding tax of $11,288).....................      653,341
                                                                     -----------
    Total Income...................................................    4,110,911
                                                                     -----------
 
EXPENSES:
Advisory fee.......................................................      517,810
Auditing and legal fees............................................       41,149
Transfer agent.....................................................       39,711
Registration and filing fees.......................................       26,771
Printing and stationery............................................       20,209
Custodian fees.....................................................       17,873
Directors' fees and expenses.......................................       13,895
Postage............................................................       10,523
Telephone..........................................................        7,764
Insurance, dues and other..........................................        6,203
                                                                     -----------
    Total Expenses Before Custody Credits..........................      701,908
    Less: Custody Credits..........................................       (7,964)
                                                                     -----------
    Total Expenses.................................................      693,944
                                                                     -----------
 
INVESTMENT INCOME--NET.............................................    3,416,967
                                                                     -----------
 
REALIZED AND UNREALIZED GAIN (LOSS) ON INVESTMENTS--NET:
  Realized Gain--Net...............................................    7,919,219
  Change in Unrealized Appreciation................................   (5,752,019)
                                                                     -----------
NET REALIZED GAIN AND CHANGE IN UNREALIZED APPRECIATION ON
  INVESTMENTS......................................................    2,167,200
                                                                     -----------
NET INCREASE IN NET ASSETS FROM OPERATIONS.........................  $ 5,584,167
                                                                     -----------
                                                                     -----------
</TABLE>
 
SEE NOTES TO FINANCIAL STATEMENTS.
 
- --------------------------------------------------------------------------------
 
                                                                               9
<PAGE>
VALUE LINE CONVERTIBLE FUND, INC.
 
STATEMENT OF CHANGES IN NET ASSETS
FOR THE YEARS ENDED APRIL 30, 1997 AND 1996
- ------------------------------------------------------------------------
 
<TABLE>
<CAPTION>
                                                  YEAR ENDED       YEAR ENDED
                                                APRIL 30, 1997   APRIL 30, 1996
<S>                                             <C>              <C>
                                                -------------------------------
OPERATIONS:
  Investment income--net......................  $   3,416,967     $  2,958,285
  Realized gain on investments--net...........      7,919,219        4,046,566
  Change in unrealized appreciation...........     (5,752,019)       6,409,849
                                                -------------------------------
  Net increase in net assets from
  operations..................................      5,584,167       13,414,700
                                                -------------------------------
 
DISTRIBUTIONS TO SHAREHOLDERS:
  Investment income--net......................     (3,158,289)      (3,024,424)
  Realized gains on investments...............     (7,350,053)              --
                                                -------------------------------
  Total distributions.........................    (10,508,342)      (3,024,424)
                                                -------------------------------
 
CAPITAL SHARE TRANSACTIONS:
  Net proceeds from sale of shares............     95,369,317       52,653,026
  Net proceeds from reinvestment of
  distributions to shareholders...............      8,470,140        2,474,940
  Cost of shares repurchased..................   (102,851,591)     (43,421,496)
                                                -------------------------------
  Increase from capital share transactions....        987,866       11,706,470
                                                -------------------------------
TOTAL (DECREASE) INCREASE.....................     (3,936,309)      22,096,746
 
NET ASSETS:
  Beginning of year...........................     72,620,114       50,523,368
                                                -------------------------------
  End of year.................................  $  68,683,805     $ 72,620,114
                                                -------------------------------
                                                -------------------------------
 
UNDISTRIBUTED INVESTMENT INCOME--NET,
  AT END OF YEAR..............................  $     440,565     $    181,887
                                                -------------------------------
                                                -------------------------------
</TABLE>
 
SEE NOTES TO FINANCIAL STATEMENTS.
 
- --------------------------------------------------------------------------------
 
10
<PAGE>
                                               VALUE LINE CONVERTIBLE FUND, INC.
 
NOTES TO FINANCIAL STATEMENTS                                     APRIL 30, 1997
- -------------------------------------------
 
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.
 
Distributions are determined in accordance with income tax regulations, which
may differ from generally accepted accounting principles.
 
(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, 1997
- -------------------------------------------
 
2. CAPITAL SHARE TRANSACTIONS.
 
Transactions in capital stock were as follows:
 
<TABLE>
<CAPTION>
                             FOR THE      FOR THE
                           YEAR ENDED   YEAR ENDED
                              1997         1996
<S>                        <C>          <C>
                           ------------------------
Shares sold..............   6,848,012    3,953,152
Shares issued to
  shareholders in
  reinvestment of
  dividends..............     640,516      194,152
                           ------------------------
                            7,488,528    4,147,304
Shares repurchased.......   7,382,823    3,281,081
                           ------------------------
Net increase.............     105,705      866,223
                           ------------------------
                           ------------------------
</TABLE>
 
3. PURCHASES AND SALES OF SECURITIES
 
Purchases and sales of investment securities, excluding short-term securities,
were as follows:
 
<TABLE>
<CAPTION>
                                            1997
<S>                                      <C>
                                         -----------
PURCHASES:
Investment Securities..................  $86,439,175
                                         -----------
                                         -----------
SALES OR REDEMPTIONS:
Investment Securities..................  $56,966,210
                                         -----------
                                         -----------
</TABLE>
 
At April 30, 1997, the aggregate cost of investment securities and repurchase
agreements securities for Federal income tax purposes was $64,912,407. The
aggregate appreciation and depreciation of investments at April 30, 1997, based
on a comparison of investment values and their costs for Federal income tax
purposes, was $2,081,552 and $780,141, respectively, resulting in a net
appreciation of $1,301,411.
 
4. INVESTMENT ADVISORY CONTRACT, MANAGEMENT FEES, AND TRANSACTIONS WITH
   AFFILIATES
 
An advisory fee of $517,810 was paid or payable to Value Line, Inc. (the
Adviser), for the year ended April 30, 1997. This was computed at the annual
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 62,518 shares of the Fund's
capital stock, representing 1.2% of the outstanding shares at April 30, 1997.
 
- --------------------------------------------------------------------------------
 
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,
                                               -------------------------------------------------------
                                                 1997          1996       1995       1994       1993
<S>                                            <C>           <C>        <C>        <C>        <C>
                                               -------------------------------------------------------
 
NET ASSET VALUE, BEGINNING OF YEAR...........  $ 14.10       $ 11.79    $ 12.26    $ 13.80    $ 12.24
                                               -------------------------------------------------------
   INCOME (LOSS) FROM INVESTMENT OPERATIONS:
      Net investment income..................      .70           .66        .74        .71        .62
      Net gains or losses on securities
        (both realized and unrealized).......      .50          2.33       (.02)       .11       1.54
                                               -------------------------------------------------------
      Total from investment operations.......     1.20          2.99        .72        .82       2.16
                                               -------------------------------------------------------
 
   LESS DISTRIBUTIONS:
      Dividends from investment
         income--net.........................     (.65)         (.68)      (.76)      (.69)      (.60)
      Distributions from capital gains.......    (1.58)           --       (.43)     (1.67)        --
                                               -------------------------------------------------------
      Total distributions....................    (2.23)         (.68)     (1.19)     (2.36)      (.60)
                                               -------------------------------------------------------
NET ASSET VALUE, END OF YEAR.................  $ 13.07       $ 14.10    $ 11.79    $ 12.26    $ 13.80
                                               -------------------------------------------------------
                                               -------------------------------------------------------
TOTAL RETURN.................................     8.80%        26.07%      6.53%      5.50%     18.16%
                                               -------------------------------------------------------
                                               -------------------------------------------------------
 
RATIOS/SUPPLEMENTAL DATA:
Net assets, end of year (in thousands).......  $68,684       $72,620    $50,523    $49,823    $43,936
Ratio of expenses to average net assets......     1.01%(1)      1.08%      1.08%      1.07%      1.10%
Ratio of net investment income
  to average net assets......................     4.94%         5.14%      6.13%      5.32%      4.80%
Portfolio turnover rate......................      164%          129%        87%       142%       146%
Average commissions paid per share of stock
  investments purchased/sold.................  $ .0500(2)        N/A        N/A        N/A        N/A
</TABLE>
 
(1)BEFORE CUSTODY CREDITS.
 
(2)DISCLOSURE EFFECTIVE FOR FISCAL YEARS BEGINNING ON OR AFTER 9/1/95.
 
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, 1997, 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, 1997 by correspondence with the custodian and brokers and the application of
alternative auditing procedures where confirmations from brokers were not
received, provide a reasonable basis for the opinion expressed above.
 
PRICE WATERHOUSE LLP
1177 AVENUE OF THE AMERICAS
NEW YORK, NY 10036
June 13, 1997
 
                 FEDERAL TAX STATUS OF DISTRIBUTIONS (UNAUDITED)
      FOR CORPORATE TAXPAYERS 8.76% OF THE ORDINARY INCOME DISTRIBUTIONS PAID
                      DURING THE CALENDAR YEAR 1996
          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.
 
1992--VALUE LINE INTERMEDIATE BOND FUND seeks high current income consistent
with low volatility of principal by investing primarily in a diversified
portfolio of investment-grade debt securities.
 
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 correct
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. READ THE PROSPECTUS CAREFULLY BEFORE YOU INVEST OR
SEND MONEY.
 
- --------------------------------------------------------------------------------
 
16


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