BURNHAM FUND INC
N-30D, 1999-02-25
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                                     [LOGO]
 
                                                                February 9, 1999
 
DEAR SHAREHOLDERS:
 
We are pleased to present to you the Annual Report of The Burnham Fund for 1998.
 
BURNHAM FUND YEAR END DATA
- --------------------------------------------------------------------------------

On December 31, 1998, The Burnham Fund's net asset value per share for Class A,
B and C shares was $34.31, $35.21 and $34.55, which represent total returns for
the year of 22.08%, 21.17%, and 21.82%, respectively. In comparison, the average
growth and income fund, according to Morningstar Inc., was up 17.77% for the
year.
 
For the year, The Burnham Fund Class A, B and C shares paid $2.03, $1.81 and
$1.81, respectively in taxable dividends per share. Of this amount, $0.24, $0.02
and $0.02 per share were from ordinary income and $1.79 from capital gains for
all share classes.
 
FOURTH QUARTER/YEAR END REVIEW
- --------------------------------------------------------------------------------
 
All domestic equity market indices showed strength in the fourth quarter after
disastrous performance in the third quarter. In the fourth quarter, the S&P 500
increased 21.3%, and the average growth and income fund, according to
CDA/Wiesenberger was up 16.8%. The Large Blend average, according to Morningstar
was up 19.9%. For the fourth quarter, The Burnham Fund Class A, B and C shares
increased 21.1%, 20.9% and 20.8%, respectively.
 
Investors shrugged off the four major crises that caused the severe market
decline in the third quarter: the Russian/Asian/Latin American financial
debacle, newsworthy hedge fund illiquidity, the Iraq impasse, and Presidential
impeachment proceedings. Despite these problems, investors demonstrated in the
fourth quarter that they are steadfast in their optimism about the U.S. economy.
In the fourth quarter, GDP rose 5.6%, up from 3.7% in the third quarter,
Personal Consumption rose, Unemployment dropped slightly, Worker Productivity
increased, and Hourly Wages rose. As expected, capacity utilization dropped
marginally, due to lower orders and deliveries of manufactured goods. Economic
indicators released on February 4, 1999 show that the domestic durable goods
sector (auto and housing-related, for example) improved at the end of the year,
but sluggish global demand is still affecting the export-sensitive heavy
industry sector. The Consumer Price Index fell further to an annualized rate of
1.8% vs. a 2.3% annualized rate over the last three years, impacted by continued
weakness in energy prices (crude oil and derivatives), flat food prices, and
lower computer equipment prices.
 
For the year, the most rewarding sectors of the markets were Computers (of any
sort -- peripherals, networking, software and services), Specialty Retail,
Communications Equipment, and Health Care. The Burnham Fund benefited from
investments in all of these sectors; some of our stronger performing stocks
included Dell Computer Corp., Lucent Technologies, Cisco Systems Inc., Gap Inc.,
Microsoft Corp., Pfizer Inc., Wal-mart Stores Inc. and Intel Corp. Merger
activity picked up its pace in the fourth quarter of the year, and several of
our investments were affected. America Online announced its acquisition of
Netscape, Exxon with Mobil, and Lucent with Ascend Communications. Contrary to
this trend, the merger of Monsanto and American Home Products (which we opposed)
was terminated, and we re-established our position in Monsanto at favorable
prices.
 
OUTLOOK FOR 1999
- --------------------------------------------------------------------------------

We start the year with optimism. In our last report, we saw a "silver lining"
in the turmoil of the third quarter, which has materialized into strong
fundamentals for the current year. The two reductions in Fed Funds rates greatly
calmed the domestic capital markets. We do not believe the Fed will raise
interest rates this year. The IMF has been refunded, and the Japanese government
is working to "reflate" its economy. We believe that the
 




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[LOGO]
 
Asian crisis is past its worst stages, and recovery in that region is likely to
occur over the course of the next few years. Europe, consolidating economically
under the Euro, will show strength in the years ahead, posing increased
competition against United States companies for both business, and also
investment capital. We believe corporate profits will continue to grow, but
investors will continue to favor those companies with unit volume and revenue
growth. Those companies with export exposure and commodity-based products will
struggle under global competitive pressures caused by the lower dollar. However,
a lower dollar also improves earnings comparisons for U.S. firms that sell
products overseas. We are not concerned about the presidential impeachment
hearings as far as the market is concerned, because we believe that the economy
will move forward regardless of its outcome. We caution that the U.S. markets
may still be sensitive to economic disruption in Latin American countries, and
emerging markets.
 
With this outlook as the foundation for new and existing investments in The
Burnham Fund, we continue to focus on the technology, telecommunications,
pharmaceutical and financial services sector. These groups are beneficiaries of
trends in which we have participated over the past several years: the
demographic changes in our country, the movement toward a service-based economy
and the value-added nature of technology to corporate productivity. Selected new
positions to the fund in the last quarter are examples of such companies. We
initiated a position in McGraw Hill because we believe the company's textbook
division will benefit from increased enrollment trends in elementary schools
nationwide. National and local initiatives are in place to improve English
language and Mathematical programs and test scores, which point to above
trendline textbook sales. As mentioned above, we re-established our position in
Monsanto, because we believe that its new anti-inflammatory (arthritis) drug
Celebrex has the potential to reach $1 billion in sales. This drug is marketed
by Pfizer -- viewed by analysts to be the most effective distributor in the
pharmaceutical industry. (The Fund also has a sizable position in Pfizer, which
markets other major drugs, and has its own strong drug pipeline.) The
fund initiated a position in Gap, Inc. during its autumn correction. We believe
that the company's rapidly growing Old Navy division and its web site will boost
revenue to above its historic growth rates. Continuing in the speciality retail
arena, we purchased Barnes & Noble, the traditional and internet book retailer
that has 15% of industry sales and is experiencing revenue growth of over 20%.
We believe that its association with America Online (which we also own) and
Bertelsmann will improve its competitive position vs. Amazon.com, and lead to a
higher p/e ratio.
 
We still have significant positions in the energy sector, which proved to be
disappointing during the past year. During 1998 we reduced our investments in
this sector, because of continuing weakness in crude prices. We have owned these
positions for many years and our cost bases are low. We believe that long term,
patient investors will enjoy high total returns from above average dividends,
and the potential for earnings leverage that may result from the global
corporate restructuring activity over the past year. Oil prices are likely to
stabilize or increase as economic activity in the Pacific Rim improves. Bank
stocks were also disappointing in the second half of the year as trading and
credit losses worked their way through their income statements. The banks in
which we invest are predominantly domestic, nevertheless, they were affected by
negative industry sentiment. We believe that 1999 will be a better year for this
group, unless there is another round of credit shocks. Financial services stocks
may show better returns in 1999.
 
As of this writing, the S&P 500 stands at approximately 24x 1999 estimates,
which is at the high end of its valuation range of the last several years. We
are positive toward equities at this time, but caution that volatility will
remain in the market, particularly in the internet related sectors which have
experienced extreme speculative attention in recent months. We continue to hold
and look for opportunities to invest in companies with earnings growth potential
of at least 15% to 20% per year for three to five years, product leadership,
innovative management with a shareholder-value orientation, superior financial
underpinnings, and a healthy dividend

                                      2

 




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                                                                          [LOGO]
 
history (when pertinent). We also search for companies whose stock is
undervalued relative to its past, or those which may benefit from restructuring
actions. We also seek companies with little or no exposure to Asia and/or Latin
America, or where the exposure is well understood or opportunistic. We are also
monitoring Year 2000 issues as they affect our investments, and to the extent to
which companies in the Fund are on track with their Y2k planning.
 
Portfolio Manager Jon Burnham continues his monthly appearances on CNBC, CNN/fn
and Bloomberg. If you would like to be notified by fax of his appearances
beforehand, please call our toll free number, 1-800-874-FUND and we would be
happy to include you on our fax broadcast of his schedule.

We appreciate your confidence in The Burnham Fund, and look forward to serving
your investment needs in the year ahead.
 
Very truly yours,

<TABLE>
<S>                              <C>
I.W. Burnham, II                                 Jon M. Burnham,
I.W. Burnham, II                                 Jon M. Burnham,
Chairman                                             President &
                                               Portfolio Manager
</TABLE>

<TABLE>
<CAPTION>
                                            CUMULATIVE PERFORMANCE COMPARISON

                                                     CUMULATIVE % CHANGE                   AVERAGE ANNUALIZED % CHANGE
                                       -------------------------------------------       ------------------------------------------

                                        1 YR       3 YR        5 YR        10 YR          1 YR        3 YR        5 YR      10 YR
                                       ------     -------     -------     -------        ------      ------      ------    --------
<S>                                     <C>        <C>         <C>         <C>            <C>         <C>         <C>       <C>
DOW JONES INDUSTRIAL AVERAGE            18.13%      89.86%     173.10%     457.87%        18.13%      23.83%      22.25%    18.76%
STANDARD & POOR'S 500 INDEX             28.58%     110.80%     193.73%     479.15%        28.58%      28.22%      24.05%    19.20%
MORNINGSTAR LARGE CAP BLEND AVERAGE     21.59%      87.80%     144.09%     365.07%        21.59%      23.38%      19.54%    16.61%
MORNINGSTAR GROWTH & INCOME AVERAGE     17.77%      82.51%     138.96%     338.95%        17.77%      22.21%      19.03%    15.94%
LEHMAN BROTHERS GOVERNMENT/CORPORATE
 BOND INDEX                              9.47%      23.63%      42.26%     144.09%         9.47%       7.33%       7.30%     9.33%
AVERAGE 3-MONTH U.S. TREASURY BILL       4.80%      15.74%      26.87%      66.59%         4.80%       4.99%       4.87%     5.23%
</TABLE>
 
The investment return and principal value of an investment will fluctuate so
that an investor's shares, when redeemed, may be worth more or less than their
original cost. Average total return for Class A shares, assuming the
reinvestment of dividends and excluding the maximum sales charge for the one,
five and ten year periods ended December 31, 1998 were 22.08%, 16.97% and
13.88%, respectively. Such performance assuming the imposition of the Class A
shares' maximum 5% sales charge for the same periods would have been 15.98%,
15.77% and 13.30%, respectively. For Class B and C shares, average total return
for the one and five year periods ended December 31, 1998 were 21.16%, 16.18%
and 21.83%, 16.27%, respectively. For Class B and C shares, average life of
class return for the period October 18, 1993 (inception date) to December 31,
1998 were 15.27% and 15.40%, respectively. Class B shares bear a maximum
contingent deferred sales charge of 5% if they are redeemed within the first
year of purchase. Such performance assuming the imposition of the contingent
deferred sales charge of 4% for the one and five year periods ended December 31,
1998, and life of class were 17.16%, 16.07% and 15.06%, respectively. Class C
shares bear a maximum contingent deferred sales charge at a rate of 1% if they
are redeemed within the first year of purchase.
 
                                      3








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[LOGO]
 
COMPARISON OF PERFORMANCE TO CERTAIN MARKET INDICES
- --------------------------------------------------------------------------------
 
Although the Fund's investment objectives do not include matching or exceeding
the performance of any securities-related index, the line graph set forth below
may be viewed as useful in that it enables an investor to compare the
performance of the Fund to certain securities-related market indices. The line
graph includes performance information relating to the Standard & Poor's 500
Index, a broad-based stock market index which is comprised of a large, unmanaged
"basket" of stocks.
 
Since the Fund is a managed investment vehicle, and its investment policies
permit it to invest in debt securities, convertible securities, warrants and
options, the Fund may be able to reduce the volatility and downside risk
inherent in an investment in an index comprised exclusively of equity
securities. In addition, the line graph sets forth information regarding the
Lehman Brothers Government/Corporate Bond Index, an index reflecting the
broad-based bond market, as well as, the average quarterly return of the 3-month
US Treasury Bills.
 
                             [COMPARISON GRAPH]

            Comparison of Change in value of $10,000 Investment
                  in the Fund to Certain Market Indices



                                  S&P 500 INDEX
<TABLE>


<S>                     <C>

DATE                     VALUE

DEC-88                  $10.000
MAR-89                  $10.707
JUN-89                  $11.652
SEP-89                  $12.900
DEC-89                  $13.167
MAR-90                  $12.771
JUN-90                  $13.573
SEP-90                  $11.707
DEC-90                  $12.756
MAR-91                  $14.610
JUN-91                  $14.576
SEP-91                  $15.356
DEC-91                  $16.643
MAR-92                  $16.224
JUN-92                  $16.532
SEP-92                  $17.050
DEC-92                  $17.909
MAR-93                  $18.695
JUN-93                  $18.784
SEP-93                  $19.268
DEC-93                  $19.716
MAR-94                  $18.969
JUN-94                  $19.048
SEP-94                  $19.978
DEC-94                  $19.975
MAR-95                  $21.920
JUN-95                  $24.012
SEP-95                  $25.920
DEC-95                  $27.481
MAR-96                  $28.955
JUN-96                  $30.253
SEP-96                  $31.189
DEC-96                  $33.790
MAR-97                  $34.695
JUN-97                  $40.753
SEP-97                  $48.309
DEC-97                  $45.068
MAR-98                  $51.355
JUN-98                  $53.052
SEP-98                  $47.777
DEC-98                  $57.948
</TABLE>

<PAGE>

                                  THE BURNHAM FUND


<TABLE>
<S>                   <C>

DATE                   VALUE

DEC-88                $ 9.500
MAR-89                $10.020
JUN-89                $10.570
SEP-89                $11.181
DEC-89                $11.663
MAR-90                $11.264
JUN-90                $11.462
SEP-90                $11.028
DEC-90                $11.456
MAR-91                $12.109
JUN-91                $12.008
SEP-91                $12.614
DEC-91                $13.515
MAR-92                $13.330
JUN-92                $13.339
SEP-92                $13.972
DEC-92                $14.556
MAR-93                $15.049
JUN-93                $15.185
SEP-93                $15.958
DEC-93                $15.920
MAR-94                $15.817
JUN-94                $15.338
SEP-94                $15.902
DEC-94                $15.636
MAR-95                $16.304
JUN-95                $17.325
SEP-95                $18.111
DEC-95                $19.459
MAR-96                $20.159
JUN-96                $20.923
SEP-96                $20.285
DEC-96                $22.884
MAR-97                $23.762
JUN-97                $25.283
SEP-97                $27.150
DEC-97                $28.543
MAR-98                $30.322
JUN-98                $32.000
SEP-98                $28.784
DEC-98                $34.850

</TABLE>
<PAGE>



                    LEHMAN BROTHERS CORP/GOVT BOND INDEX
<TABLE>

<S>                    <C>

DATE                    VALUE

DEC-88                 $10.000
MAR-89                 $10.109
JUN-89                 $10.921
SEP-89                 $11.024
DEC-89                 $11.422
MAR-90                 $11.292
JUN-90                 $11.698
SEP-90                 $11.768
DEC-90                 $12.369
MAR-91                 $12.703
JUN-91                 $12.894
SEP-91                 $13.636
DEC-91                 $14.363
MAR-92                 $14.147
JUN-92                 $14.722
SEP-92                 $15.440
DEC-92                 $15.451
MAR-93                 $16.171
JUN-93                 $16.658
SEP-93                 $17.209
DEC-93                 $17.159
MAR-94                 $16.620
JUN-94                 $16.414
SEP-94                 $16.496
DEC-94                 $16.557
MAR-95                 $17.382
JUN-95                 $18.508
SEP-95                 $18.862
DEC-95                 $19.741
MAR-96                 $19.279
JUN-96                 $19.369
SEP-96                 $19.712
DEC-96                 $20.316
MAR-97                 $20.141
JUN-97                 $20.872
SEP-97                 $21.602
DEC-97                 $22.296
MAR-98                 $22.635
JUN-98                 $23.226
SEP-98                 $24.375
DEC-98                 $24.405

</TABLE>

<PAGE>

            AVERAGE 3-MONTH U.S. TREASURY BILL RATE

<TABLE>
DATE                   VALUE 

<S>                    <C>
DEC-88                 $10.000
MAR-89                 $10.185
JUN-89                 $10.407
SEP-89                 $10.618
DEC-89                 $10.820
MAR-90                 $11.013
JUN-90                 $11.231
SEP-90                 $11.450
DEC-90                 $11.660
MAR-91                 $11.825
JUN-91                 $11.995
SEP-91                 $12.161
DEC-91                 $12.315
MAR-92                 $12.435
JUN-92                 $12.553
SEP-92                 $12.659
DEC-92                 $12.754
MAR-93                 $12.846
JUN-93                 $12.938
SEP-93                 $13.035
DEC-93                 $13.129
MAR-94                 $13.223
JUN-94                 $13.349
SEP-94                 $13.484
DEC-94                 $13.635
MAR-95                 $13.805
JUN-95                 $14.003
SEP-95                 $14.192
DEC-95                 $14.391
MAR-96                 $14.560
JUN-96                 $14.742
SEP-96                 $14.928
DEC-96                 $15.116
MAR-97                 $15.305
JUN-97                 $15.495
SEP-97                 $15.696
DEC-97                 $15.894
MAR-98                 $16.088
JUN-98                 $16.286
SEP-98                 $16.488
DEC-98                 $16.656

</TABLE>

In making any of these comparisons, it should be understood that the performance
of a market index is not adjusted to reflect the brokerage expenses that would
be incurred in purchasing and selling the securities comprising the index, and
does not include the management fees and other expenses that are generally
incurred in investing through mutual funds.
 
The performance information set forth on the line graph is based on a $10,000
investment made as of December 31, 1988, and reflects changes in value through
the 10-year period to December 31, 1998. Performance for The Burnham Fund Class
A shares is based on the imposition of a maximum initial sales charge of 5%.
Performance for other classes of the Fund will be greater or less than the line
graph shown based on the differences in sales charges and fees paid by
shareholders investing in the different classes of the Fund. Average annualized
total returns for Class B and C shares for the one, five and life of class
(inception date -- October 18, 1993), assuming the imposition of contingent
deferred sales charges were 17.16% and 21.83%, 16.07% and 16.27% and 15.06% and
15.29%, respectively.
 
PERFORMANCE ANALYSIS SECTION
- --------------------------------------------------------------------------------
 
Jon M. Burnham, Portfolio Manager of the Fund, believed that equities had a
positive total return potential for 1998. For the four quarters of 1998,
consecutively, the Fund returned 11.5%, 4.4%, (13.4%) and 21.1%. The
Morningstar, Inc. Large Blend Index, which represents its peer group, returned
consecutively, 12.5%, 1.8%, (11.4%) and 20.0%, totaling 21.8% for the year.
 
The Burnham Fund modestly underperformed its peer index in the first and third
quarters of 1998. The Fund's manager believes this first quarter was due to its
overweighted positions in Energy and REIT equities, which were subsequently
reduced. In the third quarter, the Fund was negatively impacted by the market's
extreme volatility, and poor relative performance in the financial services and
technology sectors, which are overweighted in the portfolio. Additionally, the
Investment Committee decided to become temporarily defensive, raising a higher
cash position until the global financial crisis stabilized. The Fund
outperformed its peer index in the second and fourth quarters of the year due to
strong performance in technology-related, communications and health care
equities. The Fund also benefited from various corporate merger and acquisition
activity during the year in core positions. The Fund believes its focus on
disciplined growth investing, as opposed to its historical value orientation led
it to outperform its peer group for the year, and narrow the underperformance it
had experienced in prior years.

                                      4



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                                                                          [LOGO]
 
                             INVESTMENT PERSPECTIVE
 
                         EQUITY PORTFOLIO DISTRIBUTION
                           by Industry Classification
                               December 31, 1998

<TABLE>
<CAPTION>
                                            % Total
                                        Equity Portfolio
                                        ----------------
<S>                                     <C>
Computer Products & Software..........        18.70%
Banking...............................         9.84%
Energy -- Oil & Gas Refining..........         9.18%
Pharmaceuticals.......................         8.40%
Telecommunications Network &
  Services............................         8.35%
Automotive............................         5.67%
Financial Services....................         4.99%
Real Estate Investment Trusts.........         4.49%
Telecommunications Equipment..........         3.82%
Other.................................        26.56%
                                             -------
Total Equities........................       100.00%
                                             -------
                                             -------
</TABLE>
 
                  TOTAL PORTFOLIO DISTRIBUTION BY ASSET CLASS
                               December 31, 1998

                                  [PIE CHART]

<TABLE>

<S>                                 <C>
CASH & CASH EQUIVALENTS               7%
CONVERTIBLE PREFERRED STOCKS          1%
CORPORATE & CONVERTIBLE BONDS         2%
COMMON STOCKS                        90%

</TABLE>


TOP 10 EQUITY HOLDINGS
December 31, 1998

<TABLE>
<CAPTION>
                              Number of                  % of
                               Shares       Value     Net Assets
                              ---------  -----------  ----------
<S>                           <C>        <C>          <C>
The Bank of New York Co.,
  Inc. ......................  160,000   $ 6,440,000     4.03%
Citigroup Inc. ..............  120,000   $ 5,940,000     3.72%
Cisco Systems Inc. ..........   60,000   $ 5,570,625     3.49%
Microsoft Corp. .............   40,000   $ 5,541,250     3.47%
Lucent Technologies Inc. ....   50,000   $ 5,500,000     3.44%
Ford Motor Company...........   90,000   $ 5,281,875     3.31%
Exxon Corporation............   70,000   $ 5,118,750     3.20%
Pfizer Inc. .................   40,000   $ 5,017,500     3.14%
Intel Corp. .................   40,000   $ 4,741,250     2.97%
International Business
  Machines Corp. ............   25,000   $ 4,618,750     2.89%
                                         -----------  ----------
TOP 10 EQUITY HOLDINGS                   $53,770,000    33.66%
                                         -----------  ----------
                                         -----------  ----------
</TABLE>


                         [CUMULATIVE RETURN GRAPH]

                             CUMULATIVE RETURN
                  OF A HYPOTHETICAL $10,000 INVESTMENT*
                     from inception (June 15, 1975)
                      through December 31, 1998

                         The Burnham Fund - Class A

                                    Value of hypothetical investment
                                      on December 31, 1998: $219,679

                              Life of Fund
                         Cumulative Percent Return:
                                          2,096.79%
                    Annual Compound Rate of Return:
                                             14.00%

$10,000 investment on June 15, 1975
(inception date).

<TABLE>
<S>            <C>
1975           $  9.792
1976           $ 12.130
1977           $ 11.656
1978           $ 13.168
1979           $ 16.265
1980           $ 21.777
1981           $ 21.220
1982           $ 25.928
1983           $ 29.066
1984           $ 31.166
1985           $ 41.191
1986           $ 50.170
1987           $ 53.524
1988           $ 59.883
1989           $ 73.520
1990           $ 72.217
1991           $ 85.195
1992           $ 91.758
1993           $100.355
1994           $ 98.565
1995           $122.663
1996           $144.252
1997           $179.923
1998           $219.679


</TABLE>

 
* All performance analyses shown herein represent past performance and are not
  indicative of future performance. All dividends and distributions from income
  and capital gains have been continually reinvested. Performance does not
  include the imposition of the maximum 5% sales charge. Performance for other
  classes of the Fund will be greater or less than the data shown in the graph
  and tables based on differences in sales charges and fees paid by shareholders
  investment in the different classes of the Fund.
 
                         AVERAGE ANNUAL TOTAL RETURN
                        Period ended December 31, 1998
 
<TABLE>
<S>                             <C>
One Year......................  22.08%
Five Years....................  16.97%
Ten Years.....................  13.88%
Fifteen Years.................  14.44%
Twenty Years..................  15.11%
</TABLE>

                                      5









<PAGE>

<PAGE>



[LOGO]
 
                       REPORT OF INDEPENDENT ACCOUNTANTS
 
            TO THE SHAREHOLDERS AND BOARD OF DIRECTORS OF
            THE BURNHAM FUND INC.:
 
                 In our opinion, the accompanying statement of
            assets and liabilities, the statement of net assets, and
            the related statement of operations and of changes of
            net assets and financial highlights presents fairly, in
            all material respects, the financial position of The
            Burnham Fund, as of December 31, 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 presented, 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
            audit. We conducted our audit 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
            audit, which included confirmation of securities owned
            at December 31, 1998 by correspondence with the
            custodian and brokers, provide a reasonable basis for
            the opinion expressed above.
 
            NEW YORK, NEW YORK            PRICEWATERHOUSECOOPERS LLP
            FEBRUARY 12, 1999
 
                                       6









<PAGE>

<PAGE>


                                                                          [LOGO]
 
                            STATEMENT OF NET ASSETS
                               December 31, 1998
<TABLE>
<CAPTION>
                                      NUMBER OF
                                        SHARES       VALUE
- --------------------------------------------------------------
<S>                                   <C>         <C>
COMMON STOCKS                  90.09%

AEROSPACE                       0.75%
  General Motors Corporation
    Class H..........................    30,000a  $  1,190,625
                                                  ------------
AIR FREIGHT                     1.11%
  FDX Corporation. ..................    20,000a     1,780,000
                                                  ------------
AUTOMOTIVE                      5.11%
  DaimlerChrysler Corporation........    30,000      2,881,875
  Ford Motor Company.................    90,000      5,281,875
                                                  ------------
                                                     8,163,750
                                                  ------------
BANKING                         8.87%
  The Bank of New York Co., Inc. ....   160,000      6,440,000
  Citigroup Inc. ....................   120,000      5,940,000
  Fleet Financial Group Inc. ........    40,000      1,787,500
                                                  ------------
                                                    14,167,500
                                                  ------------
BROADCASTING                    0.82%
  CBS Corp. .........................    40,000      1,310,000
                                                  ------------
COMPUTER PRODUCTS & SOFTWARE   16.85%
  BMC Software Inc. .................    25,000a     1,114,844
  Cisco Systems Inc. ................    60,000a     5,570,625
  Compaq Computer Corp. .............    40,000      1,677,500
  Dell Computer Corp. ...............    30,000a     2,196,562
  EMC Corp. .........................    25,000a     2,125,000
  International Business Machines
    Corp. ...........................    25,000      4,618,750
  Microsoft Corp. ...................    40,000a     5,541,250
  Siebel Systems Inc. ...............   120,000a     4,072,500
                                                  ------------
                                                    26,917,031
                                                  ------------
COMPUTERS - DATA PROCESSING     2.00%
  America Online Inc. ...............    20,000a     3,200,000
                                                  ------------
CONSUMER PRODUCTS               3.14%
  Blyth Industries Inc. .............    30,000a       937,500
  General Electric Co. ..............    40,000      4,082,500
                                                  ------------
                                                     5,020,000
                                                  ------------
DIVERSIFIED CHEMICALS           0.89%
  Monsanto Co. ......................    30,000      1,425,000
                                                  ------------

ENGINEERING/INDUSTRIAL
  PRODUCTION                    0.06%
  Thermolyte Corporation ............    10,000ab      100,000
                                                  ------------
ENERGY - OIL & GAS REFINING     8.27%
  Amoco Corp. .......................    10,000   $    603,750
  British Petroleum PLC ADS..........    20,000      1,792,500
  Conoco Inc. .......................    30,000a       626,250
  Exxon Corporation..................    70,000      5,118,750
  Mobil Corporation..................    40,000      3,485,000
  Texaco Inc. .......................    30,000      1,586,250
                                                  ------------
                                                    13,212,500
                                                  ------------
FINANCIAL SERVICES              4.50%
  American Express Co. ..............    40,000      4,090,000
  Associates First Capital Corp......    60,000      2,542,500
  Webster Financial Corporation......    20,000        549,375
                                                  ------------
                                                     7,181,875
                                                  ------------
FOOD AND BEVERAGE PRODUCTS      3.10%
  American Italian Pasta Co. ........   100,000a     2,637,500
  The Coca Cola Company..............    20,000      1,337,500
  Ralston Purina Co. ................    30,000        971,250
                                                  ------------
                                                     4,946,250
                                                  ------------
HEALTHCARE FACILITIES           0.74%
  Rehabcare Group Inc. ..............    63,400a     1,184,788
                                                  ------------
INSURANCE                       1.93%
  Allstate...........................    80,000      3,090,000
                                                  ------------
OIL DRILLING                    1.62%
  Diamond Offshore Drilling Inc. ....    70,000      1,658,125
  Schlumberger Ltd. .................    20,000        922,500
                                                  ------------
                                                     2,580,625
                                                  ------------
PASSENGER CRUISE LINES          0.90%
  Carnival Corp. ....................    30,000      1,440,000
                                                  ------------
PHARMACEUTICALS                 7.57%
  Merck & Co. .......................    25,000      3,692,188
  Pfizer Inc. .......................    40,000      5,017,500
  Warner Lambert Inc. ...............    45,000      3,383,437
                                                  ------------
                                                    12,093,125
                                                  ------------
PUBLISHING                      0.32%
  McGraw-Hill Cos., Inc. ............     5,000        509,375
                                                  ------------
</TABLE>

                  See notes to financial statements.

                                  7


 




<PAGE>

<PAGE>



[Logo]
                            STATEMENT OF NET ASSETS
                               December 31, 1998
<TABLE>
<CAPTION>
                                      NUMBER OF
                                        SHARES       VALUE
- --------------------------------------------------------------
<S>                                   <C>         <C>
REAL ESTATE INVESTMENT
  TRUSTS                        4.05%
  Chateau Communities Inc. ..........    40,000   $  1,172,500
  Developers Diversified Realty
    Corp. ...........................    60,000      1,065,000
  Franchise Finance Corp. ...........    70,000      1,680,000
  Golf Trust of America..............    45,000      1,248,750
  National Golf Properties, Inc. ....    45,000      1,302,187
                                                  ------------
                                                     6,468,437
                                                  ------------
RETAIL STORES                   2.70%
  Barnes & Noble Inc. ...............    30,000a     1,275,000
  GAP, Inc. .........................    25,000      1,406,250
  Wal Mart Stores Inc. ..............    20,000      1,628,750
                                                  ------------
                                                     4,310,000
                                                  ------------
SECURITY SERVICES               0.86%
  Kroll-O'Gara Co. ..................    35,000a     1,378,125
                                                  ------------
SEMICONDUCTORS                  2.97%
  Intel Corp. .......................    40,000      4,741,250
                                                  ------------
TELECOMMUNICATION EQUIPMENT     3.44%
  Lucent Technologies Inc. ..........    50,000      5,500,000
                                                  ------------
TELECOMMUNICATIONS NETWORK
  AND SERVICES                  7.52%
  ECI Telecom Ltd. ..................    60,000      2,124,375
  GTE Corp. .........................    40,000      2,600,000
  Qwest Communications International
    Inc..............................    50,000a     2,498,437
  SBC Communications Inc. ...........    60,000      3,217,500
  Telephone & Data Systems Inc. .....    35,000      1,572,813
                                                  ------------
                                                    12,013,125
                                                  ------------
  TOTAL COMMON STOCKS
    (cost: $77,914,420)..............              143,923,381
                                                  ------------
CONVERTIBLE PREFERRED
  SECURITIES                    1.44%

PASSENGER CRUISE LINES          1.44%
  Royal Caribbean Cruises,
    Conv. Preferred Cl. `A'..........    20,000      2,300,000
                                                  ------------
  TOTAL CONVERTIBLE PREFERRED
    SECURITIES (cost: $1,084,100)....                2,300,000
                                                  ------------

CORPORATE CONVERTIBLE BONDS     0.78%

DATA PROCESSING                 0.78%
  Adaptec, Inc. 4.75% sub. notes
    Conv. 2/1/04..................... $1,000,000  $    777,500
  Data General Corp., 6% sub. notes
    5/15/04..........................   500,000        471,875
                                                  ------------
  TOTAL CORPORATE CONVERTIBLE BONDS
    (cost: $1,271,000)...............                1,249,375
                                                  ------------
CORPORATE BONDS                 0.86%

HOTELS                          0.86%
  Host Marriott Corp., 9.375% senior
    notes 6/15/07.................... 1,265,000      1,371,893
                                                  ------------
  TOTAL CORPORATE BONDS (cost:
    $1,273,606)......................                1,371,893
                                                  ------------
COMMERCIAL PAPER                6.89%
  American Express Credit Corp., 6%
    01/04/99......................... 2,500,000      2,500,000
  Associates Corp. of North America
    6.03% 01/05/99................... 4,500,000      4,500,000
  General Motors Acceptance Corp.
    5.97% 01/04/99................... 4,000,000      4,000,000
                                                  ------------
  TOTAL COMMERCIAL PAPER
    (cost: $11,000,000)..............               11,000,000
                                                  ------------
TOTAL INVESTMENTS IN SECURITIES
  (cost: $92,543,126)                              159,844,649
                                                  ------------
CALL OPTIONS WRITTEN           (0.02%)
  Mobil Corp. @ 85 expiring January,
    1999............................. 100 calls        (35,000)
                                                  ------------
  TOTAL CALL OPTIONS WRITTEN
    (premium received $61,998).......                  (35,000)
                                                  ------------
TOTAL INVESTMENTS             100.04%              159,809,649
LIABILITIES LESS CASH
  AND OTHER ASSETS             (0.04%)                 (70,092)
                                                  ------------
NET ASSETS                    100.00%             $159,739,557
                                                  ------------
                                                  ------------
</TABLE>

- --------------------------------------------------------------------------------
a Non-income producing security.
b A unit consisting of one share of common stock of Thermolyte Corporation and
  one redemption right. (Note 4)
 
FEDERAL INCOME TAX BASIS OF INVESTMENT SECURITIES
For Federal income tax purposes, the tax basis of investment securities owned at
December 31, 1998 was $92,739,869. The aggregate gross unrealized appreciation
for all securities in which there was an excess of value over tax cost was
$68,192,813 and aggregate gross unrealized depreciation for all securities in
which there was excess of tax cost over value was $1,123,033.

                      See notes to financial statements.

                                       8









<PAGE>

<PAGE>


                                                                          [LOGO]
 
<TABLE>
<CAPTION>
               STATEMENT OF ASSETS AND LIABILITIES
                        December 31, 1998
- --------------------------------------------------------------
<S>                                               <C>
ASSETS:
  Investment in securities, at value
    (identified cost: $92,543,126) (Note 1)....   $159,844,649
  Dividends and interest receivable............        179,902
  Receivable for capital stock sold............        105,396
  Receivable from investment adviser...........         32,247
  Prepaid expenses.............................          8,525
  Other assets.................................          1,277
                                                  ------------
    Total assets...............................    160,171,996
                                                  ------------
LIABILITIES:
  Payable to custodian.........................         43,952
  Payable for capital stock redeemed...........        151,268
  Payable for options written
    (proceeds received $61,998)................         35,000
  Payable for investment advisory fees (Note
    6).........................................         79,468
  Payable for distribution and
    service fees (Note 7)......................         33,551
  Accrued expenses and other payables..........         89,200
                                                  ------------
    Total liabilities..........................        432,439
                                                  ------------
NET ASSETS.....................................    159,739,557
                                                  ------------
                                                  ------------
CLASS A SHARES
NET ASSET VALUE AND REDEMPTION PRICE PER SHARE
  (NOTE 2): ($156,735,682/4,567,585) shares
  outstanding).................................   $      34.31
                                                  ------------
                                                  ------------
CALCULATION OF MAXIMUM OFFERING PRICE
SALES CHARGE - 5% of public offering price:
  (Note 2): ($34.31 net asset value plus 5.0%
  of public offering price)....................   $      36.12
                                                  ------------
                                                  ------------
CLASS B SHARES
NET ASSET VALUE AND OFFERING PRICE PER SHARE:
  (NOTE 2): ($2,408,018/68,383) shares
  outstanding).................................   $      35.21
                                                  ------------
                                                  ------------
CLASS C SHARES
NET ASSET VALUE AND OFFERING PRICE PER SHARE:
  (NOTE 2): ($595,857/17,247) shares of
  capital stock outstanding)...................   $      34.55
                                                  ------------
                                                  ------------
Redemption price per share varies with the
length
of time Class B and C shares are held. (Note 7)
NET ASSETS CONSISTED OF:
  Capital paid-in..............................   $ 84,021,092
  Undistributed net investment income..........        181,652
  Accumulated net realized gains
    on investments.............................      8,208,292
  Net unrealized appreciation of investments...     67,328,521
                                                  ------------
                                                  $159,739,557
                                                  ------------
                                                  ------------
 
<CAPTION>
                    STATEMENT OF OPERATIONS
                  Year ended December 31, 1998
- ---------------------------------------------------------------
<S>                                                <C>
INVESTMENT INCOME:
  INCOME:
    Dividends...................................    $ 2,218,914
    Interest....................................        869,988
                                                    -----------
      Total income..............................      3,088,902
                                                    -----------
  EXPENSES:
    Investment advisory fees (Note 6)...........        905,674
    Distribution fee (Class A) (Note 7).........        287,261
    Distribution fee (Class B) (Note 7).........         15,193
    Distribution fee (Class C) (Note 7).........          2,327
    Service fees (Class B & C) (Note 7).........          5,839
    Transfer agent fees.........................        194,433
    Professional fees...........................        216,730
    Reports to shareholders.....................        116,721
    Directors' fees and expenses................         81,588
    Custodian fees..............................         34,809
    Registration fees and expenses..............         59,257
    Insurance expense...........................         13,140
    Miscellaneous expense.......................         45,760
                                                    -----------
      Total expenses before reimbursement.......      1,978,732
      Less: Expenses voluntarily reimbursed
         by Investment Adviser (Note 6).........        (32,247)
                                                    -----------
      Total expenses after reimbursement........      1,946,485
                                                    -----------
         Net investment income..................      1,142,417
                                                    -----------
                                                    -----------
NET REALIZED AND UNREALIZED GAIN ON INVESTMENTS:
  Realized gain from securities and options
    transactions
      Proceeds from sales.........   $83,692,941
      Cost of securities sold.....   (75,696,033)
                                     -----------
    Net realized gain from securities
      transactions..............................      7,996,908
                                                    -----------
  Increase in unrealized
    appreciation of investments
      Beginning of year...........   $46,975,277
      End of year.................    67,328,521
                                     -----------
  Increase in unrealized appreciation...........     20,353,244
                                                    -----------
Net realized and unrealized
  gain on investments...........................     28,350,152
                                                    -----------
Net increase in net assets resulting
  from operations...............................    $29,492,569
                                                    -----------
                                                    -----------
</TABLE>

                       See notes to financial statements.

                                    9



 




<PAGE>

<PAGE>



[LOGO]
 
                       STATEMENT OF CHANGES IN NET ASSETS
<TABLE>
<CAPTION>
                                    Year ended      Year ended
                                   December 31,    December 31,
                                       1998            1997
- ---------------------------------------------------------------
<S>                                <C>             <C>
INCREASE IN NET ASSETS:
  FROM OPERATIONS:
  Net investment income.........   $ 1,142,417     $ 2,087,255
  Net realized gain from
    security and option
    transactions................     7,996,908       7,595,669
  Increase in unrealized
    appreciation of
    investments.................    20,353,244      18,745,136
                                   ------------    ------------
  Net increase in net assets
    resulting from operations...    29,492,569      28,428,060
                                   ------------    ------------
DISTRIBUTIONS TO SHAREHOLDERS
  (NOTE 1):
  From net investment income:
    Class A Shares..............    (1,482,009)     (2,041,644)
    Class B Shares..............        (3,373)        (12,430)
    Class C Shares..............          (361)           (122)
  From realized gains from
    security and option
    transactions:
    Class A Shares..............    (7,404,378)     (5,310,408)
    Class B Shares..............       (85,434)        (45,808)
    Class C Shares..............        (5,196)           (152)
                                   ------------    ------------
      Total distributions to
         shareholders...........    (8,980,751)     (7,410,564)
                                   ------------    ------------
CAPITAL SHARE TRANSACTIONS
  (NOTE 2):
  Net proceeds from sale of
    shares......................     4,634,280       2,286,944
  Net asset value of shares
    issued to shareholders in
    reinvestment of dividends...     7,867,717       6,428,892
                                   ------------    ------------
                                    12,501,997       8,715,836
  Cost of shares redeemed.......   (11,425,490)    (10,050,186)
                                   ------------    ------------
  Increase (decrease) in net
    assets derived from
    capital share
    transactions................     1,076,507      (1,334,350)
                                   ------------    ------------
  Increase in net assets
    for the year................    21,588,325      19,683,146
                                   ------------    ------------
NET ASSETS:
  Beginning of year.............   138,151,232     118,468,086
                                   ------------    ------------
  End of year (including
    undistributed net invest-
    ment income of $181,652 and
    $593,535, respectively).....   $159,739,557    $138,151,232
                                   ------------    ------------
                                   ------------    ------------
</TABLE>

              See notes to financial statements.

                         NOTES TO FINANCIAL STATEMENTS
                               December 31, 1998
 
NOTE 1 -- SIGNIFICANT ACCOUNTING POLICIES
 
The Burnham Fund Inc. ("Fund") is registered under the Investment Company Act of
1940, as amended (the "1940 Act"), as a diversified, open-end management
investment company.
 
The Fund offers three classes of shares. Class A shares are sold with a
front-end sales charge of up to 5.0%. Class B shares are sold with a contingent
deferred sales charge of 5.0% which declines to zero for purchases held for more
than six years. Class C shares are sold with a contingent deferred sales charge
of 1.0%, which declines to zero if held for more than one year.
 
The following is a summary of significant accounting policies consistently
followed by the Fund in the preparation of its financial statements. The
policies are in conformity with generally accepted accounting principles.
 
A. Security valuation -- Investments in securities traded, or in options
purchased, on a national securities exchange are valued at the last reported
sales price on the primary exchange on which they are traded on the last
business day of the period. Securities traded in the over-the-counter market
(including securities listed on exchanges whose primary market is believed to be
over-the-counter) and listed securities for which no sale was reported on that
date are valued at the mean between the last reported bid and asked prices.
Short-term money market instruments which have a maturity of more than 60 days
are valued at prices based on market quotations for securities of similar type,
yield and maturity. Short-term money market instruments which have a maturity of
60 days or less are valued at amortized cost which approximates value.
 
B. Repurchase agreements -- Securities held as collateral for repurchase
agreements are held by the Federal Reserve Bank and are designated as being held
for the Fund's behalf by its custodian under the book-entry system. The Fund
monitors the adequacy of the collateral (U.S. Government securities) daily and
can require the seller to provide additional collateral in the event the market
value of the securities pledged falls below 102% of the carrying value of the
repurchase agreement.

                                      10

 




<PAGE>

<PAGE>


                                                                          [LOGO]
 
C. Federal income taxes -- It is the Fund's intent to qualify each year as a
'regulated investment company' under Subchapter M of the Internal Revenue Code.
By so qualifying, the Fund will not be subject to Federal income taxes to the
extent that its net investment income and net realized capital gains are
distributed.
 
D. Other -- Security transactions are accounted for on the date the securities
are purchased or sold. Interest income is recorded on the accrual basis and
dividend income on the ex-dividend date. Dividends and distributions to
shareholders are recorded on the ex-dividend dates.
 
The Fund may periodically make reclassifications among certain of its capital
accounts as a result of the timing and characteristics of certain income and
capital gains distributions determined annually in accordance with Federal tax
regulations which may differ from generally accepted accounting principles.
During 1998, the Fund decreased undistributed net investment income by $68,557
and increased accumulated net realized gains on investments by $68,557.
 
E. Expenses -- Expenses that are attributable to a specific class of shares will
be charged to that class. Fund-level expenses will be allocated daily based upon
the relative percentage of net assets of each class of shares.
 
F. Management's Use of Estimates -- The preparation of financial statements in
conformity with generally accepted accounting principles requires management to
make estimates and assumptions that affect the reported amounts of assets and
liabilities at the date of the financial statements and the reported amounts of
income and expenses during the reporting period. Actual results could differ
from those estimates.

G. Option Writing -- When the Fund writes a covered call option, the amount
received is included in the Statement of Assets and Liabilities as an asset and
an equivalent liability. The liability is subsequently marked to market to
reflect the current value of the option written. When a call option expires or
when the Fund enters into a closing purchase transaction, the Fund will
recognize a gain or (loss) without regard to any unrealized gain or loss on the
underlying security. When a call option is exercised, the proceeds from the
delivery of the underlying security are increased by the amount originally
received and the resulting gain or loss is recorded by the Fund.
 
Transactions in written options for the year ended December 31, 1998 were as
follows:

<TABLE>
<CAPTION>
                                          Number
                                            of
                                          Options      Premiums
                                          -------    ----------
<S>                                      <C>         <C>
Options written at December 31,
  1997...............................         0              0
Options written......................      (400)     ($222,042)
Options canceled in closing purchase
  transactions.......................       300        160,044
                                        ---------     --------
Options outstanding at December 31,
  1998...............................      (100)       $61,998
                                        ---------     --------
                                        ---------     --------
</TABLE>
 
The cost of canceling options in closing transactions was $214,775 resulting in
a net realized capital loss of $54,731.
 
NOTE 2 -- CAPITAL STOCK
 
At December 31, 1998, there were 40,000,000 shares of capital stock ($0.10 par
value) authorized, divided into four classes designated Class A, B, C and D
shares. At December 31, 1998, Class D shares were not issued.
 
Transactions in capital stock for the year ended 1998 and year ended 1997 for
Class A, B and C shares were as follows:


<TABLE>
<CAPTION>
                                                                                       Year ended                Year ended
                                                                                          1998                      1997
                                                                                 ----------------------    -----------------------
                                                                                  Shares       Amount       Shares       Amount
                                                                                 --------    ----------    --------    -----------
<S>                                                                              <C>         <C>           <C>         <C>
CLASS A SHARES
Shares sold...................................................................    118,079    $3,768,093      70,028    $ 1,866,407
Shares issued to shareholders in
  reinvestment of distributions...............................................    272,850     7,773,525     256,708      6,371,152
                                                                                 --------    ----------    --------    -----------
                                                                                  390,929    11,511,618     326,736      8,237,559
Shares redeemed...............................................................   (364,848)   11,898,527    (363,191)   (10,016,451)
                                                                                 --------    ----------    --------    -----------
Net increase (decrease).......................................................     26,081    $  143,051     (36,455)   ($1,778,892)
                                                                                 --------    ----------    --------    -----------
                                                                                 --------    ----------    --------    -----------
</TABLE>

                                     11


 




<PAGE>

<PAGE>



[LOGO]
 
<TABLE>
<CAPTION>
                                                                                       Year ended                Year ended
                                                                                          1998                      1997
                                                                                 ----------------------    -----------------------
                                                                                  Shares       Amount       Shares       Amount
                                                                                 --------    ----------    --------    -----------
<S>                                                                              <C>         <C>           <C>         <C>
CLASS B SHARES
Shares sold...................................................................     13,771    $  427,864      11,773    $   329,687
Shares issued to shareholders in
  reinvestment of distributions...............................................      3,047        88,639       2,280         57,475
                                                                                 --------    ----------    --------    -----------
                                                                                   16,818       516,504      14,053        387,162
Shares redeemed...............................................................       (848)      (26,909)     (1,130)       (32,979)
                                                                                 --------    ----------    --------    -----------
Net increase..................................................................     15,970    $  489,595      12,923    $   354,183
                                                                                 --------    ----------    --------    -----------
                                                                                 --------    ----------    --------    -----------
CLASS C SHARES
Shares sold...................................................................     13,864       438,323       3,071         90,850
Shares issued to shareholders in
  reinvestment of distributions...............................................        196         5,553          10            265
                                                                                 --------    ----------    --------    -----------
                                                                                   14,060       443,877       3,081         91,115
Shares redeemed...............................................................         (1)          (16)        (25)          (756)
                                                                                 --------    ----------    --------    -----------
Net increase..................................................................     14,059    $  443,861       3,056    $    90,359
                                                                                 --------    ----------    --------    -----------
                                                                                 --------    ----------    --------    -----------
</TABLE>
 
NOTE 3 -- PURCHASE AND SALES OF SECURITIES
 
The aggregate cost of purchases and the proceeds from sales of securities or
maturities for the year ended December 31, 1998 were:
 
<TABLE>
<CAPTION>
                                                     Proceeds
                                   Cost of          from sales
                                  purchases       or maturities
                                --------------    --------------
<S>                             <C>               <C>
Short-term money market
  instruments................   $1,540,742,528    $1,539,149,528
Common stocks and other
  securities.................   $   73,193,338    $   83,692,941
</TABLE>
 
NOTE 4 -- RESTRICTED SECURITIES
 
A restricted security is a security which has not been registered with the U.S.
Securities and Exchange Commission pursuant to the Securities Act of 1933. The
Fund may purchase restricted securities through a private offering. These
securities cannot be sold without prior registration under the Securities Act of
1933 unless such sale is pursuant to an exemption therefrom. A secondary market
exists for certain privately placed securities. At December 31, 1998, the Fund
held a restricted security with a value aggregating $100,000, representing less
than 0.1% of the Fund's net assets. Currently, a market does not exist for the
security listed below:
 
<TABLE>
<S>        <C>                   <C>            <C>          <C>
Units           Company           Acquired        Cost         Value
- ----------------------------------------------------------------------
10,000      Thermolyte Corp.     03/16/1995     $100,000      $100,000
</TABLE>
 
This security has been valued in good faith by management.
 
NOTE 5 -- OFF-BALANCE SHEET RISK IN FINANCIAL INSTRUMENTS
 
The Fund may from time to time trade in financial instruments with off-balance
sheet risks in the normal course of its investing activities to assist in
managing exposure to various market risks. These financial instruments include
written as well as purchased options, and may involve, to a varying degree,
elements of risk in excess of the amounts recognized for financial statement
purposes. The notional or contractual amounts of these instruments represent the
investment the Fund has in particular classes of financial instruments and does
not necessarily represent the amounts potentially subject to risk. The
measurement of risks associated with these instruments is meaningful only when
all related and offsetting transactions are considered.
 
NOTE 6 -- INVESTMENT ADVISORY FEES AND OTHER TRANSACTIONS
 
Burnham Asset Management Corporation, the Investment Adviser, provides research
and statistical services and makes investment recommendations to the Fund. With
its affiliate, Burnham Securities Incorporated (the "Distributor"), the
Investment Adviser supplies a staff trained in accounting and shareholder
services to aid in the Fund's administration and day-to-day operations.

                                      12


 




<PAGE>

<PAGE>


                                                                          [LOGO]
 
The Investment Adviser receives an investment advisory fee paid monthly at an
annual rate of 5/8 of 1% of the Fund's average daily net asset values. In
addition, if in any year the Fund's operating expenses, including investment
advisory fees but excluding interest, taxes and brokerage commissions, exceed
2.5% of the first $30 million of the Fund's average net assets, 2.0% of the next
$70 million and 1.5% of the remaining average net assets, the fees to be paid to
the Investment Adviser will be reduced to the extent that such expenses exceed
such limitation. For the year ended December 31, 1998, the Fund incurred fees in
the amount of $905,674. The advisory fees and the expenses of the Fund as
defined above did not exceed the maximum allowable limitation. The Investment
Adviser has voluntarily agreed to reimburse expenses of Class A, B and C shares
in order to limit such expenses to an annual rate of 1.3%, 2.3% and 2.3%,
respectively. Accordingly, the Investment Adviser has reimbursed Class A, B and
C Shares $31,196, $879 and $172, respectively.
 
NOTE 7 -- DISTRIBUTION SERVICES AGREEMENT
 
The Distributor serves as principal distributor of Fund shares. The Fund has
adopted a Distribution Service Agreement (the "Agreement") pursuant to Rule
12b-1 under the 1940 Act for Classes A, B and C shares. Under the agreement, the
Fund pays a distribution fee, subject to certain NASD sales expense limitations
on the Distributor at an annual rate of 0.25%, 0.75% and 0.75%, respectively, of
the Fund's average daily net assets attributable to each respective class. For
the year ended December 31, 1998, Class A, B and C shares incurred fees of
$287,261, $15,193, and $2,327, respectively. Class B and C shares of the Fund
will also pay a service fee at an annual rate of 0.25% of the average daily net
assets of Class B and C shares. The service fee will be used by the Distributor
to compensate broker-dealers and other NASD members for rendering continuing,
ongoing service to Class B and C shareholders. Service fees incurred for Class B
and C shares for the year ended December 31, 1998 were $5,063 and $776,
respectively. For the year ended December 31, 1998, the Distributor earned
$102,991 in brokerage commissions from Fund transactions and $15,188 in sales
commissions from the distribution of Class A shares.
 
A contingent deferred sales charge ("CDSC") at a maximum rate of 5% is imposed
on Class B shares if an investor redeems within six years of the purchase date.
A CDSC is imposed on Class C shares at a rate of 1% if shares are redeemed
within 12 months from the date of purchase.
 
A CDSC will be imposed on the proceeds of the redemptions of Class A shares
purchased aggregating $1 million or more if they are redeemed within 24 months
of the end of the calendar month of their purchase, in an amount equal to 1% if
the redemption occurs within 12 months and .50 of 1% if the redemption occurs
within the next 12 months. No CDSC will be imposed on Class A, B and C shares
derived from reinvestment of dividends or capital gain distributions, or on
amounts which represent an increase in the value of the shareholder's account
resulting from capital appreciation above the amount paid for Class A, B and C
shares purchased during the CDSC period. Any sales charge imposed on redemptions
is paid to the Distributor. For the year ended December 31, 1998, there were
$878 in CDSC charges paid to the Distributor.
 
Certain directors and officers of the Fund are also directors, officers and/or
employees of the Investment Adviser and/or Distributor. None of the directors so
affiliated received compensation for their services as directors of the Fund.
Similarly, none of the Fund's officers received compensation from the Fund.
 
NOTE 8 -- DIVIDENDS AND DISTRIBUTIONS SUBSEQUENT TO END OF REPORTING PERIOD
 
The Fund announced a per-share distribution to shareholders of record December
31, 1998. The distribution had an ex-distribution date of January 4, 1999 and
was payable January 11, 1999.
 
The distribution was as follows:
 
<TABLE>
<CAPTION>
                                   CLASS A    CLASS B    CLASS C
- ----------------------------------------------------------------
<S>                                <C>        <C>        <C>
From net investment income......    $0.04      $0.00      $0.00
From long-term capital gains....    $1.79      $1.79      $1.79
                                   -------    -------    -------
Total distributions paid........    $1.83      $1.79      $1.79
                                   -------    -------    -------
                                   -------    -------    -------
</TABLE>

                                     13


 




<PAGE>

<PAGE>



[LOGO]
 
NOTE 9 -- SPECIAL MEETING OF FUND SHAREHOLDERS
 
On November 19, 1998, the shareholders of The Burnham Fund, Inc. (the "Fund")
voted to approve the following changes, which are expected to take effect on or
about April 30, 1999.
 
1. To reorganize the Fund from a Maryland corporation to a series of a Delaware
business trust. The reorganization will be tax-free and will not change any
shareholder's economic interest in the Fund.
 
2. To convert Class C shares of the Fund to Class A shares. Class A shares have
a lower expense ratio than Class C shares.
 
3. To amend the Fund's advisory agreement with Burnham Asset Management
Corporation to reduce the advisory fee from 0.625% to 0.60% annually of the
Fund's average net assets while also excluding non-advisory administrative
services from the services covered by the advisory agreement. Burnham Asset
Management Corporation will provide these administrative services under a
separate administration agreement for an administration fee of up to 0.15%
annually of the Fund's average net assets.
 
4. To reclassify, amend or restate some of the Fund's fundamental investment
policies and restrictions.
 
The above changes were also approved by the Fund's board of directors at a
meeting held on August 27, 1998.

                                    14










<PAGE>

<PAGE>


                         NOTES TO FINANCIAL STATEMENTS
                               December 31, 1998
 
NOTE 10 -- FINANCIAL HIGHLIGHTS
- --------------------------------------------------------------------------------
<TABLE>
<CAPTION>
                                         CLASS A SHARES                                  CLASS B SHARES
                           -------------------------------------------    ---------------------------------------------
<S>                        <C>      <C>      <C>      <C>      <C>        <C>      <C>      <C>       <C>       <C>
                            1998     1997     1996     1995     1994       1998     1997     1996      1995      1994
- -----------------------------------------------------------------------------------------------------------------------
Net Asset Value,
 Beginning of Year          $30.04   $25.65   $23.19   $19.88   $21.86     $30.75   $26.31   $23.45    $19.94    $21.84
                           --------------------------------------------------------------------------------------------
INCOME FROM INVESTMENT
 OPERATIONS
Net Investment Income
 (loss)                       0.25     0.45     0.51     0.71     0.75       0.03     0.13     0.21      0.41      0.49
Net Gains or Losses on
 Securities
 (both realized and
 unrealized)                  5.97     5.54     3.36     3.91    (1.15)      6.12     5.75     3.69      4.10     (1.04)
                           --------------------------------------------------------------------------------------------
Total from Investment
 Operations                   6.22     5.99     3.87     4.62    (0.40)      6.15     5.88     3.90      4.51     (0.55)
LESS DISTRIBUTIONS
Dividends (from net
 investment income)          (0.32)   (0.44)   (0.55)   (0.75)   (0.87)     (0.06)   (0.28)   (0.18)    (0.44)    (0.64)
Distributions from Capital
 Gains (from
 securities and options
 transactions)               (1.63)   (1.16)   (0.86)   (0.56)   (0.71)     (1.63)   (1.16)   (0.86)    (0.56)    (0.71)
                           --------------------------------------------------------------------------------------------
Total Distributions          (1.95)   (1.60)   (1.41)   (1.31)   (1.58)     (1.69)   (1.44)   (1.04)    (1.00)    (1.35)
                           --------------------------------------------------------------------------------------------
Net Asset Value, End of
 Year                       $34.31   $30.04   $25.65   $23.19   $19.88     $35.21   $30.75   $26.31    $23.45    $19.94
                           --------------------------------------------------------------------------------------------
                           --------------------------------------------------------------------------------------------
Total Return                 22.08%   24.74%   17.60%   24.45%   (1.77%)    21.16%   23.60%   17.34%    23.54%    (2.52%)
                           --------------------------------------------------------------------------------------------
RATIOS/SUPPLEMENTAL DATA
Net Assets (in $millions),
 End of Year                 156.7    136.4    117.4    112.0    101.8        2.4      1.6      1.0       0.6       0.3
                           --------------------------------------------------------------------------------------------
Ratio of Expenses (net)
 to Average Net Assets [1]     1.3%     1.1%     1.3%     1.5%     1.5%       2.1%     2.0%     2.1%      2.2%      2.3%
                           --------------------------------------------------------------------------------------------
Ratio of Net Income to
 Average Net Assets            0.8%     1.6%     2.1%     3.3%     3.7%       0.0%     0.7%     1.3%      2.5%      2.9%
                           --------------------------------------------------------------------------------------------
Portfolio Turnover Rate       54.7%    59.4%    61.5%    78.3%    87.9%      54.7%    59.4%    61.5%     78.3%     87.9%
                           --------------------------------------------------------------------------------------------
 
<CAPTION>
                                             CLASS C SHARES
                             ----------------------------------------------
                             1998'DD'  1997      1996      1995      1994
- ---------------------------------------------------------------------------
<S>                        <C>       <C>       <C>       <C>       <C>
Net Asset Value,
 Beginning of Year            $30.09   $25.69    $23.10    $19.89    $21.87
                            -----------------------------------------------
INCOME FROM INVESTMENT
 OPERATIONS
Net Investment Income
 (loss)                         0.01     0.13      0.29      0.54      0.72
Net Gains or Losses on
 Securities
 (both realized and
 unrealized)                    6.18     5.62      3.37      3.91     (1.15)
                            -----------------------------------------------
Total from Investment
 Operations                     6.19     5.75      3.66      4.45     (0.43)
LESS DISTRIBUTIONS
Dividends (from net
 investment income)            (0.10)   (0.19)    (0.21)    (0.68)    (0.84)
Distributions from Capital
 Gains (from
 securities and options
 transactions)                 (1.63)   (1.16)    (0.86)    (0.56)    (0.71)
                            -----------------------------------------------
Total Distributions            (1.73)   (1.35)    (1.07)    (1.24)    (1.55)
                            -----------------------------------------------
Net Asset Value, End of
 Year                         $34.55   $30.09    $25.69    $23.10    $19.89
                            -----------------------------------------------
                            -----------------------------------------------
Total Return                   21.83%   23.59%    16.56%    23.51%    (1.95%)
                            -----------------------------------------------
 
RATIOS/SUPPLEMENTAL DATA
Net Assets (in $millions),
 End of Year                     0.6      0.1       0.0**     0.0**       0.0**
                            -----------------------------------------------
Ratio of Expenses (net)
 to Average Net Assets [1]       2.3%     2.0%      2.2%      2.3%      1.5%
                            -----------------------------------------------
Ratio of Net Income to
 Average Net Assets               --      0.5%      1.2%      2.5%      3.6%
                            -----------------------------------------------
Portfolio Turnover Rate         54.7%    59.4%     61.5%     78.3%     87.9%
                            -----------------------------------------------
 
</TABLE>
 
** Less than $100,000 of net assets. "DD" Based on average shares outstanding.
 
[1]  Had the Investment Adviser not agreed to reimburse Class C shares for
     expenses in excess of the expense limitation described in Note 6, the
     ratios of expenses to average net assets for the years ended December 31,
     1998, 1997, 1996 and 1995 would have been 2.4%, 2.5%, 2.5% and 2.5%,
     respectively, for Class C shares. For the year ended December 31, 1998, the
     Investment Adviser reimbursed Class A and B shares for expenses in excess
     of the expense limitation described in Note 6. The ratios of expenses to
     average net assets would have been 1.3% and 2.1% respectively, had the
     Investment Adviser not agreed to reimburse expenses.









<PAGE>

<PAGE>



OFFICERS OF THE FUND
I.W. Burnham, II Chairman
Jon M. Burnham, President
    and Chief Executive Officer
Michael E. Barna, Executive Vice President
    Chief Financial Officer, Treasurer and Secretary
Debra B. Hyman, Executive Vice President
Ronald M. Geffen, Vice President
Frank A. Passantino, Vice President and
    Assistant Secretary
Louis S. Rosenthal, Vice President
 
INVESTMENT ADVISER
Burnham Asset Management Corporation
1325 Avenue of the Americas
New York, New York 10019
 
DISTRIBUTOR
Burnham Securities Incorporated
1325 Avenue of the Americas
New York, New York 10019
Telephone: 1 (800) 874-FUND
 
CUSTODIAN
Investors Fiduciary Trust Co.
801 Pennsylvania
Kansas City, Missouri 64105
 
LEGAL COUNSEL
Hale & Dorr LLP
60 State Street
Boston, Massachusetts 02109
 
TRANSFER AGENT
State Street Bank and Trust Company
225 Franklin Street
Boston, Massachusetts 02110
 
SERVICING AGENT
Boston Financial Data Services, Inc.
2 Heritage Drive
North Quincy, Massachusetts 02171
 
INDEPENDENT ACCOUNTANTS
PricewaterhouseCoopers LLP
1177 Avenue of the Americas
New York, New York 10036
 
http://www.burnhamfunds.com
 
This report has been prepared for the information of shareholders of The
Burnham Fund Inc. and is not authorized for distribution to prospective
investors unless preceded or accompanied by an effective prospectus that
includes information regarding the Fund's objectives, policies, management,
records and other information.




ANNUAL REPORT


December 31, 1998


[LOGO]


BURNHAM Securities Inc.
Principal Distributor





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