MORGAN STANLEY DEAN WITTER US GOVERNMENT MONEY MARKET TRUST
N-30D, 1999-09-28
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<PAGE>   1

MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST    Two World Trade
                                                                          Center

LETTER TO THE SHAREHOLDERS July 31, 1999                New York, New York 10048

DEAR SHAREHOLDER:

For the six-month period ended July 31, 1999, Morgan Stanley Dean Witter U.S.
Government Money Market Trust produced an annualized net investment income of
4.06 percent. As of that date, the Fund had assets in excess of $1 billion and
its average life was 62 days. The Fund's annualized yield for July was 4.12
percent.

MARKET OVERVIEW

Following a five-month period of relatively stable short-term interest rates
from January through May, 1999, upward yield pressure began to manifest itself
in June, culminating with the Federal Reserve Board's decision to raise the
federal-funds rate by 25 basis points to 5.00 percent on June 30. At the same
time, the Federal Open Market Committee (FOMC) adopted a neutral stance as to
near-term policy action. Such a posture is normal after changing the
federal-funds rate and does not preclude the FOMC from changing the rate again,
as it did at its August 25th meeting, without announcing a change in its bias.
We believe that the FOMC would be more comfortable if the real rate of economic
growth in the U.S. were to slow from the 4 percent area to a more sustainable
rate of 2.5 percent to 3 percent.

In the second quarter, GDP increased at only a 1.8 percent annual rate (down
from a 4.3 percent annual rate in the first quarter). However, during the same
time frame, consumer spending remained robust and rose at a 4.6 percent annual
rate. In addition, the Employment Cost Index, a closely watched inflation
indicator, advanced at a 4.4 percent annual rate in the second quarter.
Therefore, while there are some signs of the economy slowing on its own, we
expect that further upward short-term yield pressure could surface within the
next nine months.
<PAGE>   2
MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST

LETTER TO THE SHAREHOLDERS July 31, 1999, continued



PORTFOLIO COMPOSITION AND STRUCTURE

On July 31, 1999, approximately 99 percent of the Fund's portfolio consisted of
federal agency obligations, with the remainder invested in U.S. Treasury bills.
At the end of the period under review, approximately 88 percent of the Fund's
holdings were due to mature in less than four months. Consequently, the
portfolio is well positioned for stability of value with a very high degree of
liquidity. As always, we attempt to operate the Fund in a conservative style
without the use of derivatives or structured notes that might fluctuate
excessively with changing interest rates. The Fund continues to serve as a
useful investment for liquidity, preservation of capital and a yield that
reflects prevailing money-market conditions.

LOOKING AHEAD

At this time we anticipate some moderation in the pace of economic activity
during the second half of 1999, with a rate of inflation slightly higher than
recent levels. Investment yields available to the Fund later in 1999 are likely
to be moderately higher than the averages achieved during the first half of the
year.

On May 1, 1999, Mitchell M. Merin was named President of the Morgan Stanley Dean
Witter Funds. Mr. Merin is the President and Chief Operating Officer of Asset
Management for Morgan Stanley Dean Witter & Co. and President, Chief Executive
Officer and Director of Morgan Stanley Dean Witter Advisors Inc., the Fund's
investment manager. He also serves as Chairman, Chief Executive Officer and
Director of the Fund's distributor and transfer agent.

We appreciate your ongoing support of Morgan Stanley Dean Witter U.S. Government
Money Market Trust and look forward to continuing to serve your investment needs
and objectives.

Very truly yours,

/S/ CHARLES A. FIUMEFREDDO                         /S/ MITCHELL M. MERIN
CHARLES A. FIUMEFREDDO                             MITCHELL M. MERIN
Chairman of the Board                              President





                                       2
<PAGE>   3



MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST

PORTFOLIO OF INVESTMENTS July 31, 1999 (unaudited)

<TABLE>
<CAPTION>
                                                         ANNUALIZED
PRINCIPAL                   DESCRIPTION                     YIELD
AMOUNT IN                       AND                      ON DATE OF
THOUSANDS                  MATURITY DATE                  PURCHASE         VALUE
- -------------------------------------------------------------------------------------
<C>         <S>                                          <C>           <C>
            U.S. GOVERNMENT AGENCIES (99.6%)
$ 55,000    Federal Farm Credit Bank
             12/03/99 - 05/16/00.......................  4.78 - 5.11%  $   53,440,129
 573,144    Federal Home Loan Banks
             08/02/99 - 03/16/00.......................  4.76 - 5.29      569,021,188
 228,530    Federal Home Loan Mortgage Corp.
             08/05/99 - 11/19/99.......................  4.77 - 5.19      227,179,386
 180,000    Federal National Mortgage Assoc.
             08/24/99 - 01/18/00.......................  4.81 - 5.35      178,360,508
                                                                       --------------

            TOTAL U.S. GOVERNMENT AGENCIES
            (Amortized Cost $1,028,001,211).........................    1,028,001,211
                                                                       --------------

            U.S. GOVERNMENT OBLIGATION (0.7%)
   7,000    U.S. Treasury Bill 09/02/99
             (Amortized Cost $6,970,997)...............     4.62            6,970,997
                                                                       --------------

            REPURCHASE AGREEMENT (0.3%)
   2,640    The Bank of New York due 08/02/99 (dated
             07/30/99; proceeds $2,699,367)(a)
             (Identified Cost $2,640,226)..............     5.00            2,640,226
                                                                       --------------
            TOTAL INVESTMENTS
             (Identified Cost $1,037,612,434)(b)............. 100.6%    1,037,612,434

            LIABILITIES IN EXCESS OF CASH
             AND OTHER ASSETS................................. (0.6)       (6,363,168)
                                                              -----    --------------

            NET ASSETS....................................... 100.0%   $1,031,249,266
                                                              =====    ==============
</TABLE>

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

<TABLE>
<C>   <S>
(a)   Collateralized by $2,177,178 U.S. Treasury Bond 8.125% due
      08/15/21 valued at $2,699,367.
(b)   Cost is the same for federal income tax purposes.
</TABLE>

        SEE NOTES TO FINANCIAL STATEMENTS



                                       3
<PAGE>   4



MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST

FINANCIAL STATEMENTS

<TABLE>
<S>                                                           <C>
STATEMENT OF ASSETS AND LIABILITIES
July 31, 1999 (unaudited)
ASSETS:
Investments in securities, at value
 (identified cost $1,037,612,434)...........................  $1,037,612,434
Cash........................................................          90,001
Shares of beneficial interest sold receivable...............         280,227
Prepaid expenses and other assets...........................           9,272
                                                              --------------

    TOTAL ASSETS............................................   1,037,991,934
                                                              --------------

LIABILITIES:
Payable for:
    Shares of beneficial interest repurchased...............       5,822,566
    Investment management fee...............................         378,945
    Plan of distribution fee................................          84,787
Accrued expenses and other payables.........................         456,370
                                                              --------------

    TOTAL LIABILITIES.......................................       6,742,668
                                                              --------------

    NET ASSETS..............................................  $1,031,249,266
                                                              ==============

COMPOSITION OF NET ASSETS:
Paid-in-capital.............................................  $1,031,247,744
Accumulated undistributed net investment income.............           1,522
                                                              --------------

    NET ASSETS..............................................  $1,031,249,266
                                                              ==============

NET ASSET VALUE PER SHARE,
 1,031,247,745 shares outstanding
 (unlimited shares authorized of $.01 par value)............           $1.00
                                                              ==============
</TABLE>

        SEE NOTES TO FINANCIAL STATEMENTS



                                       4
<PAGE>   5



MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST

FINANCIAL STATEMENTS, continued

<TABLE>
<S>                                                           <C>
STATEMENT OF OPERATIONS
For the six months ended July 31, 1999 (unaudited)
NET INVESTMENT INCOME:
INTEREST INCOME.............................................  $25,203,496
                                                              -----------

EXPENSES
Investment management fee...................................    2,294,383
Transfer agent fees and expenses............................    1,452,261
Plan of distribution fee....................................      376,902
Shareholder reports and notices.............................      123,971
Registration fees...........................................       69,021
Custodian fees..............................................       29,178
Professional fees...........................................       28,874
Trustees' fees and expenses.................................        8,985
Other.......................................................        4,363
                                                              -----------

    TOTAL EXPENSES..........................................    4,387,938
                                                              -----------

    NET INVESTMENT INCOME AND NET INCREASE..................  $20,815,558
                                                              ===========
</TABLE>

        SEE NOTES TO FINANCIAL STATEMENTS



                                       5
<PAGE>   6



MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST

FINANCIAL STATEMENTS, continued
<TABLE>
<CAPTION>
STATEMENT OF CHANGES IN NET ASSETS
                                                        FOR THE SIX        FOR THE YEAR
                                                        MONTHS ENDED          ENDED
                                                       JULY 31, 1999     JANUARY 31, 1999
- -----------------------------------------------------------------------------------------
                                                        (unaudited)
<S>                                                   <C>                <C>
INCREASE (DECREASE) IN NET ASSETS:
OPERATIONS:
Net investment income...............................   $   20,815,558     $   41,848,979
Net realized gain...................................        --                    40,360
                                                       --------------     --------------

    NET INCREASE....................................       20,815,558         41,889,339
                                                       --------------     --------------

DIVIDENDS AND DISTRIBUTIONS TO SHAREHOLDERS FROM:
Net investment income...............................      (20,815,675)       (41,849,500)
Net realized gain...................................        --                   (40,360)
                                                       --------------     --------------

    TOTAL DIVIDENDS AND DISTRIBUTIONS...............      (20,815,675)       (41,889,860)
                                                       --------------     --------------

Net increase from transactions in shares of
 beneficial interest................................       13,784,620        126,893,998
                                                       --------------     --------------

    NET INCREASE....................................       13,784,503        126,893,477

NET ASSETS:
Beginning of period.................................    1,017,464,763        890,571,286
                                                       --------------     --------------

    END OF PERIOD
    (Including undistributed net investment income
    of
    $1,522 and $1,639, respectively)................   $1,031,249,266     $1,017,464,763
                                                       ==============     ==============
</TABLE>

        SEE NOTES TO FINANCIAL STATEMENTS



                                       6
<PAGE>   7



MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST

NOTES TO FINANCIAL STATEMENTS July 31, 1999 (unaudited)

1. ORGANIZATION AND ACCOUNTING POLICIES

Morgan Stanley Dean Witter U.S. Government Money Market Trust (the "Fund"), is
registered under the Investment Company Act of 1940, as amended (the "Act"), as
a diversified, open-end management investment company. The Fund's investment
objectives are security of principal, high current income and liquidity. The
Fund was organized as a Massachusetts business trust on November 18, 1981 and
commenced operations on February 17, 1982.

The preparation of financial statements in accordance with generally accepted
accounting principles requires management to make estimates and assumptions that
affect the reported amounts and disclosures. Actual results could differ from
those estimates.

The following is a summary of significant accounting policies:

A. VALUATION OF INVESTMENTS -- Portfolio securities are valued at amortized
cost, which approximates market value.

B. ACCOUNTING FOR INVESTMENTS -- Security transactions are accounted for on the
trade date (date the order to buy or sell is executed). Realized gains and
losses on security transactions are determined by the identified cost method.
Premiums are amortized and discounts are accreted over the life of the
respective securities.

C. FEDERAL INCOME TAX STATUS -- It is the Fund's policy to comply with the
requirements of the Internal Revenue Code applicable to regulated investment
companies and to distribute all of its taxable income to its shareholders.
Accordingly, no federal income tax provision is required.

D. DIVIDENDS AND DISTRIBUTIONS TO SHAREHOLDERS -- The Fund records dividends and
distributions as of the close of each business day.

2. INVESTMENT MANAGEMENT AGREEMENT

Pursuant to an Investment Management Agreement with Morgan Stanley Dean Witter
Advisors Inc. (the "Investment Manager"), the Fund pays the Investment Manager a
management fee, accrued daily and payable monthly, by applying the following
annual rates to the net assets of the Fund determined as of the close of each
business day: 0.50% to the portion of the daily net assets not exceeding $500
million; 0.425% to the portion of the daily net assets exceeding $500 million
but not exceeding $750 million; 0.375% to the portion of the daily net assets
exceeding $750 million but not exceeding



                                       7
<PAGE>   8
MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST

NOTES TO FINANCIAL STATEMENTS July 31, 1999 (unaudited) continued



$1 billion; 0.35% to the portion of the daily net assets exceeding $1 billion
but not exceeding $1.5 billion; 0.325% to the portion of the daily net assets
exceeding $1.5 billion but not exceeding $2 billion; 0.30% to the portion of the
daily net assets exceeding $2 billion but not exceeding $2.5 billion; 0.275% to
the portion of the daily net assets exceeding $2.5 billion but not exceeding $3
billion; and 0.25% to the portion of the daily net assets exceeding $3 billion.

Under the terms of the Agreement, the Investment Manager maintains certain of
the Fund's books and records and furnishes, at its own expense, office space,
facilities, equipment, clerical, bookkeeping and certain legal services and pays
the salaries of all personnel, including officers of the Fund who are employees
of the Investment Manager. The Investment Manager also bears the cost of
telephone services, heat, light, power and other utilities provided to the Fund.

3. PLAN OF DISTRIBUTION

Morgan Stanley Dean Witter Distributors Inc. (the "Distributor"), an affiliate
of the Investment Manager, is the distributor of the Fund's shares and, in
accordance with a Plan of Distribution (the "Plan") pursuant to Rule 12b-1 under
the Act, finances certain expenses in connection therewith.

Under the Plan, the Distributor bears the expense of all promotional and
distribution related activities on behalf of the Fund, except for expenses that
the Trustees determine to reimburse, as described below. The following
activities and services may be provided by the Distributor, and other selected
broker-dealers under the Plan: (1) compensation to, and expenses of, Morgan
Stanley Dean Witter Financial Advisors and other selected broker-dealers; (2)
sales incentives and bonuses to sales representatives and to marketing personnel
in connection with promoting sales of the Fund's shares; (3) expenses incurred
in connection with promoting sales of the Fund's shares; (4) preparing and
distributing sales literature; and (5) providing advertising and promotional
activities, including direct mail solicitation and television, radio, newspaper,
magazine and other media advertisements.

The Fund is authorized to reimburse the Distributor for specific expenses the
Distributor incurs or plans to incur in promoting the distribution of the Fund's
shares. The amount of each monthly reimbursement payment may in no event exceed
an amount equal to a payment at the annual rate of 0.15% of the Fund's average
daily net assets during the month. Expenses incurred by the Distributor pursuant
to the Plan in any fiscal year will not be reimbursed by the Fund through
payments accrued in any subsequent fiscal year. For the six months ended July
31, 1999, the distribution fee was accrued at the annual rate of 0.07%.



                                       8
<PAGE>   9
MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST

NOTES TO FINANCIAL STATEMENTS July 31, 1999 (unaudited) continued



4. SECURITY TRANSACTIONS AND TRANSACTIONS WITH AFFILIATES

The cost of purchases and proceeds from sales/maturities of portfolio securities
for the six months ended July 31, 1999 aggregated $6,511,927,391 and
$6,522,948,208, respectively.

Morgan Stanley Dean Witter Trust FSB, an affiliate of the Investment Manager and
Distributor, is the Fund's transfer agent. At July 31, 1999, the Fund had
transfer agent fees and expenses payable of approximately $232,000.

The Fund has an unfunded noncontributory defined benefit pension plan covering
all independent Trustees of the Fund who will have served as independent
Trustees for at least five years at the time of retirement. Benefits under this
plan are based on years of service and compensation during the last five years
of service. Aggregate pension costs for the six months ended July 31, 1999
included in Trustees' fees and expenses in the Statement of Operations amounted
to $2,899. At July 31, 1999, the Fund had an accrued pension liability of
$51,306 which is included in accrued expenses in the Statement of Assets and
Liabilities.

5. SHARES OF BENEFICIAL INTEREST

Transactions in shares of beneficial interest, at $1.00 per share, were as
follows:

<TABLE>
<CAPTION>
                                                               FOR THE SIX       FOR THE YEAR
                                                               MONTHS ENDED         ENDED
                                                              JULY 31, 1999    JANUARY 31, 1999
                                                              --------------   ----------------
                                                               (unaudited)
<S>                                                           <C>              <C>
Shares sold.................................................   1,066,586,430     2,239,344,299
Shares issued in reinvestment of dividends..................      20,745,980        41,717,140
Acquisition of Dean Witter Retirement Series -- U.S.
 Government Money Market Series.............................        --                 837,211
                                                              --------------    --------------
                                                               1,087,332,410     2,281,898,650
Shares repurchased..........................................  (1,073,547,790)   (2,155,004,652)
                                                              --------------    --------------
Net increase................................................      13,784,620       126,893,998
                                                              ==============    ==============
</TABLE>



                                       9
<PAGE>   10
MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST

NOTES TO FINANCIAL STATEMENTS July 31, 1999 (unaudited) continued



6. ACQUISITION OF DEAN WITTER RETIREMENT SERIES -- U.S. GOVERNMENT MONEY MARKET
SERIES

As of the close of business on September 11, 1998, the Fund acquired all the net
assets of Dean Witter Retirement Series -- U.S. Government Money Market Series
("Retirement U.S. Government") pursuant to a plan of reorganization approved by
shareholders of Retirement U.S. Government on August 19, 1998. The acquisition
was accomplished by a tax-free exchange of 837,211 shares of the Fund at a net
asset value of $1.00 per share for 837,211 shares of Retirement U.S. Government.
The net assets of the Fund and Retirement U.S. Government immediately before the
acquisition were $942,511,862 and $837,211, respectively. Immediately after the
acquisition, the combined net assets of the Fund amounted to $943,349,073.



                                       10
<PAGE>   11



MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST

FINANCIAL HIGHLIGHTS

Selected ratios and per share data for a share of beneficial interest
outstanding throughout each period:

<TABLE>
<CAPTION>
                                                              FOR THE SIX               FOR THE YEAR ENDED JANUARY 31,
                                                             MONTHS ENDED    ----------------------------------------------------
                                                             JULY 31, 1999     1999       1998       1997       1996       1995
- ---------------------------------------------------------------------------------------------------------------------------------
                                                              (unaudited)
<S>                                                          <C>             <C>        <C>        <C>        <C>        <C>
SELECTED PER SHARE DATA:

Net asset value, beginning period..........................      $ 1.00        $ 1.00     $ 1.00    $ 1.00     $ 1.00     $ 1.00
                                                                 ------        ------     ------    ------     ------     ------

Net investment income......................................       0.020         0.045      0.046     0.043      0.049      0.034

Less dividends from net investment income..................      (0.020)       (0.045)    (0.046)   (0.043)    (0.049)    (0.034)
                                                                 ------        ------     ------    ------     ------     ------

Net asset value, end of period.............................      $ 1.00        $ 1.00     $ 1.00    $ 1.00     $ 1.00     $ 1.00
                                                                 ======        ======     ======    ======     ======     ======

TOTAL RETURN...............................................        2.38%(1)      4.63%      4.67%     4.41%      5.00%      3.47%

RATIOS TO AVERAGE NET ASSETS:
Expenses...................................................        0.86%(2)      0.94%      1.02%     1.11%      1.09%      1.08%

Net investment income......................................        4.06%(2)      4.50%      4.53%     4.29%      4.86%      3.38%

SUPPLEMENTAL DATA:
Net assets, end of period, in millions.....................      $1,031        $1,017       $891       $927       $903       $809
</TABLE>

- ---------------------
(1) Not annualized.
(2) Annualized.

                       SEE NOTES TO FINANCIAL STATEMENTS



                                       11
<PAGE>   12
TRUSTEES
- ----------------------------------
Michael Bozic
Charles A. Fiumefreddo
Edwin J. Garn
Wayne E. Hedien
Dr. Manuel H. Johnson
Michael E. Nugent
Philip J. Purcell
John L. Schroeder

OFFICERS
- ----------------------------------
Charles A. Fiumefreddo
Chairman and Chief Executive Officer

Mitchell M. Merin
President

Barry Fink
Vice President, Secretary and General Counsel

Jonathan R. Page
Vice President

Thomas F. Caloia
Treasurer

TRANSFER AGENT
- ----------------------------------
Morgan Stanley Dean Witter Trust FSB
Harborside Financial Center -- Plaza Two
Jersey City, New Jersey 07311

INDEPENDENT ACCOUNTANTS
- ----------------------------------
PricewaterhouseCoopers LLP
1177 Avenue of the Americas
New York, New York 10036

INVESTMENT MANAGER
- ----------------------------------
Morgan Stanley Dean Witter Advisors Inc.
Two World Trade Center
New York, New York 10048

The financial statements included herein have been taken from the records of the
Trust without examination by the independent accountants and accordingly they
do not express an opinion thereon.

This report is submitted for the general information of shareholders of the
Fund. For more detailed information about the Fund, its officers and trustees,
fees, expenses and other pertinent information, please see the prospectus of
the Fund.

This report is not authorized for distribution to prospective investors in the
Fund unless preceded or accompanied by an effective prospectus. Read the
prospectus carefully before investing.

MORGAN STANLEY
DEAN WITTER
U.S. GOVERNMENT
MONEY MARKET TRUST


Semiannual Report
July 31, 1999


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