MORGAN STANLEY DEAN WITTER US GOVERNMENT MONEY MARKET TRUST
N-30D, 1998-09-28
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<PAGE>

MORGAN STANLEY DEAN WITTER 
U.S. GOVERNMENT MONEY MARKET TRUST                       Two World Trade Center,
LETTER TO THE SHAREHOLDERS July 31, 1998                New York, New York 10048


DEAR SHAREHOLDER:

As of July 31, 1998, Morgan Stanley Dean Witter U.S. Government Money Market
Trust had assets in excess of $901 million, with an average life of 76 days.
The Trust's annualized net yield for the six-month fiscal period ended July 31
was 4.63 percent, and its annualized yield for the month of July was 4.61
percent.


MARKET OVERVIEW

After rising approximately 25 basis points (0.25 percentage points) late in the
first quarter of 1997, money market yields remained remarkably stable over the
past five quarters. Federal Reserve policy makers have held the target rate for
Federal funds at 5.50 percent since March 25, 1997. Overall economic conditions
in the United States continue to be good as inflation and the unemployment rate
remain low. After strong, domestic demand led economic activity in the first
quarter of 1998, the second quarter of the year began to show evidence that the
U.S. economy might be softening in response to the Asian economic situation.

The National Association of Purchasing Managers' Index fell to 49.1 percent in
July, its lowest level in more than two years, while new orders for durable
goods contracted in May and June, indicating a growing weakness in the
manufacturing sector. However, despite a sixth consecutive month of growth in
retail sales and a monthly average of 240,000 nonfarm jobs being created
year-to-date through June, inflation remains under control. Producer prices
have fallen in four of the last six months, and the Consumer Price Index was up
only 1.70 percent year over year through June.


PORTFOLIO

On July 31, 1998, approximately 99 percent of the Trust's holdings consisted of
Federal agency obligations, with the remaining 1 percent invested in U.S.
Treasury bills. At the end of this fiscal period, approximately 77 percent of
the Trust's assets were due to mature in less

<PAGE>

MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST
LETTER TO THE SHAREHOLDERS, continued

than four months. Therefore, the Trust is well positioned for stability of
value and a high degree of liquidity. We continue to manage the Trust in a
conservative manner without structured notes or derivative products that could
fluctuate excessively when interest rates change.


LOOKING AHEAD

At this time we anticipate a moderation in the pace of economic activity for
the remainder of 1998, with no major adverse surprises in the rate of
inflation. If unfavorable economic conditions in Asia, Latin America and Russia
continue to slow U.S. economic growth, the Fed might have to consider lowering
the Federal-funds target rate. As a result, investment yields available to the
Trust during the months immediately ahead may be slightly lower than those
available during the fiscal period just ended. We believe that the Trust will
continue to serve as a useful investment for liquidity, preservation of capital
and a yield that reflects prevailing money market conditions.

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
- --------------------------
CHARLES A. FIUMEFREDDO
Chairman of the Board

                                        2
<PAGE>

MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST
PORTFOLIO OF INVESTMENTS July 31, 1998 (unaudited)


<TABLE>
<CAPTION>
                                                                               ANNUALIZED
 PRINCIPAL                            DESCRIPTION                                 YIELD
 AMOUNT IN                                AND                                  ON DATE OF
 THOUSANDS                           MATURITY DATE                              PURCHASE             VALUE
- -------------------------------------------------------------------------------------------------------------
<S>           <C>                                                           <C>                <C>
              U.S. GOVERNMENT AGENCIES (99.2%)
 $ 86,442     Federal Farm Credit Bank
               08/07/98-03/29/99 ........................................       5.39-5.69%       $ 85,192,438
  415,364     Federal Home Loan Banks
               08/05/98-01/20/99 ........................................        5.40-5.53        410,377,912
  132,242     Federal Home Loan Mortgage Corp.
               08/04/98-12/07/98 ........................................        5.47-5.52        131,219,534
  235,580     Federal National Mortgage Assoc.
               08/10/98-12/15/98 ........................................        5.43-5.52        232,839,713
   34,500     Student Loan Marketing Assoc.
               08/03/98 .................................................            5.54          34,489,382
                                                                                                 ------------
              TOTAL U.S. GOVERNMENT AGENCIES
              (Amortized Cost $894,118,979)...............................................       894,118,979
                                                                                                 ------------
              U.S. GOVERNMENT OBLIGATION (1.1%)
   10,000     U.S. Treasury Bill 08/13/98
              (Amortized Cost $9,983,417)................................            5.06           9,983,417
                                                                                                 ------------
              REPURCHASE AGREEMENT (0.2%)
    1,817     The Bank of New York due 08/03/98 (dated 07/31/98; proceeds
              $1,817,777) (a) (Identified Cost $1,816,944) ..............            5.50           1,816,944
                                                                                                 ------------
              TOTAL INVESTMENTS
              (Identified Cost $905,919,340) (b).........................          100.5  %       905,919,340
              LIABILITIES IN EXCESS OF CASH AND OTHER ASSETS ............       (     0.5)         (4,466,781)
                                                                              ------------       ------------
              NET ASSETS ................................................          100.0  %      $901,452,559
                                                                              ============       ============
</TABLE>

- ---------------
(a)        Collateralized by $356,594 U.S. Treasury Bond 11.125% due 08/15/03
           valued at $460,201 and $1,065,200 U.S. Treasury Bond 11.875% due
           11/15/03 valued at $1,393,082.
(b)        Cost is the same for federal income tax purposes.

                        SEE NOTES TO FINANCIAL STATEMENTS


                                        3
<PAGE>

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

STATEMENT OF ASSETS AND LIABILITIES
July 31, 1998 (unaudited)

<TABLE>
<CAPTION>
<S>                                                                       <C>
ASSETS :
Investments in securities, at value
  (identified cost $905,919,340) ........................................ $905,919,340
Cash ....................................................................       90,453
Receivable for:
  Shares of beneficial interest sold ....................................      222,043
  Interest ..............................................................      209,381
Prepaid expenses ........................................................      172,352
                                                                          ------------
  TOTAL ASSETS ..........................................................  906,613,569
                                                                          ------------
LIABILITIES :
Payable for:
  Shares of beneficial interest repurchased .............................    4,590,157
  Investment management fee .............................................      352,849
  Plan of distribution fee ..............................................       77,107
Accrued expenses and other payables .....................................      140,897
                                                                          ------------
  TOTAL LIABILITIES .....................................................    5,161,010
                                                                          ------------
  NET ASSETS ............................................................ $901,452,559
                                                                          ============
COMPOSITION OF NET ASSETS :
Paid-in-capital ......................................................... $901,451,134
Accumulated undistributed net investment income .........................        1,425
                                                                          ------------
  NET ASSETS ............................................................ $901,452,559
                                                                          ============
NET ASSET VALUE PER SHARE,
  901,451,134 shares outstanding (unlimited shares authorized of $.01 par
  value) ................................................................        $1.00
                                                                                 =====
</TABLE>

                        SEE NOTES TO FINANCIAL STATEMENTS


                                        4
<PAGE>

MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST
FINANCIAL STATEMENTS, continued

STATEMENT OF OPERATIONS
For the six months ended July 31, 1998 (unaudited)

<TABLE>
<CAPTION>
<S>                                              <C>
NET INVESTMENT INCOME :
INTEREST INCOME ................................  $24,938,107
                                                  -----------
EXPENSES
Investment management fee ......................    2,054,421
Transfer agent fees and expenses ...............    1,449,004
Plan of distribution fee .......................      421,823
Registration fees ..............................      109,876
Shareholder reports and notices ................      102,443
Professional fees ..............................       25,824
Custodian fees .................................       22,920
Trustees' fees and expenses ....................       10,871
Other ..........................................        4,111
                                                  -----------
  TOTAL EXPENSES ...............................    4,201,293
                                                  -----------
NET INVESTMENT INCOME AND NET INCREASE .........  $20,736,814
                                                  ===========
</TABLE>

                                        

                        SEE NOTES TO FINANCIAL STATEMENTS


                                       5
<PAGE>

MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST
FINANCIAL STATEMENTS, continued

STATEMENT OF CHANGES IN NET ASSETS

<TABLE>
<CAPTION>
                                                         FOR THE SIX      FOR THE YEAR
                                                         MONTHS ENDED        ENDED
                                                        JULY 31, 1998   JANUARY 31, 1998
- ----------------------------------------------------------------------------------------
<S>                                                    <C>             <C>
                                                          (unaudited)
INCREASE (DECREASE) IN NET ASSETS :
OPERATIONS :
Net investment income and net increase ...............  $  20,736,814    $  40,709,335
Dividends from net investment income .................    (20,737,549)     (40,709,121)
Net increase (decrease) from transactions in shares of
  beneficial interest ................................     10,882,008      (36,513,549)
                                                        -------------    -------------
  NET INCREASE (DECREASE) ............................     10,881,273      (36,513,335)
NET ASSETS :
Beginning of period ..................................    890,571,286      927,084,621
                                                        -------------    -------------
  END OF PERIOD
   (Including undistributed net investment income of
   $1,425 and $2,160, respectively)...................  $ 901,452,559    $ 890,571,286
                                                        =============    =============
</TABLE>

                        SEE NOTES TO FINANCIAL STATEMENTS


                                        6
<PAGE>

MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST
NOTES TO FINANCIAL STATEMENTS July 31, 1998 (unaudited)


1. ORGANIZATION AND ACCOUNTING POLICIES

Morgan Stanley Dean Witter U.S. Government Money Market Trust (the "Trust"),
formerly Dean Witter U.S. Government Money Market Trust is registered under the
Investment Company Act of 1940, as amended (the "Act"), as a diversified,
open-end management investment company. The Trust's investment objectives are
security of principal, high current income and liquidity. The Trust 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 Trust'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 Trust 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"), formerly Dean Witter InterCapital
Inc., the Trust pays the Investment Manager a management fee, accrued daily and
payable monthly, by applying the following annual rates to the net assets of
the Trust 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 $1 billion; 0.35% to the portion of the daily net assets exceeding $1
billion but not exceeding


                                        7
<PAGE>

MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST
NOTES TO FINANCIAL STATEMENTS July 31, 1998 (unaudited) (continued)

$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 Trust'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 Trust 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
Trust.


3. PLAN OF DISTRIBUTION

Morgan Stanley Dean Witter Distributors Inc. (the "Distributor"), an affiliate
of the Investment Manager, is the distributor of the Trust'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 Trust, 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 Trust's shares; (3)
expenses incurred in connection with promoting sales of the Trust'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 Trust is authorized to reimburse the Distributor for specific expenses the
Distributor incurs or plans to incur in promoting the distribution of the
Trust'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
Trust'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 Trust through payments accrued in any subsequent fiscal year. For the six
months ended July 31, 1998, the distribution fee was accrued at the annual rate
of 0.10%.


                                        8

<PAGE>

MORGAN STANLEY DEAN WITTER U.S. GOVERNMENT MONEY MARKET TRUST
NOTES TO FINANCIAL STATEMENTS July 31, 1998 (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, 1998 aggregated $6,525,556,390 and
$6,543,369,421, respectively.

Morgan Stanley Dean Witter Trust FSB, an affiliate of the Investment Manager
and Distributor, is the Trust's transfer agent.

The Trust has an unfunded noncontributory defined benefit pension plan covering
all independent Trustees of the Trust 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, 1998
included in Trustees' fees and expenses in the Statement of Operations amounted
to $3,220. At July 31, 1998, the Trust had an accrued pension liability of
$49,311 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, 1998        JANUARY 31, 1998
                                                       -------------------   -------------------
                                                           (unaudited)
<S>                                                    <C>                   <C>
Shares sold ........................................       1,136,975,361         2,013,452,444
Shares issued in reinvestment of dividends .........          20,656,027            40,560,689
                                                           -------------         -------------
                                                           1,157,631,388         2,054,013,133
Shares repurchased .................................      (1,146,749,380)       (2,090,526,682)
                                                          --------------        --------------
Net increase (decrease) ............................          10,882,008           (36,513,549)
                                                          ==============        ==============
</TABLE>


6. SUBSEQUENT EVENT

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


                                        9

<PAGE>

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, 1998     1998       1997       1996       1995       1994
                                                    ---------------- ---------- ---------- ---------- ---------- ----------
                                                       (unaudited)
<S>                                                 <C>              <C>        <C>        <C>        <C>        <C>
PER SHARE OPERATING PERFORMANCE:
Net asset value, beginning period .................      $ 1.00         $ 1.00     $ 1.00     $ 1.00     $ 1.00     $ 1.00
                                                         ------         ------     ------     ------     ------     ------
Net investment income .............................       0.023          0.046      0.043      0.049      0.034      0.023
Less dividends from net investment income .........      (0.023)        (0.046)    (0.043)    (0.049)    (0.034)    (0.023)
                                                          -----         ------     ------     ------     ------     ------
Net asset value, end of period ....................      $ 1.00         $ 1.00     $ 1.00     $ 1.00     $ 1.00     $ 1.00
                                                         ======         ======     ======     ======     ======     ======
TOTAL INVESTMENT RETURN ...........................        2.76%(1)       4.67%      4.41%      5.00%      3.47%      2.28%
RATIOS TO AVERAGE NET ASSETS:
Expenses ..........................................        0.94%(2)       1.02%      1.11%      1.09%      1.08%      1.00%
Net investment income .............................        4.63%(2)       4.53%      4.29%      4.86%      3.38%      2.23%
SUPPLEMENTAL DATA:
Net assets, end of period, in millions ............        $901           $891       $927       $903       $809       $818
</TABLE>

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


                        SEE NOTES TO FINANCIAL STATEMENTS

                                       10


<PAGE>


TRUSTEES
- -----------------------------------------------
Michael Bozic
Charles A. Fiumefreddo
Edwin J. Garn
John R. Haire
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

Barry Fink
Vice President, Secretary and General Counsel

Johnathan 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 Fund 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.

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


SEMIANNUAL REPORT
JULY 31, 1998



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