KEMPER STRATEGIC MUNICIPAL INCOME TRUST
N-30D, 1996-07-30
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<PAGE>   1
 
KEMPER STRATEGIC
MUNICIPAL INCOME TRUST
 
SEMIANNUAL REPORT TO SHAREHOLDERS
FOR THE PERIOD ENDED MAY 31, 1996


         ". . . the [higher coupon] bonds experienced less price movement 
              as rates rose during the period. This cushioned the fund 
                 from the potential impact of rising interest rates."
<PAGE>   2
TABLE OF
Contents

2
Terms to Know
3
General
Economic Overview
6
Performance Update
7
Largest Sectors
8
Portfolio Statistics
9
Portfolio of
Investments
13
Financial Statements
15
Notes to
Financial Statements
17
Financial Highlights
 
At A Glance
- --------------------------------------------------------------------------------
TOTAL RETURNS
- --------------------------------------------------------------------------------
FOR THE PERIOD ENDED MAY 31, 1996
 
<TABLE>
<CAPTION>
                         BASED ON        BASED ON
                         NET ASSET        MARKET
                           VALUE          PRICE
<S>                      <C>             <C>
- -------------------------------------------------
KEMPER STRATEGIC
MUNICIPAL INCOME TRUST     1.32%           2.27%
- -------------------------------------------------
</TABLE>
 
NET ASSET VALUE AND MARKET PRICE
 
<TABLE>
<CAPTION>
                           AS OF      AS OF
                          5/31/96    11/30/95
- ---------------------------------------------
<S>                       <C>        <C>
NET ASSET VALUE            $11.94    $ 12.19
- ---------------------------------------------
MARKET PRICE               $12.00    $12.125
- ---------------------------------------------
</TABLE>
 
DIVIDEND REVIEW
THE FOLLOWING TABLE SHOWS PER SHARE DIVIDEND INFORMATION FOR THE FUND AS OF MAY
31, 1996.
 
<TABLE>
<S>                                      <C>
- ------------------------------------------------
SIX-MONTH INCOME:                         $0.408
- ------------------------------------------------
MAY DIVIDEND:                             $0.068
- ------------------------------------------------
ANNUALIZED DISTRIBUTION RATE:
 (BASED ON NET ASSET VALUE)                6.83%
- ------------------------------------------------
ANNUALIZED DISTRIBUTION RATE:
 (BASED ON MARKET PRICE)                   6.80%
- ------------------------------------------------
TAX EQUIVALENT DISTRIBUTION RATE:
 (BASED ON NET ASSET VALUE AND A
 37.1% FEDERAL INCOME TAX RATE AND
 AN ASSUMED $150,000 OF INCOME FOR
 A JOINT RETURN)                          10.86%
- ------------------------------------------------
TAX EQUIVALENT DISTRIBUTION RATE:
 (BASED ON MARKET PRICE AND A
 37.1% FEDERAL INCOME TAX RATE AND
 AN ASSUMED $150,000 OF INCOME FOR
 A JOINT RETURN)                          10.81%
- ------------------------------------------------
</TABLE>
 
Statistical Note: Current annualized distribution rate is the latest monthly
dividend shown as an annualized percentage of net asset value/market price on
the date shown. Distribution rate simply measures the level of dividends and is
not a complete measure of performance. Total return measures aggregate change in
net asset value/market value assuming reinvestment of dividends. Returns are
historical and do not represent future performance. Market price, net asset
value and returns fluctuate. Additional information concerning performance is
contained in the Financial Highlights appearing at the end of this report.
Income may be subject to state and local taxes and a portion of the income may
be subject to the alternative minimum tax for certain investors.
 
Terms to Know                         

DURATION Duration is a measure of the interest rate sensitivity of a fixed-
income investment or portfolio. The longer the duration, the greater the
interest rate risk.

REVENUE BOND INDEX (RBI) The average yield on 25 revenue bonds with 30-year
maturities compiled by THE BOND BUYER, a newspaper that covers the municipal
bond market.
 
TOTAL RETURN A fund's total return figure measures both the net investment
income and any realized and unrealized appreciation or depreciation of the
underlying investments in its portfolio for a specified period. Total return
assumes the reinvestment of all dividends and it represents the aggregate
percentage change in the value of an investment in the fund over the period.
Total return may be based upon net asset value or market price.
 
 
<PAGE>   3
GENERAL ECONOMIC OVERVIEW

[TIMBERS PHOTO] 

STEPHEN B. TIMBERS IS PRESIDENT, CHIEF EXECUTIVE AND CHIEF INVESTMENT OFFICER OF
ZURICH KEMPER INVESTMENTS, INC. (ZKI). ZKI AND ITS AFFILIATES MANAGE
APPROXIMATELY $78 BILLION IN ASSETS, INCLUDING $45 BILLION
IN RETAIL MUTUAL FUNDS. TIMBERS IS A GRADUATE OF YALE UNIVERSITY AND HOLDS AN
M.B.A. FROM HARVARD UNIVERSITY.

DEAR SHAREHOLDER,
 
The first six months of 1996 have provided a few surprises. As the year began,
most of us expected sluggish economic and corporate growth -- which the Federal
Reserve Board would address by reducing short-term interest rates. Yet, what we
experienced was stronger-than-anticipated economic growth, better corporate
earnings and rising interest rates. Although such surprises unsettled the bond
market, the stock market has followed a spectacular 1995 with strength so far
this year.

  Where is the economy headed now? Its direction is even less predictable as we
draw nearer to the November elections. Half of the country's leading economists
are forecasting 3 percent growth while an equal number are looking for no better
than 1 percent growth. At Kemper Funds, we suspect that the economy is growing
at a subpar rate of 2 percent. Although commodity prices may suggest otherwise,
we think inflation is holding at less than 3 percent. We see no reason to expect
the Fed to reduce rates to stimulate growth but neither is it likely to raise
rates significantly to control growth. In an environment of stable or gently
rising rates, we would expect corporate earnings to grow at a rate of about 7 to
8 percent -- that's somewhat higher than we believed likely at the start of the
year.

  Our forecast calls for a generally comfortable environment for investors. But
both the economy and the general direction of the markets are due for a
reversal. In July, the U.S. economy entered its 64th month of consecutive
growth. This is the longest expansion without a single quarter of negative
output growth since George Washington was president. Today's bull market started
in October 1990, which makes it one of the longest running bull markets in
history. By virtue of its length alone, the stock market is vulnerable to a
correction.

  As expected, volatility has returned to the market this year. For example: The
stock market's performance on March 8, the date that a surprisingly strong
employment report was released, betrayed some level of investor skittishness.
But while the Standard & Poor's lost 3.1 percent that day, it quickly regained
the ground and moved higher.

CONSUMERS AND JOB SECURITY
 
The restructuring of corporate America, which is generally credited for its
improved profitability, has been an important influence on the consumer. 
Economic growth is heavily dependent upon consumer spending which, in turn, is
a function of inflation, pay raises and fear of job loss.  While the first two
have not been a recent concern, fear of losing one's job has dampened consumer
confidence.

  Such anxiety in the workplace was the subject of a recent study by the
Council of Economic Advisors.  According to that report, more than two-thirds
of the new jobs created in the United States in 1994 and 1995 paid better than
the average job.  The report found that the rate at which jobs were eliminated
has risen slightly despite strong economic growth of recent years -- however, it
reported that the length of time most workers spent unemployed has declined.

  The graph below tracks Bureau of Labor Statistics data that show the
recent relationship between number of jobs created versus the number of jobs
lost.

                                 [LINE GRAPH]
<TABLE>
<CAPTION>
                      Jobs Created                  Jobs Lost
<S>                   <C>                           <C>
12/31/91               (300,000)                       40,000
12/31/92                120,000                       (30,000)
12/31/93                300,000                        70,000
12/31/94                180,000                        70,000
12/31/95                (80,000)                      (40,000)
3/31/96                 490,000                       (10,000)
</TABLE>

SOURCE: BUREAU OF LABOR STATISTICS
                                                                               3
<PAGE>   4
GENERAL ECONOMIC OVERVIEW

ECONOMIC GUIDEPOSTS

Economic activity is a key influence on investment performance and
shareholder decision-making. Periods of recession or boom, inflation or
deflation, credit expansion or credit crunch have a significant impact on 
mutual fund performance.  

  The following are some significant economic guideposts and their investment 
rationale that may help your investment decision-making. The 10-year Treasury 
rate and the prime rate are prevailing interest rates. The other data report 
year-to-year percentage changes.

<TABLE>
<CAPTION>
                        Now (5/31/96)   6 months ago   1 year ago   2 years ago

<S>                         <C>           <C>             <C>         <C>
10-year Treasury rate(1)     6.74           5.71            6.17        7.10    

Prime rate(2)                8.25           8.63            9.00        7.25    

Inflation rate(3)            2.96           2.60            3.04        2.56    

The U.S. dollar(4)           8.51          -2.58           -9.31        0.51    

Capital
 goods orders(5)             2.93          11.03           12.98       25.11    

Industrial production(6)     3.26           1.08            2.80        6.61    

Employment growth(7)         2.00           1.92            2.71        3.12
</TABLE>

(1) Falling interest rates in recent years have been a big plus for financial
    assets.

(2) The interest rate that commercial lenders charge their best borrowers.

(3) Inflation reduces an investor's real return. In the last five years, infla-
    tion has been as high as 6%. The low, moderate inflation of the last
    few years has meant high real returns.

(4) Changes in the exchange value of the dollar impact U.S. exporters
    and the value of U.S. firms' foreign profits.

(5) These influence corporate profits and equity performance.

(6) An influence on corporate profits and equity performance.

(7) An influence on family income and retail sales.

Source: Economics Department, Zurich Kemper Investments, Inc.
 

  Such ebb and flow is to be expected in investing, especially at this point in
the cycle. Attempting to "prepare" for a correction is futile, we believe. Those
whose caution caused them to excuse themselves from the market early this year,
for example, would have forgone its significant gain year to date.

  Several opportunities exist today for the careful investor. First, having
settled down some from a raucous 1995, the technology sector continues to enjoy
the product and market demand that make it the dominant sector of the 1990s.
Second, equity investors willing to look overseas may find opportunities in
countries whose economies today are at a point where the U.S. economy was in
1995. Our forecast assumes that strength in foreign markets could boost those
countries' currencies, which would weaken the value of the dollar.

  We expect the fixed-income markets to continue to be sensitive to interest
rate and inflation news. However, for as long as economic growth is positive and
earnings are growing, we believe the high-yield market is one market segment
that has significant potential.

  Finally, we look for political activity to have less and less bearing on the
markets' performance. Although they may continue to debate tax reform,
federal budget deficit reduction and health care reform, the incumbent
legislators are running out of time to take action before the November
elections. If there is any suspense by November, it is likely to be in whether
the Republicans can retain control of Congress. Their success would make a
balanced budget and tax reform likely agenda topics for 1997.

  With that as an economic backdrop, we encourage you to read the following
detailed report of your fund, including an interview with your fund's portfolio
management. Thank you for your continued support. We appreciate the opportunity
to serve your investment needs.
 
Sincerely,
 
/s/ Stephen B. Timbers 
 
STEPHEN B. TIMBERS
PRESIDENT, CHIEF INVESTMENT AND EXECUTIVE OFFICER
ZURICH KEMPER INVESTMENTS, INC.
 
July 2, 1996
 
4
<PAGE>   5
MANAGEMENT TEAM
 
                    KEMPER STRATEGIC MUNICIPAL INCOME TRUST
                           PORTFOLIO MANAGEMENT TEAM
 
[MIER PHOTO]

CHRIS MIER JOINED ZURICH KEMPER INVESTMENTS, INC. (ZKI) IN 1986 AND IS NOW
SENIOR VICE PRESIDENT OF ZKI AND A VICE PRESIDENT AND PORTFOLIO CO-MANAGER OF
KEMPER STRATEGIC MUNICIPAL INCOME TRUST. HE HAS BEEN PORTFOLIO MANAGER SINCE THE
FUND'S INCEPTION IN 1989. MIER RECEIVED A B.A. DEGREE IN ECONOMICS FROM THE
UNIVERSITY OF MICHIGAN AND WENT ON TO RECEIVE HIS M.M. IN FINANCE FROM THE
KELLOGG GRADUATE SCHOOL OF MANAGEMENT AT NORTHWESTERN UNIVERSITY. HE IS A
CHARTERED FINANCIAL ANALYST.
 
[BURROW PHOTO]

DALE BURROW HAS BEEN WITH ZKI SINCE 1987 AND IS A FIRST VICE PRESIDENT. HE
BECAME A VICE PRESIDENT AND PORTFOLIO CO-MANAGER OF THE FUND IN 1993. BURROW
RECEIVED A B.A. DEGREE FROM THE UNIVERSITY OF OKLAHOMA AND AN M.B.A. FROM DEPAUL
UNIVERSITY. HE IS A CHARTERED FINANCIAL ANALYST.

[WILLSON PHOTO]

STEPHEN WILLSON IS A FIRST VICE PRESIDENT OF ZKI AND HAS BEEN WITH THE COMPANY
SINCE 1985. HE BECAME A VICE PRESIDENT AND PORTFOLIO CO-MANAGER OF THE FUND IN
1993. WILLSON EARNED A B.A. IN MATHEMATICS AND A MASTER'S DEGREE IN FINANCE FROM
NORTHERN ILLINOIS UNIVERSITY AND IS A CHARTERED FINANCIAL ANALYST.
 








 
The views expressed in this report reflect those of the portfolio management
team only through the end of the period of the report, as stated on the cover.
The managers' views are subject to change at any time, based on market and 
other conditions.








                                                                              5
<PAGE>   6
PERFORMANCE UPDATE
 
THE PORTFOLIO MANAGEMENT TEAM OF KEMPER STRATEGIC MUNICIPAL INCOME TRUST
DISCUSSES THE FUND'S ABOVE-AVERAGE PERFORMANCE DURING A PERIOD OF SHIFTING
INTEREST RATES AND STRONGER ECONOMIC GROWTH.
 
Q.    HOW WOULD YOU CHARACTERIZE THE MARKET OVER THE LAST SIX MONTHS, AND HOW 
DID MUNICIPAL BONDS FARE?
 
A.    In December, at the start of the period, the market was enjoying a 
declining interest rate environment and bond yields were almost at their lowest 
point in 1995. The Bond Buyer 25- Bond Revenue Bond Index (RBI) -- a gauge of 
municipal bond interest rates -- began the period at 5.78 percent on November 
30, 1995.
 
      However, by mid-January that scenario began to change. Data began to 
indicate that the economic slowdown experienced in late 1995, which helped 
cause the decline in yields, may have been related mostly to the impact of 
severe weather as opposed to any fundamental weakness in the economy. Moreover,
with the start of the Republican party presidential primaries, focus moved away 
from the federal budget and deficit reduction proposals toward other issues. 
Yields began to rise as the focus on the deficit reduction began to fall. By 
the end of March, the RBI had risen to 6.15 percent. Although fluctuating 
somewhat throughout the rest of the period, on May 30, the RBI was 6.17 percent.
 
Q.    KEMPER STRATEGIC MUNICIPAL INCOME TRUST OUTPERFORMED THE AVERAGE RETURN 
OF ITS LIPPER PEER GROUP FOR THE SIX-MONTH PERIOD. HOW WAS THE FUND MANAGED TO
ACHIEVE THESE RESULTS?
 
A.    A good deal of the portfolio is invested in relatively high coupon bonds. 
Because of their higher coupons, the bonds experienced less price movement as 
rates rose during the period. This cushioned the fund from the potential impact 
of rising interest rates. In addition, the portfolio's high yield bonds 
provided an attractive income stream which supported the fund's total return. 
Hedging activities during the period also helped. By hedging we were able to 
support the fund's net asset value.
 
Q.    HOW DID MUNICIPAL BOND SUPPLY IMPACT THE MARKET DURING THE PERIOD?
 
A.    The volume of new supply during the period was heavier than anticipated.
As rates continued to fall early in the period, there was significant refunding 
activity in the market. When an issuer refunds debt they offer new debt at 
lower coupon rates. As market interest rates began to rise in late January and
February, the refunding activity subsided. Supply began to moderate somewhat, 
although it remained slightly ahead of 1995 levels. Demand for municipal bonds
from the mutual fund industry was relatively weak, but demand from individuals
and property casualty insurance companies was fairly strong.
 
Q.    DID TALK OF TAX REFORM CONTINUE TO IMPACT THE MUNICIPAL BOND MARKET 
DURING THE PERIOD?
 
A.    Talk of tax reform -- including a possible flat tax -- has raised 
considerable interest in the media and among municipal bond investors. At this
writing, however, it seems that the market is less confident that a flat tax 
will come to pass. President Clinton has not embraced such tax changes and 
Republican presidential candidate Robert Dole has gone on record as supporting
a "flatter" tax but not a flat tax. These factors should mitigate the risk of 
radical tax law change.
 
Q.    WHAT'S YOUR OUTLOOK FOR THE REMAINDER OF THE FISCAL YEAR?
 
A.    We anticipate continued moderate growth with inflation remaining under 
control at approximately 2.5 percent to 3.0 percent.
 
6
 
<PAGE>   7
LARGEST SECTORS
 
THE FUND'S LARGEST SECTORS*
 
Representing 61% of the fund's total net assets on May 31, 1996
 
<TABLE>
<CAPTION>
            HOLDINGS                             PERCENT
<S>    <C>                                        <C>
- --------------------------------------------------------
       SENIOR CARE BONDS                             16%
1.
- --------------------------------------------------------
       U.S. GOVERNMENT SECURED                       14%
2.
- --------------------------------------------------------
       NON-SENIOR CARE BONDS                         11%
3.
- --------------------------------------------------------
       SINGLE FAMILY STATE HOUSING BONDS             11%
4.
- --------------------------------------------------------
       HOSPITAL BONDS                                 9%
5.
- --------------------------------------------------------
</TABLE>
 
*Portfolio composition and holdings are subject to change.







                                      
                                                                              7
 
<PAGE>   8
PORTFOLIO STATISTICS
 
SECURITIES RATINGS
 
<TABLE>
<CAPTION>
                                              ON 5/31/96        ON 11/30/95
<S>                                          <C>               <C>
- ----------------------------------------------------------------------------
AAA                                                  4%                4%
- ----------------------------------------------------------------------------
AA                                                   9                10
- ----------------------------------------------------------------------------
A                                                    3                 6
- ----------------------------------------------------------------------------
BBB                                                 22                22
- ----------------------------------------------------------------------------
B                                                    2                 2
- ----------------------------------------------------------------------------
NOT RATED+                                          60                56
- ----------------------------------------------------------------------------
                                                   100%              100%
</TABLE>
 

                [PIE CHART]                [PIE CHART]

AAA
AA
A
BBB
B
Not Rated
                                                     
                ON 5/31/96                 ON 11/30/95
- -------------------------------------------------------------------------------

The ratings of Standard & Poor's Corporation (S&P) and Moody's Investors
Services, Inc. (Moody's) represent their opinions as to the quality of
securities that they undertake to rate. The percentage shown reflects the higher
of Moody's or S&P ratings. Portfolio composition will change over time. Ratings
are relative and subjective and not absolute standards of quality.
 
+These securities are not rated by S&P or Moody's, however they are rated by
Zurich Kemper Investments, Inc. as follows: AAA 9%, A 4%, BBB 9%, BB 33% and B
5%.
 
AVERAGE MATURITY
 
<TABLE>
<CAPTION>
                                              ON 5/31/96        ON 11/30/95
<S>                                          <C>               <C>
- ----------------------------------------------------------------------------
AVERAGE MATURITY                               18.0 YEARS        17.2 YEARS
- ----------------------------------------------------------------------------
</TABLE>




 
8
 
<PAGE>   9
PORTFOLIO OF INVESTMENTS
 
KEMPER STRATEGIC MUNICIPAL INCOME TRUST
 
Portfolio of Investments at May 31, 1996
(Dollars in thousands)
 
<TABLE>
<CAPTION>
- --------------------------------------------------------------------------------------------------------------------
                                                                                             PRINCIPAL 
 ISSUER                                                                                       AMOUNT       VALUE
ADVANCED REFUNDED OBLIGATIONS SECURED AS TO PRINCIPAL
AND INTEREST BY THE UNITED STATES GOVERNMENT SECURITIES--13.4%
- ----------------------------------------------------------------------------------------------------------------------
<S>                                    <C>                                                     <C>       <C>      
                                       IL, Chicago, Tax Increment Rev., 8.90%, to be called
                                         1-1-02 @ 102                                          $2,170    $  2,606
                                       IL, Itasca, Central Manufacturing District, Rev.,
                                         8.375%, to be called 12-1-2000 @ 102                   2,585       2,814
                                       IN, Indianapolis, Local Public Improvement Bond Bank,
                                         Rev., 8.50%, to be called 2-1-98 @ 102                 3,000       3,271
                                       OH, Marion County, United Church Health Care
                                         Facilities, Rev., 8.875%, to be called 12-1-99 @
                                         103                                                    2,780       3,211
                                       FL, Volusia County, Health Facilities Auth., Memorial
                                         Health Systems, Hospital Facilities, Rev., 8.25%,
                                         to be called 6-1-2000 @ 102                            2,390       2,727
                                       FL, Greater Orlando, Aviation Auth., Airport
                                         Facilities, Rev., 8.00%, to be called 10-1-98 @ 102       70          77
                                       PA, Greene County, Gen. Oblg., 8.75% to be called
                                         12-1-2000 @ 100                                        1,835       2,119
                                         -----------------------------------------------------------------------------
                                       TOTAL ADVANCED REFUNDED OBLIGATIONS
                                       (Cost: $14,767)                                                     16,825
                                         -----------------------------------------------------------------------------
OTHER MUNICIPAL OBLIGATIONS
- ----------------------------------------------------------------------------------------------------------------------
ILLINOIS--12.3%
                                       Chicago, O'Hare International Airport, American
                                         Airlines Special Facilities, Rev., 8.20%, 2018 and
                                         2024                                                   4,075       4,353
                                       Harvard, Multifamily Housing, Northfield Court Proj.,
                                         Rev., 9.50%, 2006                                      1,975       2,141
                                       Health Facilities Auth., Bethany Home and Hospital of
                                         the Methodist Church, Rev., 8.625%, 2009               2,510       2,787
                                       Lombard, Tax Increment Rev., 8.80%, 2004                 1,760       1,978
                                       St. Charles, Multifamily Housing, Wessel Court Proj.,
                                         Rev., 7.60%, 2024                                      1,985       2,016
                                       University Park, Tax Increment Rev., 8.50%, 2011         1,970       2,120
                                       -------------------------------------------------------------------------------
                                                                                                           15,395
- ----------------------------------------------------------------------------------------------------------------------
ARIZONA--7.0%
                                       Coconino County, Industrial Dev. Auth., The Guidance
                                         Center, Inc. Proj., Rev., 9.25%, 2011                  1,875       1,999
                                       Health Facilities Auth., The New Foundation,
                                         Healthcare Rev., 8.25%, 2019                           2,450       2,541
                                       Industrial Dev. Auth. of the County of Pima, Larson
                                         Company Proj., Rev., 9.50%, 2010                       2,300       2,525
                                       Maricopa County, Gen. Oblg., 8.625%, 2007                1,560       1,774
                                       -------------------------------------------------------------------------------
                                                                                                            8,839
- ----------------------------------------------------------------------------------------------------------------------
INDIANA--6.4%
                                       Fishers, Economic Dev. Water Facilities, Indianapolis
                                         Water Company, Rev., 7.875%, 2019                        685         725
                                       Health Facilities Finance Auth., Fayette Memorial
                                         Hospital, Rev., 7.20%, 2022                            2,800       2,804
                                       Housing Finance Auth., Rev., 8.375%, 2020                1,675       1,745
                                       Indianapolis Airport Auth., United Air Lines, Inc.,
                                         Indianapolis Maintenance Center Proj., 6.50%, 2031     2,900       2,805
                                       -------------------------------------------------------------------------------
                                                                                                            8,079
- ----------------------------------------------------------------------------------------------------------------------
</TABLE>
 
                                                                               9
 
<PAGE>   10
PORTFOLIO OF INVESTMENTS
 
<TABLE>
<CAPTION>
(Dollars in thousands)
                                                                                             PRINCIPAL 
                                                                                              AMOUNT       VALUE
<S>                                    <C>                                                     <C>       <C>      
NEW YORK--5.4%
                                       Medical Care Facilities Finance Agcy., Rev.,
                                         7.30%, 2021                                           $   60    $     65
                                       New York City, Gen. Oblg., 7.00% and 7.50%, 2010         3,735       3,915
                                       Port Auth., LaGuardia Airport Passenger Terminal,
                                         Rev., 9.125%, 2015                                     2,500       2,740
                                       -------------------------------------------------------------------------------
                                                                                                            6,720
- ----------------------------------------------------------------------------------------------------------------------
FLORIDA--5.1%
                                       Greater Orlando Aviation Auth., Airport Facilities,
                                         Rev., 8.00%, 2018                                        625         676
                                       Martin County Industrial Dev. Auth., Rev.,
                                         7.875%, 2025                                           1,500       1,672
                                       Nassua County, Amelia Island Proj., Rev.,
                                         9.75%, 2023                                            1,985       2,181
                                       Manatee County, First Mortgage Rev.,
                                         7.350%, 2015                                           1,775       1,821
                                       -------------------------------------------------------------------------------
                                                                                                            6,350
- ----------------------------------------------------------------------------------------------------------------------
COLORADO--4.1%
                                       Arapahoe County, Capital Improvement Trust Fund
                                         Highway, Rev., zero coupon, 2010                       5,000       1,882
                                       City and County of Denver, Airport System Rev., 7.50%
                                         to 8.75%, 2023 through 2025                            2,900       3,295
                                       -------------------------------------------------------------------------------
                                                                                                            5,177
- ----------------------------------------------------------------------------------------------------------------------
MISSOURI--4.0%
                                       St. Louis, Scullin Redevelopment Proj., Rev., 10.00%,
                                         2010                                                   2,365       2,816
                                       West Plains, Industrial Dev. Auth., Ozarks Medical
                                         Center, Hospital Rev., 8.625%, 2020                    2,000       2,180
                                       -------------------------------------------------------------------------------
                                                                                                            4,996
- ----------------------------------------------------------------------------------------------------------------------
PENNSYLVANIA--3.9%
                                       Columbia County, Industrial Dev. Auth., First
                                         Mortgage Rev., 9.00%, 2014                             1,950       2,077
                                       Lehigh County General Purpose Auth., Wiley House,
                                         Rev., 8.65%, 2004                                      2,800       2,871
                                       -------------------------------------------------------------------------------
                                                                                                            4,948
- ----------------------------------------------------------------------------------------------------------------------
OKLAHOMA--3.8%
                                       Housing Finance Agency, Single Family Mortgage Rev.,
                                         6.35%, 2027                                            1,415       1,406
                                       Woodward Municipal Auth., Hospital Rev., 8.50% and
                                         9.25%, 2014                                            3,085       3,388
                                       -------------------------------------------------------------------------------
                                                                                                            4,794
- ----------------------------------------------------------------------------------------------------------------------
MINNESOTA--3.5%
                                       Housing Finance Agcy., Single Family Mortgage Rev.,
                                         7.95%, 2022                                            2,045       2,147
                                       Sauk Rapids, Industrial Dev., Gold N Plump, Rev.,
                                         9.50%, 2005                                            2,160       2,247
                                       -------------------------------------------------------------------------------
                                                                                                            4,394
- ----------------------------------------------------------------------------------------------------------------------
IOWA--3.4%
                                       Finance Auth., On With Life, Healthcare Facility
                                         Rev., 7.25%, 2015                                      2,000       2,044
                                       Lake City, Health Care Facility, Opportunity Living
                                         Proj., Rev., 10.00%, 2015                              2,000       2,202
                                       -------------------------------------------------------------------------------
                                                                                                            4,246
- ----------------------------------------------------------------------------------------------------------------------
</TABLE>
 
10
 
<PAGE>   11
PORTFOLIO OF INVESTMENTS
 
<TABLE>
<CAPTION>
(Dollars in thousands)
                                                                                             PRINCIPAL 
                                                                                              AMOUNT        VALUE
<S>                                    <C>                                                     <C>       <C>      
MICHIGAN--2.7%
                                       Gogebic County, Grand View Hospital, Rev., 8.75%,
                                         2016                                                  $2,250    $  2,424
                                       Madison Heights, Tax Increment Finance Auth., Rev.,
                                         8.50%, 2001                                              980       1,029
                                       -------------------------------------------------------------------------------
                                                                                                            3,453
- ----------------------------------------------------------------------------------------------------------------------
OHIO--2.1%
                                       Cuyahoga County, Judson Retirement Community Center,
                                         Rev., 8.875%, 2019                                     2,500       2,669
- ----------------------------------------------------------------------------------------------------------------------
NEW MEXICO--2.0%
                                       Albuquerque Health Care Ltd., Nursing Home, Rev.,
                                         9.75%, 2014                                            1,400       1,515
                                       Truth or Consequences, Nursing Home Improvement,
                                         Sierra Health Care, Inc., Rev., 9.75%, 2014              935       1,011
                                       -------------------------------------------------------------------------------
                                                                                                            2,526
- ----------------------------------------------------------------------------------------------------------------------
WYOMING--2.0%
                                       Community Dev. Auth., Housing Rev., 6.30%, 2028          2,500       2,500
- ----------------------------------------------------------------------------------------------------------------------
CONNECTICUT--1.8%
                                       Dev. Auth., Pierce Memorial Baptist Home, Rev.,
                                         9.25%, 2018                                            2,000       2,202
- ----------------------------------------------------------------------------------------------------------------------
TEXAS--1.7%
                                       Brazos River Auth., Texas Utilities Electric Company,
                                         Pollution Control Rev., 8.25%, 2019                    2,000       2,157
- ----------------------------------------------------------------------------------------------------------------------
MASSACHUSETTS--1.7%
                                       Worcester, Briarwood Retirement Community, Rev.,
                                         9.25%, 2022                                            2,000       2,110
- ----------------------------------------------------------------------------------------------------------------------
NEW HAMPSHIRE--1.6%
                                       Higher Educational and Health Facilities Auth., Rev.,
                                         7.45%, 2025                                            2,000       1,974
- ----------------------------------------------------------------------------------------------------------------------
NEVADA--1.5%
                                       Housing Division, Single Family Program, Rev., 7.90%,
                                         2021                                                   1,865       1,945
- ----------------------------------------------------------------------------------------------------------------------
CALIFORNIA--1.4%
                                       Sacramento County, Rev., 7.20%, 2015                     1,250       1,280
                                       San Diego, Detention Facility, Certificates of
                                         Participation, Rev., 8.00%, 2002                         425         452
                                       -------------------------------------------------------------------------------
                                                                                                            1,732
- ----------------------------------------------------------------------------------------------------------------------
UTAH--1.3%
                                       Housing Finance Agency, Single Family Mortgage Rev.,
                                         6.65%, 2026                                            1,600       1,628
- ----------------------------------------------------------------------------------------------------------------------
SOUTH CAROLINA--1.3%
                                       Aiken County, Mattie C. Hall Health Care Center,
                                         Hospital Facilities, Rev., 8.625%, 2010                1,500       1,592
- ----------------------------------------------------------------------------------------------------------------------
KENTUCKY--1.3%
                                       Jefferson County, Louisville Gas and Electric,
                                         Pollution Control, Control Rev., 7.75%, 2019           1,500       1,588
- ----------------------------------------------------------------------------------------------------------------------
STATES LESS THAN
ONE PERCENT--2.6%
                                       NJ, Educational Facilities Auth., Caldwell College,
                                         Rev., 7.25%, 2025                                      1,150       1,173
                                       -------------------------------------------------------------------------------
                                       ND, Housing Finance Agcy., Single Family Mortgage
                                         Rev., 8.375%, 2021                                     1,010       1,065
                                       -------------------------------------------------------------------------------
                                       RI, Housing and Mortgage Finance Corp., Rev.,
                                         8.30%, 2011                                              565         572
                                       -------------------------------------------------------------------------------
                                       NE, Investment Finance Auth., Single Family Housing
                                         Rev., 6.70%, 2026                                        500         510
                                       -------------------------------------------------------------------------------
                                                                                                            3,320
- ----------------------------------------------------------------------------------------------------------------------
</TABLE>
 
                                                                              11
 
<PAGE>   12
PORTFOLIO OF INVESTMENTS
 
<TABLE>
<CAPTION>
(Dollars in thousands)
                                                                                            PRINCIPAL 
                                                                                             AMOUNT        VALUE
<S>                                    <C>                                                     <C>       <C>      
                                       TOTAL OTHER MUNICIPAL OBLIGATIONS--83.9%
                                       (Cost: $98,491)                                                   $105,334
                                       -------------------------------------------------------------------------------
                                       TOTAL MUNICIPAL OBLIGATIONS--97.3%
                                       (Cost: $113,258)                                                   122,159
                                       -------------------------------------------------------------------------------
- ----------------------------------------------------------------------------------------------------------------------
MONEY MARKET INSTRUMENTS--.3%
                                       Yield--3.90%
                                       Due--June 1996
                                       (Cost: $400)                                            $  400         400
                                       -------------------------------------------------------------------------------
                                       TOTAL INVESTMENTS--97.6%
                                       (Cost: $113,658)                                                   122,559
                                       -------------------------------------------------------------------------------
                                       CASH AND OTHER ASSETS, LESS LIABILITIES--2.4%                        3,071
                                       -------------------------------------------------------------------------------
                                       NET ASSETS--100%                                                  $125,630
                                       -------------------------------------------------------------------------------
</TABLE>
 
NOTE TO PORTFOLIO OF INVESTMENTS
 
Based on the cost of investments of $113,658,000 for federal income tax purposes
at May 31, 1996 the gross unrealized appreciation of investments was $9,036,000,
the gross unrealized depreciation was $135,000 and the net unrealized
appreciation of investments was $8,901,000.
 
See accompanying Notes to Financial Statements.




 
12
 
<PAGE>   13
FINANCIAL STATEMENTS
 
STATEMENT OF ASSETS AND LIABILITIES
May 31, 1996
(in thousands)
 
ASSETS
 
<TABLE>
<S>                                                                                            <C>
Investments, at value
(Cost: $113,658)                                                                               $122,559
- -------------------------------------------------------------------------------------------------------
Cash                                                                                                167
- -------------------------------------------------------------------------------------------------------
Receivable for:
  Investments sold                                                                                1,716
- -------------------------------------------------------------------------------------------------------
  Interest                                                                                        2,955
- -------------------------------------------------------------------------------------------------------
TOTAL ASSETS                                                                                    127,397
- -------------------------------------------------------------------------------------------------------
 
LIABILITIES AND NET ASSETS
 
Payable for:
  Investments purchased                                                                           1,679
- -------------------------------------------------------------------------------------------------------
  Management fee                                                                                     63
- -------------------------------------------------------------------------------------------------------
  Custodian and transfer agent fees and related expenses                                             10
- -------------------------------------------------------------------------------------------------------
  Trustees' fees and other                                                                           15
- -------------------------------------------------------------------------------------------------------
    Total liabilities                                                                             1,767
- -------------------------------------------------------------------------------------------------------
NET ASSETS APPLICABLE TO 10,526 SHARES OUTSTANDING,
$.01 PAR VALUE, EQUIVALENT TO $11.94 PER SHARE                                                 $125,630
- -------------------------------------------------------------------------------------------------------
 
ANALYSIS OF NET ASSETS
 
Paid-in capital                                                                                $116,899
- -------------------------------------------------------------------------------------------------------
Accumulated net realized loss on investments                                                       (554)
- -------------------------------------------------------------------------------------------------------
Net unrealized appreciation on investments                                                        8,901
- -------------------------------------------------------------------------------------------------------
Undistributed net investment income                                                                 384
- -------------------------------------------------------------------------------------------------------
NET ASSETS APPLICABLE TO SHARES OUTSTANDING                                                    $125,630
- -------------------------------------------------------------------------------------------------------
NET ASSET VALUE PER SHARE
($125,630 / 10,526 shares outstanding)                                                           $11.94
- -------------------------------------------------------------------------------------------------------
</TABLE>
 
See accompanying Notes to Financial Statements.



 
                                                                             13
<PAGE>   14
FINANCIAL STATEMENTS
 
STATEMENT OF OPERATIONS
Six months ended May 31, 1996
(in thousands)
 
NET INVESTMENT INCOME
 
<TABLE>
<S>                                                                                              <C>
 Interest income                                                                                 $ 4,791
- --------------------------------------------------------------------------------------------------------
 Expenses:
  Management fee                                                                                     380
- --------------------------------------------------------------------------------------------------------
  Custodian and transfer agent fees and related expenses                                              23
- --------------------------------------------------------------------------------------------------------
  Professional fees                                                                                   26
- --------------------------------------------------------------------------------------------------------
  Reports to shareholders                                                                              9
- --------------------------------------------------------------------------------------------------------
  Trustees' fees and other                                                                            43
- --------------------------------------------------------------------------------------------------------
   Total expenses                                                                                    481
- --------------------------------------------------------------------------------------------------------
NET INVESTMENT INCOME                                                                              4,310
- --------------------------------------------------------------------------------------------------------
 
 NET REALIZED AND UNREALIZED GAIN (LOSS) ON INVESTMENTS
 
 Net realized gain on sales of investments                                                           201
- --------------------------------------------------------------------------------------------------------
 Net realized gain from futures transactions                                                         166
- --------------------------------------------------------------------------------------------------------
  Net realized gain                                                                                  367
- --------------------------------------------------------------------------------------------------------
 Change in net unrealized appreciation on investments                                             (3,105)
- --------------------------------------------------------------------------------------------------------
Net loss on investments                                                                           (2,738)
- --------------------------------------------------------------------------------------------------------
NET INCREASE IN NET ASSETS RESULTING FROM OPERATIONS                                             $ 1,572
- --------------------------------------------------------------------------------------------------------
</TABLE>
 
STATEMENT OF CHANGES IN NET ASSETS
 
(in thousands)
 
<TABLE>
<CAPTION>
                                                                      SIX MONTHS
                                                                        ENDED                 YEAR ENDED
                                                                       MAY 31,               NOVEMBER 30,
                                                                         1996                    1995
OPERATIONS, DIVIDENDS AND CAPITAL SHARE ACTIVITY
<S>                                                                   <C>                    <C>
 Net investment income                                                  $ 4,310                   8,704
- ---------------------------------------------------------------------------------------------------------
 Net realized gain (loss)                                                   367                    (262)
- ---------------------------------------------------------------------------------------------------------
 Change in net unrealized appreciation                                   (3,105)                  6,961
- ---------------------------------------------------------------------------------------------------------
Net increase in net assets resulting from operations                      1,572                  15,403
- ---------------------------------------------------------------------------------------------------------
Distribution from net investment income                                  (4,294)                 (8,542)
- ---------------------------------------------------------------------------------------------------------
Proceeds from shares issued in reinvestment of dividends
41 shares and 25 shares, respectively)                                      508                     294
- ---------------------------------------------------------------------------------------------------------
TOTAL INCREASE (DECREASE) IN NET ASSETS                                  (2,214)                  7,155
- ---------------------------------------------------------------------------------------------------------
 
NET ASSETS
 
Beginning of period                                                     127,844                 120,689
- ---------------------------------------------------------------------------------------------------------
END OF PERIOD (including undistributed net investment income of
$384 and $368, respectively)                                           $125,630                 127,844
- ---------------------------------------------------------------------------------------------------------
</TABLE>




 
14
 
<PAGE>   15
NOTES TO FINANCIAL STATEMENTS
- --------------------------------------------------------------------------------
1    SIGNIFICANT
     ACCOUNTING POLICIES     DESCRIPTION OF FUND. The Fund is registered under
                             the Investment Company Act of 1940 as a
                             non-diversified, closed-end management investment
                             company.
 
                             INVESTMENT VALUATION. Investments are stated at
                             value. Fixed income securities are valued by using
                             market quotations, or independent pricing services
                             that use prices provided by market makers or
                             estimates of market values obtained from yield data
                             relating to instruments or securities with similar
                             characteristics. Exchange traded options are valued
                             at the last sale price unless there is no sale
                             price, in which event prices provided by market
                             makers are used. Over-the-counter traded options
                             are valued based upon prices provided by market
                             makers. Financial futures and options thereon are
                             valued at the settlement price established each day
                             by the board of trade or exchange on which they are
                             traded. Other securities and assets are valued at
                             fair value as determined in good faith by the Board
                             of Trustees.
 
                             INVESTMENT TRANSACTIONS AND INVESTMENT INCOME.
                             Investment transactions are accounted for on the
                             trade date (date the order to buy or sell is
                             executed). Interest income is recorded on the
                             accrual basis and includes premium and original
                             issue discount amortization on fixed income
                             securities. Realized gains and losses from
                             investment transactions are reported on an
                             identified cost basis.
 
                             FEDERAL INCOME TAXES. The Fund has complied with
                             the special provisions of the Internal Revenue Code
                             available to investment companies for the six
                             months ended May 31, 1996. The accumulated net
                             realized loss on sales of investments for federal
                             income tax purposes at May 31, 1996, amounting to
                             approximately $288,000, is available to offset
                             future taxable gains. If not applied, the loss
                             carryover expires during the period 2002 through
                             2004.
 
                             DIVIDENDS TO SHAREHOLDERS. The Fund declares and
                             pays dividends of net investment income monthly and
                             any net realized capital gains annually, which are
                             recorded on the ex-dividend date. Dividends are
                             determined in accordance with income tax principles
                             which may treat certain transactions differently
                             from generally accepted accounting principles.
 
- --------------------------------------------------------------------------------
2    TRANSACTIONS
     WITH AFFILIATES         MANAGEMENT AGREEMENT. The Fund has a management
                             agreement with Zurich Kemper Investments, Inc.
                             (ZKI) (formerly known as Kemper Financial Services,
                             Inc.), and pays a management fee at an annual rate
                             of .60% of average weekly net assets. The Fund
                             incurred a management fee of $380,000 for the six
                             months ended May 31, 1996.
 
                             SHAREHOLDER SERVICES AGREEMENT. Pursuant to a
                             services agreement with the Fund's transfer agent,
                             Kemper Service Company (KSvC) is the shareholder
                             service agent of the Fund. Under the agreement,
                             KSvC received shareholder services fees of $12,000
                             for the six months ended May 31, 1996.
 
                             OFFICERS AND TRUSTEES. Certain officers or trustees
                             of the Fund are also officers or directors of ZKI.
                             During the six months ended May 31, 1996,



 
                                                                              15
 
<PAGE>   16
NOTES TO FINANCIAL STATEMENTS
 
                             the Fund made no direct payments to its officers
                             and incurred trustees' fees of $12,000 to
                             independent trustees.
 
- --------------------------------------------------------------------------------
3    INVESTMENT
     TRANSACTIONS            For the six months ended May 31, 1996, investment
                             transactions (excluding short-term instruments) are
                             as follows (in thousands):
 
                             Purchases                                   $27,170
 
                             Proceeds from sales                          26,046










 
16
 
<PAGE>   17
FINANCIAL HIGHLIGHTS
 
<TABLE>
<CAPTION>
                                                    SIX MONTHS
                                                      ENDED                    YEAR ENDED NOVEMBER 30,
                                                     MAY 31,       ------------------------------------------------
                                                       1996         1995        1994        1993        1992
<S>                                                 <C>            <C>         <C>         <C>         <C>     <C>
 PER SHARE OPERATING PERFORMANCE
Net asset value, beginning of period                   $12.19        11.54       12.36       11.86       11.65
- -------------------------------------------------------------------------------------------------------------------
Income from investment operations:
  Net investment income                                   .41          .83         .83         .83         .84
- -------------------------------------------------------------------------------------------------------------------
  Net realized and unrealized gain (loss)               (.25)          .64        (.80)        .58         .30
- -------------------------------------------------------------------------------------------------------------------
Total from investment operations                          .16         1.47         .03        1.41        1.14
- -------------------------------------------------------------------------------------------------------------------
Less dividends:
  Distribution from net investment income                 .41          .82         .82         .89         .83
- -------------------------------------------------------------------------------------------------------------------
  Distribution from net realized gain                      --           --         .03         .02         .10
- -------------------------------------------------------------------------------------------------------------------
Total dividends                                           .41          .82         .85         .91         .93
- -------------------------------------------------------------------------------------------------------------------
Net asset value, end of period                         $11.94        12.19       11.54       12.36       11.86
- -------------------------------------------------------------------------------------------------------------------
Market value, end of period                            $12.00        12.13       11.63       12.38       12.13
- -------------------------------------------------------------------------------------------------------------------
 TOTAL RETURN (NOT ANNUALIZED)
Based on net asset value                                 1.32%       13.09         .12       12.32       10.14
- -------------------------------------------------------------------------------------------------------------------
Based on market value                                    2.27%       11.77         .71        9.51        7.86
- -------------------------------------------------------------------------------------------------------------------
 RATIOS TO AVERAGE NET ASSETS (ANNUALIZED)
Expenses                                                  .75%         .76         .75         .74         .77
- -------------------------------------------------------------------------------------------------------------------
Net investment income                                    6.80%        6.97        6.92        6.87        7.17
- -------------------------------------------------------------------------------------------------------------------
 SUPPLEMENTAL DATA
Net assets at end of period (in thousands)           $125,630      127,844     120,689     128,564     122,035
- -------------------------------------------------------------------------------------------------------------------
Portfolio turnover rate (annualized)                       42%           8          11           8          10
- -------------------------------------------------------------------------------------------------------------------
</TABLE>
 
NOTE: Total return based on net asset value reflects changes in the Fund's net
asset value during the period. Total return based on market value reflects
changes in market value. Each figure includes reinvestment of dividends. These
figures will differ depending upon the level of any discount from or premium to
net asset value at which the Fund's shares trade during the period.




 
                                                                             17
 
<PAGE>   18
SHAREHOLDERS' MEETING
 
ANNUAL SHAREHOLDERS' MEETING
 
On May 29, 1996, an annual shareholders' meeting was held. Kemper Strategic
Municipal Income Trust shareholders were asked to vote on two separate issues:
re-election of the eight members to the Board of Trustees and ratification of
Ernst & Young LLP as independent auditors. We are pleased to report that all
nominees were elected and the selection of Ernst & Young LLP as the fund's
auditors was ratified. Following are the results for each issue:
 
1) Re-election of Trustees:
 
<TABLE>
<CAPTION>
                               For        Withheld
    <S>                     <C>           <C>
    James E. Akins          8,125,773     245,272
    Arthur R. Gottschalk    8,160,095     210,950
    Frederick T. Kelsey     8,143,353     227,692
    Dominique P. Morax      8,134,144     236,901
    Fred B. Renwick         8,134,144     236,901
    Stephen B. Timbers      8,171,814     199,231
    John B. Tingleff        8,170,140     200,905
    John G. Weithers        8,171,814     199,231
</TABLE>
 
2) Ratification of the selection of Ernst & Young LLP as independent auditors
   for the fund:
 
<TABLE>
<CAPTION>
       For        Against     Abstain
   <S>            <C>         <C>
   8,224,494      61,662      84,889
</TABLE>







 
18
 
<PAGE>   19
 
                                     NOTES
 




















                                                                              19
<PAGE>   20
TRUSTEES AND OFFICERS
 
TRUSTEES                        OFFICERS
 
STEPHEN B. TIMBERS              J. PATRICK BEIMFORD, JR.     CHARLES F. CUSTER
President and Trustee           Vice President               Vice President and
                                                             Assistant Secretary
JAMES E. AKINS                  DALE R. BURROW                
Trustee                         Vice President               JEROME L. DUFFY
                                                             Treasurer
ARTHUR R. GOTTSCHALK            CHRISTOPHER J. MIER          
Trustee                         Vice President
                                 
FREDERICK T. KELSEY             JOHN E. NEAL
Trustee                         Vice President
                                 
DOMINIQUE P. MORAX              JOHN E. PETERS
Trustee                         Vice President
                                 
FRED B. RENWICK                 STEPHEN R. WILLSON
Trustee                         Vice President
                                 
JOHN B. TINGLEFF                PHILIP J. COLLORA
Trustee                         Vice President
                                and Secretary
JOHN G. WEITHERS                
Trustee

- --------------------------------------------------------------------------------
LEGAL COUNSEL                 VEDDER, PRICE, KAUFMAN & KAMMHOLZ
                              222 North LaSalle Street
                              Chicago, IL 60601
 
- --------------------------------------------------------------------------------
SHAREHOLDER SERVICE AGENT     KEMPER SERVICE COMPANY
                              P.O. Box 419066
                              Kansas City, MO 64141
 
- --------------------------------------------------------------------------------
CUSTODIAN AND TRANSFER AGENT  INVESTORS FIDUCIARY TRUST COMPANY
                              127 West 10th Street
                              Kansas City, MO 64105
 
- --------------------------------------------------------------------------------
INVESTMENT MANAGER            ZURICH KEMPER INVESTMENTS, INC.
                              120 South LaSalle Street
                              Chicago, IL 60603
                              http://www.Kemper.com
 

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