KEMPER HIGH INCOME TRUST
N-30D, 1995-08-01
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<PAGE>   1
 
DEAR SHAREHOLDER:
 
We are pleased to provide you with an overview of the performance of Kemper High
Income Trust and the high yield market.
 
PERFORMANCE HIGHLIGHTS
 
- Morningstar* gave the fund a 4-star "above average" overall rating as of
  5/26/95. The fund also received 4 stars for the 3-year and 5-year periods
  ended 4/28/95.
 
- According to Lipper Analytical Services,** the fund was ranked 15 out of 25
  closed-end high yield funds for the six-month period ended May 31, 1995.
 
- The fund returned 11.15% based on net asset value for the six-month period
  ended May 31, 1995. The fund's total return for the period based on market
  price was 14.76%.
 
- The fund's closing price on May 31, 1995, was $9.13. Based on a net asset
  value of $8.78 on this same date, the fund was trading at a 3.93% premium.
 
DIVIDEND REVIEW
 
The fund continues to deliver a high level of current income, as reflected in
its 10.25% distribution rate based on net asset value and 9.86% distribution
rate based on market price, at the end of May.
 
MARKET REVIEW
 
It is a pleasure to report that since we last wrote to you, at the end of
November of 1994, the bond market has greatly improved. To give you an idea of
the change that's occurred--the Salomon Brothers Broad Investment Grade Index+,
which is a broad measure of bond activity, rose 11.56% over the six months ended
May 31, 1995, compared to a decline of 0.04% for the six months prior to
November-end. Bond yields which move inversely to bond prices have also fallen.
For example, the yield on the 10-year Treasury fell from 7.91% at the end of
November, to 6.28% at the end of May.
 
In late November, the economic data began to suggest that the economy had slowed
from the very strong pace of earlier in 1994. As you may know, slower economic
growth is usually positive for bond prices because it implies that inflation,
which erodes the value of fixed payments, is less likely to rise. Throughout the
first quarter of 1995, economic data such as industrial production, retail
sales, employment and consumer confidence continued to be weak. Since these
suggested slower economic growth, yields declined and bond prices rallied.
 
High yield bonds, which are the fund's primary investment, beat the broader
fixed-income market according to Salomon Brothers Indices. The Salomon Brothers
Extended High Yield Index++ returned 12.84%, for the six-month period ended May
31, 1995, compared to the Salomon Brothers Broad Investment Grade Index's return
of 11.56%. High yield bonds have benefited from continued economic strength and
favorable supply and demand fundamentals. The recent decline in yields has
boosted demand for the higher income offered by corporate bonds. This and lower
supply, because of a drop in the new-issuance of corporate bonds, have supported
corporate bond prices.
 
FUND REVIEW
 
In the six-month period, we continued to position the fund more defensively,
based on our belief that the economy will slow as 1995 progresses. We increased
the portfolio's weighting in media investments, which tend to perform well in
the later stages of economic growth. We also made the fund less sensitive to
market changes by lowering its exposure to deferred-interest bonds, which by
nature tend to amplify movements in the market, and by boosting its weighting in
cash-paying securities.
 
With our goal of making the fund more defensive, we also continued to increase
its position in BB-rated bonds, when the opportunity arose. At the end of May
1994, 19% of the fund's bond holdings were BB-rated. One year later, 21% were
BB-rated. As you
 
                                        1
<PAGE>   2
 
may know, although BB-rated securities provide less income than B-rated issues,
they are higher quality bonds. As a result, their price behavior tends to be
more closely related to Treasuries, which are AAA-rated. This has been the case
over the past six-months. Treasury bonds have rallied and BB-rated securities
have outperformed B-rated bonds.
 
PORTFOLIO COMPOSITION
 
As of May 31, 1995, 95% of the fund's portfolio was invested in long-term
corporate securities, 3% preferred and common shares and cash equivalents
comprising the remainder. The corporate securities have the following ratings:
 
<TABLE>
<CAPTION>
RATING BREAKDOWN     PERCENT
-----------------    -------
<S>                  <C>
BB                      21%
B                       71
Other                    8
</TABLE>
 
The fund's primary sector weightings include the cable industry, where we find
stable cash flow and good consolidation prospects, and the telecommunications
industry, where we see growth potential. The five largest holdings in the
portfolio are K & F Industries, Owens-Illinois Inc., Gaylord Container, American
Standard Inc., and Trump Taj Mahal. The fund's average maturity is approximately
7.8 years.
 
OUTLOOK
 
We look for the high yield market to perform reasonably well in 1995, with most
of the return from income rather than price appreciation. The Fed's tightening
during 1994 should slow the economy in 1995. This poses a less favorable
scenario for high yield issuers than in recent years and limits the upside for
prices of high yield bonds. On the other hand, the Fed's actions should be
successful in restraining inflation--a positive environment for fixed-income
securities such as high yield bonds.
 
Our strategy will continue to be one of positioning the fund so that it is less
sensitive to changes in the market. We will also continue to seek buying
opportunities among higher-quality securities.
 
Once again, we appreciate having you as a shareholder of Kemper High Income
Trust, and are pleased to report our activities to you.
 
Sincerely,
 
Michael A. McNamara
Vice President and Portfolio Co-Manager
 
Harry E. Resis, Jr.
Vice President and Portfolio Co-Manager
 
Mr. McNamara became a Portfolio Manager of the fund in 1990. He is a Senior Vice
President of Kemper Financial Services, Inc. (KFS).
 
Mr. Resis became Portfolio Co-Manager of the fund in 1992. He joined KFS in 1988
and is a Senior Vice President of KFS.
 
                                        2
<PAGE>   3
 
 * Morningstar ratings range from five stars (highest) to one star (lowest) and
   represent its assessment of the historical risk level and total return
   relative to its class as a weighted average for 3- and 5-year periods.
   Ratings are not absolute or necessarily predictive of future performance.
 
** Lipper Analytical Services, Inc. rankings are based upon changes in net asset
   value with all dividends reinvested. Rankings are historical and do not
   reflect future performance.
 
 + Salomon Brothers Broad Investment Grade (BIG) Bond Index is a market
   capitalization-weighted index that covers an all-inclusive universe of
   institutionally traded U.S. Treasury, agency, mortgage, and corporate
   securities. This index includes all fixed-rate bonds with a maturity of one
   year or longer and issues with at least a $50 million amount outstanding
   ($200 million for mortgage coupons). Source is Salomon Brothers Inc.
 
++ The Salomon Brothers Extended High Yield Bond Index is computed on a total
   return basis with all dividends reinvested, and is comprised of cash pay,
   deferred interest, bankrupt and/or default securities. Source is Salomon
   Brothers Inc.
 
Statistical Note: Current annualized distribution rate is the latest 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 price 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. The
ratings of Standard and Poor's Corporation (S&P) and Moody's Investors Service,
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.
 
                                        3
<PAGE>   4
 
ANNUAL SHAREHOLDERS MEETING
 
We are pleased to report that all six trustees have been re-elected to the Board
of Trustees of Kemper High Income Trust at the annual meeting held on May 16,
1995. The Trustees are: Arthur R. Gottschalk, Frederick T. Kelsey, David B.
Mathis, Stephen B. Timbers, John B. Tingleff and John G. Weithers.
 
Along with the re-election of the Trustees, shareholders were asked to ratify
the selection of Ernst & Young LLP as the independent auditors for the fund. The
results of the shareholders' vote at the May 16, 1995 meeting were as follows:
 
- Election of Trustees
 
<TABLE>
<CAPTION>
                          For         Withheld
<S>                    <C>            <C>
Arthur R.
  Gottschalk           18,382,262     354,004
Frederick T. Kelsey    18,391,870     344,396
David B. Mathis        18,360,971     375,295
Stephen B. Timbers     18,349,527     386,739
John B. Tingleff       18,404,202     332,064
John G. Weithers       18,401,592     334,674
</TABLE>
 
- Ratification of the selection of Ernst & Young LLP as independent auditors for
  the fund
 
               For:           18,203,274
                                 
               Against:          179,849
 
                                        4
<PAGE>   5
 
PORTFOLIO OF INVESTMENTS May 31, 1995
(Dollars in thousands)
<TABLE>
<CAPTION>
                                       Principal
                                        Amount     Value
                                       ---------  --------
<S>                                    <C>        <C>
CORPORATE OBLIGATIONS
BROADCASTING, CABLESYSTEMS
AND PUBLISHING-15.9%
----------------------------------------------------------
Act III Broadcasting, Inc., 9.625%,
  2003                                 $    290   $    284
----------------------------------------------------------
Adelphia Communication Corporation,
12.50%, 2002                              1,480      1,465
----------------------------------------------------------
(b)Australis Media Ltd., units,
  14.00%, 2003                            1,570        801
----------------------------------------------------------
Affinity Group, Inc., 11.50%, 2003        1,420      1,420
----------------------------------------------------------
(b)Bell Cablemedia PLC, 11.95%, 2004      1,320        865
----------------------------------------------------------
Big Flower Press, Inc., 10.75%, 2003      1,800      1,786
----------------------------------------------------------
CF Cable TV, Inc., 11.625%, 2005            645        684
----------------------------------------------------------
Cablevision Industries Corporation,
10.75%, 2002                              1,710      1,847
----------------------------------------------------------
Cablevision Systems Company
  9.875%, 2013                              865        891
  9.875%, 2023                              220        224
----------------------------------------------------------
Century Communications Corporation,
11.875%, 2003                             2,945      3,136
----------------------------------------------------------
Comcast Corporation
  9.50%, 2008                             2,360      2,336
  10.625%, 2012                             850        901
----------------------------------------------------------
Continental Cablevision, Inc.
9.50%, 2013                               2,675      2,702
----------------------------------------------------------
Granite Broadcasting Corp., 10.375%,
  2005                                      500        500
----------------------------------------------------------
(b)International Cabletel, 12.75%,
  2005                                    2,700      1,532
----------------------------------------------------------
Katz Corporation, 12.75%, 2002            1,175      1,275
----------------------------------------------------------
(b)Neodata Services, 12.00%, 2003           940        780
----------------------------------------------------------
Rogers Cablesystems Limited
  9.625%, 2002                              650        653
  10.00%, 2005                              670        680
----------------------------------------------------------
Sinclair Broadcasting Group, Inc.,
10.00%, 2003                              1,250      1,250
----------------------------------------------------------
Summit Communications Group Inc.,
10.50%, 2005                              1,075      1,180
----------------------------------------------------------
Univision TV, 11.75%, 2001                  625        675
----------------------------------------------------------
Viacom International, Inc., 8.00%,
  2006                                    2,420      2,360
----------------------------------------------------------
Videotron Groupe, 10.625%, 2005             420        441
----------------------------------------------------------
(b)Videotron Holdings PLC, 11.12%,
  2004                                      850        544
----------------------------------------------------------
Webcraft Technologies, Inc., 9.375%,
  2002                                      660        591
----------------------------------------------------------
                                                    31,803
 
<CAPTION>
                                       Principal
                                        Amount     Value
                                       ---------  --------
<S>                                    <C>        <C>
BUSINESS SERVICES-3.5%
----------------------------------------------------------
Comdata Network, Inc.
  12.50%, 1999                         $    600   $    656
  13.25%, 2002                            1,270      1,429
----------------------------------------------------------
Computervision Corporation
  10.875%, 1997                           1,390      1,404
  11.375%, 1999                             580        561
----------------------------------------------------------
Corporate Express Inc., 9.125%, 2004        830        805
----------------------------------------------------------
Merisel, Inc., 12.50%, 2004               1,350      1,188
----------------------------------------------------------
Outdoor Systems, Inc., 10.75%, 2003       1,080      1,037
----------------------------------------------------------
                                                     7,080
CHEMICALS-4.9%
----------------------------------------------------------
Arcadian Partners, L.P., 10.75%, 2005     1,420      1,454
----------------------------------------------------------
Atlantis Group, Inc., 11.00%, 2003        1,125      1,136
----------------------------------------------------------
G-I Holdings Inc., zero coupon, 1998      1,940      1,339
----------------------------------------------------------
Pioneer Americas Acquisition
  Corporation, 13.375%, 2005              1,300      1,362
----------------------------------------------------------
Polymer Group, Inc., 12.25%, 2002           725        732
----------------------------------------------------------
Rexene Corporation, 11.75%, 2004          1,390      1,512
----------------------------------------------------------
UCC Investors Holdings, Inc.
  10.50%, 2002                            1,980      2,064
  11.00%, 2003                              260        271
----------------------------------------------------------
                                                     9,870
COMMUNICATIONS-6.5%
----------------------------------------------------------
(b)Call-Net Enterprises Inc., 13.25%,
  2004                                      840        501
----------------------------------------------------------
(b)Celcaribe S.A., 13.50%, 2004             900        756
----------------------------------------------------------
(b)Cellular, Inc., 11.75%, 2003             585        433
----------------------------------------------------------
(b)Echostar Communications units,
12.875%, 2004                             3,850      1,829
----------------------------------------------------------
Intermedia Communications Florida,
  units, 13.50%, 2005                     1,000      1,004
----------------------------------------------------------
Paging Network, Inc.
  11.75%, 2002                            1,995      2,150
(a)  9.25%, 2002                          1,000      1,000
----------------------------------------------------------
(b)PanAmSat, L.P., 11.375%, 2003          2,350      1,669
----------------------------------------------------------
Rogers Cantel, 11.125%, 2002              2,553      2,655
----------------------------------------------------------
USA Mobile Communications, Inc. II,
14.00%, 2004                                850        939
----------------------------------------------------------
                                                    12,936
</TABLE>
 
                                        5
<PAGE>   6
 
(Dollars in thousands)
<TABLE>
<CAPTION>
                                       Principal
                                        Amount     Value
                                       ---------  --------
<S>                                    <C>        <C>
CONSTRUCTION MATERIALS-5.9%
----------------------------------------------------------
American Standard Inc.
  10.875%, 1999                        $  1,838   $  1,976
  11.375%, 2004                             720        799
(b)  10.50%, 2005                           950        713
  9.25%, 2016                               660        663
----------------------------------------------------------
(b)Building Materials Corporation of
  America, 11.75%, 2004                   3,205      1,955
----------------------------------------------------------
Nortek, 9.875%, 2004                      1,400      1,330
----------------------------------------------------------
Triangle Pacific Corporation, 10.50%,
  2003                                    2,185      2,229
----------------------------------------------------------
Waxman Industries, Inc.
  12.25%, 1998                              500        480
  13.75%, 1999                              936        791
(a)(b)  12.75%, 2004, with warrants
  expiring 2004                           1,853        841
----------------------------------------------------------
                                                    11,777
CONSUMER PRODUCTS AND SERVICES-7.3%
----------------------------------------------------------
Allied Waste Industry, 12.00%, 2004         500        520
----------------------------------------------------------
Bally's Park Place Funding, Inc.,
9.25%, 2004                               2,330      2,138
----------------------------------------------------------
Beatrice Foods, Inc., 12.00%, 2001        2,350      2,162
----------------------------------------------------------
Cinemark USA, Inc., 12.00%, 2002            907        983
----------------------------------------------------------
(b)Dr. Pepper Bottling Holdings, Inc.,
11.625%, 2003                             1,165        885
----------------------------------------------------------
Empress River Casino, 10.75%, 2002        1,000      1,010
----------------------------------------------------------
Mid-American Waste Systems Inc.,
12.25%, 2003                                920        948
----------------------------------------------------------
P&C Food Markets, Inc., 11.50%, 2001        830        880
----------------------------------------------------------
Players International, 12.25%, 2005         320        324
----------------------------------------------------------
Sante Fe Hotel Inc., 11.00%, 2000,
with warrants expiring 1996                 745        687
----------------------------------------------------------
Trump Taj Mahal, PIK, 11.35%, 1999        5,398      4,082
----------------------------------------------------------
                                                    14,619
DRUGS AND HEALTH CARE-3.9%
----------------------------------------------------------
Abbey Healthcare Group Incorporated,
9.50%, 2002                                 560        574
----------------------------------------------------------
Amerisource Distribution Corp, PIK,
11.25%, 2005                                710        796
----------------------------------------------------------
Charter Medical Corporation,
11.25%, 2004                              1,440      1,526
----------------------------------------------------------
Dade International Inc., 13.00%, 2005       850        901
----------------------------------------------------------
National Medical Enterprises
  9.625%, 2002                              420        443
  10.125%, 2005                           1,240      1,183
----------------------------------------------------------
Ornda Healthcorporation
  12.25%, 2002                            1,110      1,221
  11.375%, 2004                           1,000      1,092
----------------------------------------------------------
                                                     7,736
 
<CAPTION>
                                       Principal
                                        Amount     Value
                                       ---------  --------
<S>                                    <C>        <C>
ENERGY AND RELATED SERVICES-3.5%
----------------------------------------------------------
Chesapeake Energy Corp., 10.50%, 2002  $    385   $    389
----------------------------------------------------------
Dual Drilling Company, 9.875%, 2004         330        290
----------------------------------------------------------
Empire Gas Corporation, 7.00%, 2004,
with warrants expiring 2004               1,300      1,054
----------------------------------------------------------
Gerrity Oil & Gas, 11.75%, 2004           1,970      1,852
----------------------------------------------------------
Global Marine, 12.75%, 1999                 250        275
----------------------------------------------------------
Gulf Canada Resources Limited,
9.25%, 2004                                 700        693
----------------------------------------------------------
HS Resources, 9.875%, 2003                  190        186
----------------------------------------------------------
Trans-Texas Gas Corporation, 10.50%,
  2000                                    1,590      1,713
----------------------------------------------------------
WRT Energy Corporation unit,
13.875%, 2002                               510        523
----------------------------------------------------------
                                                     6,975
FINANCIAL SERVICES, HOME BUILDING AND
REAL ESTATE DEVELOPMENT-3.2%
----------------------------------------------------------
Continental Homes Holding,
12.00%, 1999                              1,100      1,097
----------------------------------------------------------
The Forecast Group L.P., 11.375%, 2000      200        122
----------------------------------------------------------
(a)Great America Holdings, 11.00%,
  1998                                      900        905
----------------------------------------------------------
Hovnanian Kent
  11.25%, 2002                            1,138      1,044
  9.75%, 2005                               600        490
----------------------------------------------------------
J.M. Peters, 12.75%, 2002                   460        391
----------------------------------------------------------
NVR, Inc., 11.00%, 2003                   1,170      1,112
----------------------------------------------------------
Oriole Homes Corp., 12.50%, 2003            240        207
----------------------------------------------------------
The Presley Companies, 12.50%, 2001       1,200      1,008
----------------------------------------------------------
                                                     6,376
MANUFACTURING, METALS AND MINING-18.7%
----------------------------------------------------------
Aftermarket Technology, 12.00%, 2004        950      1,007
----------------------------------------------------------
Amstar Corporation, 11.375%, 1997         2,326      2,338
----------------------------------------------------------
BE Aerospace, 9.75%, 2003                   720        713
----------------------------------------------------------
Bluebird Body Company, 11.75%, 2002       1,600      1,640
----------------------------------------------------------
Day International Group, 11.125%, 2005      330        335
----------------------------------------------------------
Earle M. Jorgensen Co., 10.75%, 2000        835        827
----------------------------------------------------------
Essex Group, Incorporated,
10.00%, 2003                                880        858
----------------------------------------------------------
Exide Corporation
  10.75%, 2002                              560        591
  10.00%, 2005                              970        994
----------------------------------------------------------
Fairchild Corporation
  12.00%, 2001                            2,280      1,961
  13.00%, 2007                              249        209
----------------------------------------------------------
Fairchild Industries, 12.25%, 1999        1,770      1,788
----------------------------------------------------------
Fairfield Manufacturing Company,
11.375%, 2001                               795        755
----------------------------------------------------------
</TABLE>
 
                                        6
<PAGE>   7
 
(Dollars in thousands)
<TABLE>
<CAPTION>
                                       Principal
                                        Amount     Value
                                       ---------  --------
<S>                                    <C>        <C>
(b)Foamex - JPS Automotive L.P.,
  14.00%, 2004 with warrants expiring
  1999                                 $    950   $    541
----------------------------------------------------------
Foamex L.P.,
  11.25%, 2002                              660        673
  11.875%, 2004                           1,790      1,736
----------------------------------------------------------
Great Dane Holdings, 12.75%, 2001         2,987      3,017
----------------------------------------------------------
GS Technologies, 12.00%, 2004             1,160      1,177
----------------------------------------------------------
Gulf States Steel, units,
13.50%, 2003                                900        913
----------------------------------------------------------
Jordan Industries, 10.375%, 2003          1,370      1,308
----------------------------------------------------------
JPS Automotive Products Corporation,
11.125%, 2001                               930        930
----------------------------------------------------------
K & F Industries, Inc.
  13.75%, 2001                            3,900      4,017
  11.875%, 2003                             560        568
----------------------------------------------------------
New-Flo Corporation, 13.25%, 2002           980        975
----------------------------------------------------------
Pace Industries, Inc., 10.625%, 2002        560        538
----------------------------------------------------------
Penda Industries Inc., 10.75%, 2004         600        540
----------------------------------------------------------
RHI Holdings, 11.875%, 1999                 665        638
----------------------------------------------------------
SPX Corporation, 11.75%, 2002               490        521
----------------------------------------------------------
Sequa Corporation
  9.625%, 1999                              200        202
  8.75%, 2001                               650        626
  9.375%, 2003                              250        240
----------------------------------------------------------
Thermedyne Industries, Inc., PIK
  10.25%, 2002                              792        780
  10.75%, 2003                            1,785      1,749
----------------------------------------------------------
Unisys Corporation
  13.50%, 1997                              490        541
  10.625%, 1999                           1,150      1,219
----------------------------------------------------------
                                                    37,465
PAPER, FOREST PRODUCTS AND
CONTAINERS-8.3%
----------------------------------------------------------
Berry Plastics Corporation,
12.25%, 2004, with warrants expiring
  2004                                      400        417
----------------------------------------------------------
Container Corporation of America
11.25%, 2004                                885        947
----------------------------------------------------------
Gaylord Container Corporation,
  11.50%, 2001                              670        719
(b)  12.75%, 2005                         1,730      1,687
----------------------------------------------------------
Maxxam Group Inc.
(b)  12.25%, 2003                           620        384
  11.25%, 2003                              475        451
----------------------------------------------------------
Owens-Illinois, Inc.
  11.00%, 2003                            1,940      2,148
  9.95%, 2004                             1,440      1,480
  9.75%, 2004                               770        781
----------------------------------------------------------
 
<CAPTION>
                                       Principal
                                        Amount     Value
                                       ---------  --------
<S>                                    <C>        <C>
Repap New Brunswick, Inc., 10.625%,
  2005                                 $  1,030   $  1,045
----------------------------------------------------------
Stone-Consolidated Corporation,
10.25%, 2000                              1,150      1,190
----------------------------------------------------------
Stone Container Corporation,
10.75%, 2002                              3,570      3,775
----------------------------------------------------------
Sweetheart Cup Company Inc.,
10.50%, 2003                                700        686
----------------------------------------------------------
SD Warren Company, 12.00%, 2004             850        927
----------------------------------------------------------
                                                    16,637
RETAILING-12.1%
----------------------------------------------------------
Color Tile Inc., 10.75%, 2001             2,010      1,286
----------------------------------------------------------
Dominick's Finer Foods, 10.875%, 2005       700        711
----------------------------------------------------------
Federated Department Stores, Inc.,
convertible, 9.72%, 2004                    440        442
----------------------------------------------------------
Finlay Fine Jewelry Corporation,
10.625%, 2003                               590        572
----------------------------------------------------------
Flagstar Corporation
  10.75%, 2001                              570        529
  10.875%, 2002                             590        547
----------------------------------------------------------
Food 4 Less Supermarket
  10.45%, 2000                            1,630      1,634
  13.75%, 2001                              780        862
----------------------------------------------------------
(c)Grand Union Company, 12.25%, 2002      3,395      1,120
----------------------------------------------------------
(b)International Semi-Tech
  Microelectronics, Inc., 11.50%, 2003    1,310        655
----------------------------------------------------------
Orchard Supply Hardware Corporation,
9.375%, 2002                                860        748
----------------------------------------------------------
Pamida Holdings, 11.75%, 2003             1,915      1,819
----------------------------------------------------------
Pathmark Stores, Inc.
  12.625%, 2002                           1,100      1,173
  9.625%, 2003                            1,110      1,077
----------------------------------------------------------
Penn Traffic Company
  8.625%, 2003                              820        769
  9.625%, 2005                              630        594
----------------------------------------------------------
Ralph's Grocery Company
  9.00%, 2003                             2,505      2,562
  10.45%, 2004                            1,120      1,123
----------------------------------------------------------
Service Merchandise Company,
9.00%, 2004                                 735        588
----------------------------------------------------------
Southland Corporation, 5.00%, 2003        4,005      3,054
----------------------------------------------------------
Specialty Retailers, Inc., 11.00%,
  2003                                      950        893
----------------------------------------------------------
Thrifty Payless
  11.75%, 2003                              800        856
  12.25%, 2004                              585        608
----------------------------------------------------------
                                                    24,222
</TABLE>
 
                                        7
<PAGE>   8
 
(Dollars in thousands)
<TABLE>
<CAPTION>
                                       Principal
                                       Amount or
                                       Number of
                                        Shares     Value
                                       ---------  --------
<S>                                    <C>        <C>
TRANSPORTATION-1.5%
----------------------------------------------------------
Burlington Motor Holdings Inc.,
11.50%, 2003                           $  1,350   $  1,185
----------------------------------------------------------
OMI Corp., 10.25%, 2003                   1,630      1,369
----------------------------------------------------------
(b)Transtar Holdings, L.P., 13.375%,
  2003                                      580        348
----------------------------------------------------------
                                                     2,902
TOTAL CORPORATE OBLIGATIONS-95.2%
(Cost: $192,067)                                   190,398
----------------------------------------------------------
COMMON AND PREFERRED STOCKS
----------------------------------------------------------
BCP/Essex Holdings                       18,000  hs.   477
----------------------------------------------------------
(c)Computervision Corporation           231,191      1,300
----------------------------------------------------------
(c)Echostar Communications               23,100        254
----------------------------------------------------------
(c)Gaylord Container Corporation        210,492      1,789
----------------------------------------------------------
(c)Gillett Co.                            6,731        140
----------------------------------------------------------
(c)J.M. Peters                            3,634          4
----------------------------------------------------------
(c)Panamset Corporation, PIK              1,500        524
----------------------------------------------------------
(a)(c)Peebles, Inc.                      38,659        966
----------------------------------------------------------
(c)Specialty Equipment Companies, Inc.   15,500        183
----------------------------------------------------------
(c)Thrifty Payless Inc.                  27,550        103
----------------------------------------------------------
(c)UGI Inc.                               5,550          7
----------------------------------------------------------
(c)Walter Industries, Inc.                7,469        102
----------------------------------------------------------
 
<CAPTION>
                                       Number of
                                       Contracts
                                          or
                                       Principal
                                        Amount     Value
                                       ---------  --------
<S>                                    <C>        <C>
TOTAL COMMON AND
PREFERRED STOCKS-2.9%
(Cost: $4,139)                                    $  5,849
----------------------------------------------------------
LONG PUT OPTIONS
(Cost: $47)
Treasury Note Futures
September 1995; 108 strike              30 cts.         22
----------------------------------------------------------
MONEY MARKET INSTRUMENT-.5%
(Cost: $1,000)
Yield-6.03%
Due-June 1995
Renaissance Energy Company             $  1,000      1,000
----------------------------------------------------------
TOTAL INVESTMENTS-98.6%
(Cost $197,253)                                    197,269
----------------------------------------------------------
CASH AND OTHER ASSETS
LESS LIABILITIES-1.4%                                2,694
----------------------------------------------------------
 
NET ASSETS-100%                                   $199,963
----------------------------------------------------------
</TABLE>
 
See accompanying Notes to Portfolio of Investments.
 
                                        8
<PAGE>   9
 
NOTES TO PORTFOLIO OF INVESTMENTS
 
(a) The following securities may require registration under the Securities Act
    of 1933 or an exemption therefrom in order to effect sale in the ordinary
    course of business; they were valued at cost on the dates of acquisition.
    These securities are valued at fair value as determined in good faith by the
    Board of Trustees of the Fund. There were no market quotations available for
    unrestricted securities of the same class on the dates of acquisition or on
    May 31, 1995. At May 31, 1995, the value of the Fund's restricted securities
    was $2,878,000, which represented 1.44% of net assets.
 
<TABLE>
<CAPTION>
                                                                                                   Principal
                                                                                                    Amount
                                                                                 Date of           or Number         Unit
                            Security Description                               Acquisition         of Shares         Cost
    ------------------------------------------------------------------------------------------------------------------------
    <S>                                                                  <C>                       <C>             <C>
    Great America Holdings, 11.00%, 1998                                  July 1990-March 1992     $900,000         $  86.06
    ------------------------------------------------------------------------------------------------------------------------
    Paging Network, Inc., 9.25%, 2002                                          March 1995          1,000,000           99.75
    ------------------------------------------------------------------------------------------------------------------------
    Peebles, Inc., common stock                                           July 1989-August 1994      38,659 shs.       27.50
    ------------------------------------------------------------------------------------------------------------------------
    Waxman Industries, Inc., warrants                                           June 1994            55,106             2.00
    ------------------------------------------------------------------------------------------------------------------------
</TABLE>
 
(b) Deferred interest obligation; currently zero coupon under terms of the
    initial offering.
 
(c) Non-income producing security. In the case of a bond, generally denotes that
    issuer has defaulted on the payment of interest or has filed for bankruptcy.
 
"PIK" denotes that interest or dividends are paid in kind.
 
Based on the cost of investments of $197,253,000 for federal income tax purposes
at May 31, 1995, the aggregate gross unrealized appreciation was $7,250,000, the
aggregate gross unrealized depreciation was $7,234,000 and the net unrealized
appreciation of investments was $16,000.
 
See accompanying Notes to Financial Statements.
 
                                        9
<PAGE>   10
 
STATEMENT OF ASSETS AND LIABILITIES
May 31, 1995
(in thousands)
 
<TABLE>
<S>                                              <C>
ASSETS
----------------------------------------------------------
Investments, at value
(Cost: $197,253)                                 $ 197,269
----------------------------------------------------------
Cash                                                   688
----------------------------------------------------------
Receivable for:
  Investments sold                                   6,878
----------------------------------------------------------
  Interest and dividends                             4,765
----------------------------------------------------------
    Total assets                                   209,600
----------------------------------------------------------
LIABILITIES AND NET ASSETS
----------------------------------------------------------
Payable for:
  Investments purchased                              9,375
----------------------------------------------------------
  Management fee                                       141
----------------------------------------------------------
  Administration fee                                    70
----------------------------------------------------------
  Custodian and transfer agent
  fees and related expenses                             35
----------------------------------------------------------
  Other                                                 16
----------------------------------------------------------
    Total liabilities                                9,637
----------------------------------------------------------
Net assets applicable to 22,769 shares
outstanding, $.01 par value,
equivalent to $8.78 per share                    $ 199,963
----------------------------------------------------------
ANALYSIS OF NET ASSETS
----------------------------------------------------------
Net amount received from issuance
of shares on account of capital                  $ 242,059
----------------------------------------------------------
Accumulated net realized loss
on sales of investments                            (44,578)
----------------------------------------------------------
Unrealized appreciation of investments                  16
----------------------------------------------------------
Undistributed net investment income                  2,466
----------------------------------------------------------
Net assets applicable to shares outstanding      $ 199,963
----------------------------------------------------------
Net asset value per share ($199,963 /
22,769 shares outstanding)                           $8.78
----------------------------------------------------------
</TABLE>
 
See accompanying Notes to Financial Statements.
STATEMENT OF OPERATIONS
Six months ended May 31, 1995
(in thousands)
 
<TABLE>
<CAPTION>
INVESTMENT INCOME
<S>                                               <C>
----------------------------------------------------------
  Interest                                        $ 11,687
----------------------------------------------------------
  Dividends                                             12
----------------------------------------------------------
    Total investment income                         11,699
----------------------------------------------------------
EXPENSES
----------------------------------------------------------
  Management fee                                       818
----------------------------------------------------------
  Interest expense                                     116
----------------------------------------------------------
  Administration fee                                   186
----------------------------------------------------------
  Custodian and transfer agent fees
  and related expenses                                  82
----------------------------------------------------------
  Professional fees                                     16
----------------------------------------------------------
  Reports to shareholders                                7
----------------------------------------------------------
  Trustees' fees and other                              40
----------------------------------------------------------
    Total expenses                                   1,265
----------------------------------------------------------
Net investment income                               10,434
----------------------------------------------------------
NET REALIZED AND UNREALIZED GAIN (LOSS) ON 
  INVESTMENTS
----------------------------------------------------------
  Net realized loss on sales of investments         (5,153)
----------------------------------------------------------
  Net change in balance of unrealized
  depreciation of investments                       15,236
----------------------------------------------------------
Net gain on investments                             10,083
----------------------------------------------------------
Net increase in net assets resulting from
  operations                                      $ 20,517
----------------------------------------------------------
</TABLE>
 
                                       10
<PAGE>   11
 
STATEMENT OF CHANGES IN NET ASSETS
(in thousands)
 
<TABLE>
<CAPTION>
                                Six months
                                   ended        Year ended
                                  May 31,      November 30,
                                   1995            1994
                                -----------    ------------
<S>                             <C>            <C>
OPERATIONS
---------------------------------------------------------
  Net investment income          $  10,434         19,981
---------------------------------------------------------
  Net realized loss on
  investments                       (5,153)       (11,455)
---------------------------------------------------------
  Net change in unrealized
  depreciation                      15,236        (13,448)
---------------------------------------------------------
Net increase (decrease) in
  net assets resulting from
operations                          20,517         (4,922)
---------------------------------------------------------
Distribution from net
  investment income                (10,230)       (20,319)
---------------------------------------------------------
Proceeds from shares issued
  in reinvestment of
dividends
(159 shares in 1995 and
251 shares in 1994)                  1,382          2,341
---------------------------------------------------------
Total increase (decrease) in
net assets                          11,669        (22,900)
---------------------------------------------------------
NET ASSETS
---------------------------------------------------------
Beginning of period                188,294        211,194
---------------------------------------------------------
End of period (including
undistributed net investment
income of $2,466 in
1995 and $2,262 in 1994)         $ 199,963        188,294
---------------------------------------------------------
</TABLE>
 
NOTES TO FINANCIAL STATEMENTS
 
1. SIGNIFICANT ACCOUNTING POLICIES
 
DESCRIPTION OF FUND
 
The Fund is registered under the Investment Company Act of 1940 as a
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. Portfolio securities
that are traded on a domestic securities exchange are valued at the last sale
price on the exchange where primarily traded or, if there is no recent sale, at
the last current bid quotation. Portfolio securities that are primarily traded
on foreign securities exchanges are generally valued at the preceding closing
values of such securities on their respective exchanges where primarily traded.
Securities not so traded are valued at the last current bid quotation if market
quotations are available. 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). Dividend income is recorded on the ex-dividend date,
and interest income is recorded on the accrual basis. Interest income includes
premium and discount amortization on money market instruments; it also includes
original issue and market discount amortization on long-term fixed income
securities. Realized gains and losses from investment transactions are reported
on an identified cost basis. Realized and unrealized gains and losses on
financial futures and options
 
                                       11
<PAGE>   12
 
are included in net realized and unrealized gain (loss) on investments, as
appropriate.
 
FEDERAL INCOME TAXES AND DIVIDENDS TO SHAREHOLDERS
 
The Fund has complied with the special provisions of the Internal Revenue Code
available to investment companies for the six months ended May 31, 1995. The
accumulated net realized loss on sales of investments for federal income tax
purposes at May 31, 1995, amounting to approximately $44,570,000, is available
to offset future taxable gains. If not applied, the loss carryover expires
during the period 1997 through 2003.
 
The Fund declares and pays dividends on a monthly basis. Net realized capital
gains, if any, reduced by capital loss carryovers, will be distributed at least
annually. Dividends payable to its shareholders are recorded by the Fund on the
ex-dividend date.
 
Distributions are determined in accordance with income tax principles which may
treat certain transactions differently from generally accepted accounting
principles.
 
OTHER CONSIDERATIONS
 
The Fund invests a substantial portion of its assets in high yield bonds. These
bonds ordinarily are in the lower rating categories of recognized rating
agencies or are non-rated, and thus involve more risk than higher rated bonds.
 
Kemper Financial Services, Inc. (KFS), the Fund's investment manager, may serve
as a member of various bondholders' committees. These committees represent the
interests of bondholders in restructuring negotiations and court proceedings. As
a result of participation on such committees, KFS may receive material,
non-public information with respect to bonds the Fund owns. Accordingly, the
Fund may be temporarily precluded from effecting transactions in such bonds due
to various restraints imposed by federal and state securities laws involving the
possession of material, non-public information.
 
2. TRANSACTIONS WITH AFFILIATES
 
The Fund has a management agreement with KFS. For management services and
facilities furnished, the Fund pays a fee at an annual rate of .85% of average
weekly net assets. The Fund incurred a management fee of $818,000 for the six
months ended May 31, 1995.
 
The Fund has a custodian agreement and a transfer agent agreement with Investors
Fiduciary Trust Company (IFTC), which was 50% owned by KFS until January 31,
1995, when KFS completed the sale of IFTC to a third party. For the six months
ended May 31, 1995, the Fund incurred custodian and transfer agent fees of
$50,000 (excluding related expenses). Pursuant to a services agreement with
IFTC, Kemper Service Company (KSvC), an affiliate of KFS, is the shareholder
service agent of the Fund. For the six months ended May 31, 1995, IFTC remitted
shareholder service fees of $31,000 to KSvC.
 
Certain officers or trustees of the Fund are also officers or directors of KFS.
During the six months ended May 31, 1995, the Fund made no direct payments to
its officers and incurred trustees' fees of $5,000 to independent trustees.
 
3. ADMINISTRATOR
 
The Fund has an administration agreement with Mitchell Hutchins Asset
Management, Inc. (Administrator). For services rendered to the Fund by the
Administrator, the Fund pays an annual fee of .15 of 1% on the first
$100,000,000 of average weekly net assets and .14 of 1% of average weekly net
assets over $100,000,000. The Fund incurred an administration fee of $186,000
for the six months ended May 31, 1995.
 
4. INVESTMENT TRANSACTIONS
 
For the six months ended May 31, 1995, investment transactions (excluding money
market instruments) are as follows (in thousands):
 
<TABLE>
<S>                                              <C>
Purchases                                        $ 108,067
----------------------------------------------------------
Proceeds from sales                                118,093
----------------------------------------------------------
</TABLE>
 
5. LINE OF CREDIT FACILITY
 
The fund has a $20,000,000 line of credit facility with Bank of America which is
available until June 30, 1996. As of May 31, 1995, there were no amounts
outstanding, however, on June 29, 1995 the fund borrowed $20,000,000 under the
facility. The loan bears interest at the London Interbank Offered Rate plus .45%
which is payable quarterly.
 
                                       12
<PAGE>   13
 
FINANCIAL HIGHLIGHTS
 
<TABLE>
<CAPTION>
                                                           Six months
                                                             ended
                                                            May 31,                       Year ended November 30,
                                                              1995           1994           1993           1992           1991
                                                           ----------     ----------     ----------     ----------     ----------
<S>                                                        <C>            <C>            <C>            <C>            <C>
PER SHARE OPERATING PERFORMANCE:
Net asset value, beginning of period                           $8.33            9.45           8.70           8.28           6.25
---------------------------------------------------------------------------------------------------------------------------------
Income from investment operations:
  Net investment income                                          .46             .88            .99            .94           1.01
---------------------------------------------------------------------------------------------------------------------------------
  Net realized and unrealized gain (loss) on investments         .44           (1.10)           .71            .45           2.07
---------------------------------------------------------------------------------------------------------------------------------
Total from investment operations                                 .90            (.22)          1.70           1.39           3.08
---------------------------------------------------------------------------------------------------------------------------------
Less dividends:
  Distribution from net investment income                        .45             .90            .95            .97            .94
---------------------------------------------------------------------------------------------------------------------------------
  Distribution from paid in surplus                               --              --             --             --            .11
---------------------------------------------------------------------------------------------------------------------------------
Total dividends                                                  .45             .90            .95            .97           1.05
---------------------------------------------------------------------------------------------------------------------------------
Net asset value, end of period                                 $8.78            8.33           9.45           8.70           8.28
---------------------------------------------------------------------------------------------------------------------------------
Market value, end of period                                    $9.13            8.38           9.13           9.13           8.63
---------------------------------------------------------------------------------------------------------------------------------
 
TOTAL RETURN (%):
Based on net asset value                                       11.12           (2.55)         20.62          17.42          52.90
---------------------------------------------------------------------------------------------------------------------------------
Based on market value                                          14.76            1.28          10.14          17.50          65.03
---------------------------------------------------------------------------------------------------------------------------------
 
RATIOS TO AVERAGE NET ASSETS (%):
 
Expenses                                                        1.31            1.64           1.82           2.03           2.22
---------------------------------------------------------------------------------------------------------------------------------
Net investment income                                          10.33            9.91          11.08          10.86          13.78
---------------------------------------------------------------------------------------------------------------------------------
 
SUPPLEMENTAL DATA:
Net assets at end of period (in thousands)                  $199,963         188,294        211,194        190,950        178,145
---------------------------------------------------------------------------------------------------------------------------------
Portfolio turnover rate (%)                                       95              83             98             47             27
---------------------------------------------------------------------------------------------------------------------------------
Total debt outstanding at end of period (in thousands)      $     --          20,000         20,000         17,312         17,312
---------------------------------------------------------------------------------------------------------------------------------
Asset coverage ratio per $1,000 of debt                           --            10.4           11.6           12.0           11.3
---------------------------------------------------------------------------------------------------------------------------------
</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.
 
                                       13
 
<PAGE>   14
KEMPER HIGH INCOME TRUST                 SEMIANNUAL REPORT TO SHAREHOLDERS
                                         May 31, 1995
 
 
                                         ---------------------------------------
 
                                         KEMPER
 
                                         ---------------------------------------
 
                                         HIGH

                                         ---------------------------------------
 
                                         INCOME
 
                                         ---------------------------------------

                                         TRUST

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

Trustees                       Officers
STEPHEN B. TIMBERS             JOHN E. PETERS
President and Trustee          Vice President

ARTHUR R. GOTTSCHALK           J. PATRICK BEIMFORD, JR.
Trustee                        Vice President

FREDERICK T. KELSEY            MICHAEL A. MCNAMARA
Trustee                        Vice President

DAVID B. MATHIS                HARRY E. RESIS, JR.
Trustee                        Vice President

JOHN B. TINGLEFF               PHILIP J. COLLORA
Trustee                        Vice President
                               and Secretary
                                                       
JOHN G. WEITHERS               CHARLES F. CUSTER       
Trustee                        Vice President and      
                               Assistant Secretary     
                                                       
                               JEROME L. DUFFY
                               Treasurer      
                                              
--------------------------------------------------------------
Legal Counsel                  Investment Manager
VEDDER, PRICE, KAUFMAN         KEMPER FINANCIAL
& KAMMHOLZ                     SERVICES, INC. 
222 North LaSalle Street       120 South LaSalle Street
Chicago, IL 60601              Chicago, IL 60603
                                              
Shareholder Service Agent      Custodian and Transfer Agent
KEMPER SERVICE COMPANY         INVESTORS FIDUCIARY
P.O. Box 419430                TRUST COMPANY  
Kansas City, MO 64141          127 West 10th Street
                               Kansas City, MO 64105
                                              
                                                          240740  [KEMPER LOGO]
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