STRONG SCHAFER VALUE FUND INC
N-30D, 1998-12-03
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<PAGE>

                                  THE STRONG
                                  ----------
                                SCHAFER VALUE
                                     FUND

                      ==================================
                      ANNUAL REPORT o SEPTEMBER 30, 1998
                      ==================================



                       [PHOTO OF STRONG FUNDS BUILDING]


                                 [STRONG LOGO]
                                 STRONG FUNDS

<PAGE>
                                       8

EIGHT BASIC PRINCIPLES FOR SUCCESSFUL MUTUAL FUND INVESTING

These common-sense rules are followed by many successful investors.  They make
sense for beginners, too.  If you have a question on these principles, or would
like to discuss them with us, please contact us at 1-800-368-3863.  We're here
24 hours a day, seven days a week to take your call.

- -------------------------------------------------------------------------------
                                        [PICTURE OF FOLDER LABELED INVESTMENTS]
1. HAVE A PLAN.  Even a simple plan can help you take control of your financial
future. Review your plan once a year, or if your circumstances change.

- -------------------------------------------------------------------------------
                                                             [PICTURE OF CLOCK]
2. START INVESTING AS SOON AS POSSIBLE.  Make time a valuable ally. Let it put
the power of compounding to work for you, while helping to reduce your
potential investment risk.

- -------------------------------------------------------------------------------
                                [PICTURE OF PIE CHART OF ASSET DIVERSIFICATION]
3. DIVERSIFY YOUR PORTFOLIO.  By investing in different asset classes - stocks,
bonds, and cash - you help protect against poor performance in one type of
investment while including investments most likely to help you achieve your
important goals.

- -------------------------------------------------------------------------------
                                           [PICTURE OF MEMO REMINDER TO INVEST]
4. INVEST REGULARLY.  Investing is a process, not a one-time event. By
investing regularly over the long term, you reduce the impact of short-term
market gyrations, and you attend to your long-term plan before you're tempted
to spend those assets on short-term needs.

- -------------------------------------------------------------------------------
                                              [PICTURE OF GRAPH SLOPING UPWARD]
5. MAINTAIN A LONG-TERM PERSPECTIVE.  For most individuals, the best discipline
is staying invested as market conditions change. Reactive, emotional investment
decisions are all too often a source of regret - and of principal loss.

- -------------------------------------------------------------------------------
             [PICTURE OF PIE CHART OF ASSET DIVERSIFICATION EMPHASIZING STOCKS]
6. CONSIDER STOCKS TO HELP ACHIEVE MAJOR LONG-TERM GOALS. Over time, stocks
have provided the more powerful returns needed to help the value of your
investments stay well ahead of inflation.

- -------------------------------------------------------------------------------
                                                       [PICTURE OF DOLLAR SIGN]
7. KEEP A COMFORTABLE AMOUNT OF CASH IN YOUR PORTFOLIO.  To meet current needs,
including emergencies, use a money market fund or a bank account - not your
long-term investment assets.

- -------------------------------------------------------------------------------
                                                  [PICTURE OF MAGNIFYING GLASS]
8. KNOW WHAT YOU'RE BUYING.  Make sure you understand the potential risks and
rewards associated with each of your investments.  Ask questions...request
information...make up your own mind.  And choose a fund company that helps you
make informed investment decisions.

<PAGE>

                                  THE STRONG
                                SCHAFER VALUE
                                     FUND

                      ==================================
                      ANNUAL REPORT o SEPTEMBER 30, 1998
                      ==================================

                               TABLE OF CONTENTS

INVESTMENT REVIEW
     The Strong Schafer Value Fund............................................2

FINANCIAL INFORMATION
     Schedule of Investments..................................................5
     Statement of Assets and Liabilities......................................7
     Statement of Operations..................................................7
     Statements of Changes in Net Assets......................................8
     Notes to Financial Statements............................................9

FINANCIAL HIGHLIGHTS.........................................................11

REPORT OF INDEPENDENT ACCOUNTANTS............................................12

<PAGE>

=============================
THE STRONG SCHAFER VALUE FUND
=============================

ONE OF THE REASONS FOR OUR UNDERPERFORMANCE IN FISCAL 1998 IS THAT WE DID NOT
OWN THE VERY LARGE STOCKS IN THE S&P 500.

The Strong Schafer Value Fund seeks long-term capital appreciation principally
through investments in common stocks and other equity securities. Current income
is a secondary--but important--objective.

A LOOK BACK ON A VERY DIFFICULT YEAR
The year ended September 30, 1998 was, by far, the most challenging and
difficult year we have experienced in 24 years of portfolio management.
Similarly, the quarter just ended was the most bruising three-month period we
have been through. The Strong Schafer Value Fund was down 23.52% for the fiscal
year ended September 30, 1998. During the same period the S&P 500 Stock Index
(S&P 500), the Fund's benchmark, returned 9.05%. The S&P 500 is generally
considered to be representative of the domestic stock market. Of this return,
8.55% was contributed by the top 25 companies in the Index while the remaining
companies contributed 0.5%.

One of the reasons for our underperformance in fiscal 1998 is that we did not
own the very large stocks in the S&P 500. Because of their rising prices and
expanded price/earnings multiples (P/Es), we have been, on balance, sellers of
the largest-capitalization stocks in the S&P 500 over the past several years.
During the year just ended, for example, we sold Atlantic Richfield, Progressive
Corp., Northern Trust, and SBC Communications, Inc.

A COMMITMENT TO OUR TIME-TESTED APPROACH
Instead of owning the very largest stocks in the Index, we have continued with
the investment approach we have used since the inception of the Fund, which has
led us to a greater weighting in the mid-cap area. Our long-standing investment
approach involves owning stocks (1) whose P/E multiples are less than the P/E
of the S&P 500, and (2) whose future earnings are expected to grow faster than
those of the S&P 500.  As the larger companies mentioned above met our price
targets and were sold because the P/E rose to the level of the S&P 500, they
were largely replaced by mid-cap stocks which, while having superior
fundamentals and more attractive valuations, nonetheless performed much less
well than their large-cap counterparts. We shifted into a heavier weighting in
the mid-cap area solely because we were unable to find large-cap alternatives
that met our valuation criteria. The mid-cap stocks we have added to the
portfolio not only have lower P/Es and better earnings per share growth
prospects than the S&P 500, they generally also have less exposure to foreign
markets than those stocks in the larger-cap universe.

Finally, selected securities held within the portfolio during the year were very
harshly treated in the market place. Earnings per share shortfalls often
resulted in disproportionate moves in stocks and any exposure to trouble spots
in the world, real or imagined, generally penalized stocks severely. Our two
most heavily weighted industries, financial and energy stocks, were especially
hard hit for these reasons.

2

<PAGE>

LOOKING AHEAD
While it is clear that recent market conditions have not favored our
value-driven investment style, it seems unlikely that market valuations for the
small group of large U.S. companies can climb indefinitely. We believe that
ultimately market preferences will return to those stocks which have
above-average earnings growth prospects and are reasonably priced.

The table on the following page illustrates the valuation of the Strong Schafer
Value Fund portfolio compared to the S&P 500. The P/E ratio of the Fund is less
than 11 times our estimate of 1999 earnings, substantially below the P/E of 21
for the S&P 500. Furthermore, we believe that our holdings will show an average
earnings per share growth of more than 13% in 1999 compared to the consensus
estimate for the S&P 500 of less than 5%.

Thank you for your continued faith and perseverance during this very trying
period. We remain committed to helping you achieve your long term investment
goals.

[PHOTO OF DAVID K. SCHAFER]

Sincerely,

/s/ David K. Schafer
David K. Schafer
Portfolio Manager

================================================================================
                    GROWTH OF AN ASSUMED $10,000 INVESTMENT
================================================================================
                            From 9-30-88 to 9-30-98
[GRAPH]

                         The Strong                    Lipper Growth
                       Schafer Value      S&P 500        and Income
                           Fund            Index*       Funds Index*
          9-88            10,000          10,000           10,000
          12-88           10,260          10,309           10,219
          12-90           12,000          13,154           11,887
          12-92           20,067          18,468           16,648
          12-94           23,815          20,598           19,003
          12-96           39,348          34,845           30,073
          9-98            39,692          49,260           37,277

This graph, prepared in accordance with SEC regulations, compares a $10,000
investment in the Fund, made on 9-30-88, with similar investments in the
Standard & Poor's 500 Stock Index ("S&P 500") and the Lipper Growth & Income
Funds Index.  Results include the reinvestment of all dividends and capital
gains distributions.  Performance is historical and does not represent future
results.  Investment returns and principal value vary, and you may have a gain
or loss when you sell shares in the Fund.
================================================================================

                                              ==================================
                                                         AVERAGE ANNUAL
                                                          TOTAL RETURNS
                                              ==================================
                                                          As of 9-30-98

                                                       1-YEAR            -23.52%

                                                       5-YEAR             10.89%

                                                      10-YEAR             14.78%

                                              SINCE INCEPTION             13.56%
                                                (on 10-22-85)
                                              ==================================

* The S&P 500 is an unmanaged index generally representative of the U.S. stock
  market, without regard to company size. The Lipper Growth & Income Funds Index
  is an equally-weighted performance index of the largest qualifying funds in
  this Lipper category.  Source of the S&P index data is Standard & Poor's
  Micropal. Source of the Lipper index data is Lipper Analytical Services, Inc.

                                                                               3

<PAGE>
<TABLE>
=====================================================================================
PORTFOLIO HOLDINGS, EARNINGS PER SHARE ESTIMATES, AND PRICE/EARNINGS RATIOS AS
                            OF 9-30-98 (UNAUDITED)
=====================================================================================
<CAPTION>
                              CLOSING PRICE  EARNINGS PER SHARE  PRICE/EARNINGS RATIO
SECURITY                        (9-30-98)     1998E      1999E    1998E        1999E
<S>                            <C>            <C>        <C>      <C>          <C>
INCO                              10.25       (0.49)     (0.16)    N.M.         N.M.
 .....................................................................................
Asia Pulp & Paper                  5.31        0.78       1.27     6.8          4.2
 .....................................................................................
New Holland                       11.25        2.00       1.80     5.6          6.3
 .....................................................................................
LaSalle Re Holdings               26.62        3.15       4.00     8.5          6.7
 .....................................................................................
R&B Falcon Drilling               12.00        1.42       1.78     8.5          6.7
 .....................................................................................
Arrow Electronics                 13.13        1.56       1.94     8.4          6.8
 .....................................................................................
UCAR International                18.00        2.39       2.65     7.5          6.8
 .....................................................................................
Owens Corning                     32.56        3.50       4.35     9.3          7.5
 .....................................................................................
Borg Warner Auto                  37.06        3.96       4.84     9.4          7.7
 .....................................................................................
Cleveland-Cliffs                  39.00        4.98       5.04     7.8          7.7
 .....................................................................................
Burlington Industries              9.50        1.34       1.18     7.1          8.1
 .....................................................................................
Chase Manhattan                   43.25        4.35       5.25     9.9          8.2
 .....................................................................................
Southdown                         45.00        4.68       5.35     9.6          8.4
 .....................................................................................
Partner Re Ltd                    40.06        4.45       4.65     9.0          8.6
 .....................................................................................
Lafarge Corp                      28.56        3.04       3.28     9.4          8.7
 .....................................................................................
Ultramar Diamond                  22.75        1.66       2.59    13.7          8.8
 .....................................................................................
May Department Stores             51.50        3.11       5.78    16.6          8.9
 .....................................................................................
Ford Motor                        47.00        5.19       5.09     9.1          9.2
 .....................................................................................
Armstrong World                   53.50        5.29       5.78    10.1          9.3
 .....................................................................................
National Bank of Canada           14.66        1.38       1.55    10.6          9.5
 .....................................................................................
Northrop Grumman                  73.00        6.55       7.64    11.1          9.6
 .....................................................................................
Avnet                             36.81        4.12       3.83     8.9          9.6
 .....................................................................................
Sun Company                       32.00        2.73       3.31    11.7          9.7
 .....................................................................................
Harman International              36.69        2.86       3.73    12.8          9.8
 .....................................................................................
SLM Holdings                      32.44        2.83       3.31    11.5          9.8
 .....................................................................................
Storage Technology                25.44        2.12       2.60    12.0          9.8
 .....................................................................................
Old Republic International        22.50        2.12       2.28    10.6          9.9
 .....................................................................................
PaineWebber                       30.00        2.70       2.95    11.1         10.2
 .....................................................................................
KLM Royal Dutch Air               24.75        3.89       2.40     6.4         10.3
 .....................................................................................
Philips NV                        53.37        4.35       5.20    12.3         10.3
 .....................................................................................
Champion Enterprises              23.25        1.89       2.20    12.3         10.6
 .....................................................................................
Goodyear Tire & Rubber            51.38        4.51       4.86    11.4         10.6
 .....................................................................................
Diamond Offshore                  26.00        2.63       2.40     9.9         10.8
 .....................................................................................
BankAmerica Corp                  53.50        3.75       4.80    14.3         11.1
 .....................................................................................
FDX Corporation                   45.13        3.91       4.05    11.5         11.1
 .....................................................................................
W.R. Berkley                      29.87        2.54       2.60    11.8         11.5
 .....................................................................................
Burlington Northern               32.00        2.40       2.75    13.3         11.6
 .....................................................................................
Keycorp                           28.87        2.25       2.46    12.8         11.7
 .....................................................................................
Repsol                            42.19        3.07       3.48    13.7         12.1
 .....................................................................................
JoAnn Stores                      22.25        1.60       1.75    13.9         12.7
 .....................................................................................
IBP Corporation                   20.25        1.57       1.54    12.9         13.1
 .....................................................................................
Summit Bank                       37.50        2.65       2.85    14.2         13.2
 .....................................................................................
Kansas City Power & Light         30.44        2.17       2.27    14.0         13.4
 .....................................................................................
Western Resources                 41.37        2.67       2.81    15.5         14.7
 .....................................................................................
Mellon Bank                       55.06        3.25       3.60    16.9         15.3
 .....................................................................................
GTE Corporation                   55.00        3.06       3.48    18.0         15.8
 .....................................................................................
Norwest Corp                      35.81        2.00       2.25    17.9         15.9
 .....................................................................................
Phillips Petroleum                45.12        2.07       2.71    21.8         16.6
 .....................................................................................
Kansas City Southern Industries   35.00        1.90       2.05    18.4         17.1
 .....................................................................................
Boeing Company                    34.31        1.00       1.95    34.3         17.6
                                                                  -------------------
S&P 500 INDEX                  1,017.01       46.36      48.52    21.9         21.0
STRONG SCHAFER VALUE FUND PORTFOLIO AVERAGES                      12.2         10.6

E=ESTIMATE

4
</TABLE>

<PAGE>
<TABLE>
SCHEDULE OF INVESTMENTS IN SECURITIES                                      SEPTEMBER 30, 1998
- ---------------------------------------------------------------------------------------------
=============================================================================================
                                   STRONG SCHAFER VALUE FUND
=============================================================================================
<CAPTION>
                                     Shares or                Unit
                                     Principal    Average    Market                 Market
Security                              Amount     Unit Cost    Value   % Change       Value
- ---------------------------------------------------------------------------------------------
COMMON STOCKS 99.1%
AEROSPACE & DEFENSE 4.0%
<S>                                <C>            <C>        <C>       <C>     <C>
The Boeing Company                     835,000    $ 49.90    $34.31    -31.24%   $ 28,650,937
Northrop Grumman Corporation           390,000     107.02     73.00    -31.79      28,470,000
                                                                                 ------------
                                                                                   57,120,937
AGRICULTURAL EQUIPMENT 1.3%
New Holland NV                       1,594,700      23.88     11.25    -52.89      17,940,375

AIR TRANSPORT 2.0%
FDX Corporation (b)                    645,000      51.07     45.13    -11.63      29,105,625

AIRLINE 1.8%
KLM Royal Dutch Airlines             1,060,000      41.10     24.75    -39.78      26,235,000

AUTO PARTS 3.9%
Borg-Warner Automotive, Inc.           680,000      41.06     37.06     -9.74      25,202,500
The Goodyear Tire & Rubber Company     600,000      56.43     51.38     -8.95      30,825,000
                                                                                 ------------
                                                                                   56,027,500
AUTOMOBILE 2.6%
Ford Motor Company                     800,000      27.93     46.94     68.06      37,550,000

BANKS 13.4%
The Chase Manhattan Corporation        593,200      45.07     43.25     -4.04      25,655,900
KeyCorp                              1,100,000      26.38     28.88      9.47      31,762,500
Mellon Bank Corporation                527,100      31.46     55.06     75.02      29,023,444
National Bank of Canada (d)          2,090,000      12.27     14.66     19.47      30,636,957
NationsBank Corporation                420,000      61.84     53.50    -13.48      22,470,000
Norwest Corporation                    810,000      36.89     35.81     -2.92      29,008,125
Summit Bancorp                         620,300      39.72     37.50     -5.58      23,261,250
                                                                                 ------------
                                                                                  191,818,176
BROKERAGE 1.8%
Paine Webber Group, Inc.               875,000      18.49     30.00     62.25      26,250,000

CEMENT 4.1%
Lafarge Corporation                  1,050,000      23.61     28.56     20.96      29,990,625
Southdown, Inc.                        640,000      40.75     45.00     10.43      28,800,000
                                                                                 ------------
                                                                                   58,790,625
COMPUTER EQUIPMENT & SERVICE 1.8%
Storage Technology Corporation(b)    1,006,400      20.35     25.44     25.01      25,600,300

ELECTRIC UTILITIES 5.8%
Kansas City Power & Light Company(b) 1,269,400      30.98     30.44     -1.74      38,637,362
Western Resources, Inc.              1,070,000      36.35     41.38     13.84      44,271,250
                                                                                 ------------
                                                                                   82,908,612
ELECTRONIC EQUIPMENT & DISTRIBUTION 8.1%
Arrow Electronics, Inc.              1,900,000      27.53     13.13    -52.31      24,937,500
Avnet, Inc.                            692,600      56.33     36.81    -34.65      25,496,338
Harman International
  Industries, Inc.(c)                1,030,000      39.50     36.69     -7.12      37,788,125
Philips Electronics NV ADR             510,000      45.90     53.38     16.29      27,221,250
                                                                                 ------------
                                                                                  115,443,213
FINANCIAL SERVICES 4.0%
Kansas City Southern Industries, Inc.  900,000      35.46     35.00     -1.30      31,500,000
SLM Holding Corporation                800,000      45.59     32.44    -28.84      25,950,000
                                                                                 ------------
                                                                                   57,450,000
FOOD 2.9%
IBP, Inc.                            2,044,200      23.35     20.25    -13.28      41,395,050

HOUSING RELATED 6.7%
Armstrong World Industries, Inc.       570,800      68.29     53.50    -21.66      30,537,800
Champion Enterprises, Inc. (b)       1,082,300      16.51     23.25     40.82      25,163,475
Owens Corning                        1,205,000      35.35     32.56     -7.89      39,237,813
                                                                                 ------------
                                                                                   94,939,088

                                                                                            5

<PAGE>

SCHEDULE OF INVESTMENTS IN SECURITIES (CONTINUED)                          SEPTEMBER 30, 1998
- ---------------------------------------------------------------------------------------------
=============================================================================================
                             STRONG SCHAFER VALUE FUND (CONTINUED)
=============================================================================================
<CAPTION>
                                     Shares or                Unit
                                     Principal    Average    Market                Market
Security                              Amount     Unit Cost    Value   % Change      Value
- ---------------------------------------------------------------------------------------------
INSURANCE 7.4%
W.R. Berkley Corporation               964,200    $ 34.78   $ 29.88    -14.09% $   28,805,475
LaSalle Re Holdings, Ltd.              560,400      24.32     26.63      9.50      14,920,650
Old Republic International
  Corporation                        1,224,000      16.37     22.50     37.45      27,540,000
Partners RE, Ltd. ADR                  850,000      41.66     40.06     -3.84      34,053,125
                                                                               --------------
                                                                                  105,319,250
METALS & MINING 5.5%
Cleveland-Cliffs, Inc.(c)              577,600      42.94     39.00     -9.18      22,526,400
Inco, Ltd.                           2,428,000      19.72     10.25    -48.02      24,887,000
UCAR International, Inc. (b)         1,746,900      30.88     18.00    -41.71      31,444,200
                                                                               --------------
                                                                                   78,857,600
OIL 9.5%
Phillips Petroleum Company             890,000      48.20     45.13     -6.37      40,161,250
Repsol SA Sponsored ADR                770,000      42.44     42.19     -0.59      32,484,375
Sun Company, Inc.                    1,040,000      41.47     32.00    -22.84      33,280,000
Ultramar Diamond Shamrock
  Corporation                        1,301,100      30.59     22.75    -25.63      29,600,025
                                                                               --------------
                                                                                  135,525,650
OIL WELL EQUIPMENT & SERVICE 2.8%
Diamond Offshore Drilling, Inc.        900,000      40.83     26.00    -36.32      23,400,000
R&B Falcon Corporation(b)            1,400,000      22.46     12.00    -46.57      16,800,000
                                                                               --------------
                                                                                   40,200,000
PAPER & FOREST PRODUCTS 0.5%
Asia Pulp & Paper Company, Ltd.
  ADR(b)                             1,437,300       9.90      5.31    -46.36       7,635,656

RAILROAD 2.9%
Burlington Northern Santa Fe
  Corporation                        1,290,000      29.42     32.00      8.77      41,280,000

RETAIL 3.0%
May Department Stores Company          680,000      47.92     51.50      7.47      35,020,000
Jo-Ann Stores, Inc. Class A (b)         12,500      23.86     22.25     -6.75         278,125
Jo-Ann Stores, Inc. Class B (b)        356,500      21.73     19.00    -12.56       6,773,500
                                                                               --------------
                                                                                   42,071,625
TELECOMMUNICATION 2.5%
GTE Corporation                        637,000      46.32     55.00     18.74      35,035,000

TEXTILE & APPAREL MANUFACTURING 0.8%
Burlington Industries, Inc. (b)      1,159,400      12.15      9.50    -21.81      11,014,300
- ---------------------------------------------------------------------------------------------
TOTAL COMMON STOCKS (COST $1,589,661,819)                                       1,415,513,582
- ---------------------------------------------------------------------------------------------

SHORT-TERM INVESTMENTS (a) 2.0%
COMMERCIAL PAPER
INTEREST BEARING 2.0%
Associates Corporation of North
  America, 5.59%, Due 10/01/98     $28,400,000     100.00    100.00      0.00      28,400,000

INTEREST BEARING, DUE UPON DEMAND 0.0%
Wisconsin Electric Power
  Company, 4.96%                       564,637     100.00    100.00      0.00         564,637
- ---------------------------------------------------------------------------------------------
TOTAL SHORT-TERM INVESTMENTS (COST $28,964,637)                                    28,964,637
- ---------------------------------------------------------------------------------------------

- ---------------------------------------------------------------------------------------------
TOTAL INVESTMENTS IN SECURITIES 101.1% (COST $1,618,626,456)                    1,444,478,219
Other Assets & Liabilities, Net (1.1%)                                            (16,746,693)
- ---------------------------------------------------------------------------------------------
NET ASSETS 100.0%                                                              $1,427,731,526
=============================================================================================


LEGEND
- ---------------------------------------------------------------------------------------------
(a) Short-term investments include any security which has a maturity of less than one year.
(b) Non-income producing security.
(c) Affiliated issuer (See note 6 of Notes to Financial Statements).
(d) Foreign-denominated security.

Percentages are stated as a percent of net assets.

See Notes to Financial Statements.

6
</TABLE>

<PAGE>

STATEMENT OF ASSETS AND LIABILITIES
- -------------------------------------------------------------------------------
September 30, 1998
                                                          STRONG SCHAFER
                                                            VALUE FUND
                                                          --------------
ASSETS:
  Investments in Securities, at Market Value
    Unaffiliated Issuers (Cost of $1,553,139,892)         $1,384,163,694
    Affiliated Issuers (Cost of $65,486,564)                  60,314,525
                                                          --------------
    Total Investments in Securities                        1,444,478,219
  Receivable for Securities Sold                              51,063,130
  Receivable from Fund Shares Sold                               290,813
  Dividends and Interest Receivable                            2,376,198
  Other Assets                                                    18,268
                                                          --------------
  Total Assets                                             1,498,226,628

LIABILITIES:
  Payable for Securities Purchased                            68,481,419
  Payable for Fund Shares Redeemed                               444,354
  Accrued Operating Expenses and Other Liabilities             1,569,329
                                                          --------------
  Total Liabilities                                           70,495,102
                                                          --------------
NET ASSETS                                                $1,427,731,526
                                                          ==============
NET ASSETS CONSIST OF:
  Capital Stock (250,000,000 shares authorized,
    $.10 par value)                                       $    2,863,881
  Paid-in Capital                                          1,593,943,466
  Accumulated Net Investment Income                            2,714,501
  Accumulated Net Realized Gain                                2,358,496
  Net Unrealized Depreciation                               (174,148,818)
                                                          --------------
  Net Assets                                              $1,427,731,526
                                                          ==============
Capital Shares Outstanding                                    28,638,810

NET ASSET VALUE PER SHARE                                         $49.85
                                                                  ======


STATEMENT OF OPERATIONS
- -------------------------------------------------------------------------------
For the Year Ended September 30, 1998
                                                          STRONG SCHAFER
                                                            VALUE FUND
                                                          --------------
INCOME:
  Dividends
    Unaffiliated Issuers (net of withholding taxes
      of $730,290)                                         $ 30,698,370
    Affiliated Issuers                                          976,943
  Interest                                                    1,523,949
                                                           ------------
  Total Income                                               33,199,262

EXPENSES:
  Investment Advisory Fees                                   17,407,737
  Custodian Fees                                                 48,545
  Shareholder Servicing Costs                                 3,181,903
  Other                                                       1,007,316
                                                           ------------
  Total Expenses                                             21,645,501
                                                           ------------
NET INVESTMENT INCOME                                        11,553,761

REALIZED AND UNREALIZED GAIN (LOSS):
  Net Realized Gain on Investments                            5,547,326
  Net Change in Unrealized Appreciation/Depreciation on
    Investments                                            (478,303,192)
                                                           ------------
NET LOSS ON INVESTMENTS                                    (472,755,866)
                                                           ------------
NET DECREASE IN NET ASSETS RESULTING FROM OPERATIONS      ($461,202,105)
                                                           ============

                                                                              7

                      See Notes to Financial Statements.

<PAGE>

STATEMENTS OF CHANGES IN NET ASSETS
- --------------------------------------------------------------------------------
                                                  STRONG SCHAFER VALUE FUND
                                              ---------------------------------
                                                YEAR ENDED         YEAR ENDED
                                              SEPT. 30, 1998     SEPT. 30, 1997
                                              --------------     --------------
OPERATIONS:
  Net Investment Income                       $   11,553,761     $    6,467,778
  Net Realized Gain                                5,547,326         33,191,786
  Net Change in Unrealized
    Appreciation/Depreciation                   (478,303,192)       266,090,855
                                              --------------     --------------
  Net Increase (Decrease) in Net Assets
    Resulting from Operations                   (461,202,105)       305,750,419

DISTRIBUTIONS:
  From Net Investment Income                     (13,340,621)        (4,149,409)
  From Net Realized Gains                        (32,880,858)       (13,812,350)
                                              --------------     --------------
  Total Distributions                            (46,221,479)       (17,961,759)

CAPITAL SHARE TRANSACTIONS:
  Proceeds from Shares Sold                    1,316,428,586        856,205,901
  Proceeds from Reinvestment of Distributions     44,633,159         17,495,106
  Payment for Shares Redeemed                   (743,425,263)      (233,352,907)
                                              --------------     --------------
  Increase in Net Assets from Capital
    Share Transactions                           617,636,482        640,348,100
                                              --------------     --------------
TOTAL INCREASE IN NET ASSETS                     110,212,898        928,136,760

NET ASSETS:
  Beginning of Year                            1,317,518,628        389,381,868
                                              --------------     --------------
  End of Year                                 $1,427,731,526     $1,317,518,628
                                              ==============     ==============
TRANSACTIONS IN SHARES OF THE FUND:
  Sold                                            20,130,827         15,163,183
  Issued in Reinvestment of Distributions            712,307            340,173
  Redeemed                                       (11,784,062)        (4,159,413)
                                                  ----------         ----------
  Net Increase in Shares of the Fund               9,059,072         11,343,943
                                                  ==========         ==========

8

                      See Notes to Financial Statements.

<PAGE>

NOTES TO FINANCIAL STATEMENTS
- --------------------------------------------------------------------------------
September 30, 1998

1. ORGANIZATION
   Strong Schafer Value Fund, Inc. (the "Fund") was incorporated under the laws
   of the State of Maryland on August 12, 1985, and is registered under the
   Investment Company Act of 1940, as amended, as an open-end, diversified
   management investment company.

2. SIGNIFICANT ACCOUNTING POLICIES
   The following is a summary of significant accounting policies followed by the
   Fund in the preparation of its financial statements.
  (A) Security Valuation -- Portfolio securities traded primarily on a
      principal securities exchange are valued at the last reported sales price
      or the mean between the latest bid and asked prices where no last sales
      price is available.  Securities traded over-the-counter are valued at the
      mean of the latest bid and asked prices or the last reported sales price.
      Securities for which market quotations are not readily available, when
      held by the Funds, are valued at fair value as determined in good faith
      under consistently applied procedures established by and under the general
      supervision of the Board of Directors.  Securities which are purchased
      within 60 days of their stated maturity are valued at amortized cost,
      which approximates fair value.

  (B) Federal Income and Excise Taxes and Distributions to Shareholders -- The
      Fund intends to comply with the requirements of the Internal Revenue Code
      applicable to regulated investment companies and to distribute
      substantially all of its taxable income to its shareholders in a manner
      which results in no tax cost to the Fund.  Therefore, no federal income or
      excise tax provision is required.

      The character of distributions made during the year from net investment
      income or net realized gains may differ from the characterization for
      federal income tax purposes due to differences in the recognition of
      income and expense items for financial statement and tax purposes.  Where
      appropriate, reclassifications between net asset accounts are made for
      such differences that are permanent in nature.

  (C) Realized Gains and Losses on Investment Transactions -- Gains or losses
      realized on investment transactions are determined by comparing the
      identified cost of the security lot sold with the net sales proceeds.
 
  (D) Additional Investment Risk -- The Fund has short-term investments which
      are unsecured nonnegotiable instruments.  These instruments are rated at
      least A1 by Standard & Poor's.  However, the Fund may be susceptible to
      credit risk with respect to these securities to the extent the issuer
      defaults on its payment obligation.  The Fund's policy is to monitor the
      creditworthiness of the issuer and the Fund does not anticipate
      nonperformance by these counterparties.

      Foreign denominated assets may involve greater risks than domestic
      transactions, including currency, political and economic, regulatory and
      market risks.

  (E) Foreign Currency Translation -- Investment securities and other assets
      and liabilities initially expressed in foreign currencies are converted to
      U.S. dollars based upon current exchange rates.  Purchases and sales of
      foreign investment securities and income are converted to U.S. dollars
      based upon currency exchange rates prevailing on the respective dates
      of such transactions.  The effect of changes in foreign exchange rates is
      reflected as a component of gains or losses on investments.
 
  (F) Use of Estimates -- The preparation of financial statements in conformity
      with generally accepted accounting principles requires management to make
      estimates and assumptions that affect the reported amounts of assets and
      liabilities and disclosure of contingent assets and liabilities at the
      date of the financial statements, and the reported amounts of increases
      and decreases in net assets from operations during the reporting period.
      Actual results could differ from those estimates.
 
  (G) Other -- Investment security transactions are recorded as of the trade
      date.  Dividend income and distributions to shareholders are recorded on
      the ex-dividend date.  Interest income is recorded on the accrual basis
      and includes amortization of premiums and discounts.

                                                                               9

<PAGE>

NOTES TO FINANCIAL STATEMENTS (CONTINUED)
- -------------------------------------------------------------------------------
September 30, 1998

3. RELATED PARTY TRANSACTIONS
   Management and investment advisory services are provided to the Fund by
   Schafer Capital Management, Inc. ("Schafer").  The Investment Advisory
   Agreement provides that, subject to the direction of the Fund's Board of
   Directors, Schafer is responsible for the management of the Fund's portfolio.
   Schafer is obligated to perform certain administrative and management
   services for the Fund, except to the extent these services are provided by
   any custodian, transfer agent, registrar or administrator hired by the Fund,
   and is obligated to provide all of the office space, facilities, equipment
   and personnel necessary to perform its duties under the investment advisory
   agreement.  The agreement provides for a monthly fee computed at an annual
   rate of 1.0% of the Fund's average daily net assets.

   In January 1996, Schafer formed an alliance with Strong Capital Management,
   Inc. ("Strong").  Strong provides fund accounting services and shareholder
   recordkeeping and related services to the Fund.  Fund accounting service fees
   are contractually established based upon the net assets of the Fund.  Fund
   accounting service fees paid to Strong for the year ended September 30, 1998
   were $55,398.  Shareholder recordkeeping and related service fees are based
   upon contractually established rates for each open and closed shareholder
   account.  Shareholder recordkeeping and related service fees payable  to
   Strong at September 30, 1998 were $136,085.  In addition, Strong is
   compensated for certain other services related to costs incurred for reports
   to shareholders.  Other shareholder servicing expenses paid to Strong for the
   year ended September 30, 1998 were $18,629.

   Pursuant to a distribution agreement, an indirect subsidiary of Strong,
   Strong Funds Distributors, Inc., has agreed to act at the request of the Fund
   and Schafer as the Fund's agent to effect the distribution of the Fund's
   shares.  No expenses are incurred by the Fund with respect to this agreement

   In September, 1997, Schafer and Strong entered into a Limited Liability
   Company Agreement (the "LLC Agreement") forming Strong Schafer Capital
   Management, LLC (the "LLC").  The LLC Agreement provides that Schafer and
   Strong shall be members of the LLC, with Schafer as the managing member, and
   grants to Strong an option to purchase Schafer's interest in the LLC which
   is first exercisable on January 10, 2001, or earlier in the event of certain
   other circumstances, subject to obtaining necessary regulatory approvals,
   including approval of the Fund's shareholders.

   Effective October 15, 1998 (see Note 7), the Fund's shareholders approved the
   adoption of a new investment advisory agreement between the Fund and the LLC,
   on terms substantially the same as the prior agreement.  As managing member
   of the LLC, Schafer will provide ongoing management and investment advisory
   services to the Fund.  These changes will not affect the current investment
   approach or philosophy outlined in the Fund's Prospectus.  Schafer, through
   its sole portfolio manager and controlling person, David K. Schafer, will
   continue in its role as the Fund's investment manager in which it has served
   since the Fund's inception.  As managing member of the LLC, Schafer will
   perform all obligations of the LLC under the new investment advisory
   agreement between the Fund and the LLC.  Moreover, the investment advisory
   fee rate payable by the Fund to the LLC under the new investment advisory
   agreement is the same.

   Investment advisory fees payable to Schafer at September 30, 1998 were
   $1,205,196.  Unaffiliated directors' fees paid during the year were $15,000.

4. INVESTMENT TRANSACTIONS
   Aggregate purchases and proceeds from sales of investment securities
   (excluding short-term investments) during the year ended September 30, 1998
   were $1,239,934,827 and $656,082,720, respectively.

5. INCOME TAX INFORMATION
   At September 30, 1998, the cost of investments in securities for federal
   income tax purposes was $1,621,134,587.  Net unrealized depreciation of
   securities was $176,656,368, consisting of gross unrealized appreciation and
   depreciation of $121,464,229 and $298,120,597, respectively.

   For corporate shareholders in the Fund, the percentage of dividend income
   distributed for the year ended September 30, 1998 which is designated as
   qualifying for the dividends-received deduction is 100% (unaudited).

10

<PAGE>

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


6. INVESTMENTS IN AFFILIATES
   Affiliated issuers, as defined under the Investment Company Act of 1940,
   include those in which the Fund's holdings represent 5% or more of the
   outstanding voting securities of the issuer.  A summary of transactions in
   the securities of these issuers during the year ended September 30, 1998 is
   as follows:
<TABLE>
<CAPTION>
                                    BALANCE OF        GROSS       GROSS SALES     BALANCE OF       VALUE     DIVIDEND INCOME
                                    SHARES HELD     PURCHASES         AND         SHARES HELD    SEPT. 30,   OCT. 1, 1997 -
                                   OCT. 1, 1997   AND ADDITIONS   REDUCTIONS    SEPT. 30, 1998     1998      SEPT. 30, 1998
<S>                                   <C>            <C>              <C>         <C>           <C>             <C>
Cleveland-Cliffs, Inc.                500,300         77,300          --            577,600     $22,526,400     $807,958
Harman International Industries, Inc. 577,000        453,000          --          1,030,000      37,788,125      168,985
</TABLE>

7. SPECIAL MEETING OF SHAREHOLDERS
   At a shareholder meeting held on October 15, 1998, in Princeton, NJ,
   shareholders (1) elected a new Board of Directors, (2) approved the adoption
   of a new investment advisory agreement between the LLC and the Fund (prior to
   such meeting Schafer was the advisor to the Fund, now Schafer is the LLC's
   Managing Member - see Note 3), and (3) ratified the appointment of
   PricewaterhouseCoopers LLP as independent auditors of the Fund.
                                         STRONG SCHAFER VALUE FUND
   (UNAUDITED)                          SHARES VOTED 17,093,447.995
                                    -----------------------------------
   PROPOSALS                        AFFIRMATIVE    WITHHOLD
   ---------                        -----------    --------
   1.  Election of Directors
        David K. Schafer              98.590%       1.410%
        Timothy C. Collins            98.375        1.625
        Mary P. English               98.373        1.627
        Phillip P. Young              98.624        1.376
 
                                    AFFIRMATIVE    AGAINST      ABSTAIN
                                    -----------    -------      -------
    2. Adopt Advisory Agreement       96.322%       1.850%       1.828%

    3. Ratify Selection of Auditors   97.814        1.048        1.138


<TABLE>
FINANCIAL HIGHLIGHTS
- -----------------------------------------------------------------------------------------------------------------

STRONG SCHAFER VALUE FUND
- -----------------------------------------------------------------------------------------------------------------
                                                  SELECTED PER-SHARE DATA(a)
               -------------------------------------------------------------------------------------------------
                             INCOME FROM INVESTMENT OPERATIONS            LESS DISTRIBUTIONS
                          --------------------------------------  -----------------------------------
                                       Net Realized
               Net Asset              and Unrealized     Total                                         Net Asset
                 Value,      Net           Gains         from      From Net   From Net                  Value,
               Beginning  Investment   (Losses) on    Investment  Investment  Realized      Total       End of
  Year Ended   of Period    Income     Investments    Operations    Income      Gains   Distributions   Period
<S>             <C>         <C>         <C>            <C>         <C>         <C>         <C>          <C>
Sept. 30, 1998  $67.29      $0.40       ($15.81)       ($15.41)    ($0.59)     ($1.44)     ($2.03)      $49.85
Sept. 30, 1997   47.28       0.39         21.48          21.87      (0.43)      (1.43)      (1.86)       67.29
Sept. 30, 1996   43.46       0.47          5.00           5.47      (0.38)      (1.27)      (1.65)       47.28
Sept. 30, 1995   36.54       0.36          8.53           8.89      (0.33)      (1.64)      (1.97)       43.46
Sept. 30, 1994   36.21       0.26          1.34           1.60      (0.19)      (1.08)      (1.27)       36.54
</TABLE>

                              RATIOS AND SUPPLEMENTAL DATA
                -------------------------------------------------------
                            Net                 Ratio of Net
                          Assets,    Ratio of    Investment
                          End of     Expenses      Income     Portfolio
                 Total  Period (In  to Average   to Average   Turnover
  Year Ended    Return   Millions)  Net Assets   Net Assets     Rate
Sept. 30, 1998  -23.5%    $1,428       1.2%         0.7%        39.0%
Sept. 30, 1997  +47.5%     1,318       1.2%         0.8%        22.5%
Sept. 30, 1996  +13.0%       389       1.3%         1.2%        17.8%
Sept. 30, 1995  +26.0%       163       1.3%         1.2%        33.2%
Sept. 30, 1994   +4.4%        68       1.5%         1.0%        28.5%

(a) Information presented relates to a share of capital stock of the Fund
    outstanding for the entire period.

                                                                              11
See Notes to Financial Statements.

<PAGE>

REPORT OF INDEPENDENT ACCOUNTANTS
- --------------------------------------------------------------------------------
To the Shareholders and Board of Directors of the
Strong Schafer Value Fund, Inc.

In our opinion, the accompanying statement of assets and liabilities, including
the schedule of investments, and the related statements of operations and of
changes in net assets and the financial highlights present fairly, in all
material respects, the financial position of Strong Schafer Value Fund, Inc.
(the "Fund") at September 30, 1998, the results of its operations for the year
then ended, the changes in its net assets for each of the two years in the
period then ended and the financial highlights for the periods indicated, in
conformity with generally accepted accounting principles.  These financial
statements and financial highlights (hereafter referred to as "financial
statements") are the responsibility of the Fund's management; our responsibility
is to express an opinion on these financial statements based on our audits.  We
conducted our audits of these financial statements in accordance with generally
accepted auditing standards which require that we plan and perform the audit to
obtain reasonable assurance about whether the financial statements are free of
material misstatement.  An audit includes examining, on a test basis, evidence
supporting the amounts and disclosures in the financial statements, assessing
the accounting principles used and significant estimates made by management, and
evaluating the overall financial statement presentation.  We believe that our
audits, which included confirmation of securities at September 30, 1998 by
correspondence with the custodian and brokers, provide a reasonable basis for
the opinion expressed above.



PricewaterhouseCoopers LLP


Milwaukee, Wisconsin
November 4, 1998


12

<PAGE>


                                   DIRECTORS
                               David K. Schafer
                              Timothy C. Collins
                                Mary P. English
                               Phillip P. Young

                                   OFFICERS
                          David K. Schafer, President
                        James P. Cullen, Vice President
                 Brendan J. Spillane, Secretary and Treasurer
                  Thomas P. Lemke, Assistant Vice President
                    John S. Weitzer, Assistant Secretary

                              INVESTMENT ADVISOR
                    Strong Schafer Capital Management, LLC
             101 Carnegie Center, Suite 107, Princeton, NJ 08540

                                  DISTRIBUTOR
                        Strong Funds Distributors, Inc.
                   P.O. Box 2936, Milwaukee, Wisconsin 53201

                                   CUSTODIAN
                             Firstar Trust Company
                   P.O. Box 701, Milwaukee, Wisconsin 53201

                 TRANSFER AGENT AND DIVIDEND-DISBURSING AGENT
                       Strong Capital Management, Inc.
                  P.O. Box 2936, Milwaukee, Wisconsin 53201

                            INDEPENDENT ACCOUNTANTS
                           PricewaterhouseCoopers LLP
              411 East Wisconsin Avenue, Milwaukee, Wisconsin 53202

                                 LEGAL COUNSEL
                                Sidney & Austin
                   1 First National Plaza, Chicago, IL 60603

<PAGE>

  For a prospectus containing more complete information, including management
fees and expenses, please call 1-800-368-1030.  Please read it carefully before
 investing or sending money.  This report does not constitute an offer for the
   sale of securities.  Strong Funds are offered for sale by prospectus only.







                               [PICTURE OF TELEPHONE]
                           To order a free prospectus kit,
                                 CALL 1-800-368-1030

                            To learn more about our funds,
                             discuss an existing account,
                              or conduct a transaction,
                                 CALL 1-800-368-3863
                                 -------------------

                                    If you are a
                               Financial Professional,
                                 CALL 1-800-368-1683

                      [PICTURE OF STRONG WEB SITE ON COMPUTER]
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                                www.strongfunds.com




                                    [STRONG LOGO]

                                    STRONG FUNDS
                     P.O. Box 2936 o Milwaukee, Wisconsin 53201
                      Strong Funds Distributors, Inc. 9516J98              ASVAL



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