IDS EQUITY SELECT FUND INC
N-30D, 1999-02-03
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                                   IDS Equity
                                   Select Fund

                                         1998 ANNUAL REPORT
                                        (PROSPECTUS ENCLOSED)

The goal of IDS Equity Select Fund, Inc.
is growth of capital and income. The
Fund invests primarily in moderate growth
stocks that generally pay dividends.

(This annual report  includes a prospectus  that  describes in detail the Fund's
objective,  investment strategies,  risks, sales charges, fees and other matters
of  interest.  Please read the  prospectus  carefully  before you invest or send
money.)


                                         AMERICAN 
                                          EXPRESS 
                                              Financial 
                                              Advisors


Distributed by American Express Financial Advisors Inc.

<PAGE>


Budding Blue Chips

When most people  think of stocks,  they tend to focus on the  notable  names in
American business -- the blue chips, as they're known. But there's another group
of companies that, though smaller and less well-known, boast impressive business
histories. These mid-size companies, which we call "budding blue chips," are the
foundation of Equity Select Fund. Often, they enjoy a dominant position in their
business.  For an investor,  this means an  opportunity  to  participate  in the
growth  that's  likely for these  companies  and the  potential for rising stock
prices.



IDS EQUITY SELECT FUND      (This annual report is not part of the prospectus.)

<PAGE>

Table of Contents


1998 ANNUAL REPORT
The purpose of this annual report is to tell investors how the Fund performed.

From the Chairman                                        4
From the Portfolio Manager                               4
Fund Facts                                               6
The 10 Largest Holdings                                  7
Making the Most of the Fund                              8
The Fund's Long-term Performance                         9
Independent Auditors' Report                            10
Financial Statements                                    11
Notes to Financial Statements                           14
Investments in Securities                               21
Federal Income Tax Information                          27


1999 PROSPECTUS
The prospectus, which is bound into the middle of this annual report, describes 
the Fund in detail.

The Fund                                              3p
Goal                                                  3p
Investment Strategy                                   3p
Risks                                                 4p
Past Performance                                      5p
Fees and Expenses                                     7p
Management                                            8p
Buying and Selling Shares                             8p
Valuing Fund Shares                                   8p
Investment Options                                    9p
Purchasing Shares                                    10p
Sales Charges                                        13p
Exchanging/Selling Shares                            17p
Distributions and Taxes                              21p
Personalized Shareholder
 Information                                         23p
About the Company                                    24p
Quick Telephone Reference                            26p
Financial Highlights                                 27p


(This annual report is not part of the prospectus.)       ANNUAL REPORT -- 1998

<PAGE>

From the Chairman

(picture of) William R. Pearce
William R. Pearce
Chairman of the board

If you're an experienced investor, you know that the past 12 months was a highly
volatile period in many financial markets. But history tells us that substantial
market moves are nothing new.  Though they're often  unpredictable,  declines --
whether they're brief or  long-lasting,  moderate or substantial -- are always a
possibility.

The potential for such  volatility  reinforces  the need for investors to review
periodically  their long-term goals and examine whether their investment program
remains on track to achieving them.

Your quarterly  investment  statements are one part of that monitoring  process.
The other is a meeting  with  your  American  Express  financial  advisor.  That
becomes  even  more  important  if  there's  a major  change  in your  financial
situation or in the financial markets.


(signature of) W.R. Pearce
William R. Pearce



From the Portfolio Manager

(picture of) Betty J. Tebault
Betty J. Tebault
Portfolio manager

IDS Equity  Select Fund had a  productive  fiscal  year,  although  its gain was
substantially  reduced by a sharp  downturn in the U.S. stock market late in the
period. For the 12 months -- December 1997 through November 1998 -- investors in
the Fund's Class A shares  realized a total  return of 9.96%.  (A portion of the
return came in the form of a capital  gain,  which was paid to  shareholders  in
December  1997 and reduced the Fund's net asset value by the same amount at that
time.)

The period began with considerable  uncertainty,  as investors tried to sort out
the potential  longer-term effects of a meltdown in Asian financial markets that
had taken place only weeks  earlier.  By February,  though,  they  evidently had
decided that the U.S.  companies would weather the storm  relatively  well, and,
with support from ongoing  reports of subdued  inflation and a growing  economy,
they sent stocks soaring through March.

The environment changed  dramatically in mid-summer,  however. By that time, the
"Asian flu" had made its way to Russia and Latin America,  re-igniting fear that
American  companies'  profits  would  decline  as a result of  reduced  overseas
revenues.  Investors  reacted to this development  with wholesale  stock-selling
that drove the market down by nearly 20% through late September. The fiscal year
did  end on a  positive  note,  though,  as  stocks  rebounded  strongly  in the
following two months,  thanks chiefly to three interest-rate cuts by the Federal
Reserve.

LARGE-CAPS LEAD
Carrying on the tradition of recent years,  large-capitalization stocks remained
at the forefront of the market's advances, a reflection of investors' preference
for the  more-predictable  earnings  patterns and liquidity of large-cap issues.
For the Fund, this continued to be a mixed blessing,  as its portfolio contained
a blend of large- and small/mid-cap  stocks.  Overall, the smaller issues, while
they made a positive contribution to performance, simply couldn't keep pace with
their bigger  brethren.  In addition,  because of recent market  conditions,  it
became  increasingly  difficult  to find  small-  and  mid-cap  stocks  that pay
dividends.

Most productive for the Fund were its holdings among pharmaceutical,  retailing,
grocery,  insurance,  telecommunications  and brokerage  stocks,  with large-cap
names such as General Electric, Gillette, Coca-Cola,  Travelers, Carnival Cruise
Lines and Federated  Department  Stores  registering some of the greatest gains.
Technology,  another fairly  substantial area of investment for the Fund, proved
to be a mixed bag. Although several holdings performed well overall, steep drops
in a few stocks negated much of those gains. I increased the technology exposure
in the  latter  part  of the  year,  taking  advantage  of low  prices  on  some
high-quality stocks.

As we begin a new fiscal year, the biggest question confronting the stock market
is how strong corporate  profits will be. In light of that, I have  concentrated
the  portfolio  in a diverse mix of  companies  that appear best able to produce
solid  profit  growth  and  whose  stock  prices  still  offer  reasonably  good
investment value.


(signature of)
Betty J. Tebault

(This annual report is not part of the prospectus.)       ANNUAL REPORT -- 1998

<PAGE>

Fund Facts

Class A -- 12-month performance
(All figures per share)

Net asset value (NAV)     
Nov. 30, 1998                                                       $14.59
Nov. 30, 1997                                                       $15.76
Decrease                                                            $ 1.17

Distributions -- Dec. 1, 1997 - Nov. 30, 1998
From income                                                         $ 0.09
From capital gains                                                  $ 2.40
Total distribution                                                  $ 2.49

Total return*                                                       +9.96%**

Class B -- 12-month performance
(All figures per share)

Net asset value (NAV)
Nov. 30, 1998                                                       $14.34
Nov. 30, 1997                                                       $15.60
Decrease                                                            $ 1.26

Distributions -- Dec. 1, 1997 - Nov. 30, 1998
From income                                                         $ 0.06
From capital gains                                                  $ 2.40
Total distribution                                                  $ 2.46

Total return*                                                       +9.12%**

Class Y -- 12-month performance
(All figures per share)

Net asset value (NAV)
Nov. 30, 1998                                                       $14.60
Nov. 30, 1997                                                       $15.77
Decrease                                                            $ 1.17

Distributions -- Dec. 1, 1997 - Nov. 30, 1998
From income                                                         $ 0.10
From capital gains                                                  $ 2.40
Total distribution                                                  $ 2.50

Total return*                                                      +10.03%**

*The  prospectus  discusses the effect of sales charges,  if any, on the various
classes.

**The  total  return  is  a  hypothetical   investment  in  the  Fund  with  all
distributions reinvested.


IDS EQUITY SELECT FUND      (This annual report is not part of the prospectus.)
<PAGE>

The 10 Largest Holdings


                                      Percent                    Value
                               (of net assets)    (as of Nov. 30, 1998)
 Tyco Intl                              4.97%              $55,881,393
 Immunex                                3.28                36,849,999
 Safeway                                2.87                32,215,624
 Estee Lauder Cl A                      2.17                24,357,781
 Arterial Vascular Engineering          2.13                23,948,749
 Cisco Systems                          2.11                23,743,124
 Martin Marietta Materials              1.96                22,062,650
 Rite Aid                               1.94                21,810,163
 ACE                                    1.92                21,600,000
 Fort James                             1.76                19,758,125  

For further detail about these  holdings,  please refer to the section  entitled
"Investments in securities" herein.


(icon of) pie chart
                                    The 10 holdings listed here
                                    make up 25.11% of net assets


(This annual report is not part of the prospectus.)       ANNUAL REPORT -- 1998

<PAGE>

Making the Most of the Fund

BUILD YOUR ASSETS SYSTEMATICALLY
One of the best  ways to  invest in the Fund is by  dollar-cost  averaging  -- a
time-tested  strategy  that  can make  market  fluctuations  work  for  you.  To
dollar-cost  average,  simply invest a fixed amount of money  regularly.  You'll
automatically  buy more shares when the Fund's share price is low,  fewer shares
when it is high. The chart below shows how dollar-cost averaging works. In these
three  hypothetical   scenarios,   you  will  see  six  months  of  share  price
fluctuations.

This strategy  does not ensure a profit or avoid a loss if the market  declines.
But, if you can continue to invest regularly  through changing market conditions
even when the price of your  shares  fall or the market  declines,  it can be an
effective way to accumulate shares to meet your long-term goals.

How dollar-cost averaging works

     Jan  Feb  Mar  Apr  May  Jun      
$15                 $16  $18  $20
$10  $10  $12  $14  
$ 5

Accumulated shares*       Average market           Your average 
                          price per share          cost per share

      42.25                    $15                    $14.20
- -------------------------------------------------------------------------------

     Jan  Feb  Mar  Apr  May  Jun      
$15  
$10  $10  $8             $8   $10
$ 5            $5   $5   

Accumulated shares*       Average market           Your average 
                          price per share          cost per share

      85.0                     $7.66                  $7.05
- -------------------------------------------------------------------------------

     Jan  Feb  Mar  Apr  May  Jun
$15
$10  $10  $8   $6             $7
$ 5                 $4   $4

Accumulated shares*       Average market           Your average 
                          price per share          cost per share

     103.5                    $6.50                    $5.80
- -------------------------------------------------------------------------------
$100 invested per month. Total invested: $600

*Shares purchased is determined by dividing the amount invested per month by the
current share price.

THREE WAYS TO BENEFIT FROM A MUTUAL FUND:
o your shares increase in value when the Fund's investments do well
o you  receive  capital  gains  when the gains on  investments  sold by the Fund
exceed losses 
o you receive income when the Fund's stock dividends, interest and
short-term gains exceed its expenses.

All  three  make up  your  total  return.  You  potentially  can  increase  your
investment if, like most investors, you reinvest your dividends and capital gain
distributions to buy additional shares of the Fund or another fund.


IDS EQUITY SELECT FUND       (This annual report is not part of the prospectus.)

<PAGE>

The Fund's Long-term Performance

                    How $10,000 has grown in IDS Equity Select Fund

$50,000
                                    S&P 500 Index
$40,000

$30,000
                                                                       $41,283
$20,000                                                                 Equity
                                                                   Select Fund
$10,000                            Lipper Growth & Income              Class A
$9,500                                         Fund Index
     '88    '89    '90    '91    '92    '93    '94    '95    '96    '97    '98

 Average annual total return (as of Nov. 30, 1998)

              1 year         Since            5 years       10 years
                          inception*
 Class A      +4.46%             --%          +15.03%        +15.23%
 Class B      +5.44%        +20.99%               --%            --%
 Class Y      +10.03%       +22.49%               --%            --%

*Inception date was March 20, 1995.

Assumes:  Holding period from 12/1/88 to 11/30/98.  Returns do not reflect taxes
payable  on   distributions.   Reinvestment  of  all  income  and  capital  gain
distributions for the Fund, with a value of $24,145. Also see "Past Performance"
in the Fund's current prospectus.

On the graph above you can see how the Fund's total returncompared to two widely
cited performance  indexes,  the Standard & Poor's 500 Index (S&P 500 Index) and
the Lipper Growth & Income Fund Index. In comparing Equity Select Fund (Class A)
to the two  indexes,  you  should  take into  account  the fact that the  Fund's
performance  reflects the maximum sales charge of 5%, while such charges are not
reflected in the performance of the indexes.

Your investment and return values fluctuate so that your shares,  when redeemed,
may be worth more or less than the original  cost.  Average  annual total return
figures reflect the impact of the applicable sales charge up to a maximum of 5%.
This was a period of widely fluctuating  security prices. Past performance is no
guarantee of future results.

S&P 500 Index,  an unmanaged  list of common  stocks,  is  frequently  used as a
general  measure  of market  performance.  However,  the S&P 500  companies  are
generally larger than those in which the Fund invests.

Lipper  Growth & Income Fund Index,  an  unmanaged  index,  published  by Lipper
Analytical  Services,  Inc., includes 30 funds that are generally similar to the
Fund,  although some funds in the index may have somewhat  different  investment
policies or objectives.

(This annual report is not part of the prospectus.)        ANNUAL REPORT -- 1998

<PAGE>
The financial statements contained in Post-Effective Amendment #88 to 
Registration Statement No. 2-13188 filed on or about January 26, 1999, are
incorporated herein by reference.
<PAGE>

Federal Income Tax Information

The  Fund is  required  by the  Internal  Revenue  Code  of  1986  to  tell  its
shareholders  about the tax treatment of the dividends it pays during its fiscal
year.  The  dividends  listed  below  were  reported  to you on  Form  1099-DIV,
Dividends and Distributions. Shareholders should consult a tax advisor on how to
report distributions for state and local purposes.

IDS Equity Select Fund, Inc.
Fiscal year ended Nov. 30, 1998

Class A

Income  distributions  taxable  as  dividend  income,   100.00%  qualifying  for
deduction by corporations.

Payable date                                                   Per share

Dec. 29, 1997                                                   $0.07520
March 27, 1998                                                   0.01053
June 26, 1998                                                    0.00510
Sept. 25, 1998                                                   0.00322
Total                                                           $0.09405

Capital gain distribution taxable as long-term capital gain.

Payable date                                                   Per share

Dec. 29, 1997                                                   $2.39599
Total distributions                                             $2.49004

The  distribution  of $2.47119 per share,  payable  Dec. 29, 1997,  consisted of
$0.01375  derived  from net  investment  income,  $0.06145  from net  short-term
capital gains (a total of $0.07520 taxable as dividend income) and $2.39599 from
net long-term capital gains.

The long-term  capital gains  distribution is divided into two rate  categories:
28% -- $1.48456 and 20% -- $0.91143.

(This annual report is not part of the prospectus.)      ANNUAL REPORT -- 1998

<PAGE>

Class B

Income  distribution   taxable  as  dividend  income,   100.00%  qualifying  for
deductions by corporations.

Payable date                                                   Per share

Dec. 29, 1997                                                   $0.06145

Capital gain distribution taxable as long-term capital gain.

Payable date                                                   Per share

Dec. 29, 1997                                                   $2.39599
Total distributions                                             $2.45744

The  distribution  of $2.45744 per share,  payable  Dec. 29, 1997,  consisted of
$0.06145  derived  from net  short-term  capital  gains  and  $2.39599  from net
long-term capital gains.

The long-term  capital gains  distribution is divided into two rate  categories:
28% -- $1.48456 and 20% -- $0.91143.


IDS EQUITY SELECT FUND       (This annual report is not part of the prospectus.)

<PAGE>

Class Y

Income  distributions  taxable  as  dividend  income,   100.00%  qualifying  for
deduction by corporations.

Payable date                                                   Per share

Dec. 29, 1997                                                   $0.07806
March 27, 1998                                                   0.01337
June 26, 1998                                                    0.00804
Sept. 25, 1998                                                   0.00577
Total                                                           $0.10524

Capital gain distribution taxable as long-term capital gain.


Payable date                                                   Per share

Dec. 29, 1997                                                   $2.39599
Total distributions                                             $2.50123

The  distribution  of $2.47405 per share,  payable  Dec. 29, 1997,  consisted of
$0.01661  derived  from net  investment  income,  $0.06145  from net  short-term
capital gains (a total of $0.07806 taxable as dividend income) and $2.39599 from
net long-term capital gains.

The long-term  capital gains  distribution is divided into two rate  categories:
28% -- $1.48456 and 20% -- $0.91143.

(This annual report is not part of the prospectus.)       ANNUAL REPORT -- 1998
<PAGE>

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<PAGE>

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<PAGE>
                                   AMERICAN
                                   EXPRESS
IDS Equity Select Fund                  Financial
IDS Tower 10                            Advisors
Minneapolis, MN 55440-0010
                                                                S-6426 N (1/99)
<PAGE>


STATEMENT OF DIFFERENCES

Difference                                       Description

1)   The layout is different                     1)  Some of the layout in the
     throughout the annual report.                   annual report to
                                                     shareholders is in two
                                                     columns.

2)   There are pictures, icons                   2)  Each picture, icon and
     and graphs throughout the                       graph is described in
     annual report.                                  parentheses.
 



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