DIME BANCORP INC
SC TO-I, EX-99.A.1.E, 2000-08-01
SAVINGS INSTITUTION, FEDERALLY CHARTERED
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<PAGE>   1
                                                              Exhibit (a)(1)(E)
                               DIME BANCORP, INC.

                           OFFER TO PURCHASE FOR CASH
                                       BY

                               DIME BANCORP, INC.
                  UP TO 13,607,664 SHARES OF ITS COMMON STOCK
           (INCLUDING THE ASSOCIATED PREFERRED STOCK PURCHASE RIGHTS)
   AT A PURCHASE PRICE NOT GREATER THAN $18.00 NOR LESS THAN $16.00 PER SHARE

THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY
TIME ON MONDAY, AUGUST 28, 2000, UNLESS THE OFFER IS EXTENDED. DIME MAY EXTEND
THE OFFER PERIOD AT ANY TIME.

                                                                  August 1, 2000
To Our Clients:

     Enclosed for your consideration are the offer to purchase, dated August 1,
2000, and the related letter of transmittal in connection with the offer by Dime
Bancorp, Inc., a Delaware corporation, to purchase for cash 13,607,664 shares of
its common stock, par value $0.01 per share, at a price not greater than $18.00
nor less than $16.00 per share, net to the seller in cash, without interest, as
specified by stockholders tendering their shares.

     Given the prices specified by tendering stockholders and the number of
shares tendered and not properly withdrawn, Dime will select the lowest purchase
price between $18.00 and $16.00 net per share in cash, without interest, that
will allow it to purchase 13,607,664 shares, or, if a lesser number of shares
are properly tendered, all shares that are properly tendered. All shares
acquired in the tender offer will be purchased at the same price.

     Dime's offer is being made upon the terms and subject to the conditions set
forth in its offer to purchase, dated August 1, 2000, and in the related letter
of transmittal which, as they may be amended and supplemented from time to time,
together constitute the tender offer. All shares tendered and purchased will
include the associated preferred stock purchase rights issued under the
Stockholder Protection Rights Agreement, dated as of October 20, 1995, as
amended, between Dime and The Dime Savings Bank of New York, FSB, as rights
agent, and, unless the context requires otherwise, all references to shares
shall include the associated preferred stock purchase rights.

     Only shares properly tendered at prices equal to or below the purchase
price and not properly withdrawn will be purchased. However, because of the
proration provisions described in the offer to purchase, all of the shares
tendered at or below the purchase price may not be purchased if more than
13,607,664 shares are properly tendered. All shares tendered and not purchased,
including shares tendered at prices above the purchase price and shares not
purchased because of proration or the conditional tender procedures, will be
returned at Dime's expense as soon as practicable following the expiration date.

     Dime reserves the right, in its sole discretion, to purchase more than
13,607,664 shares pursuant to the offer, subject to applicable law.

     Upon the terms and conditions of Dime's offer, if more than 13,607,664
shares are properly tendered at prices equal to or below the purchase price and
not properly withdrawn, Dime will purchase properly tendered shares in the
following order:

     - First, all shares properly tendered and not properly withdrawn by any
       "odd lot holder" (as defined below) who:

        - tenders all shares owned (beneficially or of record) by the odd lot
          holder at a price equal to or below the purchase price (tenders of
          less than all the shares owned will not qualify for this preference);
          and

        - completes the section entitled "Odd Lots" in the letter of transmittal
          and, if applicable, in the notice of guaranteed delivery; and

     - Second, after the purchase of all the shares properly tendered by odd lot
       holders and subject to the conditional tender procedures described in
       section 6 of the offer to purchase, all other shares properly tendered at
       prices equal to or below the purchase price, on a pro rata basis with
       appropriate adjustments to avoid purchases of fractional shares.
<PAGE>   2

     A TENDER OF YOUR SHARES CAN BE MADE ONLY BY US AS THE HOLDER OF RECORD AND
PURSUANT TO YOUR INSTRUCTIONS. THE LETTER OF TRANSMITTAL IS FURNISHED TO YOU FOR
YOUR INFORMATION ONLY AND CANNOT BE USED BY YOU TO TENDER YOUR SHARES HELD BY US
FOR YOUR ACCOUNT.

     Accordingly, please use the attached "Instruction Form" to instruct us as
to whether you wish us to tender any or all of the shares we hold for your
account on the terms and subject to the conditions of the tender offer.

     WE CALL YOUR ATTENTION TO THE FOLLOWING:

      1.  You may tender shares at prices not in excess of $18.00 nor less than
          $16.00 per share as indicated in the attached Instruction Form, net to
          you in cash, without interest.

      2.  You should consult with your broker regarding the possibility of
          designating the priority in which your shares will be purchased in the
          event of proration.

      3.  The tender offer is not conditioned upon any minimum number of shares
          being tendered. The tender offer is, however, subject to certain other
          conditions described in the offer to purchase.

      4.  The tender offer and withdrawal rights will expire at 12:00 midnight,
          New York City time, on Monday August 28, 2000, unless Dime extends the
          tender offer.

      5.  The tender offer is for 13,607,664 shares, constituting approximately
          12.45% of the shares outstanding as of July 6, 2000.

      6.  Tendering stockholders who are registered stockholders or who tender
          their shares directly to EquiServe Trust Company, N.A. as the
          depositary, will not be obligated to pay any brokerage commissions or
          fees, solicitation fees, or, except as set forth in the offer to
          purchase and the letter of transmittal, stock transfer taxes on Dime's
          purchase of shares under the tender offer.

      7.  If you are an odd lot holder, meaning that you own beneficially or of
          record an aggregate of fewer than 100 shares (including shares held in
          the Dime Dividend Reinvestment and Optional Cash Purchase Program, but
          not including shares held in the Retirement 401(k) Investment Plan of
          Dime or the North American Mortgage Company Retirement and 401(k)
          Savings Plan), and you instruct us to tender on your behalf all such
          shares at or below the purchase price before the expiration date and
          check the box captioned "Odd Lots" in the attached instruction form,
          Dime, upon the terms and subject to the conditions of the tender
          offer, will accept all such shares for purchase before proration, if
          any, of the purchase of other shares properly tendered at or below the
          purchase price and not properly withdrawn.

      8.  If you wish to tender portions of your shares at different prices, you
          must complete a separate Instruction Form for each price at which you
          wish to tender each such portion of your shares. We must submit
          separate letters of transmittal on your behalf for each price you will
          accept.

      9.  The board of directors of Dime has approved the tender offer. However,
          neither Dime nor its board of directors nor either dealer manager nor
          the information agent makes any recommendation to stockholders as to
          whether they should tender or not tender their shares or as to the
          price or prices at which stockholders may choose to tender their
          shares. Stockholders must make their own decision as to whether to
          tender their shares and, if so, how many shares to tender and the
          price or prices at which such shares should be tendered. Dime's
          directors and executive officers have advised Dime that they do not
          intend to tender any shares in the tender offer.

     10.  If you wish to have us tender any or all of your shares, please so
          instruct us by completing, executing, detaching and returning to us
          the attached Instruction Form. If you authorize us to tender your
          shares, we will tender all such shares unless you specify otherwise on
          the attached Instruction Form.

     Please forward your Instruction Form to us as soon as possible to allow us
ample time to tender your shares on your behalf prior to the expiration of the
offer.

     The tender offer is being made solely under the offer to purchase and the
related letter of transmittal and is being made to all record holders of shares.
The tender offer is not being made to, nor will tenders be accepted from or on
behalf of, holders of shares residing in any jurisdiction in which the making of
the tender offer or acceptance thereof would not be in compliance with the
securities, blue sky or other laws of such jurisdiction.

                                        2
<PAGE>   3

                                INSTRUCTION FORM

            INSTRUCTIONS FOR TENDER OF SHARES OF DIME BANCORP, INC.

     By signing this instruction form you acknowledge receipt of our letter and
the enclosed offer to purchase, dated August 1, 2000, and the related letter of
transmittal in connection with the offer by Dime Bancorp, Inc., a Delaware
corporation, to purchase shares of its common stock, $0.01 par value per share.
Dime is offering to purchase up to 13,607,664 shares at a price not greater than
$18.00 nor less than $16.00 per share, net to the seller in cash, without
interest, as specified by stockholders tendering their shares. Dime's offer is
being made upon the terms and subject to the conditions set forth in the offer
to purchase and in the related letter of transmittal, which, as they may be
amended or supplemented from time to time, together constitute the offer. All
shares tendered and purchased will include the associated preferred stock
purchase rights issued pursuant to the Stockholder Protection Rights Agreement,
dated as of October 20, 1995, as amended, between Dime and The Dime Savings Bank
of New York, FSB, as rights agent, and, unless the context otherwise requires,
all references to shares include the associated preferred stock purchase rights.

     This will instruct us to tender to Dime, on your behalf, the number of
shares indicated below (or if no number is indicated below, all shares) which
are beneficially owned by you but registered in our name, upon the terms and
subject to the conditions of the offer.

     Number of shares to be tendered:
     ----------------- shares. (Unless otherwise indicated, it will be assumed
that all shares held by us for your account are to be tendered.)

                        PRICE AT WHICH YOU ARE TENDERING
                (SEE INSTRUCTION 5 TO THE LETTER OF TRANSMITTAL)
You must check one box and only one box if you want to tender your shares. If
more than one box is checked or if no box is checked, your shares will not be
properly tendered.

SHARES TENDERED AT A PRICE DETERMINED BY YOU:

By checking one of the following boxes below instead of the box under "Shares
tendered at a price determined pursuant to the offer," you are tendering shares
at the price checked. This action could result in none of your shares being
purchased if the purchase price selected by Dime for the shares is less than the
price checked below. If you want to tender portions of your shares at more than
one price, you must complete a separate letter of transmittal for each price at
which you tender shares. The same shares cannot be tendered at more than one
price.

        PRICE (IN DOLLARS) PER SHARE AT WHICH SHARES ARE BEING TENDERED

<TABLE>
<S>  <C>      <C>  <C>      <C>  <C>      <C>  <C>
[ ]  $16.000  [ ]  $16.500  [ ]  $17.000  [ ]  $17.500
[ ]  $16.125  [ ]  $16.625  [ ]  $17.125  [ ]  $17.625
[ ]  $16.250  [ ]  $16.750  [ ]  $17.250  [ ]  $17.750
[ ]  $16.375  [ ]  $16.875  [ ]  $17.375  [ ]  $17.875
                     [ ] $18.000
</TABLE>

                                       OR

SHARES TENDERED AT A PRICE DETERMINED PURSUANT TO THE OFFER:

[ ]  By checking this one box instead of one of the price boxes above, you are
     tendering shares and are willing to accept the purchase price selected by
     Dime in accordance with the terms of the offer. This action will maximize
     the chance of having Dime purchase your shares (subject to the possibility
     of proration). Note this action could result in your receiving a price per
     share as low as $16.00.

                                        3
<PAGE>   4

                                    ODD LOTS
                (SEE INSTRUCTION 8 TO THE LETTER OF TRANSMITTAL)

Complete this section only if you own, or are tendering on behalf of a person
who owns, beneficially or of record, an aggregate of fewer than 100 shares
(including any shares held in The Dime Dividend Reinvestment and Optional Cash
Purchase Program, but not including any shares held in the North American
Mortgage Company Retirement and 401(k) Savings Plan or the Retirement 401(k)
Investment Plan of Dime Bancorp, Inc.) and are tendering all shares.

You either (check one box):

[ ]  are the beneficial or record owner of an aggregate of fewer than 100
     shares, all of which are being tendered; or

[ ]  are a broker, dealer, commercial bank, trust company, or other nominee that
     (a) is tendering for the beneficial owner(s), shares with respect to which
     it is the record holder, and (b) believes, based upon representations made
     to it by the beneficial owner(s), that each such person is the beneficial
     owner of an aggregate of fewer than 100 shares and is tendering all of the
     shares.

                               CONDITIONAL TENDER
               (SEE INSTRUCTION 15 TO THE LETTER OF TRANSMITTAL)

You may condition your tender of shares on Dime purchasing a specified minimum
number of your tendered shares, all as described in section 6 of the offer to
purchase. Unless the minimum number of shares you indicate below is purchased by
Dime in the offer, none of the shares you tendered will be purchased. It is your
responsibility to calculate that minimum number of shares that must be purchased
if any are purchased, and you are urged to consult your own tax advisor before
completing this section. Unless this box has been checked and a minimum number
of shares specified, your tender will be deemed unconditional.

[ ]  The minimum number of shares that must be purchased, if any are purchased,
     is:
     ----------------- shares.

If because of proration, the minimum number of shares that you designated above
will not be purchased, Dime may accept conditional tenders by random lot, if
necessary. However, to be eligible for purchase by random lot, you must have
tendered all your shares and checked this box:

[ ]  The tendered shares represent all shares held by me.

     THE METHOD OF DELIVERY OF THIS DOCUMENT IS AT THE OPTION AND RISK OF THE
TENDERING STOCKHOLDER. IF DELIVERY IS BY MAIL, REGISTERED MAIL WITH RETURN
RECEIPT REQUESTED, PROPERLY INSURED, IS RECOMMENDED. IN ALL CASES, SUFFICIENT
TIME SHOULD BE ALLOWED TO ASSURE DELIVERY.

SIGN HERE:

Signature(s):
--------------------------------------------------------------------------------

Print Name(s):
--------------------------------------------------------------------------------

Address(es):
--------------------------------------------------------------------------------

Area Code and Telephone Number:
---------------------------------------------------------------------------

Taxpayer Identification or Social Security Number:
----------------------------------------------------------

Date:
-------------------------, 2000

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