<PAGE>   1
                                                        EXHIBIT INDEX ON PAGE 17


                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM 10-Q


         [XX]     QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15 (d) OF THE
                  SECURITIES EXCHANGE ACT OF 1934

For the quarterly period ended:               SEPTEMBER 30, 1998

                                       or

         [  ]     TRANSITION REPORT PURSUANT TO SECTION 13 OR 15 (d) OF THE 
                  SECURITIES EXCHANGE ACT OF 1934

For the transition period from                      to                         


Commission File Number:   1-6064

                                ALEXANDER'S, INC.
             (Exact name of registrant as specified in its charter)


               DELAWARE                                       51-0100517
(State or other jurisdiction of incorporation              (I.R.S. Employer
               or organization)                         Identification Number)

PARK 80 WEST, PLAZA II, SADDLE BROOK, NEW JERSEY                07663
    (Address of principal executive offices)                 (Zip Code)

                                  (201)587-8541
              (Registrant's telephone number, including area code)



              (Former name, former address and former fiscal year,
                         if changed since last report)

                 Indicate by check mark whether the registrant (1) has filed all
reports required to be filed by Section 13 or 15(d) of the Securities Exchange
Act of 1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.
                                                 [X] Yes    [ ] No

                APPLICABLE ONLY TO ISSUERS INVOLVED IN BANKRUPTCY
                   PROCEEDINGS DURING THE PRECEDING FIVE YEARS

                 Indicate by check mark whether the registrant has filed all
reports required to be filed by Sections 12, 13 or 15(d) of the Securities
Exchange Act of 1934 subsequent to the distribution of securities under a plan
confirmed by a court.
                                                 [ ] Yes    [ ] No

                 As of October 23, 1998 there were 5,000,850 common shares
outstanding.

                                     Page 1
<PAGE>   2
                                ALEXANDER'S, INC.

                                      INDEX


<TABLE>
<CAPTION>
                                                                                                     Page Number
                                                                                                     -----------
<S>              <C>                                                                                 <C>
PART I.          FINANCIAL INFORMATION:

        Item 1.    Financial Statements:

                   Consolidated Balance Sheets as of September 30, 1998
                   and December 31, 1997...........................................................      3

                   Consolidated Statements of Operations for the Three and
                   Nine Months Ended September 30, 1998 and September 30, 1997.....................      4

                   Consolidated Statements of Cash Flows for the Nine
                   Months Ended September 30, 1998 and September 30, 1997..........................      5

                   Notes to Consolidated Financial Statements......................................      6

        Item 2.    Management's Discussion and Analysis of Financial
                   Condition and Results of Operations.............................................     10

        Item 3.    Quantitative and Qualitative Disclosures About Market Risks.....................     14


PART II.           OTHER INFORMATION:

        Item 6.    Exhibits and Reports on Form 8-K................................................     15


Signatures         ................................................................................     16

Exhibit Index      ................................................................................     17
</TABLE>

                                     Page 2
<PAGE>   3
PART I.  FINANCIAL INFORMATION

                                ALEXANDER'S, INC.
                                AND SUBSIDIARIES

                           CONSOLIDATED BALANCE SHEETS
                   (AMOUNTS IN THOUSANDS EXCEPT SHARE AMOUNTS)


<TABLE>
<CAPTION>
                                                         SEPTEMBER 30,           DECEMBER 31,
                                                             1998                   1997
                                                             ----                   ----
<S>                                                      <C>                     <C>
ASSETS:

Real estate, at cost:
     Land                                                 $  69,557               $  45,571
     Buildings, leaseholds and improvements                 147,337                 123,612
     Capitalized expenses and predevelopment
         costs                                               52,616                  47,163
                                                          ---------               ---------
              Total                                         269,510                 216,346
     Less accumulated depreciation and
         amortization                                       (50,611)                (35,224)
                                                          ---------               ---------
                                                            218,899                 181,122

     Investment in unconsolidated joint
         venture                                                 --                  10,611
                                                          ---------               ---------
     Real estate, net                                       218,899                 191,733

Cash and cash equivalents                                    14,466                   2,691
Restricted cash                                              11,175                   1,872
Receivable arising from condemnation
     proceedings                                                 --                  14,700
Accounts receivable, net of allowance for
     doubtful accounts of $631 and $147                       4,490                   1,064
Receivable arising from the straight-lining
     of rents, net                                           11,881                   7,805
Deferred lease and other expenses                            28,857                  12,443
Deferred debt expense                                         3,098                     783
Other assets                                                  6,289                   1,983
                                                          ---------               ---------

TOTAL ASSETS                                              $ 299,155               $ 235,074
                                                          =========               =========

                                                         SEPTEMBER 30,           DECEMBER 31,
                                                             1998                   1997
                                                             ----                   ----

LIABILITIES AND STOCKHOLDERS'
     EQUITY:

Debt                                                      $ 262,269               $ 208,087
Amounts due to Vornado Realty Trust and
     its affiliate                                            5,840                   6,888
Accounts payable and accrued liabilities                     10,143                   4,174
Other liabilities                                            17,178                   2,296
Minority interest                                               600                     600
                                                          ---------               ---------

     TOTAL LIABILITIES                                      296,030                 222,045
                                                          ---------               ---------

Commitments and contingencies

Stockholders' Equity:

Common stock; $1.00 par value per share;
     authorized 10,000,000 shares;
     issued 5,173,450                                         5,174                   5,174
Additional capital                                           24,843                  24,843
Deficit                                                     (25,932)                (16,028)
                                                          ---------               ---------
                                                              4,085                  13,989
Less treasury shares, 172,600 shares
     at cost                                                   (960)                   (960)
                                                          ---------               ---------
     Total stockholders' equity                               3,125                  13,029
                                                          ---------               ---------


TOTAL LIABILITIES AND STOCKHOLDERS'
     EQUITY                                               $ 299,155               $ 235,074
                                                          =========               =========
</TABLE>

                 See notes to consolidated financial statements.

                                     Page 3
<PAGE>   4
                                ALEXANDER'S, INC.
                                AND SUBSIDIARIES

                      CONSOLIDATED STATEMENTS OF OPERATIONS


(amounts in thousands except per share amounts)
<TABLE>
<CAPTION>
                                                               FOR THE THREE MONTHS              FOR THE NINE MONTHS
                                                                      ENDED                             ENDED                    
                                                          SEPTEMBER 30,     SEPTEMBER 30,    SEPTEMBER 30,    SEPTEMBER 30,
                                                               1998             1997             1998              1997 
                                                               ----             ----             ----              ---- 
<S>                                                       <C>               <C>              <C>              <C>
Revenues:
    Property rentals                                         $ 11,100         $  4,317         $ 23,451         $ 13,167
    Expense reimbursements                                      5,101              419            7,711            1,713
    Equity in income of unconsolidated
       joint venture                                               --            1,280            2,519            3,895
                                                             --------         --------         --------         --------
Total revenues                                                 16,201            6,016           33,681           18,775
                                                             --------         --------         --------         --------

Expenses:
    Operating (including management fee to Vornado
       of $210 and $630 each for the three and nine
        months ended in 1998 and 1997, respectively)            6,951            1,501           11,964            5,378
    General and administrative (including management
       fee to Vornado of $540 and $1,620 each for the
       three and nine months ended in 1998 and
       1997, respectively)                                        869            1,026            3,106            3,039
    Depreciation and amortization                               1,219              588            2,910            1,741
                                                             --------         --------         --------         --------
Total expenses                                                  9,039            3,115           17,980           10,158
                                                             --------         --------         --------         --------

Operating income                                                7,162            2,901           15,701            8,617

Write-off of the carrying value of the
    Lexington Avenue building and related
    predevelopment costs                                      (15,096)              --          (15,096)              --
Interest and debt expense
    (including interest on loan from Vornado)                  (4,336)          (3,250)         (11,261)          (9,855)
Interest and other income, net                                    328              214              752            1,078
                                                             --------         --------         --------         --------

Net loss                                                     $(11,942)        $   (135)        $ (9,904)        $   (160)
                                                             ========         ========         ========         ========

Net loss per share - basic                                   $  (2.39)        $   (.03)        $  (1.98)        $   (.03)
                                                             ========         ========         ========         ========

Net loss per share - diluted                                 $  (2.39)        $   (.03)        $  (1.98)        $   (.03)
                                                             ========         ========         ========         ========
</TABLE>

                 See notes to consolidated financial statements.

                                     Page 4
<PAGE>   5
                                ALEXANDER'S, INC.
                                AND SUBSIDIARIES

                      CONSOLIDATED STATEMENTS OF CASH FLOWS

(amounts in thousands)

<TABLE>
<CAPTION>
                                                                      FOR THE NINE MONTHS ENDED   
                                                                     SEPTEMBER 30,   SEPTEMBER 30,
                                                                        1998              1997  
                                                                        ----              ----  
<S>                                                                  <C>             <C>
CASH FLOWS FROM OPERATING ACTIVITIES:
  Net loss                                                            $ (9,904)        $   (160)
  Adjustments to reconcile net income (loss) to net
    cash provided by (used in) operating activities:
      Depreciation and amortization
        (including debt issuance costs)                                  3,937            3,089
      Straight-lining of rental income                                  (4,076)          (1,024)
      Write-off of the carrying value of the
         Lexington Avenue building and related
         predevelopment costs                                           15,096               --
  Change in assets and liabilities:
      Accounts receivable                                                 (472)            (465)
      (Investment) distributions in excess of equity in income
        of unconsolidated joint venture                                   (386)           1,481
      Amounts due to Vornado Realty Trust and its affiliate             (1,048)          (1,787)
      Accounts payable and accrued liabilities                          (1,299)             606
      Other liabilities                                                   (120)            (317)
      Other                                                             (4,632)          (2,320)
                                                                      --------         --------


Net cash used in operating activities                                   (2,904)            (897)
                                                                      --------         --------

CASH FLOWS FROM INVESTING ACTIVITIES:
  Acquisition of Kings Plaza Mall                                      (28,000)              --
  Additions to real estate                                             (10,656)         (16,323)
  Collection of condemnation proceeds                                   14,700               --
  Cash restricted for construction and development                      (9,237)             928
  Cash restricted for operating liabilities                                (66)             557
                                                                      --------         --------
Net cash used in investing activities                                  (33,259)         (14,838)
                                                                      --------         --------

CASH FLOWS FROM FINANCING ACTIVITIES:
  Issuance of debt                                                      90,000           16,667
  Debt repayments                                                      (38,720)            (792)
  Deferred debt expense                                                 (3,342)            (199)
                                                                      --------         --------
Net cash provided by financing activities                               47,938           15,676
                                                                      --------         --------

Net increase in cash and cash equivalents                               11,775              (59)
Cash and cash equivalents at beginning of period                         2,691            5,480
                                                                      --------         --------

Cash and cash equivalents at end of period                            $ 14,466         $  5,421
                                                                      ========         ========

SUPPLEMENTAL DISCLOSURE OF CASH FLOW INFORMATION:
  Cash payments for interest (including capitalized
    interest of $5,529 and $6,982)                                    $ 15,762         $ 15,489
                                                                      ========         ========
</TABLE>

                 See notes to consolidated financial statements.

                                     Page 5
<PAGE>   6
                                ALEXANDER'S, INC.
                                AND SUBSIDIARIES

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS



1.  CONSOLIDATED FINANCIAL STATEMENTS

      The Consolidated Balance Sheet as of September 30, 1998, the Consolidated
    Statements of Operations for the Three and Nine Months Ended September 30,
    1998 and 1997, and the Consolidated Statements of Cash Flows for the Nine
    Months Ended September 30, 1998 and 1997 are unaudited. In the opinion of
    management, all adjustments (which include only normal recurring
    adjustments) necessary to present fairly the financial position, results of
    operations and changes in cash flows have been made.

      Certain information and footnote disclosures normally included in
    financial statements prepared in accordance with generally accepted
    accounting principles have been condensed or omitted. These condensed
    consolidated financial statements should be read in conjunction with the
    financial statements and notes thereto included in the Company's 1997 Annual
    Report to Shareholders. The results of operations for the three and nine
    months ended September 30, 1998 are not necessarily indicative of the
    operating results for the full year.


2.  ACQUISITION OF KINGS PLAZA MALL AND RELATED FINANCING TRANSACTIONS

      On June 18, 1998, the Company increased its interest in the Kings Plaza
    Mall (the "Mall") to 100% by acquiring Federated Department Store's
    ("Federated") 50% interest. The purchase price was approximately
    $28,000,000, which was paid in cash. In addition, the Company has agreed to
    pay Federated $15,000,000 to renovate its Macy's store in the Mall in
    exchange for certain modifications to the Kings Plaza Operating Agreement.
    The Company has accrued this liability as part of "Other liabilities" and
    the consideration as part of "Deferred lease and other expenses" on the
    Consolidated Balance Sheet. Prior to June 18, 1998, the Company owned a 50%
    interest in the Mall (since it was built in 1970) and accounted for this
    investment under the equity method.

      In connection with the acquisition, the Company completed a $90,000,000
    three-year mortgage loan with Union Bank of Switzerland. The loan is
    collateralized by the Kings Plaza Mall and the Company's anchor store and
    bears interest at LIBOR plus 1.25% (currently 6.91%). The proceeds from the
    borrowing were also used to repay $34,900,000 of existing debt ($32,000,000
    of which was due in the next year). In addition, the Company expects to
    complete a $30,000,000 construction loan on this property with Union Bank of
    Switzerland, of which approximately $15,000,000 will be used to partially
    fund a renovation of the Mall, and $15,000,000 will be used to pay the
    liability to Federated noted above.

      Set forth below is the unaudited pro forma condensed consolidated
    statements of operations for the Company for the nine months ended September
    30, 1998 and 1997 as if the acquisition of the Kings Plaza Mall and the
    related financing transactions had occurred on January 1, 1997.


                                     Page 6
<PAGE>   7
                                ALEXANDER'S, INC.
                                AND SUBSIDIARIES

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

    (Amounts in thousands, except per share amounts)

<TABLE>
<CAPTION>
                                                    PRO FORMA FOR THE NINE MONTHS ENDED 
                                                     SEPTEMBER 30,        SEPTEMBER 30,
                                                         1998                 1997           
                                                         ----                 ----           
<S>                                                 <C>                   <C>
       Revenues                                       $ 45,327             $ 30,301
                                                      ========             ========
                                                                           
       Net (loss) income                              $ (6,708)            $ 12,685
                                                      ========             ========
                                                                           
       Net (loss) income per share - basic            $  (1.34)            $    .54
                                                      ========             ========
                                                                           
       Net (loss) income per share - diluted          $  (1.34)            $    .54
                                                      ========             ========
</TABLE>                                                                   
                                                                       

    The pro forma results for the nine months ended September 30, 1998 include
    the write-off of the carrying value of the Lexington Avenue building and
    related predevelopment costs of $15,096,000.

3.  RELATIONSHIP WITH VORNADO REALTY TRUST ("Vornado")

      Vornado owns 29.3% of the Company's Common Stock. The Company is managed
    by and its properties are redeveloped and leased by Vornado, pursuant to
    agreements with a one-year term expiring in March of each year which are
    automatically renewable. Under these agreements, the Company incurred fees
    of $1,563,000 in each of the three month periods ended September 30, 1998
    and 1997 and $4,688,000 in the nine months ended September 30, 1998 and
    1997. In addition, Vornado is due $3,221,000 at September 30, 1998 under the
    leasing agreement, subject to the payment of rents by tenants.

      Vornado lent the Company $45,000,000, the subordinated tranche of a
    $75,000,000 loan, in 1995. The loan, which had a three-year term expiring on
    March 15, 1998, has been extended for an additional year and the interest
    rate has been reset from 15.60% per annum to 13.87% per annum. The Company
    incurred interest on its loan from Vornado of $1,595,000 and $1,794,000 in
    the three months ended September 30, 1998 and 1997, of which $976,000 and
    $1,317,000 were capitalized. Interest on the loan was $4,891,000 and
    $5,420,000 in the nine months ended September 30, 1998 and 1997, of which
    $2,785,000 and $3,796,000 were capitalized.


4.  COMMITMENTS AND CONTINGENCIES

      Lexington Avenue

      The Company is continuing to evaluate redevelopment plans for this site,
    which may include developing a large multi-use building requiring capital in
    excess of $300,000,000 to be expended. No development decisions have been
    finalized. In September 1998, the Company commenced the process of razing
    the existing building and accordingly, the carrying value of the building
    and related predevelopment costs of $15,096,000 were written-off.


                                     Page 7
<PAGE>   8
                                ALEXANDER'S, INC.
                                AND SUBSIDIARIES

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS



      Environmental Matters

     In June 1997, the Kings Plaza Shopping Center (the "Center"), commissioned
     an Environmental Study and Contamination Assessment Site Investigation (the
     Phase II "Study") to evaluate and delineate environmental conditions
     disclosed in a Phase I study. The results of the Study indicate the
     presence of petroleum and other hydrocarbons in the soil and groundwater.
     The Study recommends a remedial approach, but agreement has not yet been
     reached with the New York State Department of Environmental Conservation
     ("NYDEC") on the finalization of the approach. The Center accrued
     $1,500,000 at December 31, 1997, for its estimated obligation with respect
     to the clean up of the site, which includes costs of (i) remedial
     investigation, (ii) feasibility study, (iii) remedial design, (iv) remedial
     action and (v) professional fees. If the NYDEC insists on a more extensive
     remediation approach, the Center could incur additional obligations.

     Such contamination may have resulted from activities of third parties;
     however, the sources of the contamination have not been fully identified.
     Although the Center intends to pursue all available remedies against any
     potentially responsible third parties, there can be no assurance that such
     parties will be identified, or if identified, whether these potentially
     responsible third parties will be solvent. In addition, the costs
     associated with pursuing any potentially responsible parties may be cost
     prohibitive. The Center has not recorded an asset as of September 30, 1998
     for potential recoveries of environmental remediation costs from other
     parties.

     Compliance with applicable provisions of federal, state and local laws
     regulating the discharge of materials into the environment or otherwise
     relating to the protection of the environment have not had, and, although
     there can be no assurance, are not expected to have, a material effect on
     the Company's operations, earnings, competitive position or capital
     expenditures.

5.   LOSS PER SHARE

     The following table set for the computation of basic and diluted loss per
share:

<TABLE>
<CAPTION>
                                                         FOR THE THREE MONTHS              FOR THE NINE MONTHS
                                                                 ENDED                             ENDED
                                                     September 30,     September 30,   September 30,    September 30,
                                                         1998             1997             1998             1997
                                                         ----             ----             ----             ----
<S>                                                  <C>               <C>             <C>              <C>
     Numerator:
          Net loss                                     $(11,942)        $   (135)        $ (9,904)        $   (160)
                                                       --------         --------         --------         -------- 

     Denominator:
     Denominator for basic earnings per share --
                    weighted average shares               5,001            5,001            5,001            5,001

     Effect of dilutive securities:
                    Employee stock options*                  --               --               --               --
                                                       --------         --------         --------         -------- 

     Denominator for diluted earnings per share --
     adjusted weighted average shares and
     assumed conversions                                  5,001            5,001            5,001            5,001
                                                       --------         --------         --------         -------- 

     Net loss per share - basic                        $  (2.39)        $   (.03)        $  (1.98)        $   (.03)
                                                       --------         --------         --------         -------- 

     Net loss per share - diluted                      $  (2.39)        $   (.03)        $  (1.98)        $   (.03)
                                                       --------         --------         --------         -------- 
</TABLE>

    * The effect of employee stock options is anti-dilutive.


                                     Page 8
<PAGE>   9
                                ALEXANDER'S, INC.
                                AND SUBSIDIARIES

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS



6.  SUBSEQUENT EVENT

    On October 16, 1998, the non-affiliated limited partners of the Seven Thirty
One Limited Partnership (the "Partnership"), which owns the Company's Lexington
Avenue property, exercised the right to put their remaining 7.64% interest to
the Partnership in exchange for a five year $15,000,000 Note. The Note bears
interest at Prime plus 1% (currently 9%) and is prepayable without penalty.





                                     Page 9
<PAGE>   10
                                ALEXANDER'S, INC.
                                AND SUBSIDIARIES

                     MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                  FINANCIAL CONDITION AND RESULTS OF OPERATIONS

RESULTS OF OPERATIONS

         The Company's revenues, which consist of property rentals, tenant
expense reimbursements and equity in income of unconsolidated joint venture were
$16,201,000 in the quarter ended September 30, 1998, compared to $6,016,000 in
the prior year's quarter, an increase of $10,185,000. Revenues were $33,681,000
for the nine months ended September 30, 1998, compared to $18,775,000 for the
prior year's nine months, an increase of $14,906,000.

         Property rentals were $11,100,000 in the quarter ended September 30,
1998, compared to $4,317,000 in the prior year's quarter, an increase of
$6,783,000. Property rentals were $23,451,000 for the nine months ended
September 30, 1998, compared to $13,167,000 for the prior year's nine months, an
increase of $10,284,000. These increases resulted from:


<TABLE>
<CAPTION>
                                                                              FOR THE                  FOR THE
                                                                           THREE MONTHS              NINE MONTHS
                                                       EFFECTIVE               ENDED                    ENDED
                                                          DATE           SEPTEMBER 30, 1998      SEPTEMBER 30, 1998
                                                          ----           ------------------      ------------------
<S>                                                   <C>                <C>                     <C>
      Rent from new tenants:
         Kings Plaza Store Property                   October 1997           $1,361,000              $3,577,000
         Rego Park I                                  March and
                                                      May 1997                   --                   1,232,000
      Acquisition of additional 50%
         interest in the Kings Plaza Mall             June 1998               2,118,000               2,353,000
      Consolidation of Kings Plaza Mall
         Operations previously recorded on
         the equity method                            June 1998               2,118,000               2,353,000
      Caldor's rejection of its Fordham
         Road lease                                   June 1997                  --                  (1,609,000)
      Parking lot revenue                                                       813,000               1,642,000
      Other                                                                     373,000                 736,000
                                                                            -----------             -----------
                                                                            $ 6,783,000             $10,284,000
                                                                            ===========             ===========
</TABLE>

         Tenant expense reimbursements were $5,101,000 in the quarter ended
September 30, 1998, compared to $419,000 in the prior year's quarter, an
increase of $4,682,000. Tenant expense reimbursements were $7,711,000 for the
nine months ended September 30, 1998, compared to $1,713,000 for the prior
year's nine months, an increase of $5,998,000 These increases reflect (i)
corresponding increases in operating expenses passed through to tenants as a
result of leases commencing subsequent to March 31, 1997 at the Rego Park I
property, (ii) the commencement of operations at the Kings Plaza Store property
and (iii) the acquisition of an additional 50% interest in the Kings Plaza Mall
and the consolidation of its operations after June 18, 1998.

         The decreases in equity in income of unconsolidated joint venture (the
Kings Plaza Mall) resulted from the consolidation of the joint venture's
operations as noted above. Total income at the Kings Plaza Mall did not change
significantly between 1997 and 1998.



                                    Page 10
<PAGE>   11
                                ALEXANDER'S, INC.
                                AND SUBSIDIARIES

                     MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                  FINANCIAL CONDITION AND RESULTS OF OPERATIONS

         Operating expenses were $6,951,000 in the quarter ended September 30,
1998, compared to $1,501,000 in the prior year's quarter, an increase of
$5,450,000. Operating expenses were $11,964,000 for the nine months ended
September 30, 1998, compared to $5,378,000 in the prior year's nine months, an
increase of $6,586,000. These increases resulted primarily from (i) real estate
taxes which previously had been capitalized, being charged to income due to the
commencement of operations at the Kings Plaza Store property and (ii) the
acquisition of an additional 50% interest in the Kings Plaza Mall and the
consolidation of the Kings Plaza Mall's operations after June 18, 1998,
partially offset by (iii) a $667,000 charge to bad debt expense in the prior
year's nine months in connection with Caldor's rejection of its Fordham Road
lease.

         General and administrative expenses were $869,000 in the quarter ended
September 30, 1998, compared to $1,026,000 in the prior year's quarter, a
decrease of $157,000. This decrease was primarily attributable to lower
professional fees and corporate office expenses. General and administrative
expenses were $3,106,000 for the nine months ended September 30, 1998, compared
to $3,039,000 in the prior year's nine months, an increase of $67,000.

         Depreciation and amortization expense increased in 1998, compared to
1997 as a result of the Kings Plaza Mall acquisition in June 1998 and the
commencement of operations at the Kings Plaza Store property in October 1997.

         In September 1998, the Company commenced the process of razing its
Lexington Avenue building and accordingly, the carrying value of the building
and related predevelopment costs of $15,096,000 were written-off.

         Interest and debt expense was $4,336,000 in the quarter ended September
30, 1998, compared to $3,250,000 in the prior year's quarter, an increase of
$1,086,000. Interest and debt expense was $11,261,000 for the nine months ended
September 30, 1998, compared to $9,855,000 in the prior year's nine months, an
increase of $1,406,000. These increases resulted primarily from interest
allocated to the Kings Plaza Store property which previously had been
capitalized, being charged to income in 1998 and a decrease in amortization of
debt issuance costs.

         Interest and other income was $328,000 in the quarter ended September
30, 1998, compared to $214,000 in the prior year's quarter, an increase of
$114,000. This increase resulted primarily from an increase in interest income
this year due to higher average investments. Interest and other income was
$752,000 for the nine months ended September 30, 1998, compared to $1,078,000 in
the prior year's nine months, a decrease of $326,000. This decrease resulted
from non-recurring items in the prior year's nine months.

LIQUIDITY AND CAPITAL RESOURCES

         In the aggregate, Alexander's current operating properties (six of its
nine properties) do not generate sufficient cash flow to pay all of its
expenses. The Company's three non-operating properties (Lexington Avenue,
Paramus, and Rego Park II) are in various stages of redevelopment. As rents
commence from a portion of the redevelopment properties, the Company expects
that cash flow will become positive.

         On June 18, 1998, the Company increased its interest in the Kings Plaza
Mall (the "Mall") to 100% by acquiring Federated Department Store's
("Federated") 50% interest. The purchase price was approximately $28,000,000,
which was paid in cash. In addition, the Company has agreed to pay Federated
$15,000,000 to renovate its Macy's store in the Mall in exchange for certain
modifications to the Kings Plaza Operating Agreement.

         In connection with the acquisition, the Company completed a $90,000,000
three-year mortgage loan with Union Bank of Switzerland. The loan is
collateralized by the Kings Plaza Mall and the Company's anchor store and bears
interest at LIBOR plus 1.25% (currently 6.91%). The proceeds from the borrowing
were also used to repay $34,900,000 of existing debt ($32,000,000 of which was
due in the next year). In addition, the Company expects to complete a
$30,000,000 construction loan with Union Bank of Switzerland, of which
approximately $15,000,000 will be used in the future to partially fund a
renovation of the Mall (estimated to cost $20,000,000 in total) and $15,000,000
will be used to pay the liability to Federated noted above.


                                    Page 11
<PAGE>   12
                                ALEXANDER'S, INC.
                                AND SUBSIDIARIES

                     MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                  FINANCIAL CONDITION AND RESULTS OF OPERATIONS

         The Company estimates that its capital expenditure requirements for the
redevelopment of its Paramus property, will cost approximately $100,000,000. The
Company is evaluating development plans for the Lexington Avenue site, which may
include a large multi-use building requiring capital in excess of $300,000,000
to be expended. While the Company anticipates that financing will be available
after tenants have been obtained for these redevelopment projects, there can be
no assurance that such financing will be obtained or if obtained, that such
financings will be on terms that are acceptable to the Company. In addition, it
is uncertain as to when these projects will commence.

         Property rentals from Caldor, which filed for relief under Chapter 11
of the United States Bankruptcy Code in September 1995, represented
approximately 9% and 22% of the Company's consolidated revenues for the nine
months ended September 30, 1998 and for the year ended December 31, 1997. Caldor
rejected its Fordham Road lease effective June 6, 1997 and accordingly, no
longer pays rent. Alexander's has filed a claim for damages based on such
rejection. The annual base rental revenue under this lease was $3,537,000. The
loss of property rental payments, if any, under the Caldor lease for the
Flushing property, could have a material adverse affect on the Company's
financial condition and results of operations.

         The Company's $75,000,000 loan, collateralized by a mortgage on its 
Rego Park I property, which was scheduled to mature on September 30, 1998, has 
been extended to March 30, 1999. The loan bears interest at LIBOR plus 1.00% 
(currently 6.64%) and is guaranteed by the Company. In connection with the loan 
extension, the Company paid a fee of 1/8%. The Company expects to refinance 
this loan through the issuance of public or private debt.          

         On October 16, 1998, the non-affiliated limited partners of the Seven
Thirty One Limited Partnership (the "Partnership"), which owns the Company's
Lexington Avenue property, exercised the right to put their remaining 7.64%
interest to the Partnership in exchange for a five year $15,000,000 Note. The
Note bears interest at Prime plus 1% (currently 9%) and is prepayable without
penalty.

         The Company estimates that the fair market values of its assets are
substantially in excess of their historical cost and that it has additional
borrowing capacity. Alexander's continues to evaluate its needs for capital
which may be raised through (a) property specific or corporate borrowing, (b)
the sale of securities and (c) asset sales.

         Although there can be no assurance, the Company believes that these
cash sources will be adequate to fund cash requirements until its operations
generate adequate cash flow.


    CASH FLOWS

    Nine Months Ended September 30, 1998
         Cash used in operating activities of $2,904,000 was comprised of (i) a
net loss of $9,904,000 and (ii) the net change in operating assets and
liabilities of $7,957,000, offset by (iii) non-cash items of $14,957,000. The
adjustments for non-cash items are comprised of (i) the write-off of the
carrying value of the Lexington Avenue building and related predevelopment costs
of $15,096,000 and (ii) depreciation and amortization of $3,937,000, offset by
(iii) the effect of straight-lining of rental income of $4,076,000.

         Net cash used in investing activities of $33,259,000 was primarily
comprised of (i) $28,000,000 for the acquisition of the remaining 50% interest
in the Kings Plaza Mall, (ii) the escrowing of cash from the condemnation of a
portion of the Paramus property ($4,172,000) and cash from the proceeds from the
Kings Plaza Shopping Center loan ($5,131,000) which is restricted as to its use
and (iii) capital expenditures of $10,656,000, partially offset by (iv) proceeds
from the condemnation of a portion of the Paramus property of $14,700,000.

         Net cash provided by financing activities of $47,938,000 was comprised
of (i) proceeds from the issuance of debt on the Kings Plaza Center of
$90,000,000, offset by (ii) repayments of debt of $38,720,000 and (iii) debt
issuance costs of $3,342,000.


                                    Page 12
<PAGE>   13
                                ALEXANDER'S, INC.
                                AND SUBSIDIARIES

                     MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                  FINANCIAL CONDITION AND RESULTS OF OPERATIONS




Nine Months Ended September 30, 1997
         Cash used in operating activities of $897,000 was comprised of a net
loss of $160,000 and the net change in operating assets and liabilities of
$2,802,000, partially offset by the net change in non-cash items of $2,065,000.
The adjustments for non-cash items are comprised of depreciation and
amortization of $3,089,000, offset by the effect of straight-lining of rental
income of $1,024,000.

         Net cash used in investing activities of $14,838,000 was comprised of
capital expenditures of $16,323,000, offset by the releases of $1,485,000 of
restricted cash.

         Net cash provided by financing activities of $15,676,000 was comprised
of borrowings under the Rego Park I construction loan of $16,468,000 (net of
debt issuance cost), offset by repayment of debt of $792,000.

Funds from Operations for the Three and Nine Months Ended September 30, 1998
and 1997 

         Funds from operations were $2,707,000 in the quarter ended September
30, 1998, an increase of $3,182,000 over the prior year's quarter. Funds from
operations were $4,108,000 in the nine months ended September 30, 1998, an
increase of $4,516,000 over the prior year's nine months. The following table
reconciles funds from operations and net loss:

<TABLE>
<CAPTION>
                                                    For The Three Months Ended                     For The Nine Months Ended  
                                              September 30, 1998     September 30, 1997   September 30, 1998     September 30, 1997
                                              ------------------     ------------------   ------------------     ------------------
<S>                                           <C>                    <C>                  <C>                    <C>          
Net loss                                         $(11,942,000)          $   (135,000)        $ (9,904,000)          $   (160,000)
Depreciation and amortization of
     real property                                  1,219,000                588,000            2,910,000              1,741,000
Straight-lining of property rentals
     for rent escalations                          (1,165,000)              (611,000)          (2,946,000)            (1,024,000)
Leasing fees paid in excess
     of expense recognized                           (501,000)              (538,000)          (1,488,000)            (1,618,000)
Write-off of the carrying value of the
     Lexington Avenue building
     and related predevelopment costs              15,096,000                     --           15,096,000                     --
Proportionate share of adjustments
     to equity in income of unconsolidated
     joint venture to arrive at funds from
     operations                                            --                221,000              440,000                653,000
                                                 ------------           ------------         ------------           ------------
                                                 $  2,707,000           $   (475,000)        $  4,108,000           $   (408,000)
                                                 ============           ============         ============           ============
</TABLE>


                                    Page 13
<PAGE>   14
                                ALEXANDER'S, INC.
                                AND SUBSIDIARIES

                     MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                  FINANCIAL CONDITION AND RESULTS OF OPERATIONS





          Funds from operations does not represent cash generated from operating
activities in accordance with generally accepted accounting principles and is
not necessarily indicative of cash available to fund cash needs, which is
disclosed in the Consolidated Statements of Cash Flows for the applicable
periods. There are no material legal or functional restrictions on the use of
funds from operations. Funds from operations should not be considered as an
alternative to net income as an indicator of the Company's operating performance
or as an alternative to cash flows as a measure of liquidity. Management
considers funds from operations a relevant supplemental measure of operating
performance because it provides a basis for comparison among REITs; however,
funds from operations may not be comparable to similarly titled measures
reported by other REITs since the Company's method of calculating funds from
operations is different from that used by NAREIT. Funds from operations, as
defined by NAREIT, represents net income before depreciation and amortization,
extraordinary items and gains or losses on sales of real estate. Funds from
operations as disclosed above has been modified to adjust for the effect of
straight-lining of property rentals for rent escalations and leasing fee
expenses. Below are the cash flows provided by (used in) operating, investing
and financing activities:


<TABLE>
<CAPTION>
                                       For The Three Months Ended                   For The Nine Months Ended  
                                September 30, 1998      September 30, 1997    September 30, 1998      September 30, 1997
                                ------------------      ------------------    ------------------      ------------------
<S>                             <C>                     <C>                   <C>                    <C>
      Operating activities          $ (2,936,000)          $ (1,211,000)          $ (2,904,000)          $   (897,000)
                                    ============           ============           ============           ============

      Investing activities          $ (2,856,000)          $ (7,441,000)          $(33,259,000)          $(14,838,000)
                                    ============           ============           ============           ============

      Financing activities          $   (756,000)          $   (131,000)          $ 47,938,000           $ 15,676,000
                                    ============           ============           ============           ============
</TABLE>


    Year 2000 Issues

         The Company is managed by Vornado Realty Trust. Vornado initiated its
Year 2000 compliance programs and information systems modifications in early
1998 in an attempt to ensure that these systems and key processes will remain
functional. This objective is expected to be achieved either by modifying
present systems using existing internal and external programming resources or by
installing new systems, and by monitoring supplier and other third-party
interfaces. In many cases, the Company will be relying on statements from
outside vendors as to the Year 2000 readiness of their systems, and will not, in
many circumstances, attempt any independent verification. Review of the systems
affecting the Company and its properties is progressing. The Company does not
expect that the cost of modifications to its systems, if any, will have a
material adverse effect on its financial position, results of operations or
liquidity. The Company has contingency plans for its own day-to-day operational
systems and management is in the process of updating these plans for possible
Year 2000 specific operational requirements.              

    Recently Issued Accounting Standards

         In June of 1998, the Financial Accounting Standards Board issued
Statement of Financial Accounting Standards No. 133, "Accounting for Derivative
Instruments and Hedging Activities". This statement establishes accounting and
reporting standards for derivative instruments, including certain derivative
instruments embedded in other contracts, and for hedging activities. It is
effective for all fiscal quarters of fiscal years beginning after June 15, 1999.
Because the Company does not currently utilize derivatives or engage in hedging
activities, management does not anticipate that implementation of this statement
will have a material effect on the Company's financial statements.

    Quantitative and Qualitative Disclosures About Market Risks

         The Company has no material exposure to market risk sensitive
investments.


                                    Page 14
<PAGE>   15
                                ALEXANDER'S, INC.



        PART II.    OTHER INFORMATION


              ITEM 6.    EXHIBITS AND REPORTS ON FORM 8-K.

                    (a)  Exhibits: The following exhibits are filed with this 
                         Quarterly Report on Form 10-Q.

                         27  Financial Data Schedule

                    (b)  Reports on Form 8-K

                         During the quarter ended September 30, 1998, the
                         Company filed the reports on Form 8-K described below:

<TABLE>
<CAPTION>
       Date of Report                   
     (Date of Earliest
      Event Reported)                  Item Reported                    Date Filed
      ---------------                  -------------                    ----------
<S>                            <C>                                      <C>
       June 18, 1998           Agreement to purchase 50%                July 2, 1998
                               interest in Kings Plaza

       June 18, 1998           Amendment to Kings Plaza                 July 31, 1998
                               Form 8-K and financial
                               statements and pro forma in
                               connection therewith
</TABLE>



                                    Page 15
<PAGE>   16
                                ALEXANDER'S, INC.

                                   SIGNATURES





              Pursuant to the requirements of the Securities Exchange Act of
1934, the registrant has duly caused this report to be signed on its behalf by
the undersigned thereunto duly authorized.




                                                 ALEXANDER'S, INC.          
                                                 -----------------
                                                  (Registrant)



Date: November 6, 1998                         /s/ Joseph Macnow               
                                   --------------------------------------------
                                                 JOSEPH MACNOW
                                         Vice President - Chief Financial
                                       Officer and Chief Accounting Officer



                                    Page 16
<PAGE>   17
                                ALEXANDER'S, INC.

                                  EXHIBIT INDEX



         EXHIBIT NO.

            27           Financial Data Schedule