<PAGE>   1
                                                        EXHIBIT INDEX ON PAGE 16


                       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:              JUNE 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)

<TABLE>
<CAPTION>
<S>                                                       <C>
                  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)
</TABLE>


                                 (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 July 24, 1998 there were 5,000,850 common shares outstanding.



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

                                      INDEX

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

        Item 1.    Financial Statements:

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

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

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

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

        Item 2.    Management's Discussion and Analysis of Financial
                   Condition and Results of Operations.............................................      9


PART II.           OTHER INFORMATION:

        Item 4.    Submission of Matters to a Vote of Security Holders.............................     14

        Item 6.    Exhibits and Reports on Form 8-K................................................     14


Signatures         ................................................................................     15

Exhibit Index      ................................................................................     16
</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>
                                                    JUNE 30,        DECEMBER 31,
                                                      1998              1997
                                                    ---------         ---------
<S>                                                 <C>               <C>
ASSETS:

Real estate, at cost:
     Land                                           $  62,964         $  45,571
     Buildings, leaseholds and improvements           167,804           123,612
     Capitalized expenses and predevelopment
         costs                                         54,373            47,163
                                                    ---------         ---------
              Total                                   285,141           216,346
     Less accumulated depreciation and
         amortization                                 (54,953)          (35,224)
                                                    ---------         ---------
                                                      230,188           181,122

     Investment in unconsolidated joint
         venture                                           --            10,611
                                                    ---------         ---------
     Real estate, net                                 230,188           191,733

Cash and cash equivalents                              21,014             2,691
Restricted cash                                        12,264             1,872
Receivable arising from condemnation
     proceedings                                           --            14,700
Accounts receivable, net of allowance for
     doubtful accounts of $358 and $147                 3,574             1,064
Receivable arising from the straight-lining
     of rents, net                                     10,528             7,805
Deferred lease and other expenses                      28,984            12,443
Deferred debt expense                                   2,906               783
Other assets                                            3,102             1,983
                                                    ---------         ---------

TOTAL ASSETS                                        $ 312,560         $ 235,074
                                                    =========         =========
</TABLE>

<TABLE>
<CAPTION>
                                                 JUNE 30,        DECEMBER 31,
                                                   1998              1997
                                                ---------         ---------
<S>                                             <C>               <C>
LIABILITIES AND STOCKHOLDERS'
     EQUITY:

Debt                                            $ 262,405         $ 208,087
Amounts due to Vornado Realty Trust and
     its affiliate                                  6,184             6,888
Accounts payable and accrued liabilities           11,075             4,174
Other liabilities                                  17,229             2,296
Minority interest                                     600               600
                                                ---------         ---------

     TOTAL LIABILITIES                            297,493           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                                           (13,990)          (16,028)
                                                ---------         ---------
                                                   16,027            13,989
Less treasury shares, 172,600 shares
     at cost                                         (960)             (960)
                                                ---------         ---------
     Total stockholders' equity                    15,067            13,029
                                                ---------         ---------


TOTAL LIABILITIES AND STOCKHOLDERS'
     EQUITY                                     $ 312,560         $ 235,074
                                                =========         =========
</TABLE>

                 See notes to consolidated financial statements.
<PAGE>   4
<TABLE>
<CAPTION>
                                                          ALEXANDER'S, INC.
                                                          AND SUBSIDIARIES

                                                CONSOLIDATED STATEMENTS OF OPERATIONS


(amounts in thousands except per share amounts)
                                                                       FOR THE THREE MONTHS                 FOR THE SIX MONTHS
                                                                               ENDED                               ENDED
                                                                     JUNE 30,          JUNE 30,          JUNE 30,          JUNE 30,
                                                                       1998              1997              1998              1997
                                                                     --------          --------          --------          --------
<S>                                                                  <C>               <C>               <C>               <C>
Revenues:
    Property rentals                                                 $  6,720          $  4,630          $ 12,351          $  8,850
    Expense reimbursements                                              1,612               803             2,610             1,294
    Equity in income of unconsolidated
       joint venture                                                    1,141             1,328             2,519             2,615
                                                                     --------          --------          --------          --------
Total revenues                                                          9,473             6,761            17,480            12,759
                                                                     --------          --------          --------          --------

Expenses:
    Operating (including management fee to Vornado
       of $210 and $420 each for the three and six
        months ended in 1998 and 1997, respectively)                    2,993             2,265             5,013             3,877
    General and administrative (including
       management fee to Vornado of $540 and $1,080
       each for the three and six months ended in 1998
        and 1997, respectively)                                         1,371             1,032             2,237             2,013
    Depreciation and amortization                                         893               582             1,691             1,153
                                                                     --------          --------          --------          --------
Total expenses                                                          5,257             3,879             8,941             7,043
                                                                     --------          --------          --------          --------

Operating income                                                        4,216             2,882             8,539             5,716

Interest and debt expense
    (including interest on loan from Vornado)                          (3,260)           (3,311)           (6,925)           (6,605)
Interest and other income, net                                            160               612               424               864
                                                                     --------          --------          --------          --------

Net income (loss)                                                    $  1,116          $    183          $  2,038          $    (25)
                                                                     ========          ========          ========          ========

Net income (loss) per share - basic                                  $    .22          $    .04          $    .41          $   (.01)
                                                                     ========          ========          ========          ========

Net income (loss) per share - diluted                                $    .22          $    .04          $    .40          $   (.01)
                                                                     ========          ========          ========          ========
</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 SIX MONTHS ENDED
                                                                       ------------------------
                                                                      JUNE 30,          JUNE 30,
                                                                        1998             1997
                                                                      --------         --------
CASH FLOWS FROM OPERATING ACTIVITIES:
<S>                                                                   <C>              <C>
  Net income (loss)                                                   $  2,038         $    (25)
  Adjustments to reconcile net income (loss) to net
    cash provided by (used in) operating activities:
      Depreciation and amortization
        (including debt issuance costs)                                  2,290            2,069
      Straight-lining of rental income                                  (2,723)            (413)
  Change in assets and liabilities:
      Accounts receivable                                               (1,548)            (327)
      (Investment) distributions in excess of equity in income
        of unconsolidated joint venture                                   (386)           1,660
      Amounts due to Vornado Realty Trust and its affiliate               (704)          (1,090)
      Accounts payable and accrued liabilities                           1,018             (321)
      Other liabilities                                                    (67)            (283)
      Other                                                                114             (956)
                                                                      --------         --------


Net cash provided by operating activities                                   32              314
                                                                      --------         --------

CASH FLOWS FROM INVESTING ACTIVITIES:
  Acquisition of Kings Plaza Mall                                      (28,000)              --
  Additions to real estate                                              (6,711)          (8,930)
  Collection of condemnation proceeds                                   14,700               --
  Cash restricted for construction and development                     (10,349)             965
  Cash restricted for operating liabilities                                (43)             568
                                                                      --------         --------
Net cash used in investing activities                                  (30,403)          (7,397)
                                                                      --------         --------

CASH FLOWS FROM FINANCING ACTIVITIES:
  Issuance of debt                                                      90,000           16,667
  Debt repayments                                                      (38,584)            (661)
  Deferred debt expense                                                 (2,722)            (199)
                                                                      --------         --------
Net cash provided by financing activities                               48,694           15,807
                                                                      --------         --------

Net increase in cash and cash equivalents                               18,323            8,724
Cash and cash equivalents at beginning of period                         2,691            5,480
                                                                      --------         --------

Cash and cash equivalents at end of period                            $ 21,014         $ 14,204
                                                                      ========         ========

SUPPLEMENTAL DISCLOSURE OF CASH FLOW INFORMATION:
  Cash payments for interest (including capitalized
    interest of $3,721 and $4,579)                                    $ 10,073         $ 10,268
                                                                      ========         ========
</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 June 30, 1998, the Consolidated
    Statements of Operations for the Three and Six Months Ended June 30, 1998
    and 1997, and the Consolidated Statements of Cash Flows for the Six Months
    Ended June 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 six
    months ended June 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 six months ended June 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 SIX MONTHS ENDED
                                               JUNE 30,                JUNE 30,
                                                1998                    1997
                                           ---------------        ---------------
<S>                                        <C>                    <C>
     Revenues                              $        30,600        $        24,700
                                           ===============        ===============

     Net income                            $         3,700        $         1,300
                                           ===============        ===============

     Net income per share - basic          $           .75        $           .25
                                           ===============        ===============

     Net income per share - diluted        $           .74        $           .25
                                           ===============        ===============
</TABLE>

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 June 30, 1998 and
    1997 and $3,126,000 in the six months ended June 30, 1998 and 1997. In
    addition, Vornado is due $3,689,000 at June 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 $1,578,000 and $1,775,000 in
    the three months ended June 30, 1998 and 1997, of which $902,000 and
    $1,250,000 were capitalized. Interest on the loan was $3,296,000 and
    $3,626,000 in the six months ended June 30, 1998 and 1997, of which
    $1,809,000 and $2,479,000 were capitalized.


4.  COMMITMENTS AND CONTINGENCIES

     Lexington Avenue

     The Company is evaluating redevelopment plans for this site, which may
     involve razing the existing buildings (in which case, the carrying cost of
     approximately $15,000,000 would be written-off) and developing a large
     multi-use building requiring capital in excess of $300,000,000 to be
     expended. No development decisions have been finalized.



                                     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 June 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.   EARNINGS PER SHARE

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

<TABLE>
<CAPTION>
                                                             FOR THE THREE MONTHS              FOR THE SIX MONTHS
                                                                   ENDED                              ENDED
                                                        JUNE  30,          JUNE 30,           JUNE 30,       JUNE 30,
                                                           1998              1997               1998          1997
                                                         -------        --------------        -------        -------
<S>                                                      <C>            <C>                   <C>            <C>
     Numerator:
       Net income (loss)                                 $ 1,116        $          183        $ 2,038        $   (25)
                                                         =======        ==============        =======        =======

     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                              61                    --             65             --
                                                         -------        --------------        -------        -------

       Denominator for diluted earnings per share-
          adjusted weighted average shares and
          assumed conversions                              5,062                 5,001          5,066          5,001
                                                         =======        ==============        =======        =======

     Net income (loss) per share - basic                 $   .22        $          .04        $   .41        $  (.01)
                                                         =======        ==============        =======        =======

     Net income (loss) per share - diluted               $   .22        $          .04        $   .40        $  (.01)
                                                         =======        ==============        =======        =======
</TABLE>

                                     Page 8
<PAGE>   9
                                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
$9,473,000 in the quarter ended June 30, 1998, compared to $6,761,000 in the
prior year's quarter, an increase of $2,712,000. Revenues were $17,480,000 for
the six months ended June 30, 1998, compared to $12,759,000 for the prior year's
six months, an increase of $4,721,000.

         Property rentals were $6,720,000 in the quarter ended June 30, 1998,
compared to $4,630,000 in the prior year's quarter, an increase of $2,090,000.
Property rentals were $12,351,000 for the six months ended June 30, 1998,
compared to $8,850,000 for the prior year's six months, an increase of
$3,501,000. These increases resulted from:

<TABLE>
<CAPTION>
                                                                              FOR THE                  FOR THE
                                                                           THREE MONTHS              SIX MONTHS
                                                        EFFECTIVE              ENDED                    ENDED
                                                          DATE             JUNE 30, 1998            JUNE 30, 1998
                                                    ----------------       -------------            -------------
<S>                                                 <C>                    <C>                      <C>
      Rent from new tenants:
         Kings Plaza Store Property                   October 1997           $1,149,000              $2,216,000
         Rego Park I                                  March/
                                                      May 1997                  341,000               1,232,000
      Acquisition of additional 50%
         interest in the Kings Plaza Mall             June 1998                 235,000                 235,000
      Consolidation of Kings Plaza Mall
         Operations previously recorded on
         the equity method                            June 1998                 235,000                 235,000
      Caldor's rejection of its Fordham
         Road lease                                   June 1997               (644,000)             (1,609,000)
      Parking lot revenue (primarily from the
           re-opening of the Lexington Avenue
           parking lot)                                                         570,000                 829,000
      Other                                                                     204,000                 363,000
                                                                           ------------            ------------
                                                                             $2,090,000              $3,501,000
                                                                             ==========              ==========
</TABLE>

         Tenant expense reimbursements were $1,612,000 in the quarter ended June
30, 1998, compared to $803,000 in the prior year's quarter, an increase of
$809,000. Tenant expense reimbursements were $2,610,000 for the six months ended
June 30, 1998, compared to $1,294,000 for the prior year's six months, an
increase of $1,316,000. 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.

         Equity in income of unconsolidated joint venture (the Kings Plaza Mall)
was $1,141,000 in the quarter ended June 30, 1998, compared to $1,328,000 in the
prior year's quarter, a decrease of $187,000. Equity in income of the Kings
Plaza Mall was $2,519,000 for the six months ended June 30, 1998, compared to
$2,615,000 in the prior year's six months, a decrease of $96,000. Total income
at the Kings Plaza Mall did not change significantly between 1997 and 1998. The
decreases in equity in income of unconsolidated joint venture resulted primarily
from the consolidation of the joint venture's operations as noted above.



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

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

         Operating expenses were $2,993,000 in the quarter ended June 30, 1998,
compared to $2,265,000 in the prior year's quarter, an increase of $728,000.
Operating expenses were $5,013,000 for the six months ended June 30, 1998 ,
compared to $3,877,000 in the prior year's six months, an increase of
$1,136,000. 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 quarter in connection
with Caldor's rejection of its Fordham Road lease.

         General and administrative expenses were $1,371,000 in the quarter
ended June 30, 1998, compared to $1,032,000 in the prior year's quarter, an
increase of $339,000. General and administrative expenses were $2,237,000 for
the six months ended June 30, 1998, compared to $2,013,000 in the prior year's
six months, an increase of $224,000. These increases resulted primarily from
higher professional fees.

         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.

         Interest and debt expense was $3,260,000 in the quarter ended June 30,
1998, compared to $3,311,000 in the prior year's quarter, a decrease of $51,000.
Interest and debt expense was $6,925,000 for the six months ended June 30, 1998,
compared to $6,605,000 in the prior year's six months, an increase of $320,000.
These changes 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 $160,000 in the quarter ended June 30,
1998, compared to $612,000 in the prior year's quarter, a decrease of $452,000.
Interest and other income was $424,000 for the six months ended June 30, 1998,
compared to $864,000 in the prior year's six months, a decrease of $440,000.
These decreases resulted primarily from non-recurring items in the prior year's
quarter.

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 10
<PAGE>   11
                                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 $90,000,000 to
$100,000,000. Further, the Company is evaluating redevelopment plans for the
Lexington Avenue site, which may involve razing the existing buildings (in which
case, the carrying cost of approximately $15,000,000 would be written-off) and
developing 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 12% and 22% of the Company's consolidated revenues for the six
months ended June 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 non-affiliated limited partners of the Seven Thirty One Limited
partnership (the "Partnership"), a limited partnership which owns the Company's
Lexington Avenue property, have the right to put their remaining 7.64% interest
to the Partnership until October 3, 1998, in exchange for a five year secured
note in the principal amount of $15,000,000, bearing annual interest at Prime
plus 1%.

         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

    Six Months Ended June 30, 1998
         Cash provided by operating activities of $32,000 was comprised of (i)
net income of $2,038,000, offset by (ii) non-cash items of $433,000, and (iii)
the net change in operating assets and liabilities of $1,573,000. The
adjustments for non-cash items are comprised of the effect of straight-lining of
rental income of $2,723,000, offset by depreciation and amortization of
$2,290,000.

         Net cash used in investing activities of $30,403,000 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 ($5,341,000) and cash from the proceeds from the
Kings Plaza Shopping Center loan ($5,008,000) which is restricted as to its use
and (iii) capital expenditures of $6,711,000, 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 $48,694,000 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 $38,584,000 and (iii) debt
issuance costs of $2,722,000.



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

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




Six Months Ended June 30, 1997

         Cash provided by operating activities of $314,000 was comprised of
$3,291,000 from results of operations (net loss of $25,000 offset by non-cash
items of $3,316,000), partially offset by the net change in operating assets and
liabilities of $2,977,000. The adjustments for non-cash items are comprised of
(i) depreciation and amortization of $2,069,000 and (ii) equity in income of
unconsolidated joint venture of $1,660,000, offset by the effect of
straight-lining of rental income of $413,000.

         Net cash used in investing activities of $7,397,000 was comprised of
capital expenditures of $8,930,000, offset by the release of $1,533,000 of
restricted cash.

         Net cash provided by financing activities of $15,807,000 was comprised
of proceeds from the issuance of debt (net of deferred debt expense) of
$16,468,000 on the Rego Park I property, offset by repayments of debt of
$661,000.

Funds from Operations for the Three and Six Months Ended June 30, 1998 and 1997

         Funds from operations were $838,000 in the quarter ended June 30, 1998,
compared to $534,000 in the prior year's quarter, an increase of $304,000. Funds
from operations were $1,401,000 in the six months ended June 30, 1998, compared
to $67,000 in the prior year's six months, an increase of $1,334,000. The
following table reconciles funds from operations and net income (loss):

<TABLE>
<CAPTION>
                                                     For The Three Months Ended               For The Six Months Ended
                                                    June 30, 1998   June 30, 1997         June 30, 1998      June 30, 1997
                                                    -------------   -------------         -------------      -------------
<S>                                                  <C>              <C>                  <C>               <C>
     Net income (loss)                               $1,116,000       $  183,000           $2,038,000        $  (25,000)
     Depreciation and amortization of
          real property                                 893,000          582,000            1,691,000         1,153,000
     Straight-lining of property rentals
          for rent escalations                         (883,000)          99,000           (1,781,000)         (413,000)
     Leasing fees paid in excess
          of expense recognized                        (497,000)        (550,000)            (987,000)       (1,080,000)
     Proportionate share of adjustments
          to equity in income of unconsolidated
          joint venture to arrive at funds from
          operations                                    209,000          220,000              440,000           432,000
                                                    -----------      -----------         ------------      ------------
                                                     $  838,000       $  534,000           $1,401,000      $     67,000
                                                     ==========       ==========           ==========      ============
</TABLE>


                                     Page 12
<PAGE>   13
                                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 Six Months Ended
                                                June 30, 1998    June 30, 1997         June 30, 1998   June 30, 1997
                                                -------------    -------------      ----------------   -------------
<S>                                            <C>               <C>                <C>                <C>
          Operating activities                 $      835,000    $    794,000       $        32,000    $     314,000
                                               ===============   =============      ================   =============

          Investing activities                   $(35,163,000)    $(3,580,000)         $(30,403,000)    $ (7,397,000)
                                                 =============    ============         =============    =============

          Financing activities                   $ 52,642,000    $   (364,000)         $ 48,694,000      $15,807,000
                                                 =============   =============         =============     ===========
</TABLE>


    Year 2000 Issues

         The Company is managed by Vornado Realty Trust. Vornado is continuing
to address the Year 2000 issues. Review of the systems effecting the Company is
progressing. During the six months ended June 30, 1998, the Company has not
incurred substantial costs related to its Year 2000 efforts. 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.



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



        PART II.    OTHER INFORMATION

              ITEM 4.    SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

                    On May 27, 1998, the Company held its annual meeting of
                stockholders. The stockholders voted, in person or by proxy, for
                the election of the three nominees listed in the Proxy Statement
                to serve on the Board of Directors for a term of three years, or
                until their respective successors are duly elected and qualify.
                The three nominees were elected. The results of the voting are
                shown below:

<TABLE>
<CAPTION>
                         Election of Directors
                                                                Votes Cast
                                                                Against or
                      Directors           Votes Cast For         Withheld
                ---------------------     --------------        ----------
<S>                                       <C>                   <C>
                Michael D. Fascitelli         4,153,143            1,277
                David Mandelbaum              4,153,253            1,167
                Richard West                  4,153,263            1,157
</TABLE>


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

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

                           10       Term Loan Agreement dated as of June 18,
                                    1998 among Alexander's Kings Plaza Center,
                                    Inc., Kings Plaza Corp., and Alexander's
                                    Department Stores of Brooklyn, Inc., as
                                    Borrower, Union Bank of Switzerland, as
                                    Lender

                           27       Financial Data Schedule

                   (b)     Reports on Form 8-K

                           None



                                     Page 14
<PAGE>   15
                                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:  August 6, 1998                           /s/ Joseph Macnow
                                        ------------------------------------
                                                  JOSEPH MACNOW
                                          Vice President - Chief Financial
                                        Officer and Chief Accounting Officer



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

                                  EXHIBIT INDEX



         EXHIBIT NO.

                  10       Term Loan Agreement dated as of June 18, 1998 among
                           Alexander's Kings Plaza Center, Inc., Kings Plaza
                           Corp., and Alexander's Department Stores of Brooklyn,
                           Inc., as Borrower, Union Bank of Switzerland, as
                           Lender

                  27       Financial Data Schedule



                                     Page 16