<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:                      MARCH 31, 1999   
                              ------------------------------------------------

                                       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 May 1, 1999 there were 5,000,850 common shares outstanding.
<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 March 31, 1999
                   and December 31, 1998...........................................................      3

                   Consolidated Statements of Operations for the Three
                   Months Ended March 31, 1999 and March 31, 1998..................................      4

                   Consolidated Statements of Cash Flows for the Three
                   Months Ended March 31, 1999 and March 31, 1998..................................      5

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

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

        Item 3.    Quantitative and Qualitative
                   Disclosures about Market Risk...................................................     13


PART II.           OTHER INFORMATION:


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


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

Exhibit Index      ................................................................................     16

Exhibit 27         ................................................................................     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>
                                                           MARCH 31,       DECEMBER 31, 
                                                             1999             1998
                                                          ---------        ----------
<S>                                                       <C>               <C>      
ASSETS:
Real estate, at cost:
     Land                                                 $  83,957         $  83,957
     Buildings leaseholds and improvements                  149,145           149,054
     Capitalized expenses and predevelopment
         costs                                               61,680            57,675
                                                          ---------         ---------
               Total                                        294,782           290,686
     Less accumulated depreciation and
         amortization                                       (52,429)          (51,529)
                                                          ---------         ---------
     Real estate, net                                       242,353           239,157

Cash and cash equivalents                                    15,076            15,363
Restricted cash                                               8,855             9,402

Accounts receivable, net of allowance for doubtful
  accounts of $684 in 1999 and $841 in 1998                   4,065             3,303
Receivable arising from the straight-lining
  of rents, net                                              11,060            13,036
Deferred lease and other property costs                      26,018            27,921
Deferred debt expense                                         2,574             2,693
Other assets                                                  6,870             6,168
                                                          ---------         ---------
TOTAL ASSETS                                              $ 316,871         $ 317,043
                                                          =========         =========
</TABLE>


<TABLE>
<CAPTION>
                                                 MARCH 31,       DECEMBER 31, 
                                                  1999             1998
                                                ---------        -----------
<S>                                             <C>               <C>
 LIABILITIES AND SHAREHOLDERS' EQUITY:

Debt (including $45,000 due to Vornado)         $ 276,962         $ 277,113
Amounts due to Vornado Realty Trust and
     its affiliate                                  4,153             5,840
Accounts payable and accrued liabilities           10,354            10,113
Other liabilities                                  16,953            17,003
                                                ---------         ---------

     TOTAL LIABILITIES                            308,422           310,069
                                                ---------         ---------

Commitments and contingencies
Stockholders' Equity:
                                                    5,174             5,174
Common stock; $1.00 par value per share;
     authorized 10,000,0000 shares;
     issued 5,173,450
Additional capital                                 24,843            24,843
Deficit                                           (20,608)          (22,083)
                                                ---------         ---------
                                                    9,409             7,934

Less treasury shares, 172,600 shares
      at cost                                        (960)             (960)
                                                ---------         ---------
Total shareholders' equity                          8,449             6,974
                                                ---------         ---------

TOTAL LIABILITIES AND STOCKHOLDERS'
     EQUITY                                     $ 316,871         $ 317,043
                                                =========         =========
</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 ENDED
                                                                    --------------------------
                                                                  MARCH 31, 1999   MARCH 31, 1998
                                                                  --------------   -------------
<S>                                                               <C>              <C>     
Revenues:
     Property rentals ......................................        $ 11,388         $  5,631
     Expense reimbursements ................................           5,235              998
     Equity in income of unconsolidated
         joint venture .....................................            --              1,378
                                                                    --------         --------
Total revenues .............................................          16,623            8,007
                                                                    --------         --------

Expenses:
     Operating (including management fee to Vornado of $327
         and $210 in 1999 and 1998) ........................           8,996            2,020
     General and administrative (including
         management fee to Vornado of $540 in 1998 and 1999)             979              866
     Depreciation and amortization .........................           1,338              798
                                                                    --------         --------
Total expenses .............................................          11,313            3,684
                                                                    --------         --------

Operating income ...........................................           5,310            4,323

Interest and debt expense
     (including interest on loan from Vornado) .............          (3,761)          (3,665)
Other, net .................................................             (74)             264
                                                                    --------         --------

Net income .................................................        $  1,475         $    922
                                                                    ========         ========

Net income per share (basic and diluted) ...................        $    .29         $    .18
                                                                    ========         ========
</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 THREE MONTHS ENDED
                                                                         --------------------------
                                                                       MARCH 31, 1999    MARCH 31, 1998
                                                                       --------------    --------------
<S>                                                                    <C>               <C>     
CASH FLOWS FROM OPERATING ACTIVITIES:
    Net income ..................................................        $  1,475         $    922
Adjustments to reconcile net income to net
cash provided by operating activities:
    Depreciation and amortization
     (including debt issuance costs) ............................           1,749            1,169
    Straight-lining of rental income ............................          (1,024)            (898)
    Write-off of the asset arising from the straight-lining
     of rents ...................................................           3,000             --
Change in assets and liabilities:
    Accounts receivable .........................................            (762)             589
    Amounts due to Vornado Realty Trust and its affiliate .......            (427)            (527)
    Accounts payable and accrued liabilities ....................             241               92
    Other liabilities from discontinued operations ..............             (50)             (58)
    Note receivable .............................................            --             14,700
    Investment in excess of equity in income
     of unconsolidated joint venture ............................            --                (98)
    Other .......................................................            (340)          (1,994)
                                                                         --------         --------

Net cash provided by operating activities .......................           3,862           13,897
                                                                         --------         --------

CASH FLOWS FROM INVESTING ACTIVITIES:
    Additions to real estate ....................................          (4,096)          (3,603)
    Cash restricted for construction and development ............             469           (6,326)
    Cash restricted for operating liabilities ...................             (79)             (11)
                                                                         --------         --------
Net cash used in investing activities ...........................          (3,706)          (9,940)
                                                                         --------         --------

CASH FLOWS FROM FINANCING ACTIVITIES:
    Debt repayments .............................................            (151)          (3,729)
    Deferred debt expense .......................................            (292)            (219)
                                                                         --------         --------
    Net cash used in financing activities .......................            (443)          (3,948)
                                                                         --------         --------

Net (decrease) increase in cash and cash equivalents ............            (287)               9
Cash and cash equivalents at beginning of period ................          15,363            2,691
                                                                         --------         --------

Cash and cash equivalents at end of period ......................        $ 15,076         $  2,700
                                                                         ========         ========

SUPPLEMENTAL DISCLOSURE OF CASH FLOW INFORMATION:
    Cash payments for interest (including capitalized interest of
     $2,245 and $1,765) .........................................        $  5,595         $  5,060
                                                                         ========         ========
</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 March 31, 1999, the consolidated
    statements of operations for the three months ended March 31, 1999, and the
    consolidated statements of cash flows for the three months ended March 31,
    1999 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 1998 Annual
    Report to Shareholders. The results of operations for the three months ended
    March 31, 1999 are not necessarily indicative of the operating results for
    the full year.


2. ACQUISITION OF KINGS PLAZA MALL

     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, plus the Company has agreed to pay Federated
  $15,000,000 to renovate its Macy's store in the Mall and Federated agreed to
  certain modifications to the Kings Plaza Operating Agreement.

     Set forth below is the pro forma condensed consolidated statement of
   operations data for the Company for the three months ended March 31, 1998 as
   if the acquisition of the Kings Plaza Mall and the related financing
   transactions had occurred on January 1, 1998.
<TABLE>

<S>                                                      <C>        
         Revenues ...............................        $14,734,000
                                                         ===========

         Net income .............................        $ 1,788,000
                                                         ===========

         Net income per share - basic and diluted        $       .35
                                                         ===========
</TABLE>


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

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS


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 $1,679,000 and $1,563,000 in each of the three month periods ended March
     31, 1999 and 1998. In addition, Vornado is due $3,448,000 at March 31, 1999
     under the leasing agreement, subject to the payment of rents by tenants.

      The Company is indebted to Vornado in the amount of $45,000,000, the
     subordinated tranche of a $65,000,000 secured financing. The Company
     incurred interest on its loan from Vornado of $1,561,000 and $1,718,000 in
     the three months ended March 31, 1999 and 1998, of which $1,164,000 and
     $907,000 was capitalized.


4. LEASES

       In the first quarter of 1999, Caldor closed all of its stores. Caldor
     previously sub-leased its Flushing store from the Company. Caldor rejected
     the Flushing lease effective March 29, 1999. In connection therewith the
     Company wrote-off the $3,000,000 asset arising from the straight-lining of
     Caldor's rent.


5. COMMITMENTS AND CONTINGENCIES

       In June 1997, the Kings Plaza Regional 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 has accrued $1,500,000 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 December 31, 1998
     for potential recoveries of environmental remediation costs from other
     parties.


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

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS


6. EARNINGS PER SHARE

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

<TABLE>
<CAPTION>
                                                                             FOR THE THREE MONTHS ENDED
                                                                             --------------------------
                                                                          MARCH 31, 1999    MARCH 31, 1998
                                                                          --------------    --------------
<S>                                                                       <C>               <C>       
         Numerator:
            Net income .............................................        $1,475,000        $  922,000
                                                                            ==========        ==========
         Denominator:
            Denominator for basic earnings per share --
             weighted average shares ...............................         5,000,850         5,000,850
            Effect of dilutive securities:
             Employee stock options ................................             1,183            67,335
                                                                            ----------        ----------

         Denominator for diluted earnings per share --
            adjusted weighted average shares and assumed conversions         5,002,033         5,068,185
                                                                            ==========        ==========

         Basic and diluted earnings per share ......................        $      .29        $      .18
                                                                            ==========        ==========
</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 had net income of $1,475,000 in the quarter ended March 31,
1999, compared to $922,000 in the quarter ended March 31, 1998, an increase of
$553,000. Operating income, before depreciation and amortization and the effect
of the straight-lining of property rentals for rent escalations, was $5,624,000
in 1999, compared to $4,384,000 in 1998, an increase of $1,240,000.

         Property rentals were $11,388,000 in quarter ended March 31, 1999,
compared to $5,631,000 in the quarter ended March 31, 1998, an increase of
$5,757,000. This increase resulted from:
<TABLE>
<CAPTION>
                                                          Effective
                                                             Date             Amount
                                                          ---------         ----------
<S>                                                       <C>               <C>
         Rent from new tenants                                              $  615,000
         Acquisition of the remaining 50%
             interest in the Kings Plaza Mall             June 1998          2,646,000
         Consolidation of 50% interest in the
             Kings Plaza Mall previously recorded
             on the equity method                         June 1998          2,646,000
         Other                                                                (150,000)
                                                                            ----------
                                                                            $5,757,000
                                                                            ==========
</TABLE>

         Tenant expense reimbursements were $5,235,000 in the quarter ended
March 31, 1999, compared to $998,000 in the quarter ended March 31, 1998, an
increase of $4,237,000. This increase resulted primarily from the acquisition of
the remaining 50% interest in the Kings Plaza Mall and the resulting
consolidation of the Mall's operations after June 18, 1998.

         The decrease in equity in income of unconsolidated joint venture
resulted from the consolidation of the Mall's operations as noted above.

         Operating expenses were $8,996,000 in the quarter ended March 31, 1999,
compared to $2,020,000 in the quarter ended March 31, 1998, an increase of
$6,976,000. Of this increase: (i) $4,064,000 is attributable to the acquisition
of the remaining 50% interest in the Kings Plaza Mall and the resulting
consolidation of the Mall's operations after June 18, 1998 and (ii) $3,000,000
resulted from the write-off of the asset arising from the straight-lining of
rents due to Caldor's rejection of its Flushing lease.

         General and administrative expenses were $979,000 in the quarter ended
March 31, 1999, compared to $866,000 in the quarter ended March 31, 1998.

         Depreciation and amortization expense increased primarily as a result
of the Kings Plaza Mall acquisition in June 1998.

         Interest and debt expense was $3,761,000 in the quarter ended March 31,
1999, compared to $3,665,000 in the quarter ended 1998, an increase of $96,000.
The increase results from higher average debt in 1999, partially offset by a
greater amount of interest capitalized on redevelopment projects.



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

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


LIQUIDITY AND CAPITAL RESOURCES

         In the aggregate, Alexander's current operating properties (five of the
eight 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.

    In connection with the acquisition of the remaining 50% interest in the
Kings Plaza Mall, the Company completed a $90,000,000 three-year mortgage loan
with Union Bank of Switzerland. The Company expects to increase this loan by
$30,000,000 of which approximately $15,000,000 will be used to partially fund a
renovation of the Mall (estimated to cost $30,000,000 in total) and $15,000,000
will be used to pay its liability to Federated.

         The Company estimates that capital expenditure requirements for the
redevelopment of its Paramus property, will approximate $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.

         In the first quarter of 1999, Caldor closed all of its stores. Caldor
previously sub-leased its Flushing Store from the Company. Caldor rejected the
Flushing lease effective March 29, 1999. The annual base rental under the lease
was $2,963,000.

         On May 12, 1999, the Company, through a newly formed subsidiary,
completed an $82,000,000 refinancing of its subsidiary's Rego Park I property 
and repaid the then existing $75,000,000 debt on the property from the proceeds
of the new loan. The new 10-year debt, which is an obligation of the subsidiary,
matures in May 2009 and bears interest at 7.25%. 
                                         


                                    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 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

    Three Months Ended March 31, 1999

    Cash provided by operating activities of $3,862,000 was comprised of (i) net
income of $1,475,000, (ii) non-cash items of $3,725,000, offset by (iii) the net
change in operating assets and liabilities of $1,338,000. The adjustments for
non-cash items are comprised of (i) the write-off of the asset arising from the
straight-lining of rents of $3,000,000 and (ii) depreciation and amortization of
$1,749,000, offset by (iii) the effect of straight-lining of rental income of
$1,024,000.

    Net cash used in investing activities of $3,706,000 was primarily comprised
of capital expenditures.

    Net cash used in financing activities of $443,000 was comprised primarily of
(i) debt issuance costs of $292,000 and (ii) repayments of debt of $151,000.

    Three Months Ended March 31, 1998

    Cash provided by operating activities of $13,897,000 was comprised of (i)
net income of $922,000, (ii) proceeds from the condemnation of a portion of the
Paramus property of $14,700,000 and (iii) non-cash items of $271,000, offset by
(iv) the net change in operating assets and liabilities of $1,169,000, offset by
the effect of straight-lining of rental income of $898,000.

    Net cash used in investing activities of $9,940,000 was primarily comprised
of (i) cash from the condemnation of a portion of the Paramus property
restricted for construction and development of $6,326,000 and (ii) capital
expenditures of $3,603,000.

    Net cash used in financing activities of $3,948,000 was comprised primarily
of repayments of debt.

Funds from Operations for the Three Months Ended March 31, 1999 and 1998

         Funds from operations was $4,679,000 in the three months ended March
31, 1999, an increase of $4,116,000 over the prior year. The following table
reconciles funds from operations and net income:


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

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

<TABLE>
<CAPTION>
                                                          Three Months Ended March 31,
                                                          ----------------------------
                                                            1999                 1998
                                                        -----------         -----------
<S>                                                     <C>                 <C>        
         Net income                                     $ 1,475,000         $   922,000
         Depreciation and amortization of
               real property                              1,338,000             798,000
         Straight-lining of property rentals
               for rent escalations                      (1,024,000)           (898,000)
         Leasing fees paid in excess
               of expense recognized                       (110,000)           (490,000)
         Proportionate share of adjustments
               to equity in income of previously
               unconsolidated joint venture to
               arrive at funds from operations                 --               231,000
         Write-off of asset arising from the
               straight-lining of rents                   3,000,000                --
                                                        -----------         -----------
                                                        $ 4,679,000         $   563,000
                                                        ===========         ===========
</TABLE>

         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>
                                         Three months Ended March 31,
                                         ----------------------------
                                         1999               1998
                                     -----------          ------------
<S>                                  <C>                  <C>         
         Operating activities        $  3,862,000         $ 13,897,000
                                     ============         ============

         Investing activities        $ (3,706,000)        $ (9,940,000)
                                     ============         ============

         Financing activities        $   (443,000)        $ (3,948,000)
                                     ============         ============
</TABLE>


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

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


    Year 2000 Issues

         The Company is managed by Vornado Realty Trust. Vornado has advised the
Company that Vornado initiated its Year 2000 compliance programs and information
systems modifications in early 1998 to ensure that its systems and key processes
will remain functional. Vornado expects this objective 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 certain cases, Vornado will be relying on statements
from outside vendors as to the Year 2000 readiness of its systems.

         The Company is not aware of any operational systems within its control
that are not Year 2000 compliant. In the event that a third-party service is
interrupted due to a Year 2000 issue, the Company will seek to obtain such
service from another third-party provider.

    Recently Issued Accounting Standards

         In June 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.


ITEM 3.  QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

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


                                    Page 13
<PAGE>   14
                                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

                            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:  May 12, 1999                                   /s/ Joseph Macnow      
                                               --------------------------------
                                               Joseph Macnow, Vice President,
                                               Chief Financial Officer


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

                                  EXHIBIT INDEX
                                                                   PAGE NUMBER
                                                                        IN
                                                                    SEQUENTIAL
         EXHIBIT NO.                                                NUMBERING  
         -----------                                                ---------  


            27           Financial Data Schedule                    17


                                    Page 16