<PAGE>   1
                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                   FORM 10-KSB

Annual Report under Section 13 or 15(d) of the Securities Exchange Act of 1934
For the fiscal year ended September 30, 1998

Commission File Number: 0-9116

                            PANHANDLE ROYALTY COMPANY
            (Exact name of small business registrant in its charter)

           OKLAHOMA                                              73-1055775
(State or other jurisdiction of                               (I.R.S. Employer
 incorporation or organization)                              Identification No.)

Grand Centre Suite 210, 5400 N Grand Blvd., Okla. City, OK  73112
(Address of principal executive offices)                  (Zip code)

Registrant's telephone number   (405) 948-1560

Securities registered under Section 12(B) of the Exchange Act:  NONE

Securities registered under Section 12(g) of the Exchange Act:
                            (Title of Class)
             CLASS A COMMON STOCK (VOTING)         .10 par value
                            (Title of Class)
             CLASS B COMMON STOCK (NON-VOTING)   $1.00 par value

Check whether the registrant (1) has filed all reports required to be filed by
Section 13 or 15(d) of the Exchange Act during the past 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

Check if there is no disclosure of delinquent filers in response to Item 405 of
Regulation SB contained in this form, and no disclosure will be contained, to
the best of registrant's knowledge, in the definitive proxy or information
statements incorporated by reference in Part III of this Form 10-KSB or any
amendment to this Form 10-KSB. [X]

Registrant's revenues for fiscal year-end September 30, 1998, were $5,440,182.

The aggregate market value of the voting stock held by non-affiliates of the
registrant, computed by using the closing price of registrant's common stock, at
December 2, 1998, was $16,380,816. As of December 2, 1998, 682,534 class A
common shares were outstanding.

Documents Incorporated By Reference ..... NONE
<PAGE>   2
                                TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                            PAGE
                                                                            ----
<S>                                                                        <C>
PART I

Item 1.  Description of Business ........................................    1-4

Item 2.  Description of Properties.......................................   4-10

Item 3.  Legal Proceedings...............................................     10

Item 4.  Submission of Matters to a Vote of
           Security Holders..............................................     10

PART II

Item 5.  Market for Common Equity and
           Related Stockholder Matters...................................  10-11

Item 6.  Management's Discussion and Analysis
           or Plan of Operations.........................................  11-14

Item 7.  Financial Statements............................................  14-31

Item 8.  Changes in and Disagreements with
           Accountants on Accounting and
           Financial Disclosure..........................................     32

PART III

Item 9.  Directors, Executive Officers, Promoters
           and Control Persons; Compliance with
           Section 16(a) of the Exchange Act.............................  32-34

Item 10. Executive Compensation..........................................  34-35

Item 11. Security Ownership of Certain Beneficial
           Owners and Management.........................................  35-36

Item 12. Certain Relationships and Related
           Transactions..................................................     36

Item 13. Exhibits and Reports on Form 8-K................................  36-37

Exhibit 21 ..............................................................     37

Signature Page ..........................................................     38
</TABLE>


                                      (i)

<PAGE>   3

                                     PART I


ITEM 1.         DESCRIPTION OF BUSINESS

                FORWARD-LOOKING STATEMENTS

                Forward-looking statements for 1999 and later periods are made
throughout this document. Such statements represent estimates of management
based on the Company's historical operating trends, its proved oil and gas
reserves and other information currently available to management. The Company
cautions that the forward-looking statements provided herein are subject to all
the risks and uncertainties incident to the acquisition, development and
marketing of, and exploration for oil and gas reserves. These risks include, but
are not limited to oil and natural gas price risk, environmental risk, drilling
risk, reserve quantity risk and operations and production risks. For all the
above reasons, actual results may vary materially from the forward-looking
statements and there is no assurance that the assumptions used are necessarily
the most likely to occur.

                BUSINESS DEVELOPMENT

                Panhandle Royalty Company ("Panhandle" or the "Company") is an
Oklahoma Corporation, organized in 1926 as Panhandle Cooperative Royalty
Company. In 1979, Panhandle Cooperative Royalty Company was merged into
Panhandle Royalty Company. Panhandle's authorized and registered stock consisted
of 100,000 shares of $1.00 par value class A common stock. In 1982, the Company
split the stock on a 10-for-1 basis and reduced the par value to $.10, resulting
in 1,000,000 shares of authorized class A common stock. Since its formation, the
Company has been involved in the acquisition and management of mineral interests
and the exploration for, and development of, oil and gas properties, principally
involving wells located on the Company's mineral interests. Panhandle's mineral
properties and other oil and gas interests are located primarily in Oklahoma,
New Mexico and Texas. Properties are also located in twelve other states. The
majority of the Company's oil and gas production is from wells located in the
Anadarko Basin of western Oklahoma and the Dagger Draw Field in Eddy County, New
Mexico. In 1988, the Company merged with New Mexico Osage Royalty Company, thus
acquiring most of its New Mexico mineral interests. The Company's offices are
located at Grand Centre Suite 210, 5400 N. Grand Blvd., Oklahoma City, OK 73112
(405)948-1560, FAX (405)948-2038.

                BUSINESS OF ISSUER

                The majority of Panhandle's revenues are derived from the
production and sale of oil and natural gas. See "Item 7 - Financial Statements".
The Company's oil and gas holdings, including its mineral interests and its
interests in producing wells, both working interests and royalty interests, are
centered in Oklahoma with increasingly more activity, in recent years, in New
Mexico and Texas. See "Item 2 Description of Properties". Exploration and
development of the Company's oil and gas properties is conducted in association
with operating oil and gas companies, including major and independent companies.
The Company does not operate any of its oil and gas properties. Drilling
operations have been active the last five years with wells drilled on the
Company's mineral properties and on third party drilling prospects. A large
percentage of the Company's recent drilling participations have been on
properties in which


                                      (1)
<PAGE>   4

the Company has mineral interests and in many cases already owns an interest in
a producing well in the unit. This "increased density" drilling has accounted
for a majority of the successful oil and gas wells completed in the last five
years and has added significant reserves for the Company. The Company continues
to acquire additional mineral interest properties, both producing and
non-producing. Several of the mineral properties purchased in the last five
years have been in areas where the Company had no mineral holdings, thus
expanding the Company's area of interest.

                PRINCIPAL PRODUCTS AND MARKETS

                The Company's principal products are crude oil and natural gas.
These products are sold to various purchasers, including pipeline companies,
which are generally located in and service the areas where the Company's
producing wells are located. The Company does not act as operator for any of the
properties in which it owns an interest, thus it relies on the operating
expertise of numerous companies that operate in the area where the Company owns
mineral interests. This expertise includes drilling operations and completions,
producing well operations and, in some cases, the marketing or purchasing of the
well's production. Natural gas sales are contracted by either the Company or the
well operator and are contracted principally on a monthly basis with third party
gas marketers and pipeline companies. Payment for gas sold is received either
from the contracted purchasers or the well operator. Crude oil sales are
generally handled by the well operator and payment for oil sold is received from
the well operator or from the crude oil purchaser.

                COMPETITIVE BUSINESS CONDITIONS

                The oil and gas industry is highly competitive, both in the
search for new oil and gas reserves and the marketing of the production from
wells. There are many factors affecting Panhandle's competitive position and the
market for its products which are beyond its control. Some of these factors are
quantity and price of foreign oil imports, changes in prices received for its
oil and gas production, business and consumer demand for refined oil products
and natural gas, and the effects of federal and state regulation of oil and gas
sales. Changes in existing economic conditions, weather patterns and actions
taken by OPEC and other oil-producing countries have dramatic influence on the
price Panhandle receives for its oil and gas production. The Company relies
heavily on companies with greater resources, staff, equipment, research, and
experience for operation of wells and the development and drilling of subsurface
prospects. The Company uses its strong financial base and its mineral property
ownership to participate in drilling operations with these larger companies.
This method allows the Company to effectively compete in drilling operations it
could not undertake on its own due to financial and personnel limits and to
maintain low overhead costs.


                                      (2)
<PAGE>   5

                SOURCES AND AVAILABILITY OF RAW MATERIALS

                The existence of commercial oil and gas reserves is essential to
the ultimate realization of value from the Company's mineral properties and
these mineral properties may be considered a raw material to its business. The
production and sale of oil and natural gas from the Company's oil and gas
properties is essential to provide the cash flow necessary to sustain the
ongoing viability of the Company. The Company continues to reinvest a large
portion of its cash flow in the purchase of additional mineral properties to
assure the continued availability of acreage with which to participate in
exploration, drilling, and development operations and subsequently the
production and sale of oil and gas. This participation in exploration and
production and the purchasing of additional mineral interests will continue to
supply the Company with the raw materials with which to generate additional cash
flow. Mineral purchases are made from varied owners, and the Company does not
rely on any particular companies or individuals for these acquisitions.

                MAJOR CUSTOMERS

                The Company's oil and gas production is sold to many different
purchasers on a well-by-well basis. No one purchaser accounts for a major
percentage of the Company's revenues. Generally, if one purchaser declines to
continue purchasing the Company's oil and/or natural gas, several other
purchasers can be located. Pricing is usually reasonably consistent from
purchaser to purchaser.

                PATENTS, TRADEMARKS, LICENSES, FRANCHISES AND
                ROYALTY AGREEMENTS

                The Company does not own any patents, trademarks, licenses or
franchises. Royalty agreements on producing oil and gas wells stemming from the
Company's ownership of mineral interests generate a substantial portion of the
Company's revenues. These royalties are tied to the ownership of the mineral
interests and this ownership is perpetual, unless sold by the Company. Royalties
are due and payable to the Company whenever oil and/or gas is produced from
wells located on the Company's mineral properties.

                GOVERNMENTAL REGULATION

                Oil and gas production is subject to various taxes, such as
gross production taxes and, in some cases, ad valorem taxes.

                The State of Oklahoma and other states require permits for
drilling operations, drilling bonds and reports concerning operations and impose
other requirements relating to the exploration and production of oil and gas.
Such states also have regulations addressing conservation matters, including
provisions for the unitization or pooling of oil and gas properties, the
establishment of maximum rates of production from oil and gas wells and the
regulation of spacing, plugging and abandonment of such wells. These statutes
and regulations currently limit the rate at which oil and gas can be produced
from certain of the Company's properties, especially in the Dagger Draw field of
New Mexico.


                                      (3)
<PAGE>   6

                Federal tax law allows producers of "tight gas" to utilize an
approximate $.52/MMBTU tax credit for gas produced from approved wells. The
credit is a direct reduction of regular federal income tax. Panhandle began
receiving revenues from "tight gas" wells during fiscal 1992. This credit will
be available for all tight gas sold prior to January 1, 2003, and is expected to
reduce the Company's cash outlay for income taxes.

                ENVIRONMENTAL MATTERS

                As the Company is directly involved in the extraction and use of
natural resources, it is subject to various federal, state and local provisions
regarding environmental and ecological matters. Compliance with these laws may
necessitate significant capital outlays, however, to date the Company's cost of
compliance has been insignificant. The Company is currently aware of one
potential environmental claim against the operator on a property where the
Company owns a working interest of less than 5%. The operator believes the claim
to be without merit. See Note 1. of Notes to Consolidated Financial Statements.
The Company does not feel the existence of these environmental laws will
materially hinder or adversely affect the Company's business operations;
however, there can be no assurances of future events. Since the Company does not
operate any wells in which it owns an interest, actual compliance with
environmental laws is controlled by others, with Panhandle being responsible for
its proportionate share of the costs involved. Panhandle carries liability
insurance and to the extent available at reasonable cost, pollution control
coverage. However, all risks are not insured due to insurance availability
and/or cost thereof.

                EMPLOYEES

                At September 30, 1998, Panhandle employed nine persons on a
full-time basis and has no part-time employees. Three of the employees are
executive officers and one is also a director of the Company.

ITEM 2.         DESCRIPTION OF PROPERTIES

                As of September 30, 1998, Panhandle's principal properties
consisted of perpetual ownership of 179,841 net mineral acres, held in tracts in
Alabama, Arkansas, Colorado, Idaho, Kansas, Illinois, Indiana, Montana,
Nebraska, New Mexico, North Dakota, Oklahoma, Tennessee and Texas. The Company
also held leases on 6,033 net acres of minerals in Louisiana, Oklahoma and
Texas. At September 30, 1998, Panhandle held royalty and/or working interests in
1,462 producing oil or gas wells, 36 successfully completed but not yet
producing wells, and 22 wells in the process of being drilled or completed.


                                      (4)
<PAGE>   7

                Panhandle does not have current abstracts or title opinions on
all mineral properties owned and, therefore, cannot warrant that it has
unencumbered title to all of its properties. In the period from 1927 through
1937, the Company lost title to a number of its then owned mineral acres through
foreclosures and tax sales of the surface acreage overlying its minerals. In
recent years, few challenges have been made against the Company's fee title to
its properties.

                Panhandle pays ad valorem taxes on its minerals owned in
Arkansas, Colorado, Idaho, Indiana, Illinois, Kansas, Tennessee and
Texas.

                ACREAGE

                The following table of mineral interests owned reflects, as of
September 30, 1998, in each respective state, the number of net and gross acres,
net and gross producing acres, net and gross acres leased, and net and gross
acres open (unleased).

                                MINERAL INTERESTS

<TABLE>
<CAPTION>
                           Net      Gross      Net      Gross       Net       Gross
                          Acres     Acres     Acres     Acres      Acres      Acres
        Net      Gross    Prod'g    Prod'g    Leased    Leased     Open       Open
St.    Acres     Acres     (1)       (1)       (2)       (2)        (3)        (3)
---    -----     -----    ------    ------    ------    ------     -----      ------
<S>    <C>       <C>      <C>       <C>       <C>       <C>        <C>        <C>
AL          5       479                                                 5        479
AR      5,890    32,016       64       220        40        80      5,786     31,716
CO      8,176    38,600                                             8,176     38,600
ID         30       880                                                30        880
IL      1,018     4,393                                             1,018      4,393
IN         27       262                                                27        262
KS        620     5,360       60       480                            560      4,880
MT        422     7,960                                               422      7,960
NE        439     5,960                                               439      5,960
ND        292     5,036                           37       320        255      4,716
NM     53,324   153,073    1,150     4,949     2,639     7,137     49,535    140,987
OK     85,280   645,843   16,207    84,884     2,038    23,173     67,035    537,786
TN      1,543     3,087                                             1,543      3,087
TX     22,775   213,021    1,094    34,072       233     3,329     21,448    175,620
      ------- ---------   ------   -------    ------    ------    -------    -------
TOT:  179,841 1,115,970   18,575   124,605     4,987    34,039    156,279    957,326
      ------- ---------   ------   -------    ------    ------    -------    -------
</TABLE>

(1)     "Producing" represents the mineral acres in which Panhandle owns a
        royalty or working interest in a producing well.

(2)     "Leased" represents the mineral acres, owned by Panhandle, that are
        leased to third parties but not producing.

(3)     "Open" represents mineral acres owned by Panhandle that are not leased
        or in production.

                This table reflects net mineral acres leased from others, lease
expiration dates, and net leased acres held by production.

                                           LEASES

<TABLE>
<CAPTION>
                                       Net Acres Leases        
                                           Expiring            Net Acres
                            Net      --------------------       Held By
                 State     Acres     1999    2000     2001    Production
                 -----    -------    ----    ----    -----    ----------
                 <S>      <C>        <C>     <C>     <C>      <C>  
                 LA           271                                   271
                 OK         5,623     891    2,542     420        1,770
                 TX           139      66       20                   53
                            -----     ---    -----     ---        -----
                 TOT:       6,033     957    2,562     420        2,094
                          -------   -----    ------   -------    ------
</TABLE>


                                      (5)
<PAGE>   8

                PROVED RESERVES

                The following table summarizes estimates of the proved reserves
of oil and gas held by Panhandle. All reserves are located within the United
States. Because the Company's nonproducing mineral and leasehold interests
consist of various small interests in numerous tracts located primarily in
Oklahoma, New Mexico and Texas and because the Company is a non-operator and
must rely on third parties to propose and drill wells, it is not feasible to
provide estimates of all proved undeveloped reserves and associated future net
revenues. Prior to fiscal 1995, the Company did not provide estimates of any
proved undeveloped reserves. Since 1995 the Company has provided estimates of
proved undeveloped reserves for certain areas of western Oklahoma where a large
amount of increased density gas drilling has taken place during the prior few
years. In 1996 estimates of certain proved undeveloped reserves in the Dagger
Draw field in southeastern New Mexico were added. Production in this field has
grown rapidly over the last five years and numerous undrilled well locations are
situated on minerals owned by Panhandle. Due to field production allowable rules
in Dagger Draw, only those proved undeveloped reserves which the Company felt
could be drilled, under existing allowable rules, have been included. Should the
allowable rules be amended and/or production volumes change significantly,
additional proved undeveloped reserves may be added in the future. The Company,
in both cases, expects drilling to continue for the next several years, and thus
made the decision to provide proved undeveloped reserve estimates for these
areas. All reserve quantity estimates were prepared by Campbell & Associates,
Inc., an independent petroleum engineering firm. The Company's reserve estimates
were not filed with any other federal agency.

<TABLE>
<CAPTION>
    Proved Developed Reserves      Barrels of Oil      MCF of Gas
                                   --------------      ----------
<S>                                <C>                 <C>      
    September 30, 1995                454,577           7,618,673
    September 30, 1996                641,213           8,200,957
    September 30, 1997                625,370           9,707,242
    September 30, 1998                497,263          10,103,355

    Proved Undeveloped Reserves

    September 30, 1995                 10,339           1,570,440
    September 30, 1996                297,582           1,638,104
    September 30, 1997                278,438           1,559,860
    September 30, 1998                279,824           1,557,965

    Total Proved Reserves

    September 30, 1995                464,916           9,189,113
    September 30, 1996                938,795           9,839,061
    September 30, 1997                903,808          11,267,102
    September 30, 1998                777,087          11,661,320
</TABLE>

                Because the determination of reserves is a function of testing,
evaluating, developing oil and gas reservoirs and establishing a production
decline history, along with product price fluctuations, it would be expected
that estimates will change as future information concerning those reservoirs is
developed and as market conditions change. Estimated reserve quantities and
future net revenues are affected by changes in product prices, and these prices
have varied substantially in recent years. Proved developed 


                                      (6)
<PAGE>   9

reserves are those expected to be recovered through existing well bores under
existing economic and operating conditions. Proved undeveloped reserves are
reserves that may be recovered from undrilled acreage, but are usually limited
to those sites directly offsetting established production units and have
sufficient geological data to indicate a reasonable expectation of commercial
success.

                ESTIMATED FUTURE NET CASH FLOWS

                Set forth below are estimated future net cash flows with respect
to Panhandle's proved reserves (based on the estimated units set forth in the
immediately preceding table) as of year ends, and the present value of such
estimated future net cash flows, computed by applying a ten (10) percent
discount factor as required by the rules and regulations of the Securities and
Exchange Commission. Estimated future net cash flows have been computed by
applying current year-end prices to future production of proved reserves less
estimated future expenditures (based on costs as of year end) to be incurred
with respect to the development and production of such reserves. Such pricing is
based on SEC guidelines. No federal income taxes are included in estimated
costs. However, the amounts are net of production taxes levied by respective
states. Prices used for determining future cash flows from oil and natural gas
for the periods ended September 30, 1998, 1997 and 1996 were as follows: 1998 -
$14.45, $1.63; 1997 - $19.12, $2.48; 1996 - $23.88, $1.84. These future net cash
flows should not be construed as the fair market value of the Company's
reserves. A market value determination would need to include many additional
factors, including anticipated oil and gas price increases or decreases.

Estimated Future Net Cash Flows

<TABLE>
<CAPTION>
                          9-30-98         9-30-97         9-30-96
                        -----------    -----------     -----------
<S>                     <C>            <C>             <C>        
 Proved Developed       $18,256,510    $29,186,367     $25,166,810
 Proved Undeveloped     $ 4,868,946    $ 7,188,163     $ 8,363,380
                        -----------    -----------     -----------
 Total Proved (1)       $23,125,456    $36,374,530     $33,530,190
</TABLE>


10% Discounted Present Value of Estimated Future Net Cash Flows

<TABLE>
<CAPTION>
                          9-30-98         9-30-97         9-30-96
                        -----------    -----------     -----------
<S>                     <C>            <C>             <C>        
  Proved Developed      $12,469,019    $19,890,600     $17,827,160
  Proved Undeveloped    $ 2,929,190    $ 4,430,870     $ 5,328,364
                        -----------    -----------     -----------
  Total Proved (1)      $15,398,209    $24,321,470     $23,155,524
</TABLE>

               (1)  The decrease in value from September 30, 1997 to September
                    30, 1998 is principally attributable to the lower oil and
                    gas prices used in the 1998 reserve report verses the prices
                    used in the 1997 reserve report.


                                      (7)
<PAGE>   10

OIL AND GAS PRODUCTION

                The following table sets forth the Company's net production of
oil and gas for the fiscal periods indicated.

<TABLE>
<CAPTION>
                            Year            Year            Year
                            Ended           Ended           Ended
                           9-30-98         9-30-97         9-30-96
                         ---------       ---------       ---------
<S>                      <C>             <C>             <C>    
Bbls - Oil                 103,989         147,734         145,301
MCF - Gas                1,710,264       1,600,247       1,551,147
</TABLE>

Average Sales Prices and Production Costs

                The following table sets forth unit price and cost data for the
fiscal periods indicated.

<TABLE>
<CAPTION>
                            Year            Year            Year
                            Ended           Ended           Ended
  Average Sales Price      9-30-98         9-30-97         9-30-96
                         ---------       ---------       ---------
<S>                      <C>             <C>             <C>    
  Per Bbl. Oil           $   15.16       $   21.21       $   19.93
  Per MCF Gas            $    2.20       $    2.39       $    1.95

  Average Production (Lifting Cost)

  Per Equivalent
  Bbl. Oil (1)(2)        $    2.47       $    2.54       $    2.46
</TABLE>

  (1)  Gas production is converted to barrel equivalents at the rate of 6 MCF
       per barrel, representing the estimated relative energy content of
       natural gas and oil.

  (2)  Includes well operating costs and production taxes.

                Average production costs are influenced by the fact that the
Company bears no costs of production on many of its well interests, as a large
part of the Company's producing well interests are royalty interests, which bear
no share of the operating costs.

                GROSS AND NET PRODUCTIVE WELLS AND DEVELOPED ACRES

                The following table sets forth Panhandle's gross and net
productive oil and gas wells as of September 30, 1998. Panhandle owns fractional
royalty interests or fractional working interests in these wells. The Company
does not operate any wells.

<TABLE>
<CAPTION>
                           Gross Wells          Net Wells
                           -----------          ---------
<S>                        <C>                  <C>      
            Oil                426              13.990492
            Gas              1,036              18.564742
                             -----              ---------
            TOTAL            1,462              32.555234
</TABLE>

                Information on multiple completions is not available from
Panhandle's records, but the number of such is insignificant.


                                      (8)
<PAGE>   11

                As of September 30, 1998, Panhandle owned 124,605 gross
developed mineral acres and 18,575 net developed mineral acres. Panhandle has
also leased from others 44,103 gross developed acres which contain 2,094 net
developed acres.

                UNDEVELOPED ACREAGE

                As of September 30, 1998, Panhandle owned 991,365 gross and
161,266 net undeveloped mineral acres, and leases on 30,025 gross and 3,939 net
acres.

                DRILLING ACTIVITY

                The following net productive development and exploratory wells
and net dry development and exploratory wells, in which the Company had a
fractional royalty or working interest, were drilled and completed during the
fiscal years indicated. Also shown are the net wells purchased during these
periods.

<TABLE>
<CAPTION>
                              Net Productive        Net Dry
Development Wells                 Wells              Wells
                              --------------        -------
<S>                           <C>                   <C>
     Fiscal year ending
       September 30, 1996        1.614002           .485562

     Fiscal year ending
       September 30, 1997        2.630851           .659734

     Fiscal year ending
       September 30, 1998        1.548498           .608732

Exploratory Wells

     Fiscal year ending
       September 30, 1996         .456455           .231341

     Fiscal year ending
       September 30, 1997         .627670           .477731

     Fiscal year ending
       September 30, 1998         .953696           .566764

Purchased Wells

     Fiscal year ending
       September 30, 1996        1.542173                 0

     Fiscal year ending
       September 30, 1997         .798765                 0

     Fiscal year ending
       September 30, 1998         .174667                 0
</TABLE>


                                      (9)
<PAGE>   12

                PRESENT ACTIVITIES

                The following table sets forth the gross and net oil and gas
wells drilling or testing as of September 30, 1998, in which Panhandle owns a
royalty or working interest.

<TABLE>
<CAPTION>
                           Gross Wells          Net Wells
                           -----------          ---------
<S>                        <C>                  <C>    
            Oil                  3                .252061
            Gas                 19                .615659
</TABLE>

                The Company has very small interests in three waterflood
operations in Oklahoma and Texas which have negligible revenues and expenses to
the Company. No additional purchases or start-ups of waterflood, pressure
maintenance or other related operations are currently planned.

ITEM 3.         LEGAL PROCEEDINGS

                There were no material legal proceedings involving Panhandle or
its subsidiary, PHC, Inc., as of the date of this report.

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

                No matters were submitted to a vote of Panhandle's security
holders during the fourth quarter of the fiscal year ended September 30, 1998.

                                     PART II

ITEM 5.         MARKET FOR COMMON EQUITY AND RELATED STOCKHOLDER MATTERS

                The Company's common stock is listed on the NASDAQ Small-Cap
Market (symbol PANRA). The following table sets forth the high and low trade
prices of the Company's common stock during the periods indicated:

<TABLE>
<CAPTION>
                  Quarter Ended                 HIGH           LOW
                  -------------                 ----           ---
<S>               <C>                          <C>            <C>  
                  December 31, 1996            37-3/4         20-3/4
                  March 31, 1997               33             24
                  June 30, 1997                36             24
                  September 30, 1997           33             25
                  December 31, 1997            42-1/2         28
                  March 31, 1998               33-1/2         26
                  June 30, 1998                34-1/16        28
                  September 30, 1998           29-1/8         25-3/4
</TABLE>

                As of November 30, 1998, the approximate number of holders of
shares of Panhandle stock were:

<TABLE>
<CAPTION>
                   Title of Class                             Number of Holders
                   --------------                             -----------------
<S>                                                           <C>  
                   Class A Common (Voting)...................      2,300
</TABLE>




                                      (10)
<PAGE>   13

                During the past two years, cash dividends have been paid as
follows on the class A common stock:

<TABLE>
<CAPTION>
                         DATE                         RATE PER SHARE
                    -------------                     --------------
<S>                                                   <C>
                    December 1996                         $ .20
                    March 1997                            $ .20
                    June 1997                             $ .20
                    September 1997                        $ .20
                    December 1997                         $ .20
                    March 1998                            $ .30
                    June 1998                             $ .20
                    September 1998                        $ .20
</TABLE>

                The Company's line of credit loan agreement contains a provision
limiting the paying or declaring of a cash dividend to fifty percent of cash
flow, as defined, of the preceding twelve-month period. See Note 3 to the
consolidated financial statements contained herein at "Item 7 - Financial
Statements", for a further discussion of the loan agreement.

ITEM 6.         MANAGEMENT'S DISCUSSION AND
                ANALYSIS OR PLAN OF OPERATIONS

                LIQUIDITY AND CAPITAL RESOURCES

                At September 30, 1998, the Company had positive working capital
of $452,270, a decrease of $501,258, compared to year end September 30, 1997.
Cash flow from operating activities also decreased to $3,458,521, as compared to
$4,675,180, for fiscal 1997. These decreases were a result of a decline in oil
and gas sales revenues during fiscal 1998. The revenue decreases are discussed
in detail in "Results of Operations."

                Capital expenditures on oil and gas activities in fiscal 1998
amounted to $3,395,945, an increase of $496,529, over the 1997 amount. Leases,
drilling and equipping wells accounted for $2,656,781 while $739,164 was spent
acquiring new mineral properties. This increased spending on oil and gas
property development is a continuation of the Company's business strategy which
is to actively pursue the development of the Company's oil and gas properties by
participating in additional drilling of wells on these properties. The Company
has historically funded the majority of its capital expenditures and working
capital requirements with cash flow from operations. The bank line of credit was
utilized in fiscal 1996 to make a large mineral property purchase, with all
borrowings repaid in fiscal 1997. As of September 30, 1998, the Company had no
debt outstanding.

                The Company expects to continue its business strategy of
aggressive drilling participation through fiscal 1999, and for several
additional years. At September 30, 1998, the Company had remaining projected
costs of $1,288,247, for its share of drilling and equipment costs on working
interest wells which have been proposed or were in the process of being drilled
or completed. Management currently expects to spend a total of approximately
$2,500,000, for exploration and development well costs in fiscal 1999. The above
capital costs, overhead expenses and dividend payments are to be funded by cash
flow and from borrowings under the Company's bank line of credit.


                                      (11)
<PAGE>   14

                The current low oil sales prices and resulting lower oil
production, experienced in fiscal 1998 is expected to continue into fiscal 1999,
see "Results of Operations." This means the Company's expected cash flow in
fiscal 1999 may be less than the amount needed to fully fund all drilling
obligations, overhead and dividend payments. Thus, the bank line of credit will
be utilized, on an as needed basis, to allow the Company to continue its
aggressive approach of developing its oil and gas properties. The line of credit
and expected cash flow are more than sufficient to meet all expected capital
obligations. The above-mentioned capital expenditure amounts may vary due to
many factors, including drilling results, oil and gas prices, industry
conditions and acquisition opportunities, among others. A significant
acquisition of producing properties could increase capital expenditures greatly
and would be financed by additional debt or possibly debt and equity.

RESULTS OF OPERATIONS

                Revenues decreased $1,576,296 or 22% in fiscal 1998 as compared
to fiscal 1997. The reduction in revenues was attributable to a $1,621,357
reduction in oil and gas sales revenues offset somewhat by small increases in
other revenues. The oil and gas sales revenue decease was a result of decreased
sales prices for both oil and natural gas, decreased oil sales volumes, slightly
offset by increased natural gas sales volumes. The chart below summarizes the
Company's production and average sales prices for oil and natural gas in fiscal
1998 and 1997.

                                   PRODUCTION

<TABLE>
<CAPTION>
                              OIL                         GAS
                              -----------------------     -----------------------
                              Total         Average       Total         Average
                              BBLS          Price/BBL     MCF           Price/MCF
                              -------       ---------     ---------     ---------
<S>                           <C>           <C>           <C>           <C>   
  Year Ended 9/30/98          103,989       $ 15.16       1,710,264     $ 2.20
  Year Ended 9/30/97          147,734       $ 21.21       1,600,247     $ 2.39
</TABLE>

                As can readily be seen from the above chart, the decrease in oil
sales volumes along with the decreased average oil sales price were the primary
reasons for the oil and gas revenue decrease. Oil sales prices decreased
steadily through fiscal 1998 and the posted price per barrel has decreased to
$8.50 in early December 1998. An oversupply of crude oil worldwide and a
declining demand for oil in many developing countries apparently caused the
price drop. The average natural gas sales prices in 1998 was 8% lower than
fiscal 1997. This price reduction was basically offset by a 6.9% increase in
natural gas production volume.

                In addition to the above, oil sales volumes were adversely
affected by a production allowable limitations in the Dagger Draw Field of New
Mexico (the Company's major oil producing field) during the first half of the
year. In May 1998, the majority operator of the same field elected to shut in
those wells during the last half of the year due to low crude oil prices. In
October 1998, certain of these wells were put back on production. Management is
uncertain as to when full production will resume.


                                      (12)
<PAGE>   15

                Shut-in oil wells along with current low oil sales prices could
reduce the Company's oil and gas sales revenues well into fiscal 1999. However,
several new gas wells should come on line in fiscal 1999, thus, increasing gas
sales volumes, and if gas sales prices remain steady, should reduce the impact
of lost oil sales revenues, in fiscal 1999.

                COSTS AND EXPENSES decreased slightly (1%), during fiscal 1998
as compared to fiscal 1997. Lease operating expenses and production taxes
decreased $92,107, principally due to decreased severance taxes paid on reduced
oil and gas sales. Severance taxes are a percentage of oil and gas sales
revenues.

                Depreciation, depletion, amortization and impairment costs
(DD&A) decreased slightly, $36,790, in fiscal 1998 as compared to fiscal 1997.
The Company's units of production DD&A was decreased by lower production volumes
in fiscal 1998, however, decreases in well reserves (caused by lower prices for
oil and gas in the 1998 reserve report compared to the 1997 reserve report)
caused many well DD&A percentages in 1998 to be higher than those in 1997. In
addition, the Company recognized a SFAS No. 121 impairment provision (see Note
1, Summary of Significant Accounting Policies, to the Financial Statements
contained herein at Item 7.) of $149,851 in fiscal 1998 as compared to an
impairment provision of $115,734 on 1997.

                Exploration costs increased 4.6% in fiscal 1998 as compared to
fiscal 1997. These costs are dry hole costs and seismic costs and vary from year
to year. The Company utilizes the successful effort's method of accounting for
oil and gas operations, thus, dry holes are a result of drilling unsuccessful
exploratory wells. There is no way to accurately estimate exploration costs from
year to year. The Company will continue exploratory well participations, thus,
future exploration costs can be expected.

                General and administrative costs increased $93,060 or 9.2% in
fiscal 1998. The increase was due to the addition of one employee during the
year; increased salaries for existing personnel and increased office space
leased during fiscal 1998. Interest expense was down due to the line of credit
being paid off in fiscal 1997. The interest paid in fiscal 1998 was a commitment
fee charged on the line of credit.

                The provision for income taxes is lower in fiscal 1998 due to
lower pretax income in fiscal 1998 and the continuing utilization of excess
percentage depletion and "tight gas sands" production tax credits.

                As discussed above, the decline in net income is attributable to
decreased oil and gas sales revenues, caused by lower oil production and lower
average oil and gas sales prices in fiscal 1998 as compared to fiscal 1997.
Management has no control over the market prices of oil or gas and currently
expects the depressed oil price to continue further into fiscal 1999. Fiscal
1999 earnings will be impacted by continued low oil prices. Continued
investments in exploratory drilling also carry certain risks, principally dry
hole costs as discussed above, the results of which can adversely affect
earnings.


                                      (13)
<PAGE>   16

YEAR 2000 ISSUES

                Much of the computer software in use today may not be able to
accurately process data beyond the year 1999. The majority of computer systems
process data using two digits for the year of transaction, rather than the full
four digits. This may cause many systems to be unable to accurately process year
2000 transactions.

                The Company has completed its assessment of both its computer
("IT systems") and operational equipment ("non-IT systems") as of June 30, 1998.
The Company has replaced its computer system hardware with new hardware which
has operating systems which are represented as being year 2000 compliant. The
Company's software supplier is in the process of revising software licenced by
the Company which is represented to be year 2000 compliant. The system software
reprogramming is expected to be complete in early 1999 with installation and
testing by the Company by June 1999. The Company has no non-IT systems which are
expected to be impacted in any material manner by Year 2000.

                The cost of replacement of the Company's IT systems noted above
was less than $25,000. Cost of the year 2000 compliant system software will be
included in the Company's standard annual license fee. Other costs to assess the
Year 2000 matter or become compliant therewith are not expected to be
significant.

                Should any of the operators of the properties in which the
Company has an interest, purchasers who buy oil and gas from the Company's
properties or financial institutions ("External Agents") used by the Company not
properly address the Year 2000 matter, there could be some delay in the Company
receiving payment for the sale of oil and gas. Should this occur, the Company
may be required to borrow additional amounts on its available line of credit,
thus incurring additional interest expense over that otherwise anticipated.
However, the Company does not expect the Year 2000 will have a material impact
on its financial position of results of operations. The Company has no systems
which directly interface with External Agents.

ITEM 7.         FINANCIAL STATEMENTS

<TABLE>
<S>                                                                        <C>
                Report of Independent Auditors............................    15

                Consolidated Balance Sheets
                         As of September 30, 1998 and 1997 ...............    16

                Consolidated Statements of Income For The
                         Years Ended September 30, 1998 and 1997 .........    17

                Consolidated Statements of Stockholders' Equity For
                         The Years Ended September 30, 1998 and 1997 .....    18

                Consolidated Statements of Cash Flows For
                         The Years Ended September 30, 1998 and 1997 .....    19

                Notes To Consolidated Financial Statements ............... 20-31
</TABLE>


                                      (14)
<PAGE>   17
                         Report of Independent Auditors

Board of Directors and Stockholders
Panhandle Royalty Company

We have audited the accompanying consolidated balance sheets of Panhandle
Royalty Company as of September 30, 1998 and 1997, and the related consolidated
statements of income, stockholders' equity and cash flows for the years then
ended. These financial statements are the responsibility of the Company's
management. Our responsibility is to express an opinion on these financial
statements based on our audits.

We conducted our audits in accordance with generally accepted auditing
standards. Those standards require that we plan and perform the audit to obtain
reasonable assurance about whether the financial statements are free of material
misstatement. An audit includes examining, on a test basis, evidence supporting
the amounts and disclosures in the financial statements. An audit also includes
assessing the accounting principles used and significant estimates made by
management, as well as evaluating the overall financial statement presentation.
We believe that our audits provide a reasonable basis for our opinion.

In our opinion, the financial statements referred to above present fairly, in
all material respects, the consolidated financial position of Panhandle Royalty
Company at September 30, 1998 and 1997, and the consolidated results of its
operations and its cash flows for the years then ended in conformity with
generally accepted accounting principles.


                                       ERNST & YOUNG LLP

Oklahoma City, Oklahoma
December 2, 1998


                                      (15)
<PAGE>   18

                            Panhandle Royalty Company

                           Consolidated Balance Sheets

<TABLE>
<CAPTION>
                                                                         SEPTEMBER 30,
                                                                     1998            1997
                                                                 -----------     -----------
<S>                                                              <C>             <C>        
ASSETS
Current assets:
   Cash and cash equivalents                                     $   320,210     $   872,797
   Oil and gas sales and other receivables                           716,648         893,779
   Income taxes receivable                                           152,090              --
   Prepaid expenses                                                   27,391           4,929
                                                                 -----------     -----------
Total current assets                                               1,216,339       1,771,505

Property and equipment, at cost, based on successful efforts
  accounting:
     Producing oil and gas properties                             22,360,790      20,063,953
     Nonproducing oil and gas properties                           5,693,399       5,068,467
     Furniture and fixtures                                          241,567         213,474
                                                                 -----------     -----------
                                                                  28,295,756      25,345,894
     Less accumulated depreciation, depletion and amortization    16,600,499      15,127,925
                                                                 -----------     -----------
Net properties and equipment                                      11,695,257      10,217,969

Other assets                                                         107,716         107,716
                                                                 -----------     -----------
                                                                 $13,019,312     $12,097,190
                                                                 ===========     ===========

LIABILITIES AND STOCKHOLDERS' EQUITY 

Current liabilities:
   Accounts payable and accrued liabilities                      $   576,033     $   351,405
   Gas imbalance liability                                            44,380          44,380
   Dividends payable                                                  31,656          29,856
   Income taxes payable                                                   --         112,336
   Deferred income taxes                                             112,000         280,000
                                                                 -----------     -----------
Total current liabilities                                            764,069         817,977

Deferred income taxes                                              1,451,000       1,247,000

Stockholders' equity:
   Class A voting common stock (one vote per stockholder), 
     $.10 par value; 1,000,000 shares authorized,
     682,534 issued and outstanding (679,820 in 1997)                 68,254          67,982
   Capital in excess of par value                                    515,823         445,306
   Retained earnings                                              10,220,166       9,518,925
                                                                 -----------     -----------
Total stockholders' equity                                        10,804,243      10,032,213
                                                                 -----------     -----------
                                                                 $13,019,312     $12,097,190
                                                                 ===========     ===========
</TABLE>

See accompanying notes.


                                      (16)
<PAGE>   19

                            Panhandle Royalty Company

                        Consolidated Statements of Income


<TABLE>
<CAPTION>
                                                             YEAR ENDED SEPTEMBER 30,
                                                               1998           1997
                                                            ----------     ----------
<S>                                                         <C>            <C>       
Revenues:
   Oil and gas sales                                        $5,337,832     $6,959,189
   Lease bonuses and rentals                                    44,269         14,469
   Interest                                                     45,929         17,372
   Other                                                        12,152         25,448
                                                            ----------     ----------
                                                             5,440,182      7,016,478

Costs and expenses:
   Lease operating expenses and production taxes               961,929      1,054,036
   Exploration costs                                           481,244        459,861
   Depreciation, depletion, amortization and impairment      1,437,413      1,474,203
   General and administrative                                1,099,636      1,006,576
   Interest expense                                              3,125         29,960
                                                            ----------     ----------
                                                             3,983,347      4,024,636
                                                            ----------     ----------
Income before provision for income taxes                     1,456,835      2,991,842

Provision for income taxes                                     142,000        693,000
                                                            ----------     ----------
Net income                                                  $1,314,835     $2,298,842
                                                            ==========     ==========

Basic earnings per share                                    $     1.93     $     3.39
                                                            ==========     ==========

Diluted earnings per share                                  $     1.92     $     3.38
                                                            ==========     ==========
</TABLE>


See accompanying notes.


                                      (17)
<PAGE>   20

                            Panhandle Royalty Company

                 Consolidated Statements of Stockholders' Equity


<TABLE>
<CAPTION>
                                                   COMMON STOCK              CAPITAL IN
                                             -------------------------        EXCESS OF         RETAINED
                                              SHARES         AMOUNT           PAR VALUE         EARNINGS           TOTAL
                                             -------      ------------      ------------      ------------      ------------
<S>                                          <C>          <C>               <C>               <C>               <C>         
Balances at September 30, 1996               677,846      $     67,785      $    383,790      $  7,763,391      $  8,214,966

Purchase and cancellation of common
   shares                                       (446)              (45)          (10,237)               --           (10,282)
Issuance of common shares to ESOP              2,420               242            71,753                --            71,995
Dividends declared ($.80 per share)               --                --                --          (543,308)         (543,308)
Net income                                        --                --                --         2,298,842         2,298,842
                                             -------      ------------      ------------      ------------      ------------
Balances at September 30, 1997               679,820            67,982           445,306         9,518,925        10,032,213

Purchase and cancellation of common
   shares                                       (111)              (11)           (3,358)               --            (3,369)
Issuance of common shares to ESOP              2,825               283            73,875                --            74,158
Dividends declared ($.90 per share)               --                --                --          (613,594)         (613,594)
Net income                                        --                --                --         1,314,835         1,314,835
                                             -------      ------------      ------------      ------------      ------------

Balances at September 30, 1998               682,534      $     68,254      $    515,823      $ 10,220,166      $ 10,804,243
                                             =======      ============      ============      ============      ============
</TABLE>


See accompanying notes.


                                      (18)
<PAGE>   21

                            Panhandle Royalty Company

                      Consolidated Statements of Cash Flows

<TABLE>
<CAPTION>
                                                                       YEAR ENDED SEPTEMBER 30,
                                                                        1998             1997
                                                                    -----------      -----------
<S>                                                                 <C>              <C>        
CASH FLOWS FROM OPERATING ACTIVITIES
Net income                                                          $ 1,314,835      $ 2,298,842
Adjustments to reconcile net income to net cash provided by
   operating activities:
     Depreciation, depletion, amortization, and impairment            1,437,413        1,474,203
     Deferred income taxes                                               36,000          369,000
     Exploration costs, exclusive of seismic                            481,244          405,072
     Common stock issued to Employee Stock Ownership Plan                74,158           71,995
     Cash provided (used) by changes in assets and liabilities:
       Oil and gas sales and other receivables                          177,131          (76,521)
       Income taxes receivable                                         (152,090)              --
       Prepaid expenses                                                 (22,462)            (409)
       Accounts payable and accrued liabilities                         224,628          185,505
       Income taxes payable                                            (112,336)         (52,507)
                                                                    -----------      -----------
Total adjustments                                                     2,143,686        2,376,338
                                                                    -----------      -----------
Net cash provided by operating activities                             3,458,521        4,675,180

CASH FLOWS FROM INVESTING ACTIVITIES OF PROPERTY AND
  EQUIPMENT
Capital expenditures, including dry hole costs                       (3,395,945)      (2,899,416)
                                                                    -----------      -----------
Net cash used in investing activities                                (3,395,945)      (2,899,416)

CASH FLOWS FROM FINANCING ACTIVITIES
Principal payments on line of credit                                         --         (750,000)
Purchase and cancellation of common shares                               (3,369)         (10,282)
Payments of dividends                                                  (611,794)        (542,108)
                                                                    -----------      -----------
Net cash used in financing activities                                  (615,163)      (1,302,390)
                                                                    -----------      -----------
Increase (decrease) in cash and cash equivalents                       (552,587)         473,374

Cash and cash equivalents at beginning of year                          872,797          399,423
                                                                    -----------      -----------
Cash and cash equivalents at end of year                            $   320,210      $   872,797
                                                                    ===========      ===========

SUPPLEMENTAL DISCLOSURES OF CASH FLOW INFORMATION
Interest paid                                                       $     3,125      $    29,960
Income taxes paid                                                       370,426          376,507
</TABLE>


See accompanying notes.


                                      (19)
<PAGE>   22

                            Panhandle Royalty Company

                   Notes to Consolidated Financial Statements

                           September 30, 1998 and 1997


1. SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

PRINCIPLES OF CONSOLIDATION

The consolidated financial statements include the accounts of Panhandle Royalty
Company and its wholly-owned subsidiary, P.H.C., Inc. All material intercompany
transactions have been eliminated in the accompanying consolidated financial
statements.

CASH EQUIVALENTS

All highly liquid short-term investments with original maturities of three
months or less at the date of purchase by the Company are considered to be cash
equivalents. Cash equivalents at September 30, 1997 included certificates of
deposit of $200,000 (none at September 30, 1998) which are valued at cost
(approximates market) and had original maturities of 90 days or less.

OIL AND GAS SALES RECEIVABLE

The Company sells oil and natural gas to various customers. Substantially all of
the Company's accounts receivable are due from purchasers of oil and natural
gas. Oil and natural gas sales are generally unsecured. The Company has not
experienced significant credit losses in prior years and is not aware of any
significant uncollectible accounts at September 30, 1998.

OIL AND GAS PRODUCING ACTIVITIES

The Company follows the successful efforts method of accounting for oil and gas
producing activities. Intangible drilling and other costs of successful wells
and development dry holes are capitalized and amortized. The costs of
exploratory wells are initially capitalized, but charged against income if and
when the well is determined to be nonproductive. Oil and gas mineral and
leasehold costs are capitalized when incurred. Impairment of unproved properties
is generally assessed on a property-by-property basis.

DEPRECIATION, DEPLETION, AMORTIZATION AND IMPAIRMENT

Depreciation, depletion and amortization of the costs of producing oil and gas
properties are computed using the units of production method primarily on a
separate-property basis using proved reserves as estimated annually by an
independent petroleum engineer. Depreciation of furniture and fixtures is
computed using the straight-line method over estimated productive lives of five
to eight years.


                                      (20)
<PAGE>   23
                            Panhandle Royalty Company

             Notes to Consolidated Financial Statements (continued)


1. SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES (CONTINUED)

The Company has significant royalty interests in wells for which the Company
does not share in the costs associated with the wells. Estimated costs of future
dismantlement, restoration and abandonment of wells in which the Company owns a
working interest are not expected to differ significantly from the estimated
salvage value of equipment from such wells and, accordingly, no accrual of such
costs is included in the accompanying consolidated financial statements.

Nonproducing oil and gas properties include nonproducing minerals, which have a
net book value of $4,207,114 at September 30, 1998, consisting of perpetual
ownership of mineral interests in several states, including Oklahoma, Texas and
New Mexico. These costs are being amortized over a thirty-three year period
using the straight-line method. An ultimate determination of whether these
properties contain recoverable reserves in economical quantities can generally
be made within this time frame. Impairment of nonproducing oil and gas
properties is recognized based on experience and management judgment.

In accordance with the provisions of Financial Accounting Standards (SFAS) No.
121, "Accounting for the Impairment of Long-Lived Assets and for Long-Lived
Assets to Be Disposed Of," the Company recognizes impairment losses for
long-lived assets when indicators of impairment are present and the undiscounted
cash flows are not sufficient to recover the assets' carrying amount. The
impairment loss is measured by comparing the fair value of the asset to its
carrying amount. Fair values are based on discounted future cash flows or
information provided by sales and purchases of similar assets. The Company's oil
and gas properties were reviewed for indicators of impairment on a
field-by-field basis, resulting in the recognition of impairment provisions of
$149,851 and $115,734, respectively, for 1998 and 1997, which are included in
depreciation, depletion, amortization and impairment expense.

ENVIRONMENTAL COSTS

Environmental liabilities, which historically have not been material, are
recognized when it is probable that a loss has been incurred and the amount of
that loss is reasonably estimable. Environmental liabilities, when accrued, are
based upon estimates of expected future costs without discounting. At September
30, 1998, there were no such costs accrued.

In December 1998, the Company was notified by an operator of a claim on a
producing property in which the Company owns a 4.7% working interest. The
operator has indicated the claim to be without merit. While the Company believes
this claim will not have a material impact on the Company's financial position
or results of operations, the ultimate outcome cannot presently be determined.


                                      (21)
<PAGE>   24
                            Panhandle Royalty Company

             Notes to Consolidated Financial Statements (continued)


1. SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES (CONTINUED)


USE OF ESTIMATES

The preparation of financial statements in conformity with generally accepted
accounting principles requires management to make estimates and assumptions that
affect the amounts reported in the consolidated financial statements and
accompanying notes. Actual results could differ from those estimates.

PRODUCTION IMBALANCES

During the course of normal production operations, joint interest owners will,
from time to time, take more or less than their ownership share of natural gas
volumes from jointly-owned wells. These volumetric imbalances are monitored over
the life of the well to achieve balancing, or to minimize imbalances, by the
time reserves are depleted, with final cash settlements made under a variety of
arrangements at that time. The Company follows the sales method of accounting
for imbalances. A liability is recorded only if takes of natural gas volumes
from jointly-owned wells exceed the Company's interest in the well's remaining
estimated natural gas reserves. At September 30, 1998 and 1997, the Company's
net liability for production imbalances of approximately 28,000 mcf of natural
gas was $44,380.

EARNINGS PER SHARE OF COMMON STOCK

In February 1997, the Financial Accounting Standards Board issued Statement No.
128, "Earnings Per Share." Statement 128 replaced the calculation of primary and
fully diluted earnings per share with basic and diluted earnings per share.
Unlike primary earnings per share, basic earnings per share excludes any
dilutive effects of options, warrants and convertible securities. Diluted
earnings per share is very similar to the previously reported fully diluted
earnings per share. All earnings per share amounts for all periods have been
presented and, where appropriate, restated to conform to the Statement 128
requirements.

FAIR VALUES OF FINANCIAL INSTRUMENTS

The following information is provided regarding the estimated fair value of the
Company's financial instruments at September 30, 1998 and 1997:

         Cash and cash equivalents, receivables, prepaid expenses, accounts
         payable and accrued liabilities are each estimated to have a fair value
         approximating the carrying amount due to the short maturity of those
         instruments.


                                      (22)
<PAGE>   25

                            Panhandle Royalty Company

             Notes to Consolidated Financial Statements (continued)


2. INCOME TAXES

The Company's provision (benefit) for income taxes is detailed as follows:

<TABLE>
<CAPTION>
                                              1998                1997
                                           ---------            --------
<S>                                        <C>                  <C>     
                  Current:
                     Federal               $  91,000            $279,000
                     State                    15,000              45,000
                                           ---------            --------
                                             106,000             324,000

                  Deferred:
                     Federal                  46,000             316,000
                     State                   (10,000)             53,000
                                           ---------            --------
                                              36,000             369,000
                                           ---------            --------
                                            $142,000            $693,000
                                            ========            ========
</TABLE>

The difference between the provision for income taxes and the amount which would
result from the application of the federal statutory rate to income before
provision for income taxes is analyzed below:

<TABLE>
<CAPTION>
                                                    1998             1997
                                                  --------        ----------
<S>                                               <C>             <C>       
Provision for income taxes at statutory rate      $509,892        $1,017,226
Percentage depletion                              (298,167)         (316,586)
Tight-sands gas credits                            (63,838)          (73,822)
State income taxes, net of federal benefit           2,948            64,680
Other                                               (8,835)            1,502
                                                  --------        ----------
                                                  $142,000        $  693,000
                                                  ========        ==========
</TABLE>


                                      (23)
<PAGE>   26
                            Panhandle Royalty Company

             Notes to Consolidated Financial Statements (continued)


2. INCOME TAXES (CONTINUED)

Deferred tax assets and liabilities, resulting from differences between the
financial statement carrying amounts and the tax bases of assets and
liabilities, consist of the following:

<TABLE>
<CAPTION>
                                                                1998          1997
                                                             ----------    ----------
<S>                                                          <C>           <C>       
Deferred tax liabilities:
   Capitalized costs and related depreciation, depletion,
     amortization and impairment                             $1,509,000    $1,351,000
   Cash basis of accounting for income tax purposes             112,000       280,000
                                                             ----------    ----------
                                                              1,621,000     1,631,000

Deferred tax assets:
   Percentage depletion carryforward                             58,000             -
   Alternative minimum tax credit carryforwards                       -       104,000
                                                             ----------    ----------
Net deferred tax liabilities                                 $1,563,000    $1,527,000
                                                             ==========    ==========
</TABLE>

3. LONG-TERM DEBT

The Company has a revolving line of credit agreement with a bank, which extends
through January 3, 2001, for borrowings, which bear interest at the bank's base
rate plus .2% (8.70% at September 30, 1998), of up to $2,500,000. Any
outstanding borrowings are unsecured but subject to a negative pledge on all of
the Company's oil and gas properties and are payable in full, with accrued and
unpaid interest, January 3, 2001. The Company is required to pay an annual fee
of .125% for the unused portion of the line of credit. There was no balance
outstanding at September 30, 1998 and 1997.

The agreement contains various restrictions which, among other things, require
the Company to maintain, at the end of each quarter, positive net income for the
preceding twelve-month period. Additionally, the Company is restricted from
incurring certain indebtedness, selling oil and gas properties for which the
proceeds received exceed $100,000, acquiring treasury stock in any one year in
excess of $150,000 and paying or declaring cash dividends exceeding fifty
percent of the cash flow from operations, as defined, of the preceding
twelve-month period.

4. DIVIDENDS PAYABLE

Dividends payable represent accrued dividends which are due and payable, but
have not been paid for various reasons, including questions concerning estates
of deceased stockholders, unlocatable shareholders or questions of ownership of
the underlying shares.


                                      (24)
<PAGE>   27
                            Panhandle Royalty Company

             Notes to Consolidated Financial Statements (continued)


5. EARNINGS PER SHARE

The following table sets forth the computation of basic and diluted earnings per
share. The Company's diluted earnings per share calculation takes into account
certain shares that may be issued under the Non-Employee Directors' Deferred
Compensation Plan (Note 7).

<TABLE>
<CAPTION>
                                                              YEAR ENDED SEPTEMBER 30,
                                                                1998           1997
                                                             ----------     ----------
<S>                                                          <C>            <C>       
Numerator for primary and diluted earnings per share:
   Net income                                                $1,314,835     $2,298,842
                                                             ==========     ==========

Denominator:
   For basic earnings per share--weighted average shares        679,764        677,627
   Effect of potential diluted shares:
     Directors' deferred compensation shares                      4,358          2,970
                                                             ----------     ----------
Denominator for diluted earnings per share--adjusted
   weighted average shares and potential shares                 684,122        680,597
                                                             ==========     ==========

Basic earnings per share                                     $     1.93     $     3.39
                                                             ==========     ==========

Diluted earnings per share                                   $     1.92     $     3.38
                                                             ==========     ==========
</TABLE>

6. EMPLOYEE STOCK OWNERSHIP PLAN

The Company has an employee stock ownership plan that covers substantially all
employees and is established to provide such employees with a retirement
benefit. These benefits become fully vested after three years of employment.
Contributions to the plan are at the discretion of the Board of Directors and
can be made in cash (none in 1998 or 1997) or the Company's common stock. For
contributions of common stock, the Company records as expense, the fair market
value of the stock at the time of contribution. The 30,934 shares of the
Company's common stock held by the plan as of September 30, 1998, are allocated
to individual participant accounts, are included in the weighted average shares
outstanding for purposes of earnings per share computations and receive
dividends. Contributions to the plan consisted of:

<TABLE>
<CAPTION>
                  YEAR                      SHARES           AMOUNT
                  ----                      ------          -------
<S>                                         <C>             <C>
                  1998                       2,825          $74,158
                  1997                       2,420          $71,995
</TABLE>


                                      (25)
<PAGE>   28

                            Panhandle Royalty Company

             Notes to Consolidated Financial Statements (continued)


7. DEFERRED COMPENSATION PLAN FOR DIRECTORS

Effective November 1, 1994, the Company formed the Panhandle Royalty Company
Deferred Compensation Plan for Non-Employee Directors (the "Plan"). The Plan
provides that each eligible director can individually elect to receive shares of
Company stock rather than cash for board meeting fees and board committee
meeting fees. These shares are unissued and vest at the date of grant. The
shares are credited to each director's deferred fee account at the fair market
value of the stock at the date of grant and are adjusted for changes in market
value subsequent thereto. Upon retirement, termination or death of the director,
or upon change in control of the Company, the shares accrued under the Plan will
be either issued to the director or may be converted to cash, at the director's
discretion, for the fair market value of the shares on the conversion date as
defined by the Plan. As of September 30, 1998, 4,358 shares (2,968 shares at
September 30, 1997) are included in the Plan. The Company has accrued $123,655
at September 30, 1998 ($86,455 at September 30, 1997) in connection with the
Plan which is included in accrued liabilities in the accompanying consolidated
balance sheet.

8. INFORMATION ON OIL AND GAS PRODUCING ACTIVITIES

All oil and gas producing activities of the Company are conducted within the
United States (principally Oklahoma and New Mexico) and represent substantially
all of the business activities of the Company.

AGGREGATE CAPITALIZED COSTS

The aggregate amount of capitalized costs of oil and gas properties and related
accumulated depreciation, depletion and amortization is as follows:

<TABLE>
<CAPTION>
                                                                  SEPTEMBER 30,
                                                             1998              1997
                                                         ------------      ------------
<S>                                                      <C>               <C>         
Producing properties                                     $ 22,360,790      $ 20,063,953
Nonproducing properties                                     5,693,399         5,068,467
                                                         ------------      ------------
                                                           28,054,189        25,132,420
Accumulated depreciation, depletion and amortization      (16,416,872)      (14,960,593)
                                                         ------------      ------------
Net capitalized costs                                    $ 11,637,317      $ 10,171,827
                                                         ============      ============
</TABLE>


                                      (26)
<PAGE>   29

                            Panhandle Royalty Company

             Notes to Consolidated Financial Statements (continued)


8. INFORMATION ON OIL AND GAS PRODUCING ACTIVITIES (CONTINUED)

COSTS INCURRED

During the reporting period, the Company incurred the following costs in oil and
gas producing activities:

<TABLE>
<CAPTION>
                                                                      1998           1997
                                                                   ----------     ----------
<S>                                                                <C>            <C>       
Property acquisition costs (principally nonproducing minerals)     $  739,164     $  224,224
Exploration costs                                                   1,181,110        967,456
Development costs                                                   1,475,671      1,676,841
                                                                   ----------     ----------
                                                                   $3,395,945     $2,868,521
                                                                   ==========     ==========
</TABLE>

9. SUPPLEMENTARY INFORMATION ON OIL AND GAS RESERVES (UNAUDITED)

The following unaudited information regarding the Company's oil and natural gas
reserves is presented pursuant to the disclosure requirements promulgated by the
Securities and Exchange Commission ("SEC") and SFAS No. 69, "Disclosures About
Oil and Gas Producing Activities."

Proved reserves are estimated quantities of crude oil and natural gas which
geological and engineering data demonstrate with reasonable certainty to be
recoverable in future years from known reservoirs under existing economic and
operating conditions. Proved developed reserves are those proved reserves that
can be expected to be recovered through existing wells with existing equipment
and operating methods. Because the Company's nonproducing mineral and leasehold
interests consist of various small interests in numerous tracts located
primarily in Oklahoma, New Mexico, Louisiana and Texas, it is not economically
feasible for the Company to provide estimates of all proved undeveloped
reserves. However, in 1995 the Company directed its independent petroleum
engineering firm to include proved undeveloped reserves in certain areas of
Western Oklahoma in the scope of properties which they evaluate for the Company
and, in 1996, the Company included certain proved undeveloped reserves in areas
of New Mexico within the scope of evaluated properties. Due to field production
allowable rules in the Dagger Draw field of New Mexico only those proved
undeveloped reserves which the Company felt could be drilled, under existing
allowable rules, have been included. Should the allowable rules be amended
and/or production volumes change significantly, additional proved undeveloped
reserves in the Dagger Draw field of New Mexico may be added in the future.

The Company's net proved (including certain undeveloped reserves described
above) oil and gas reserves as of September 30, 1998 and 1997 have been
estimated by Campbell & Associates, Inc., an independent petroleum engineering
firm. All studies have been prepared in accordance 


                                      (27)
<PAGE>   30

                            Panhandle Royalty Company

             Notes to Consolidated Financial Statements (continued)


9. SUPPLEMENTARY INFORMATION ON OIL AND GAS RESERVES (UNAUDITED) (CONTINUED)

with regulations prescribed by the Securities and Exchange Commission. The
reserve estimates were based on economic and operating conditions existing at
September 30, 1998 and 1997. Since the determination and valuation of proved
reserves is a function of testing and estimation, the reserves presented should
be expected to change as future information becomes available.

ESTIMATED QUANTITIES OF PROVED OIL AND GAS RESERVES

The following table presents the Company's net proved (including certain
undeveloped reserves described above) oil and gas reserve quantities as
estimated by Campbell & Associates, Inc., an independent petroleum engineering
firm, as of September 30, 1998 and 1997, and the changes in reserves for the
years then ended:

<TABLE>
<CAPTION>
                                                           PROVED RESERVES
                                                       ------------------------
                                                          OIL            GAS
                                                       (Mbarrels)       (Mmcf)
                                                       ----------       -------
<S>                                                    <C>              <C>  
September 30, 1996                                         939            9,839

Revisions of previous estimates (1)                       (243)             956
Purchases of reserves in place                               8               64
Extensions and discoveries                                 348            2,008
Production                                                (148)          (1,600)
                                                       -------          -------
September 30, 1997                                         904           11,267

Revisions of previous estimates (2)                       (102)            (746)
Purchases of reserves in place                              13               33
Extensions and discoveries                                  66            2,817
Production                                                (104)          (1,710)
                                                       -------          -------
September 30, 1998                                         777           11,661
                                                       =======          =======
</TABLE>

(1)      Oil and gas revisions are primarily related to those reserves which
         were economically recoverable at the higher prices which existed at
         September 30, 1996 which are not economically recoverable at prices
         existing at September 30, 1997.

(2)      Oil and gas revisions are primarily related to those reserves which
         were economically recoverable at the higher prices which existed at
         September 30, 1997 which are not economically recoverable at prices
         existing at September 30, 1998.


                                      (28)
<PAGE>   31
                            Panhandle Royalty Company

             Notes to Consolidated Financial Statements (continued)


9. SUPPLEMENTARY INFORMATION ON OIL AND GAS RESERVES (UNAUDITED) (CONTINUED)

<TABLE>
<CAPTION>
                                      PROVED DEVELOPED RESERVES    PROVED UNDEVELOPED RESERVES
                                      -------------------------    ---------------------------
                                         OIL              GAS         OIL                GAS
                                      (Mbarrels)         (Mmcf)    (Mbarrels)           (Mmcf)
                                      ----------         ------    ----------           ------
<S>                                   <C>                <C>       <C>                  <C>  
September 30, 1996                       641              8,201       298                1,638
                                         ===              =====       ===                =====

September 30, 1997                       625              9,707       279                1,560
                                         ===              =====       ===                =====

September 30, 1998                       498             10,103       279                1,558
                                         ===              =====       ===                =====
</TABLE>

STANDARDIZED MEASURE OF DISCOUNTED FUTURE NET CASH FLOWS

Estimates of future cash flows from proved oil and gas reserves, based on
current prices and costs, are shown in the following table. Estimated income
taxes are calculated by (i) applying the appropriate year-end tax rates to the
estimated future pretax net cash flows less depreciation of the tax basis of
properties and statutory depletion allowances and (ii) reducing the amount in
(i) for estimated tax credits to be realized in the future for gas produced from
"tight-sands."

<TABLE>
<CAPTION>
                                                                     SEPTEMBER 30,
                                                                 1998            1997
                                                              -----------     -----------
<S>                                                           <C>             <C>        
Future cash inflows                                           $30,120,490     $45,015,420
Future production costs                                         5,815,190       7,481,181
Future development costs                                        1,179,844       1,159,709
                                                              -----------     -----------
Future net cash inflows before future income tax expenses      23,125,456      36,374,530

Future income tax expense                                       5,945,839       8,971,733
                                                              -----------     -----------
Future net cash flows                                          17,179,617      27,402,797

10% annual discount                                             5,846,105       8,660,434
                                                              -----------     -----------
Standardized measure of discounted future net cash flows      $11,333,512     $18,742,363
                                                              ===========     ===========
</TABLE>


                                      (29)
<PAGE>   32

                            Panhandle Royalty Company

             Notes to Consolidated Financial Statements (continued)


9. SUPPLEMENTARY INFORMATION ON OIL AND GAS RESERVES (UNAUDITED) (CONTINUED)

Changes in the standardized measure of discounted future net cash flows are as
follows:

<TABLE>
<CAPTION>
                                                           1998              1997
                                                       ------------      ------------
<S>                                                    <C>               <C>         
Beginning of year                                      $ 18,742,363      $ 16,287,311
Changes resulting from:
   Sales of oil and gas, net of production costs         (4,375,903)       (5,850,364)
   Net change in sales prices and production costs       (8,305,058)          387,598
   Future development costs                                 (13,875)          (49,806)
   Extensions and discoveries                             3,186,652         6,163,526
   Revisions of quantity estimates                       (1,451,226)         (780,082)
   Purchases of minerals-in-place                           111,795           157,667
   Accretion of discount                                  1,874,236         2,315,552
   Net change in income taxes                             2,281,936           521,575
   Change in timing and other, net                         (717,408)         (410,614)
                                                       ------------      ------------
End of year                                            $ 11,333,512      $ 18,742,363
                                                       ============      ============
</TABLE>

10. QUARTERLY RESULTS OF OPERATIONS (UNAUDITED)

The following is a summary of the Company's unaudited quarterly results of
operations. The fiscal 1997 earnings per share amounts have been restated to
comply with Financial Accounting Standards Board No. 128, "Earnings Per Share."

<TABLE>
<CAPTION>
                                                           FISCAL 1998
                                   ------------------------------------------------------------
                                                          QUARTER ENDED
                                   ------------------------------------------------------------
                                   DECEMBER 31      MARCH 31         JUNE 30       SEPTEMBER 30
                                   -----------     -----------     -----------     ------------
<S>                                <C>             <C>             <C>             <C>        
Revenues                           $ 1,826,939     $ 1,335,664     $ 1,199,739     $ 1,077,840
Income (loss) before provision
   for income taxes (A)                751,541         369,716         341,193          (5,615)
Net income (B)                         586,541         299,716         296,193         132,385
Basic earnings per share           $       .86     $       .44     $       .44     $       .19
Diluted earnings per share         $       .86     $       .44     $       .43     $       .19
</TABLE>


                                      (30)
<PAGE>   33

                            Panhandle Royalty Company

             Notes to Consolidated Financial Statements (continued)


10. QUARTERLY RESULTS OF OPERATIONS (UNAUDITED) (CONTINUED)

<TABLE>
<CAPTION>
                                                      FISCAL 1997
                                --------------------------------------------------------
                                                     QUARTER ENDED
                                --------------------------------------------------------
                                DECEMBER 31     MARCH 31       JUNE 30      SEPTEMBER 30
                                -----------    ----------     ----------    ------------
<S>                             <C>            <C>            <C>            <C>       
Revenues                        $1,557,539     $2,511,315     $1,475,773     $1,471,851
Income before provision for
   income taxes (A)                582,102      1,407,716        648,708        353,316
Net income (B)                     476,102      1,082,716        513,708        226,316
Basic earnings per share        $      .70     $     1.60     $      .76     $      .33
Diluted earnings per share      $      .70     $     1.59     $      .76     $      .33
</TABLE>

(A)  Fourth quarter income before provision for income taxes includes an SFAS
     121 charge of $59,851 and $115,734 for 1998 and 1997, respectively.

(B)  Year-end adjustments to the Company's provision for income taxes caused the
     effective rate for 1998 to be less than (more than in 1997) that estimated
     during the previous three quarters. The effect of this difference is
     reflected in the fourth quarter net income above.


                                      (31)
<PAGE>   34

ITEM 8.         CHANGES IN AND DISAGREEMENTS WITH ACCOUNTANTS ON
                ACCOUNTING AND FINANCIAL DISCLOSURE

                                     N O N E


                                    PART III

ITEM 9.         DIRECTORS, EXECUTIVE OFFICERS, PROMOTERS AND
                CONTROL PERSONS; COMPLIANCE WITH SECTION 16(a)
                OF THE EXCHANGE ACT

                Listed below are the names, ages and positions, as of December
1, 1998, of the directors and executive officers of the Company. The Company's
bylaws provide for seven directors who are elected for staggered three-year
terms. Executive officers are appointed by the board of directors to serve in
their respective capacities until their successors are duly appointed by the
directors.

                                    DIRECTORS

<TABLE>
<CAPTION>
                         A                                   Served As
                         g                          Term     Director
Name                     e    Position & Offices   Expires     Since
----                     -    ------------------   -------   ---------
<S>                      <C>                       <C>       <C> 
Michael A. Cawley (b)    51   Director              2001        1991

Sam J. Cerny (a)         66   Director              2000        1993

E. Chris Kauffman (b)(c) 58   Director              2000        1991

H W Peace II (b)         63   Director, Chief       1999        1991
                              Executive Officer,
                              President

Ray H. Potts (c)         66   Director              2001        1997

Robert A. Reece (a)(c)   54   Director              1999        1986

Jerry L. Smith (a)       58   Director, Chairman    1999        1987
                              of the Board
</TABLE>

    (a)   Member of Audit Committee
    (b)   Member of Compensation Committee
    (c)   Member of Retirement Committee


                                      (32)
<PAGE>   35

                               EXECUTIVE OFFICERS

<TABLE>
<CAPTION>
                                                                    Held Office
Name                          Age        Position & Offices            Since
----                          ---        ------------------         -----------
<S>                           <C>        <C>                        <C>
Jerry L. Smith                58         Chairman of the                1997
                                         Board, Director

H W Peace II                  63         Director, Chief                1991
                                         Executive Officer,
                                         President

Michael C. Coffman            45         Vice President,                1990
                                         Chief Financial Officer,
                                         Secretary/Treasurer

Wanda C. Tucker               61         Vice President of              1990
                                         Land
</TABLE>

                BUSINESS EXPERIENCE

                Michael A. Cawley is an attorney and is the president and chief
executive officer of the Samuel Roberts Noble Foundation, Inc. He has been
employed by the Noble Foundation for the last six years. Prior to joining the
Noble Foundation, he was engaged in the practice of law in Ardmore, Oklahoma
with the firm of Thompson & Cawley. He is also a director of Noble Drilling
Corporation and Noble Affiliates Inc.

                Sam J. Cerny is a geological engineer and has been employed by
Shell Oil Company, Cleary Petroleum Corporation and its successor company, Grace
Petroleum Corporation, where he served as President/CEO from 1976 to 1991. He is
a past president of the Oklahoma Independent Petroleum Association and for the
last five years has been active as a petroleum management consultant.

                E. Chris Kauffman is a vice-president of Campbell-Kauffman,
Inc., an independent insurance agency in Oklahoma City. He has been involved
with the agency since it was formed in 1981. In addition, he is the chief
financial officer and treasurer of The Insurance Center Agency, Inc. He is also
a director of First State Bank in Oklahoma City and a trustee of the Central
Oklahoma Transportation & Parking Authority.

                Robert A. Reece is an attorney, and for the last five years has
been of counsel with the firm of Crowe & Dunlevy. He is also active in the
management of his family's investments.

                H W Peace II holds bachelors and masters degrees in geology. For
thirty-four years he has been employed as a geologist, in management or as an
officer and/or director in the petroleum industry. He has been employed by Union
Oil Company of California, Cotton Petroleum and Hadson Petroleum Corporation. He
has been president of the Company since 1991.


                                      (33)
<PAGE>   36

                Ray H. Potts holds a master's degree in geology from the
University of Missouri. He was employed for six years as an exploration
geologist for the Pure Oil Company and in 1967 formed Potts-Stephenson
Exploration Company, later changed to PSEC, Inc. In 1997 PSEC, Inc. was sold to
ONEOK Resources Company. Mr. Potts is currently active in the oil and gas
industry and has been involved in several national and state trade associations,
geological societies and numerous civic activities.

                Jerry L. Smith for the last eight years has been the owner of
Smith Capital Corporation in Dallas. This corporation is a private investment
firm focusing on commercial real estate and securities. Mr. Smith also serves as
Treasurer and as a Director of the Association of Graduates of the United States
Air Force Academy.

                Michael C. Coffman is a certified public accountant. Since 1975,
he has worked in public accounting and as a financial officer of three publicly
owned companies involved in the oil and gas industry. He has been employed by
the Company for the last eight years.

                Wanda C. Tucker has been a full-time employee of the Company
since 1978, has served in various positions with the Company and is currently
vice president of land.

                None of the organizations described in the business experiences
of company directors and officers are parents, subsidiaries or affiliates of
Panhandle Royalty Company.


ITEM 10.        EXECUTIVE COMPENSATION


                           Summary Compensation Table

<TABLE>
<CAPTION>
Name and
Principal                                                      All Other
Position          Year        Salary          Bonus          Compensation
--------          ----        ------          -----          ------------
<S>               <C>        <C>             <C>             <C>       
H W Peace II      1998       $122,500        $25,600          $22,215(1)
President &       1997       $113,750        $25,600          $20,903(1)
Chief Exec.       1996       $108,750        $15,600          $18,653(1)
Officer
</TABLE>

    (1)         Represents the value of 846 shares for 1998,
                702 shares for 1997, and 888 shares for 1996,
                of Company stock contributed to the Panhandle
                Employee Stock Ownership Plan (ESOP) on Mr.
                Peace's behalf.  The ESOP is a defined
                contribution plan, non-voluntary and non-
                contributory and serves as the retirement plan
                for the Company's employees.  Contributions
                are at the discretion of the board of
                directors and, to date, all contributions have
                been made in shares of Company stock.
                Contributions are allocated to all
                participants in proportion to their salaries
                for the plan year and 100% vesting occurs
                after three years' of service.


                                      (34)
<PAGE>   37

                DIRECTORS FEES

                Outside directors of the Company are paid $1,000 plus travel
expenses for attending each meeting of the board of directors and $200 for
attending each committee meeting of the board. Any director who travels in
excess of 50 miles to attend a meeting receives an additional $100 for each
meeting. Outside directors can elect to be included in the Panhandle Royalty
Company Deferred Compensation Plan For Non-Employee Directors (the "Plan"). The
Plan provides that each eligible director can individually elect to receive
shares of Company stock rather than cash for board meeting fees and board
committee meeting fees. These unissued shares are credited to each director's
deferred fee account at the fair market value of the shares on the date of the
meeting. Upon retirement, termination or death of the director, or upon a change
in control of the Company, the shares accrued under the Plan will be either
issued to the director or may be converted to cash, at the directors'
discretion, at the fair market value of the shares on the conversion date, as
defined. All outside directors are participating in this Plan.

                In addition to the above, Jerry Smith, chairman of the board of
directors, who is not an employee of the Company, is entitled to receive a $100
per hour fee for time spent, other than board or committee meetings, on Company
business. During fiscal 1998 and 1997, no payments were made to Mr. Smith under
this arrangement.

ITEM 11.        SECURITY OWNERSHIP OF CERTAIN
                BENEFICIAL OWNERS AND MANAGEMENT

                SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS

                As of December 4, 1998, no person or "group" as that term is
used in Section 13(d)(3) of the Securities Exchange Act of 1934, was known to
Panhandle to be the beneficial owner of more than five percent of the
outstanding shares of Panhandle's class A common stock.

                SECURITY OWNERSHIP OF MANAGEMENT

                The following table sets forth, as of September 30, 1998, all
shares of class A common stock held beneficially, directly or indirectly by each
director and by all directors and officers as a group.



                                      (35)
<PAGE>   38

<TABLE>
<CAPTION>
                            Amount And Nature Of             Percent Of
        Name                Beneficial Ownership                Class
        ----                --------------------             ----------
<S>                         <C>                              <C>      
Michael A. Cawley (A)       100 shares, sole voting               *
                            and investment powers

Sam J. Cerny (B)            1,200 shares, sole voting             *
                            and investment powers

E. Chris Kauffman (C)       3,100 shares, shared voting           *
                            and investment powers

H W Peace II (D)            8,371 shares, shared voting          1.2%
                            and investment powers

Ray H. Potts (E)            160 shares, sole voting               *
                            and investment powers

Robert A. Reece (F)         5,848 shares, sole voting             *
                            and investment powers

Jerry L. Smith (G)          7,024 shares, sole voting            1.0%
                            and investment powers

All directors and           10,392 shares, shared                1.5%
officers as a               voting and investment
group (9 persons)           powers

                            27,103 shares, sole voting           4.0%
                            and investment powers

                            37,495 shares total                  5.5%

                                                     * less than 1.0%
</TABLE>



(A) P.O. Box 2180, Ardmore, OK  73402
(B) 3330 Liberty Twr, 100 N. Broadway, Okla. City, OK 73102 
(C) 9705 North Broadway Ext. - Suite #200, Okla. City, OK 73114 
(D) 5400 N.W. Grand Blvd - Suite #210, Okla. City, OK 73112 
(E) 100 N. Broadway - Suite #3200, Okla. City, OK 73102 
(F) 6403 N. Grand Blvd. - Suite #204, Okla. City, OK 73116 
(G) 5944 Luther Lane - Suite #401, Dallas, TX 75225


ITEM 12.        CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS

                                    N O N E


ITEM 13.        EXHIBITS AND REPORTS ON FORM 8-K

                (3)      Articles of Incorporation (Incorporated by
                         reference to Exhibit attached to Form 10 filed
                         January 27, 1980, and to Forms 8-K dated June 1,
                         1982 and December 3, 1982)

                         By-Laws as amended (Incorporated by reference to
                         Form 8-K dated October 31, 1994)

                (4)      Instruments defining the rights of security
                         holders (Incorporated by reference to Articles of
                         Incorporation and By-Laws listed above)


                                      (36)
<PAGE>   39

                (10)     Agreement indemnifying directors and officers
                         (Incorporated by reference to Form 10-K dated September
                         30, 1989)

                (21)     Subsidiaries of the Registrant

                (27)     Financial Data Schedule


                REPORTS ON FORM 8-K

                No reports on Form 8-K were filed during the quarter ended
September 30, 1998.


                                   EXHIBIT 21

                    SUBSIDIARIES OF PANHANDLE ROYALTY COMPANY
                              AT SEPTEMBER 30, 1998

                The following table sets forth certain information with respect
to Panhandle's subsidiary:

                                   CORPORATION

                                    PHC, INC.

                PHC, Inc. was incorporated in Oklahoma and is included in
Panhandle's consolidated financial statements.  PHC, Inc. is inactive,
and has never done any business.


                                      (37)
<PAGE>   40

                                   SIGNATURES

                Pursuant to the requirements of Section 13 or 15(d) of the
Exchange Act, the registrant caused this report to be signed on its behalf by
the undersigned, thereunto duly authorized.

                                       PANHANDLE ROYALTY COMPANY


                                       By: /s/ H W Peace II
                                           -------------------------------------
                                           H W Peace II, Chief
                                           Executive Officer,
                                           President, Director

                                       Date: December 15, 1998
                                             -----------------------------------

                In accordance with the Exchange Act, this report has been signed
below by the following persons on behalf of the registrant and in the capacities
and on the dates indicated.


   /s/ Jerry L. Smith                               /s/ E. Chris Kauffman
-----------------------------------              -------------------------------
Jerry L. Smith, Chairman of Board                E. Chris Kauffman, Director

Date  December 15, 1998                          Date  December 15, 1998
      -----------------------------                    -------------------------


   /s/ Robert A. Reece                              /s/ Ray H. Potts
-----------------------------------              -------------------------------
Robert A. Reece, Director                        Ray H. Potts, Director

Date  December 15, 1998                          Date  December 15, 1998
      -----------------------------                    -------------------------


   /s/ Sam J. Cerny                                 /s/ Michael A. Cawley
-----------------------------------              -------------------------------
Sam J. Cerny, Director                           Michael A. Cawley, Director

Date  December 15, 1998                          Date  December 15, 1998
      -----------------------------                    -------------------------


   /s/ Michael C. Coffman
-----------------------------------
Michael C. Coffman, Vice President
Treasurer and Secretary
(Principal Financial and Accounting
 Officer)

Date  December 15, 1998
      ----------------------------- 


                                      (38)
<PAGE>   41
                                 EXHIBIT INDEX

<TABLE>
<CAPTION>
EXHIBIT 
NUMBER          DESCRIPTION
-------         -----------
<S>       <C>                                                            
  (3)     Articles of Incorporation (Incorporated by reference to Exhibit
          attached to Form 10 filed January 27, 1980, and to Forms 8-K dated
          June 1, 1982 and December 3, 1982)

          By-Laws as amended (Incorporated by reference to Form 8-K dated
          October 31, 1994)

  (4)     Instruments defining the rights of security holders (Incorporated by
          reference to Articles of Incorporation and By-Laws listed above)

  (10)    Agreement indemnifying directors and officers (Incorporated by
          reference to Form 10-K dated September 30, 1989)

  (21)    Subsidiaries of the Registrant

  (27)    Financial Data Schedule
</TABLE>