<PAGE>   1
                                                                   EXHIBIT 10(m)


                             STOCK OPTION AGREEMENT


         THIS AGREEMENT, made as of August 27, 1996, between Plains Resources
Inc., a Delaware corporation (the "Company"), and William C. Egg, Jr. (the
"Optionee").

         WHEREAS, on May 23, 1996, the Board of Directors (the "Board") of the
Company authorized and empowered the Compensation Committee of the Board (the
"Compensation Committee") to grant to William C. Egg, Jr., Senior Vice
President  of the Company, an option for the purchase of 200,000 shares of the
Company's common stock, $.10 per share par value ("Common Stock"), upon such
terms and provisions as the Compensation Committee deems to be in the best
interest of the Company; and

         WHEREAS,  pursuant to the authority granted by the Board, the
Compensation Committee has determined to grant an option to the Optionee as
provided herein.

         NOW THEREFORE, the parties hereto agree as follows:

         1.      GRANT OF OPTION.

         The Company hereby grants to the Optionee the right and option (the
"Option") to purchase, from time to time, all or any part of an aggregate of
200,000 whole shares of Common Stock (the "Option Shares") subject to, and in
accordance with, the terms and provisions set forth in this Agreement.

         2.      EXERCISE PRICE.

         The price at which the Optionee shall be entitled to purchase the
Option Shares upon the exercise of the Option shall be $13.50 per share (the
"Exercise Price"), subject to adjustment from time to time in accordance with
the terms and provisions of this Agreement..

         3.      EXPIRATION DATE.

         The Option shall be exercisable to the extent and in the manner
provided herein until 5:00 p.m., Houston time, on August 27, 2001 (the
"Expiration Date"): provided, however, that the Option may be earlier
terminated as provided in Paragraph 7 hereof.

         4.      EXERCISABILITY OF OPTION.

         The Option shall not be exercisable by the Optionee, his guardian or
his legal representative unless and until one of the following events (a
"Vesting Event") occurs on or before the Expiration Date:

         (a)     The Per Share Market Value (as defined below) of the Common
                 Stock equals or exceeds the Vesting Price (as defined below)
                 for any 20 Trading Days (as defined below) in any 30
                 consecutive Trading Days.

         (b)     The distribution to the holders of the Company's Common Stock,
                 in connection with
<PAGE>   2
                 a merger or consolidation of the Company with another
                 corporation or entity, whether or not the Company is the
                 surviving entity, or the liquidation of the Company or the
                 sale or other disposition of substantially all of its assets
                 (such merger, consolidation, liquidation, or disposition of
                 assets being herein referred to as a "Transaction"), of
                 securities, cash or property having a value per share of such
                 Common Stock equal to or exceeding the Vesting Price.
                 Notwithstanding any other provision herein to the contrary, in
                 the event a Transaction is consummated (the date of such
                 consummation herein referred to as the "Consummation Date") on
                 or before August 27, 1999, the Option shall become exercisable
                 on the Consummation Date, if:

                          (i)   the Per Share Market Value of the Common Stock
                          on the day prior to the Consummation Date equals or
                          exceeds $20.00 per share;

                          (ii)   prior to the Consummation Date, the Per Share
                          Market Value of the Common Stock equals or exceeds
                          $20.00 per share for any 20 Trading Days in any 30
                          consecutive Trading Days; or

                          (iii) the securities, cash or property distributed in
                          such Transaction to the holders of the Company's
                          Common Stock has a value per share of such Common
                          Stock of $20.00 or more.

                 For purposes of this Paragraph 4 (b), the value of any
                 securities so distributed shall be determined on the same
                 basis set forth herein for determining the Per Share Market
                 Value of a share of Common Stock, and the value of any other
                 property so distributed shall be determined by a nationally
                 recognized or major regional investment banking firm or firm
                 of independent certified public accountants of recognized
                 standing (which may be the firm that regularly examines the
                 financial statements of the Company) selected in good faith by
                 the Board of Directors of the Company.

         (c)     The death of the Optionee.

         (d)     The Disability (as defined below) of the Optionee.

         (e)     The Company terminates the employment of the Optionee, without
                 Cause (as defined below), in connection with or in
                 anticipation of a Change in Control (as defined below) of the
                 Company.

         (f)     A Change in Control of the Company occurs subsequent to 
                 August 27, 2000.

         (g)     Subsequent to August 27,1996, the Company terminates the
                 employment of the Optionee for any reason other than (i) Cause
                 or, (ii) a determination by at least a majority of the
                 Incumbent Board (as hereinafter defined), evidenced by a Board
                 resolution, that the Optionee has failed to perform his duties
                 consistent with the goals set forth in the Five Year Strategic
                 Plan adopted by the Board on November 9, 1995, and modified on
                 February 8, 1996, provided however, this clause (ii) shall be
                 null and void if the foregoing determination by the Incumbent
                 Board is made during a period within which Optionee could have
                 terminated his employment for Good Reason (as hereinafter
                 defined).





                                       2
<PAGE>   3
         (h)     The Optionee terminates his employment with the Company for
                 Good Reason prior to August 27, 1999, and the Per Share Market
                 Value of the Common Stock prior to such date has equaled or
                 exceeded $20.00 per share for any 20 Trading Days in any 30
                 consecutive Trading Days.

From the date of the occurrence of a Vesting Event, the Option shall remain
exercisable until the Expiration Date unless the Company terminates the
Optionee's employment for Cause, in which case the Option will terminate in
accordance with Paragraph 7.1 below.

         As used herein, the term "CAUSE" shall mean (i) the willful engaging
by the Optionee in gross misconduct resulting in demonstrable material injury
to the Company, or (ii) the nonappealable conviction of the Optionee of a
felony involving moral turpitude.  For purposes of this definition, no act or
failure to act on the Optionee's part shall be considered "willful" unless
done, or omitted to be done, by him not in good faith and without reasonable
belief that his act or omission was in the best interest of the Company or
otherwise likely to result in no material injury thereto.

         As used herein a "CHANGE IN CONTROL" shall be deemed to have occurred
if, prior to the Expiration Date of the Option;

          (i) Any "person" for purposes of Section 13(d) or 14(d) of the
         Securities Exchange Act of 1934, as amended (the "1934 Act"), (A)
         acquires beneficial ownership (within the meaning of Rule 13d-3
         promulgated under the 1934 Act) of shares of the Company's capital
         stock having 25% or more of the total number of votes that may be cast
         in the election of directors of the Company ("Voting Stock"),  and (B)
         such person seeks to elect or cause to be elected two or more members
         of the Company's Board of Directors or otherwise exerts or attempts to
         exert a controlling influence on the management of the Company;
         provided, however, that if the transaction in which such person
         becomes the beneficial owner of 25% or more of the Voting Stock is
         approved by a majority of the Incumbent Board (as defined below), such
         transaction shall not be deemed to constitute a Change in Control, or

         (ii) The individuals who are directors of the Company on the date
         hereof (the "Incumbent Board") cease to constitute a majority of the
         Board of Directors of the Company, provided, however, that if either
         the election of any new director or the nomination for election of any
         new director was approved by a majority of the Incumbent Board, such
         new director shall be considered as a member of the Incumbent Board.

Notwithstanding the foregoing, a "Change in Control" of the Company shall not
be deemed to have occurred solely as a result of (i) a restructuring of the
Company as a wholly-owned subsidiary of another corporation in a transaction in
which the owners of shares of capital stock of the Company become the owners,
in substantially identical proportions, of all or substantially all of the
shares of capital stock of such other corporation or (ii) the issuance of the
authorized and unissued capital stock of the Company or of any parent of the
Company in connection with a financing or acquisition initiated by the Company
or such parent.





                                       3
<PAGE>   4
         As used herein, the term "DISABILITY" shall mean a physical or mental
infirmity which impairs the Optionee's ability to perform substantially his
duties for a period of one hundred eighty (180) consecutive days or which the
Board determines constitutes a Disability.

         As used herein, the term "PER SHARE MARKET VALUE" for any particular
date shall mean, (a) the last sale price per share of the Common Stock on such
date on the principal stock exchange on which the Common Stock has been listed
or if there is no such price on such date, then the last price on such exchange
on the date nearest preceding such date, or (b) if the Common Stock is not
listed on any stock exchange, the average between the high and low prices for a
share of Common Stock in the over-the -counter market, as reported by the
Nasdaq National Market at the close of business on such date, or the last sales
price if such price is reported and high and low prices are not available, or
(c) if the Common Stock is not quoted on the Nasdaq National Market, the
average between the high and low prices for a share of Common Stock in the
over-the-counter market as reported by the National Quotation Bureau
Incorporated (or any similar organization or agency succeeding to its functions
of reporting prices), or (d) if the Common Stock is no longer publicly traded,
as determined by a nationally recognized or major regional investment banking
firm or firm of independent certified public accountants of recognized standing
(which may be the firm that regularly examines the financial statements of the
Company) selected in good faith by the Board of Directors of the Company,
provided that none of the transactions related to the foregoing shall include
purchases by the Optionee or any "affiliate" (as such term is defined in the
General Rules and Regulations under the Securities Act of 1933) of the Company.

         As used herein, the term "VESTING PRICE" shall mean $24.00 per share
of Common Stock.  Upon any adjustment of the Exercise Price pursuant to
Paragraph 10 hereof, the Vesting Price shall be adjusted, as of the date of
such adjustment of the Exercise Price, to that price determined by multiplying
the Vesting Price in effect immediately prior to such adjustment of the
Exercise Price by a fraction (i) the numerator of which shall be the Exercise
Price in effect immediately after such adjustment of the Exercise Price, and
(ii) the denominator of which shall be the Exercise Price in effect immediately
prior to such adjustment.

         As used herein, the term "TRADING DAY" shall mean (a) a day on which
the Common Stock is traded on the principal stock exchange on which the Common
Stock has been listed, or (b) if the Common Stock is not listed on any stock
exchange, a day on which the Common Stock is traded in the over-the-counter
market, as reported by the Nasdaq National Market, or (c) if the Common Stock
is not quoted on the Nasdaq National Market, a day on which the Common Stock is
traded in the over-the-counter market as reported by the National Quotation
Bureau Incorporated (or any similar organization or agency succeeding to its
functions of reporting prices).

         5.      MANNER OF EXERCISE AND PAYMENT.

         5.1     Subject to the terms and conditions of this Agreement, the
Option may be exercised by delivery of written notice to the Company, at its
principal executive office.  Such notice shall state





                                       4
<PAGE>   5
that the Optionee is electing to exercise the Option and the number of Option
Shares in respect of which the Option is being exercised and shall be signed by
the person or persons exercising the Option.

         5.2     The notice of exercise shall be accompanied by the full
purchase price for the Option Shares in respect of which the Option is being
exercised, (i) in cash, (ii) by check or (iii) by transferring  shares of
Common Stock to the Company (other than shares held by the Optionee for less
than 6 months prior to the date of exercise) the number of which shares shall
be determined by dividing the full purchase price for the Option Shares in
respect of which the Option is being exercised by the Per Share Market Value of
the Common Stock on the Trading Day preceding the date of exercise.

         5.3     Upon receipt of the notice of exercise and full payment for
the Option Shares in respect of which the Option is being exercised, the
Company shall take such action as may be necessary promptly to effect the
transfer to the Optionee of the number of Option Shares as to which such
exercise was effective.

         5.4     The Optionee shall not be deemed to be the holder of, or to
have any of the rights of a holder with respect to any Option Shares subject to
the Option until (i) the Option shall have been exercised pursuant to the terms
of this Agreement and the Optionee shall have paid the full purchase price for
the number of Option Shares in respect of which the Option was exercised, (ii)
the Company shall have issued and delivered the Option Shares to the Optionee,
and (iii) the Optionee's name shall have been entered as a stockholder of
record on the books of the Company, whereupon the Optionee shall have full
voting and other ownership rights with respect to such Option Shares.

         6.      COMPLIANCE WITH LAWS, RULES AND REGULATIONS.

         Notwithstanding any other provision of this Agreement to the contrary,
the obligation of the Company to sell or issue any Option Shares under the
Option shall be suspended during any period of time when the issuance of such
Option Shares would constitute a violation by Optionee or the Company of any
provisions of any law or regulation of any governmental authority.  The Option
shall be subject to the requirements that, if at any time the Board shall, in
good faith and upon a reasonable basis, determine that the listing,
registration or qualification of the Option Shares upon any stock exchange or
under any state or federal law of the United States or any governmental
subdivision thereof, or the consent or approval of any governmental regulatory
body, or investment or other representation, are necessary or desirable in
connection with the issue or purchase of Option Shares, the Option may not be
exercised in whole or in part unless such listing, registration, qualification,
consent, approval or representations shall have been effected or obtained free
of any conditions not acceptable to the Board acting reasonably and in good
faith.  In the event the Option Shares issuable on exercise of an Option are
not registered under the Securities Act of 1933, as amended (the "Act"), the
Company may imprint on the certificate for such Option Shares the following
legend which counsel for the Company considers necessary or advisable to comply
with the Act:





                                       5
<PAGE>   6
         "The shares represented by this certificate have not been registered
         under the Securities Act  of 1933 or under the securities laws of any
         state and may reoffered or sold only if registered or if an exemption
         from registration is available."

         Notwithstanding any other provision in this Agreement to the contrary,
if within 10 days preceding the Expiration Date, the Company is unable to issue
Option Shares under the Option, the term of the Option shall be extended and
written notice given to Optionee (at least 7 days prior to the Expiration Date)
of such extension so as to provide a reasonable opportunity for Optionee to
exercise the Option; provided, however, in no event shall such extension exceed
the period during which the Company was unable to issue Option Shares under the
Option plus 10 days.


         7.      TERMINATION OF OPTION

         7.1     Notwithstanding any other provision in this Agreement to the
contrary, if on or before the Expiration Date of the Option, the Company
terminates the Optionee's employment with the Company, with Cause, the Option
shall terminate on the date of such termination and after such date no rights
thereunder may be exercised.

         7.2     Notwithstanding any other provision in this Agreement to the
contrary, if  prior to the date the Option becomes exercisable and on or before
the Expiration Date of the Option, the Optionee terminates his employment with
the Company, other than for Good Reason (as defined below) or as a result of
his Disability, the Option shall terminate on the date of such termination and
after such date no rights thereunder may be exercised.

                 As used herein, the term "GOOD REASON" shall mean (i) any
removal of the Optionee from, or any failure to re-elect the Optionee to the
positions of President and Chief Executive Officer of the Company, except in
connection with termination of Optionee's employment for Cause, (ii) a material
breach by the Company of the Optionee's Employment Agreement with the Company
dated as of March 1, 1993, as amended or replaced prior to the Expiration Date
of the Option, or (iii) a Change in Control of the Company.

         8.      NONTRANSFERABILITY.

         The Option shall not be transferrable other than by will or by the
laws of descent and distribution.  During the lifetime of the Optionee, the
Option shall be exercisable only by the Optionee or his guardian or legal
representative.

         9.      NO RIGHT TO CONTINUED EMPLOYMENT.

         Nothing in this Agreement shall be interpreted or construed to confer
upon the Optionee any right with respect to continuance of employment with the
Company, nor shall this Agreement





                                       6
<PAGE>   7
interfere in any way with the right of the Company to terminate the Optionee's
employment at any time.

         10.     ADJUSTMENTS UPON CHANGES IN THE COMPANY'S CAPITAL STRUCTURE.

         10.1    If the Company shall effect a subdivision or consolidation of
the Common Stock or other capital readjustment, the payment of a stock
dividend, or other increase or reduction of the number of shares of Common
Stock outstanding, without receiving compensation therefor in money, services,
or property, then the number of Option Shares purchasable under the Option and
the Exercise Price shall be appropriately adjusted in such a manner as to
entitle the Optionee to receive, upon exercise of the Option, for the same
aggregate consideration, the same total number of Option Shares and other
securities as he would have received after the happening of any of the events
described above had he exercised the Option in full immediately prior to such
event.

         10.2    If  (i) a Transaction described in Paragraph 4(b) is
consummated  while the Option remains outstanding, and (ii) the Option becomes
exercisable as a result of such Transaction, (x) Optionee shall be entitled
upon exercise of the Option, to receive, in lieu of Option Shares, the number
and class or classes of shares of such stock or other securities or property to
which Optionee would have been entitled if, immediately prior to such
Transaction, Optionee had been the holder of the Option Shares or (y) the
Option may be canceled by the Board as of the Consummation Date of any such
Transaction upon payment to Optionee in cash equal to the amount by which the
value (as determined in good faith by the Board) of the securities or property
to which Optionee would have been entitled if, immediately prior to such
Transaction, Optionee had been the holder of the Option Shares exceeds the
aggregate Exercise Price of the Option Shares.

         10.3    If  the Company shall issue rights or warrants to all holders
of Common Stock entitling them to subscribe for or purchase shares of Common
Stock at a price less than the  Per Share Market Value of Common Stock on the
record date of such issuance, the Exercise Price shall be reduced by
multiplying the Exercise Price in effect prior to such record date by a
fraction, of which the denominator shall be the number of shares of Common
Stock (excluding treasury shares, if any) outstanding on the date of such
issuance of such rights or warrants plus the number of additional shares of
Common Stock offered for subscription or purchase, and of which the numerator
shall be the number of shares of Common Stock (excluding treasury shares, if
any) outstanding on the date of issuance of such rights or warrants plus the
number of shares which the aggregate offering price of the total number of
shares so offered would purchase at such Per Share Market Price.  Such
adjustment shall be made whenever such rights or warrants are issued, and shall
become effective immediately after the record date for the determination of
stockholders entitled to receive such rights or warrants.  However, upon the
expiration of any right or warrant to purchase Common Stock, the issuance of
which resulted in an adjustment in the Exercise Price pursuant to this
paragraph 10.3, if any such right or warrant shall expire and shall not have
been exercised, the Exercise Price shall immediately upon such expiration be
recomputed and effective immediately upon such expiration be  increased to the
price which it would have been had the adjustment of the Exercise Price made
upon the issuance of such rights or warrants been made on the basis of offering
for subscription or purchase only that number of shares of Common Stock
actually purchased upon the exercise of such rights or warrants actually
exercised.





                                       7
<PAGE>   8
         10.4    If the Company shall distribute to all holders of Common Stock
evidences of its indebtedness or assets (excluding cash dividends or cash
distributions paid out of earned surplus) or rights or warrants to subscribe
for or purchase any security (excluding those referred to in paragraph 10.3
above) then in each such case the Exercise Price shall be determined by
multiplying the Exercise Price in effect prior to the record date fixed for
determination of stockholders entitled to receive such distribution by a
fraction, of which the denominator shall be the Per Share Market Value of the
Common Stock on the record date, and of which the numerator shall be such Per
Share Market Value of the Common Stock, less the then fair market value (as
determined by the Board of the Company  in good faith, whose determination
shall be conclusive if made in good faith;  provided, however that in the event
of a distribution or series of related distributions exceeding 10% of the net
assets of the Company, then such fair market value shall be determined by a
nationally recognized or major regional investment banking firm or firm of
independent certified public accountants of recognized standing (which may be
the firm that regularly examines the financial statements of the Company)
selected in good faith by the Board of the Company, and in either case shall be
described in a statement provided to the Optionee) of the portion of assets or
evidences of indebtedness so distributed or such subscription rights applicable
to one share of Common Stock.  Such adjustment shall be made whenever any such
distribution is made and shall become effective immediately after the record
date mentioned above.

         10.5    If conditions shall arise by reason of action taken by the
Company, which, in the opinion of the Board of the Company, are not adequately
covered by the other provisions hereof and which might reasonably be expected
to materially and adversely affect the rights of the Optionee hereunder, or if
any such conditions are expected to arise by reason of any action contemplated
by the Company, the Board of the Company shall appoint a firm of independent
certified public accountants of recognized standing (which may be the firm that
regularly examines the financial statements of the Company), who shall give
their opinion as to the adjustment, if any (not inconsistent  with the
standards established in this paragraph 10), of the Exercise Price (including,
if necessary, any adjustment as to the securities which may be purchased
hereunder) which is or would be required to preserve without dilution the
rights of the Optionee hereunder.  The Board of the Company shall make the
adjustment recommended forthwith upon receipt of such opinion or the taking of
any such action contemplated, as the case may be: provided, however, that no
such adjustment of the Exercise Price shall be made which in the opinion of the
investment banking firm or firm of accountants giving the aforesaid opinion
would result in an increase of the Exercise Price to more than the Exercise
Price then in effect.

         Except as hereinbefore expressly provided, the issue by the Company of
shares of any class, or securities convertible into shares of any class, for
cash or property, or for labor or services either upon direct sale or upon the
exercise of rights or warrants to subscribe therefor, or upon conversion of
shares or obligations of the Company convertible into such shares or other
securities, shall not affect, and no adjustment by reason thereof shall be made
with respect to the number or exercise price of Option Shares then subject to
the Option.





                                       8
<PAGE>   9
         11.     WITHHOLDING OF TAXES.

         Prior to the issuance of the Option Shares for an exercise of the
Option, the Optionee shall pay to the Company any federal, state and local
income taxes and other amounts (the "Withholding Taxes") as may be required by
law to be withheld.  In satisfaction of the Withholding Taxes, the Optionee may
transfer shares of Common Stock to the Company (other than shares held by
Optionee for less than 6 months prior to the date of exercise) the number of
which shares shall be determined by dividing the total amount of the
Withholding Taxes by the Per Share Market Value on the Trading Day preceding
the date of exercise.

         12.     MODIFICATION OF AGREEMENT.

         This Agreement may be modified, amended, suspended or terminated, and
any terms and conditions may be waived, but only by a written instrument
executed by the parties hereto.


         13.     SEVERABILITY.

         Should any provision of the Agreement be held by a court of competent
jurisdiction to be unenforceable or invalid for any reason, the remaining
provisions of this Agreement shall not be affected by such holding and shall
continue in full force in accordance with their terms.

         14.     GOVERNING LAW.

         The validity, interpretation, construction and performance of this
Agreement shall be governed by the laws of the State of Delaware without giving
effect to the conflicts of laws principles thereof.

         15.     SUCCESSORS IN INTEREST.

         This Agreement shall inure to the benefit of and be binding upon any
successor to the Company.  This Agreement shall inure to the benefit of the
Optionee's legal representatives.  All obligations imposed upon the Optionee
and all rights granted to the Company under this Agreement shall be final,
binding and conclusive upon the Optionee's heirs, executors, administrators and
legal representatives.



<TABLE>
         <S>                                                <C>
         Attest:                                            PLAINS RESOURCES INC.

              /s/ Michael R. Patterson                      by:     /s/ Tom H. Delimitros         
         -------------------------------                        ----------------------------------
         Secretary                                          Chairman of the Compensation Committee


                                                                /s/ William C. Egg, Jr.               
                                                            ------------------------------------------
                                                            William C. Egg, Jr., OPTIONEE
</TABLE>





                                       9