<PAGE>


                                                                   EXHIBIT 10.39








                              CERIDIAN CORPORATION

                        UK COMPENSATION SHARE OPTION PLAN



                     ADOPTED BY THE COMPANY ON 27 APRIL 2001
















                                KPMG
                                1 PUDDLE DOCK
                                LONDON
                                EC4V 3PD
                                REF:  CERIDIAN/SS/REPORTS/COMPENSATIONFINAL.DOC



<PAGE>



       RULES OF THE CERIDIAN CORPORATION UK COMPENSATION SHARE OPTION PLAN

                                      INDEX
<Table>
<Caption>
                                                                              PAGE
                                                                              ----
<S>                                                                           <C>
 1   Definitions ........................................................      2
 2   Time of grant of Options ...........................................      7
 3   Conditions on the grant of Options .................................      7
 4   Grant of Options ...................................................      7
 5   Limitations on Grant ...............................................      8
 6   Exercise of Options ................................................      8
 7   Take-overs, Reconstructions and Liquidations .......................     10
 8   Variation of Share Capital .........................................     11
 9   Manner of Exercise of Options ......................................     12
10   Administration and Amendment .......................................     13
11   Compliance with Laws and Regulations ...............................     14
12   Loss of Office or Employment .......................................     14
</Table>




                                       1
<PAGE>


                        RULES OF THE CERIDIAN CORPORATION
                        UK COMPENSATION SHARE OPTION PLAN

DEFINITIONS

         In these Rules the following words and expressions shall have, where
         the context so admits, the following meanings:

<Table>
<S>                                        <C>        <C>
         "Accounting Period"               -          an accounting reference period of the Company;

         "Act"                             -          the Income and Corporation Taxes Act 1988;

         "Acquiring Company"               -          where the conditions of paragraph 15 of Schedule
                                                      9 to the Act are met, either such company as
                                                      shall be at any time the "Acquiring Company" as
                                                      defined in that paragraph, or some other company
                                                      falling within sub-paragraph (b) or sub-paragraph
                                                      (c) of paragraph 10 of Schedule 9 in relation to
                                                      the Acquiring Company over whose shares an Option
                                                      has been granted;

         "Administrator"                              an Administrator appointed by the Committee;

         "Adoption Date"                   -          the date on which the Plan is adopted by resolution
                                                      of the Board;

         "Associated Company"              -          has the same meaning as in section 416 of the Act;

         "Auditors"                        -          the auditors for the time being of the Company
                                                      (acting as experts and not as arbitrators);

         "Board"                           -          the Board of directors of the Company or a
                                                      committee of the Board;
</Table>



                                       2
<PAGE>

<Table>
<S>                                        <C>        <C>
         "Ceridian Old SAYE Plan"          -          the plan now known as the Ceridian Amended
                                                      Savings-Related Share Option Plan adopted on
                                                      15 December 1997 and amended on 14 February 2001;

         "Committee"                       -          a duly constituted committee of the Board
                                                      delegated with the authority to consider the
                                                      remuneration of Group Employees;

         "Company"                         -          the company known after 30 March 2001 as Ceridian
                                                      Corporation, incorporated under the laws of
                                                      Delaware in the United States of America or save
                                                      for Rules 2, 3, 4, 5 and 10.2 the Acquiring
                                                      Company;

         "Control"                         -          has the same meaning as in section 840 of the Act;

         "Corresponding Option"            -          an option granted under Rule 4.2A of the Ceridian
                                                      Old SAYE Plan;

         "Date of Grant"                   -          the date on which an Option is, was or is to be
                                                      granted to an Eligible Employee under the Plan,
                                                      pursuant to Rule 4.1, or on which an Option is or
                                                      was treated as being granted pursuant to Rule 4.2;

         "Eligible Employee"               -          any Group Employee who validly accepts an offer
                                                      of the type referred to in Rule 4.2A of the
                                                      Ceridian Old SAYE Plan;

         "Exercise Number"                 -          on a date, the maximum number of Shares which may be
                                                      acquired on the exercise of an Option on that
                                                      date;
</Table>



                                       3
<PAGE>

<Table>
<S>                                        <C>        <C>
         "Exercise Price"                  -          the price at which an Eligible Employee may
                                                      acquire a Share on the exercise of an Option as
                                                      determined by the Board

         "Group"                           -          the Company and any other company which is a Subsidiary of
                                                      the Company and which is for the time being
                                                      nominated by the Board to be a participating
                                                      company  under the Plan and the phrase "Group
                                                      Company" shall be construed accordingly;

         "Group Employee"                  -          a director or employee of any and all Group Companies;

         "Injury or Disability"            -          the cessation of employment or office by reason
                                                      of injury or disability provided the Committee
                                                      are satisfied, on production of such evidence as
                                                      it may reasonably require:

                                                      (i)      that the individual has ceased to
                                                               exercise and, by reason of injury or
                                                               disability, is incapable of exercising
                                                               that office or employment; and

                                                      (ii)     that the individual is likely to remain
                                                               so incapable for the foreseeable future;

         "Maturity Date"                   -          a date set by the Committee pursuant to Rule 4.1
                                                      being the date on which the Exercise Number is
                                                      equal to the total number of Shares under an
                                                      Option;

         "New Option"                      -          an option over shares in the Acquiring Company
                                                      meeting the requirements of sub-paragraphs
                                                      15(3)(a) to (d) of Schedule 9, granted in
                                                      consideration for the release of a Subsisting
                                                      Option within the "appropriate
</Table>



                                       4
<PAGE>

<Table>
<S>                                        <C>        <C>
                                                      period" (as defined by paragraph 15(2) of Schedule 9);

         "Option"                          -          a right to acquire Shares granted or to be granted
                                                      pursuant to Rules 4.1 or 4.2;

         "Option Certificate"              -          an option certificate in a form approved by the
                                                      Committee from time to time;

         "Option Holder"                   -          a person who has been granted an Option or (where
                                                      the context admits) his legal personal
                                                      representative(s);

         "Option to Subscribe"             -          an Option to subscribe for Shares granted by the
                                                      Company;

         "Plan"                            -          this Ceridian Corporation UK Compensation Share
                                                      Option Plan constituted and governed by the Rules;

         "Redundancy"                      -          the cessation of employment or office by reason
                                                      of redundancy within the meaning of the
                                                      Employment Rights Act 1996;

         "Retirement"                      -          the cessation of employment or office by reason
                                                      of retirement either at the Specified Age or any
                                                      other age at which the individual is bound to
                                                      retire in accordance with the terms of his
                                                      contract of employment;

         "Rules"                           -          the rules of the Plan as the same may be amended
                                                      from time to time;

         "Share"                           -          a share in the common stock of the Company, a
                                                      share in which is within the meaning of ordinary
                                                      share capital in section 832(1) of the Act;
</Table>



                                       5
<PAGE>

<Table>
<S>                                        <C>        <C>
         "Specified Age"                   -         age 60;

         "Subsidiary"                      -         a company which is under the Control of the
                                                     Company and which is a subsidiary of the Company
                                                     within the meaning of section 736 of the
                                                     Companies Act 1985;

         "Subsisting Option"               -         an Option which has been granted and which has
                                                     not lapsed, been surrendered, renounced or been
                                                     exercised in full;

         "Transaction"                     -         the reverse spin off undertaken by the company
                                                     which on 30 March 2001 was known as Ceridian
                                                     Corporation whereby, inter alia, the  Company
                                                     acquired Control of Ceridian Holdings UK Limited
                                                     on 28 March 2001.
</Table>

1.2      In these Rules, except insofar as the context otherwise requires:

         (i)      words denoting the singular shall include the plural
                  and vice versa;

         (ii)     words importing a gender shall include every gender and
                  references to a person shall include bodies corporate and
                  unincorporated and vice versa;

         (iii)    reference to any enactment shall be construed as a reference
                  to that enactment as from time to time amended, modified,
                  extended or re-enacted and shall include any orders,
                  regulations, instruments or other sub-ordinate legislation
                  made under the relevant enactment;

         (iv)     words have the same meanings as in Schedule 9 unless the
                  context otherwise requires; and

         (v)      headings and captions are provided for reference only and
                  shall not be considered as part of the Plan.

2.       TIME OF GRANT OF OPTIONS



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<PAGE>

         At any time Corresponding Options are granted the Committee may grant
         any Eligible Employee an Option pursuant to Rule 4.1 below.

3.       CONDITIONS ON THE GRANT OF OPTIONS

3.1      The grant of every Option to any Eligible Employee pursuant to Rule 4.1
         below shall be conditional on that Eligible Employee executing a valid
         election in the form envisaged in Paragraph 3 (B)(1) of Schedule 1 to
         the Social Security Contribution and Benefits Act 1992 no later than 30
         days after the Date of Grant.

3.2      On the failure of the Eligible Employee to execute an election within
         the time limit required by Rule 3.1 above, the Option shall for all
         purposes be taken never to have been granted.

4.       GRANT OF OPTION

4.1      The Committee may grant to any Eligible Employee within six months of
         the completion of the Transaction an Option over such number of Shares
         and at such Exercise Price as it determines. At the time of such grant
         the Committee shall also determine the Maturity Date of each Option,
         and the rate at which the Exercise Number shall accrue, and these shall
         be notified to each Option Holder by letter as soon as reasonably
         practicable following the Date of Grant.

4.2      Where the circumstances noted in Rule 7 apply New Options may be
         granted in consideration for the release of Options previously granted
         under this Plan. Such New Options are deemed to be equivalent to the
         old Options and to have been granted within the terms of this Plan.

4.3      No Option may be transferred, assigned or charged and any purported
         transfer, assignment or charge shall be void ab initio. Each Option
         Certificate shall carry a statement to this effect. For the avoidance
         of doubt, this Rule 4.3 shall not prevent the Option of a deceased
         Option Holder being exercised by his personal representative(s) within
         the terms of these Rules.

4.4      Options shall be granted by deed and as soon as possible after Options
         have been granted the Administrator shall issue an Option Certificate
         specifying the Date of Grant, the number of Shares subject to Option,
         the Exercise Price and the Maturity Date.



                                       7
<PAGE>



5.       LIMITATIONS ON GRANT

         The Committee may determine a limit on the number of Shares which are
         to be available in respect of Options granted under this Plan.

6.       EXERCISE OF OPTIONS

6.1      Subject to each of the succeeding sections of this Rule 6 and Rule 9
         any Subsisting Option may be exercised by the Option Holder or, if
         deceased, by his personal representatives in whole or in part at the
         time of or at any time following the occurrence of the earliest of the
         following events:

         (i)    the Maturity Date;

         (ii)   the death of the Option Holder;

         (iii)  upon the Option Holder ceasing to be a director or employee of
                the Group where that cessation was by reason of Injury or
                Disability, Redundancy or Retirement;

         (iv)   an opportunity to exercise the Option pursuant to Rule 7;

         (v)    upon the Option Holder ceasing to be a Group Employee, where
                that cessation was by reason only that the Company has ceased to
                have Control of such company, or that the office or employment
                relates to a business or part of a business which is transferred
                to a person who is neither an associated company (within the
                meaning of section 416 of the Act) of the Company nor a company
                of which the Company has Control;

         (vi)   the relevant Maturity Date, where the Option Holder holds an
                office or employment in a company which is not a Group Company
                but which is:

                  (a)      an Associated Company of the Company; or

                  (b)      a company of which the Company has Control.

6.2      An Option shall lapse and become thereafter incapable of exercise on
         the earliest of the following events:



                                       8
<PAGE>

         (i)      except where the Option Holder has died, the expiry of six
                  months following the Maturity Date;

         (ii)     where the Option Holder died within six months following the
                  Maturity Date, the first anniversary of the Maturity Date;

         (iii)    where the Option Holder has died before the Maturity Date, the
                  first anniversary of his death;

         (iv)     unless the Option Holder has died, on the expiry of six months
                  after the Option has become exercisable by virtue of Paragraph
                  (iii) and (v) of Rule 6.1;

         (v)      save in the circumstances in Rule 6.1 (ii), (iii), (iv) and
                  (v) above, and subject to Rule 6.5, immediately following the
                  Option Holder ceasing to be a Group Employee;

         (vi)     the expiry of six months after the Option has first become
                  exercisable in accordance with Rule 7; and

         (vii)    the Option Holder being adjudicated bankrupt.

6.4      If an Option Holder continues to be employed by a Group Company after
         the date on which he reaches the Specified Age he may exercise any
         Subsisting Option within six months following that date.

6.5      No person shall be treated for the purposes of this Rule 6 as ceasing
         to be a Group Employee until he is no longer a director or employee of
         the Company, any Associated Company or a company of which the Company
         has Control.

7.       TAKE-OVERS, RECONSTRUCTIONS AND LIQUIDATIONS

7.1      If any person obtains Control of the Company as a result of making:

         (i)      a general offer to acquire the whole of the issued share
                  capital of the Company (other than that which is already owned
                  by him) which is unconditional or which is made on a condition
                  such that if it is satisfied the person making the offer will
                  have Control of the Company; or



                                       9
<PAGE>

         (ii)     a general offer to acquire all the shares (other than shares
                  which are already owned by him) in the Company which are of
                  the same class as Shares subject to a Subsisting Option

         then the Committee shall notify all Option Holders as soon as is
         practicable of the offer in accordance with Rule 10.4. Any Subsisting
         Option may be exercised from the date of the receipt of that
         notification up to the expiry of a period ending six months from the
         time when the person making the offer has obtained Control of the
         Company and any condition subject to which the offer is made has been
         satisfied.

7.2      If as a result of the events specified in Rule 7.1 an Acquiring Company
         has obtained Control of the Company, the Option Holder may, if the
         Acquiring Company so agrees, release any Subsisting Option he holds in
         consideration for the grant of a New Option.

         A New Option issued in consideration of the release of an Option shall
         be evidenced by an Option Certificate which shall import the relevant
         provisions of these Rules.

         A New Option shall, for all other purposes of this Plan, be treated as
         having been acquired at the same time as the corresponding released
         Option and the definition of Date of Grant shall be construed
         accordingly.

7.3      If the Company passes a resolution for voluntary winding up, any
         Subsisting Option may be exercised within 6 months of the passing of
         the resolution.

7.4      The periods of exercisability under Rule 6.1(iv) and the date of lapse
         under Rule 6.2 (vi) are those of whichever of the pre-conditions of
         Rules 7.1 or 7.3 are first achieved. The subsequent achievement of any
         other pre-conditions will not cause a period of exercisability to begin
         nor a date of lapse to arise.

7.5      For the purpose of this Rule 7 other than Rule 7.2 a person shall be
         deemed to have obtained Control of a Company if he and others acting in
         concert with him have together obtained Control of it.

7.6      The exercise of an Option pursuant to the preceding provisions of this
         Rule 7 shall be subject to the provisions of Rule 9.

7.7      A New Option shall not be exercisable by virtue of the event pursuant
         to which it was granted.



                                       10
<PAGE>

8.       VARIATION OF SHARE CAPITAL

8.1      In the event of any variation of the share capital of the Company,
         including, but without prejudice to the generality of the preceding
         words, any capitalisation or rights issue or any consolidation,
         sub-division or reduction of capital by the Company, the number and
         nominal amount of Shares subject to any Option and the Exercise Price
         may be adjusted (including retrospective adjustments) by the Committee
         in such manner as is fair and reasonable provided that:

         (i)      the aggregate amount payable on the exercise of an Option in
                  full is neither materially changed nor increased; and

         (ii)     the Exercise Price for a Share subject to an Option to
                  Subscribe is not reduced below its nominal value unless (and
                  to the extent that) the Company is authorised to capitalise
                  from its undistributed profits or reserves upon the exercise
                  of such Option an amount equal to the difference between the
                  aggregate Exercise Price and the aggregate nominal value of
                  the Shares to be issued upon such exercise and to apply such
                  sum in paying up the difference.

         Such variation shall be deemed to be effective from the record date at
         which the respective variation applied to other shares of the same
         class as the Shares. Any Options exercised within that period shall be
         treated as exercised with the benefit of the variation confirmed by the
         Auditors.

8.3      The Administrator shall take such steps as he considers necessary to
         notify Option Holders of any adjustment made under Rule 8.1 and may
         call in, cancel, endorse, issue or reissue any Option Certificate
         consequent upon such adjustment.

9.       MANNER OF EXERCISE OF OPTIONS

9.1      An Option shall be exercised by the Option Holder, or as the case may
         be by his personal representatives, delivering a notice in writing to
         the Treasurer of the Company, detailing the number of Shares, not to
         exceed the Exercise Number, in respect of which he wishes to exercise
         the Option accompanied by the appropriate payment or authority to the
         Company to arrange the sale of such number of Shares as is necessary to
         satisfy the Option and the relevant Option Certificate and shall be
         effective on the date of its receipt by the Treasurer of the Company.

9.2      The number of Shares specified in the notice of exercise given in
         accordance with Rule 9.1 shall be allotted and issued to the Option
         Holder or at his direction (if such Option Holder shall have



                                       11
<PAGE>

         given notice that he wishes to sell some or all of the Shares so
         acquired) immediately following such acquisition within 30 days of the
         date of exercise and the Company shall arrange for the delivery of a
         definitive share certificate in respect thereof or, as the case may be,
         the appropriate changes to the books of the Company to reflect such
         allotment and issue of Shares. Save for any rights determined by
         reference to a record date preceding the date of allotment or transfer,
         such Shares shall rank pari passu with the other Shares of the same
         class in issue at the date of allotment or transfer.

9.3      When an Option is exercised only in part, it shall lapse to the extent
         of the unexercised balance.

9.4      If an Option is exercised and the Option Holder is liable to tax,
         duties or other amounts on such exercise and his employer or former
         employer being a Group Company is liable to make a payment to the
         appropriate authorities on account of that liability the Option Holder
         shall grant to the Company the irrevocable authority, as agent of the
         Option Holder and on his behalf, to sell or procure the sale of
         sufficient of the Shares subject to such Option so that the net
         proceeds payable to the employer or former employer are so far as
         possible equal to but not less than the amount payable to the
         appropriate authorities and the Company shall account to the Option
         Holder for any balance.

         No Shares shall be allotted to the Option Holder until the employer or
         former employer has received payment. This Rule 9.4 shall not apply if
         the Option Holder makes alternative arrangements to the satisfaction of
         his employer or former employer and the Company is informed by the
         employer or former employer that the arrangements are satisfactory or
         the Option Holder pays to the Company, as applicable, in Pounds
         Sterling, (whether by cheque or by banker's draft) the amount necessary
         to satisfy such liabilities.

9.5      If an Option is exercised then the Option Holder shall grant and shall
         be deemed to have granted to the Company the irrevocable authority, as
         agent of the Option Holder and on his behalf, to sell or procure the
         sale of sufficient of the Shares subject to such Option so that the net
         proceeds payable to the Group Company are so far as possible equal to
         but not less than the amount of the secondary NIC which the Option
         Holder is liable for and the Company shall account to the Option Holder
         for any balance.

         No shares shall be allotted to the Option Holders until the Group
         Company has received payment. This Rule 9.5 shall not apply if the
         Option Holder makes alternative arrangements to the satisfaction of his
         employer or former employer and the Company is informed by that Group
         Company that the arrangements are satisfactory.



                                       12
<PAGE>

10.      ADMINISTRATION AND AMENDMENT

10.1     The Plan shall be administered by the Committee in conjunction with the
         Administrator and the Committee's decision on all disputes shall be
         final save where the Rules require the concurrence of the Auditors.

10.2     The Board may from time to time amend these Rules provided that:

         (i)      no amendment may materially affect an Option Holder as regards
                  an Option granted prior to the amendment being made unless 75%
                  of such Option Holders consent in writing to such amendment;

         (ii)     no amendment may be made which would make the terms on which
                  Options may be granted materially more generous or would
                  increase the limits specified in Rule 5 without the prior
                  approval of the Board;

         (iii)    no amendment may be made to the advantage of participants
                  without the prior approval of the Board (except for minor
                  amendments to benefit the administration of the Plan or to
                  take account of a change in legislation and amendments to
                  obtain or maintain favourable tax, exchange control or
                  regulatory treatment for participants in the Plan, the Company
                  or for Group Companies).

10.3     The cost of establishing and operating the Plan shall be borne by the
         Group Companies in such proportions as the Board shall determine.

10.4     Any notice or other communication under or in connection with the Plan
         may be given by the Company either personally or by post, and to the
         Company either personally or by post for the attention of: Corporate
         Treasury, Ceridian Corporation, 3311 East, Old Shakopee Road,
         Minneapolis, Minnesota 55425; items sent by airmail post shall be
         pre-paid and shall be deemed to have been received 7 days after posting
         and items sent by pre-paid Federal Express or similar shall be deemed
         to have been received 5 days after posting.

10.5     The Company shall at all times keep available sufficient authorised and
         unissued Shares to satisfy the exercise to the full extent of all
         Subsisting Options, taking account of any other obligations of the
         Company to issue unissued shares of the same class as Shares.



                                       13
<PAGE>

11.      COMPLIANCE WITH LAWS AND REGULATIONS

11.1     The exercise of any Subsisting Option and the issuance or transfer of
         Shares pursuant to Rule 9 shall be subject to compliance by the Company
         and by the Option Holder with all applicable requirements of law
         relating thereto and with all applicable regulations of any stock
         exchange on which the Shares of the Company may be listed at the time
         of such exercise by the Option Holder.

11.2     Prior to exercise of an Option, the Company may request the Option
         Holder to execute and deliver to the Company such representations in
         writing in order that the Company and the Option Holder comply with the
         applicable requirements of federal and state securities law.

12.      LOSS OF OFFICE OR EMPLOYMENT

         The rights and obligations of any individual under the terms of his
         office or employment with any Group Company shall not be affected by
         his participation in the Plan or any right which he may have to
         participate therein, and an individual who participates therein shall
         waive any and all rights to compensation or damages in consequence of
         the termination of his office or employment for any reason whatsoever
         insofar as those rights arise or may arise from his ceasing to have
         rights under or be entitled to exercise any Option under the Plan as a
         result of such termination.




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