CARDINAL HEALTH, INC. 2007 NONEMPLOYEE DIRECTORS EQUITY INCENTIVE PLAN

Exhibit 10.4

CARDINAL HEALTH, INC.

2007 NONEMPLOYEE DIRECTORS EQUITY INCENTIVE PLAN

SECTION 1 | PURPOSE

The purpose of the Cardinal Health, Inc. 2007 Nonemployee Directors Equity Incentive Plan (the “Plan”) is to assist Cardinal Health, Inc. (the “Company”) in attracting and retaining qualified members of its Board of Directors (the “Board”). The Plan provides for equity ownership opportunities to directors in order to encourage and enable them to participate in the Company’s future prosperity and growth and to match the interests of directors with those of shareholders.

These objectives will be promoted through the granting to Nonemployee Directors (defined below) of equity-based awards (“awards”). The types of awards that may be granted under the Plan are options (“Stock Options”) to purchase Shares (defined below) and grants of Shares or Share Units subject to Section 6 (“Restricted Shares” or “Restricted Share Units”).

SECTION 2 | ADMINISTRATION

The Plan shall be administered by the Human Resources and Compensation Committee (the “Committee”) of the Board, which shall have the power and authority to grant Stock Options, Restricted Shares and Restricted Share Units to members of the Board who do not serve as employees of the Company (“Nonemployee Directors”). In particular, the Committee shall have the authority to: (i) select Nonemployee Directors as recipients of awards; (ii) determine the number and type of awards to be granted; (iii) determine the terms and conditions, not inconsistent with the terms hereof, of any award; (iv) adopt, alter and repeal such administrative rules, guidelines and practices governing the Plan as it shall, from time to time, deem advisable; (v) interpret the Plan and any award granted and any agreements relating thereto; and (vi) take any other actions the Committee considers appropriate in connection with, and otherwise supervise the administration of, the Plan. All decisions made by the Committee pursuant to the provisions hereof shall be made in the Committee’s sole discretion and shall be final and binding on all persons.

SECTION 3 | ELIGIBILITY

Only Nonemployee Directors are eligible to receive awards under the Plan. Members of the Committee who are Nonemployee Directors are eligible to receive awards.

SECTION 4 | SHARES SUBJECT TO PLAN

The total number of the common shares of the Company, without par value (“Shares”), reserved and available for issuance pursuant to awards hereunder (“Available Shares”) shall be 750,000. The Available Shares may consist of authorized but unissued Shares or treasury Shares, including Shares purchased on the open market. For purposes of this Section 4, the aggregate number of Available Shares under the Plan at any time shall not be reduced by Shares subject to awards that have been cancelled, expired or forfeited. Shares granted under the Plan shall not be counted as used unless and until they are

actually issued and delivered to a Nonemployee Director. Notwithstanding anything to the contrary contained herein, the following Shares shall not become available for awards under the Plan: (i) Shares subject to awards that have been retained by the Company in payment or satisfaction of the exercise price of an award, or (ii) Shares that have been delivered (either actually or constructively by attestation) to the Company in payment or satisfaction of the exercise price of an award.

In the event of (i) a stock dividend, stock split, reverse stock split, share combination, or recapitalization or similar event affecting the capital structure of the Company (each, a “Share Change”), or (ii) a merger, consolidation, acquisition of property or shares, separation, spinoff, reorganization, stock rights offering, liquidation, disaffiliation from the Company of a Subsidiary or division (“Disaffiliation”), or similar event affecting the Company or any of its subsidiaries (each, an “Organic Change”), the Committee shall make such substitutions or adjustments as it deems appropriate and equitable to the aggregate number of Shares reserved for issuance under the Plan, the number and exercise price of Shares subject to outstanding Stock Options, the purchase price, if any, for Restricted Shares or Restricted Share Units, and the number of Shares subject to a Restricted Share or Restricted Share Unit award. In the case of Organic Changes, such adjustments may include, without limitation, (x) the cancellation of outstanding awards in exchange for payments of cash, property or a combination thereof having an aggregate value equal to the value of such awards, as determined by the Committee in its sole discretion (it being understood that in the case of an Organic Change with respect to which shareholders receive consideration other than publicly traded equity securities of the ultimate surviving entity, any such determination by the Administrator that the value of a Stock Option shall for this purpose be deemed to equal the excess, if any, of the value of the consideration being paid for each Share pursuant to such Organic Change over the exercise price of such Stock Option shall conclusively be deemed valid), (y) the substitution of other property (including, without limitation, cash or other securities of the Company and securities of entities other than the Company) for the Shares subject to outstanding awards, and (z) in connection with any Disaffiliation, arranging for the assumption of awards, or replacement of awards with new awards based on other property or other securities (including, without limitation, other securities of the Company and securities of entities other than the Company), by the affected subsidiary, affiliate or division or by the entity that controls such subsidiary, affiliate or division following such Disaffiliation (as well as any corresponding adjustments to awards that remain based upon Company securities).

SECTION 5 | STOCK OPTIONS

Any Stock Options granted under the Plan shall be in such form as the Committee may from time to time approve, and the provisions of Stock Option awards need not be the same with respect to each optionee. Stock Options granted under the Plan will be options that are not intended to qualify as incentive stock options under Section 422 of the Internal Revenue Code of 1986, as amended (the “Code”).

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Stock Options granted under the Plan shall be subject to the following terms and conditions and shall contain such additional terms and conditions not inconsistent with the terms of the Plan as the Committee deems appropriate.

(a) Eligibility and Grant. All Stock Options shall be evidenced by a written agreement, which shall be dated as of the date on which a Stock Option is granted, signed (electronically or otherwise) by an officer of the Company authorized by the Committee, and which the Committee may also require the Nonemployee Director to sign (electronically or otherwise). Such agreement shall describe the Stock Options and state that such Stock Options are subject to the Plan.

(b) Exercise of Stock Options. Stock Options shall become exercisable at such time or times and subject to such terms and conditions (including, without limitation, installment or cliff exercise provisions) as shall be determined by the Committee. The Committee shall have the authority, in its discretion, to accelerate the time at which a Stock Option shall be exercisable whenever it may determine that such action is appropriate by reason of changes in applicable tax or other law or other changes in circumstances occurring after the award of such Stock Option.

(c) Exercise Price. The exercise price per Share purchasable under a Stock Option shall be determined by the Committee, except that the per Share exercise price shall be no less than 100% of the fair market value per Share as of the day the Stock Option is granted. Unless otherwise determined by the Committee, the fair market value shall be the closing price for the Shares reported on a consolidated basis on the New York Stock Exchange on the relevant date, or if there were no sales on such date, the closing price on the nearest preceding date on which sales occurred.

(d) No Stock Option Repricing. Subject to Section 4 of the Plan, the exercise price of any Stock Option may not be reduced without shareholder approval.

(e) Maximum Term. Each Stock Option shall be exercisable for 10 years from the date of grant or such shorter period of time as may be provided in the Stock Option agreement.

(f) Transferability of Stock Options. Except as otherwise provided hereunder, Stock Options shall be transferable by the Nonemployee Director only with prior approval of the Committee. Any attempted transfer without Committee approval shall be null and void. Unless Committee approval of the transfer shall have been obtained, all Stock Options shall be exercisable during the Nonemployee Director’s lifetime only by the Nonemployee Director or the Nonemployee Director’s legal representative. Without limiting the generality of the foregoing, the Committee may, in the manner established by the Committee, provide for the irrevocable transfer, without payment of consideration, of any Stock Option by a Nonemployee Director to a member of the Nonemployee Director’s family or to a family entity. In such case, the Stock Option shall be exercisable only by such transferee. For purposes of this provision: (i) a Nonemployee Director’s “family” shall include the Nonemployee Director’s child, stepchild, grandchild, parent, stepparent, grandparent, spouse, former spouse, sibling, niece,

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nephew, mother-in-law, father-in-law, son-in-law, daughter-in-law, brother-in-law, or sister-in-law, including through adoptive relationships, and any person sharing the Nonemployee Director’s household (other than a tenant or employee); and (ii) a “family entity” shall include a trust in which the foregoing persons have more than fifty percent (50%) of the beneficial interest, a foundation in which the foregoing persons (or the Nonemployee Director) control the management of assets, and any other entity in which the foregoing persons (or the Nonemployee Director) own more than fifty percent (50%) of the voting interests; and (iii) neither a transfer under a domestic relations order in settlement of marital property rights nor a transfer to an entity in which more than fifty percent (50%) of the voting interests are owned by family members (or the Nonemployee Director) in exchange for an interest in that entity shall be considered to be a transfer for consideration.

(g) Method of Exercise. Stock Options may be exercised in whole or in part by giving written notice of exercise to the Company specifying the number of Shares to be purchased. No Shares shall be transferred until full payment therefor has been made. Payment for exercise of a Stock Option may be made (i) in cash, (ii) by delivery of Shares already owned by the Nonemployee Director, (iii) by attestation of ownership of such already-owned Shares, (iv) to the extent permitted by law, by delivery of cash from the proceeds of a sale through a bank or broker on a date satisfactory to the Company of some or all of the shares to which such exercise relates, or (v) by any combination of the foregoing.

(h) Termination of Option. Except as otherwise provided herein, unless otherwise determined by the Committee at or after grant or termination, if a Nonemployee Director ceases to be a member of the Board for any reason, then all Stock Options or any unexercised portion of such Stock Options which otherwise are exercisable shall remain exercisable until expiration of the original term of such Stock Options.

SECTION 6 | RESTRICTED SHARES AND RESTRICTED SHARE UNITS

Restricted Shares or Restricted Share Units may be granted to Nonemployee Directors alone or in addition to other awards granted under the Plan. For purposes of the Plan, “Restricted Shares” shall mean Shares issued to Nonemployee Directors subject to a “substantial risk of forfeiture” within the meaning of Section 83 of the Code and a prohibition on transfer, which may also be subject to such other restrictions as the Committee may impose, and “Restricted Share Units” shall mean a grant of a right to receive Shares in the future, with such units subject to a risk of forfeiture or other restrictions that will lapse at the end of a specified period or upon the achievement of performance or other objectives. Any Restricted Shares or Restricted Share Units granted under the Plan shall be subject to the following restrictions and conditions, and shall contain such additional terms and conditions in the applicable award agreement, not inconsistent with the terms of the Plan, as the Committee deems appropriate. The provisions of Restricted Share or Restricted Share Unit awards need not be the same with respect to each recipient.

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(a) Restricted Share and Restricted Share Unit Award Agreement. Each Restricted Share or Restricted Share Unit grant shall be evidenced by an agreement executed on behalf of the Company by an officer designated by the Committee. Such Restricted Share Award Agreement or Restricted Share Unit Award Agreement shall describe the Restricted Shares or Restricted Share Units and state that such Restricted Shares or Restricted Share Units are subject to the Plan and shall contain such other terms and provisions, consistent with the Plan, as the Committee may approve. At the time any Restricted Shares or Restricted Share Units are awarded, the Committee may determine that such Restricted Shares or Restricted Share Units shall, after vesting, be further restricted as to transferability or be subject to repurchase by the Company upon occurrence of certain events determined by the Committee, in its sole discretion, and specified in the applicable Restricted Share Award Agreement or Restricted Share Unit Award Agreement. Awards of Restricted Shares or Restricted Share Units must be accepted by a grantee thereof within the period of time specified by the Committee at grant, if any, by executing the Restricted Share Award Agreement or Restricted Share Unit Award Agreement and paying the purchase price, if any, of such award. The prospective recipient of a Restricted Share or Restricted Share Unit award shall not have any rights with respect to such award, unless such recipient executes an agreement evidencing the award and delivers a fully executed copy thereof to the Company, and otherwise complies with the applicable terms and conditions of such award.

(b) Share Restrictions. Subject to the provisions of the Plan and the applicable Restricted Share Award Agreement or Restricted Share Unit Award Agreement, during a period set by the Committee commencing with the date of such award and ending on such date as determined by the Committee at grant (the “Restriction Period”), the Nonemployee Director shall not be permitted to sell, transfer, pledge, assign or otherwise encumber Restricted Shares or Restricted Share Units awarded under the Plan. No Restriction Period shall be less than one year, except in the event of a change of control of the Company or upon the death, disability or retirement of a Nonemployee Director; provided that the period of time from one annual meeting of shareholders to the next shall be considered one year whether or not it includes 365 calendar days. Unless otherwise determined by the Committee at or after grant or termination of service, if a Nonemployee Director’s service to the Company terminates during the Restriction Period, all Restricted Shares or Restricted Share Units held by such Nonemployee Director still subject to restriction shall be forfeited by the Nonemployee Director.

(c) Stock Certificate and Legends. Each Nonemployee Director receiving a Restricted Share award shall be issued a stock certificate or book-entry account on the Company’s transfer agent’s records in respect of such Restricted Shares. Such certificate or book entry shall be registered in the name of the Nonemployee Director. The Committee may require that any stock certificates evidencing such Restricted Shares be held in custody by the Company until the restrictions thereon shall have lapsed, and that, as a condition of any Restricted Shares award, the Nonemployee Director shall have delivered a stock power, endorsed in blank, relating to the Restricted Shares covered by such award.

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(d) Shareholder Rights. Except as provided in this Section 6, the Nonemployee Director shall have, with respect to the Restricted Shares covered by any award, all of the rights of a shareholder of the Company, including the right to vote the Shares, and the right to receive any dividends or other distributions, with respect to the Shares, but subject, however, to those restrictions placed on such Restricted Shares pursuant to the Plan and as specified by the Committee in the Restricted Share Award Agreement. A Nonemployee Director shall not have any rights as a shareholder of the Company with respect to the Restricted Share Units unless and until the Shares underlying such Restricted Share Units have been issued or transferred and registered in the name of such Nonemployee Director; provided that a Restricted Share Unit Award Agreement may provide for dividend equivalents to be paid with respect to outstanding Restricted Share Units.

(e) Expiration of Restriction Period. If and when the Restriction Period expires without a prior forfeiture of the Restricted Shares subject to such Restriction Period, unrestricted certificates for such shares shall be delivered to the Nonemployee Director. Unrestricted shares subject to vested Restricted Share Units shall be delivered to the Nonemployee Director pursuant to the terms of the applicable Restricted Share Unit Award Agreement (which may, subject to Section 10(f), provide for deferral of such delivery to a date that is later than the date of vesting).

SECTION 7 | CHANGE OF CONTROL

(a) In the event of a Change of Control (as defined below), unless otherwise determined by the Committee at the time of grant and subject to Section 7(c), the following provisions shall apply:

(i) On the date that such Change of Control occurs, any or all Stock Options not previously exercisable and vested shall become fully exercisable and vested, and all outstanding Stock Options shall remain exercisable for the remainder of their original term.

(ii) On the date that such Change of Control occurs, the restrictions applicable to any or all Restricted Shares and Restricted Share Units shall lapse and such awards shall be fully vested.

(b) For purposes of the Plan, “Change of Control” means any of the following:

(i) the acquisition by any individual, entity or group (within the meaning of Section 13(d)(3) or 14(d)(2) of the Exchange Act) (a “Person”) of beneficial ownership (within the meaning of Rule 13d-3 promulgated under the Securities Exchange Act of 1934, as amended (the “Exchange Act”)) of twenty-five percent (25%) or more of either (x) the then-outstanding Shares of the Company (the “Outstanding Company Common Shares”), or (y) the combined voting power of the then-outstanding voting securities of the Company entitled to vote generally in the election of directors (the “Outstanding Company Voting Securities”); provided, however, that for purposes of this subsection (i), the following

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acquisitions shall not constitute a Change of Control: (A) any acquisition directly from the Company or any corporation controlled by the Company, (B) any acquisition by the Company or any corporation controlled by the Company, (C) any acquisition by any employee benefit plan (or related trust) sponsored or maintained by the Company or any corporation controlled by the Company, or (D) any acquisition by any corporation that is a Non-Control Acquisition (as defined in subsection (iii) of this Section 7(b)); or

(ii) individuals who, as of the effective date of the Plan, constitute the Board (the “Incumbent Board”) cease for any reason to constitute at least a majority of the Board; provided, however, that any individual becoming a director subsequent to the effective date whose election, or nomination for election by the Company’s shareholders, was approved by a vote of at least a majority of the directors then comprising the Incumbent Board shall be considered as though such individual were a member of the Incumbent Board, but excluding, for this purpose, any such individual whose initial assumption of office occurs as a result of an actual or threatened election contest with respect to the election or removal of directors or other actual or threatened solicitation of proxies or consents by or on behalf of a Person other than the Board; or

(iii) consummation of a reorganization, merger or consolidation or sale or other disposition of all or substantially all of the assets of the Company or the acquisition by the Company of assets or shares of another corporation (a “Business Combination”), unless such Business Combination is a Non-Control Acquisition. A “Non-Control Acquisition” shall mean a Business Combination where: (x) all or substantially all of the individuals and entities who were the beneficial owners, respectively, of the Outstanding Company Common Shares and Outstanding Company Voting Securities immediately prior to such Business Combination beneficially own, directly or indirectly, more than fifty percent (50%) of, respectively, the then-outstanding shares of common stock and the combined voting power of the then-outstanding voting securities entitled to vote generally in the election of directors, as the case may be, of the corporation resulting from such Business Combination (including, without limitation, a corporation which as a result of such transaction owns the Company or all or substantially all of the Company’s assets either directly or through one or more subsidiaries) in substantially the same proportions as their ownership immediately prior to such Business Combination of the Outstanding Company Common Shares and Outstanding Company Voting Securities, as the case may be, (y) no Person (excluding any employee benefit plan (or related trust) of the Company or such corporation resulting from such Business Combination) beneficially owns, directly or indirectly, twenty-five percent (25%) or more of, respectively, the then-outstanding shares of common stock of the corporation resulting from such Business Combination or the combined voting power of the then-outstanding voting securities of such corporation except to the extent that such ownership existed prior to the Business Combination (including any ownership that existed in the Company or the company being acquired, if any), and (z) at least a majority of the members of the board of directors of the corporation resulting from such

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Business Combination were members of the Incumbent Board at the time of the execution of the initial agreement, or of the action of the Board, providing for such Business Combination; or

(iv) approval by the shareholders of the Company of a complete liquidation or dissolution of the Company.

SECTION 8 | AMENDMENTS AND TERMINATION

(a) The Board may amend, alter or discontinue the Plan; provided, however, that no amendment, alteration or discontinuation shall be made (i) which would impair the rights of an optionee, participant or permitted transferee under any award theretofore granted without the optionee’s, participant’s or transferee’s consent, except for amendments made to cause the Plan or such award to comply with applicable law, stock exchange rules or accounting rules; or (ii) without the approval of the Company’s shareholders to the extent such approval is required by applicable law, regulation or stock exchange rule.

In addition, without limiting the foregoing, unless approved by the Company’s shareholders and subject to Section 4 of the Plan, no such amendment or alteration shall be made that would: (i) increase the maximum aggregate number of Available Shares under the Plan; (ii) reduce the minimum exercise price for Stock Options granted under the Plan; or (iii) reduce the exercise price of outstanding Stock Options.

Subject to the above provisions, the Board shall have authority to amend the Plan in any respect, including, without limitation, to take into account changes in applicable tax and securities laws and accounting rules, as well as other developments.

SECTION 9 | UNFUNDED STATUS OF PLAN

The Plan is intended to constitute an “unfunded” plan for incentive and deferred compensation. With respect to any payments or deliveries of Shares not yet made by the Company to a participant, optionee or transferee, nothing contained herein shall give any such participant, optionee or transferee any rights that are greater than those of a general creditor of the Company. The Committee may authorize the creation of trusts or other arrangements to meet the obligations created under the Plan to deliver Shares or payments hereunder consistent with the foregoing.

SECTION 10 | GENERAL PROVISIONS

(a) Additional Awards Permitted. Nothing contained in the Plan shall prevent the Company from adopting other or additional compensation arrangements for its employees, consultants or Nonemployee Directors.

(b) Additional Restrictions Permitted. The Committee may specify on the date an award is granted that part or all of the Shares that are (i) to be issued or transferred by the Company upon the exercise of Stock Options or upon the termination of the Restriction Period applicable to Restricted Share Units or (ii) Restricted Shares no longer subject to

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the substantial risk of forfeiture and restrictions on transfer referred to in Section 6 of the Plan, will be subject to further restrictions on transfer.

(c) Beneficiaries. The Committee may establish such procedures as it deems appropriate for a Nonemployee Director to designate a beneficiary to whom any amounts or benefits payable in the event of the Nonemployee Director’s death are to be paid.

(d) Laws Governing. The Plan and all awards made and action taken thereunder shall be governed by and construed in accordance with the internal substantive laws, but not the choice of law rules, of the State of Ohio, except to the extent superseded by federal law.

(e) Government Regulation. Notwithstanding any provisions of the Plan or any agreement made pursuant to the Plan, the Company’s obligations under the Plan and such agreement shall be subject to all applicable laws, rules and regulations and to such approvals as may be required by any governmental or regulatory agencies.

(f) Section 409A. It is the intention of the Company that no award shall be “deferred compensation” subject to Section 409A of the Code (“Section 409A”), unless and to the extent that the Committee specifically determines otherwise, and the Plan and the terms and conditions of all awards shall be interpreted accordingly. The terms and conditions governing any awards that the Committee determines will be subject to Section 409A, including any rules for elective or mandatory deferral of the delivery of cash or Shares pursuant thereto, shall be set forth in the applicable award agreement, and shall comply in all respects with Section 409A.

SECTION 11 | EFFECTIVE DATE

The Plan shall become effective on the date when it is approved by the shareholders of the Company. No new awards shall be granted under the Cardinal Health, Inc. Amended and Restated Outside Directors Equity Incentive Plan after this Plan becomes effective.

SECTION 12 | TERM OF PLAN

No award shall be granted pursuant to the Plan more than 10 years after the date on which the Plan is first approved by the shareholders of the Company unless it is terminated earlier under Section 8 of the Plan, but awards granted prior to such date may extend beyond that date.

SECTION 13 | INDEMNIFICATION

No member of the Board or the Committee shall be liable for any action or determination made in good faith with respect to the Plan or any award granted under the Plan. Each person who is or shall have been a member of the Committee or of the Board shall be indemnified and held harmless by the Company against and from any loss, cost, liability or expense that may be imposed upon or reasonably incurred by him or her in connection with or resulting from any claim, action, suit or proceeding to which he may be a party or in which he may be involved by reason of any action taken or failure to act under or in

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connection with the Plan or any award granted under the Plan and against and from any and all amounts paid by him or her in settlement thereof, with the Company’s approval, or paid by him or her, except a judgment based upon a finding of bad faith, provided he or she shall give the Company an opportunity, at its own expense, to handle and defend the same before he or she undertakes to handle and defend it on his or her own behalf. The foregoing right of indemnification shall not be exclusive of any other rights of indemnification to which such person may be entitled under the Company’s Articles of Incorporation or Code of Regulations, contained in any indemnification agreements, as a matter of law, or otherwise, or any power that the Company may have to indemnify him or her or hold him or her harmless.

SECTION 14 | SAVINGS CLAUSE

In case any one or more of the provisions of the Plan shall be held invalid, illegal or unenforceable in any respect, the validity, legality and enforceability of the remaining provisions shall not in any way be affected or impaired thereby and the invalid, illegal or unenforceable provision shall be deemed null and void; however, to the extent permissible by law, any provision which could be deemed null and void shall first be construed, interpreted or revised retroactively to permit the Plan to be construed so as to foster the intent of the Plan.

SECTION 15 | AWARDS TO NONEMPLOYEE DIRECTORS OUTSIDE OF UNITED STATES

The Committee may modify the terms of any award under the Plan granted to a Nonemployee Director who, at the time of grant or during the term of the award, is resident or employed outside of the United States in any manner deemed by the Committee to be necessary or appropriate in order to accommodate differences in local law, regulation, tax policy or custom, or so that the value and other benefits of the award to the Nonemployee Director, as affected by foreign tax laws and other restrictions applicable as a result of the Nonemployee Director’s residence or employment abroad, will be comparable to the value of such an award to a Nonemployee Director who is resident or employed in the United States. Moreover, the Committee may approve such supplements to, or amendments, restatements or alternative versions of, the Plan as it may consider necessary or appropriate for such purposes without thereby affecting the terms of the Plan as in effect for any other purpose; provided that no such supplements, amendments, restatements or alternative versions shall include any provisions that are inconsistent with the terms of the Plan, as then in effect, unless the Plan could have been amended to eliminate such inconsistency without further approval of the shareholders of the Company.

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