Exhibit 10.4

AMENDED AND RESTATED

1998 MOODY’S CORPORATION

NON-EMPLOYEE DIRECTORS’ STOCK INCENTIVE PLAN

(Adopted September 8, 2000; Amended and Restated as of December 11, 2012, October 20, 2015 and December 14, 2015)

1. Purpose of the Plan

The purpose of the Plan is to aid the Company in attracting, retaining and compensating non-employee directors and to enable them to increase their ownership of Shares. The Plan will be beneficial to the Company and its stockholders since it will allow non-employee directors of the Board to have a greater personal financial stake in the Company through the ownership of Shares, in addition to underscoring their common interest with stockholders in increasing the value of the Shares on a long-term basis.

2. Definitions

The following capitalized terms used in the Plan have the respective meanings set forth in this Section:

(a) Act: The Securities Exchange Act of 1934, as amended, or any successor thereto.

(b) Award: An Option, Share of Restricted Stock or Performance Share granted pursuant to the Plan.

(c) Beneficial Owner: As such term is defined in Rule 13d-3 under the Act (or any successor rule thereto).

(d) Board: The Board of Directors of the Company.

(e) Change in Control: The occurrence of a change in ownership of Moody’s Corporation, a change in the effective control of Moody’s Corporation, or a change in the ownership of a substantial portion of the assets of Moody’s Corporation. For this purpose, a change in the ownership of Moody’s Corporation occurs on the date that any one person, or more than one person acting as a group (as determined pursuant to the regulations under Section 409A), acquires ownership of stock of Moody’s Corporation that, together with stock held by such person or group, constitutes more than 50 percent of the total fair market value or total voting power of the stock of Moody’s Corporation. A change in effective control of Moody’s Corporation occurs on either of the following dates: (1) the date any one person, or more than one person acting as a group acquires (or has acquired during the 12-month period ending on the date of the most recent acquisition by such person or persons) ownership of stock of Moody’s Corporation possessing 50 percent or more of the total voting power of the stock of Moody’s Corporation, or (2) the date a majority of members of the Board is replaced during any 12-month period by directors whose appointment or election is not endorsed by a majority of the members of the Board before the date of the appointment or election. A change in the ownership of a substantial portion of the assets of Moody’s Corporation occurs on the date that any one person, or more than one person acting as a group, acquires (or has acquired during the 12-month period ending on the date of the most recent acquisition by such person or persons) assets from Moody’s Corporation that have a total gross fair market value (as determined pursuant to the regulations under Section 409A) equal to or more than 40 percent of the total gross fair market value of all of the assets of Moody’s Corporation immediately before such acquisition or acquisitions.

(f) Code: The Internal Revenue Code of 1986 and the regulations thereunder, as amended from time to time.

(g) Committee: The Governance and Compensation Committee of the Board, or any successor thereto or other committee designated by the Board to assume the obligations of the Committee hereunder.

(h) Company: Moody’s Corporation.

(i) Disability: Inability to continue to serve as a non-employee director due to a medically determinable physical or mental impairment which constitutes a permanent and total disability, as determined by the Committee (excluding any member thereof whose own Disability is at issue in a given case) based upon such evidence as it deems necessary and appropriate.

(j) Effective Date: The date on which the Plan takes effect, as defined pursuant to Section 14 of the Plan.

(k) Fair Market Value: On a given date, the arithmetic mean of the high and low prices of the Shares as reported on such date on the Composite Tape of the principal national securities exchange on which such Shares are listed or admitted to trading, or, if no Composite Tape exists for such national securities exchange on such date, then on the principal national securities exchange on which such Shares are listed or admitted to trading, or, if the Shares are not listed or admitted on a national securities exchange, the arithmetic mean of the per Share closing bid price and per Share closing asked price on such date as quoted on the National Association of Securities Dealers Automated Quotation System (or such market in which such prices are regularly quoted), or, if there is no market on which the Shares are regularly quoted, the Fair Market Value shall be the value established by the Committee in good faith. If no sale of Shares shall have been reported on such Composite Tape or such national securities exchange on such date or quoted on the National Association of Securities Dealers Automated Quotation System on such date, then the immediately preceding date on which sales of the Shares have been so reported or quoted shall be used.

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(l) Option: A stock option granted pursuant to Section 6 of the Plan.

(m) Option Price: The purchase price per Share of an Option, as determined pursuant to Section 6(b) of the Plan.

(n) Participant: Any director of the Company who is not an employee of the Company or any Subsidiary of the Company as of the date that an Award is granted.

(o) Performance Period: The calendar year or such other period of at least 12 consecutive months as shall be designated by the Committee from time to time.

(p) Performance Share: A periodic bonus award, payable in unrestricted Shares, granted pursuant to Section 8(a) of the Plan.

(q) Person: As such term is used for purposes of Section 13(d) or 14(d) of the Act (or any successor section thereto).

(r) Plan: The 1998 Moody’s Corporation Non-Employee Directors’ Stock Incentive Plan, as amended and restated.

(s) Restricted Stock: A Share of restricted stock granted pursuant to Section 7 of the Plan.

(t) Retirement: Termination of service with the Company after such Participant has attained age 70, regardless of the length of such Participant’s service; or, with the prior written consent of the Committee (excluding any member thereof whose own Retirement is at issue in a given case), termination of service at an earlier age after the Participant has completed six or more years of service with the Company.

(u) Section 409A: Section 409A of the Code and applicable guidance issued thereunder.

(v) Service Period: The period of time designated by the Committee from time to time during which services must be rendered and at the end of which Restricted Stock grants shall vest.

(w) Shares: Shares of common stock, par value $0.01 per share, of the Company.

(x) Subsidiary: A subsidiary corporation, as defined in Section 424(f) of the Code (or any successor section thereto).

(y) Termination of Service: A Participant’s “separation from service” with the Company as determined pursuant to Section 409A.

3. Shares Subject to the Plan

The total number of Shares which may be issued under the Plan is 1,700,000 (subject to adjustment in accordance with the provisions of Section 9 hereof). The Shares may consist, in whole or in part, of unissued Shares or treasury Shares. The issuance of Awards shall reduce the total number of Shares available under the Plan. Shares which are subject to Awards which terminate or lapse may be granted again under the Plan.

4. Administration

The Plan shall be administered by the Committee, which may delegate its duties and powers in whole or in part to any subcommittee thereof consisting solely of at least two “non-employee directors” within the meaning of Rule 16b-3 under the Act (or any successor rule thereto); provided, however, that any action permitted to be taken by the Committee may be taken by the Board, in its discretion. The Committee is authorized to interpret the Plan, to establish, amend and rescind any rules and regulations relating to the Plan, and to make any other determinations that it deems necessary or desirable for the administration of the Plan. The Committee may correct any defect or omission or reconcile any inconsistency in the Plan in the manner and to the extent the Committee deems necessary or desirable. Any decision of the Committee in the interpretation and administration of the Plan, as described herein, shall lie within its sole and absolute discretion and shall be final, conclusive and binding on all parties concerned (including, but not limited to, Participants and their beneficiaries or successors).

5. Eligibility/Annual Limitation on Grants

All Participants shall be eligible to participate under this Plan. In no event shall the number of Shares subject to Awards granted to any Participant in a calendar year exceed the lesser of (a) 20,000 Shares and (b) Shares with a Fair Market Value of $400,000.

6. Terms and Conditions of Options

Options granted under the Plan shall be non-qualified stock options for federal income tax purposes, as evidenced by the related Option agreements, and shall be subject to the foregoing and the following terms and conditions and to such other terms and conditions, not inconsistent therewith, as the Committee shall determine:

(a) Grants. A Participant may receive, on such dates as determined by the Committee in its sole discretion, grants consisting of such number of Options as determined by the Committee in its sole discretion.

(b) Option Price. The Option Price per Share shall be determined by the Committee, but shall not be less than 100% of the Fair Market Value of the Shares on the date an Option is granted.

(c) Exercisability. Options granted under the Plan shall be exercisable at such time and upon such terms and conditions as may be determined by the Committee, but in no event shall an Option be exercisable more than ten years after the date it is granted.

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(d) Exercise of Options. Except as otherwise provided in the Plan or in a related Option agreement, an Option may be exercised for all, or from time to time any part, of the Shares for which it is then exercisable. For purposes of Section 6 of the Plan, the exercise date of an Option shall be the later of the date a notice of exercise is received by the Company and, if applicable, the date payment is received by the Company pursuant to clauses (i), (ii) or (iii) in the following sentence. The purchase price for the Shares as to which an Option is exercised shall be paid to the Company in full at the time of exercise at the election of the Participant (i) in cash, (ii) in Shares, having a Fair Market Value equal to the aggregate Option Price for the Shares being purchased and satisfying such other requirements as may be imposed by the Committee, (iii) partly in cash and partly in such Shares, or (iv) through the delivery of irrevocable instructions to a broker to deliver promptly to the Company an amount equal to the aggregate Option Price for the Shares being purchased. No Participant shall have any rights to dividends or other rights of a stockholder with respect to Shares subject to an Option until the occurrence of the exercise date (determined as set forth above) and, if applicable, the satisfaction of any other conditions imposed by the Committee pursuant to the Plan.

(e) Exercisability Upon Termination of Service by Death. Upon a Termination of Service by reason of death after the first anniversary of the date on which an Option is granted, the unexercised portion of such Option shall immediately vest in full and may thereafter be exercised during the shorter of the remaining term of the Option or five years after the date of death.

(f) Exercisability Upon Termination of Service by Disability or Retirement. Upon a Termination of Service by reason of Disability or Retirement after the first anniversary of the date on which an Option is granted, the unexercised portion of such Option may thereafter be exercised during the shorter of the remaining term of the Option or five years after the date of such Termination of Service; provided, however, that if a Participant dies within a period of five years after such Termination of Service, the unexercised portion of the Option shall immediately vest in full and may thereafter be exercised, during the shorter of the remaining term of the Option or the period that is the longer of five years after the date of such Termination of Service or one year after the date of death.

(g) Effect of Other Termination of Service. Upon a Termination of Service by reason of Disability or Retirement prior to the first anniversary of the date on which an Option is granted (as described above), then, a pro rata portion of such Option shall immediately vest in full and may be exercised thereafter, during the shorter of (A) the remaining term of such Option or (B) five years after the date of such Termination of Service, for a prorated number of Shares (rounded down to the nearest whole number of Shares), equal to (i) the number of Shares subject to such Option multiplied by (ii) a fraction the numerator of which is the number of days the Participant served on the Board subsequent to the date on which such Option was granted and the denominator of which is 365. The portion of such Option which is not so exercisable shall terminate as of the date of Disability or Retirement. Upon a Termination of Service for any other reason prior to the first anniversary of the date on which an Option is granted, such Option shall thereupon terminate. Upon a Termination of Service for any reason other than death, Disability or Retirement after the first anniversary of the date on which an Option is granted, the unexercised portion of such Option shall thereupon terminate.

(h) Nontransferability of Stock Options. Except as otherwise provided in this Section 6(h), an Option shall not be transferable by the optionee otherwise than by will or by the laws of descent and distribution and during the lifetime of an optionee an Option shall be exercisable only by the optionee. An Option exercisable after the death of an optionee or a transferee pursuant to the following sentence may be exercised by the legatees, personal representatives or distributees of the optionee or such transferee. The Committee may, in its discretion, authorize all or a portion of the Options previously granted or to be granted to an optionee to be on terms which permit irrevocable transfer for no consideration by such optionee to any child, stepchild, grandchild, parent, stepparent, grandparent, spouse, sibling, mother-in-law, father-in-law, son-in-law, daughter-in-law, brother-in-law, or sister-in-law, including adoptive relationships, of the optionee, trusts for the exclusive benefit of these persons, and any other entity owned solely by these persons (“Eligible Transferees”), provided that (x) the stock option agreement pursuant to which such Options are granted must be approved by the Committee, and must expressly provide for transferability in a manner consistent with this Section and (y) subsequent transfers of transferred Options shall be prohibited except those in accordance with the first sentence of this Section 6(h). The Committee may, in its discretion, amend the definition of Eligible Transferees to conform to the coverage rules of Form S-8 under the Securities Act of 1933 or any comparable Form from time to time in effect. Following transfer, any such Options shall continue to be subject to the same terms and conditions as were applicable immediately prior to transfer. The events of Termination of Service of Sections 6(e), 6(f) and 6(g) hereof shall continue to be applied with respect to the original optionee, following which the Options shall be exercisable by the transferee only to the extent, and for the periods specified, in Sections 6(e), 6(f) and 6(g). The Committee may delegate to a committee consisting of employees of the Company the authority to authorize transfers, establish terms and conditions upon which transfers may be made and establish classes of Options eligible to transfer Options, as well as to make other determinations with respect to Option transfers.

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7. Terms and Conditions of Restricted Stock

Restricted Stock granted under the Plan shall be subject to the foregoing and the following terms and conditions and to such other terms and conditions, not inconsistent therewith, as the Committee shall determine:

(a) Grants. A Participant may receive, on such dates as determined by the Committee in its sole discretion, grants consisting of such amounts of Restricted Stock as determined by the Committee in its sole discretion.

(b) Restrictions. Restricted Stock granted under the Plan may not be sold, transferred, pledged, assigned or otherwise disposed of under any circumstances; provided, however, that the foregoing restrictions shall lapse at such time and upon such terms and conditions as may be specified by the Committee in the related Award agreement(s).

(c) Vesting. Any grant of Restricted Stock under the Plan shall be subject to a minimum one-year vesting requirement.

(d) Forfeiture of Grants. Except to the extent otherwise specified by the Committee in a related Award agreement(s), all Shares of Restricted Stock as to which restrictions have not previously lapsed pursuant to Section 7(b) of the Plan shall be forfeited upon a Participant’s Termination of Service for any reason (including, without limitation, by reason of death, Disability or Retirement).

(e) Other Provisions. During the period prior to the date on which the foregoing restrictions lapse, Shares of Restricted Stock shall be registered in the Participant’s name and such Participant shall have voting rights and receive dividends with respect to such Restricted Stock.

(f) Authorization for Committee to Permit Deferral. Notwithstanding anything in this Section 7 to the contrary, a Participant may, if and to the extent permitted by the Committee, elect to defer receipt of any Restricted Stock granted under the Plan; provided, however, that any such election must be made and become irrevocable not later than the close of the calendar year next preceding the year in which the Service Period commences; and further provided, that any such deferral shall be effected in accordance with the requirements of Section 409A of the Code. Any and all Restricted Stock for which a deferral election is made shall be contributed to a grantor “rabbi” trust established by the Company prior to the date on which the restrictions on such Restricted Stock lapse, which trust shall be administered by an independent trustee; provided, however, that distributions of Restricted Stock by such a trust to a Participant following the Participant’s Termination of Service will satisfy the Company’s obligations to the Participant with respect to Restricted Stock awarded under this Plan to the extent of such distributions.

8. Terms and Conditions of Performance Shares

(a) Establishment of Annual Performance Target Levels and Number of Performance Shares. Prior to the commencement of a given Performance Period, the Committee shall establish organizational or individual performance criteria within the meaning of Section 409A relating to such Performance Period (“Performance Goals”). The Committee shall also establish the number of Performance Shares that would be payable to Participants upon the attainment of various Performance Goals during such Performance Period.

(b) Payment in Unrestricted Shares. As soon as practicable following a given Performance Period, but in no event later than 30 days after the end of such Performance Period, Participants shall receive unrestricted Shares equal to the number of Performance Shares earned by such Participant during such Performance Period. A Participant who did not serve on the Board during an entire Performance Period shall receive a prorated number of Shares (rounded down to the nearest whole number of Shares) based upon (i) the number of days during the Performance Period during which such Participant served on the Board and (ii) the actual performance results.

(c) Authorization for Committee to Permit Deferral. Notwithstanding Section 8(b) of the Plan, a Participant may, if and to the extent permitted by the Committee, elect to defer payment of any unrestricted Shares payable as a result of any Performance Shares earned by such Participant; provided, however, that any such election must be made and become irrevocable (i) on or before the date that is six months before the end of the Performance Period, provided that the Participant performs services continuously from the later of the beginning of the Performance Period or the date the Performance Goals are established through the date an election is made pursuant to this Section 8(c), and (ii) in accordance with such terms and conditions as are established by the Committee in its sole discretion. Any and all Shares earned pursuant to Section 8(b) and the receipt of which is deferred by election pursuant to this Section 8(c) shall be distributed in accordance with the requirements of Section 409A of the Code.

(d) Vesting. Any grant of Performance Shares under the Plan shall be subject to a minimum one-year vesting requirement.

9. Adjustments Upon Certain Events

Notwithstanding any other provisions in the Plan to the contrary, the following provisions shall apply to all Awards granted under the Plan:

(a) Generally. In the event of any change in the outstanding Shares after the Effective Date by reason of any Share dividend or split, reorganization, recapitalization, merger, consolidation, spin-off, combination or exchange of Shares or other

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corporate exchange or similar transaction, or any distribution to stockholders of Shares other than regular cash dividends, the Committee shall adjust the following to the extent necessary to achieve an equitable result: (i) the number or kind of Shares or other securities issued or reserved for issuance pursuant to the Plan or pursuant to outstanding Awards, (ii) the Option Price, and/or (iii) any other affected terms of such Awards.

(b) Change in Control. Upon the occurrence of a Change in Control, (i) all restrictions on Shares of Restricted Stock shall lapse, (ii) each Participant shall receive the target number of Performance Shares for the Performance Period in which the Change in Control occurs (or, if no target number has been established for such Performance Period, the target number for the immediately preceding Performance Period shall be used), and (iii) all Stock Options shall vest and become exercisable.

10. Successors and Assigns

The Plan shall be binding on all successors and assigns of the Company and a Participant, including, without limitation, the estate of such Participant and the executor, administrator or trustee of such estate, or any receiver or trustee in bankruptcy or representative of the Participant’s creditors.

11. Amendments or Termination

The Committee may amend, alter or discontinue the Plan, but no amendment, alteration or discontinuation shall be made which would impair the rights of any Participant under any Award theretofore granted without such Participant’s consent.

12. Nontransferability of Awards

Except as provided in Section 6(h) of the Plan, an Award shall not be transferable or assignable by the Participant otherwise than by will or by the laws of descent and distribution. During the lifetime of a Participant, an Award shall be exercisable only by such Participant. An Award exercisable after the death of a Participant may be exercised by the legatees, personal representatives or distributees of the Participant. Notwithstanding anything to the contrary herein, the Committee, in its sole discretion, shall have the authority to waive this Section 12 (or any part thereof) to the extent that this Section 12 (or any part thereof) is not required under the rules promulgated under any law, rule or regulation applicable to the Company.

13. Choice of Law

The Plan shall be governed by and construed in accordance with the laws of the State of Delaware applicable to contracts made and to be performed in the State of Delaware.

14. Effectiveness of the Plan

The amendment and restatement of the Plan shall be effective as of December 14, 2015.

15. Section 409A

The Plan is intended to comply with the provisions of Section 409A in order to avoid taxation of amounts deferred hereunder before such amounts are distributed from the Plan, and the Plan will be interpreted accordingly.

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