IDT CORPORATION 2005 STOCK OPTION AND INCENTIVE PLAN

EXHIBIT 10.04

IDT CORPORATION

2005 STOCK OPTION AND INCENTIVE PLAN

(Amended and Restated on February 24, 2009)

The purpose of the IDT Corporation 2005 Stock Option and Incentive Plan (the “Plan”) is to provide incentives to executive officers, employees, directors and consultants of IDT Corporation (the “Company”), or any subsidiary of the Company which now exists or hereafter is organized or acquired by the Company, to acquire a proprietary interest in the Company, to continue as officers, employees, directors or consultants, to increase their efforts on behalf of the Company and to promote the success of the Company’s business. The provisions of the Plan are intended to satisfy the requirements of Section 16(b) of the Securities Exchange Act of 1934, as amended, and of Section 162(m) of the Internal Revenue Code of 1986, as amended, and shall be interpreted in a manner consistent with the requirements thereof.

As used in this Plan, the following words and phrases shall have the meanings indicated:

(a) “Agreement” shall mean a written agreement entered into between the Company and a Grantee in connection with an award under the Plan.

(b) “Board” shall mean the Board of Directors of the Company.

(c) “Change in Control” means a change in ownership or control of the Company effected through either of the following:

(i) any “person,” as such term is used in Sections 13(d) and 14(d) of the Exchange Act (other than (A) the Company, (B) any trustee or other fiduciary holding securities under an employee benefit plan of the Company, (C) any corporation or other entity owned, directly or indirectly, by the stockholders of the Company in substantially the same proportions as their ownership of common stock, or (D) any person who, immediately prior to the Initial Public Offering, owned more than 25% of the combined voting power of the Company’s then outstanding voting securities), is or becomes the “beneficial owner” (as defined in Rule 13d-3 under the Exchange Act), directly or indirectly, of securities of the Company (not including in the securities beneficially owned by such person any securities acquired directly from the Company or any of its affiliates other than in connection with the acquisition by the Company or its affiliates of a business) representing 25% or more of the combined voting power of the Company’s then outstanding voting securities; or

(ii) during any period of not more than two consecutive years, not including any period prior to the initial adoption of this Plan by the Board, individuals who at the beginning of such period constitute the Board, and any new director (other than a director whose initial assumption of office is in connection with an actual or threatened election contest, including, but not limited to a consent solicitation, relating to the election of directors of the Company) whose election by the Board or nomination for election by the Company’s stockholders was approved by a vote of at least two-thirds (2/3) of the directors then still in office who either were directors at the beginning of the period or whose election or nomination for election was previously so approved, cease for any reason to constitute at least a majority thereof.

(d) “Class B Common Stock” shall mean shares of Class B Common Stock, par value $.01 per share, of the Company.

(e) “Code” shall mean the Internal Revenue Code of 1986, as amended from time to time.

(f) “Committee” shall mean the Compensation Committee of the Board or such other committee as the Board may designate from time to time to administer the Plan.

(g) “Common Stock” shall mean shares of Common Stock, par value $.01 per share, of the Company.

(h) “Company” shall mean IDT Corporation, a corporation incorporated under the laws of the State of Delaware, or any successor corporation.

(i) “Continuous Service” means that the provision of services to the Company or a Related Entity in any capacity of officer, employee, director or consultant is not interrupted or terminated. Continuous Service shall not be considered interrupted in the case of (i) any approved leave of absence, (ii) transfers between locations of the Company or among the Company, any Related Entity or any successor in any capacity of officer, employee, director or consultant, or (iii) any change in status as long as the individual remains in the service of the Company or a Related Entity in any capacity of officer, employee, director or consultant (except as otherwise provided in the applicable Agreement). An approved leave of absence shall include sick leave, maternity leave, military leave (including without limitation service in the National Guard or the Army Reserves) or any other personal leave approved by the Committee. For purposes of Incentive Stock Options, no such leave may exceed ninety (90) days unless reemployment upon expiration of such leave is guaranteed by statute or contract.

(j) “Corporate Transaction” means any of the following transactions:

(i) a merger or consolidation of the Company with any other corporation or other entity, other than (A) a merger or consolidation which would result in the voting securities of the Company outstanding immediately prior thereto continuing to represent (either by remaining outstanding or by being converted into voting securities of the surviving or parent entity) 80% or more of the combined voting power of the voting securities of the Company or such surviving or parent entity outstanding immediately after such merger or consolidation or (B) a merger or consolidation effected to implement a recapitalization of the Company (or similar transaction) in which no “person” (as defined in the Exchange Act) acquired 25% or more of the combined voting power of the Company’s then outstanding securities; or

(ii) a plan of complete liquidation of the Company or an agreement for the sale or disposition by the Company of all or substantially all of its assets (or any transaction having a similar effect).

(k) “Deferred Stock Units” mean a Grantee’s rights to receive shares of Class B Common Stock or Common Stock, as applicable, on a deferred basis, subject to such restrictions, forfeiture provisions and other terms and conditions as shall be determined by the Committee.

(l) “Disability” shall mean a Grantee’s inability to perform his or her duties with the Company or any of its affiliates by reason of any medically determinable physical or mental impairment, as determined by a physician selected by the Grantee and acceptable to the Company.

(m) “Exchange Act” shall mean the Securities Exchange Act of 1934, as amended from time to time.

(n) “Fair Market Value” per share as of a particular date shall mean (i) the closing sale price per share of Class B Common Stock or Common Stock, as applicable, on the national securities exchange on which the Class B Common Stock or Common Stock, as applicable, is principally traded for the last preceding date on which there was a sale of such Class B Common Stock or Common Stock, as applicable, on such exchange, or (ii) if the shares of Class B Common Stock or Common Stock, as applicable, are then traded in an over-the-counter market, the average of the closing bid and asked prices for the shares of Class B Common Stock or Common Stock, as applicable, in such over-the-counter market for the last preceding date on which there was a sale of such Class B Common Stock or Common Stock, as applicable, in such market, or (iii) if the shares of Class B Common Stock or Common Stock, as applicable, are not then listed on a national securities exchange or traded in an over-the-counter market, such value as the Committee, in its sole discretion, shall determine.

(o) “Grantee” shall mean a person who receives a grant of Options, Stock Appreciation Rights, Limited Rights, Deferred Stock Units or Restricted Stock under the Plan.

(p) “Incentive Stock Option” shall mean any option intended to be, and designated as, an incentive stock option within the meaning of Section 422 of the Code.

(q) “Insider” shall mean a Grantee who is subject to the reporting requirements of Section 16(a) of the Exchange Act.

(r) “Insider Trading Policy” shall mean the Insider Trading Policy of the Company, as may be amended from time to time.

(s) “Limited Right” shall mean a limited stock appreciation right granted pursuant to Section 10 of the Plan.

(t) “Non-Employee Director” means a member of the Board or the board of directors of any Subsidiary (other than Net2Phone, Inc., Film Roman, Inc. or any other Subsidiary that has either (A) a class of “equity securities” (as defined in Rule 3a11-1 promulgated under the Exchange Act) registered under the Exchange Act or a similar foreign statute or (B) adopted any stock option plan, equity compensation plan or similar employee benefit plan in which non-employee directors of such Subsidiary are eligible to participate) who is not an employee of the Company or any Subsidiary.

(u) “Non-Employee Director Annual Grant” shall mean an award of 4,166 shares of Restricted Stock.

(v) “Non-Employee Director Grant Date” shall mean January 5 of the applicable year (or the following business day if January 5 is not a business day).

(w) “Nonqualified Stock Option” shall mean any option not designated as an Incentive Stock Option.

(x) “Option” or “Options” shall mean a grant to a Grantee of an option or options to purchase shares of Class B Common Stock or Common Stock, as applicable.

(y) “Option Agreement” shall have the meaning set forth in Section 6 of the Plan.

(z) “Option Price” shall mean the exercise price of the shares of Class B Common Stock or Common Stock, as applicable, covered by an Option.

(aa) “Parent” shall mean any company (other than the Company) in an unbroken chain of companies ending with the Company if, at the time of granting an award under the Plan, each of the companies other than the Company owns stock possessing fifty percent (50%) or more of the total combined voting power of all classes of stock in one of the other companies in such chain.

(bb) “Plan” means this IDT Corporation 2005 Stock Option and Incentive Plan, as amended or restated from time to time.

(cc) “Related Entity” means any Parent, Subsidiary or any business, corporation, partnership, limited liability company or other entity in which the Company, a Parent or a Subsidiary holds a substantial ownership interest, directly or indirectly.

(dd) “Related Entity Disposition” means the sale, distribution or other disposition by the Company of all or substantially all of the Company’s interest in any Related Entity effected by a sale, merger or consolidation or other transaction involving such Related Entity or the sale of all or substantially all of the assets of such Related Entity.

(ee) “Restricted Period” shall have the meaning set forth in Section 11(b) of the Plan.

(ff) “Restricted Stock” means shares of Class B Common Stock or Common Stock, as applicable, issued under the Plan to a Grantee for such consideration, if any, and subject to such restrictions on transfer, rights of refusal, repurchase provisions, forfeiture provisions and other terms and conditions as shall be determined by the Committee.

(gg) “Retirement” shall mean a Grantee’s retirement in accordance with the terms of any tax-qualified retirement plan maintained by the Company or any of its affiliates in which the Grantee participates.

(hh) “Rule 16b-3” shall mean Rule 16b-3, as from time to time in effect, promulgated under the Exchange Act, including any successor to such Rule.

(ii) “Stock Appreciation Right” shall mean the right, granted to a Grantee under Section 9 of the Plan, to be paid an amount measured by the appreciation in the Fair Market Value of a share of Class B Common Stock or Common Stock, as applicable, from the date of grant to the date of exercise of the right, with payment to be made in cash or Class B Common Stock or Common Stock, as applicable, as specified in the award or determined by the Committee.

(jj) “Subsidiary” shall mean any company (other than the Company) in an unbroken chain of companies beginning with the Company if each of the companies other than the last company in the unbroken chain owns stock possessing fifty percent (50%) or more of the total combined voting power of all classes of stock in one of the other companies in such chain.

(kk) “Tax Event” shall have the meaning set forth in Section 17 of the Plan.

(ll) “Ten Percent Stockholder” shall mean a Grantee who at the time an Incentive Stock Option is granted, owns stock possessing more than ten percent (10%) of the total combined voting power of all classes of stock of the Company or any Parent or Subsidiary.

(a) The Plan shall be administered by the Committee, the members of which may be composed of (i) “non-employee directors” under Rule 16b-3 and “outside directors” under Section 162(m) of the Code, or (ii) any other members of the Board.

(b) The Committee shall have the authority in its discretion, subject to and not inconsistent with the express provisions of the Plan, to administer the Plan and to exercise all the powers and authorities either specifically granted to it under the Plan or necessary or advisable in the administration of the Plan, including, without limitation, the authority to grant Options, Stock Appreciation Rights, Limited Rights, Deferred Stock Units and Restricted Stock; to determine which options shall constitute Incentive Stock Options and which Options shall constitute Nonqualified Stock Options; to determine which Options (if any) shall be accompanied by Limited Rights; to determine the purchase price of the shares of Class B Common Stock or Common Stock, as applicable, covered by each Option; to determine the persons to whom, and the time or times at which awards shall be granted; to determine the number of shares to be covered by each award; to interpret the Plan and any award under the Plan; to reconcile any inconsistent terms in the Plan or any award under the Plan; to prescribe, amend and rescind rules and regulations relating to the Plan; to determine the terms and provisions of the Agreements (which need not be identical) and to cancel or suspend awards, as necessary; and to make all other determinations deemed necessary or advisable for the administration of the Plan.

(c) All decisions, determination and interpretations of the Committee shall be final and binding on all Grantees of any awards under this Plan. No member of the Board or Committee shall be liable for any action taken or determination made in good faith with respect to the Plan or any award granted hereunder.

(d) The Committee may delegate to one or more executive officers of the Company the authority to (i) grant awards under the Plan to employees of the Company and its Subsidiaries who are not officers or directors of the Company, (ii) execute and deliver documents or take such other ministerial actions on behalf of the Committee with respect to awards and (iii) to make interpretations of the Plan. The grant of authority in

this Section 3(d) shall be subject to such conditions and limitations as may be determined by the Committee. If the Committee delegates authority to any such executive officer or executive officers of the Company pursuant to this Section 3(d), and such executive officer or executive officers grant awards pursuant to such delegated authority, references in this Plan to the “Committee” as they relate to such awards shall be deemed to refer to such executive officer or executive officers, as applicable.

Awards may be granted to executive officers, employees, directors and consultants of the Company or of any Subsidiary. In addition to any other awards granted to Non-Employee Directors hereunder, awards shall be granted to Non-Employee Directors pursuant to Section 14 of the Plan. In determining the persons to whom awards shall be granted and the number of shares to be covered by each award, the Committee shall take into account the duties of the respective persons, their present and potential contributions to the success of the Company and such other factors as the Committee shall deem relevant in connection with accomplishing the purposes of the Plan.

(a) The maximum number of shares of Class B Common Stock reserved for the grant of awards under the Plan shall be 3,166,666, subject to adjustment as provided in Section 12 of the Plan. Such shares may, in whole or in part, be authorized but unissued shares or shares that shall have been or may be reacquired by the Company.

(b) The maximum number of shares of Common Stock reserved for the grant of awards under the Plan shall be 1,000,000, subject to adjustment as provided in Section 12 of the Plan. Such shares may, in whole or in part, be authorized but unissued shares or shares that shall have been or may be reacquired by the Company.

(c) If any outstanding award under the Plan should, for any reason expire, be canceled or be forfeited (other than in connection with the exercise of a Stock Appreciation Right or a Limited Right), without having been exercised in full, the shares of Class B Common Stock or Common Stock allocable to the unexercised, canceled or terminated portion of such award shall (unless the Plan shall have been terminated) become available for subsequent grants of awards under the Plan, unless otherwise determined by the Committee.

(a) OPTION AGREEMENT. Each Option granted pursuant to the Plan shall be evidenced by a written agreement between the Company and the Grantee (the “Option Agreement”), in such form and containing such terms and conditions as the Committee shall from time to time approve, which Option Agreement shall comply with and be subject to the following terms and conditions, unless otherwise specifically provided in such Option Agreement. For purposes of interpreting this Section 6, a director’s service as a member of the Board or a consultant’s service shall be deemed to be employment with the Company.

(b) NUMBER OF SHARES. Each Option Agreement shall state the number of shares of Class B Common Stock or Common Stock, as applicable, to which the Option relates.

(c) TYPE OF OPTION. Each Option Agreement shall specifically state that the Option constitutes an Incentive Stock Option or a Nonqualified Stock Option. In the absence of such designation, the Option will be deemed to be a Nonqualified Stock Option.

(d) OPTION PRICE. Each Option Agreement shall state the Option Price, which, in the case of an Incentive Stock Option, shall not be less than one hundred percent (100%) of the Fair Market Value of the shares of Class B Common Stock or Common Stock, as applicable, covered by the Option on the date of grant. The Option Price shall be subject to adjustment as provided in Section 12 of the Plan.

(e) MEDIUM AND TIME OF PAYMENT. The Option Price shall be paid in full, at the time of exercise, in cash or in shares of Class B Common Stock or Common Stock, as applicable, having a Fair Market Value equal to such Option Price or in a combination of cash and Class B Common Stock or Common Stock, as applicable, including a cashless exercise procedure through a broker-dealer; provided, however, that in the case of an Incentive Stock Option, the medium of payment shall be determined at the time of grant and set forth in the applicable Option Agreement.

(f) TERM AND EXERCISABILITY OF OPTIONS. Each Option Agreement shall provide the exercise schedule for the Option as determined by the Committee, provided, that, the Committee shall have the authority to accelerate the exercisability of any outstanding option at such time and under such circumstances as it, in its sole discretion, deems appropriate. The exercise period will be ten (10) years from the date of the grant of the option unless otherwise determined by the Committee; provided, however, that in the case of an Incentive Stock Option, such exercise period shall not exceed ten (10) years from the date of grant of such Option. The exercise period shall be subject to earlier termination as provided in Sections 6(g) and 6(h) of the Plan. An Option may be exercised, as to any or all full shares of Class B Common Stock or Common Stock, as applicable, as to which the Option has become exercisable, by written notice delivered in person or by mail to the Company’s transfer agent or other administrator designated by the Company, specifying the number of shares of Class B Common Stock or Common Stock, as applicable, with respect to which the Option is being exercised.

(g) TERMINATION. Except as provided in this Section 6(g) and in Section 6(h) of the Plan, an Option may not be exercised unless the Grantee is then in the employ of or maintaining a director or consultant relationship with the Company or a Subsidiary thereof (or a company or a Parent or Subsidiary of such company issuing or assuming the Option in a transaction to which Section 424(a) of the Code applies), and unless the Grantee has remained in Continuous Service with the Company or any Subsidiary since the date of grant of the Option. In the event that the employment or consultant relationship of a Grantee shall terminate (other than by reason of death, Disability or Retirement), all Options of such Grantee that are exercisable at the time of Grantee’s termination may, unless earlier terminated in accordance with their terms, be exercised within 180 days after the date of termination (or such different period as the Committee shall prescribe).

(h) DEATH, DISABILITY OR RETIREMENT OF GRANTEE. If a Grantee shall die while employed by, or maintaining a director or consultant relationship with, the Company or a Subsidiary thereof, or within thirty (30) days after the date of termination of such Grantee’s employment, director or consultant relationship (or within such different period as the Committee may have provided pursuant to Section 6(g) of the Plan), or if the Grantee’s employment, director or consultant relationship shall terminate by reason of Disability, all Options theretofore granted to such Grantee (to the extent otherwise exercisable) may, unless earlier terminated in accordance with their terms, be exercised by the Grantee or by the Grantee’s estate or by a person who acquired the right to exercise such Options by bequest or inheritance or otherwise by result of death or Disability of the Grantee, at any time within 180 days after the death or Disability of the Grantee (or such different period as the Committee shall prescribe). In the event that an Option granted hereunder shall be exercised by the legal representatives of a deceased or former Grantee, written notice of such exercise shall be accompanied by a certified copy of letters testamentary or equivalent proof of the right of such legal representative to exercise such Option. In the event that the employment or consultant relationship of a Grantee shall terminate on account of such Grantee’s Retirement, all Options of such Grantee that are exercisable at the time of such Retire