EXHIBIT 10.13

THE STOCK OPTION EVIDENCED BY THIS AGREEMENT HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933 OR QUALIFIED UNDER APPLICABLE STATE SECURITIES LAWS AND MAY NOT BE SOLD OR OTHERWISE TRANSFERRED EXCEPT AS PERMITTED UNDER SECTION 10 OF THIS AGREEMENT

KEMPHARM, INC.

NON-QUALIFIED STOCK OPTION AGREEMENT

THIS KEMPHARM, INC. NON-QUALIFIED STOCK OPTION AGREEMENT is entered into by and between KEMPHARM, INC., an Iowa corporation with its principal office at 2656 Crosspark Road, Suite 100, Coralville, IA 52241, and                 , whose address is set forth beneath the Participant’s signature page hereto.

1. DEFINITIONS. As used in this Agreement, the following capitalized terms have shall the following meanings. Capitalized terms used but not defined in this Agreement shall have the meaning ascribed to them in the Plan.

(a) Agreement. “Agreement” means this Non-qualified Stock Option Agreement.

(b) Cause. “Cause” means: (i) acts of willful malfeasance, gross misconduct or neglect with respect to the performance of the Participant’s duties and responsibilities as an employee, consultant, officer or director of the Company or its Affiliates, (ii) conduct that results in or is reasonably likely to result in harm to the reputation or business of the Company or any of its affiliates, (iii) the commission of, or plea of guilty or no contest to, a crime constituting a felony, or (vi) the material breach of any contractual obligation to the Company which is not remedied within the time specified under the contract at issue.

(c) Change of Control. “Change of Control” means the occurrence of any of the following:

(1) the acquisition by any person, or group of persons acting in concert (other than the Company or any Affiliate), of beneficial ownership (as determined under Rule 13d-3 of the Exchange Act) of 50.01% or more (on a fully diluted basis) of the then-Outstanding Company Common Stock and/or the then-Outstanding Company Voting Stock (a “Stock Sale”; or

(2) the direct or indirect sale, transfer, license, conveyance or other disposition (other than by way of merger or consolidation), in one or a series of related transactions, of all or substantially all of the properties or assets of the Company and its subsidiaries, taken as a whole, to any person, or group of persons acting in concert, that is not a subsidiary of the Company (an “Asset Sale”); or

(3) the consummation of a reorganization, merger, consolidation, statutory share exchange or similar form of corporate transaction involving the Company that requires the approval of the Company’s shareholders, whether for such transaction or the issuance of securities in the transaction (a “Business Combination”);

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provided, however, that a Stock Sale, Asset Sale or Business Combination shall not constitute a Change of Control if immediately following such Stock or Asset Sale or Business Combination at least 50.01% of the total voting power eligible to elect at least a majority of the directors of (A) the purchasing entity in such Stock or Asset Sale, or the entity resulting from such Business Combination (in each case the “Surviving Company”), or (B) if applicable, the ultimate parent entity that directly or indirectly has beneficial ownership of sufficient voting securities eligible to elect a majority of the members of the board of directors (or the analogous governing body) of the Surviving Company (the “Parent Company”), is represented by the Outstanding Company Voting Stock that was outstanding immediately prior to such Stock or Asset Sale or Business Combination (or, if applicable, is represented by shares into which the Outstanding Company Voting Stock were converted pursuant to such Stock or Asset Sale or Business Combination), and such voting power among the holders thereof is in substantially the same proportion as the Outstanding Company Voting Securities among the holders thereof immediately prior to the Stock or Asset Sale or Business Combination.

(d) Company. “Company” means KemPharm, Inc.

(e) Continuous Service. “Continuous Service” for the Company means the Participant’s performance, without interruption or termination, of ongoing services to the Company or any Affiliate in the capacity of an (i) employee, (ii) officer, (iii) member of the Board, (iv) consultant pursuant to a written consultant or services agreement, or (v) member of an advisory board of the Company.

(f) Exchange Act. The “Exchange Act” means the Securities Exchange Act of 1934, as amended.

(g) Exercise Agreement. “Exercise Agreement” has the meaning ascribed to it in Section 6(a) hereof.

(h) Exercise Price. “Exercise Price” means the price per share at which the Option may be exercised to purchase Option Shares.

(i) Expiration Date. “Expiration Date” means the expiration date set forth above.

(j) Holder. “Holder” means the Participant and the Participant’s permitted assigns and successors in interest.

(k) Net Exercise. “Net Exercise” has the meaning ascribed to it in Section 6(c).

(l) Option. “Option” means the option to purchase up to the maximum number of Option Shares granted under this Agreement to the Holder.

(m) Option Shares. “Option Shares” means the shares of Common stock which the Holder may purchase by exercise of the Option (subject to adjustment and substitution pursuant to Section 7).

(n) Outstanding Company Common Stock. “Outstanding Company Common Stock” means, at any given time, the outstanding shares of Common Stock taking into account as outstanding for this purpose such Common Stock issuable upon the exercise of options or warrants, the conversion of convertible stock or debt, and the exercise of any similar right to acquire such Common Stock.

(o) Outstanding Company Voting Stock. “Outstanding Company Voting Stock” means, at any given time, the then-outstanding voting securities of the Company entitled to vote generally in the election of at least a majority of the Company’s directors, taking into account as outstanding for this purpose such voting securities as are issuable upon the exercise of options or warrants, the conversion of convertible stock or debt, and the exercise of any similar right to acquire such voting securities.

(p) Participant. “Participant” means the individual named in the first unnumbered paragraph of this Agreement.

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(q) Plan. The “Plan” means the Company’s Incentive Stock Plan, a copy of which has been made available to the Participant, as may be amended by the Company at any time, in its discretion.

(r) Securities Act. “Securities Act” means the Securities Act of 1933, as amended.

(s) Service Termination Date. “Service Termination Date” means the effective date of the termination of the Participant’s Continuous Service.

(t) Stock Certificate. “Stock Certificate” means a certificate issued by the Company representing the ownership of the Option Shares purchased by the exercise of the Option.

2. GRANT OF NON-QUALIFIED STOCK OPTION.

(a) Grant of Option. The Company hereby grants to the Holder the Option to purchase up to the total number of shares set forth above of Common Stock at the Exercise Price. The effective date of the grant of the Option is the date set forth above. The grant of the Option is made pursuant to and subject to the terms and conditions of Plan, which may be amended from time to time, as well as the terms and conditions set forth in this Agreement.

(b) Type of Grant. The Option is intended to be a non-qualified stock option and not an incentive stock option within the meaning of Code Section 422 or any section or sections of future legislation that amend, supplement or supersede that section.

(c) Consideration. The grant of the Option is made in consideration of the Continuous Service to be rendered by the Participant to the Company. The Administrator shall determine, in its sole discretion, whether Continuous Service shall be considered interrupted and the effective date of any termination in the Participant’s Continuous Service and the Service Termination Date.

3. EXERCISE PRICE. The Exercise Price at which the Option may be exercised is the exercise price set forth above, which is equal to the fair market value of a share of Common Stock as of the effective date of the grant of the Option. The exercise price established pursuant to the preceding sentence shall be adjusted from time to time pursuant to Sections 7 and 8(b) hereof. For all purposes of this Agreement, the fair market value, at any given time, of a share of Common Stock shall be determined by the Administrator in accordance with the terms and conditions of the Plan.

4. VESTING.

(a) Vesting Schedule. Subject to Section 8(a), the Holder’s right to purchase the Option Shares will become vested, such that the Holder shall have the vested right to purchase such Option Shares by exercise of the Option in accordance with the following schedule:

(b) Unvested Portion of the Option. At any given time, the Holder may exercise only the vested portion of the Option, and may not exercise the portion of the Option which is unvested. Upon the Participant’s Service Termination Date for any reason, the portion of the Option which is not vested as of such date shall be immediately forfeited.

5. EXPIRATION.

(a) Expiration Date. The Option will expire and all rights of the Holder granted hereunder will become null and void at the close of business on the Expiration Date or earlier as provided in this Agreement or the Plan.

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(b) Termination of Continuous Service without Cause. If the Participant’s Continuous Service terminates for any reason other than death or removal for Cause, then the Holder may exercise the vested portion of the Option (determined as of the Service Termination Date), in whole or in part, but only within such period of time ending on the Expiration Date.

(c) Termination due to Death. If the Participant’s Continuous Service terminates as a result of the Participant’s death, then the parties identified in this Section 5(c) may exercise the vested portion of the Option (determined as of the Service Termination Date), in whole or in part, but only within such period of time ending on the earlier of (1) the one year anniversary of the Service Termination Date or (2) the Expiration Date. The parties who may exercise the Option pursuant to this Section 5(b) shall be (i) the court-appointed representative of the Participant’s estate, (ii) if the Participant’s estate is administered with a will, by the persons or persons to whom the Participant’s rights in the Option pass under such will, or (iii) if the Participant’s estate is administered intestate, by the person or persons to whom the Participant’s rights in the Option pass under the applicable intestacy laws. Any person exercising the Option pursuant to this Section 5(c) shall demonstrate to the satisfaction of the Company that he or she has sufficient power and authority under applicable state law to exercise the Option.

(d) Termination for Cause. If the Participant’s Continuous Service is terminated by the Company or any Affiliate for Cause, then the Option (whether vested or unvested) shall immediately terminate and cease to be exercisable as of the Service Termination Date. The Administrator, in its absolute discretion, shall determine the effect of all matters and questions relating to whether the Participant was discharged for Cause.

(e) Breach of Contract. Notwithstanding the forgoing, if at any time following the Service Termination Date, the Administrator determines, in its absolute discretion, that the Participant has materially breached any of the Participant’s obligations to the Company pursuant any written agreement between the Company and the Participant, then the entire Option shall be forfeited immediately as of the date of such determination by the Administrator, and the Holder may thereafter not exercise any portion of the Option.

6. MANNER OF EXERCISE.

(a) Election to Exercise. To exercise the Option, the Holder must deliver to the Company an executed stock option exercise agreement in such form as is approved by the Administrator from time to time (the “Exercise Agreement”), which shall set forth the Holder’s election to exercise the Option, the number of Option Shares being purchased, any restrictions imposed on the Option Shares, and any representations, warranties, and agreements regarding the Holder’s investment intent and access to information as may be required by the Company, in its discretion, to comply with applicable securities laws. If someone other than the Participant exercises thee Option, then such person must submit documentation reasonably acceptable to the Company verifying that such person has the legal right to exercise the Option.

(b) Cash Exercise. Unless the Holder elects to exercise the Option on a Net Exercise basis in accordance with Section 5(c) hereof, the Holder must pay in cash or check at the time the Option is exercised an amount equal to the aggregate Exercise Price for the number of Option Shares being purchased.

(c) Net Issue (Cashless Exercise) Election. In lieu of exercising the Option to purchase the Options Shares on a cash basis, the Holder may elect to receive, without the payment by the Holder of any additional consideration, shares of Common Stock equal to the value of the Option Shares or any portion thereof (the “Net Exercise”). Upon exercise of the Option on a Net Exercise basis, the Company will issue to the Holder such number of fully paid and nonassessable shares of Common Stock as is equal to the difference of the total number of Options Shares with respect to which the Net Exercise is made minus a number of shares with an aggregate fair market value equal to the aggregate Exercise Price at the time of exercise. The Board will promptly respond in writing to an inquiry by the Holder as to the fair market value of one share of Common Stock.

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(d) No Fractional Shares. No fractional shares of Common Stock may be purchased by exercise of the Option, and when any provision hereof may entitle the Participant to a fractional share, such fraction shall be disregarded.

(e) Partial Exercises. A partial exercise of the Option to purchase less than the entire vested portion of the Option shall not affect the Holder’s rights to exercise the Option with respect to the remainder of the vested portion of the Option, subject to the terms and conditions of the Plan and this Agreement.

(f) Effective Date of Issuance. The Option Shares acquired upon exercise of the Option shall be deemed to be issued as of the close of business on the date on which the Company receives from the Holder the duly executed Exercise Agreement and, except in the case of a Net Exercise purchase, payment in cash or by check in the amount equal to the aggregate Exercise Price for the Option Shares being, or such later date as is stated in the Exercise Agreement, which shall in any event be not more than thirty (30) days following the date on which the Exercise Agreement is delivered to the Company; provided that if any law or regulation requires the Company to take any action with respect to the Option Shares to be purchased before the Company’s issuance of such shares, then the date of issuance of such Option Shares shall be extended for the period necessary to take such action, and further provided that the Holder has made appropriate arrangements with the Company for any applicable Federal, state and local taxes withholding required by law.

(g) Withholding Taxes. The Company shall not issue any shares of Common Stock being purchased pursuant to the exercise of the Option unless the Company has received payment for all applicable withholding taxes or arrangements satisfactory to the Company for the payment thereof have been made.

7. Adjustments upon Stock Dividends, Etc. In the event of changes in the outstanding Common Stock or in the capital structure of the Company by reason of any stock dividend, stock split, reverse stock split, an extraordinary corporate transaction such as any recapitalization, reorganization, merger, consolidation, combination, exchange, or other relevant change in the Company’s capitalization after the effective date of the grant of the Option, the Administrator shall, in its absolute discretion, equitably adjust or substitute the Exercise Price and the maximum number and kind of shares of capital stock for which the Option may be exercised to the extent necessary to preserve the original economic intent of the grant of the Option. In the case of any adjustment pursuant to this Section 7, unless the Administrator specifically determines, in its absolute discretion, that such adjustment is in the best interests of the Company or its Affiliates, the Administrator shall ensure that such adjustment (i) will not constitute a modification of the Option within the meaning of Code Section 409A, and (ii) will be made in a manner which does not adversely affect any applicable exemption provided pursuant to Rule 16b-3 under the Exchange Act. The Company shall give the Holder notice of an adjustment pursuant to this Section 7, and, upon notice, such adjustment shall be conclusive and binding upon the Company and the Holder for all purposes.

8. Effect of Change in Control.

(a) Acceleration of Vesting. If a Change of Control occurs and the Participant’s Continuous Service is terminated by the Company (other than for death or Cause) within twenty-four (24) months following the Change of Control, the Holder’s right to purchase the Option Shares will become immediately 100% vested and exercisable.

(b) Cash-out. In the event of a Change of Control, the Administrator, in its discretion and upon at least 10 days’ advance notice to the Holder, cancel the Option and pay to the Holder the value of the Option (treated as if the Option was 100% vested at such time) based upon the price per share of Common Stock received or to be received by other shareholders of the Company in the event.

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(c) Determination. The Administrator, in its absolute discretion, shall determine the effect of all matters and questions relating to whether a Change of Control has occurred.

9. Shareholder Rights upon Exercise.

(a) Delivery of Certificates. As soon as practical after the effective date of issuance of Option Shares purchased by exercise of the Option, in accordance with section 6(f) hereof, the Company will cause to be issued in the name of and delivered to the Holder, or as otherwise directed in the duly executed Exercise Agreement, one or more Stock Certificates representing the purchased Option Shares. The Stock Certificate shall contain such restrictive legends or other conditions and restrictions governing the disposition of the Shares as may be reasonably required by this Agreement, the Company’s articles of incorporation and bylaws, applicable securities laws or any other law or regulation. The Company shall have the sole discretion to determine whether a legend, restriction or condition is reasonable in light of the facts and circumstances involved in each situation.

(b) Shareholder Status. The Holder shall have no rights or privileges of a shareholder of the Company with respect to any of the Option Shares issuable on the exercise of this Option unless and until the Company has issued and delivered to the Holder one or more Stock Certificates.

(c) Shareholder Agreements. Immediately upon exercise of the Option, the Participant shall be subject to all the terms and conditions of any shareholders’ agreement (or similar agreement) entered into by the Company’s shareholders and in effect at that time. The Company may refuse to issue a Stock Certificate pursuant to this Agreement until the Holder signs and agrees to be bound by any such agreement.

10. Lock Up Agreement. The Holder agrees that, if so requested by the Company and an underwriter of securities of the Company pursuant to the registration of such securities under the Securities Act, the Holder shall not sell or otherwise transfer or dispose of any Option Shares purchased by exercise of the Option (other than those included in the registration) for a period specified by the underwriter not to exceed 180 days following the effective date of a registration statement of the Company filed under said Act, provided that: (a) such agreement shall apply to the Company’s initial public offering only; and (b) all officers and directors of the Company enter into similar agreements. The obligations described in this Section 9 shall not apply to a registration relating solely to employee benefit plans on Form S-1 or S-8 or similar forms that may be promulgated in the future, or a registration relating solely to a Securities and Exchange Commission Rule 145 transaction on Form S-4 or similar forms that may be promulgated in the future. The Company may impose stop-transfer instructions with respect to the Shares (or other securities) subject to the foregoing restriction until the end of said 180 day period.

11. Nontransferability of Option. The Option has not been registered under the Securities Act. Neither this Option nor the rights and privileges conferred by this Agreement may be transferred, assigned, pledged or hypothecated in any manner (whether by operation of law or otherwise) other than by will or by the applicable laws of descent and distribution.

12. Transfer Restrictions on Stock Imposed by the Securities Act.

(a) Restriction on Transfer. Notwithstanding any other provision of this Agreement, no transfer for value of any shares of stock acquired upon exercise of the Option shall be valid unless (i) there is an effective registration statement under the Securities Act covering the stock issuable by exercise the Option; or (ii) the Holder has furnished the Company with an opinion of counsel satisfactory to the Company that such transfer will not violate the registration requirements of the Securities Act or any applicable state law regulating the sale of securities.

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(b) Legend. The face of each certificate representing shares of stock issued upon the exercise of the Option shall bear a legend substantially similar to the following:

THE SHARES OF STOCK REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933 OR THE SECURITIES LAWS OF ANY STATE AND MAY NOT BE SOLD, TRANSFERRED OR PLEDGED IN THE ABSENCE OF AN EFFECTIVE REGISTRATION STATEMENT UNDER SUCH ACT AND STATUTES UNLESS PRIOR TO ANY SALE, TRANSFER OR PLEDGE, THE ISSUER RECEIVES AN OPINION OF COUNSEL, IN FORM AND SUBSTANCE SATISFACTORY TO THE ISSUER, THAT THE REGISTRATION IS NOT REQUIRED UNDER SUCH ACT AND STATUTES AND THE RULES PROMULGATED THEREUNDER.

(c) Investment Intent. If there is not an effective registration statement under the Securities Act covering the shares of the stock to be issued by exercise of the Option, the Holder may acquire such shares upon exercise of the Option only for the Holder’s own account and not with a view to, or for resale in connection with, any distribution thereof within the meaning of the Securities Act.

13. Continuation of Service. Nothing contained in this Agreement shall confer upon the Participant the right to be retained by the Company or its Affiliates, or upon the Company and its Affiliates the obligation to retain the Participant, in any position as an employee, consultant, officer or director of the Company. Further, noting in the Plan or this Agreement shall be construed to limit or interfere in any way with the right of the Company or any of its Affiliates to reduce the Participant’s compensation or to terminate Participant’s Continuous Service at any time, with or without Cause.

14. Administration; the Plan. The Company shall have the authority to construe the terms of this Agreement and to prescribe rules and regulations relating to the administration of this Option. The terms and provisions of the Plan are incorporated herein by reference. To the extent any provision of this Agreement is inconsistent or in conflict with any term or provision of the Plan, the Plan shall govern.

15. Notice. All notices, demands and other communications shall be in writing and given via personal delivery, overnight, next-day or second-day delivery by a national delivery service, confirmed email, confirmed facsimile, or mailed through the U.S. postal service, proper postage prepaid to, in the case of the Company, addressed to the Company’s principal office marked attention to the Company’s president, or to the president’s primary Company email address, and in the case of the Holder, addressed to the postal address or email address set forth beneath the Participant’s signature hereto, and in each case to such other mail address, email address or facsimile number as may hereafter be furnished in writing by either party to the other party. Any such notice, demand or communication shall be deemed received by the addressee (i) upon actual receipt in the case of personal delivery or overnight, next-day or second-day delivery by a national delivery service, (ii) the next business day immediately following the date on which notice is transmitted, in the case of notice by confirmed email or facsimile, or (iii) in the case of notice mailed through the U.S. postal service, on the third business day following the deposit of such notice in the mail.

16. Governing Law; Jurisdiction. This Agreement shall be governed by and construed and enforced in accordance with the laws of the State of Iowa. The litigation of any disputes arising out of this Agreement shall take place in the appropriate federal or state court located in Johnson County, Iowa. The parties, to the extent they can legally do so, hereby consent to service of process, and to be sued in the State of Iowa and consent to the exclusive jurisdiction of the courts of the State of Iowa and the United States District Court for the Southern District of Iowa, as well as to the jurisdiction of all courts to which an appeal may be taken from such courts, for the purpose of any suit, action or other proceeding arising out of any of their obligations hereunder or with respect to the transactions contemplated hereby, and expressly waive any and all objections they may have to venue in such courts.

17. Successors. The provisions of this Agreement shall be binding upon and inure to the benefit of (a) each Holder hereunder, the Participant’s heirs, personal representatives, executors, estate administrators, successors and permitted assigns, and any receiver, trustee in bankruptcy or representative of creditors of

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a Holder, and (b) any successor corporation of the Company, or upon any successor corporation or organization succeeding to all or substantially all of the assets and business of the Company and its Affiliates, taken as a whole.

18. Entire Agreement. This Agreement, subject to the terms and conditions of the Plan, contain the entire understanding of the parties to this Agreement with respect to the grant of the Option hereunder, and supersedes and replaces all former agreements or understandings, oral or written, between Company and the Participant regarding the subject matter hereof.

19. Modification and Waiver. This Agreement may not be amended except by a written instrument signed by both Parties which specifically refers to the particular provision or provisions being amended. No provision of this Agreement may be waived except in a written instrument that specifically refers to the particular provision or provisions being waived and is signed by the Party against whom the waiver is being asserted. No waiver by any Party of any right, power or privilege hereunder shall constitute a waiver of any other right, power or privilege hereunder, and no waiver by any party of any breach of a provision hereunder shall constitute a waiver of any other breach of that or any other provision of this Agreement.

20. Severability. If any one or more of the provisions of this Agreement are determined to be unenforceable, in whole or in part, for any reason, shall be unaffected and shall be enforceable as if the void, invalid or unenforceable part was not a provision of the Agreement.

21. Headings. The captions and headings of this Agreement are for convenience of reference only and shall not affect the interpretation of this Agreement.

22. Counterparts. This Agreement may be executed in counterparts, including by transmission of facsimile or PDF copies of signature pages, each of which shall for all purposes are deemed to be an original and all of which shall constitute on instrument. All signatures of the parties transmitted by facsimile or PDF shall be deemed to be their original signatures for all purposes.

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SIGNATURE PAGE TO

KEMPHARM, INC. NON-QUALIFIED STOCK OPTION AGREEMENT

IN WITNESS WHEREOF, the parties have executed this Agreement as of                             , 20     

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OPTION EXERCISE RECORD

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