PRIVATE PLACEMENT WARRANTS PURCHASE AGREEMENT

Exhibit 10.4

PRIVATE PLACEMENT WARRANTS PURCHASE AGREEMENT

THIS PRIVATE PLACEMENT WARRANTS PURCHASE AGREEMENT, dated as of October 10, 2016 (as it may from time to time be amended, this “Agreement”), is entered into by and between Avista Healthcare Public Acquisition Corp., a Cayman Islands exempted company (the “Company”), Avista Acquisition Corp., a Cayman Islands exempted company (the “Sponsor”) and the other parties listed on the signature pages hereto (collectively with the Sponsor, the “Purchasers” and each, a “Purchaser”).

WHEREAS:

The Company intends to consummate an initial public offering of the Company’s units (the “Public Offering”), each unit consisting of one Class A ordinary share of the Company, par value $0.0001 per share (each, a “Share”), and one warrant;

Each warrant entitles the holder to purchase one-half of one Share at an exercise price of $5.75 (or $11.50 per whole Share); and

The Purchasers have agreed to purchase an aggregate of 16,000,000 warrants (or up to 17,800,000 warrants if the over-allotment option in connection with the Public Offering is exercised in full) (the “Private Placement Warrants”), each Private Placement Warrant entitling the holder to purchase one-half of one Share at an exercise price of $5.75 (or $11.50 per whole Share).

NOW THEREFORE, in consideration of the mutual promises contained in this Agreement and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties to this Agreement hereby, intending legally to be bound, agree as follows:

AGREEMENT

Section 1.  Authorization, Purchase and Sale; Terms of the Private Placement Warrants.

A.  Authorization of the Private Placement Warrants.  The Company has duly authorized the issuance and sale of the Private Placement Warrants to the Purchasers.

B.  Purchase and Sale of the Private Placement Warrants.

(i)  On the date that is one business day prior to the date of the consummation of the Public Offering or on such earlier time and date as may be mutually agreed by the Purchasers and the Company (the “Initial Closing Date”), the Company shall issue and sell to the Purchasers, and the Purchasers shall purchase from the Company, an aggregate of 16,000,000 Private Placement Warrants at a price of $0.50 per warrant for an aggregate purchase price of $8,000,000 (the “Purchase Price”), as set forth on Annex I hereto, which shall be paid by wire transfer of immediately available funds to the Company in accordance with the Company’s wiring instructions.  On the Initial Closing Date, upon the payment by the Purchasers of the Purchase Price by wire transfer of immediately available funds to the Company, the Company, at its option, shall deliver a certificate evidencing the Private Placement Warrants purchased on

such date duly registered in such Purchaser’s name to such Purchaser or effect such delivery in book-entry form.

(ii)  On the date that is one business day prior to the date of the consummation of the closing of the over-allotment option in connection with the Public Offering (the “Over-Allotment Option”) or on such earlier time and date as may be mutually agreed by the Purchasers and the Company (each such date, an “Over-allotment Closing Date,” and each Over-allotment Closing Date (if any) and the Initial Closing Date being sometimes referred to herein as a “Closing Date”), the Company shall issue and sell to the Purchasers, and the Purchasers shall purchase from the Company, an aggregate of up to 1,800,000 Private Placement Warrants at a price of $0.50 per warrant for an aggregate purchase price of up to $900,000 (if the over-allotment option in connection with the Public Offering is exercised in full) (the “Over-allotment Purchase Price”), as set forth on Annex II hereto, which shall be paid by wire transfer of immediately available funds to the Company in accordance with the Company’s wiring instructions.  On the Over-allotment Closing Date, upon the payment by the Purchasers of the Over-allotment Purchase Price by wire transfer of immediately available funds to the Company, the Company shall, at its option, deliver a certificate evidencing the Private Placement Warrants purchased on such date duly registered in such Purchaser’s name to such Purchaser or effect such delivery in book-entry form.

C.  Terms of the Private Placement Warrants.

(i)  Each Private Placement Warrant shall have the terms set forth in a Warrant Agreement to be entered into by the Company and a warrant agent, in connection with the Public Offering (a “Warrant Agreement”).

(ii)  At the time of the closing of the Public Offering, the Company and the Purchasers shall enter into a registration rights agreement (the “Registration Rights Agreement”) pursuant to which the Company will grant certain registration rights to the Purchasers relating to the Private Placement Warrants and the Shares underlying the Private Placement Warrants.

Section 2.  Representations and Warranties of the Company.  As a material inducement to the Purchasers to enter into this Agreement and purchase the Private Placement Warrants, the Company hereby represents and warrants to the Purchasers (which representations and warranties shall survive each Closing Date) that:

A.  Organization and Corporate Power.  The Company is an exempted company duly incorporated, validly existing and in good standing under the laws of the Cayman Islands and is qualified to do business in every jurisdiction in which the failure to so qualify would reasonably be expected to have a material adverse effect on the financial condition, operating results or assets of the Company.  The Company possesses all requisite corporate power and authority necessary to carry out the transactions contemplated by this Agreement and the Warrant Agreement.

B.  Authorization; No Breach.

(i)  The execution, delivery and performance of this Agreement and the Private Placement Warrants have been duly authorized by the Company as of the Closing Date.  This

2

Agreement constitutes the valid and binding obligation of the Company, enforceable in accordance with its terms.  Upon issuance in accordance with, and payment pursuant to, the terms of the Warrant Agreement and this Agreement, the Private Placement Warrants will constitute valid and binding obligations of the Company, enforceable in accordance with their terms as of the Closing Dates.

(ii)  The execution and delivery by the Company of this Agreement and the Private Placement Warrants, the issuance and sale of the Private Placement Warrants, the issuance of the Shares upon exercise of the Private Placement Warrants and the fulfillment, of and compliance with, the respective terms hereof and thereof by the Company, do not and will not as of the Closing Dates (a) conflict with or result in a breach of the terms, conditions or provisions of, (b) constitute a default under, (c) result in the creation of any lien, security interest, charge or encumbrance upon the Company’s share capital or assets under, (d) result in a violation of, or (e) require any authorization, consent, approval, exemption or other action by or notice or declaration to, or filing with, any court or administrative or governmental body or agency pursuant to the memorandum and articles of association of the Company (in effect on the date hereof or as may be amended prior to completion of the contemplated Public Offering), or any material law, statute, rule or regulation to which the Company is subject, or any agreement, order, judgment or decree to which the Company is subject, except for any filings required after the date hereof under federal or state securities laws.

C.  Title to Securities.  Upon issuance in accordance with, and payment pursuant to, and registration in the register of members of the Company, the terms hereof and the Warrant Agreement, the Shares issuable upon exercise of the Private Placement Warrants will be duly and validly issued, fully paid and nonassessable.  Upon issuance in accordance with, and payment pursuant to, the terms hereof and the Warrant Agreement, the Purchasers will have good title to the Private Placement Warrants and the Shares issuable upon exercise of such Private Placement Warrants, free and clear of all liens, claims and encumbrances of any kind, other than (i) transfer restrictions hereunder and under the other agreements contemplated hereby, (ii) transfer restrictions under federal and state securities laws, and (iii) liens, claims or encumbrances imposed due to the actions of the Purchasers.

D.  Governmental Consents.  No permit, consent, approval or authorization of, or declaration to or filing with, any governmental authority is required in connection with the execution, delivery and performance by the Company of this Agreement or the consummation by the Company of any other transactions contemplated hereby.

Section 3.  Representations and Warranties of the Purchasers.  As a material inducement to the Company to enter into this Agreement and issue and sell the Private Placement Warrants to the Purchasers, each Purchaser severally and not jointly hereby represents and warrants to the Company (which representations and warranties shall survive each Closing Date) that:

A.  Organization and Requisite Authority.  The Purchaser possesses all requisite power and authority necessary to carry out the transactions contemplated by this Agreement.

3

B.  Authorization; No Breach.

(i)  This Agreement constitutes a valid and binding obligation of the Purchaser, enforceable in accordance with its terms, subject to bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other laws of general applicability relating to or affecting creditors’ rights and to general equitable principles (whether considered in a proceeding in equity or law).

(ii)  The execution and delivery by the Purchaser of this Agreement and the fulfillment of and compliance with the terms hereof by the Purchaser does not and shall not as of each Closing Date conflict with or result in a breach by the Purchaser of the terms, conditions or provisions of any agreement, instrument, order, judgment or decree to which the Purchaser is subject.

C.  Investment Representations.

(i)  The Purchaser is acquiring the Private Placement Warrants and, upon exercise of the Private Placement Warrants, the Shares issuable upon such exercise (collectively, the “Securities”), for the Purchaser’s own account, for investment purposes only and not with a view towards, or for resale in connection with, any public sale or distribution thereof.

(ii)  The Purchaser is an “accredited investor” as such term is defined in Rule 501(a)(3) of Regulation D under the Securities Act of 1933, as amended (the “Securities Act”).

(iii)  The Purchaser understands that the Securities are being offered and will be sold to it in reliance on specific exemptions from the registration requirements of the United States federal and state securities laws and that the Company is relying upon the truth and accuracy of, and the Purchaser’s compliance with, the representations and warranties of the Purchaser set forth herein in order to determine the availability of such exemptions and the eligibility of the Purchaser to acquire such Securities.

(iv)  The Purchaser decided to enter into this Agreement not as a result of any general solicitation or general advertising within the meaning of Rule 502(c) under the Securities Act.

(v)  The Purchaser has been furnished with all materials relating to the business, finances and operations of the Company and materials relating to the offer and sale of the Securities which have been requested by the Purchaser.  The Purchaser has been afforded the opportunity to ask questions of the executive officers and directors of the Company.  The Purchaser understands that its investment in the Securities involves a high degree of risk and it has sought such accounting, legal and tax advice as it has considered necessary to make an informed investment decision with respect to the acquisition of the Securities.

(vi)  The Purchaser understands that no United States federal or state agency or any other government or governmental agency has passed on or made any recommendation or endorsement of the Securities or the fairness or suitability of the investment in the Securities by the Purchaser nor have such authorities passed upon or endorsed the merits of the offering of the Securities.

4

(vii)  The Purchaser understands that: (a) the Securities have not been and are not being registered under the Securities Act or any state securities laws, and may not be offered for sale, sold, assigned or transferred unless (1) subsequently registered thereunder or (2) sold in reliance on an exemption therefrom; and (b) except as specifically set forth in the Registration Rights Agreement, neither the Company nor any other person is under any obligation to register the Securities under the Securities Act or any state securities laws or to comply with the terms and conditions of any exemption thereunder.  In this regard, the Purchaser understands that the Securities and Exchange Commission (the “SEC”) has taken the position that promoters or affiliates of a blank check company and their transferees, both before and after a Business Combination, are deemed to be “underwriters” under the Securities Act when reselling the securities of a blank check company.  Based on that position, Rule 144 adopted pursuant to the Securities Act would not be available for resale transactions of the Securities despite technical compliance with the requirements of such Rule, and the Securities can be resold only through a registered offering or in reliance upon another exemption from the registration requirements of the Securities Act.

(viii)  The Purchaser has such knowledge and experience in financial and business matters, knows of the high degree of risk associated with investments in the securities of companies in the development stage such as the Company, is capable of evaluating the merits and risks of an investment in the Securities and is able to bear the economic risk of an investment in the Securities in the amount contemplated hereunder for an indefinite period of time.  The Purchaser has adequate means of providing for its current financial needs and contingencies and will have no current or anticipated future needs for liquidity which would be jeopardized by the investment in the Securities.  The Purchaser can afford a complete loss of its investments in the Securities.

Section 4.  Conditions of the Purchaser’s Obligations.  The obligations of each Purchaser to purchase and pay for the Private Placement Warrants are subject to the fulfillment, on or before each Closing Date, of each of the following conditions:

A.  Representations and Warranties.  The representations and warranties of the Company contained in Section 2 shall be true and correct at and as of such Closing Date as though then made.

B.  Performance.  The Company shall have performed and complied with all agreements, obligations and conditions contained in this Agreement that are required to be performed or complied with by it on or before such Closing Date.

C.  No Injunction.  No litigation, statute, rule, regulation, executive order, decree, ruling or injunction shall have been enacted, entered, promulgated or endorsed by or in any court or governmental authority of competent jurisdiction or any self-regulatory organization having authority over the matters contemplated hereby, which prohibits the consummation of any of the transactions contemplated by this Agreement or the Warrant Agreement.

D.  Warrant Agreement.  The Company shall have entered into a Warrant Agreement with a warrant agent on terms satisfactory to each Purchaser.

5

Section 5.  Conditions of the Company’s Obligations.  The obligations of the Company to each Purchaser under this Agreement are subject to the fulfillment, on or before each Closing Date, of each of the following conditions:

A.  Representations and Warranties.  The representations and warranties of such Purchaser contained in Section 3 shall be true and correct at and as of such Closing Date as though then made.

B.  Performance.  Such Purchaser shall have performed and complied with all agreements, obligations and conditions contained in this Agreement that are required to be performed or complied with by such Purchaser on or before such Closing Date.

C.  No Injunction.  No litigation, statute, rule, regulation, executive order, decree, ruling or injunction shall have been enacted, entered, promulgated or endorsed by or in any court or governmental authority of competent jurisdiction or any self-regulatory organization having authority over the matters contemplated hereby, which prohibits the consummation of any of the transactions contemplated by this Agreement or the Warrant Agreement.

D.  Warrant Agreement.  The Company shall have entered into a Warrant Agreement with a warrant agent on terms satisfactory to the Company.

Section 6.  Call Right and Forfeitures. (A) Each Purchaser, other than the Sponsor, agrees that if such Purchaser resigns from the board of directors of the Company for any reason or is removed from the board of directors of the Company for Cause (as defined in Section 9 hereof), in each case, prior to the Company’s initial business combination, Thompson Dean and David Burgstahler, or either of them, shall have the right, but not the obligation, to purchase the Private Placement Warrants held by such Purchaser at $0.50 per Private Placement Warrant.

B.  In the event the Sponsor is required to forfeit any of the Private Placement Warrants held by it at the time of the Company’s initial business combination in connection therewith, or otherwise transfer any such Private Placement Warrants to any seller or funding source participating therein, whether or not for value, each other Purchaser shall forfeit or otherwise transfer the Private Placement Warrants held by it on a pro rata basis on the same terms and conditions as the Sponsor.

Section 7.  Termination.  This Agreement may be terminated at any time after December 31, 2016 upon the election by either the Company or any Purchaser solely as to itself upon written notice to the other parties if the closing of the Public Offering does not occur prior to such date.

Section 8.  Survival of Representations and Warranties.  All of the representations and warranties contained herein shall survive each Closing Date.

Section 9.  Definitions.  Terms used but not otherwise defined in this Agreement shall have the meaning assigned to such terms in the registration statement on Form S-1 the Company has filed with the SEC, under the Securities Act.

“Cause” shall mean: (i) the Purchaser has committed a deliberate and premeditated act against the interests of the Company including, without limitation; an act of fraud, embezzlement,

6

misappropriation or breach of fiduciary duty against the Company, including, but not limited to, the offer, payment, solicitation or acceptance of any unlawful bribe or kickback with respect to the Company’s business; or (ii) the Purchaser has been convicted by a court of competent jurisdiction of, or pleaded guilty or nolo contendere to, any felony or any crime involving moral turpitude; or (iii) the Purchaser has failed to perform or neglected the material duties incident to his position as a director of the Company and such refusal or failure shall have continued for a period of twenty (20) days after written notice to the Purchaser specifying such refusal or failure in reasonable detail (other than a failure resulting from the Purchaser’s permanent and total disability as defined under Section 22(e)(3) of the Internal Revenue Code of 1986, as amended); or (iv) the Purchaser has become an officer or director of another blank check company in violation of the letter agreement to be entered into at the time of the Public Offering among the Company, the Sponsor, each Purchaser and the other parties signatory thereto; or (v) the Purchaser has engaged in conduct that violated the Company’s then existing written internal policies or procedures that have been provided to the Purchaser in writing prior to such conduct and which is materially detrimental to the business and reputation of the Company; or (vi) the Purchaser has engaged in (x) the unlawful use (including being under the influence) or possession of illegal drugs on the Company’s premises or (y) habitual drunkenness on the Company’s premises.

Section 10.  Miscellaneous.

A.  Successors and Assigns.  Except as otherwise expressly provided herein, all covenants and agreements contained in this Agreement by or on behalf of any of the parties hereto shall bind and inure to the benefit of the respective successors of the parties hereto whether so expressed or not.  Notwithstanding the foregoing or anything to the contrary herein, the parties may not assign this Agreement, other than assignments by any Purchaser to affiliates thereof.

B.  Severability.  Whenever possible, each provision of this Agreement shall be interpreted in such manner as to be effective and valid under applicable law, but if any provision of this Agreement is held to be prohibited by or invalid under applicable law, such provision shall be ineffective only to the extent of such prohibition or invalidity, without invalidating the remainder of this Agreement.

C.  Counterparts.  This Agreement may be executed simultaneously in two or more counterparts, none of which need contain the signatures of more than one party, but all such counterparts taken together shall constitute one and the same agreement.

D.  Descriptive Headings; Interpretation.  The descriptive headings of this Agreement are inserted for convenience only and do not constitute a substantive part of this Agreement.  The use of the word “including” in this Agreement shall be by way of example rather than by limitation.

E.  Governing Law.  This Agreement shall be deemed to be a contract made under the laws of the State of New York and for all purposes shall be construed in accordance with the internal laws of the State of New York.

7

F.  Amendments.  This Agreement may not be amended, modified or waived as to any particular provision, except by a written instrument executed by all parties hereto.

[Signature page follows]

8

IN WITNESS WHEREOF, the parties hereto have executed this Agreement to be effective as of the date first set forth above.

[Signature page to Private Placement Warrants Purchase Agreement]

[Signature page to Private Placement Warrants Purchase Agreement]

ANNEX I

ANNEX II

If the Over-Allotment Option is not exercised in full, each Purchaser will purchase its pro rata number of Private Placement Warrants relative to the portion of the Over-Allotment Option exercised.