Private Placement Warrant Subscription Agreement, dated October 28, 2021, among the CompanyB. Riley Principal Investments, LLC and Continental Stock Transfer & Trust Company

Exhibit 10.4

PRIVATE PLACEMENT WARRANT SUBSCRIPTION AGREEMENT

This PRIVATE PLACEMENT WARRANT SUBSCRIPTION AGREEMENT (this “Agreement”) is made as of the 28th day of October, 2021, by and between AltEnergy Acquisition Corp, a Delaware corporation (the “Company”), and B. Riley Principal Investments, LLC (the “Subscriber”).

WHEREAS, the Company has filed with the Securities and Exchange Commission (“SEC”) a Registration Statement on Form S-1 (the “Registration Statement”) in connection with an underwritten initial public offering (“IPO”) of 23,000,000 units of the Company (the “Public Units”) (including up to 3,000,000 Public Units to the extent the over-allotment option of the underwriters of the IPO is exercised (the “Over-allotment Option”)), with each such Public Unit consisting of one share of Class A common stock, par value $0.0001 per share (the “Class A Common Stock”, together with the Class B common stock, par value $0.0001 per share (the “Class B Common Stock”), of the Company, the “Common Stock”), of the Company and one-half of one redeemable warrant, where each whole warrant entitles the holder to purchase one share of Class A Common Stock (“Warrant”) at an exercise price of $11.50 per share (subject to adjustments);

WHEREAS, the Company desires to sell to the Subscriber on a private placement basis an aggregate of 400,000 Private Placement Warrants (the “Private Placement Warrants”) of the Company for a purchase price of $1.00 per Private Placement Warrant, each Private Placement Warrant exercisable to purchase one share of Class A Common Stock. The shares of Class A Common Stock underlying the Private Placement Warrants are hereinafter referred to as the “Private Shares.” The Private Placement Warrants and Private Shares, collectively, are hereinafter referred to as the “Securities.” Each Private Placement Warrant is exercisable to purchase one share of Class A Common Stock at an exercise price of $11.50, subject to the adjustments as set forth in the Warrant Agreement (as defined below), during the period commencing 30 days following the consummation of the Company’s initial business combination (the “Business Combination”), as such term is defined in the Registration Statement, and expiring on the fifth anniversary of the consummation of the Business Combination or earlier upon redemption or liquidation; and

WHEREAS, the Subscriber wishes to purchase an aggregate of 400,000 Private Placement Warrants for the purchase price of $1.00 per Private Placement Warrant, and the Company wishes to accept such subscription from the Subscriber.

NOW, THEREFORE, in consideration of the premises and the mutual covenants hereinafter set forth and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Company and the Subscriber hereby, intending legally to be bound, agree as follows:

1. Agreement to Subscribe.

1.1 Purchase and Issuance of the Private Placement Warrants. Upon the terms and subject to the conditions of this Agreement:

(a) The Company has duly authorized the issuance and sale of the Warrants to the Subscriber.

(b) The Subscriber hereby agrees to purchase from the Company, and the Company hereby agrees to sell to the Subscriber, on the Closing Date (as defined below) 400,000 Private Placement Warrants, for $1.00 per Private Placement Warrant, payable by the Subscriber by wire transfer of immediately available funds or by such other method as may be reasonably acceptable to the Company as follows: (i) $400,000 to the trust account (the “Trust Account”) at a financial institution to be chosen by the Company, maintained by Continental Stock Transfer & Trust Company, acting as trustee (“Continental”), at least one (1) business day prior to the Closing Date, and (ii) $0 to the Company, at a financial institution to be chosen by the Company, on the Closing Date. On the Closing Date, the Company shall, subject to receipt of funds pursuant to the immediately prior sentence, at its option, deliver to the Subscriber the certificates representing the Private Placement Warrants purchased by the Subscriber or effect such delivery in book-entry form.

1.2 Closing. The closing of the purchase and sale of the Private Placement Warrants shall take place substantially simultaneously with the closing of the IPO (the “Closing Date”). The closing of the purchase and sale of the Private Placement Warrants shall take place at the offices of Morrison Cohen, LLP, 909 Third Avenue, New York, New York 10022, or such other place as may be agreed upon by the parties hereto.

1.3 Conditions to Closing. The obligation of the Subscriber to purchase and pay for the Private Placement Warrants as provided herein shall be subject to the satisfaction of the conditions set forth in the Underwriting Agreement, dated the date hereof (the “Underwriting Agreement”), by and between the Company and B. Riley Securities, Inc., as representative of the several underwriters named therein.

1.4 Termination. This Agreement and each of the obligations of the undersigned shall be null and void and without effect if the Closing Date does not occur on prior to November 2, 2021 or if the Underwriting Agreement is terminated for any reason.

2. Representations and Warranties of the Subscriber.

The Subscriber represents and warrants to the Company as follows:

2.1 Organization and Authority. The Subscriber is duly organized, validly existing and in good standing under the laws of its jurisdiction of organization and it possesses all requisite power and authority necessary to carry out the transactions contemplated by this Agreement.

2.2 Authority. This Agreement has been validly authorized, executed and delivered by the Subscriber and is a valid and binding agreement of the Subscriber, enforceable against the Subscriber in accordance with its terms, subject to the general principles of equity and to bankruptcy or other laws affecting the enforcement of creditors’ rights generally.

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2.3 No Conflicts. The execution, delivery and performance of this Agreement and the Private Placement Warrants and the consummation by the Subscriber of the transactions contemplated hereby do not violate, conflict with or constitute a default under (i) the Subscriber’s organizational documents, (ii) any material agreement or instrument to which the Subscriber is a party or (iii) any law, statute, rule or regulation to which the Subscriber is subject, or any agreement, order, judgment or decree to which the Subscriber is subject.

2.4 Accredited Investor. The Subscriber represents that it is an “accredited investor” as such term is defined in Rule 501(a) of Regulation D under the Securities Act of 1933, as amended (the “Securities Act”), and acknowledges that the sale contemplated hereby is being made in reliance, among other things, on a private placement exemption to “accredited investors” under the Securities Act and similar exemptions under state law.

2.5 Intent. The Subscriber is purchasing the Securities solely for investment purposes, for the Subscriber’s own account (and/or for the account or benefit of its members or affiliates, as permitted, pursuant to the terms hereof), and not with a view to the distribution thereof and the Subscriber has no present arrangement to sell the Securities to or through any person or entity except as may be permitted hereunder.

2.6 Restrictions on Transfer. The Subscriber acknowledges and understands the Securities are being offered in a transaction not involving a public offering in the United States within the meaning of the Securities Act. The Securities have not been registered under the Securities Act or any state securities laws, and may be offered, resold, pledged or otherwise transferred only (i) pursuant to an effective registration statement filed under the Securities Act, (ii) pursuant to an exemption from registration under Rule 144 promulgated under the Securities Act, if available, or (iii) pursuant to any other available exemption from the registration requirements of the Securities Act, and in each case in accordance with any applicable securities laws of any state or any other jurisdiction.

2.7 Sophisticated Investor.

(a) The Subscriber is sophisticated in financial matters and is able to evaluate the risks and benefits of the investment in the Securities.

(b) The Subscriber is aware that an investment in the Securities is highly speculative and subject to substantial risks because, among other things, (i) the Securities are subject to transfer restrictions and have not been registered under the Securities Act and therefore cannot be sold unless subsequently registered under the Securities Act or an exemption from such registration is available and (ii) the Securities held by the Subscriber are not entitled to, and have no right, interest or claim to any monies held in the Trust Account, and the Subscriber may suffer a loss of a portion or all of its investment in the Securities. The Subscriber is able to bear the economic risk of its investment in the Securities for an indefinite period of time.

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2.8 Reliance on Representations and Warranties. The Subscriber understands the Private Placement Warrants are being offered and sold to the Subscriber in reliance on exemptions from the registration requirements under the Securities Act, and analogous provisions in the laws and regulations of various states, and that the Company is relying upon the truth and accuracy of the representations, warranties, agreements, acknowledgments and understandings of the Subscriber set forth in this Agreement in order to determine the applicability of such provisions.

2.9 No General Solicitation. The Subscriber is not subscribing for the Private Placement Warrants as a result of or subsequent to any general solicitation or general advertising, including but not limited to any advertisement, article, notice or other communication published in any newspaper, magazine, or similar media or broadcast over television or radio, or presented at any seminar or meeting or in the Registration Statement.

2.10 Legend. Subscriber acknowledges and agrees the book-entries or certificates, if any, evidencing each of the Securities shall bear a restrictive legend (the “Legend”), in form and substance substantially as set forth in Section 4 hereof.

3. Representations, Warranties and Covenants of the Company.

The Company represents and warrants to, and agrees with, the Subscriber that:

3.1 Organization and Qualification. The Company is a corporation duly incorporated, validly existing and in good standing under the laws of the State of Delaware and has the requisite corporate power to own its properties and assets and to carry on its business as now being conducted.

3.2 Authorization; Enforcement. (i) The Company has the requisite corporate power and authority to enter into and perform its obligations under this Agreement and to issue the Securities in accordance with the terms hereof, (ii) the execution, delivery and performance of this Agreement by the Company and the consummation by it of the transactions contemplated hereby have been duly authorized by all necessary corporate action, and no further consent or authorization of the Company or its Board of Directors or stockholders is required, and (iii) this Agreement constitutes valid and binding obligations of the Company enforceable against the Company in accordance with its terms, except as such enforceability may be limited by applicable bankruptcy, insolvency, fraudulent conveyance, moratorium, reorganization, or similar laws relating to, or affecting generally the enforcement of, creditors’ rights and remedies or by equitable principles of general application and except as enforcement of rights to indemnity and contribution may be limited by federal and state securities laws or principles of public policy.

3.3 No Conflicts. The execution, delivery and performance of this Agreement and the consummation by the Company of the transactions contemplated hereby do not (i) result in a violation of the Company’s certificate of incorporation or by-laws, (ii) conflict with, or constitute a default under any agreement or instrument to which the Company is a party or (iii) any law statute, rule or regulation to which the Company is subject or any agreement, order, judgment or decree to which the Company is subject. Other than any SEC or state securities filings which may be required to be made by the Company subsequent to the Closing Date, and any registration statement which may be filed pursuant thereto, the Company is not required under

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federal, state or local law, rule or regulation to obtain any consent, authorization or order of, or make any filing or registration with, any court or governmental agency or self-regulatory entity in order for it to perform any of its obligations under this Agreement or issue the Private Placement Warrants or Warrant Shares in accordance with the terms hereof.

3.4 Valid Issuance of Capital Stock. The total number of shares of all classes of capital stock which the Company has authority to issue is 100,000,000 shares of Class A Common Stock, 10,000,000 shares of Class B Common Stock and 1,000,000 shares of preferred stock, $0.0001 par value per share (“Preferred Stock”). As of the date hereof, the Company has issued and outstanding 5,750,000 shares of Class B Common Stock (of which up to 750,000 shares are subject to forfeiture as described in the Registration Statement), no shares of Class A Common Stock and no shares of Preferred Stock. All of the issued shares of capital stock of the Company have been duly authorized, validly issued, and are fully paid and non-assessable.

3.5 Title to Securities. Upon issuance in accordance with, and payment pursuant to, the terms hereof and that certain warrant agreement (the “Warrant Agreement”) to be entered into between the Company and Continental, as warrant agent, as the case may be, each of the Private Placement Warrants and Warrant Shares will be duly and validly issued, fully paid and non-assessable. On the date of issuance of the Private Placement Warrants, the Warrant Shares shall have been reserved for issuance. Upon issuance in accordance with, and payment pursuant to, the terms hereof and the Warrant Agreement, as the case may be, the Subscriber will have or receive good title to the Private Placement Warrants free and clear of all liens, claims and encumbrances of any kind, other than (i) transfer restrictions hereunder and (ii) transfer restrictions under federal and state securities laws.

3.6 Additional Representations and Warranties. The representations and warranties of the Company set forth in the Underwriting Agreement are hereby incorporated herein and are true and correct with the same force and effect as though expressly made herein as of the date hereof.

4. Legend.

4.1 Legend. The Company will issue the Private Placement Warrants, and when issued, the Warrant Shares, purchased by the Subscriber in the name of the Subscriber. The Securities will bear the following Legend and appropriate “stop transfer” instructions:

“THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “SECURITIES ACT”), OR ANY STATE SECURITIES LAWS AND NEITHER THE SECURITIES NOR ANY INTEREST THEREIN MAY BE OFFERED, SOLD, TRANSFERRED, PLEDGED OR OTHERWISE DISPOSED OF EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES ACT OR SUCH LAWS OR AN EXEMPTION FROM REGISTRATION UNDER THE SECURITIES ACT AND SUCH LAWS WHICH, IN THE OPINION OF COUNSEL FOR THIS CORPORATION, IS AVAILABLE.”

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“THE SECURITIES REPRESENTED BY THIS CERTIFICATE ARE SUBJECT TO LOCK-UP PURSUANT TO A PRIVATE PLACEMENT WARRANT SUBSCRIPTION AGREEMENT BETWEEN ALTENERGY ACQUISITION CORP. AND THE SUBSCRIBER PARTY THERETO AND MAY ONLY BE OFFERED, SOLD, TRANSFERRED, PLEDGED OR OTHERWISE DISPOSED DURING THE TERM OF THE LOCK-UP PURSUANT TO THE TERMS SET FORTH IN THE PRIVATE PLACEMENT WARRANT SUBSCRIPTION AGREEMENT.”

4.2 Subscriber’s Compliance. Nothing in this Section 4 shall affect in any way the Subscriber’s obligations and agreements to comply with all applicable securities laws upon resale of the Private Placement Warrants or any securities underlying the Private Placement Warrants.

4.3 Registration Rights. The Subscriber shall be entitled to certain registration rights relating to the Private Placement Warrants and the Private Shares that will be governed by a registration rights agreement (“Registration Rights Agreement”) to be entered into among the Company, the Subscriber and the other security holders party thereto, on or prior to the effective date of the Registration Statement.

5. Waiver of Liquidation Distributions.

In connection with the Securities purchased pursuant to this Agreement, the Subscriber hereby waives any and all right, title, interest or claim of any kind in or to any distributions of the amounts in the Trust Account with respect to the Securities, whether (i) in connection with the exercise of redemption rights if the Company consummates the Business Combination, (ii) in connection with any tender offer conducted by the Company prior to a Business Combination, (iii) upon the Company’s redemption of shares of Common Stock sold in the Company’s IPO upon the Company’s failure to timely complete the Business Combination or (iv) in connection with a stockholder vote to approve an amendment to the Company’s amended and restated certificate of incorporation, (A) to modify the substance or timing of the Company’s obligation to allow redemption in connection with the Business Combination or to redeem 100% of the Company’s public shares if the Company does not timely complete the Business Combination or (B) with respect to any other provision relating to stockholders’ rights or pre-Business Combination activity. In the event Subscriber purchases shares of Common Stock in the IPO or in the aftermarket, any additional shares so purchased shall be eligible to receive the redemption value of such shares of Common Stock upon the same terms offered to all other purchasers of Common Stock in the IPO in the event the Company fails to consummate the Business Combination.

6. Terms of Private Placement Warrants. Each Private Placement Warrant shall have the terms set forth in the Warrant Agreement.

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7. Lock-Up Period.

7.1 The Subscriber agrees that it shall not Transfer any Securities until 30 days following the consummation of the Business Combination; provided, however, that Transfers of Securities are permitted (i) to the Company’s officers or directors, any affiliates or family members of any of the Company’s officers or directors, any members of the Subscriber, or any affiliates of the Subscriber, as well as affiliates of such members and funds and accounts advised by such members; (ii) in the case of an individual, by gift to a member of the individual’s immediate family or to a trust, the beneficiary of which is a member of the individual’s immediate family, an affiliate of such person or to a charitable organization; (iii) in the case of an individual, by virtue of laws of descent and distribution upon death of the individual; (iv) in the case of an individual, pursuant to a qualified domestic relations order; (v) by private sales or transfers made in connection with any forward purchase agreement or similar arrangement or in connection with the consummation of the Business Combination at prices no greater than the price at which the shares or warrants were originally purchased; (vi) in the event of the Company’s liquidation prior to the completion of the Business Combination; (vii) by virtue of the laws of the State of Delaware or the Subscriber’s limited liability company agreement upon dissolution of the Subscriber; or (viii) in the event of the Company’s liquidation, merger, capital stock exchange, reorganization or other similar transaction which results in all of the Company’s stockholders having the right to exchange their shares of Common Stock for cash, securities or other property subsequent to the completion of the Business Combination, provided, however, that in the case of clauses (i) through (v) or (vii), these permitted transferees must enter into a written agreement with the Company agreeing to be bound by the Transfer and other restrictions contained herein.

7.2 For purposes of Section 7.1, the term “Transfer” shall mean the (i) sale of, offer to sell, contract or agreement to sell, hypothecate, pledge, grant of any option to purchase or otherwise dispose of or agreement to dispose of, directly or indirectly, or establishment or increase of a put equivalent position or liquidation with respect to or decrease of a call equivalent position within the meaning of Section 16 of the Securities Exchange Act of 1934, as amended, and the rules and regulations of the SEC promulgated thereunder with respect to, any of the Securities, (ii) entry into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of any of the Securities, whether any such transaction is to be settled by delivery of such Securities, in cash or otherwise, or (iii) public announcement of any intention to effect any transaction specified in clause (i) or (ii).

8. Terms of the Private Placement Warrants.

8.1 The Private Placement Warrants are substantially identical to the warrants included in the units to be offered in the IPO except that: (i) the Private Placement Warrants and Warrant Shares are subject to the transfer restrictions described in Section 7 hereof, (ii) the Private Placement Warrants will be non-redeemable and may be exercisable on a “cashless” basis if held by a Subscriber or its permitted transferees, as further described in the Warrant Agreement, and (iii) the Private Placement Warrants and Warrant Shares are being purchased pursuant to an exemption from the registration requirements of the Securities Act and will become freely tradable only after the expiration of the lockup described above in clause (i) and they are registered pursuant to the Registration Rights Agreement or an exemption from registration is available, and the restrictions described above in clause (i) have expired.

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9. Governing Law; Jurisdiction; Waiver of Jury Trial.

This Agreement shall be governed by and construed in accordance with the laws of the State of New York for agreements made and to be wholly performed within such state. THE PARTIES HERETO HEREBY WAIVE ANY RIGHT TO A JURY TRIAL IN CONNECTION WITH ANY LITIGATION PURSUANT TO THIS AGREEMENT AND THE TRANSACTIONS CONTEMPLATED HEREBY.

10. Assignment; Entire Agreement; Amendment.

10.1 Assignment. Neither this Agreement nor any rights hereunder may be assigned by any party to any other person other than by the Subscriber to a person agreeing to be bound by the terms hereof, including the transfer restrictions contained in Section 7 hereof.

10.2 Entire Agreement. This Agreement sets forth the entire agreement and understanding between the parties as to the subject matter thereof and merges and supersedes all prior discussions, agreements and understandings of any and every nature among them.

10.3 Amendment. Except as expressly provided in this Agreement, neither this Agreement nor any term hereof may be amended, waived, discharged or terminated other than by a written instrument signed by all of the parties hereto.

10.4 Binding upon Successors. This Agreement shall be binding upon and inure to the benefit of the parties hereto and to their respective heirs, legal representatives, successors and permitted assigns.

11. Notices.

11.1 Notices. Unless otherwise provided herein, any notice or other communication to a party hereunder shall be sufficiently given if in writing and personally delivered or sent by facsimile or other electronic transmission with copy sent in another manner herein provided or sent by courier (which for all purposes of this Agreement shall include Federal Express or other recognized overnight courier) or mailed to said party by certified mail, return receipt requested, at its address provided for herein or such other address as either may designate for itself in such notice to the other. Communications shall be deemed to have been received when delivered personally, on the scheduled arrival date when sent by next day or 2nd-day courier service, or if sent by facsimile upon receipt of confirmation of transmittal or, if sent by mail, then three days after deposit in the mail. If given by electronic transmission, such notice shall be deemed to be delivered (i) if by electronic mail, when directed to an electronic mail address at which the stockholder has consented to receive notice; (ii) if by a posting on an electronic network together with separate notice to the stockholder of such specific posting, upon the later of (1) such posting and (2) the giving of such separate notice; and (iii) if by any other form of electronic transmission, when directed to the stockholder.

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12. Counterparts.

This Agreement may be executed in one or more counterparts, all of which when taken together shall be considered one and the same agreement and shall become effective when counterparts have been signed by each party and delivered to the other party, it being understood that both parties need not sign the same counterpart. In the event that any signature is delivered by facsimile transmission or by e-mail delivery of a “pdf” format data file, such signature shall create a valid and binding obligation of the party executing (or on whose behalf such signature is executed) with the same force and effect as if such facsimile or “.pdf” signature page were an original thereof.

13. Survival; Severability.

13.1 Survival. The representations, warranties, covenants and agreements of the parties hereto shall survive the Closing Date.

13.2 Severability. In the event that any provision of this Agreement becomes or is declared by a court of competent jurisdiction to be illegal, unenforceable or void, this Agreement shall continue in full force and effect without said provision; provided that no such severability shall be effective if it materially changes the economic benefit of this Agreement to any party.

14. Headings.

The titles and subtitles used in this Agreement are used for convenience only and are not to be considered in construing or interpreting this Agreement.

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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 Warrant Subscription Agreement]