Warrant Exercise Agreement, dated as of March 4, 2024, by and between BigBear.ai and the Investor

Exhibit 10.1

BIGBEAR.AI HOLDINGS, INC.

March 4, 2024

Holder of January 2023 Common Stock Purchase Warrant

Re: Inducement Offer to Exercise January 2023 Common Stock Purchase Warrant

Dear Holder:

BigBear.ai Holdings, Inc., a Delaware corporation (the “Company”), is pleased to offer to you an opportunity to exercise in full the Common Stock Purchase Warrant issued on January 19, 2023, which is exercisable for up to 13,888,889 shares of the Company’s common stock, par value $0.0001 per share (the “Common Stock”) (with a current exercise price of $2.39 per share) (the “Existing Warrants”) currently held by you (the “Holder”). The resale of the shares of Common Stock underlying the Existing Warrants (“Warrant Shares”) has been registered pursuant to a registration statement on Form S-3 (File No. 333-269465) (the “Registration Statement”). The Registration Statement is currently effective and, upon exercise of the Existing Warrants pursuant to this letter agreement, will be effective for the issuance or sale, as the case may be, of the Warrant Shares underlying the Existing Warrants (the “Existing Warrant Shares”). Capitalized terms not otherwise defined herein shall have the meanings set forth in the Existing Warrants.

In consideration for exercising in full the Existing Warrants held by the Holder as set forth on the signature page hereto (the “Warrant Exercise”), the Company hereby offers the Holder to issue the Holder or its designee a new unregistered Common Stock Purchase Warrant (the “New Warrant”) pursuant to Section 4(a)(2) of the Securities Act of 1933, as amended, (the “Securities Act”), to purchase up to 9,000,000 shares (the “New Warrant Shares”) of Common Stock, which New Warrant shall be substantially in the form of Exhibit A attached hereto and will be exercisable commencing upon the date that is six (6) months from the date of issuance, with an expiration date of five years after the date of issuance with an exercise price per share equal to $4.75.

The New Warrant certificates shall be delivered within two (2) Trading Days following the Warrant Exercise, and the resale of the New Warrant Shares, shall be registered under the Securities Act pursuant to the Resale Registration Statement (as defined hereinafter). Notwithstanding anything herein to the contrary, in the event that any Warrant Exercise would otherwise cause the Holder to exceed the beneficial ownership limitations (“Beneficial Ownership Limitation”) set forth in Section 2(e) of the Existing Warrant (or, if applicable and at the Holder’s election, 9.99%), the Company shall only issue such number of Warrant Shares to the Holder that would not cause the Holder to exceed the maximum number of Warrant Shares permitted thereunder, as directed by the Holder, with the balance to be held in abeyance until notice from the Holder that the balance (or portion thereof) may be issued in compliance with such limitations, which abeyance shall be evidenced through the Existing Warrant which shall be deemed prepaid thereafter (including the payment in full of the exercise price), and exercised pursuant to a Notice of Exercise in the Existing Warrant (provided no additional exercise price shall be due and payable). The parties hereby agree that the Beneficial Ownership Limitation for purposes of the Existing Warrant is as set forth on the Holder’s signature page hereto.

Expressly subject to the paragraph immediately following this paragraph below, the Holder may accept this offer by signing this letter below, with such acceptance constituting the Holder’s exercise in full of the Existing Warrant for an aggregate exercise price set forth on the Holder’s signature page hereto (the “Existing Warrant Exercise Price”) on or before 11:59 p.m. ET on March 4, 2024.

Additionally, the Company agrees to the representations, warranties and covenants set forth on Annex A attached hereto. Holder represents and warrants that it is an “accredited investor” as defined in Rule 501 of the Securities Act, and agrees that the New Warrants will contain restrictive legends when issued, and neither the New Warrants nor the Common Stock issuable upon exercise of the New Warrants will initially be registered under the Securities Act.

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The Holder understands that the New Warrants and the New Warrant Shares are not, and may never be, registered under the Securities Act, or the securities laws of any state and, accordingly, each certificate, if any, representing such securities shall bear a legend substantially similar to the following:

“NEITHER THIS SECURITY NOR THE SECURITIES FOR WHICH THIS SECURITY IS EXERCISABLE HAVE BEEN REGISTERED WITH THE SECURITIES AND EXCHANGE COMMISSION OR THE SECURITIES COMMISSION OF ANY STATE IN RELIANCE UPON AN EXEMPTION FROM REGISTRATION UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “SECURITIES ACT”), AND, ACCORDINGLY, MAY NOT BE OFFERED OR SOLD EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES ACT OR PURSUANT TO AN AVAILABLE EXEMPTION FROM, OR IN A TRANSACTION NOT SUBJECT TO, THE REGISTRATION REQUIREMENTS OF THE SECURITIES ACT AND IN ACCORDANCE WITH APPLICABLE STATE SECURITIES LAWS. THIS SECURITY AND THE SECURITIES ISSUABLE UPON EXERCISE OF THIS SECURITY MAY BE PLEDGED IN CONNECTION WITH A BONA FIDE MARGIN ACCOUNT OR OTHER LOAN SECURED BY SUCH SECURITIES.”

Certificates evidencing the New Warrant Shares shall not contain any legend (including the legend set forth above), (i) while a registration statement covering the resale of such New Warrant Shares is effective under the Securities Act and following the delivery of a legal opinion from counsel to the Company to Continental Stock Transfer & Trust Company, the current transfer agent of the Company, affirming that the New Warrant Shares are eligible for sale without such legends under the provisions of the effective registration statement, (ii) following any sale of such New Warrant Shares pursuant to Rule 144 under the Securities Act (“Rule 144”), (iii) if such New Warrant Shares are eligible for sale under Rule 144 (assuming cashless exercise of the New Warrants), without the requirement for the Company to be in compliance with the current public information required under Rule 144 as to such New Warrant Shares and without volume or manner-of-sale restrictions, (iv) if such New Warrant Shares may be sold under Rule 144 (assuming cashless exercise of the New Warrants) and the Company is then in compliance with the current public information required under Rule 144 as to such New Warrant Shares, or (v) if such legend is not required under applicable requirements of the Securities Act (including judicial interpretations and pronouncements issued by the staff of the Securities and Exchange Commission (the “Commission”) and the earliest of clauses (i) through (v), the “Delegend Date”). The Company shall cause its counsel to issue a legal opinion to Continental Stock Transfer & Trust Company, the current transfer agent of the Company, and any successor transfer agent of the Company (the “Transfer Agent”) promptly after the Delegend Date if required by the Company and/or the Transfer Agent to effect the removal of the legend hereunder, which opinion shall be in form and substance reasonably acceptable to the Holder. If all or any portion of the New Warrants are exercised at a time when the New Warrant Shares may be sold under Rule 144 and the Company is then in compliance with the current public information required under Rule 144 (assuming cashless exercise of the New Warrants), or if the New Warrant Shares may be sold under Rule 144 without the requirement for the Company to be in compliance with the current public information required under Rule 144 as to such New Warrant Shares or if such legend is not otherwise required under applicable requirements of the Securities Act (including judicial interpretations and pronouncements issued by the staff of the Commission) then such New Warrant Shares shall be issued free of all legends. The Company agrees that following the Delegend Date or at such time as such legend is no longer required under this paragraph, it will, no later than two (2) Trading Days following the delivery by the Holder to the Company or the Transfer Agent of a certificate representing the New Warrant Shares issued with a restrictive legend, deliver or cause to be delivered to the Holder a certificate representing such shares that is free from all restrictive and other legends or, at the request of the Holder shall credit the account of the Holder’s prime broker with the Depository Trust Company System as directed by the Holder.

In addition to the Holder’s other available remedies, the Company shall pay to a Holder, in cash, (i) as partial liquidated damages and not as a penalty, for each $1,000 of New Warrant Shares (based on the VWAP of the Common Stock on the date such New Warrant Shares are submitted to the Transfer Agent) delivered for removal of the restrictive legend, $5 per Trading Day (increasing to $10 per Trading Day seven (7) Trading Days after such damages have begun to accrue) for each Trading Day following two (2) Trading Days after the delivery date (the “Legend Removal Date”) until such certificate is delivered without a legend and (ii) if the Company fails to (a) issue and deliver (or cause to be delivered) to the Holder by the Legend Removal Date a certificate representing the New Warrant Shares so delivered to the Company by the Holder that is free from all restrictive and other legends and (b) if after the Legend Removal Date the Holder purchases (in an open market transaction or otherwise) shares of

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Common Stock to deliver in satisfaction of a sale by the Holder of all or any portion of the number of shares of Common Stock, or a sale of a number of shares of Common Stock equal to all or any portion of the number of shares of Common Stock that the Holder anticipated receiving from the Company without any restrictive legend, then, an amount equal to the excess of the Holder’s total purchase price (including brokerage commissions and other out-of-pocket expenses, if any) for the shares of Common Stock so purchased (including brokerage commissions and other out-of-pocket expenses, if any) (the “Buy-In Price”) over the product of (A) such number of New Warrant Shares that the Company was required to deliver to the Holder by the Legend Removal Date and for which the Holder was required to purchase shares to timely satisfy delivery requirements, multiplied by (B) the weighted average price at which the Holder sold that number of shares of Common Stock.

From the date hereof until thirty (30) days after the Closing Date, neither the Company nor any Subsidiary shall (A) issue, enter into any agreement to issue or announce the issuance or proposed issuance of any Common Stock or Common Stock Equivalents or (B) file any registration statement or any amendment or supplement to any existing registration statement (other than the resale registration statement referred to herein or prospectus supplements to the Registration Statements to reflect the transactions contemplated hereby).

From the date hereof until sixty (60) days after the Closing Date, the Company shall be prohibited from effecting or entering into an agreement to effect any issuance by the Company or any of its Subsidiaries of shares of Common Stock or Common Stock Equivalents (or a combination of units thereof) involving a Variable Rate Transaction. “Variable Rate Transaction” is defined herein as a transaction in which the Company (i) issues or sells any debt or equity securities that are convertible into, exchangeable or exercisable for, or include the right to receive additional shares of Common Stock either (A) at a conversion price, exercise price or exchange rate or other price that is based upon and/or varies with the trading prices of or quotations for the Common Stock at any time after the initial issuance of such debt or equity securities, or (B) with a conversion, exercise or exchange price that is subject to being reset at some future date after the initial issuance of such debt or equity security (other than in connection with a stock split or stock dividend or similar event) or upon the occurrence of specified or contingent events directly or indirectly related to the business of the Company or the market for shares of Common Stock or (ii) enters into, or effects a transaction under, any agreement, including, but not limited to, an equity line of credit or an “at-the-market offering,” whereby the Company may issue securities at a future determined price regardless of whether shares pursuant to such agreement have actually been issued and regardless of whether such agreement is subsequently canceled. The Holder shall be entitled to obtain injunctive relief against the Company to preclude any such issuance, which remedy shall be in addition to any right to collect damages.

If this offer is accepted and the transaction documents are executed on or before 11:59 p.m. ET on March 4, 2024, then on or before 8:30 a.m. ET on the next Trading Day, the Company shall issue a press release or file a Form 8-K with the Commission disclosing all material terms of the transactions contemplated hereunder. From and after the issuance of such press release or the filing of such Form 8-K, the Company represents to the Holder that it shall have publicly disclosed all material, non-public information delivered to the Holder by the Company, or any of its respective officers, directors, employees or agents in connection with the transactions contemplated hereunder. In addition, effective upon the issuance of such press release or the filing of such Form 8-K, the Company acknowledges and agrees that any and all confidentiality or similar obligations under any agreement, whether written or oral, between the Company, any of its subsidiaries or any of their respective officers, directors, agents, employees or Affiliates on the one hand, and the Holder and its Affiliates on the other hand, shall terminate. The Company represents, warrants and covenants that, upon acceptance of this offer, the shares of Common Stock underlying the Existing Warrants shall be issued free of any legends or restrictions on resale by the Holder and shall be delivered two Business Days after the date the Company receives the Existing Warrant Exercise Price (or, with respect to the Warrant Shares underlying the Existing Warrant that would otherwise be in excess of the Beneficial Ownership Limitation, within two Business Days of the date the Company is notified by the Holder that its ownership is less than the Beneficial Ownership Limitation).

As soon as practicable (and in any event within 30 calendar days of the date of this letter agreement (the “Filing Date”), the Company shall file a resale registration statement (the “Resale Registration Statement”) on Form S-1 or Form S-3, if eligible, providing for the resale by the Purchaser of the New Warrant Shares issued and issuable upon exercise of the New Warrants. The Company shall use reasonable best efforts to cause the Resale Registration Statement to become effective within 45 calendar days following the date hereof (or, in the event of a “full review” by the Commission, the 60th calendar day following the date hereof hereof) (the “Effectiveness Date”) and to keep

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the Resale Registration Statement effective at all times until no holder of the New Warrants owns any New Warrants or New Warrant Shares. In the event that the Resale Registration Statement is not (i) filed by the Filing Date or (ii) declared effective by the Commission by the Effectiveness Date, then, in addition to any other rights the holders of New Warrants may have hereunder or under applicable law, on the Filing Date or the Effectiveness Date (each such date being referred to herein as an “Event Date”) and on each monthly anniversary of such Event Date (if the Resale Registration Statement shall not have been filed or declared effective by the applicable Event Date) until the Resale Registration Statement is filed or declared effective, the Company shall pay to each holder of New Warrants an amount in cash, as partial liquidated damages and not as a penalty, equal to the product of 1.0% multiplied by the aggregate exercise price of the New Warrants held by each holder of the New Warrants. The parties agree that the maximum aggregate liquidated damages payable to a holder of the New Warrants shall be 5.0% of the aggregate exercise price of the New Warrants. Held by each holder of the New Warrants. If the Company fails to pay any partial liquidated damages pursuant to this Section in full within seven days after the date payable, the Company will pay interest thereon at a rate of 12% per annum (or such lesser maximum amount that is permitted to be paid by applicable law) to the holders of the New Warrants, accruing daily from the date such partial liquidated damages are due until such amounts, plus all such interest thereon, are paid in full. The partial liquidated damages pursuant to the terms hereof shall apply on a daily pro rata basis for any portion of a month prior to the Resale Registration Statement being filed or declared effective, as the case may be.

Within one Business Day from the Holder’s execution of this letter, the Holder shall make available for “Delivery Versus Payment” to the Company immediately available funds equal to the number of Existing Warrants being exercised multiplied by the exercise price per share as set forth above and the Company shall deliver the Warrant Shares via “Delivery Versus Payment” to the Holder and shall deliver the New Warrants registered in the name of the Holder. The date of the closing of the exercise of the Existing Warrant (the “Closing”) shall be referred to as the “Closing Date.”

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Accepted and Agreed to:

[Signature Page to Warrant Exercise Agreement]

Annex A

Representations, Warranties and Covenants of the Company. The Company hereby makes the following representations and warranties to the Holder:

SEC Reports. The Company has filed all reports, schedules, forms, statements and other documents required to be filed by the Company under the Exchange Act, including pursuant to Section 13(a) or 15(d) thereof, for the one year preceding the date hereof (or such shorter period as the Company was required by law or regulation to file such material) (the foregoing materials, including the exhibits thereto and documents incorporated by reference therein, being collectively referred to herein as the “SEC Reports”). As of their respective dates, the SEC Reports complied in all material respects with the requirements of the Exchange Act and none of the SEC Reports, when filed, contained any untrue statement of a material fact or omitted to state a material fact required to be stated therein or necessary in order to make the statements therein, in the light of the circumstances under which they were made, not misleading. The Company is not currently an issuer identified in Rule 144(i) under the Securities Act.

Authorization; Enforcement. The Company has the requisite corporate power and authority to enter into and to consummate the transactions contemplated by this letter agreement and otherwise to carry out its obligations hereunder and thereunder. The execution and delivery of this letter agreement by the Company and the consummation by the Company of the transactions contemplated hereby have been duly authorized by all necessary action on the part of the Company and no further action is required by the Company, its board of directors or its stockholders in connection therewith. This letter agreement has been duly executed by the Company and, when delivered in accordance with the terms hereof, will constitute the valid and binding obligation of the Company enforceable against the Company in accordance with its terms, except (i) as limited by general equitable principles and applicable bankruptcy, insolvency, reorganization, moratorium and other laws of general application affecting enforcement of creditors’ rights generally, (ii) as limited by laws relating to the availability of specific performance, injunctive relief or other equitable remedies and (iii) insofar as indemnification and contribution provisions may be limited by applicable law.

No Conflicts. The execution, delivery and performance of this letter agreement by the Company and the consummation by the Company of the transactions contemplated hereby do not and will not: (i) conflict with or violate any provision of the Company’s certificate or articles of incorporation, bylaws or other organizational or charter documents; or (ii) conflict with, or constitute a default (or an event that with notice or lapse of time or both would become a default) under, result in the creation of any liens, claims, security interests, other encumbrances or defects upon any of the properties or assets of the Company in connection with, or give to others any rights of termination, amendment, acceleration or cancellation (with or without notice, lapse of time or both) of, any material agreement, credit facility, debt or other material instrument (evidencing Company debt or otherwise) or other material understanding to which such Company is a party or by which any property or asset of the Company is bound or affected; or (iii) conflict with or result in a violation of any law, rule, regulation, order, judgment, injunction, decree or other restriction of any court or governmental authority to which the Company is subject (including federal and state securities laws and regulations), or by which any property or asset of the Company is bound or affected, except, in the case of each of clauses (ii) and (iii), such as would not have or reasonably be expected to result in a material adverse effect upon the business, prospects, properties, operations, condition (financial or otherwise) or results of operations of the Company, taken as a whole, or in its ability to perform its obligations under this letter agreement.

Trading Market. The transactions contemplated under this letter agreement comply with all the rules and regulations of the New York Stock Exchange.

Filings, Consents and Approvals. The Company is not required to obtain any consent, waiver, authorization or order of, give any notice to, or make any filing or registration with, any court or other federal, state, local or other governmental authority or other Person in connection with the execution, delivery and performance by the Company of this letter agreement, other than: (i) the filings required pursuant to this letter agreement, (ii) application(s) and/or notice to each applicable Trading Market for the listing of the New Warrants and New Warrant Shares for trading thereon in the time and manner required thereby, and (iii) the filing of Form D with the Commission and such filings as are required to be made under applicable state and federal securities laws.

Listing of Common Stock. The Company hereby agrees to use commercially reasonable efforts to maintain the listing or quotation of the Common Stock on the Trading Market on which it is currently listed, and concurrently with the Closing, the Company shall apply to list or quote all of the New Warrant Shares on such Trading Market and promptly secure the listing of all of the New Warrant Shares on such Trading Market. The Company further agrees, if the Company applies to have the Common Stock traded on any other Trading Market, it will then include in such application all of the New Warrant Shares, and will take such other action as is necessary to cause all of the New Warrant Shares to be listed or quoted on such other Trading Market as promptly as possible. The Company will then take all action reasonably necessary to continue the listing and trading of its Common Stock on a Trading Market and will comply in all respects with the Company’s reporting, filing and other obligations under the bylaws or rules of the Trading Market. The Company agrees to maintain the eligibility of the Common Stock for electronic transfer through the Depository Trust Company or another established clearing corporation, including, without limitation, by timely payment of fees to the Depository Trust Company or such other established clearing corporation in connection with such electronic transfer.

Form D; Blue Sky Filings. If required, the Company agrees to timely file a Form D with respect to the New Warrants and New Warrant Shares as required under Regulation D and to provide a copy thereof, promptly upon request of the Holder. The Company shall take such action as the Company shall reasonably determine is necessary in order to obtain an exemption for, or to qualify the New Warrants and New Warrant Shares for, sale to the Holder at Closing under applicable securities or “Blue Sky” laws of the states of the United States, and shall provide evidence of such actions promptly upon request of the Holder.

Exhibit A

Form of New Warrant