Document:

Exhibit 10.4

 

May 24, 2021

 

Fifth Wall Acquisition Corp. III

6060 Center Drive 10th Floor

Los Angeles, California 90045

 

Re:      Initial Public Offering

 

Ladies and Gentlemen:

 

This letter (this “Letter Agreement”)
is being delivered to you in accordance with the Underwriting Agreement (the “Underwriting Agreement”) entered
into by and among Fifth Wall Acquisition Corp. III, a Cayman Islands exempted company (the “Company”), Deutsche
Bank Securities Inc., Goldman Sachs & Co. LLC and BofA Securities, Inc. as representatives (the “Representatives”)
of the several underwriters (each, an “Underwriter” and collectively, the “Underwriters”),
relating to an underwritten initial public offering (the “Public Offering”), of up to 28,750,000 of the Company’s
shares (the “Shares”) of Class A ordinary shares, par value $0.0001 (the “Class A Ordinary Shares”),
including up to 3,750,000 Shares that may be purchased to cover over-allotments, if any. The Shares will be sold in the Public Offering
pursuant to a registration statement on Form S-1 and prospectus (the “Prospectus”) filed by the Company with
the U.S. Securities and Exchange Commission (the “Commission”) and the Company has applied to have the Shares
listed on the Nasdaq Capital Market. Certain capitalized terms used herein are defined in paragraph 11 hereof.

 

In order to induce the Company and the Underwriters
to enter into the Underwriting Agreement and to proceed with the Public Offering and for other good and valuable consideration, the receipt
and sufficiency of which are hereby acknowledged, each of Fifth Wall Acquisition Sponsor III LLC (the “Sponsor”)
and the undersigned individuals, each of whom is a member of the Company’s board of directors and/or management team (each of the
undersigned individuals, an “Insider” and collectively, the “Insiders”), hereby agrees
with the Company as follows:

 

		1.	The Sponsor and each Insider agrees that if the Company seeks shareholder approval of a proposed Business Combination, then in connection
with such proposed Business Combination, it, he or she shall (i) vote any Ordinary Shares (as defined below) owned by it, him or her in
favor of any proposed Business Combination and (ii) not redeem any Ordinary Shares owned by it, him or her in connection with such shareholder
approval. If the Company seeks to consummate a proposed Business Combination by engaging in a tender offer, the Sponsor and each Insider
agrees that it, he or she will not sell or tender any Ordinary Shares owned by it, him or her in connection therewith.

 

     

     

    

 

		2.	The Sponsor and each Insider hereby agrees that in the event that the Company fails to consummate a Business Combination within 24
months from the closing of the Public Offering, or such later period approved by the Company’s shareholders in accordance with the
Company’s amended and restated memorandum and articles of association (as it may be amended from time to time, the “Articles”), the Sponsor and
each Insider shall take all reasonable steps to cause the Company to (i) cease all operations except for the purpose of winding up, (ii)
as promptly as reasonably possible but not more than ten business days thereafter, redeem 100% of the Class A Ordinary Shares sold in
the Public Offering (the “Offering Shares”), at a per-share price, payable in cash, equal to the aggregate amount
then on deposit in the Trust Account (as defined below), including interest earned on the funds held in the Trust Account and not previously
released to the Company to pay its taxes (less taxes payable and up to $100,000 of interest to pay dissolution expenses), divided by the
number of then outstanding Offering Shares, which redemption will completely extinguish all Public Shareholders’ (as defined below)
rights as shareholders (including the right to receive further liquidating distributions, if any), and (iii) as promptly as reasonably
possible following such redemption, subject to the approval of the Company’s remaining shareholders and the Company’s board
of directors, liquidate and dissolve, subject in each case to the Company’s obligations under Cayman Islands law to provide for
claims of creditors and other requirements of applicable law. The Sponsor and each Insider agrees to not propose any amendment to the
Articles to modify the substance or timing of the Company’s obligation to redeem 100% of the Offering Shares if the Company does
not complete a Business Combination within the required time period set forth in the Articles or with respect to any other material provisions
relating to shareholders’ rights or pre-initial business combination activity, unless the Company provides its Public Shareholders
with the opportunity to redeem their Offering Shares upon approval of any such amendment at a per-share price, payable in cash, equal
to the aggregate amount then on deposit in the Trust Account, including interest earned on the funds held in the Trust Account and not
previously released to the Company to pay its taxes, divided by the number of then outstanding Offering Shares.

  

The Sponsor and each Insider acknowledges that it, he or she
has no right, title, interest or claim of any kind in or to any monies held in the Trust Account or any other asset of the Company as
a result of any liquidation of the Company with respect to the Founder Shares (as defined below) held by it, him or her. The Sponsor
and each Insider hereby further waives, with respect to any Ordinary Shares held by it, him or her, if any, any redemption rights it,
he or she may have in connection with (A) the consummation of a Business Combination, including, without limitation, any such rights
available in the context of a shareholder vote to approve such Business Combination, or (B) a shareholder vote to approve an amendment
to the Articles to modify the substance or timing of the Company’s obligation to redeem 100% of the Offering Shares if the Company
has not consummated a Business Combination within the time period set forth in the Articles or with respect to any other material provisions
relating to shareholders’ rights or pre-initial business combination activity or in the context of a tender offer made by the Company
to purchase Offering Shares (although the Sponsor, the Insiders and their respective affiliates shall be entitled to redemption and liquidation
rights with respect to any Offering Shares it or they hold if the Company fails to consummate a Business Combination within the time period
set forth in the Articles).

 

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		3.	During the period commencing on the effective date of the Underwriting Agreement and ending 180 days after such date, the Sponsor
and each Insider shall not, without the prior written consent of the Representatives, (i) sell, offer to sell, contract or agree to sell,
hypothecate, pledge, grant any option to purchase or otherwise dispose of or agree to dispose of, directly or indirectly, or establish
or increase a put equivalent position or liquidate or decrease a call equivalent position within the meaning of Section 16 of the Securities
Exchange Act of 1934, as amended (the “Exchange Act”), and the rules and regulations of the Commission promulgated
thereunder, with respect to, any Ordinary Shares (including, but not limited to, Founder Shares) or any securities convertible into, or
exercisable, or exchangeable for, Ordinary Shares owned by it, him or her, (ii) enter into any swap or other arrangement that transfers
to another, in whole or in part, any of the economic consequences of ownership of any Ordinary Shares (including, but not limited to,
Founder Shares) or any securities convertible into, or exercisable, or exchangeable for, Ordinary Shares owned by it, him or her, whether
any such transaction is to be settled by delivery of such securities, in cash or otherwise, or (iii) publicly announce any intention to
effect any transaction specified in clause (i) or (ii); provided, however, that the foregoing does not apply to the forfeiture of any
Founder Shares pursuant to their terms or any transfer of Founder Shares to any current or future independent director of the company
(as long as such current or future independent director transferee is subject to this Letter Agreement or executes an agreement substantially
identical to the terms of this Letter Agreement, as applicable to directors and officers at the time of such transfer; and as long as,
to the extent any Section 16 reporting obligation is triggered as a result of such transfer, any related Section 16 filing includes a
practical explanation as to the nature of the transfer). Each of the Insiders and the Sponsor acknowledges and agrees that, prior to the
effective date of any release or waiver, of the restrictions set forth in this paragraph 3 or paragraph 7 below, the Company shall announce
the impending release or waiver by press release through a major news service at least two business days before the effective date of
the release or waiver. Any release or waiver granted shall only be effective two business days after the publication date of such press
release. The provisions of this paragraph will not apply if the release or waiver is effected solely to permit a transfer not for consideration
and the transferee has agreed in writing to be bound by the same terms described in this Letter Agreement to the extent and for the duration
that such terms remain in effect at the time of the transfer. Notwithstanding the foregoing, nothing in this Section 3 will prohibit (1)
the issuance and sale of Private Placement Shares (as defined below), (2) the issuance and sale of any Shares in the Public Offering,
including any Shares issued and sold to cover over-allotments, if any, (3) the registration with the SEC pursuant to an agreement to be
entered into concurrently with the execution of this Agreement, the resale of the Private Placement Shares and the Founder Shares and
(4) issuance of securities in connection with a Business Combination.

 

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		4.	In the event of the liquidation of the Trust Account upon the failure of the Company to consummate its initial Business Combination
within the time period set forth in the Articles, the Sponsor (the “Indemnitor”) agrees to indemnify and hold
harmless the Company against any and all loss, liability, claim, damage and expense whatsoever (including, but not limited to, any and
all legal or other expenses reasonably incurred in investigating, preparing or defending against any litigation, whether pending or threatened)
to which the Company may become subject as a result of any claim by (i) any third party for services rendered or products sold to the
Company or (ii) any prospective target business with which the Company has entered into a written letter of intent, confidentiality or
other similar agreement or Business Combination agreement (a “Target”); provided, however, that
such indemnification of the Company by the Indemnitor (x) shall apply only to the extent necessary to ensure that such claims by a third
party or a Target do not reduce the amount of funds in the Trust Account to below the lesser of (i) $10.00 per Offering Share and (ii)
the actual amount per Offering Share held in the Trust Account as of the date of the liquidation of the Trust Account, if less than $10.00
per Offering Share is then held in the Trust Account due to reductions in the value of the trust assets, less taxes payable, (y) shall
not apply to any claims by a third party or a Target which executed a waiver of any and all rights to the monies held in the Trust Account
(whether or not such waiver is enforceable) and (z) shall not apply to any claims under the Company’s indemnity of the Underwriters
against certain liabilities, including liabilities under the Securities Act of 1933, as amended. The Indemnitor shall have the right to
defend against any such claim with counsel of its choice reasonably satisfactory to the Company if, within 15 days following written receipt
of notice of the claim to the Indemnitor, the Indemnitor notifies the Company in writing that it shall undertake such defense.

 

		5.	To the extent that the Underwriters do not exercise their over-allotment option to purchase up to an additional 3,750,000 Shares within
45 days from the date of the Prospectus (and as further described in the Prospectus), the Sponsor agrees to forfeit, at no cost, a number
of Founder Shares in the aggregate equal to 937,500 multiplied by a fraction, (i) the numerator of which is 3,750,000 minus the number
of Shares purchased by the Underwriters upon the exercise of their over-allotment option, and (ii) the denominator of which is 3,750,000.
The forfeiture will be adjusted to the extent that the over-allotment option is not exercised in full by the Underwriters so that the
Founder Shares will represent an aggregate of 20.0% of the Company’s issued and outstanding Class A Ordinary Shares after the Public
Offering (not including the Private Placement Shares (as defined below)). The Sponsor further agrees that to the extent that the size
of the Public Offering is increased or decreased, the Company will purchase or sell Shares or effect a share repurchase or share capitalization,
as applicable, immediately prior to the consummation of the Public Offering in such amount as to maintain the ownership of the Initial
Shareholders prior to the Public Offering at 20.0% of its issued and outstanding Capital Shares upon the consummation of the Public Offering.
In connection with such increase or decrease in the size of the Public Offering, then (A) the references to 3,750,000 in the numerator
and denominator of the formula in the first sentence of this paragraph shall
be changed to a number equal to 15% of the number of Public Shares issued in the Public Offering and (B) the reference to 937,500 in the
formula set forth in the first sentence of this paragraph shall be adjusted to such number of Founder Shares that the Sponsor would have
to surrender to the Company in order for the Initial Shareholders to hold an aggregate of 20.0% of the Company’s issued and outstanding
Class A Ordinary Shares after the Public Offering (not including Private Placement Shares).

 

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		6.	The Sponsor and each Insider hereby agrees and acknowledges that: (i) the Underwriters and the Company would be irreparably injured
in the event of a breach by such Sponsor or an Insider of its, his or her obligations under paragraphs 1, 2, 3, 4, 5, 7(a), and 7(b),
as applicable, of this Letter Agreement (ii) monetary damages may not be an adequate remedy for such breach and (iii) the non-breaching
party shall be entitled to injunctive relief, in addition to any other remedy that such party may have in law or in equity, in the event
of such breach.

 

		7.	               (a)              The Sponsor and each Insider agrees that it, he or she shall not Transfer any Founder Shares (or any Class A Ordinary Shares
issuable upon conversion thereof) until the earliest of (A) one year after the completion of the Company’s initial Business Combination
or (B) subsequent to the Company’s initial Business Combination, (x) the date on which the Company completes a liquidation, merger,
share exchange, reorganization or other similar transaction that results in all of the Company’s shareholders having the right to
exchange their Class A Ordinary Shares for cash, securities or other property or (y) if the closing price of the Company’s Class
A Ordinary Shares equals or exceeds $12.00 per share (as adjusted for share sub-divisions, share capitalizations, reorganizations, recapitalizations
and the like) for any 20 trading days within any 30-trading day period commencing at least 150 days after the Company’s initial
Business Combination (the “Founder Shares Lock-up Period”).

 

(b)              
The Sponsor and each Insider agrees that it, he or she shall not Transfer any Private Placement Shares, until 30 days after the
completion of a Business Combination (the “Private Placement Shares Lock-up Period”, together with the Founder
Shares Lock-up Period, the “Lock-up Periods”).

 

(c)              
Notwithstanding the provisions set forth in paragraphs 7(a) and (b), Transfers of the Founder Shares, Private Placement Shares
or the Founder Shares that are held by the Sponsor, any Insider or any of their permitted transferees (that have complied with this paragraph
7(c)), are permitted (a) to the Company’s officers or directors, any affiliates or family members of any of the Company’s
officers or directors, to the Sponsor, any members or partners of the Sponsor or their affiliates, or any affiliates of the Sponsor;
(b) in the case of an individual, by gift to a member of such individual’s immediate family or to a trust, the beneficiary of which
is a member of such individual’s immediate family, an affiliate of such individual or to a charitable organization; (c) in the
case of an individual, by virtue of laws of descent and distribution upon death of such individual; (d) in the case of an individual,
pursuant to a qualified domestic relations order; (e) by private sales or transfers made in connection with any forward purchase agreement
or similar arrangement or in connection with the consummation of an initial Business Combination at prices no greater than the price
at which the securities were originally purchased; (f) by virtue of the laws of the Cayman Islands or the Sponsor’s limited liability
company agreement upon dissolution of the Sponsor; (g) to the Company for no value for cancellation in connection with the consummation
of a Business Combination; (h) in the event of the Company’s liquidation prior to the consummation of a Business Combination; or
(i) in the event of the Company’s liquidation, merger, share exchange or other similar transaction which results in all of the
Company’s shareholders having the right to exchange their Class A Ordinary Shares for cash, securities or other property subsequent
to the Company’s completion of an initial Business Combination; provided, however, that in the case of clauses (a)
through (f), these permitted transferees must enter into a written agreement with the Company agreeing to be bound by the transfer restrictions
herein and the other restrictions contained in this Agreement (including provisions relating to voting, the Trust Account and liquidating
distributions).

 

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		8.	The Sponsor and each Insider represents and warrants that it, he or she has never been suspended or expelled from membership in any
securities or commodities exchange or association or had a securities or commodities license or registration denied, suspended or revoked.
Each Insider’s biographical information furnished to the Company (including any such information included in the Prospectus) is
true and accurate in all respects and does not omit any material information with respect to the Insider’s background. The Sponsor
and each Insider’s questionnaire furnished to the Company is true and accurate in all respects. The Sponsor and each Insider represents
and warrants that: it, he or she is not subject to or a respondent in any legal action for, any injunction, cease-and-desist order or
order or stipulation to desist or refrain from any act or practice relating to the offering of securities in any jurisdiction; it, he
or she has never been convicted of, or pleaded guilty to, any crime (i) involving fraud, (ii) relating to any financial transaction or
handling of funds of another person, or (iii) pertaining to any dealings in any securities and it, he or she is not currently a defendant
in any such criminal proceeding.

 

		9.	Except as disclosed in the Prospectus, neither the Sponsor nor any officer, nor any affiliate of the Sponsor or any officer, nor any
director of the Company, shall receive from the Company any finder’s fee, reimbursement, consulting fee, non-cash payments, monies
in respect of any repayment of a loan or other compensation prior to, or in connection with any services rendered in order to effectuate,
the consummation of the Company’s initial Business Combination (regardless of the type of transaction that it is), other than the
following, none of which will be made from the proceeds held in the Trust Account prior to the completion of the initial Business Combination:
repayment of a loan and advances up to an aggregate of $300,000 made to the Company by the Sponsor; payment of up to $17,500 per month, for up to 24 months, for
office space and professional, secretarial, administrative and support services; reimbursement for any reasonable out-of-pocket expenses
related to identifying, investigating, negotiating and completing an initial Business Combination, and repayment of loans, if any, and
on such terms as to be determined by the Company from time to time, made by the Sponsor or an affiliate of the Sponsor or any of the Company’s
officers or directors to finance transaction costs in connection with an intended initial Business Combination, provided, that, if the
Company does not consummate an initial Business Combination, a portion of the working capital held outside the Trust Account may be used
by the Company to repay such loaned amounts so long as no proceeds from the Trust Account are used for such repayment. Up to $1,500,000
of such loans may be convertible into shares at a price of $10.00 per share at the option of the lender. Such shares would be identical
to the Private Placement Shares.

 

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		10.	The Sponsor and each Insider has full right and power, without violating any agreement to which it is bound (including, without limitation,
any non-competition or non-solicitation agreement with any employer or former employer), to enter into this Letter Agreement and, as applicable,
to serve as an officer and/or director on the board of directors of the Company and hereby consents to being named in the Prospectus as
an officer and/or director of the Company.

 

		11.	As used herein, (i) “Business Combination” shall mean a merger, share exchange, asset acquisition, share
purchase, reorganization or similar business combination, involving the Company and one or more businesses; (ii) “Ordinary
Shares” shall mean the Class A ordinary shares and Class B ordinary shares; (iii) “Founder Shares”
shall mean the 7,187,500 Class B ordinary shares issued and outstanding (up to 937,500 Shares of which are subject to complete or partial
forfeiture if the over-allotment option is not exercised by the Underwriters); (iv) “Initial Shareholders” shall
mean the Sponsor and any Insider that holds Founder Shares; (v) “Private Placement Shares” shall mean the up
to 857,000 shares (or up to 932,000 shares if the over-allotment option is exercised in full) that the Sponsor has agreed to purchase
for an aggregate purchase price of $8,570,000 (or $9,320,000 if the over-allotment option is exercised in full), or $10.00 per Share,
in a private placement that shall occur simultaneously with the consummation of the Public Offering; (vi) “Public Shareholders”
shall mean the holders of securities issued in the Public Offering; (vii) “Trust Account” shall mean the trust
fund into which a portion of the net proceeds of the Public Offering and the sale of the Private Placement Shares shall be deposited;
(viii) “Transfer” shall mean the (a) 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 Exchange Act, and the rules and regulations of the Commission promulgated thereunder with respect to, any security, (b) 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 security,
whether any such transaction is to be settled by delivery of such securities, in cash or otherwise, or (c) public announcement of any
intention to effect any transaction specified in clause (a) or (b); and (ix) “Shares” shall mean the Private
Placement Shares and public shares.

 

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		12.	The Company will maintain an insurance policy or policies providing directors’ and officers’ liability insurance, and
each Director shall be covered by such policy or policies, in accordance with its or their terms, to the maximum extent of the coverage
available for any of the Company’s directors or officers.

 

		13.	This Letter Agreement constitutes the entire agreement and understanding of the parties hereto in respect of the subject matter hereof
and supersedes all prior understandings, agreements, or representations by or among the parties hereto, written or oral, to the extent
they relate in any way to the subject matter hereof or the transactions contemplated hereby. This Letter Agreement may not be changed,
amended, modified or waived (other than to correct a typographical error) as to any particular provision, except by a written instrument
executed by all parties hereto.

 

		14.	No party hereto may assign either this Letter Agreement or any of its rights, interests, or obligations hereunder without the prior
written consent of the other parties. Any purported assignment in violation of this paragraph shall be void and ineffectual and shall
not operate to transfer or assign any interest or title to the purported assignee. This Letter Agreement shall be binding on the Sponsor
and each Insider and their respective successors, heirs and assigns and permitted transferees.

 

		15.	Nothing in this Letter Agreement shall be construed to confer upon, or give to, any person or corporation other than the parties hereto
any right, remedy or claim under or by reason of this Letter Agreement or of any covenant, condition, stipulation, promise or agreement
hereof. All covenants, conditions, stipulations, promises and agreements contained in this Letter Agreement shall be for the sole and
exclusive benefit of the parties hereto and their successors, heirs, personal representatives and assigns and permitted transferees.

 

		16.	This Letter Agreement may be executed in any number of original or facsimile counterparts and each of such counterparts shall for
all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument.

 

		17.	This Letter Agreement shall be deemed severable, and the invalidity or unenforceability of any term or provision hereof shall not
affect the validity or enforceability of this Letter Agreement or of any other term or provision hereof. Furthermore, in lieu of any such
invalid or unenforceable term or provision, the parties hereto intend that there shall be added as a part of this Letter Agreement a provision as similar in terms to such invalid or unenforceable
provision as may be possible and be valid and enforceable.

 

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		18.	This Letter Agreement shall be governed by and construed and enforced in accordance with the laws of the State of New York. The parties
hereto (i) all agree that any action, proceeding, claim or dispute arising out of, or relating in any way to, this Letter Agreement shall
be brought and enforced in the courts of New York City or in the State of New York, and irrevocably submit to such jurisdiction and venue,
which jurisdiction and venue shall be exclusive and (ii) waive any objection to such exclusive jurisdiction and venue or that such courts
represent an inconvenient forum.

 

		19.	Any notice, consent or request to be given in connection with any of the terms or provisions of this Letter Agreement shall be in
writing and shall be sent by express mail or similar private courier service, by certified mail (return receipt requested), by hand delivery
or facsimile transmission.

 

		20.	Each party hereto shall not be liable for any breaches or misrepresentations contained in this Letter Agreement by any other party
to this Letter Agreement, and no party shall be liable or responsible for the obligations of another party, including, without limitation,
indemnification obligations and notice obligations.

 

		21.	This Letter Agreement shall terminate on the earlier of (i) the expiration of the Lock-up Periods or (ii) the liquidation of the Company;
provided, however, that this Letter Agreement shall earlier terminate in the event that the Public Offering is not consummated and closed
by December 31, 2021; provided further that paragraph 4 of this Letter Agreement shall survive such liquidation.

 

[Signature Page Follows]

 

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	 	Sincerely,
	 	 
	 	FIFTH WALL ACQUISITION SPONSOR III LLC
	 	 
	 	By:	/s/
    Brendan Wallace
	 	 	Name:  Brendan Wallace
	 	 	Title:   Manager 

 

	Acknowledged and Agreed:	 
	 	 
	FIFTH WALL ACQUISITION CORP. III	 
	 	 
	By:	/s/
    Brendan Wallace	 
	 	Name: Brendan Wallace	 
	 	Title: Chief Executive Officer	 
	  	 
	/s/ Brendan Wallace	 
	Brendan Wallace	 
	 	 
	/s/ Andriy Mykhaylovskyy	 
	Andriy Mykhaylovskyy	 
	 	 
	/s/ Adeyemi Ajao	 
	Adeyemi Ajao	 
	 	 
	/s/ Alana Beard	 
	Alana Beard	 
	 	 
	/s/ Poonam Sharma Mathis	 
	Poonam Sharma Mathis	 
	 	 
	/s/ Amanda Parness	 
	Amanda Parness	 

 

[Signature
Page to Letter Agreement]Exhibit 10.5

 

PRIVATE PLACEMENT SHARES PURCHASE AGREEMENT

 

THIS PRIVATE PLACEMENT SHARES PURCHASE AGREEMENT
(as it may from time to time be amended and including all exhibits referenced herein, this “Agreement”), dated
as of May 24, 2021 (the “Effective Date”), is entered into by and between among Fifth Wall Acquisition Corp.
III, a Cayman Islands exempted company (the “Company”), and Fifth Wall Acquisition Sponsor III LLC, a Cayman
Islands limited liability company (the “Purchaser”).

 

WHEREAS, the Company intends to consummate an initial
public offering (the “Public Offering”) of the Company’s Class A ordinary shares, par value $0.0001 (each,
a “Share”), as set forth in the Company’s Registration Statement on Form S-1, filed with the U.S. Securities
and Exchange Commission (the “SEC”), File Number 333-255292 (the “Registration Statement”),
under the Securities Act of 1933, as amended (the “Securities Act”).

 

WHEREAS, the Purchaser has agreed to purchase an
aggregate of 857,000 Shares (and up to 932,000 Shares if the underwriters in the Public Offering exercise their option to purchase additional
Shares in full) (the “Private Placement Shares”).

 

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 Shares.

 

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

 

B.                Purchase
and Sale of the Private Placement Shares.

 

(i)             On
the date of the consummation of the Public Offering (the “IPO Closing Date”), the Company shall issue and sell
to the Purchaser, and the Purchaser shall purchase from the Company, 857,000 Private Placement Shares at a price of $10.00 per Private
Placement Share for an aggregate purchase price of $8,570,000 (the “Purchase Price”). The Purchaser shall pay
the Purchase Price by wire transfer of immediately available funds to the Company at in accordance with the Company’s wiring instructions,
at least one (1) business day prior to the date of effectiveness of the Registration Statement filed in connection with the Public Offering.
On the IPO Closing Date, subject to the receipt of funds pursuant to the immediately prior sentence, the Company, at its option, shall
deliver a certificate evidencing the Private Placement Shares purchased by the Purchaser on such date duly registered in the Purchaser’s
name to the Purchaser or effect such delivery in book-entry form.

 

     

     

    

 

(ii)            On the date of any closing of the option to purchase additional Shares, if any, in connection with the Public Offering or on such
earlier time and date as may be mutually agreed by the Purchaser and the Company (each such date, an “Option Closing Date”,
and each Option Closing Date (if any) and the IPO Closing Date, a “Closing Date”), the Company shall issue
and sell to the Purchaser, and the Purchaser shall purchase from the Company, up to 75,000 Private Placement Shares (or, to the extent
the option to purchase additional Shares is not exercised in full, a lesser number of Private Placement Shares in proportion to portion
of the option that is exercised) at a price of $10.00 per Private Placement Share for an aggregate purchase price of up to $750,000 (the
 “Option Purchase Price”). The Purchaser shall pay the Option Purchase Price in accordance with the Company’s
wire instruction by wire transfer of immediately available funds to the Company. On each Option Closing Date (if any), subject to the
receipt of funds pursuant to the immediately prior sentence, the Company shall, at its option, deliver a certificate evidencing the Private
Placement Shares purchased on such date duly registered in the Purchaser’s name to the Purchaser or effect such delivery in book-entry
form.

 

C.                Terms
of the Private Placement Shares.

 

(i)             The
Private Placement Shares are substantially identical to the Shares to be offered in the Public Offering except: (a) as provided in that
letter agreement, dated as of the date hereof (the “Letter Agreement”), by and among the Company, the Purchaser
and each of the Company’s officers, directors and director nominees, and (b) the Private Placement 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 the Letter Agreement and they are registered pursuant to the Registration and Shareholder Rights Agreement
(as defined below) or an exemption from registration is available, and the restrictions described above in clause (a) have expired.

 

(ii)            On the Effective Date, the Company and the Purchaser shall enter into a registration and shareholder rights agreement (the “Registration
and Shareholder Rights Agreement”) pursuant to which the Company will grant certain registration rights to the Purchaser
relating to the Private Placement Shares.

 

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

 

A.                Incorporation
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.

 

    2

     

    

 

B.                Authorization; No Breach.

 

(i)             The
execution, delivery and performance of this Agreement and the Private Placement Shares have been duly authorized by the Company as of
the Closing Date. This 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 this Agreement, the Private Placement Shares will constitute
valid and binding obligations of the Company, enforceable in accordance with their terms as of the Closing Date.

 

(ii)            The execution and delivery by the Company of this Agreement and the Private Placement Shares, the issuance and sale of the Private
Placement Shares and the fulfillment of and compliance with the respective terms hereof and thereof by the Company, do not and will not
as of each Closing Date (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 amended and restated 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, the terms hereof, the Private Placement Shares will be
duly and validly issued, fully paid and nonassessable. Upon issuance in accordance with, and payment pursuant to, the terms hereof, the
Purchaser will have good title to the Private Placement Shares purchased by it, 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 Purchaser.

 

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.

 

E.                 Regulation
D Qualification. Neither the Company nor, to its actual knowledge, any of its affiliates, members, officers, directors or beneficial
shareholders of 20% or more of its outstanding securities, has experienced a disqualifying event as enumerated pursuant to Rule 506(d)
of Regulation D under the Securities Act.

 

Section 3.              Representations
and Warranties of the Purchaser. As a material inducement to the Company to enter into this Agreement and issue and sell the Private
Placement Shares to the Purchaser, the Purchaser hereby represents and warrants to the Company (which representations and warranties
shall survive each Closing Date) that:

 

    3

     

    

 

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

 

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 that would materially impact its
ability to perform its obligations hereunder.

 

C.                Investment
Representations.

 

(i)             The Purchaser is acquiring the Private Placement Shares for its 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, and the Purchaser has not experienced a disqualifying event as enumerated pursuant to Rule 506(d) of Regulation D
under the Securities Act.

 

(iii)           The
Purchaser understands that the Private Placement Shares 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 Private Placement Shares.

 

(iv)          The
Purchaser did not decide to enter into this Agreement as a result of any general solicitation or general advertising within the meaning
of Rule 502(c) of Regulation D 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 Private Placement Shares 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 Private Placement Shares 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 Private Placement Shares.

 

    4

     

    

 

(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 Private Placement Shares or the fairness or suitability of the investment in the Private Placement
Shares by the Purchaser nor have such authorities passed upon or endorsed the merits of the offering of the Private Placement Shares.

 

(vii)         The Purchaser understands that: (a) the Private Placement Shares 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 and Shareholder Rights
Agreement, neither the Company nor any other person is under any obligation to register the Private Placement Shares under the Securities
Act or any state securities laws or to comply with the terms and conditions of any exemption thereunder. While the Purchaser understands
that Rule 144 under the Securities Act is not available for the resale of securities initially issued by shell companies (other than business
combination related shell companies) or issuers that have been at any time previously a shell company, the Purchaser understands that
Rule 144 includes an exception to this prohibition if the following conditions are met: (i) the issuer of the securities that was formerly
a shell company has ceased to be a shell company; (ii) the issuer of the securities is subject to the reporting requirements of Section
13 or 15(d) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”); (iii) the issuer of the securities has
filed all Exchange Act reports and material required to be filed, as applicable, during the preceding 12 months (or such shorter period
that the issuer was required to file such reports and materials), other than Form 8-K reports; and (iv) at least one year has elapsed
from the time that the issuer filed current Form 10 type information with the SEC reflecting its status as an entity that is not a shell
company.

 

(viii)        The
Purchaser has such knowledge and experience in financial and business matters, knowledge 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 Private Placement Shares and is able to bear the economic risk of an investment in the Private Placement Shares 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 Private Placement Shares. The Purchaser can afford a complete loss of its investments in the Private Placement Shares.

 

(ix)           The
Purchaser understands that the Private Placement Shares shall bear the following legend and appropriate “stop transfer restrictions”:

 

“THE SECURITIES
REPRESENTED HEREBY HAVE NOT BEEN REGISTERED UNDER THE UNITED STATES SECURITIES ACT OF 1933, AS AMENDED, 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 SUCH ACT OR SUCH LAWS OR AN EXEMPTION FROM REGISTRATION UNDER SUCH ACT AND
SUCH LAWS WHICH, IN THE OPINION OF COUNSEL, IS AVAILABLE.

 

    5

     

    

 

THE SECURITIES REPRESENTED BY THIS CERTIFICATE
ARE SUBJECT TO LOCKUP PROVISIONS AND MAY NOT BE OFFERED, SOLD, TRANSFERRED, PLEDGED OR OTHERWISE DISPOSED OF DURING THE TERM OF THE LOCKUP.”

 

Section 4.              Conditions
of the Purchaser’s Obligations. The obligations of the Purchaser to purchase and pay for the Private Placement Shares 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.

 

D.                Registration
and Shareholder Rights Agreement. The Company shall have entered into the Registration and Shareholder Rights Agreement on terms
satisfactory to the Purchaser.

 

Section 5.              Conditions
of the Company’s Obligations. The obligations of the Company to the 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 the Purchaser contained in Section 3 shall be true and correct at and
as of such Closing Date as though then made.

 

B.                 Performance.
The 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 the Purchaser on or before such Closing Date.

 

C.                 Corporate
Consents. The Company shall have obtained the consent of its board of directors authorizing the execution, delivery and performance
of this Agreement and the issuance and sale of the Private Placement Shares hereunder.

 

    6

     

    

 

D.                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.

 

Section 6.               Termination.
This Agreement may be terminated at any time after December 31, 2022 upon the election by either the Company or the Purchaser upon written
notice to the other party if the closing of the IPO does not occur prior to such date.

 

Section 7.               Survival
of Representations and Warranties. All of the representations and warranties contained herein shall survive each Closing Date.

 

Section 8.               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 plans to file under the Securities Act.

 

Section 9.               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 without the prior
written consent of the other party hereto, other than assignments by the Purchaser to its affiliates thereof (including, without limitation
one or more of its members).

 

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. In the event that any signature is delivered
by via 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.

 

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.

 

    7

     

    

 

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, without giving effect to conflicts of law principles that
would result in the application of the laws of another jurisdiction.

 

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

 

[Signature page follows]

 

    8

     

    

 

IN WITNESS WHEREOF, the undersigned have duly executed
this Agreement as of the date first written above.

 

	 	COMPANY:
	 	 
	 	FIFTH WALL ACQUISITION CORP.
    III,
	 	a Cayman Islands exempted company
	 	 
	 	 
	 	By:	/s/ Brendan Wallace
	 	 	Name: 	Brendan Wallace
	 	 	Title:	Chief Executive Officer
	 	 
	 	PURCHASER:
	 	 
	 	FIFTH WALL ACQUISITION SPONSOR
    III LLC,
	 	a Cayman Islands limited liability
    company
	 	 
	 	 
	 	By:	/s/ Brendan Wallace
	 	 	Name:	Brendan Wallace
	 	 	Title:	Manager

 

[Signature Page to Private Placement Shares Purchase Agreement]

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