Exhibit 10.4


 





HENNESSY
CAPITAL ACQUISITION CORP. IV


3485
N. Pines Way, Suite 110


Wilson,
Wyoming 83014


 


February
28, 2019


 


Hennessy
Capital LLC


3485
N. Pines Way, Suite 110


Wilson,
Wyoming 83014


 


Re: Administrative
Support Agreement


 


Ladies
and Gentlemen:


 


This
letter agreement by and between Hennessy Acquisition Corp. IV (the “Company”) and Hennessy Capital LLC (“Hennessy
Capital”), dated as of the date hereof, will confirm our agreement that, commencing on the date the securities of the
Company are first listed on The Nasdaq Capital Market (the “Listing Date”), pursuant to a Registration Statement
on Form S-1 and prospectus filed with the U.S. Securities and Exchange Commission (the “Registration Statement”)
and continuing until the earlier of the consummation by the Company of an initial business combination or the Company’s
liquidation (in each case as described in the Registration Statement) (such earlier date hereinafter referred to as the “Termination
Date”):


 


(i)
Hennessy Capital shall make available, or cause to be made available, to the Company, at 3485 N. Pines Way, Suite 110, Wilson,
Wyoming 83014 (or any successor location of Hennessy Capital), certain office space, utilities and secretarial and administrative
support as may be reasonably required by the Company. In exchange therefor, the Company shall pay Hennessy Capital the sum of
$15,000 per month on the Listing Date and continuing monthly thereafter until the Termination Date; and


 


(ii) Hennessy
Capital hereby irrevocably waives any and all right, title, interest, causes of action and claims of any kind as a result of,
or arising out of, this letter agreement (each, a “Claim”) in or to, and any and all right to seek payment
of any amounts due to it out of, the trust account established for the benefit of the public stockholders of the Company and into
which substantially all of the proceeds of the Company’s initial public offering will be deposited (the “Trust
Account”) as a result of, or arising out of, this letter agreement, and hereby irrevocably waives any Claim it may have
in the future, which Claim would reduce, encumber or otherwise adversely affect the Trust Account or any monies or other assets
in the Trust Account, and further agrees not to seek recourse, reimbursement, payment or satisfaction of any Claim against the
Trust Account or any monies or other assets in the Trust Account for any reason whatsoever.


 


This
letter agreement constitutes the entire agreement and understanding of the parties hereto in respect of its subject matter 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 amended, modified or waived as to any particular provision, except by a written instrument executed
by the parties hereto.


 


No
party hereto may assign either this letter agreement or any of its rights, interests, or obligations hereunder without the prior
written approval of the other party. 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 constitutes the entire relationship of the parties hereto, and any litigation between the parties (whether grounded
in contract, tort, statute, law or equity) shall be governed by, construed in accordance with, and interpreted pursuant to the
laws of the State of New York, without giving effect to its choice of law principles.


  


[Signature
Page Follows]


 




     


     


    

 


	 	Very truly yours,
	 	 
	 	HENNESSY CAPITAL ACQUISITION
    CORP. IV
	 	 	 
	 	By:	/s/ Daniel J. Hennessy
	 	 	Name: Daniel J. Hennessy
	 	 	Title: Chief Executive Officer








 





	AGREED TO AND ACCEPTED BY:  
	 
	HENNESSY CAPITAL LLC  


 


	By:	/s/ Daniel J. Hennessy	 
	Name:	Daniel J. Hennessy	 
	Title:	Managing Member	 


 


 







 


 


[Signature
Page to Administrative Support Agreement]