POWER OF ATTORNEY

        Know all by these presents, that the undersigned hereby constitutes and
appoints each of Michael C. Mauer and Christopher E. Jansen, and with full power
of substitution, the undersigned's true and lawful attorney-in-fact to:

        (1)     prepare, execute in the undersigned's name and on the
                undersigned's behalf, and submit to the U.S. Securities and
                Exchange Commission (the "SEC") a Form ID, including amendments
                thereto, and any other documents necessary or appropriate to
                obtain codes and passwords enabling the undersigned to make
                electronic filings with the SEC of reports required by Section
                16(a) of the Securities Exchange Act of 1934 or any rule or
                regulation of the SEC;

        (2)     execute for and on behalf of the undersigned, in the
                undersigned's capacity as an officer and/or director of CM
                Finance Inc (the "Company"), Forms 3, 4, and 5 in accordance
                with Section 16(a) of the Securities Exchange Act of 1934 and
                the rules thereunder;

        (3)     do and perform any and all acts for and on behalf of the
                undersigned which may be necessary or desirable to complete and
                execute any such Form 3, 4, or 5, complete and execute any
                amendment or amendments thereto, and timely file such form with
                the SEC and any stock exchange or similar authority; and

        (4)     take any other action of any type whatsoever in connection with
                the foregoing which, in the opinion of such attorney-in-fact,
                may be of benefit to, in the best interest of, or legally
                required by, the undersigned, it being understood that the
                documents executed by such attorney-in-fact on behalf of the
                undersigned pursuant to this Power of Attorney shall be in such
                form and shall contain such terms and conditions as such
                attorney-in-fact may approve in such attorney-in-fact's
                discretion.

        The undersigned hereby grants to the foregoing attorney-in-fact full
power and authority to do and perform any and every act and thing whatsoever
requisite, necessary, or proper to be done in the exercise of any of the rights
and powers herein granted, as fully to all intents and purposes as the
undersigned might or could do if personally present, with full power of
substitution or revocation, hereby ratifying and confirming all that such
attorney-in-fact, or such attorney-in-fact's substitute or substitutes, shall
lawfully do or cause to be done by virtue of this power of attorney and the
rights and powers herein granted. The undersigned acknowledges that the
foregoing attorney-in-fact, in serving in such capacity at the request of the
undersigned, are not assuming, nor is the Company assuming, any of the
undersigned's responsibilities to comply with Section 16 of the Securities
Exchange Act of 1934.

        This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4, and 5 with respect to the
undersigned's holdings of and transactions in securities issued by the Company,
unless earlier revoked by the undersigned in a signed writing delivered to the
foregoing attorney-in-fact.

        IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed as of this 12th day of September, 2014.

                                        /s/ Jai Agarwal
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                                        Jai Agarwal