<PAGE>

                                                                    Exhibit 10.5

               Confidential treatment has been requested for portions of this
               exhibit. The copy filed herewith omits the information subject to
               the confidentiality request. Omissions are designated as [*]. A
               complete version of this exhibit has been filed separately with
               the Securities and Exchange Commission.



January 7, 2002

Mr. Morgan Guenther
Senior Vice President, Business Development
TiVo, Inc.
2160 Gold Street
PO Box 2160
Alviso, CA  95002

References: Letter Agreement between TiVo, Inc. and DIRECTV, Inc. dated
            September 28, 2001 (the "Buy-Down Agreement")
            Warrant and Registration Rights Agreement between TiVo, Inc. and
            DIRECTV, Inc. dated October 6, 2000 (the "Warrant Agreement")
            Marketing Agreement between TiVo, Inc. and DIRECTV, Inc. dated April
            13, 1999 the "Marketing Agreement")

Dear Morgan:

This letter amends and supplements the Buy-Down Agreement, which previously
amended and supplemented both the Warrant Agreement and Marketing Agreement.

     1. The third paragraph in Section 2 ("DIRECTV/TiVo Buy-Down Contribution")
     of the Buy-Down Agreement is hereby deleted in its entirety and replaced in
     its entirety with the following paragraph:

          "Following the Term (January 31, 2002) and through March 15, 2002,
          DIRECTV agrees to contribute [*] and TiVo agrees to contribute [*] for
          each DIRECTV with TiVo receiver sold by all authorized DIRECTV dealers
          ("Reno Box"). After March 15, 2002 through [*], TiVo will have no
          obligation to contribute any Buy Down funds for the sale of DIRECTV
          with TiVo combination boxes."

     2. A new third paragraph shall be added to Section 3 ("Consideration to
     DIRECTV") which shall read as follows:

          " - In the event DIRECTV contributes to the buy-down for any DIRECTV
          with TiVo receivers after the March 15, 2002 through [*] in addition
          to the current [*] TiVo revenue share paid to DIRECTV, TiVo will pay
          DIRECTV an incremental revenue share of [*] (for a total of [*]) with
          respect to each receiver for which DIRECTV provides a buy-down
          contribution after the March 15, 2002 date and through [*]. This
          consideration shall replace the previous TiVo warrant structure

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[*] Certain information on this page has been omitted and filed separately with
the Securities and Exchange Commission. Confidential treatment has been
requested with respect to the omitted portions.

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          and TiVo shall not be obligated to contribute a buy-down payment after
          the March 15, 2002 date through [*]."

     3. In the last sentence of the last paragraph of Section 5
     "Administration", the word "TiVo" shall be replaced with the word
     "DIRECTV".

     4. Immediately upon execution of the letter dated January 7, 2002, DIRECTV
     shall communicate to authorized DIRECTV dealers the extension of the
     Buy-Down program through approximately [*].

     5. Except as otherwise set forth above, the terms and conditions of the
     Buy-Down Agreement remain in full force and effect.

Please indicate TiVo's agreement to the above by signing this letter amending
the Buy-Down Agreement as indicated below.

DIRECTV, Inc.


By:    /s/ Larry N. Chapman
       --------------------
Name:  Larry N. Chapman
Title: Executive Vice President


ACKNOWLEDGED AND AGREED:
TiVo, Inc.


By:    /s/ Morgan Guenther                                   Date: 01/07/02
       -------------------                                         --------
Name:  Morgan Guenther
Title: President

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[*] Certain information on this page has been omitted and filed separately with
the Securities and Exchange Commission. Confidential treatment has been
requested with respect to the omitted portions.