CALIX NETWORKS, INC.

Exhibit 4.12

THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AND HAVE BEEN ACQUIRED FOR INVESTMENT AND NOT WITH A VIEW TO, OR IN CONNECTION WITH, THE SALE OR DISTRIBUTION THEREOF. NO SUCH SALE OR DISTRIBUTION MAY BE EFFECTED WITHOUT AN EFFECTIVE REGISTRATION STATEMENT RELATED THERETO OR AN OPINION OF COUNSEL IN A FORM SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION IS NOT REQUIRED UNDER THE SECURITIES ACT OF 1933.

CALIX NETWORKS, INC.

Common Stock Purchase Warrant

Calix Networks, Inc. (the “Company”), for value received, hereby certifies that Timothy P. Willis, or his registered assigns (the “Registered Holder”), is entitled, subject to the terms set forth below, to purchase from the Company, on or before the Expiration Date (as defined in Section 7 below), up to 10,000 shares (as adjusted from time to time pursuant to the provisions of this Warrant) of Common Stock of the Company, at a purchase price of $0.89 per share. The shares purchasable upon exercise of this Warrant and the purchase price per share shall be adjusted from time to time pursuant to the provisions of this Warrant and are hereinafter referred to as the “Warrant Stock” and the “Purchase Price,” respectively.

1. Exercise.

(a) Manner of Exercise. Subject to the terms hereof, this Warrant may be exercised by the Registered Holder, in whole or in part, by surrendering this Warrant, with the purchase form appended hereto as Exhibit A duly executed by such Registered Holder or by such Registered Holder’s duly authorized attorney, at the principal office of the Company, or at such other office or agency as the Company may designate, accompanied by payment in full of the Purchase Price payable in respect of the number of shares of Warrant Stock purchased upon such exercise. The Purchase Price may be paid by cash, check, wire transfer or by the surrender of promissory notes or other instruments representing indebtedness of the Company to the Registered Holder.

(b) Effective Time of Exercise. Each exercise of this Warrant shall be deemed to have been effected immediately prior to the close of business on the day on which this Warrant shall have been surrendered to the Company as provided in Section 1(a) above. Notwithstanding the foregoing, in the event that this Warrant is submitted for exercise in connection with an Exercise Event (as defined in Section 2(b) below), the exercise will be conditioned on, and will be effected immediately prior to, the occurrence of such Exercise Event. At such time, the person or persons in whose name or names any certificates for Warrant Stock shall be issuable upon such exercise as provided in Section 1(d) below shall be deemed to have become the holder or holders of record of the Warrant Stock represented by such certificates.

(c) Net Issue Exercise.

(i) In lieu of exercising this Warrant in the manner provided above in Section 1(a), the Registered Holder may elect to receive shares equal to the value of this Warrant (or the portion thereof being canceled) by surrender of this Warrant at the principal office of the Company together with notice of such election on the form attached as Exhibit A duly executed in which event the Company shall issue to the Registered Holder a number of shares of Common Stock computed using the following formula:

(ii) For purposes of this Section 1(c), the fair market value of one share of Common Stock on the date of calculation shall mean:

(A) if the exercise is in connection with an initial public offering of the Company’s Common Stock, and if the Company’s Registration Statement relating to such public offering has been declared effective by the Securities and Exchange Commission, then the fair market value per share of Common Stock shall be the initial “Price to Public” specified in the final prospectus with respect to the offering;

(B) if this Warrant is exercised after, and not in connection with, the Company’s initial public offering, and if the Company’s Common Stock is traded on a securities exchange or The Nasdaq Stock Market or actively traded over-the-counter:

(1) if the Company’s Common Stock is traded on a securities exchange or The Nasdaq Stock Market, the fair market value shall be deemed to be the average of the closing prices over a thirty (30) day period ending three days before date of calculation; or

(2) if the Company’s Common Stock is actively traded over-the-counter, the fair market value shall be deemed to be the average of the closing bid or sales price (whichever is applicable) over the thirty (30) day period ending three days before the date of calculation, or

(C) if neither (A) nor (B) is applicable, the fair market value shall be at the highest price per share which the Company could obtain on the date of calculation

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from a willing buyer (not a current employee or director) for shares of Common Stock sold by the Company, from authorized but unissued shares, as determined in good faith by the Board of Directors, unless the Company is at such time subject to an acquisition as described in Section 2(b) below, in which case the fair market value per share of Common Stock shall be deemed to be the value of the consideration per share received by the holders of such stock pursuant to such acquisition.

(d) Delivery to Holder. As soon as practicable after the exercise of this Warrant in whole or in part, and in any event within ten (10) days thereafter, the Company at its expense will cause to be issued in the name of, and delivered to, the Registered Holder, or as such Holder (upon payment by such Holder of any applicable transfer taxes) may direct:

(i) a certificate or certificates for the number of shares of Warrant Stock to which such Registered Holder shall be entitled; and

(ii) in case such exercise is in part only, a new warrant or warrants (dated the date hereof) of like tenor, calling in the aggregate on the face or faces thereof for the number of shares of Warrant Stock equal (without giving effect to any adjustment therein) to the number of such shares called for on the face of this Warrant minus the number of such shares purchased by the Registered Holder upon such exercise as provided in Section 1(a) above.

2. Restrictions on Exercise.

(a) Vesting. This Warrant shall only be exercisable for the number of shares of Warrant Stock that have vested as of the date of exercise. As of the initial date of issuance of this Warrant, as set forth above (the “Date of Issuance”), 3,000 shares of the Warrant Stock shall have vested. The remaining 7,000 shares of Warrant Stock shall vest during such period of time as Tim Willis shall be providing services to the Company pursuant to the terms of that certain Independent Contractor agreement dated December 1, 2001 between the Company and Tim Willis, as such agreement may be amended from time to time (the “Services Agreement”) as follows: 2,333 shares of Warrant Stock shall vest upon Company equipment shipment to SBC for use in an SBC TRI lab evaluation. The next 2,333 shares of Warrant Stock shall vest upon turn up of Company equipment for [SBC]’s First Office Application, provided that the agreement has not been terminated prior to such completion or purchase. The last 2,334 shares of Warrant Stock shall vest upon the effective date of SBC’s Product Approval Letter for the use of Calix equipment in the SBC network. In the event that, on the [third (3^rd)] anniversary of the Date of Issuance of this Warrant, the Warrant Stock has not fully vested pursuant to the vesting schedule in the immediately preceding sentence and the Services Agreement has not been terminated prior to such date, any remaining shares of Warrant Stock that have not yet vested shall then become vested. In the event that the Services Agreement does not contain a procedure for termination, the Services Agreement will be considered terminated for purposes of this Warrant upon delivery of a notice of termination by the Company to Tim Willis. From and after the termination of the Services Agreement, no additional Warrant Stock shall vest.

(b) Exercisability. Notwithstanding any other provision of this Warrant, this Warrant shall not be exercisable until immediately prior to the occurrence of the earlier to occur of the following events (each, an “Exercise Event”): (i) the closing of the sale, conveyance, or

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disposal of all or substantially all of the Company’s property or business, or the Company’s merger into or consolidation with any other corporation as a result of which the holders of the Company’s outstanding stock immediately prior to such transaction hold, immediately after such transaction, stock representing less than 50% of the voting power of the surviving corporation (or its parent corporation if the surviving corporation is wholly owned by the parent corporation) in such transaction; provided, however, that this Section 2(b) shall not apply to a merger effected exclusively for the purpose of changing the domicile of the Company, or (ii) the closing of a firm commitment underwritten public offering of the Company’s Common Stock pursuant to a registration statement under the Securities Act of 1933, as amended (the “Securities Act”). As set forth in Section 2(a) above, this Warrant shall only be exercisable for the number of shares of Warrant Stock that have vested as of the date of exercise.

3. Adjustments.

(a) Stock Splits and Dividends. If outstanding shares of the Company’s Common Stock shall be subdivided into a greater number of shares or a dividend in Common Stock shall be paid in respect of Common Stock, the Purchase Price in effect immediately prior to such subdivision or at the record date of such dividend shall simultaneously with the effectiveness of such subdivision or immediately after the record date of such dividend be proportionately reduced. If outstanding shares of Common Stock shall be combined into a smaller number of shares, the Purchase Price in effect immediately prior to such combination shall, simultaneously with the effectiveness of such combination, be proportionately increased. When any adjustment is required to be made in the Purchase Price, the number of shares of Warrant Stock purchasable upon the exercise of this Warrant shall be changed to the number determined by dividing (i) an amount equal to the number of shares issuable upon the exercise of this Warrant immediately prior to such adjustment, multiplied by the Purchase Price in effect immediately prior to such adjustment, by (ii) the Purchase Price in effect immediately after such adjustment.

(b) Reclassification, Etc. In case of any reclassification or change of the outstanding securities of the Company or of any reorganization of the Company (or any other corporation the stock or securities of which are at the time receivable upon the exercise of this Warrant) or any similar corporate reorganization on or after the date hereof, then and in each such case the Registered Holder of this Warrant, upon the exercise hereof at any time after the consummation of such reclassification, change, or reorganization shall be entitled to receive, in lieu of the stock or other securities and property receivable upon the exercise hereof prior to such consummation, the stock or other securities or property to which such holder would have been entitled upon such consummation if such holder had exercised this Warrant immediately prior thereto, all subject to further adjustment pursuant to the provisions of this Section 3.

(c) Adjustment Certificate. When any adjustment is required to be made in the Warrant Stock or the Purchase Price pursuant to this Section 3, the Company shall promptly mail to the Registered Holder a certificate setting forth (i) a brief statement of the facts requiring such adjustment, (ii) the Purchase Price after such adjustment and (iii) the kind and amount of stock or other securities or property into which this Warrant shall be exercisable after such adjustment.

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4. Transfers.

(a) Unregistered Security. Each holder of this Warrant acknowledges that this Warrant and the Warrant Stock have not been registered under the Securities Act, and agrees not to sell, pledge, distribute, offer for sale, transfer or otherwise dispose of this Warrant or any Warrant Stock issued upon its exercise in the absence of (i) an effective registration statement under the Act as to this Warrant or such Warrant Stock and registration or qualification of this Warrant or such Warrant Stock under any applicable U.S. federal or state securities law then in effect or (ii) an opinion of counsel, satisfactory to the Company, that such registration and qualification are not required. Each certificate or other instrument for Warrant Stock issued upon the exercise of this Warrant shall bear a legend substantially to the foregoing effect.

(b) Transferability. Subject to the provisions of Section 4(a) hereof, this Warrant and all rights hereunder are transferable only with the written consent of the Company; provided that any assignee shall be bound by the terms hereof. Notwithstanding the foregoing, this Warrant may not be transferred to any individual or entity engaged in any business that competes with any business of the Company, and any purported transfer to such individual or entity shall be void. A permitted transfer of this Warrant shall be effected by surrendering the Warrant with a properly executed assignment (in the form of Exhibit B hereto) at the principal office of the Company, provided that the assignee has agreed in writing to be bound by the terms hereof (including, without limitation, Section 19 below). This Warrant may not be transferred in part.

(c) Warrant Register. The Company will maintain a register containing the names and addresses of the Registered Holders of this Warrant. Until any transfer of this Warrant is made in the warrant register, the Company may treat the Registered Holder of this Warrant as the absolute owner hereof for all purposes; provided, however, that if this Warrant is properly assigned in blank, the Company may (but shall not be required to) treat the bearer hereof as the absolute owner hereof for all purposes, notwithstanding any notice to the contrary. Any Registered Holder may change such Registered Holder’s address as shown on the warrant register by written notice to the Company requesting such change.

5. Representations and Warranties of Holder. The Registered Holder hereby represents and warrants to the Company as follows:

(a) Purchase Entirely for Own Account. The Registered Holder acknowledges that this Warrant is given to the Registered Holder in reliance upon the Registered Holder’s representation to the Company, which by its acceptance of this Warrant the Registered Holder hereby confirms, that the Warrant, and the Warrant Stock (collectively, the “Securities”) being acquired by the Registered Holder are being acquired for investment for the Registered Holder’s own account, not as a nominee or agent, and not with a view to the resale or distribution of any part thereof, and that the Registered Holder has no present intention of selling, granting any participation in, or otherwise distributing the same. By executing this Agreement, the Registered Holder further represents that the Registered Holder does not presently have any contract, undertaking, agreement or arrangement with any person to sell, transfer or grant participations to such person or to any third person, with respect to any of the Securities. The Registered Holder represents that it has full power and authority to execute this Warrant. The Registered Holder has not been formed for the specific purpose of acquiring any of the Securities.

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(b) Disclosure of Information. The Registered Holder has had an opportunity to discuss the Company’s business, management, financial affairs and the terms and conditions of the offering of the Securities with the Company’s management. The Registered Holder understands that such discussions, as well as any written information issued by the Company, were intended to describe the aspects of the Company’s business which it believes to be material.

(c) Restricted Securities. The Registered Holder understands that the Securities have not been, and will not be, registered under the Securities Act, by reason of a specific exemption from the registration provisions of the Securities Act which depends upon, among other things, the bona fide nature of the investment intent and the accuracy of the Registered Holder’s representations as expressed herein. The Registered Holder understands that the Securities are “restricted securities” under applicable U.S. federal and state securities laws and that, pursuant to these laws, the Registered Holder must hold the Securities indefinitely unless they are registered with the Securities and Exchange Commission and qualified by state authorities, or an exemption from such registration and qualification requirements is available. The Registered Holder acknowledges that the Company has no obligation to register or qualify the Securities for resale. The Registered Holder further acknowledges that if an exemption from registration or qualification is available, it may be conditioned on various requirements including, but not limited to, the time and manner of sale, the holding period for the Securities, and on requirements relating to the Company which are outside of the Registered Holder’s control, and which the Company is under no obligation and may not be able to satisfy.

(d) No Public Market. The Registered Holder understands that no public market now exists for any of the securities issued by the Company, that the Company has made no assurances that a public market will ever exist for the Securities.

(e) Legends. The Registered Holder understands that the Securities, and any securities issued in respect of or exchange for the Securities, may bear one or all of the following legends:

(i) “THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AND HAVE BEEN ACQUIRED FOR INVESTMENT AND NOT WITH A VIEW TO, OR IN CONNECTION WITH, THE SALE OR DISTRIBUTION THEREOF. NO SUCH SALE OR DISTRIBUTION MAY BE EFFECTED WITHOUT AN EFFECTIVE REGISTRATION STATEMENT RELATED THERETO OR AN OPINION OF COUNSEL IN A FORM SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION IS NOT REQUIRED UNDER THE SECURITIES ACT OF 1933.”

(ii) Any legend required by the Blue Sky laws of any state to the extent such laws are applicable to the shares represented by the certificate so legended.

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(f) Accredited Investor. The Registered Holder is an accredited investor as defined in Rule 501(a) of Regulation D promulgated under the Securities Act, a copy of which is attached hereto as Exhibit C.

6. No Impairment. The Company will not, by amendment of its charter or through reorganization, consolidation, merger, dissolution, sale of assets or any other voluntary action, avoid or seek to avoid the observance or performance of any of the terms of this Warrant, but will at all times in good faith assist in the carrying out of all such terms and in the taking of all such action as may be necessary or appropriate in order to protect the rights of the holder of this Warrant against impairment.

7. Termination. This Warrant (and the right to purchase securities upon exercise hereof) shall terminate upon the earliest to occur of the following (the “Expiration Date”): (a) the tenth (10th) anniversary of the Date of Issuance, (b) the closing of the sale, conveyance, or disposal of all or substantially all of the Company’s property or business, or the Company’s merger into or consolidation with any other corporation as a result of which the holders of the Company’s outstanding stock immediately prior to such transaction hold, immediately after such transaction, stock representing less than 50% of the voting power of the surviving corporation (or its parent corporation if the surviving corporation is wholly owned by the parent corporation) in such transaction; provided, however, that this Section 7(b) shall not apply to a merger effected exclusively for the purpose of changing the domicile of the Company or (c) two (2) years following the closing of a firm commitment underwritten public offering of the Company’s Common Stock pursuant to a registration statement under the Securities Act.

8. Notices of Certain Transactions. In case:

(a) the Company shall take a record of the holders of its Common Stock (or other stock or securities at the time deliverable upon the exercise of this Warrant) for the purpose of entitling or enabling them to receive any dividend or other distribution, or to receive any right to subscribe for or purchase any shares of stock of any class or any other securities, or to receive any other right, to subscribe for or purchase any shares of stock of any class or any other securities, or to receive any other right, or

(b) of any capital reorganization of the Company, any reclassification of the capital stock of the Company, any consolidation or merger of the Company with or into another corporation (other than a consolidation or merger in which the Company is the surviving entity), or any transfer of all or substantially all of the assets of the Company, or

(c) of the voluntary or involuntary dissolution, liquidation or winding-up of the Company.

then, and in each such case, the Company will mail or cause to be mailed to the Registered Holder of this Warrant a notice specifying, as the case may be, (i) the date on which a record is to be taken for the purpose of such dividend, distribution or right, and stating the amount and character of such dividend, distribution or right or (ii) the effective date on which such reorganization, reclassification, consolidation, merger, transfer, dissolution, liquidation or winding-up is to take place, and the time, if any is to be fixed, as of which the holders of record

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of Common Stock (or such other stock or securities at the time deliverable upon such reorganization, reclassification, consolidation, merger, transfer, dissolution, liquidation or winding-up) are to be determined. Such notice shall be mailed at least ten (10) days prior to the record date or effective date for the event specified in such notice.

9. Reservation of Stock. The Company will at all times reserve and keep available, solely for the issuance and delivery upon the exercise of this Warrant, such shares of Warrant Stock and other stock, securities and property, as from time to time shall be issuable upon the exercise of this Warrant.

10. Exchange of Warrants. Upon the surrender by the Registered Holder of any Warrant or Warrants, properly endorsed, to the Company at the principal office of the Company, the Company will, subject to the provisions of Section 4 hereof, issue and deliver to or upon the order of such Holder, at the Company’s expense, a new Warrant or Warrants of like tenor, in the name of such Registered Holder or as such Registered Holder (upon payment by such Registered Holder of any applicable transfer taxes) may direct, calling in the aggregate on the face or faces thereof for the number of shares of Common Stock called for on the face or faces of the Warrant or Warrants so surrendered.

11. Replacement of Warrants. Upon receipt of evidence reasonably satisfactory to the Company of the loss, theft, destruction or mutilation of this Warrant and (in the case of loss, theft or destruction) upon delivery of an indemnity agreement (with surety if reasonably required) in an amount reasonably satisfactory to the Company, or (in the case of mutilation) upon surrender and cancellation of this Warrant, the Company will issue, in lieu thereof, a new Warrant of like tenor.

12. Notices. Any notice required or permitted by this Warrant shall be in writing and shall be deemed sufficient upon receipt, when delivered personally or by courier, overnight delivery service or confirmed facsimile or other electronic transmission, or forty-eight (48) hours after being deposited in the regular mail as certified or registered mail (airmail if sent internationally) with postage prepaid, addressed (a) if to the Registered Holder, to the address of the Registered Holder most recently furnished in writing to the Company and (b) if to the Company, to the address set forth below or subsequently modified by written notice to the Registered Holder.

13. No Rights as Stockholder. Until the exercise of this Warrant, the Registered Holder of this Warrant shall not have or exercise any rights by virtue hereof as a stockholder of the Company.

14. Services Agreement. Nothing in this Warrant shall affect in any manner whatsoever the right or power of the Company to terminate the Services Agreement in accordance with the terms thereof.

15. No Fractional Shares. No fractional shares of Common Stock will be issued in connection with any exercise hereunder. In lieu of any fractional shares which would otherwise be issuable, the Company shall pay cash equal to the product of such fraction multiplied by the fair market value of one share of Common Stock on the date of exercise, as determined in good faith by the Company’s Board of Directors.

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16. Amendment or Waiver. Any term of this Warrant may be amended or waived only by an instrument in writing signed by the party against which enforcement of the amendment or waiver is sought.

17. Headings. The headings in this Warrant are for purposes of reference only and shall not limit or otherwise affect the meaning of any provision of this Warrant.

18. Governing Law. This Warrant shall be governed, construed and interpreted in accordance with the laws of the State of California, without giving effect to principles of conflicts of law.

19. “Market Stand-Off” Agreement. The Registered Holder hereby agrees that, during the period of duration (up to, but not exceeding, 180 days) specified by the Company and an underwriter of Common Stock or other securities of the Company, following the effective date of a registration statement of the Company filed under the Securities Act, it shall not, to the extent requested by the Company and such underwriter, directly or indirectly sell, offer to sell, contract to sell (including, without limitation, any short sale), grant any option to purchase or otherwise transfer or dispose of (other than to donees who agree to be similarly bound) any securities of the Company held by it at any time during such period except Common Stock included in such registration.

In order to enforce the foregoing covenant, the Company may impose stop-transfer instructions with respect to the Warrant Stock (and the shares or securities of every other person subject to the foregoing restriction) until the end of such period, and the Registered Holder agrees that, if so requested, such Holder will execute an agreement in the form provided by the underwriter containing terms which are essentially consistent with the provisions of this Section 19.

[Signature Page Follows]

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EXHIBIT A

PURCHASE FORM

The undersigned, pursuant to the provisions set forth in the attached Warrant hereby irrevocably elects to purchase              shares of the Common Stock covered by the attached Warrant and (please indicate either (a) or (b) below):

The undersigned further acknowledges that it has reviewed the representations and warranties contained in Section 5 of the Warrant and the covenants contained in Section 19 of the Warrant, and by its signature below the undersigned hereby makes such representations, warranties and covenants as of the date hereof.

EXHIBIT B

ASSIGNMENT FORM

FOR VALUE RECEIVED,                          hereby sells, assigns and transfers all of the rights of the undersigned under the attached Warrant with respect to the number of shares of Common Stock covered thereby set forth below, unto:

EXHIBIT C

Rule 501(a) under the Securities Act of 1933, as amended:

(a) Accredited Investor. “Accredited investor” shall mean any person who comes within any of the following categories, or who the issuer reasonably believes comes within any of the following categories, at the time of the sale of the securities to that person:

(1) Any bank as defined in Section 3(a)(2) of the Act or any savings and loan association or other institution as defined in Section 3(a)(5)(A) of the Act whether acting in its individual or fiduciary capacity; any broker dealer registered pursuant to Section 15 of the Securities Exchange Act of 1934; any insurance company as defined in Section 2(13) of the Act; any investment company registered under the Investment Company Act of 1940 or a business development company as defined in Section 2(a)(48) of that Act; any Small Business Investment Company licensed by the U.S. Small Business Administration under Section 301(c) or (d) of the Small Business Investment Act of 1958; any plan established and maintained by a state, its political subdivisions, or any agency or instrumentality of a state or its political subdivisions, for the benefit of its employees, if such plan has total assets in excess of $5,000,000; any employee benefit plan within the meaning of the Employee Retirement Income Security Act of 1974, if the investment decision is made by a plan fiduciary, as defined in Section 3(21) of such Act, which is either a bank, savings and loan association, insurance company, or registered investment adviser, or if the employee benefit plan has total assets in excess of $5,000,000, or, if a self-directed plan, with investment decisions made solely by persons that are accredited investors;

(2) Any private business development company as defined in Section 202(a)(22) of the Investment Advisers Act of 1940;

(3) Any organization described in Section 501(c)(3) of the Internal Revenue Code, corporation, Massachusetts or similar business trust, or partnership, not formed for the specific purpose of acquiring the securities offered, with total assets in excess of $5,000,000;

(4) Any director, executive officer, or general partner of the issuer of the securities being offered or sold, or any director, executive officer, or general partner of a general partner of that issuer;

(5) Any natural person whose individual net worth, or joint net worth with that person’s spouse, at the time of his purchase exceeds $1,000,000;

(6) Any natural person who had an individual income in excess of $200,000 in each of the two most recent years or joint income with that person’s spouse in excess of $300,000 in each of those years and has a reasonable expectation of reaching the same income level in the current year;

(7) Any trust with total assets in excess of $5,000,000, not formed for the specific purpose of acquiring the securities offered, whose purchase is directed by a sophisticated person as described in Rule 506(b)(2)(ii); and

(8) Any entity in which all of the equity owners are accredited investors.