Document:

exv4w1

Exhibit 4.1

SECOND AMENDMENT TO THE

THIRD AMENDED AND RESTATED RIGHTS AGREEMENT

     This Second Amendment to the Third Amended and Restated Rights Agreement dated as of July 15,
2008 (the “Amendment”), is between Intervoice, Inc., a Texas corporation (the
“Company”), and Computershare Trust Company, N.A., successor rights agent to Computershare
Investor Services, LLC, a Delaware limited liability company, as rights agent (the “Rights
Agent”).

RECITALS:

     WHEREAS, the Company and the Rights Agent are parties to that certain Third Amended and
Restated Rights Agreement dated as of May 1, 2001, as amended by the First Amendment to Third
Amended and Restated Rights Agreement dated as of May 29, 2002 (the “Agreement”).

     WHEREAS, the Company, Convergys Corporation, an Ohio corporation (“Parent”), and
Dialog Merger Sub, Inc., a Texas corporation and a wholly-owned subsidiary of Parent (“Merger
Sub”), are entering into an Agreement and Plan of Merger (the “Merger Agreement”) dated
as of the date hereof, pursuant to which Merger Sub will merge into the Company (the
“Merger”).

     WHEREAS, the Company was formerly referred to as Intervoice-Brite, Inc. in the Agreement.

     WHEREAS, the Board of Directors of the Company deems it desirable to amend the Agreement
pursuant to the provisions of Section 27 of the Agreement to make certain modifications to the
Agreement in the manner set forth below.

     NOW, THEREFORE, in consideration of the foregoing and the mutual covenants and agreements
contained herein, and intending to be legally bound hereby, the parties hereto agree as follows:

     Section 1. Defined Terms. Except as amended hereby, capitalized terms used but not
defined herein shall have the meaning ascribed to such terms in the Agreement.

     Section 2. Amendments to Preamble.

     (a) The preamble shall be amended and restated in its entirety to read as follows:

     Third Amended and Restated Rights Agreement, dated as of May 1, 2001 (this
“Agreement”), between Intervoice, Inc., a Texas corporation (the “Company”), and
Computershare Trust Company, N.A., successor rights agent to Computershare Investor
Services, LLC, a Delaware limited liability company (the “Rights Agent”).

     Section 3. Amendments to Section 1.

     (a) Section 1 of the Agreement is amended by adding the following defined terms:

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     “Merger Agreement” means that certain Agreement and Plan of Merger dated as of the date
hereof by and among the Company, Parent and Merger Sub, as it may be amended from time to
time.

     “Merger” means the merger of Merger Sub into the Company pursuant to the Merger
Agreement.

     “Offer” means a cash tender offer made by the Purchaser (the “Offer”) to acquire all of
the Company Shares that are issued and outstanding for $8.25 per Share net to the
seller in cash, without interest, upon the terms and subject to the conditions of the Merger
Agreement.

     “Parent” means Convergys Corporation, an Ohio corporation.

     “Merger Sub” means Dialog Merger Sub, Inc., a Texas corporation.

     “Tender and Voting Agreement” means that certain Tender and Voting Agreement dated as
of the date hereof by and among certain shareholders of the Company, Parent and Merger Sub,
as it may be amended from time to time.

     (b) The definition of “Acquiring Person” in Section 1 of the Agreement is amended to
add the following language at the end of such definition:

     Notwithstanding anything contained in this Agreement to the contrary, neither Parent,
Merger Sub nor any of their respective Affiliates or Associates shall become or be an
Acquiring Person solely by virtue of:

     (i) the execution, delivery and performance of the Merger Agreement, as it may
be amended from time to time hereafter; or

     (ii) the consummation of the transactions contemplated by the Merger Agreement;
or

     (iii) without limiting the generality of clauses (i) and (ii) above, the
Beneficial Ownership by any of such Persons of shares of Common Shares as a result
of its beneficial ownership of shares of Parent Common Shares.

     (c) The definition of “Business Day” in Section 1 of the Agreement is hereby amended to
delete the term “State of Delaware” in its entirety and replace it with “Commonwealth of
Massachusetts.”

     Section 4. Amendment to Section 2. Section 2 is hereby amended in its entirety to read
as follows:

     Section 2. Appointment of Rights Agent. The Company hereby appoints the Rights Agent
to act as agent for the Company in accordance with the terms and conditions hereof, and the
Rights Agent hereby accepts such appointment. The Company may from time to time appoint such co-Rights Agents as it may deem necessary or
desirable, upon ten (10) days’ prior written notice to the Rights Agent. The Rights Agent

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shall have no duty to supervise, and shall in no event be liable for, the acts or omissions
of any such co-Rights Agents.

     Section 5. Amendments to Section 3. Section 3(a) is hereby amended in its entirety to
read as follows:

     Until the earlier of (i) the close of business on the tenth day after the Shares
Acquisition Date or (ii) the close of business on the tenth business day (or such later date
as may be determined by action of the Board of Directors prior to such time as any person
becomes an Acquiring Person) after the date of the commencement by any Person (other than
the Company, any Subsidiary of the Company, any employee benefit plan of the Company or of
any Subsidiary of the Company, any entity holding Common Shares for or pursuant to the terms
of any such plan, and other than Parent, Merger Sub or any of their respective Affiliates or
Associates if such commencement is in connection with the Merger or the Offer as
contemplated by the Merger Agreement) of, or of the first public announcement of the
intention of any Person (other than the Company, any Subsidiary of the Company, any employee
benefit plan of the Company or of any Subsidiary of the Company, any entity holding Common
Shares for or pursuant to the terms of any such plan, and other than Parent, Merger Sub or
any of their respective Affiliates or Associates if such announcement is in connection with
the Merger or the Offer as contemplated by the Merger Agreement) to commence, a tender or
exchange offer the consummation of which would result in any Person becoming the Beneficial
Owner of Common Shares aggregating 20% or more of the then outstanding Common Shares
(including any such date which is after the date of this Agreement and prior to the issuance
of the Rights; the earlier of such dates being herein referred to as the “Distribution
Date”), (x) the Rights will be evidenced (subject to the provisions of Section 3(b) hereof)
by the certificates for Common Shares registered in the names of the holders thereof (which
certificates shall also be deemed to be Right Certificates) and not by separate Right
Certificates, and (y) the right to receive Right Certificates will be transferable only in
connection with the transfer of Common Shares. As soon as practicable after the Distribution
Date, the Company will prepare and execute, the Rights Agent will countersign, and the
Company will send or cause to be sent (and the Rights Agent will, if requested and at the
expense of the Company, send) by first-class, insured, postage-prepaid mail, to each record
holder of Common Shares as of the close of business on the Distribution Date, at the address
of such holder shown on the records of the Company, a Right Certificate, in substantially
the form of Exhibit A hereto (a “Right Certificate”), evidencing one Right for each Common
Share so held. As of the Distribution Date, the Rights will be evidenced solely by such
Right Certificates.

     Section 6. Amendments to Section 7. Section 7(a) is hereby amended in its entirety to
read as follows:

     The registered holder of any Right Certificate may exercise the Rights evidenced
thereby (except as otherwise provided herein) in whole or in part at any time after the
Distribution Date upon surrender of the Right Certificate, with the form of election to
purchase on the reverse side thereof duly executed, to the Rights Agent at the principal
office or offices of the Rights Agent designated for such purpose, together with payment
of the Purchase Price for each one eight-hundredths of a Preferred Share (or other
securities, cash or other assets, as the case may be) as to which the Rights are exercised,

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at or prior to the earliest of (i) the close of business on May 10, 2011 (the “Final
Expiration Date”), (ii) the time at which the Rights are redeemed as provided in Section 23
hereof (the “Redemption Date”), (iii) the time at which such Rights are exchanged as
provided in Section 24 hereof, or (iv) the time immediately prior to the Effective Time (as
defined in the Merger Agreement), but only if the Effective Time shall occur.

     Section 7. Amendment to Section 21. Section 21 is hereby amended to add the following
new sentence after the existing first sentence:

     In the event the transfer agency relationship in effect between the Company and the
Rights Agent terminates, the Rights Agent will be deemed to have resigned automatically
and be discharged from its duties under this Agreement as of the effective date of such
termination, and the Company shall be responsible for sending any required notice.

     Section 8. Amendment to Section 26. Section 26 is hereby amended to delete the Rights
Agent notice address in its entirety and replace it with the following:

Computershare Trust Company, N.A.

350 Indiana Street, Suite 800

Golden, CO 80401

Attention: Client Services

     Section 9. Addition of Section 34. Section 34 is hereby added to the Agreement to read
as follows:

     Section 34. Exception for Certain Transactions. Notwithstanding any provision of this
Agreement to the contrary, (i) none of Parent, Merger Sub or any of their Affiliates or
Associates shall be deemed an Acquiring Person, (ii) none of a Distribution Date, Flip-In
Event, Flip-In Trigger Date, Flip-Over Event nor a Shares Acquisition Date shall be deemed
to occur or to have occurred and (iii) no holder of any Rights shall be entitled to exercise
such Rights under, or be entitled to any rights under, the Agreement, including, without
limitation, pursuant to Section 7 of this Agreement, in any such case by reason of (a) the
approval, execution or delivery of the Merger Agreement or the Tender and Voting Agreement,
or any amendments thereof approved in advance by the Board of Directors of the Company, (b)
the public announcement by any of the Company, Parent or Merger Sub that Parent, Merger Sub
or any of their respective Affiliates or Associates is to commence a tender or exchange
offer the consummation of which would result in any Person becoming the Beneficial Owner of
Common Shares aggregating 20% or more of the then outstanding Common Shares in accordance
with the Merger Agreement, (c) the public announcement of the Merger, (d) the adoption of
the Merger Agreement by the Company’s shareholders, (e) the exchange of Common Shares
(including the Rights) pursuant to the Merger Agreement, or (f) the consummation or public
announcement of any transaction contemplated by the Merger Agreement in accordance with the
provisions thereof, including the Merger provided for in the Merger Agreement.

     Section 10. Addition of Section 35. Section 35 is hereby added to the Agreement to read
as follows:

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     Notice to Rights Agent. Promptly following the Effective Time (as defined in the
Merger Agreement) the Company shall provide the Rights Agent with written notice of the
occurrence of the Merger.

     Section 11. Amendments to Summary of Rights. Exhibit B to the Agreement shall be deemed
amended in a manner consistent with this Amendment.

     Section 12. Severability. If any term, provision, covenant or restriction of this
Amendment is held by a court of competent jurisdiction or other authority to be invalid, void
or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this
Amendment shall remain in full force and effect and shall in no way be affected, impaired or
invalidated.

     Section 13. Governing Law. This Amendment shall be deemed to be a contract made under
the laws of the State of Texas and for all purposes shall be governed by and construed in
accordance with the laws of such State applicable to contracts made and to be performed
entirely within such State.

     Section 14. Counterparts. This Amendment may be executed in any number of 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.

     Section 15. Effect of Amendment. Except as expressly modified herein, the Agreement
shall remain in full force and effect.

[Signature Page Follows.]

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     IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed as of
the day and year first above written.

	 	 	 	 	 
	 	Intervoice, Inc.

 	 
	 	By:  	/s/
Robert E. Ritchey	 
	 	 	Name:  	Robert E. Ritchey	 
	 	 	Title:  	Chief Executive Officer	 
	 

	 	 	 	 	 
	 	Computershare Trust Company, N.A.

 	 
	 	By:  	/s/
Kellie Gwinn	 
	 	 	Name:  	Kellie Gwinn	 
	 	 	Title:  	Vice President	 
	 

6exv10w1

Exhibit 10.1

AMENDMENT NO. 2 TO

THE BOARD REPRESENTATION AND

GOVERNANCE AGREEMENT

     This AMENDMENT NO.2 (the “Amendment”) to the Board Representation and Governance
Agreement (the “Governance Agreement”), dated as of June 22, 2007, as amended by Amendment
No.1 to the Governance Agreement, dated as of July 1, 2007, by and between Intervoice, Inc., a
Texas corporation (the “Company” or “Intervoice”) and David W. Brandenburg, a
natural person residing in the State of Florida (“David Brandenburg”), is being entered
into as of July 15, 2008.

RECITALS:

     WHEREAS, the Company, Convergys Corporation, an Ohio corporation (“Parent”), and
Dialog Merger Sub, Inc., a Texas corporation and a wholly-owned subsidiary of Parent (“Merger
Sub”), are entering into an Agreement and Plan of Merger (the “Merger Agreement”) dated
as of the date hereof, pursuant to which Merger Sub will merge into the Company (the
“Merger”).

     WHEREAS, the Merger Agreement provides that, among other things, the Company will amend the
Governance Agreement.

     NOW, THEREFORE, in consideration of the foregoing and the mutual covenants and agreements
contained herein, and intending to be legally bound hereby, the parties hereto agree as follows:

     Section 1. Definitions; References. Unless otherwise specifically defined herein, each term
used herein shall have the meaning assigned to such term in the Governance Agreement. Each
reference to “hereof”, “herein”, “hereunder”, “hereby” and “this Agreement” shall from and after
the date hereof refer to the Governance Agreement as amended by this Amendment.

     Section 2. Amendment to Section 1.2. The definition of “Brandenburg Representation Period”
in Section 1.2 of the Governance Agreement is hereby amended and restated in its entirety to read
as follows:

     “Brandenburg Representation Period” shall mean the period commencing with the appointment of
the Brandenburg Nominees to the Board and ending on the earlier of the Effective Time (as defined
in the Merger Agreement) or the conclusion of the 2008 Annual Meeting of Shareholders.

     Section 3. Addition of Section 4.16. Section 4.16 is hereby added to the Governance
Agreement to read as follows:

     This Agreement, all of the terms and conditions herein, and the rights and obligations
of the parties hereunder, will terminate as of the earlier of the Effective Time (as
defined in the Merger Agreement) or the conclusion of the 2008 Annual Meeting of
Shareholders; except that notwithstanding the foregoing,

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(i) Section 2.1(i) shall remain in full force and effect as long as the Brandenburg
Nominees remain members of the board of the Company; and (ii) Sections 3.4, 3.5 and 3.6
shall survive the termination of this Agreement.

     Section 4. No Further Amendment. Except as otherwise provided herein, the Governance
Agreement shall remain unchanged and in full force and effect.

     Section 5. Effect of Amendment. From and after the execution of this Amendment by the parties
hereto, any references to the Governance Agreement shall be deemed a reference to the Governance
Agreement as amended hereby.

     Section 6. Governing Law. This Amendment shall be governed by, enforced under and construed
in accordance with the laws of the State of Texas, without giving effect to any choice or conflict
of law provision or rule thereof or of any other jurisdiction.

     Section 7. Counterparts. This Amendment may be executed in any number of counterparts, each
of which shall be deemed an original, but all of which together shall constitute one and the same
instrument.

     Section 8. Descriptive Headings. The descriptive headings herein are inserted for
convenience of reference only and shall in no way be construed to define, limit, describe, explain,
modify, amplify, or add to the interpretation, construction or meaning of any provision of, or
scope or intent of, this Amendment or the Governance Agreement nor in any way affect this Amendment
or the Governance Agreement.

[Signature Page Follows.]

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     IN WITNESS WHEREOF, each of the undersigned has caused this Amendment to be signed by its duly
authorized officer as of the date first above written.

	 	 	 	 	 
	 	INTERVOICE, INC.

 	 
	 	By:  	/s/
Robert E. Ritchey	 
	 	 	Name:  	Robert E. Ritchey	 
	 	 	Title:  	Chief Executive Officer	 
	 	 	 	 	 
	 	 	 	 	 
	 	
	 	/s/ David W. Brandenburg 	 
	 	David W. Brandenburg 	 
	 

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