Document:

<PAGE>   1

                                                                    EXHIBIT 4.11

                   FORM OF SERIES 1998A CONVERTIBLE DEBENTURE

                            PETER KIEWIT SONS', INC.
                             A DELAWARE CORPORATION

Registered Debenture No.                                $
7.35% Convertible Debenture                                Due: October 31, 2010

     PETER KIEWIT SONS', INC., a corporation organized and existing under the
laws of the State of Delaware, and having its principal place of business in the
City of Omaha, Nebraska (hereinafter called the "Corporation"), for the value
received, hereby promises to pay to                or registered assigns
(hereinafter called the "Debentureholder") on October 31, 2010, the principal
sum of           ($          ) Dollars.

     This debenture is one of the 1998A issue of registered convertible
debentures of the Corporation, due October 31, 2010 unless previously redeemed
or converted, limited to the aggregate principal amount of           and No/100
($          ) Dollars, all issued or to be issued pursuant to an indenture,
dated as of July 1, 1986, executed and delivered by Peter Kiewit Sons', Inc.
(now Level 3 Communications, Inc.) ("PKS") and FirstTier Bank, N.A. Omaha, as
trustee, as amended pursuant to a First Supplemental Indenture between the
Corporation, PKS and U.S. Bank National Association (hereinafter referred to as
"Trustee"), as successor trustee dated as of March 31, 1998. Reference is hereby
made to the indenture, and all indentures supplemental thereto, for a
description of the rights, limitations, obligations and immunities of the
Corporation, the holders of the debentures and the Trustee.

          (1) TYPE OF PAYMENT:  Payment of interest and principal shall be in
     any coin or currency of the United States of America which at the time of
     payment shall be legal tender for the payment of public or private debts.

          (2) INTEREST:  Except as hereinafter provided, the Corporation
     promises to pay to the registered owner hereof or his registered assigns,
     interest on the principal sum of this debenture, at the rate of seven and
     thirty five hundredths (7.35) percent per annum until the Corporation's
     obligation with respect to the payment of the principal amount shall have
     been discharged. Interest shall accrue upon this debenture from the most
     recent date to which interest has been paid, or if no interest has been
     paid, from the date of original issuance. In the event of conversion as
     provided in paragraph (7) hereof, interest shall cease accruing on the
     principal amount of the debenture on June 30, 2003. Interest on this
     debenture shall be paid annually on each November 1st, commencing November
     1, 2000.

          (3) PLACE OF PAYMENT:  The principal and interest on this debenture
     shall be payable at the office of the Corporation in Omaha, Nebraska.

          (4) DEFAULT:  This debenture shall be deemed to be in default whenever
     the principal sum and/or interest becomes payable and remains unpaid for a
     period of sixty (60) days.

          (5) REDEMPTION:  This debenture is subject to redemption at any time
     prior to the date of maturity at its principal amount plus all unpaid
     interest to the date of redemption provided, however, that the entire
     series is redeemed. This debenture may not be redeemed during the
     thirty-one (31) day conversion period provided for in paragraph (7) hereof.
     Redemption shall be preceded by notice thereof, given to the registered
     holder by registered mail no later than ten (10) days preceding the date of
     redemption.

          (6) TRANSFER:  The debenture may be transferred by the registered
     holder at the principal office of the Corporation in Omaha, Nebraska on
     registry books kept for such purpose at such office, upon surrender and
     cancellation of this debenture, and the payment of applicable charges. The
     Corporation and the Trustee may treat the registered holder of this
     debenture as the absolute owner for all purposes.
<PAGE>   2

          (7) CONVERSION:  (a) This debenture is convertible into the $0.01 par
     value common stock ("Common Stock") of the Corporation on the following
     basis: the debenture is not convertible, in whole or in part, for the
     period commencing on the date of issuance and ending on September 30, 2003.
     During the period commencing on October 1, 2003 and ending on October 31,
     2003, the registered holder may convert the entire principal amount of the
     debenture plus a cash payment in the amount of                multiplied by
     the formula value of the Common Stock on the date of conversion, into
               (          ) shares of Common Stock of the Corporation. During
     the period commencing on November 1, 2003 and ending on October 31, 2010,
     the date of maturity, the debenture is not convertible, in whole or in
     part. The conversion privilege shall be deemed exercised by submission of
     the debenture with a written request for conversion during the applicable
     thirty-one (31) day period at the principal office of the Corporation. The
     Corporation shall thereafter, within a sixty (60) day period, issue the
     Common Stock of the Corporation into which the debenture shall have been
     converted. As a condition precedent to the rights of conversion granted in
     this paragraph, the Debentureholder agrees to execute the Corporation's
     applicable Stock Repurchase Agreement. The debenture shall only be
     convertible by the registered holder if the registered holder is otherwise
     eligible to own shares of Common Stock of the Corporation as provided in
     the Corporation's Restated Certificate of Incorporation.

          (b) In case the Corporation shall change the stock issuable upon
     conversion into the same or different number of new shares of the same or
     of any other class or classes, the Debentureholder, upon conversion, shall
     be entitled to receive, in lieu of the old stock which he would have been
     entitled to receive but for such change, a number of shares of the new
     stock equivalent to the number of shares of new stock that would have been
     issued to him in exchange for such number of shares of old stock which he
     would have been entitled to receive if the conversion privilege had been
     exercisable and exercised immediately prior to such change.

          (c) In case at any time or from time to time the Corporation shall
     declare and pay on or in respect of the class of stock issuable upon
     conversion, any dividend of shares of stock of any class or classes, the
     Debentureholder, upon exercising the conversion privilege, after the date
     of record of the holders of stock to whom such stock dividend is payable,
     shall be entitled to receive the shares of stock theretofore issuable upon
     conversion, together with the dividend stock which would have been issuable
     if the conversion privilege had been exercisable and exercised immediately
     prior to the record date.

          (d) The Corporation covenants and agrees that in case it shall
     consolidate or merge with, or shall sell its property as an entirety, or
     substantially as an entirety to any other corporation, proper provision
     will be made as part of the terms of such consolidation, merger or sale,
     that the holder of any convertible debenture will thereafter be entitled to
     convert it into the same kind and amount of securities and any other assets
     as may be issuable or distributable by the terms of such consolidation,
     merger or sale with respect to the number of shares of Common Stock into
     which this debenture is convertible at the time of such consolidation,
     merger or sale; provided, however, that the surviving corporation with
     which the Corporation consolidates, merges or sells its property shall
     succeed to all of the rights provided for in this debenture, including the
     right of redemption.

          (8) SUBORDINATION:  In the payment of their claims, all creditors of
     the Corporation shall rank equally with the holders of convertible
     debentures. All claims of the convertible Debentureholders against earnings
     or assets are hereby made superior to those of stockholders, and the
     Corporation agrees that as long as any of its convertible debentures are
     outstanding, it will not pay any dividends on its stock until all liability
     for unpaid interest on its debentures has been paid. In the event of
     dissolution or liquidation of the Corporation, the holders of all
     debentures shall be entitled to be paid in full, both principal and
     interest, before any assets of the Corporation are distributed to any
     stockholder.

          (9) OWNERSHIP:  The Corporation may treat the registered owner of the
     debenture as the absolute owner of this debenture.

          (10) LIQUIDATION OF LIABILITY:  No recourse shall be had for the
     payment of the principal or interest of this debenture, against any
     incorporator, stockholder, officer, or director, past,

                                        2
<PAGE>   3

     present, or future, of the Corporation, all such liability being expressly
     waived by the owner of this debenture.

          (11) VALIDATION:  This debenture shall not be valid or become
     obligatory for any purpose until the certificate of authentication thereon
     shall have been signed by the Trustee.

     IN WITNESS WHEREOF, Peter Kiewit Sons', Inc. has caused this debenture to
become signed and its corporate seal to be hereunto affixed by its officers duly
authorized thereunto, all as of the                day of             , 2000.

<TABLE>
<S>                                                    <C>
ATTEST:                                                PETER KIEWIT SONS', INC.

-----------------------------------------------------  By --------------------------------------------------
Assistant Secretary                                    President
</TABLE>

TRUSTEE'S CERTIFICATE OF AUTHENTICATION:  This is one of the debentures
described in the Trust Indenture, dated as of July 1, 1986, by and between Peter
Kiewit Sons', Inc. (now Level 3 Communications, Inc.) ("PKS") and FirstTier
Bank, N.A. Omaha, as trustee, as amended pursuant to a First Supplemental
Indenture between the Corporation, PKS and U.S. Bank National Association, as
successor trustee dated as of March 31, 1998.

<TABLE>
<S>                                                    <C>
Dated -----------------------------------------------  By --------------------------------------------------
                                                       Authorized Officer
</TABLE>

This Debenture and the transfer thereof are subject to restrictions which are
stated in an Agreement between the Debentureholder(s) whose name(s) appear(s)
hereon and PETER KIEWIT SONS', INC., dated November 1, 1998.

                                        3<PAGE>   1

                                                                    EXHIBIT 4.12

                   FORM OF SERIES 1999A CONVERTIBLE DEBENTURE
                            PETER KIEWIT SONS', INC.
                             A DELAWARE CORPORATION

Registered Debenture No.                                $
8.25% Convertible Debenture                                Due: October 31, 2010

     PETER KIEWIT SONS', INC., a corporation organized and existing under the
laws of the State of Delaware, and having its principal place of business in the
City of Omaha, Nebraska (hereinafter called the "Corporation"), for the value
received, hereby promises to pay to                or registered assigns
(hereinafter called the "Debentureholder") on October 31, 2010, the principal
sum of                ($          ) Dollars.

     This debenture is one of the 1999A series of registered convertible
debentures of the Corporation, due October 31, 2010 unless previously redeemed
or converted, limited to the aggregate principal amount of                and
No/100 ($          ) Dollars, all issued or to be issued pursuant to an
indenture, dated as of July 1, 1986, executed and delivered by Peter Kiewit
Sons', Inc. (now Level 3 Communications, Inc.) ("PKS") and FirstTier Bank, N.A.
Omaha, as trustee, as amended pursuant to a First Supplemental Indenture between
the Corporation, PKS and U.S. Bank National Association (hereinafter referred to
as "Trustee"), as successor trustee dated as of March 31, 1998. Reference is
hereby made to the indenture, and all indentures supplemental thereto, for a
description of the rights, limitations, obligations and immunities of the
Corporation, the holders of the debentures and the Trustee.

          (1) TYPE OF PAYMENT:  Payment of interest and principal shall be in
     any coin or currency of the United States of America which at the time of
     payment shall be legal tender for the payment of public or private debts.

          (2) INTEREST:  Except as hereinafter provided, the Corporation
     promises to pay to the registered holder hereof or his registered assigns,
     interest on the principal sum of this debenture at the rate of eight and
     twenty-five hundredths percent (8.25%) per annum until the Corporation's
     obligation with respect to the payment of the principal amount shall have
     been discharged. Interest shall accrue upon this debenture from the most
     recent date to which interest has been paid, or if no interest has been
     paid, from the date of original issuance. In the event of conversion as
     provided in paragraph (7) hereof, interest shall cease accruing on the
     principal amount of the debenture on June 30, 2004. Interest on this
     debenture shall be paid annually each November 1st, commencing on November
     1, 2000.

          (3) PLACE OF PAYMENT:  The principal and interest on this debenture
     shall be payable at the office of the Corporation in Omaha, Nebraska.

          (4) DEFAULT:  This debenture shall be deemed to be in default whenever
     the principal sum and/or interest becomes payable and remains unpaid for a
     period of sixty (60) days.

          (5) REDEMPTION:  This debenture is subject to redemption at any time
     prior to the date of maturity at its principal amount plus all unpaid
     interest to the date of redemption; provided, however, that the entire
     series is redeemed. This debenture may not be redeemed during the
     thirty-one (31) day conversion period provided for in paragraph (7) hereof.
     Redemption shall be preceded by notice thereof, given to the registered
     holder by registered mail no later than ten (10) days preceding the date of
     redemption.

          (6) TRANSFER:  The debenture may be transferred by the registered
     holder at the principal office of the Corporation in Omaha, Nebraska on
     registry books kept for such purpose at such office, upon surrender and
     cancellation of this debenture, and the payment of applicable charges. The
     Corporation and the Trustee may treat the registered holder of this
     debenture as the absolute owner for all purposes.

          (7) CONVERSION:  (a) This debenture is convertible into the $0.01 par
     value common stock ("Common Stock") of the Corporation on the following
     basis: the debenture is not convertible, in whole or in part, for the
     period commencing on the date of issuance and ending on September 30, 2004.
     During
<PAGE>   2

     the period commencing on October 1, 2004 and ending on October 31, 2004,
     the registered holder may convert the entire principal amount of the
     debenture plus a cash payment in the amount of                multiplied by
     the formula value of the Common Stock on the date of conversion, into
                    (               ) shares of Common Stock of the Corporation.
     During the period commencing on November 1, 2004 and ending on October 31,
     2010, the date of maturity, the debenture is not convertible, in whole or
     in part. The conversion privilege shall be deemed exercised by submission
     of the debenture with a written request for conversion during the
     applicable thirty-one (31) day period at the principal office of the
     Corporation. The Corporation shall thereafter, within a sixty (60) day
     period, issue the Common Stock into which the debenture shall have been
     converted. As a condition precedent to the rights of conversion granted in
     this paragraph, the Debentureholder agrees to execute the Corporation's
     applicable Stock Repurchase Agreement. The debenture shall only be
     convertible by the registered holder if the registered holder is otherwise
     eligible to own shares of Common Stock of the Corporation as provided in
     the Corporation's Restated Certificate of Incorporation.

          (b) In case the Corporation shall change the stock issuable upon
     conversion into the same or different number of new shares of the same or
     of any other class or classes, the Debentureholder, upon conversion, shall
     be entitled to receive, in lieu of the old stock which he would have been
     entitled to receive but for such change, a number of shares of the new
     stock equivalent to the number of shares of new stock that would have been
     issued to him in exchange for such number of shares of old stock which he
     would have been entitled to receive if the conversion privilege had been
     exercisable and exercised immediately prior to such change.

          (c) In case at any time or from time to time the Corporation shall
     declare and pay on or in respect of the class of stock issuable upon
     conversion, any dividend of shares of stock of any class or classes, the
     Debentureholder, upon exercising the conversion privilege, after the date
     of record of the holders of stock to whom such stock dividend is payable,
     shall be entitled to receive the shares of stock theretofore issuable upon
     conversion, together with the dividend stock which would have been issuable
     if the conversion privilege had been exercisable and exercised immediately
     prior to the record date.

          (d) The Corporation covenants and agrees that in case it shall
     consolidate or merge with, or shall sell its property as an entirety, or
     substantially as an entirety to any other corporation, proper provision
     will be made as part of the terms of such consolidation, merger or sale,
     that the holder of any convertible debenture will thereafter be entitled to
     convert it into the same kind and amount of securities and any other assets
     as may be issuable or distributable by the terms of such consolidation,
     merger or sale with respect to the number of shares of Common Stock into
     which this debenture is convertible at the time of such consolidation,
     merger or sale; provided, however, that the surviving corporation with
     which the Corporation consolidates, merges or sells its property shall
     succeed to all of the rights provided for in this debenture, including the
     right of redemption.

          (8) SUBORDINATION:  In the payment of their claims, all creditors of
     the Corporation shall rank equally with the holders of convertible
     debentures. All claims of the convertible Debentureholders against earnings
     or assets are hereby made superior to those of stockholders, and the
     Corporation agrees that as long as any of its convertible debentures are
     outstanding, it will not pay any dividends on its stock until all liability
     for unpaid interest on its debentures has been paid. In the event of
     dissolution or liquidation of the Corporation, the holders of all
     debentures shall be entitled to be paid in full, both principal and
     interest, before any assets of the Corporation are distributed to any
     stockholder.

          (9) OWNERSHIP:  The Corporation may treat the registered owner of the
     debenture as the absolute owner of this debenture.

          (10) LIQUIDATION OF LIABILITY:  No recourse shall be had for the
     payment of the principal or interest of this debenture, against any
     incorporator, stockholder, officer, or director, past, present, or future,
     of the Corporation, all such liability being expressly waived by the owner
     of this debenture.

                                        2
<PAGE>   3

          (11) VALIDATION:  This debenture shall not be valid or become
     obligatory for any purpose until the certificate of authentication thereon
     shall have been signed by the Trustee.

     IN WITNESS WHEREOF, Peter Kiewit Sons', Inc. has caused this debenture to
become signed and its corporate seal to be hereunto affixed by its officers duly
authorized thereunto, all as of the                day of             , 2000.

<TABLE>
<S>                                                    <C>
ATTEST:                                                PETER KIEWIT SONS', INC.
                                                       By
-----------------------------------------------------  --------------------------------------------------
Assistant Secretary                                    President
</TABLE>

TRUSTEE'S CERTIFICATE OF AUTHENTICATION:  This is one of the debentures
described in the Trust Indenture, dated as of July 1, 1986, by and between Peter
Kiewit Sons', Inc. (now Level 3 Communications, Inc.) ("PKS") and FirstTier
Bank, N.A. Omaha, as trustee, as amended pursuant to a First Supplemental
Indenture between the Corporation, PKS and U.S. Bank National Association, as
successor trustee dated as of March 31, 1998.

<TABLE>
<S>                                                    <C>

Dated                                                  By
-----------------------------------------------        --------------------------------------------------
                                                       Authorized Officer
</TABLE>

This Debenture and the transfer thereof are subject to restrictions which are
stated in an Agreement between the Debentureholder(s) whose name(s) appear(s)
hereon and PETER KIEWIT SONS', INC., dated November 1, 1999.

                                        3

Source: [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00012-of-00352.parquet"}, [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00012-of-00352.parquet"}]]