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1 Vol. 78 Wednesday, No. 147 July 31, 2013 Part II Department of the Treasury Fiscal Service 31 CFR Part 356 Sale and Issue of Marketable Book-Entry Treasury Bills, Notes, and Bonds; Final Rule VerDate Mar<15> :04 Jul 30, 2013 Jkt PO Frm Fmt 4717 Sfmt 4717 E:\FR\FM\31JYR2.SGM 31JYR2

8 46432 Federal Register / Vol. 78, No. 147 / Wednesday, July 31, 2013 / Rules and Regulations Computing the Projected Cash Flows The following table presents the future interest payment dates and the number of days between them. TABLE 2 PAYMENT DATES Dates Days between dates Issue Date: T 0 = 7/31/ st Interest Date: T 1 = 10/31/ T 1 T 0 = 92 2nd Interest Date: T 2 = 1/31/ T 2 T 1 = 92 3rd Interest Date: T 3 = 4/30/ T 3 T 2 = 89 4th Interest Date: T 4 = 7/31/ T 4 T 3 = 92 5th Interest Date: T 5 = 10/31/ T 5 T 4 = 92 6th Interest Date: T 6 = 1/31/ T 6 T 5 = 92 7th Interest Date: T 7 = 4/30/ T 7 T 6 = 89 8th Interest & Maturity Dates: T 8 = 7/31/ T 8 T 7 = 92 Let a i = 100 max(r + s,0)/360 and A i = a i (T i T i 1) {i=8} a i represents the daily projected interest, for a \$100 par value, that will accrue between the future interest payment dates T i 1 and T i, where i = 1,2,...,8. a i s are computed using the spread s = 0.120% obtained at the auction, and the fixed index rate of r = % applicable to the issue date (7/31/2012). For example: a 1 = 100 max( ,0)/ 360 = A i represents the projected cash flow the floating rate note holder will receive, for a \$100 par value, at the future interest payment date T i, where i = 1,2,...,8. T i T i 1 is the number of days between the future VerDate Mar<15> :04 Jul 30, 2013 Jkt PO Frm Fmt 4701 Sfmt 4700 E:\FR\FM\31JYR2.SGM 31JYR2 interest payment dates T i 1 and T i. To account for the payback of the par value, the variable 1 {i=8} takes the value 1 if the payment date is the maturity date, or 0 otherwise. For example: A i = = and A 8 = = ER31JY13.001</GPH>

9 Federal Register / Vol. 78, No. 147 / Wednesday, July 31, 2013 / Rules and Regulations Let B i = 1 + (r + m) (T i T i 1)/360 B i represents the projected compound factor between the future dates T i 1 and T i, where i = 1,2,...,8. All B i s are computed using the discount margin m = 0.120% (equals the spread determined at the auction), and the fixed index rate of r = % applicable to the issue date (7/31/2012). For example: B 3 = 1 + ( ) 89/360 = The following table shows the projected daily accrued interest values for \$100 par value (a i s), cash flows at interest payment dates (A i s), and the compound factors between payment dates (B i s). TABLE 3 PROJECTED CASH FLOWS AND COMPOUND FACTORS i a i A i B i Computing the Price The price is computed as follows: B. For newly issued floating rate notes issued at a premium: Formula: VerDate Mar<15> :04 Jul 30, 2013 Jkt PO Frm Fmt 4701 Sfmt 4700 E:\FR\FM\31JYR2.SGM 31JYR2 ER31JY13.002</GPH>

10 46434 Federal Register / Vol. 78, No. 147 / Wednesday, July 31, 2013 / Rules and Regulations Example: The purpose of this example is to demonstrate how a floating rate note auction can result in a price at a premium given a negative discount margin and spread at auction. For a new two-year floating rate note auctioned on July 25, 2012, and issued on July 31, 2012, with a maturity date of July 31, 2014, solve for the price per 100 (P). In a new issue (not a reopening) of a floating rate note, the discount margin established at auction will be equal to the spread. In this example, the discount margin determined at auction is 0.150%, but the floating rate note is subject to a daily interest rate accrual minimum of 0.000%. Definitions: TABLE 1 13-WEEK BILL AUCTION DATA T 0 = July 31, N = 8. T N = July 31, r = %. s = 0.150%. m = 0.150%. As of the issue date the latest 13-week bill, auctioned at least two days prior, has the following information: Auction date Issue date Maturity date Auction clearing price Auction high rate Index rate 7/23/2012 7/26/ /25/ % % Computing the Projected Cash Flows The following table presents the future interest payment dates and the number of days between them. TABLE 2 PAYMENT DATES Dates Days between dates Issue Date: T 0 = 7/31/ st Interest Date: T 1 = 10/31/ T 1 T 0 = 92 2nd Interest Date: T 2 = 1/31/ T 2 T 1 = 92 3rd Interest Date: T 3 = 4/30/ T 3 T 2 = 89 4th Interest Date: T 4 = 7/31/ T 4 T 3 = 92 5th Interest Date: T 5 = 10/31/ T 5 T 4 = 92 6th Interest Date: T 6 = 1/31/ T 6 T 5 = 92 7th Interest Date: T 7 = 4/30/ T 7 T 6 = 89 8th Interest & Maturity Dates: T 8 = 7/31/ T 8 T 7 = 92 VerDate Mar<15> :04 Jul 30, 2013 Jkt PO Frm Fmt 4701 Sfmt 4700 E:\FR\FM\31JYR2.SGM 31JYR2 ER31JY13.003</GPH> ER31JY13.004</GPH>

11 Federal Register / Vol. 78, No. 147 / Wednesday, July 31, 2013 / Rules and Regulations Let a i = 100 max(r + s,0)/360 and A i = a i (T i T i 1) {i=8} a i Represents the daily projected interest, for a \$100 par value, that will accrue between the future interest payment dates T i 1 and T i where i = 1,2,...,8. a i s are computed using the spread s = 0.150%, and the fixed index rate of r = % applicable to the issue date (7/31/2012). For example: a i = 100 max( ,0)/ 360 = 100 0/360 = A i represents the projected cash flow the floating rate note holder will receive, for a \$100 par value, at the future interest payment date T i, where i = 1,2,..., 8. T i T i 1 is the number of days between the future interest payment dates T i 1 and T i. To account for the payback of the par value, the variable 1 {i= 8} takes the value 1 if the payment date is the maturity date, or 0 otherwise. For example: A 1 = = and A 8 = = Let B i = 1 + (r + m) (T i T i 1)/360 B i represents the projected compound factor between the future dates T i 1 and T i, where i = 1,2,..., 8. All B i s are computed using the discount margin m = 0.150% (equals the spread obtained at the auction), and the fixed index rate of r = % applicable to the issue date (7/31/2012). For example: B 3 = 1 + ( ) 89/360 = The following table shows the projected daily accrued interests for \$100 par value (a i s), cash flows at interest payment dates (A i s), and the compound factors between payment dates (B i s). TABLE 3 PROJECTED CASH FLOWS AND COMPOUND FACTORS i a i A i B i Computing the Price The price is computed as follows: Definitions for Reopenings of Floating Rate Notes and Calculation of Interest Payments IP i = the quarterly interest payment at date T i. P D = the price that includes the accrued interest per \$100 par value as of the reopening issue date. AI = accrued interest per \$100 par value as of the reopening issue date. P C = the price without accrued interest per \$100 par value as of the reopening issue date. T 1 = the dated date if the reopening occurs before the first interest payment date, or, otherwise, the latest interest payment date prior to the reopening issue date. T 0 = the reopening issue date. N = the total number of remaining quarterly interest payments as of the reopening issue date. i and k = indexes that identify the sequence of interest payment dates relative to the issue date. For example T 1, T 2, and T 3 represent the first, second, and the third VerDate Mar<15> :04 Jul 30, 2013 Jkt PO Frm Fmt 4701 Sfmt 4700 E:\FR\FM\31JYR2.SGM 31JYR2 interest payment dates after the issue date respectively, while T 1 represents the preceding interest payment date before the issue date. j = an index that identifies days between consecutive interest payment dates. T i = the i th remaining quarterly interest payment date. T i T i 1 = the number of days between the interest payment date T i and the preceding interest payment date. T N = the maturity date. ER31JY13.005</GPH>

12 46436 Federal Register / Vol. 78, No. 147 / Wednesday, July 31, 2013 / Rules and Regulations r j s = the effective index rates for days between the last interest payment date and the reopening issue date. r = the index rate applicable to the reopening issue date. s = the spread. m = the discount margin. C. Pricing and accrued interest for reopened floating rate notes Formula: Example: The purpose of this example is to determine the floating rate note prices with and without accrued interest at the time of the reopening auction. For a two-year floating rate note that was originally auctioned on July 25, 2012, with an issue date of July 31, 2012, reopened in an auction on August 30, 2012 and issued on August 31, 2012, with a maturity date of July 31, 2014, solve for accrued interest per 100 (AI), the price with accrued interest per 100 (P D) and the price without accrued interest per 100 (P C). Since this is a reopening of an original issue from the prior month, Table 2 as shown in the example is used for accrued interest calculations. In the case of floating rate note reopenings, the spread on the security remains equal to the spread that was established at the original auction of the floating rate notes. TABLE 1 13-WEEK BILL AUCTION DATA Definitions: T 1 = July 31, T 0 = August 31, N = 8. T N = July 31, r = %. s = 0.120%. m = 0.100%. The following table shows the past results for the 13-week bill auction. Auction date Issue date Maturity date Auction clearing price Auction high rate (percent) Index rate (percent) 7/23/ /26/ /25/ /30/ /2/ /1/ /6/ /9/ /8/ /13/ /16/ /15/ /20/ /23/ /23/ /27/ /30/ /29/ VerDate Mar<15> :04 Jul 30, 2013 Jkt PO Frm Fmt 4701 Sfmt 4700 E:\FR\FM\31JYR2.SGM 31JYR2 ER31JY13.006</GPH>

13 Federal Register / Vol. 78, No. 147 / Wednesday, July 31, 2013 / Rules and Regulations The following table shows the index rates applicable for the accrued interest. TABLE 2 APPLICABLE INDEX RATE Accrual starts Accrual ends Number of days in accrual period Applicable floating rate Auction date Index rate (percent) 7/31/ /31/ /23/ /1/ /6/ /30/ /7/ /13/ /6/ /14/ /20/ /13/ /21/ /27/ /20/ /28/ /30/ /27/ Computing the Accrued Interest The accrued interest as of the new issue date (8/31/2012) for a \$100 par value is: AI = max ( max ( max ( max ( max ( max ( AI = TABLE 3 PAYMENT DATES Dates AI = AI = = \$ Computing the Projected Cash Flows The following table presents the future interest payment dates and the number of days between them. Days between dates Original Issue Date: T 1 = 7/31/ New Issue Date: T 0 = 8/31/ T 0 T 1 = 31 1st Interest Date: T 1 = 10/31/ T 1 T 0 = 61 2nd Interest Date: T 2 = 1/31/ T 2 T 1 = 92 3rd Interest Date: T 3 = 4/30/ T 3 T 2 = 89 4th Interest Date: T 4 = 7/31/ T 4 T 3 = 92 5th Interest Date: T 5 = 10/31/ T 5 T 4 = 92 6th Interest Date: T 6 = 1/31/ T 6 T 5 = 92 7th Interest Date: T 7 = 4/30/ T 7 T 6 = 89 8th Interest & Maturity Dates: T 8 = 7/31/ T 8 T 7 = 92 Let a 1 = 100 max(r + s, 0)/360 and A i = a i (T i T i 1) {i=8} a 1 represents the daily projected interest, for a \$100 par value, that will accrue between the future interest payment dates T i 1 and T 1, where i=1,2,...,8. a i s are computed using the spread s = 0.120% obtained at the original auction, and the fixed index rate of VerDate Mar<15> :04 Jul 30, 2013 Jkt PO Frm Fmt 4701 Sfmt 4700 E:\FR\FM\31JYR2.SGM 31JYR2 r = % applicable to the new issue date (8/31/2012). For example: a i = 100 max( ,0)/ 360 = A i represents the projected cash flow the floating rate note holder will receive, less ER31JY13.007</GPH>

14 46438 Federal Register / Vol. 78, No. 147 / Wednesday, July 31, 2013 / Rules and Regulations accrued interest, for a \$100 par value, at the future interest payment date T i, where i=1,2,...,8. T i 1 is the number of days between the future interest payment dates T i 1 and T i. To account for the payback of the par value, the variable 1 {i=8} takes the value 1 if the payment date is the maturity date, or 0 otherwise. For example: A i = = and A 8 = = Let B i = 1 + (r + m) (T i 1)/360 B i represents the projected compound factor between the future dates T i 1 and T i, where i=1,2,...,8. All B i s are computed using the discount margin m = 0.100% obtained at the reopening auction, and the fixed index rate of r = % applicable to the new issue date (8/31/2012). For example: B 3 = 1 + ( ) 89/360 = The following table shows the projected daily accrued interests for \$100 par value (a i s), cash flows at interest payment dates (A i s), and the compound factors between payment dates (B i s). TABLE 4 PROJECTED CASH FLOWS AND COMPOUND FACTORS i a i A i B i Computing the Price The price with accrued interest is computed as follows: VerDate Mar<15> :04 Jul 30, 2013 Jkt PO Frm Fmt 4701 Sfmt 4725 E:\FR\FM\31JYR2.SGM 31JYR2 ER31JY13.008</GPH>

15 Federal Register / Vol. 78, No. 147 / Wednesday, July 31, 2013 / Rules and Regulations D. For calculating interest payments: Example: For a new issue of a two-year floating rate note auctioned on July 25, 2012, and issued on July 31, 2012, with a maturity date of July 31, 2014, and a first interest payment date of October 31, 2012, calculate the quarterly interest payments (IP I) per 100. In a new issuance (not a reopening) of a new floating rate note, the discount margin determined at auction will be equal to the spread. The interest accrual rate used for this floating rate note on the issue date is % (index rate of % plus a spread of 0.120%) and this rate is used for each daily interest accrual over the life of the security for the purposes of this example. Example 1: Projected interest payment as of the original issue date. T 0 = July 31, N = 8. T N = July 31, r = %. s = 0.120%. m = 0.120%. TABLE 1 13-WEEK BILL AUCTION DATA As of the issue date the latest 13-week bill, auctioned at least two days prior, has the following information: Auction date Issue date Maturity date Auction clearing price Auction high rate Index rate 7/23/ /26/ /25/ % % Computing the Projected Cash Flows The following table presents the future interest payment dates and the number of days between them. TABLE 2 PAYMENT DATES Dates Days between dates Issue Date: T 0 = 7/31/ st Interest Date: T 1 = 10/31/ T 1 T 0 = 92 2nd Interest Date: T 2 = 1/31/ T 2 T 1 = 92 3rd Interest Date: T 3 = 4/30/ T 3 T 2 = 89 4th Interest Date: T 4 = 7/31/ T 4 T 3 = 92 5th Interest Date: T 5 = 10/31/ T 5 T 4 = 92 6th Interest Date: T 6 = 1/31/ T 6 T 5 = 92 7th Interest Date: T 7 = 4/30/ T 7 T 6 = 89 8th Interest & Maturity Dates: T 8 = 7/31/ T 8 T 7 = 92 VerDate Mar<15> :04 Jul 30, 2013 Jkt PO Frm Fmt 4701 Sfmt 4700 E:\FR\FM\31JYR2.SGM 31JYR2 ER31JY13.010</GPH> ER31JY13.011</GPH>

16 46440 Federal Register / Vol. 78, No. 147 / Wednesday, July 31, 2013 / Rules and Regulations Using the spread s = 0.120%, and the fixed index rate of r = % applicable to the issue date (7/31/2012), the first and seventh projected interest payments are computed as follows: IP 1 = 92 [100 max( ] IP 1 = = IP 7 = 89 [100 max( ] IP 7 = = The following table shows all projected interest payments as of the issue date. TABLE 3 PROJECTED INTEREST PAYMENTS i Dates IP i /31/ /31/ /30/ TABLE 3 PROJECTED INTEREST PAYMENTS Continued i Dates IP i /31/ /31/ /31/ /30/ /31/ Example 2: Projected interest payment as of the reopening issue date (intermediate values, including rates in percentage terms, are rounded to nine decimal places). This example demonstrates the calculations required to determine the interest payment due when the reopened floating rate note is issued. This example also demonstrates the need to calculate accrued interest at the time of a floating rate reopening auction. Since this is a reopening TABLE 4 13-WEEK BILL AUCTION DATA of an original issue from 31 days prior, Table 5 as shown in the example is used for accrued interest calculations. For a two-year floating rate note originally auctioned on July 25, 2012 with an original issue date of July 31, 2012, reopened by an auction on August 30, 2012 and issued on August 31, 2012, with a maturity date of July 31, 2014, calculate the quarterly interest payments (IP I) per 100. T 1 is the dated date if the reopening occurs before the first interest payment date, or otherwise the latest interest payment date prior to the new issue date. T 1 = July 31, T 0 = August 31, N = 8. T N = July 31, r = %. s = 0.120%. m = 0.100%. The following table shows the past results for the 13-week bill auction. Auction date Issue date Maturity date Auction clearing price Auction high rate (percent) Index rate (percent) 7/23/ /26/ /25/ /30/ /2/ /1/ /6/ /9/ /8/ /13/ /16/ /15/ /20/ /23/ /23/ /27/ /30/ /29/ The following table shows the index rates applicable for the accrued interest. TABLE 5 APPLICABLE INDEX RATE Accrual starts Accrual ends Number of days in accrual period Applicable floating rate Auction date Index rate (percent) 7/31/ /31/ /23/ /1/ /6/ /30/ /7/ /13/ /6/ /14/ /20/ /13/ /21/ /27/ /20/ VerDate Mar<15> :04 Jul 30, 2013 Jkt PO Frm Fmt 4701 Sfmt 4700 E:\FR\FM\31JYR2.SGM 31JYR2 ER31JY13.012</GPH>

17 Federal Register / Vol. 78, No. 147 / Wednesday, July 31, 2013 / Rules and Regulations TABLE 5 APPLICABLE INDEX RATE Continued Accrual starts Accrual ends Number of days in accrual period Applicable floating rate Auction date Index rate (percent) 8/28/ /30/ /27/ Computing the accrued interest The accrued interest as of 8/31/2012 for a \$100 par value is: AI = max ( max ( max ( max ( max ( max ( AI = TABLE 6 PAYMENT DATES Dates AI = AI = = \$ The following table presents the future interest payment dates and the number of days between them. Days between dates Original Issue Date: T 1 = 7/31/ New Issue Date: T 0 = 8/31/ T0 T 1 = 31 1st Interest Date: T 1 = 10/31/ T 1 T 0 = 61 2nd Interest Date: T 2 = 1/31/ T 2 T 1 = 92 3rd Interest Date: T 3 = 4/30/ T 3 T 2 = 89 4th Interest Date: T 4 = 7/31/ T 4 T 3 = 92 5th Interest Date: T 5 = 10/31/ T 5 T 4 = 92 6th Interest Date: T 6 = 1/31/ T 6 T 5 = 92 7th Interest Date: T 7 = 4/30/ T 7 T 6 = 89 8th Interest & Maturity Dates: T 8 = 7/31/ T 8 T 7 = 92 Using the original spread s = 0.120% (obtained on 7/25/2012), and the fixed index rate of r = % applicable to the new issue date (8/31/2012), the first and eighth projected interest payments are computed as follows: IP 1 = [100 max ( ] IP 1 = IP 1 = = and IP 8 = 92 [100 max ( ] IP 8 = = The following table shows all projected interest payments as of the new issue date. TABLE 7 PROJECTED INTEREST PAYMENTS i Dates IP i /31/ TABLE 7 PROJECTED INTEREST PAYMENTS Continued i Dates IP i /31/ /30/ /31/ /31/ /31/ /30/ /31/ Definitions for Newly Issued Floating Rate Notes with an Issue Date that Occurs after the Dated Date P D = the price that includes accrued interest from the dated date to the issue date per \$100 par value as of the issue date. AI = the accrued interest per \$100 par value as of the issue date. P C = the price without accrued interest per \$100 par value as of the issue date. T 1 = the dated date. T 0 = the issue date. N = the total number of remaining quarterly interest payments as of the new issue date. i and k = indexes that identify the sequence of interest payment dates. j = an index that identifies days between the dated date and the issue date. T i = the i th quarterly future interest payment date. T i T i 1 = the number of days between the interest payment date T i and the preceding interest payment date. T N = the maturity date. r j s = the effective index rates for days between the dated date and the issue date. r = the index rate applicable to the issue date. s = the spread. m = the discount margin. E. Pricing and accrued interest for new issue floating rate notes with an issue date that occurs after the dated date Formula: VerDate Mar<15> :04 Jul 30, 2013 Jkt PO Frm Fmt 4701 Sfmt 4700 E:\FR\FM\31JYR2.SGM 31JYR2

18 46442 Federal Register / Vol. 78, No. 147 / Wednesday, July 31, 2013 / Rules and Regulations Example: The purpose of this example is to demonstrate how a floating rate note can have a price without accrued interest of less than \$100 par value when the issue date occurs after the dated date. An original issue two-year floating rate note is auctioned on December 29, 2011, with a dated date of December 31, 2011, an issue date of January 3, 2012, and a maturity date of December 31, Definitions: Dated date = 12/31/2011. Issue date = 1/3/2012. Maturity date = 12/31/2013. Spread = 1.000% at auction. Discount margin = 1.000%. As of the issue date the latest 13-week bill, auctioned at least two days prior, has the following information: TABLE 1 13-WEEK BILL AUCTION DATA Auction date Issue date Maturity date Auction clearing price Auction high rate Index rate 12/27/ /29/2011 3/29/ % % The following table shows the index rates applicable for the accrued interest. Accrual starts TABLE 2 APPLICABLE INDEX RATE Accrual ends Number of days in accrual period Applicable floating rate Auction date Index rate 12/31/ /2/ /27/ % VerDate Mar<15> :04 Jul 30, 2013 Jkt PO Frm Fmt 4701 Sfmt 4700 E:\FR\FM\31JYR2.SGM 31JYR2 ER31JY13.013</GPH> ER31JY13.014</GPH>

19 Federal Register / Vol. 78, No. 147 / Wednesday, July 31, 2013 / Rules and Regulations Computing the accrued interest The accrued interest as of the new issue date (1/3/2012) for a \$100 par value is: AI = max ( ,0)/360 AI = AI = = \$ TABLE 3 PAYMENT DATES Dates Computing the Projected Cash Flows The following table presents the future interest payment dates and the number of days between them. Days between dates Dated Date: = T 1 = 12/31/ Issue Date: T 0 = 1/3/ T 0 T 1 = 3 1st Interest Date: T 1 = 3/31/ T 1 T 0 = 88 2nd Interest Date: T 2 = 6/30/ T 2 T 1 = 91 3rd Interest Date: T 3 = 9/30/ T 3 T 2 = 92 4th Interest Date: T 4 = 12/31/ T 4 T 3 = 92 5th Interest Date: T 5 = 3/31/ T 5 T 4 = 90 6th Interest Date: T 6 = 6/30/ T 6 T 5 = 91 7th Interest Date: T 7 = 9/30/ T 7 T 6 = 92 8th Interest & Maturity Dates: T 8 = 12/31/ T 8 T 7 = 92 Let a i = 100 max(r + s, 0)/360 and A i = a i (T i T i 1) {i=8} a i represents the daily projected interest, for a \$100 par value, that will accrue between the future interest payment dates T i 1 and T i, where i = 1,2,...,8. a i s are computed using the spread s = 1.000% obtained at the auction, and the fixed index rate of r = % applicable to the issue date (1/3/2012). For example: a 1 = 100 max( ,0)/ 360 = A i represents the projected cash flow the floating rate note holder will receive, less accrued interest, for a \$100 par value, at the future interest payment date T i, where i = 1,2,...,8. T i T i 1 is the number of days between the future interest payment dates T i 1 and T 1. To account for the payback of the par value, the variable 1 {i=8} takes the value 1 if the payment date is the maturity date, or 0 otherwise. For example: A 1 = = and A 8 = = Let B i = 1 + (r + m) (T i T i 1)/360 B i represents the projected compound factor between the future dates T i 1 and T i, where i = 1,2,...,8. All B i s are computed using the discount margin m = 1.000% (equals the spread obtained at the auction), and the fixed index rate of r = % applicable to the issue date (1/3/2012). For example: B 3 = 1 + ( ) 92/360 = The following table shows the projected daily accrued interests for \$100 par value (a i s), cash flows at interest payment dates (A i s), and the compound factors between payment dates (B i s). TABLE 4 PROJECTED CASH FLOWS AND COMPOUND FACTORS i a i A i B i Computing the price The price with accrued interest is computed as follows: VerDate Mar<15> :04 Jul 30, 2013 Jkt PO Frm Fmt 4701 Sfmt 4700 E:\FR\FM\31JYR2.SGM 31JYR2

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