31 CFR Part 356 — Sale and Issue of Marketable Book-Entry Treasury Bills, Notes, and Bonds (Department of the Treasury Circular, Fiscal Service Series No. 1-93)

PART 356—SALE AND ISSUE OF MARKETABLE BOOK-ENTRY TREASURY BILLS, NOTES, AND BONDS (DEPARTMENT OF THE TREASURY CIRCULAR, FISCAL SERVICE SERIES NO. 1-93) Authority: 5 U.S.C. 301; 31 U.S.C. 3102, et seq.; Source: 69 FR 45202, July 28, 2004, unless otherwise noted. Editorial Note: Nomenclature changes to part 356 appear at 70 FR 57439, Sept. 30, 2005. Subpart A—General Information § 356.0 What authority does the Treasury have to sell and issue securities? Chapter 31 of Title 31 of the United States Code authorizes the Secretary of the Treasury to issue United States obligations, and to offer them for sale with the terms and conditions that the Secretary prescribes. § 356.1 To which securities does this circular apply? The provisions in this part, including the appendices, and each individual auction announcement govern the sale and issuance of marketable Treasury securities issued on or after March 1, 1993. This part also governs all securities eligible for the STRIPS (Separate Trading of Registered Interest and Principal of Securities) Program (See § 356.31.). In addition, these provisions and the auction announcements govern any other types of securities we may issue under this part. § 356.2 What definitions do I need to know to understand this part? 13-week bill Accrued interest Adjusted value (1) Multiplying the semiannual interest rate by the par amount, and then (2) Multiplying this value by: 100 divided by the Reference CPI of the original issue date (or dated date, when the dated date is different from the original issue date). (See appendix B, section V of this part for an example of how to calculate the adjusted value.) Auction Autocharge agreement (1) Deliver awarded securities to the book-entry securities account of a designated depository institution in the commercial book-entry system, and (2) Charge a funds account of a designated depository institution for the settlement amount of the securities. Bid Bid-to-cover ratio Bidder, Bidder Identification Number Book-entry security See Business day Call Certificate of indebtedness Clearing corporation Competitive bid Consumer Price Index Corpus CUSIP number Customer Dated date Dealer Delivery and payment agreement Depository institution (1) An entity described in Section 19(b)(1)(A), excluding subparagraph (vii), of the Federal Reserve Act (12 U.S.C. 461(b)(1)(A)). (2) Any agency or branch of a foreign bank as defined by the International Banking Act of 1978, as amended (12 U.S.C. 3101). Discount Discount amount Discount margin Discount rate Funds account Index Index rate See Index ratio Inflation-adjusted principal Interest rate Intermediary Issue date Marketable security Maturity date Minimum to bid Multiple to bid Multiple-price auction Noncompetitive bid Offering amount Par Par amount Person Premium Premium amount Price Real yield Reference CPI Reopening Security Settlement Settlement amount Single-price auction Spread i.e. STRIPS Submitter TINT We Weighted-average Yield You [69 FR 45202, July 28, 2004, as amended at 70 FR 57439, Sept. 30, 2005; 73 FR 14938, Mar. 20, 2008; 76 FR 18063, Apr. 1, 2011; 78 FR 46428, July 31, 2013; 81 FR 43070, July 1, 2016; 87 FR 40439, July 7, 2022] § 356.3 What is the role of the Federal Reserve Banks in this process? The Treasury Department authorizes Federal Reserve Banks, as fiscal agents of the United States, to perform all activities necessary to carry out the provisions of this part, any auction announcements, and applicable regulations. § 356.4 What are the book-entry systems in which auctioned Treasury securities may be issued or maintained? We issue marketable Treasury securities into the commercial book-entry system and into accounts maintained directly on the records of the Department of the Treasury (“securities held directly with Treasury”). (a) The commercial book-entry system. (b) Securities held directly with Treasury. See [69 FR 45202, July 28, 2004, as amended at 70 FR 57439, Sept. 30, 2005; 72 FR 2193, Jan. 18, 2007; 71 FR 2928, Jan. 23, 2007; 73 FR 14938, Mar. 20, 2008; 76 FR 18063, Apr. 1, 2011; 87 FR 40439, July 7, 2022] § 356.5 What types of securities does the Treasury auction? We offer securities under this part exclusively in book-entry form and as direct obligations of the United States issued under Chapter 31 of Title 31 of the United States Code. When we issue additional securities with the same CUSIP number as outstanding securities, we consider them to be the same securities as the outstanding securities. (a) Treasury bills. (2) Are redeemed at their par amount at maturity; and (3) Have maturities of not more than one year. (b) Treasury notes. 1 1 (i) Are issued with a stated rate of interest to be applied to the par amount; (ii) Have interest payable semiannually; (iii) Are redeemed at their par amount at maturity; (iv) Are sold at discount, par, or premium, depending upon the auction results; and (v) Have maturities of at least one year, but of not more than ten years. (2) Treasury inflation-protected notes. (ii) Have interest payable semiannually; (iii) Are redeemed at maturity at their inflation-adjusted principal, or at their par amount, whichever is greater; (iv) Are sold at discount, par, or premium, depending on the auction results (See appendix B for price and interest payment calculations and appendix C for Investment Considerations.); and (v) Have maturities of at least one year, but not more than ten years. (vi) Are only reopened as scheduled or announced. (3) Treasury floating rate notes. (ii) Have a zero-percent minimum daily interest accrual rate; (iii) Have interest payable quarterly; (iv) Are redeemed at their par amount at maturity; (v) Are sold at discount, par, or premium depending on the auction results (See appendix B for price and interest payment calculations and appendix C for Investment Considerations.); and (vi) Have maturities of at least one year, but not more than ten years. (c) Treasury bonds. (ii) Have interest payable semiannually; (iii) Are redeemed at their par amount at maturity; (iv) Are sold at discount, par, or premium, depending on the auction results; and (v) Have maturities of more than ten years. (2) Treasury inflation-protected bonds. (ii) Have interest payable semiannually; (iii) Are redeemed at maturity at their inflation-adjusted principal, or at their par amount, whichever is greater; (iv) Are sold at discount, par, or premium, depending on the auction results; and (v) Have maturities of more than ten years. (See appendix B for price and interest payment calculations and appendix C for Investment Considerations.) (vi) Are only reopened as scheduled or announced. [69 FR 45202, July 28, 2004, as amended at 70 FR 57439, Sept. 30, 2005; 74 FR 26086, June 1, 2009; 78 FR 46428, 46429, July 31, 2013; 87 FR 40439, July 7, 2022] Subpart B—Bidding, Certifications, and Payment § 356.10 What is the purpose of an auction announcement? By issuing an auction announcement, we provide public notice of the sale of bills, notes, and bonds. The auction announcement lists the specifics of each auction, e.g., offering amount, term and type of security, CUSIP number, and issue and maturity dates. The auction announcement and this part, including the Appendices, specify the terms and conditions of sale. If anything in the auction announcement differs from this part, the auction announcement will control. If you intend to bid, you should read the applicable auction announcement along with this part. § 356.11 How are bids submitted in an auction? (a) General. See (2) We must receive competitive and noncompetitive bids prior to their respective closing times, which are stated in the auction announcement. We will not include late bids in the auction. For bids other than those submitted on paper forms, our computer time stamp will establish the receipt time. You are bound by your bids after the closing time. (3) We are not responsible for any delays, errors, or omissions. We are not responsible for any failures or disruptions of equipment or communications facilities used for participating in Treasury auctions. (4) Submitters are responsible for bids submitted using computer equipment on their premises, whether or not such bids are authorized. (b) Commercial book-entry system. (2) You must have an agreement on file with us under which you agree to our terms and conditions for access to our system for participating in our auctions. (3) In contingency situations, such as a power outage, we may accept bids by a telephone call to designated Treasury employees if you submit them prior to the relevant bidding deadline. (c) Securities held directly with Treasury. [69 FR 45202, July 28, 2004, as amended at 70 FR 57440, Sept. 30, 2005; 87 FR 40439, July 7, 2022] § 356.12 What are the different types of bids and do they have specific requirements or restrictions? (a) General. (b) Noncompetitive bids Maximum bid. (2) Additional restrictions. (i) That require delivery of the specific security being auctioned; (ii) For which the security being auctioned is one of several securities that may be delivered; or (iii) That are cash-settled. (c) Competitive bids Bid format Treasury bills. (ii) Treasury non-indexed securities. (iii) Treasury inflation-protected securities. (iv) Treasury floating rate notes. (2) Maximum recognized bid. (3) Additional restrictions. [69 FR 45202, July 28, 2004, as amended at 69 FR 53621, Sept. 2, 2004; 70 FR 57440, Sept. 30, 2005; 74 FR 26086, June 1, 2009; 78 FR 46428, 46429, July 31, 2013; 87 FR 40439, July 7, 2022] § 356.13 When must I report my net long position and how do I calculate it? (a) Net long position reporting threshold. See If . . . And if . . . Then . . . (i) the total of your bids and your net long position in the security being auctioned equals or exceeds the reporting threshold you must report your net long position (which does not include your bids). (ii) the total of your bids in the auction equals or exceeds the reporting threshold you have no position or a net short position in the security being auctioned you must report a zero. (iii) the total of your bids and your net long position in the security being auctioned is less than the reporting threshold you may either report nothing (leave the field blank) or report your net long position. (2) Also, if you have more than one bid in an auction and you must report either your net long position or a zero, you must report that figure only once. Finally, if you are a customer and must report either your net long position or a zero, you must report that figure through only one depository institution or dealer. (See § 356.14(d).) (b) “As of” time for calculating net long position. (c) Components of the net long position. (1) Your holdings of outstanding securities with the same CUSIP number as the security being auctioned; (2) Your holdings of STRIPS principal components of the security being auctioned, and; (3) Your positions, in the security being auctioned, in: (i) When-issued trading, including when-issued trading positions of the STRIPS principal components; (ii) Futures contracts that require delivery of the specific security being auctioned (but not futures contracts for which the security being auctioned is one of several securities that may be delivered, and not futures contracts that are cash-settled); and (iii) Forward contracts that require delivery of the specific security being auctioned or of the STRIPS principal component of that security. (d) Calculating the net long position in a reopening. (1) Your holdings of the outstanding securities (paragraph (c)(1) of this section) combined with (2) Your holdings of STRIPS principal components of the security being auctioned (paragraph (c)(2) of this section). We will specify the amount of holdings that you may exclude from the net long position calculation in the auction announcement. You may not take the exclusion if your combined holdings are zero or less. The exclusion is optional, but if you take the exclusion, you must include any holdings that exceed the exclusion amount in calculating your net long position. If the exclusion amount is greater than your combined holdings (paragraphs (c)(1) and (2) of this section), you may calculate the combined holdings as zero, but they cannot be included in the calculation as a negative number. § 356.14 What are the requirements for submitting bids for customers? (a) Institutions that may submit bids for customers. see (b) Payment. (c) Identifying customers. (1) The full name or title of the trustee or fiduciary; (2) A reference to the document creating the trust or fiduciary estate with date of execution; and (3) The employer identification number (not social security number) of the trust or fiduciary estate. We do not consider trusts to be a separate bidder that have not been assigned, or that do not provide, an employer identification number. (d) Competitive customer bids. (e) Noncompetitive customer bids. [69 FR 45202, July 28, 2004, as amended at 74 FR 26086, June 1, 2009; 78 FR 46429, July 31, 2013; 87 FR 40440, July 7, 2022] § 356.15 What rules apply to bids submitted by investment advisers? (a) General. (b) Bidding options. An investment adviser may bid for a controlled account . . . In such cases, we consider the bidder to be . . . (i) in the investment adviser's own name the investment adviser. (ii) in the name of the controlled account the controlled account. (2) Using the first option (paragraph (b)(1)(i)), an investment advisor could bid noncompetitively up to the noncompetitive bidding limit only for itself, as a single bidder. Using the second option (paragraph (b)(1)(ii)), an investment adviser could bid noncompetitively for each separately named controlled account up to the noncompetitive bidding limit. The investment adviser could also bid noncompetitively in its own name in the same auction up to the noncompetitive bidding limit. An investment adviser may not bid for a controlled account both noncompetitively and competitively in the same auction. If an investment adviser is bidding competitively in the name of a controlled account, the controlled account is subject to the award limitations of § 356.22(b). (c) Reporting net long positions. If an investment adviser is bidding competitively, and . . . Then . . . (1) the investment adviser has a net long position for its own account that position must be included in the investment adviser's net long position calculation. (2) the investment adviser's competitive bid is for a controlled account any net long position of that account must be included in the investment adviser's net long position calculation. (3) the investment adviser is not bidding competitively for a controlled account and . . . (i) the controlled account has a net long position of $100 million or more that position must be included in the investment adviser's net long position calculation. (ii) the controlled account has a net long position that is less than $100 million that position may be excluded from the investment adviser's net long position calculation. (iii) any net long position is excluded under paragraph (b)(3)(ii) of this table all net short positions of controlled accounts under $100 million must also be excluded. (d) Certifications. (e) Proration of awards. [69 FR 45202, July 28, 2004, as amended at 78 FR 46429, July 31, 2013] § 356.16 Do I have to make any certifications? (a) Submitters. (1) You are in compliance with this part and the auction announcement; (2) The information provided with regard to any bids for your own account is accurate and complete; and (3) The information provided with regard to any bids for customers accurately and completely reflects information provided by your customers or intermediaries. (b) Intermediaries. (1) You are in compliance with this part and the applicable auction announcement; and (2) That the information you provided to a submitter or other intermediary with regard to bids for customers accurately and completely reflects information provided by those customers or intermediaries. (c) Customers. (1) You are in compliance with this part and the auction announcement and; (2) The information you provided to the submitter or intermediary in connection with the bid is accurate and complete. [69 FR 45202, July 28, 2004, as amended at 72 FR 14938, Mar. 20, 2008] § 356.17 How and when do I pay for securities awarded in an auction? (a) General. (b) Securities held directly with Treasury. See (c) Commercial book-entry system. (1) A submitter that does not have a funds account at a Federal Reserve Bank or that chooses not to pay by charge to its own funds account must have an approved autocharge agreement on file with us before submitting any bids. Any depository institution whose funds account will be charged under an autocharge agreement will receive advance notice from us of the total par amount of, and price to be charged for, securities awarded as a result of the submitter's bids. (2) A submitter that is a member of a clearing corporation may instruct that delivery and payment be made through the clearing corporation for securities awarded to the submitter for its own account. To do this, the following requirements must be met prior to submitting any bids: (i) We must have acknowledged and have on file an autocharge agreement between the clearing corporation and a depository institution. By entering into such an agreement, the clearing corporation authorizes us to provide aggregate par and price information to the depository institution whose funds account will be charged under the agreement. The clearing corporation is responsible for remitting payment for auction awards of the clearing corporation member. (ii) We must have acknowledged and have on file a delivery and payment agreement between the submitter and the clearing corporation. By entering into such an agreement, the submitter authorizes us to provide award and payment information to the clearing corporation. [69 FR 45202, July 28, 2004, as amended at 70 FR 57440, Sept. 30, 2005; 70 FR 71401, Nov. 29, 2005; 73 FR 14938, Mar. 20, 2008; 87 FR 40440, July 7, 2022] Subpart C—Determination of Auction Awards; Settlement § 356.20 How does the Treasury determine auction awards? (a) Determining the range and amount of accepted competitive bids Accepting bids. (2) Accepting bids at the high yield, discount rate, or discount margin. (b) Determining the interest rate for new non-indexed and inflation-protected note and bond issues. 1/8 See (1) Single-price auctions. (2) Multiple-price auctions. (c) Determining the interest rate for floating rate notes. (d) Determining purchase prices for awarded securities. (1) Single-price auctions. (2) Multiple-price auctions Competitive bids. (ii) Noncompetitive bids. [69 FR 45202, July 28, 2004, as amended at 69 FR 53621, Sept. 2, 2004; 76 FR 11080, Mar. 1, 2011; 78 FR 46429, July 31, 2013; 87 FR 40440, July 7, 2022] § 356.21 How are awards at the high yield, discount rate, or discount margin calculated? (a) Awards to submitters. (b) Awards to customers. [69 FR 45202, July 28, 2004, as amended at 74 FR 26086, June 1, 2009; 78 FR 46430, July 31, 2013] § 356.22 Does the Treasury have any limitations on auction awards? (a) Awards to noncompetitive bidders. (b) Awards to competitive bidders. [69 FR 45202, July 28, 2004, as amended at 69 FR 53622, Sept. 2, 2004; 70 FR 57440, Sept. 30, 2005; 87 FR 40440, July 7, 2022] § 356.23 How are the auction results announced? (a) After the conclusion of the auction, we will make the auction results available on our website at http://www.treasurydirect.gov. (b) The auction results will include such information as: (1) The amounts of bids we accepted and the amount of securities we awarded; (2) The range of accepted yields, discount rates, or discount margins. (3) The proration percentage; (4) The interest rate for a note or bond; (5) A breakdown of the amounts of noncompetitive and competitive bids we accepted from, and awarded to, the public; (6) The amounts of bids tendered and accepted from the Federal Reserve Banks for their own accounts; (7) The bid-to-cover ratio; and (8) Other information that we may decide to include. [69 FR 45202, July 28, 2004, as amended at 74 FR 26086, June 1, 2009; 78 FR 46430, July 31, 2013; 87 FR 40440, July 7, 2022] § 356.24 Will I be notified directly of my awards and, if I am submitting bids for others, do I have to provide confirmations? (a) Notice of awards Notice to submitters. (2) Notice to clearing corporations. (b) Notification of awards to customers. (c) Notification of awards and settlement amounts to a depository institution having an autocharge agreement with a submitter or a clearing corporation. (d) Customer confirmation Customer requirements When and how must a customer confirm its awards? (ii) What must the customer include in its confirmation? (A) A confirmation of the awarded bid(s), including the name of each submitter that submitted the bid(s) on the customer's behalf, and (B) A statement indicating whether the customer had a reportable net long position as defined in § 356.13. If a position had to be reported, the statement must provide the amount of the position and the name of the submitter that the customer requested to report the position. (2) Submitter or intermediary requirements. [69 FR 45202, July 28, 2004, as amended at 71 FR 76151, Dec. 20, 2006; 74 FR 26086, June 1, 2009; 74 FR 47100, Sept. 15, 2009] § 356.25 How does the settlement process work? Securities bought in the auction must be paid for by the issue date. The payment amount for awarded securities will be the settlement amount as defined in § 356.2. (See formulas in appendix B.) There are several ways to pay for securities: (a) Payment by debit entry to a deposit account. (b) Payment by authorized charge to a funds account. (c) Payment through a certificate of indebtedness. [69 FR 45202, July 28, 2004, as amended at 70 FR 57440, Sept. 30, 2005; 73 FR 14938, Mar. 20, 2008; 87 FR 40440, July 7, 2022] Subpart D—Miscellaneous Provisions § 356.30 When does the Treasury pay principal and interest on securities? (a) General. (b) Treasury inflation-protected securities. At maturity, if . . . then . . . (i) the inflation-adjusted principal is equal to or more than the par amount of the security. we will pay the inflation-adjusted principal. (ii) the inflation-adjusted principal is less than the par amount of the security, and the security has not been stripped. we will pay an additional amount so that the additional amount plus the inflation-adjusted principal equals the par amount. (iii) the inflation-adjusted principal is less than the par amount of the security, and the security has been stripped. to holders of principal components only we will pay an additional amount so that the additional amount plus the inflation-adjusted principal equals the par amount. (2) Regardless of whether or not we pay an additional amount, we will base the final interest payment on the inflation-adjusted principal at maturity. (c) Discharge of payment obligations The commercial book-entry system. (i) That does not have an account at a Federal Reserve Bank, or (ii) With respect to any accounts not maintained at a Federal Reserve Bank. (2) Securities held directly with Treasury. [69 FR 45202, July 28, 2004, as amended at 70 FR 57441, Sept. 30, 2005; 78 FR 46430, July 31, 2013; 87 FR 40440, July 7, 2022] § 356.31 How does the STRIPS program work? (a) General. http://www.treasurydirect.gov. (b) Treasury non-indexed securities (notes and bonds other than Treasury inflation-protected securities or Treasury floating rate notes) Minimum par amounts required for STRIPS. (2) Principal components. (3) Interest components. (i) They are maintained in accounts, and transferred, at their original payment value, which is derived by multiplying the semiannual interest rate and the par amount; (ii) Their interest payment date becomes the maturity date for the component; (iii) All interest components with the same maturity date have the same CUSIP number, regardless of the underlying security from which the interest payments were stripped, and therefore are fungible (interchangeable). (iv) the CUSIP numbers of interest components are different from the CUSIP numbers of principal components and fully constituted securities, even if they have the same maturity date, and therefore are not fungible. (c) Treasury inflation-protected securities Minimum par amounts required for STRIPS. (2) Principal components. (3) Interest components Adjusted value. (ii) CUSIP numbers. (iii) Payment at maturity. (iv) Rebasing of the CPI. (d) Reconstituting a security. (e) Applicable regulations. [69 FR 45202, July 28, 2004, as amended at 73 FR 14939, Mar. 20, 2008; 74 FR 26086, June 1, 2009; 78 FR 46428, 46430, July 31, 2013; 81 FR 43070, July 1, 2016] § 356.32 What tax rules apply? (a) General. (b) Treasury inflation-protected securities. (c) Treasury floating rate notes. [69 FR 45202, July 28, 2004, as amended at 78 FR 46430, July 31, 2013] § 356.33 Does the Treasury have any discretion in the auction process? (a) We have the discretion to: (1) Accept, reject, or refuse to recognize any bids submitted in an auction; (2) Award more or less than the amount of securities specified in the auction announcement; (3) Waive any provision of this part for any bidder or submitter; and (4) Change the terms and conditions of an auction. (b) Our decisions under this part are final. We will provide a public notice if we change any auction provision, term, or condition. (c) We reserve the right to modify the terms and conditions of new securities and to depart from the customary pattern of securities offerings at any time. § 356.34 What could happen if someone does not fully comply with the auction rules or fails to pay for securities? (a) General. (b) Liquidated damages. § 356.35 Who approved the information collections? The Office of Management and Budget approved the collections of information contained in §§ 356.11, 356.12, 356.13, 356.14, and 356.15 and in appendix A of this part under control number 1535-0112. Appendix A to Part 356—Bidder Categories I. Categories of Eligible Bidders We describe below various categories of bidders eligible to bid in Treasury auctions. You may use them to determine whether we consider you and other persons or entities to be one bidder or more than one bidder for auction bidding and compliance purposes. For example, we use these definitions to apply the competitive and noncompetitive award limitations and for other requirements. Notwithstanding these definitions, we consider any persons or entities that intentionally act together with respect to bidding in a Treasury auction to collectively be one bidder. Even if an auction participant does not fall under any of the categories listed below, it is our intent that no auction participant receives a larger auction award by acquiring securities through others than it could have received had it been considered one of these types of bidders. (a) Corporation • Entity that is more than 50-percent owned, directly or indirectly, by the corporation; • Entity that is more than 50-percent owned, directly or indirectly, by any other affiliate of the corporation; • Person or entity that owns, directly or indirectly, more than 50 percent of the corporation; • Person or entity that owns, directly or indirectly, more than 50 percent of any other affiliate of the corporation; or • Entity, a majority of whose board of directors or a majority of whose general partners are directors or officers of the corporation, or of any affiliate of the corporation. An entity that is more than 50-percent owned as described in this definition is not an affiliate, however, if: • The purpose of such ownership is to seek a return on investment and not to engage in the business of the entity; • The owner does not routinely exercise operational or management control over the entity; • The owner does not exercise any control over investment decisions of the entity regarding U.S. Treasury securities; • The corporation has written policies or procedures, including ongoing compliance monitoring processes, that are designed to prevent it from acting together with the entity regarding participation in Treasury auctions or investment strategies regarding Treasury securities being auctioned; and • The corporation submits notice and certification to us, as provided in this appendix A. A corporation that plans to make use of this exception to the definition of “affiliate” must inform us of this fact in writing and provide the following certification: [Name of corporation] hereby certifies that, with regard to any entity of which it owns more than 50 percent as defined in appendix A to 31 CFR part 356, but for which the purpose of such ownership is to seek a return on investment and not to engage in the business of the entity: • We do not routinely exercise operational or management control over the entity; • We do not exercise any control over investment decisions of the entity regarding U.S. Treasury securities; • We have written policies or procedures, including ongoing compliance monitoring processes, that are designed to prevent the corporation from acting together with the entity regarding participation in Treasury auctions or investment strategies regarding Treasury securities being auctioned; and • We will continue to meet the terms of this certification until we notify the Treasury of a change. (b) Partnership An affiliate is any: • Entity that is more than 50-percent owned, directly or indirectly, by the partnership; • Entity that is more than 50-percent owned, directly or indirectly, by any other affiliate of the partnership; • Person or entity that owns, directly or indirectly, more than 50 percent of the partnership; • Person or entity that owns, directly or indirectly, more than 50 percent of any other affiliate of the partnership; or • Entity, a majority of whose general partners or a majority of whose board of directors are general partners or directors of the partnership or of any affiliate of the partnership. An entity that is more than 50-percent owned as described in this definition is not an affiliate, however, if: • The purpose of such ownership is to seek a return on investment and not to engage in the business of the entity; • The owner does not routinely exercise operational or management control over the entity; • The owner does not exercise any control over investment decisions of the entity regarding U.S. Treasury securities; • The partnership has written policies or procedures, including ongoing compliance monitoring processes, that are designed to prevent it from acting together with the entity regarding participation in Treasury auctions or investment strategies regarding Treasury securities being auctioned; and • The partnership submits notice and certification to us, as provided in this appendix A. A partnership that plans to make use of this exception to the definition of “affiliate” must inform us of this fact in writing and provide the following certification: [Name of partnership] hereby certifies that, with regard to any entity of which it owns more than 50 percent as defined in appendix A to 31 CFR part 356, but for which the purpose of such ownership is to seek a return on investment and not to engage in the business of the entity: • We do not routinely exercise operational or management control over the entity; • We do not exercise any control over investment decisions of the entity regarding U.S. Treasury securities; • We have written policies or procedures, including ongoing compliance monitoring processes, that are designed to prevent the partnership from acting together with the entity regarding participation in Treasury auctions or investment strategies regarding Treasury securities being auctioned; and • We will continue to meet the terms of this certification until we notify the Treasury of a change. (c) Government-related entity (1) A state government or the government of the District of Columbia (2) A unit of local government, including any county, city, municipality, or township, or other unit of general government as defined by the Bureau of the Census for statistical purposes. (3) A commonwealth, territory, or possession of the United States. (4) A governmental entity, body, or corporation established under Federal, State, or local law. (5) A foreign central bank, the government of a foreign state, or an international organization in which the United States holds membership. This type of entity applies only when such entity is not using an account at the Federal Reserve Bank of New York (See paragraph (f).). We generally consider an investment, reserve, or other fund of one of the above government-related entities as part of that entity and not a separate bidder. We will consider a government-related entity's fund to be a separate bidder if it meets the definition of the “trust or other fiduciary estate” category, or if applicable law requires that the investments of such fund be made separately. (d) Trust or other fiduciary estate • The legal entity must be able to be identified by: 1. The name or title of the trustee or fiduciary; 2. Specific reference to the trust instrument, court order, or legal authority under which the trustee or fiduciary is acting; and 3. The unique IRS-assigned employer identification number (not social security number) for the entity. • The trustee or fiduciary must make the decisions on participating in auctions on behalf of the trust or fiduciary estate. (e) Individual (f) Foreign and International Monetary Authority (“FIMA”) (1) A foreign central bank or regional central bank. (2) A foreign governmental monetary or finance entity. (3) A non-governmental international financial organization that is not private in nature (for example, the International Monetary Fund, the World Bank, the Inter-American Development Bank, and the Asian Development Bank). (4) A non-financial international organization that the United States participates in (for example, the United Nations). (5) A multi-party arrangement of a governmental ministry and/or a foreign central bank or monetary authority with a United States Government Department and/or the Federal Reserve Bank of New York. (6) A foreign or international monetary entity or an entity authorized by statute or by us to open accounts at the Federal Reserve Bank of New York. (g) Other Bidder II. How To Obtain Separate Bidder Recognition Under certain circumstances, we may recognize a major organizational component (e.g., the parent or a subsidiary) in a corporate or partnership structure as a bidder separate from the larger corporate or partnership structure. We also may recognize two or more major organizational components collectively as one bidder. All of the following criteria must be met for such component(s) to qualify for recognition as a separate bidder: (a) Such component(s) must be prohibited by law or regulation from exchanging, or must have established written internal procedures designed to prevent the exchange of, information related to bidding in Treasury auctions with any other component in the corporate or partnership structure; (b) Such component(s) must not be created for the purpose of circumventing our bidding and award limitations; (c) Decisions related to purchasing Treasury securities at auction and participation in specific auctions must be made by employees of such component(s). Employees of such component(s) that make decisions to purchase or dispose of Treasury securities must not perform the same function for other components within the corporate or partnership structure; and (d) The records of such component(s) related to the bidding for, acquisition of, and disposition of Treasury securities must be maintained by such component(s). Those records must be identifiable—separate and apart from similar records for other components within the corporate or partnership structure. To obtain recognition as a separate bidder, each component or group of components must request such recognition from us, provide a description of the component or group and its position within the corporate or partnership structure, and provide the following certification: [Name of the bidder] hereby certifies that to the best of its knowledge and belief it meets the criteria for a separate bidder as described in appendix A to 31 CFR part 356. The above-named bidder also certifies that it has established written policies or procedures, including ongoing compliance monitoring processes, that are designed to prevent the component or group of components from: (1) Exchanging any of the following information with any other part of the corporate [partnership] structure: (a) Yields, discount rates, or discount margins at which it plans to bid; (b) amounts of securities for which it plans to bid; (c) positions that it holds or plans to acquire in a security being auctioned; and (d) investment strategies that it plans to follow regarding the security being auctioned, or (2) In any way intentionally acting together with any other part of the corporate [partnership] structure with respect to formulating or entering bids in a Treasury auction. The above-named bidder agrees that it will promptly notify the Department in writing when any of the information provided to obtain separate bidder status changes or when this certification is no longer valid. [69 FR 45202, July 28, 2004, as amended at 70 FR 29456, May 23, 2005; 78 FR 46430, July 31, 2013] Appendix B to Part 356—Formulas and Tables I. Computation of Interest on Treasury Bonds and Notes. II. Formulas for Conversion of Non-indexed Security Yields to Equivalent Prices. III. Formulas for Conversion of Inflation-Protected Security Yields to Equivalent Prices. IV. Formulas for Conversion of Floating Rate Note Discount Margins to Equivalent Prices V. Computation of Adjusted Values and Payment Amounts for Stripped Inflation-Protected Interest Components. VI. Computation of Purchase Price, Discount Rate, and Investment Rate (Coupon-Equivalent Yield) for Treasury Bills. The examples in this appendix are given for illustrative purposes only and are in no way a prediction of interest rates on any bills, notes, or bonds issued under this part. In some of the following examples, we use intermediate rounding for ease in following the calculations. I. Computation of Interest on Treasury Bonds and Notes A. Treasury Non-indexed Securities 1. Regular Half-Year Payment Period. 2. Daily Interest Decimal. Table 1 Interest period Beginning and ending days are 1st or 15th of the months listed under interest period Beginning and ending days are the last days of the months listed under interest period Regular year Leap year Regular year Leap year January to July 181 182 181 182 February to August 181 182 184 184 March to September 184 184 183 183 April to October 183 183 184 184 May to November 184 184 183 183 June to December 183 183 184 184 July to January 184 184 184 184 August to February 184 184 181 182 September to March 181 182 182 183 October to April 182 183 181 182 November to May 181 182 182 183 December to June 182 183 181 182 Table 2 below shows the daily interest decimals covering interest from 1/8 1/8 1/181 1/182 1/183 1/184 Table 2 [Decimal for one day's interest on $1,000 at various rates of interest, payable semiannually or on a semiannual basis, in regular years of 365 days and in years of 366 days (to determine applicable number of days, see table 1.)] Rate per annum (percent) Half-year of 184 days Half-year of 183 days Half-year of 182 days Half-year of 181 days 1 8 0.003396739 0.003415301 0.003434066 0.003453039 1 4 0.006793478 0.006830601 0.006868132 0.006906077 3 8 0.010190217 0.010245902 0.010302198 0.010359116 1 2 0.013586957 0.013661202 0.013736264 0.013812155 5 8 0.016983696 0.017076503 0.017170330 0.017265193 3 4 0.020380435 0.020491803 0.020604396 0.020718232 7 8 0.023777174 0.023907104 0.024038462 0.024171271 1 0.027173913 0.027322404 0.027472527 0.027624309 1 1 8 0.030570652 0.030737705 0.030906593 0.031077348 1 1 4 0.033967391 0.034153005 0.034340659 0.034530387 1 3 8 0.037364130 0.037568306 0.037774725 0.037983425 1 1 2 0.040760870 0.040983607 0.041208791 0.041436464 1 5 8 0.044157609 0.044398907 0.044642857 0.044889503 1 3 4 0.047554348 0.047814208 0.048076923 0.048342541 1 7 8 0.050951087 0.051229508 0.051510989 0.051795580 2 0.054347826 0.054644809 0.054945055 0.055248619 2 1 8 0.057744565 0.058060109 0.058379121 0.058701657 2 1 4 0.061141304 0.061475410 0.061813187 0.062154696 2 3 8 0.064538043 0.064890710 0.065247253 0.065607735 2 1 2 0.067934783 0.068306011 0.068681319 0.069060773 2 5 8 0.071331522 0.071721311 0.072115385 0.072513812 2 3 4 0.074728261 0.075136612 0.075549451 0.075966851 2 7 8 0.078125000 0.078551913 0.078983516 0.079419890 3 0.081521739 0.081967213 0.082417582 0.082872928 3 1 8 0.084918478 0.085382514 0.085851648 0.086325967 3 1 4 0.088315217 0.088797814 0.089285714 0.089779006 3 3 8 0.091711957 0.092213115 0.092719780 0.093232044 3 1 2 0.095108696 0.095628415 0.096153846 0.096685083 3 5 8 0.098505435 0.099043716 0.099587912 0.100138122 3 3 4 0.101902174 0.102459016 0.103021978 0.103591160 3 7 8 0.105298913 0.105874317 0.106456044 0.107044199 4 0.108695652 0.109289617 0.109890110 0.110497238 4 1 8 0.112092391 0.112704918 0.113324176 0.113950276 4 1 4 0.115489130 0.116120219 0.116758242 0.117403315 4 3 8 0.118885870 0.119535519 0.120192308 0.120856354 4 1 2 0.122282609 0.122950820 0.123626374 0.124309392 4 5 8 0.125679348 0.126366120 0.127060440 0.127762431 4 3 4 0.129076087 0.129781421 0.130494505 0.131215470 4 7 8 0.132472826 0.133196721 0.133928571 0.134668508 5 0.135869565 0.136612022 0.137362637 0.138121547 5 1 8 0.139266304 0.140027322 0.140796703 0.141574586 5 1 4 0.142663043 0.143442623 0.144230769 0.145027624 5 3 8 0.146059783 0.146857923 0.147664835 0.148480663 5 1 2 0.149456522 0.150273224 0.151098901 0.151933702 5 5 8 0.152853261 0.153688525 0.154532967 0.155386740 5 3 4 0.156250000 0.157103825 0.157967033 0.158839779 5 7 8 0.159646739 0.160519126 0.161401099 0.162292818 6 0.163043478 0.163934426 0.164835165 0.165745856 6 1 8 0.166440217 0.167349727 0.168269231 0.169198895 6 1 4 0.169836957 0.170765027 0.171703297 0.172651934 6 3 8 0.173233696 0.174180328 0.175137363 0.176104972 6 1 2 0.176630435 0.177595628 0.178571429 0.179558011 6 5 8 0.180027174 0.181010929 0.182005495 0.183011050 6 3 4 0.183423913 0.184426230 0.185439560 0.186464088 6 7 8 0.186820652 0.187841530 0.188873626 0.189917127 7 0.190217391 0.191256831 0.192307692 0.193370166 7 1 8 0.193614130 0.194672131 0.195741758 0.196823204 7 1 4 0.197010870 0.198087432 0.199175824 0.200276243 7 3 8 0.200407609 0.201502732 0.202609890 0.203729282 7 1 2 0.203804348 0.204918033 0.206043956 0.207182320 7 5 8 0.207201087 0.208333333 0.209478022 0.210635359 7 3 4 0.210597826 0.211748634 0.212912088 0.214088398 7 7 8 0.213994565 0.215163934 0.216346154 0.217541436 8 0.217391304 0.218579235 0.219780220 0.220994475 8 1 8 0.220788043 0.221994536 0.223214286 0.224447514 8 1 4 0.224184783 0.225409836 0.226648352 0.227900552 8 3 8 0.227581522 0.228825137 0.230082418 0.231353591 8 1 2 0.230978261 0.232240437 0.233516484 0.234806630 8 5 8 0.234375000 0.235655738 0.236950549 0.238259669 8 3 4 0.237771739 0.239071038 0.240384615 0.241712707 8 7 8 0.241168478 0.242486339 0.243818681 0.245165746 9 0.244565217 0.245901639 0.247252747 0.248618785 9 1 8 0.247961957 0.249316940 0.250686813 0.252071823 9 1 4 0.251358696 0.252732240 0.254120879 0.255524862 9 3 8 0.254755435 0.256147541 0.257554945 0.258977901 9 1 2 0.258152174 0.259562842 0.260989011 0.262430939 9 5 8 0.261548913 0.262978142 0.264423077 0.265883978 9 3 4 0.264945652 0.266393443 0.267857143 0.269337017 9 7 8 0.268342391 0.269808743 0.271291209 0.272790055 10 0.271739130 0.273224044 0.274725275 0.276243094 10 1 8 0.275135870 0.276639344 0.278159341 0.279696133 10 1 4 0.278532609 0.280054645 0.281593407 0.283149171 10 3 8 0.281929348 0.283469945 0.285027473 0.286602210 10 1 2 0.285326087 0.286885246 0.288461538 0.290055249 10 5 8 0.288722826 0.290300546 0.291895604 0.293508287 10 3 4 0.292119565 0.293715847 0.295329670 0.296961326 10 7 8 0.295516304 0.297131148 0.298763736 0.300414365 11 0.298913043 0.300546448 0.302197802 0.303867403 11 1 8 0.302309783 0.303961749 0.305631868 0.307320442 11 1 4 0.305706522 0.307377049 0.309065934 0.310773481 11 3 8 0.309103261 0.310792350 0.312500000 0.314226519 11 1 2 0.312500000 0.314207650 0.315934066 0.317679558 11 5 8 0.315896739 0.317622951 0.319368132 0.321132597 11 3 4 0.319293478 0.321038251 0.322802198 0.324585635 11 7 8 0.322690217 0.324453552 0.326236264 0.328038674 12 0.326086957 0.327868852 0.329670330 0.331491713 12 1 8 0.329483696 0.331284153 0.333104396 0.334944751 12 1 4 0.332880435 0.334699454 0.336538462 0.338397790 12 3 8 0.336277174 0.338114754 0.339972527 0.341850829 12 1 2 0.339673913 0.341530055 0.343406593 0.345303867 12 5 8 0.343070652 0.344945355 0.346840659 0.348756906 12 3 4 0.346467391 0.348360656 0.350274725 0.352209945 12 7 8 0.349864130 0.351775956 0.353708791 0.355662983 13 0.353260870 0.355191257 0.357142857 0.359116022 13 1 8 0.356657609 0.358606557 0.360576923 0.362569061 13 1 4 0.360054348 0.362021858 0.364010989 0.366022099 13 3 8 0.363451087 0.365437158 0.367445055 0.369475138 13 1 2 0.366847826 0.368852459 0.370879121 0.372928177 13 5 8 0.370244565 0.372267760 0.374313187 0.376381215 13 3 4 0.373641304 0.375683060 0.377747253 0.379834254 13 7 8 0.377038043 0.379098361 0.381181319 0.383287293 14 0.380434783 0.382513661 0.384615385 0.386740331 14 1 8 0.383831522 0.385928962 0.388049451 0.390193370 14 1 4 0.387228261 0.389344262 0.391483516 0.393646409 14 3 8 0.390625000 0.392759563 0.394917582 0.397099448 14 1 2 0.394021739 0.396174863 0.398351648 0.400552486 14 5 8 0.397418478 0.399590164 0.401785714 0.404005525 14 3 4 0.400815217 0.403005464 0.405219780 0.407458564 14 7 8 0.404211957 0.406420765 0.408653846 0.410911602 15 0.407608696 0.409836066 0.412087912 0.414364641 15 1 8 0.411005435 0.413251366 0.415521978 0.417817680 15 1 4 0.414402174 0.416666667 0.418956044 0.421270718 15 3 8 0.417798913 0.420081967 0.422390110 0.424723757 15 1 2 0.421195652 0.423497268 0.425824176 0.428176796 15 5 8 0.424592391 0.426912568 0.429258242 0.431629834 15 3 4 0.427989130 0.430327869 0.432692308 0.435082873 15 7 8 0.431385870 0.433743169 0.436126374 0.438535912 16 0.434782609 0.437158470 0.439560440 0.441988950 16 1 8 0.438179348 0.440573770 0.442994505 0.445441989 16 1 4 0.441576087 0.443989071 0.446428571 0.448895028 16 3 8 0.444972826 0.447404372 0.449862637 0.452348066 16 1 2 0.448369565 0.450819672 0.453296703 0.455801105 16 5 8 0.451766304 0.454234973 0.456730769 0.459254144 16 3 4 0.455163043 0.457650273 0.460164835 0.462707182 16 7 8 0.458559783 0.461065574 0.463598901 0.466160221 17 0.461956522 0.464480874 0.467032967 0.469613260 17 1 8 0.465353261 0.467896175 0.470467033 0.473066298 17 1 4 0.468750000 0.471311475 0.473901099 0.476519337 17 3 8 0.472146739 0.474726776 0.477335165 0.479972376 17 1 2 0.475543478 0.478142077 0.480769231 0.483425414 17 5 8 0.478940217 0.481557377 0.484203297 0.486878453 17 3 4 0.482336957 0.484972678 0.487637363 0.490331492 17 7 8 0.485733696 0.488387978 0.491071429 0.493784530 18 0.489130435 0.491803279 0.494505495 0.497237569 18 1 8 0.492527174 0.495218579 0.497939560 0.500690608 18 1 4 0.495923913 0.498633880 0.501373626 0.504143646 18 3 8 0.499320652 0.502049180 0.504807692 0.507596685 18 1 2 0.502717391 0.505464481 0.508241758 0.511049724 18 5 8 0.506114130 0.508879781 0.511675824 0.514502762 18 3 4 0.509510870 0.512295082 0.515109890 0.517955801 18 7 8 0.512907609 0.515710383 0.518543956 0.521408840 19 0.516304348 0.519125683 0.521978022 0.524861878 19 1 8 0.519701087 0.522540984 0.525412088 0.528314917 19 1 4 0.523097826 0.525956284 0.528846154 0.531767956 19 3 8 0.526494565 0.529371585 0.532280220 0.535220994 19 1 2 0.529891304 0.532786885 0.535714286 0.538674033 19 5 8 0.533288043 0.536202186 0.539148352 0.542127072 19 3 4 0.536684783 0.539617486 0.542582418 0.545580110 19 7 8 0.540081522 0.543032787 0.546016484 0.549033149 20 0.543478261 0.546448087 0.549450549 0.552486188 3. Short First Payment Period. Example A 2-year note paying 8 3/8 3/8 4. Long First Payment Period. Example A 5-year 2-month note paying 7 7/8 7/8 B. Treasury Inflation-Protected Securities 1. Indexing Process. 2. Index Ratio. Date Where Date = valuation date 3. Reference CPI. Therefore the Ref CPI and the Index Ratio for a particular date will be expressed to five decimal places. (i) The formula for the Ref CPI for a specific date is: Where Date = valuation date D = the number of days in the month in which Date falls t = the calendar day corresponding to Date CPI M Ref CPI M April1 January Ref CPI M + 1 (ii) For example, the Ref CPI for April 15, 1996 is calculated as follows: where D = 30, t = 15 Ref CPI April 1, 1996 Ref CPI May 1, 1996 (iii) Putting these values in the equation in paragraph (ii) above: This value truncated to six decimals is 154.633333; rounded to five decimals it is 154.63333. (iv) To calculate the Index Ratio for April 16, 1996, for an inflation-protected security issued on April 15, 1996, the Ref CPI April 16, 1996 April 16, 1996 The Index Ratio for April 16, 1996 is: Index Ratio April 16, 1996 This value truncated to six decimals is 1.000107; rounded to five decimals it is 1.00011. 4. Index Contingencies. (i) If a previously reported CPI is revised, we will continue to use the previously reported (unrevised) CPI in calculating the principal value and interest payments. If the CPI is rebased to a different year, we will continue to use the CPI based on the base reference period in effect when the security was first issued, as long as that CPI continues to be published. (ii) We will replace the CPI with an appropriate alternative index if, while an inflation-protected security is outstanding, the applicable CPI is: • Discontinued, • In the judgment of the Secretary, fundamentally altered in a manner materially adverse to the interests of an investor in the security, or • In the judgment of the Secretary, altered by legislation or Executive Order in a manner materially adverse to the interests of an investor in the security. (iii) If we decide to substitute an alternative index we will consult with the Bureau of Labor Statistics or any successor agency. We will then notify the public of the substitute index and how we will apply it. Determinations of the Secretary in this regard will be final. (iv) If the CPI for a particular month is not reported by the last day of the following month, we will announce an index number based on the last available twelve-month change in the CPI. We will base our calculations of our payment obligations that rely on that month's CPI on the index number we announce. (a) For example, if the CPI for month M is not reported timely, the formula for calculating the index number to be used is: (b) Generalizing for the last reported CPI issued N months prior to month M: (c) If it is necessary to use these formulas to calculate an index number, we will use that number for all subsequent calculations that rely on the month's index number. We will not replace it with the actual CPI when it is reported, except for use in the above formulas. If it becomes necessary to use the above formulas to derive an index number, we will use the last CPI that has been reported to calculate CPI numbers for months for which the CPI has not been reported timely. 5. Computation of Interest for a Regular Half-Year Payment Period. Specifically, we compute a semiannual interest payment on the basis of one-half of one year's interest regardless of the actual number of days in the half-year. Example A 10-year inflation-protected note paying 3 7/8% IssueDate Date C. Treasury Floating Rate Notes 1. Indexing and Interest Payment Process. 2. Interest Rate. 3. Interest Accrual. 4. Index Contingencies. (i) If Treasury were to discontinue auctions of 13-week bills, the Secretary has authority to determine and announce a new index for outstanding floating rate notes. (ii) If Treasury were to not conduct a 13-week bill auction in a particular week, then the interest rate in effect for the notes at the time of the last 13-week bill auction results announcement will remain in effect until such time, if any, as the results of a 13-week Treasury auction are again announced by Treasury. Treasury reserves the right to change the index rate for any newly issued floating rate note. D. Accrued Interest 1. You will have to pay accrued interest on a Treasury bond or note when interest accrues prior to the issue date of the security. Because you receive a full interest payment despite having held the security for only a portion of the interest payment period, you must compensate us through the payment of accrued interest at settlement. 2. For a Treasury non-indexed security, if accrued interest covers a fractional portion of a full half-year period, the number of days in the full half-year period and the stated interest rate will determine the daily interest decimal to use in computing the accrued interest. We multiply the decimal by the number of days for which interest has accrued. 3. If a reopened bond or note has a long first interest payment period (a “long coupon”), and the dated date for the reopened issue is less than six full months before the first interest payment, the accrued interest will fall into two separate half-year periods. A separate daily interest decimal must be multiplied by the respective number of days in each half-year period during which interest has accrued. 4. We round all accrued interest computations to five decimal places for a $1,000 par amount, using normal rounding procedures. We calculate accrued interest for a par amount of securities greater than $1,000 by applying the appropriate multiple to accrued interest payable for a $1,000 par amount, rounded to five decimal places. We calculate accrued interest for a par amount of securities less than $1,000 by applying the appropriate fraction to accrued interest payable for a $1,000 par amount, rounded to five decimal places. 5. For an inflation-protected security, we calculate accrued interest as shown in section III, paragraphs A and B of this appendix. Examples: (1) Treasury Non-indexed Securities—(i) Involving One Half-Year: 3/4% (2) Involving Two Half-Years: A 10 3/4% 6. For a floating rate note, if accrued interest covers a portion of a full quarterly interest payment period, we calculate accrued interest as shown in section IV, paragraphs C and D of this appendix. II. Formulas for Conversion of Non-indexed Security Yields to Equivalent Prices Definitions P = price per 100 (dollars), rounded to six places, using normal rounding procedures. C = the regular annual interest per $100, payable semiannually, e.g., 6.125 (the decimal equivalent of a 6 1/8 i = nominal annual rate of return or yield to maturity, based on semiannual interest payments and expressed in decimals, e.g., .0719. n = number of full semiannual periods from the issue date to maturity, except that, if the issue date is a coupon frequency date, n will be one less than the number of full semiannual periods remaining to maturity. Coupon frequency dates are the two semiannual dates based on the maturity date of each note or bond issue. For example, a security maturing on November 15, 2015, would have coupon frequency dates of May 15 and November 15. r = (1) number of days from the issue date to the first interest payment (regular or short first payment period), or (2) number of days in fractional portion (or “initial short period”) of long first payment period. s = (1) number of days in the full semiannual period ending on the first interest payment date (regular or short first payment period), or (2) number of days in the full semiannual period in which the fractional portion of a long first payment period falls, ending at the onset of the regular portion of the first interest payment. v n n a n n 2 3 n Special Case: n n n n i.e. 2 3 n n A = accrued interest. A. For non-indexed securities with a regular first interest payment period: Formula: P[1 + (r/s)(i/2)] = (C/2)(r/s) + (C/2)a n n Example: For an 8 3/4 Definitions:G12752 C = 8.75. i = .0884. r = 184 (May 15 to November 15, 1990). s = 184 (May 15 to November 15, 1990). n = 59 (There are 60 full semiannual periods, but n is reduced by 1 because the issue date is a coupon frequency date.) v n 59 a n Resolution: P[1 + (r/s)(i/2)] = (C/2)(r/s) + (C/2)a n n P[1 + (184/184)(.0884/2)] = (8.75/2)(184/184) + (8.75/2)(20.8610780353) + 100(.0779403508). (1) P[1 + .0442] = 4.375 + 91.2672164044 + 7.7940350840. (2) P[1.0442] = 103.4362514884. (3) P = 103.4362514884 / 1.0442. (4) P = 99.057893. B. For non-indexed securities with a short first interest payment period: Formula: P[1 + (r/s)(i/2)] = (C/2)(r/s) + (C/2)a n n Example: For an 8 1/2 Definitions: C = 8.50. i = .0859. n = 3. r = 181 (April 2 to September 30, 1990). s = 183 (March 31 to September 30, 1990). v n 3 a n Resolution: P[1 + (r/s)(i/2)] = (C/2)(r/s) + (C/2)a n n P[1 + (181/183)(.0859/2)] = (8.50/2)(181/183) + (8.50/2)(2.7596261590) + 100(.8814740565). (1) P[1 + .042480601] = 4.2035519126 + 11.7284111757 + 88.14740565. (2) P[1.042480601] = 104.0793687354. (3) P = 104.0793687354 / 1.042480601. (4) P = 99.838183. C. For non-indexed securities with a long first interest payment period: Formula: P[1 + (r/s)(i/2)] = [(C/2)(r/s)]v + (C/2)a n n Example: For an 8 1/2 Definitions: C = 8.50. i = .0853. n = 10. r = 75 (March 1 to May 15, 1990, which is the fractional portion of the first interest payment). s = 181 (November 15, 1989, to May 15, 1990). v = 1 / (1 + .0853/2), or .9590946147. v n 10 a n Resolution: P[1 + (r/s)(i/2)] = [(C/2)(r/s)]v + (C/2)a n n P[1 + (75/181)(.0853/2)] = [(8.50/2)(75/181)].9590946147 + (8.50/2)(8.0049454082) + 100(.6585890783). (1) P[1 + .017672652] = 1.6890133062 + 34.0210179850 + 65.8589078339. (2) P[1.017672652] = 101.5689391251. (3) P = 101.5689391251 / 1.017672652. (4) P = 99.805118. D. (1) For non-indexed securities reopened during a regular interest period where the purchase price includes predetermined accrued interest. (2) For new non-indexed securities accruing interest from the coupon frequency date immediately preceding the issue date, with the interest rate established in the auction being used to determine the accrued interest payable on the issue date. Formula: (P + A)[1 + (r/s)(i/2)] = C/2 + (C/2)a n n Where: A = [(s−r)/s](C/2). Example: For a 9 1/2 Definitions: C = 9.50. i = .0954. n = 19. r = 167 (November 29, 1985, to May 15, 1986). s = 181 (November 15, 1985, to May 15, 1986). v n 19 a n A = [(181 − 167) / 181](9.50/2), or .367403. Resolution: (P + A)[1 + (r/s)(i/2)] = C/2 + (C/2)a n n (P + .367403)[1 + (167/181)(.0954/2)] = (9.50/2) + (9.50/2)(12.3150859630) + 100(.4125703996). (1) (P + .367403)[1 + .044010497] = 4.75 + 58.4966583243 + 41.25703996. (2) (P + .367403)[1.044010497] = 104.5036982843. (3) (P + .367403) = 104.5036982843 / 1.044010497. (4) (P + .367403) = 100.098321. (5) P = 100.098321 −.367403. (6) P = 99.730918. E. For non-indexed securities reopened during the regular portion of a long first payment period: Formula: (P + A)[1 + (r/s)(i/2)] = (r′s″)(C/2) + C 2 + (C/2)a n n Where: A = AI′ + AI, AI′ = (r′/s″)(C/2), AI = [(s−r) / s](C/2), and r = number of days from the reopening date to the first interest payment date, s = number of days in the semiannual period for the regular portion of the first interest payment period, r′ = number of days in the fractional portion (or “initial short period”) of the first interest payment period, s″ = number of days in the semiannual period ending with the commencement date of the regular portion of the first interest payment period. Example: A 10 3/4 Definitions: C = 10.75. i = .1047. n = 39. r = 103 (November 4, 1985, to February 15, 1986). s = 184 (August 15, 1985, to February 15, 1986). r′ = 44 (July 2 to August 15, 1985). s″ = 181 (February 15 to August 15, 1985). v n 39 a n AI′ = (44 / 181)(10.75 / 2), or 1.306630. AI = [(184 − 103) / 184](10.75 / 2), or 2.366168. A = AI′ + AI, or 3.672798. Resolution: (P + A)[1 + (r/s)(i/2)] = (r′/s″)(C/2) + C/2 + (C/2)a n n (P + 3.672798)[1 + (103/184)(.1047/2)] = (44/181)(10.75/2) + 10.75/2 + (10.75/2)(16.4910258142) + 100(.1366947986). (1) (P + 3.672798)[1 + .02930462] = 1.3066298343 + 5.375 + 88.6392637512 + 13.6694798628. (2) (P + 3.672798)[1.02930462] = 108.9903734482. (3) (P + 3.672798) = 108.9903734482 / 1.02930462. (4) (P + 3.672798) = 105.887384. (5) P = 105.887384 −3.672798. (6) P = 102.214586. F. For non-indexed securities reopened during a short first payment period: Formula: (P + A)[1 + (r/s)(i/2)] = (r′/s)(C/2) + (C/2)a n n Where: A = [(r′ − r)/s](C/2) and r′ = number of days from the original issue date to the first interest payment date. Example: For a 10 1/2 Definitions: C = 10.50. i = .1053. n = 15. r = 92 (August 15, 1983, to November 15, 1983). s = 184 (May 15, 1983, to November 15, 1983). r′ = 183 (May 16, 1983, to November 15, 1983). v n 15 a n A = [(183 − 92) / 184](10.50 / 2), or 2.596467. Resolution: (P + A)[1 + (r/s)(i/2)] = (r′/s)(C/2) + (C/2)a n n (P + 2.596467)[1 + (92/184)(.1053/2)] = (183/184)(10.50/2) + (10.50/2)(10.1962082956) + 100(.4631696332). (1) (P + 2.596467)[1 + .026325] = 5.2214673913 + 53.5300935520 + 46.31696332. (2) (P + 2.596467)[1.026325] = 105.0685242633. (3) (P + 2.596467) = 105.0685242633 / 1.026325. (4) (P + 2.596467) = 102.373541. (5) P = 102.373541 − 2.596467. (6) P = 99.777074. G. For non-indexed securities reopened during the fractional portion (initial short period) of a long first payment period: Formula: (P + A)[1 + (r/s)(i/2)] = [(r′/s)(C/2)]v + (C/2)a n n Where: A = [(r′ − r)/s](C/2), and r = number of days from the reopening date to the end of the short period. r′ = number of days in the short period. s = number of days in the semiannual period ending with the end of the short period. Example: For a 9 3/4 Definitions: C = 9.75. i = .0979. n = 12. r = 30 (November 15, 1988, to December 15, 1988). s = 183 (June 15, 1988, to December 15, 1988). r′ = 61 (October 15, 1988, to December 15, 1988). v = 1 / (1 + .0979/2), or .9533342867. v n 12 a n A = [(61 − 30)/183](9.75/2), or .825820. Resolution: (P + A)[1 + (r/s)(i/2)] = [(r′/s)(C/2)]v + (C/2)a n n (P + .825820)[1 + (30/183)(.0979/2)] = [(61/183)(9.75/2)](.9533342867) + (9.75/2)(8.9159733613) + 100(.5635631040). (1) (P + .825820)[1 + .00802459] = 1.549168216 + 43.4653701362 + 56.35631040. (2) (P + .825820)[1.00802459] = 101.3708487520. (3) (P + .825820) = 101.3708487520 / 1.00802459. (4) (P + .825820) = 100.563865. (5) P = 100.563865 −. 825820. (6) P = 99.738045. III. Formulas for Conversion of Inflation-Indexed Security Yields to Equivalent Prices Definitions P = unadjusted or real price per 100 (dollars). P adj Date A = unadjusted accrued interest per $100 original principal. A adj Date SA = settlement amount including accrued interest in current dollars per $100 original principal; P adj adj r = days from settlement date to next coupon date. s = days in current semiannual period. i = real yield, expressed in decimals (e.g., 0.0325). C = real annual coupon, payable semiannually, in terms of real dollars paid on $100 initial, or real, principal of the security. n = number of full semiannual periods from issue date to maturity date, except that, if the issue date is a coupon frequency date, n will be one less than the number of full semiannual periods remaining until maturity. Coupon frequency dates are the two semiannual dates based on the maturity date of each note or bond issue. For example, a security maturing on July 15, 2026 would have coupon frequency dates of January 15 and July 15. v n n a n n 2 3 ... n Special Case: If i = 0, then a n n n n i.e. 2 3 ... n n Date = valuation date. D = the number of days in the month in which Date falls. t = calendar day corresponding to Date. CPI = Consumer Price Index number. CPI M Ref CPI M April 1 January Ref CPI M + 1 Ref CPI Date M M + 1 M Index Ratio Date Date IssueDate Note: When the Issue Date is different from the Dated Date, the denominator is the Ref CPI DatedDate A. For inflation-protected securities with a regular first interest payment period: Formulas: P adj Date A = [(s−r)/s] × (C/2). A adj Date SA = P adj adj Index Ratio Date Date IssueDate Example: We issued a 10-year inflation-protected note on January 15, 1999. The note was issued at a discount to yield of 3.898% (real). The note bears a 3 7/8 Definitions: C = 3.875. i = 0.03898. n = 19 (There are 20 full semiannual periods but n is reduced by 1 because the issue date is a coupon frequency date.). r = 181 (January 15, 1999 to July 15, 1999). s = 181 (January 15, 1999 to July 15, 1999). Ref CPI Date Ref CPI IssueDate Resolution: Index Ratio Date Date IssueDate A = [(181 − 181)/181] × 3.875/2 = 0. A adj v n n 19 a n n Formula: P = 99.811030. P adj Date P adj SA = P adj adj SA = 99.811030 + 0 = 99.811030. Note: For the real price (P), we have rounded to six places. These amounts are based on 100 par value. B. (1) For inflation-protected securities reopened during a regular interest period where the purchase price includes predetermined accrued interest. (2) For new inflation-protected securities accruing interest from the coupon frequency date immediately preceding the issue date, with the interest rate established in the auction being used to determine the accrued interest payable on the issue date. Bidding: Formulas: P adj Date A = [(s−r)/s] × (C/2). A adj Date SA = P adj adj. Index Ratio Date Date IssueDate Example: We issued a 3 5/8 Definitions: C = 3.625. i = 0.0365. n = 18. r = 92 (October 15, 1998 to January 15, 1999). s = 184 (July 15, 1998 to January 15, 1999). Ref CPI Date Ref CPI IssueDate Resolution: Index Ratio Date Date IssueDate v n n 18 a n n Formula: P = 100.703267 − 0.906250. P = 99.797017. P adj Date P adj P adj A = [(184−92)/184] × 3.625/2 = 0.906250. A adj Date A adj A adj SA = P adj adj SA = 101.784820. Note: For the real price (P), and the inflation-adjusted price (P adj adj IV. Formulas for Conversion of Floating Rate Note Discount Margins to Equivalent Prices Definitions for Newly Issued Floating Rate Notes P = the price per $100 par value. T 0 N = the total number of quarterly interest payments. i k T i th T i i-1 i T N r = the index rate applicable to the issue date. s = the spread. m = the discount margin. A. For newly issued floating rate notes issued at par: Formula: Example: The purpose of this example is to demonstrate how a floating rate note price is derived at the time of original issuance. Additionally, this example depicts the association of the July 31, 2012 issue date and the two-business-day lockout period. 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, and an interest accrual rate on the issue date of 0.215022819% (index rate of 0.095022819% plus a spread of 0.120%), solve for the price per 100 (P). This interest accrual rate is used for each daily interest accrual over the life of the security for the purposes of this example. In a new issuance (not a reopening) of a floating rate note, the discount margin determined at auction will be equal to the spread. Definitions: T 0 N = 8. T N r s m 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 Auction high rate Index rate 7/23/2012 7/26/2012 10/25/2012 99.975986 0.095% 0.095022819% The rationale for using a 13-week bill auction that has occurred at least two days prior to the issue date is due to the two-business-day lockout period. This lockout period applies only to the issue date and interest payment dates, thus any 13-week bill auction that occurs during the two-day lockout period is not used for calculations related to the issue date and interest payment dates. The following sample calendar depicts this relationship for the floating rate note issue date. 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 1st Interest Date: T 1 T 1 T 0 2nd Interest Date: T 2 T 2 T 1 3rd Interest Date: T 3 T 3 T 2 4th Interest Date: T 4 T 4 T 3 5th Interest Date: T 5 T 5 T 4 6th Interest Date: T 6 T 6 T 5 7th Interest Date: T 7 T 7 T 6 8th Interest & Maturity Dates: T 8 T 8 T 7 Let a i r s, and A i a i T i T i −1 {i = 8} a i T i −1 T i i a i s r a 1 A i T i i T i T i −1 T i −1 T i {i = 8} A i and A 8 Let B i r m T i T i − 1 B i T i −1 T i i i m r B 3 The following table shows the projected daily accrued interest values for $100 par value ( a i A i B i Table 3—Projected Cash Flows and Compound Factors i a i A i B i 1 0.000597286 0.054950312 1.000549503 2 0.000597286 0.054950312 1.000549503 3 0.000597286 0.053158454 1.000531584 4 0.000597286 0.054950312 1.000549503 5 0.000597286 0.054950312 1.000549503 6 0.000597286 0.054950312 1.000549503 7 0.000597286 0.053158454 1.000531584 8 0.000597286 100.054950312 1.000549503 Computing the Price The price is computed as follows: B. For newly issued floating rate notes issued at a premium: Formula: 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: T 0 N = 8. T N r s m 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 Auction high rate Index rate 7/23/2012 7/26/2012 10/25/2012 99.975986 0.095% 0.095022819% 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 1st Interest Date: T 1 T 1 T 0 2nd Interest Date: T 2 T 2 T 1 3rd Interest Date: T 3 T 3 T 2 4th Interest Date: T 4 T 4 T 3 5th Interest Date: T 5 T 5 T 4 6th Interest Date: T 6 T 6 T 5 7th Interest Date: T 7 T 7 T 6 8th Interest & Maturity Dates: T 8 T 8 T 7 Let a i r s, and A i a i T i − T i − 1 {i = 8} a i T i − 1 T i i a i s r a i A i T i i T i T i −1 T i −1 T i { i 8} A 1 and A 8 Let B i r m T i T i −1 B i T i −1 T i i B i m r B 3 The following table shows the projected daily accrued interests for $100 par value ( a i A i B i Table 3—Projected Cash Flows and Compound Factors i a i A i B i 1 0.000000000 0.000000000 0.999859503 2 0.000000000 0.000000000 0.999859503 3 0.000000000 0.000000000 0.999864084 4 0.000000000 0.000000000 0.999859503 5 0.000000000 0.000000000 0.999859503 6 0.000000000 0.000000000 0.999859503 7 0.000000000 0.000000000 0.999864084 8 0.000000000 100.000000000 0.999859503 Computing the Price The price is computed as follows: Definitions for Reopenings of Floating Rate Notes and Calculation of Interest Payments IP i i P D AI P C T −1 T 0 N = the total number of remaining quarterly interest payments as of the reopening issue date. i k 1 2 3 −1 j T i th T i i−1 i T N r j r s m 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 C Definitions: T −1 T 0 N = 8. T N r s m The following table shows the past results for the 13-week bill auction. Table 1—13-Week Bill Auction Data Auction date Issue date Maturity date Auction Auction Index rate 7/23/2012 7/26/2012 10/25/2012 99.975986 0.095 0.095022819 7/30/2012 8/2/2012 11/1/2012 99.972194 0.110 0.110030595 8/6/2012 8/9/2012 11/8/2012 99.974722 0.100 0.100025284 8/13/2012 8/16/2012 11/15/2012 99.972194 0.110 0.110030595 8/20/2012 8/23/2012 11/23/2012 99.973167 0.105 0.105028183 8/27/2012 8/30/2012 11/29/2012 99.973458 0.105 0.105027876 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 7/31/2012 7/31/2012 1 7/23/2012 0.095022819 8/1/2012 8/6/2012 6 7/30/2012 0.110030595 8/7/2012 8/13/2012 7 8/6/2012 0.100025284 8/14/2012 8/20/2012 7 8/13/2012 0.110030595 8/21/2012 8/27/2012 7 8/20/2012 0.105028183 8/28/2012 8/30/2012 3 8/27/2012 0.105027876 Computing the Accrued Interest The accrued interest as of the new issue date (8/31/2012) for a $100 par value is: AI + 6 × 100 × max (0.00110030595 + 0.00120,0)/360 + 7 × 100 × max (0.00100025284 + 0.00120,0)/360 + 7 × 100 × max (0.00110030595 + 0.00120,0)/360 + 7 × 100 × max (0.00105028183 + 0.00120,0)/360 + 3 × 100 × max (0.00105027876 + 0.00120,0)/360 AI + 6 × 0.000638974 + 7 × 0.000611181 + 7 × 0.000638974 + 7 × 0.000625078 + 3 × 0.000625077 AI AI Computing the Projected Cash Flows The following table presents the future interest payment dates and the number of days between them. Table 3—Payment Dates Dates Days between dates Original Issue Date: T −1 New Issue Date: T 0 T 0 T −1 1st Interest Date: T 1 T 1 T 0 2nd Interest Date: T 2 T 2 T 1 3rd Interest Date: T 3 T 3 T 2 4th Interest Date: T 4 T 4 T 3 5th Interest Date: T 5 T 5 T 4 6th Interest Date: T 6 T 6 T 5 7th Interest Date: T 7 T 7 T 6 8th Interest & Maturity Dates: T 8 T 8 T 7 Let a i r s and A i a i T i T i −1 { i = 8} a i T i −1 T i i a i s r a i A i T i i T i T i - 1 T i −1 T i { i = 8} A 1 and A 8 Let B i r m T i T i -1 B i T i −1 T i i B i m r B 3 The following table shows the projected daily accrued interests for $100 par value ( a i A i B i Table 4—Projected Cash Flows and Compound Factors i a i A i B i 1 0.000625077 0.038129697 1.000347408 2 0.000625077 0.057507084 1.000523960 3 0.000625077 0.055631853 1.000506874 4 0.000625077 0.057507084 1.000523960 5 0.000625077 0.057507084 1.000523960 6 0.000625077 0.057507084 1.000523960 7 0.000625077 0.055631853 1.000506874 8 0.000625077 100.057507084 1.000523960 Computing the Price The price with accrued interest is computed as follows: 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 Example 1: Projected interest payment as of the original issue date. T 0 N = 8. T N r = 0.095022819%. s = 0.120%. m = 0.120%. 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 Auction high rate Index rate 7/23/2012 7/26/2012 10/25/2012 99.975986 0.095% 0.095022819% 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 1st Interest Date: T 1 T 1 T 0 2nd Interest Date: T 2 T 2 T 1 3rd Interest Date: T 3 T 3 T 2 4th Interest Date: T 4 T 4 T 3 5th Interest Date: T 5 T 5 T 4 6th Interest Date: T 6 T 6 T 5 7th Interest Date: T 7 T 7 T 6 8th Interest & Maturity Dates: T 8 T 8 T 7 Using the spread s r IP 1 IP 1 IP 7 IP 7 The following table shows all projected interest payments as of the issue date. Table 3—Projected Interest Payments i Dates IP i 1 10/31/2012 0.054950312 2 1/31/2013 0.054950312 3 4/30/2013 0.053158454 4 7/31/2013 0.054950312 5 10/31/2013 0.054950312 6 1/31/2014 0.054950312 7 4/30/2014 0.053158454 8 7/31/2014 0.054950312 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 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 −1 T −1 T 0 N = 8. T N r = 0.105027876%. s = 0.120%. m = 0.100%. The following table shows the past results for the 13-week bill auction. Table 4—13-Week Bill Auction Data Auction date Issue date Maturity date Auction Auction Index rate 7/23/2012 7/26/2012 10/25/2012 99.975986 0.095 0.095022819 7/30/2012 8/2/2012 11/1/2012 99.972194 0.110 0.110030595 8/6/2012 8/9/2012 11/8/2012 99.974722 0.100 0.100025284 8/13/2012 8/16/2012 11/15/2012 99.972194 0.110 0.110030595 8/20/2012 8/23/2012 11/23/2012 99.973167 0.105 0.105028183 8/27/2012 8/30/2012 11/29/2012 99.973458 0.105 0.105027876 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 Applicable floating rate Auction date Index rate 7/31/2012 7/31/2012 1 7/23/2012 0.095022819 8/1/2012 8/6/2012 6 7/30/2012 0.110030595 8/7/2012 8/13/2012 7 8/6/2012 0.100025284 8/14/2012 8/20/2012 7 8/13/2012 0.110030595 8/21/2012 8/27/2012 7 8/20/2012 0.105028183 8/28/2012 8/30/2012 3 8/27/2012 0.105027876 Computing the accrued interest The accrued interest as of 8/31/2012 for a $100 par value is: AI + 6 × 100 × max (0.00110030595 + 0.00120,0)/360 + 7 × 100 × max (0.00100025284 + 0.00120,0)/360 + 7 × 100 × max (0.00110030595 + 0.00120,0)/360 + 7 × 100 × max (0.00105028183 + 0.00120,0)/360 + 3 × 100 × max (0.00105027876 + 0.00120,0)/360 AI + 6 × 0.000638974 + 7 × 0.000611181 + 7 × 0.000638974 + 7 × 0.000625078 + 3 × 0.000625077 AI AI The following table presents the future interest payment dates and the number of days between them. Table 6—Payment Dates Dates Days between dates Original Issue Date: T − 1 New Issue Date: T 0 T 0 T −1 1st Interest Date: T 1 T 1 T 0 2nd Interest Date: T 2 T 2 T 1 3rd Interest Date: T 3 T 3 T 2 4th Interest Date: T 4 T 4 T 3 5th Interest Date: T 5 T 5 T 4 6th Interest Date: T 6 T 6 T 5 7th Interest Date: T 7 T 7 T 6 8th Interest & Maturity Dates: T 8 T 8 T 7 Using the original spread s r IP 1 IP 1 IP 1 and IP 8 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 1 10/31/2012 0.057562689 2 1/31/2013 0.057507084 3 4/30/2013 0.055631853 4 7/31/2013 0.057507084 5 10/31/2013 0.057507084 6 1/31/2014 0.057507084 7 4/30/2014 0.055631853 8 7/31/2014 0.057507084 Definitions for Newly Issued Floating Rate Notes with an Issue Date that Occurs after the Dated Date P D AI P C T −1 T 0 N i k j T i i th T i T i−1 T i T N r j r s m E. Pricing and accrued interest for new issue floating rate notes with an issue date that occurs after the dated date Formula: 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, 2013. 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 Auction high rate Index rate 12/27/2011 12/29/2011 3/29/2012 99.993681 0.025% 0.025001580% 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 Applicable floating rate Auction date Index rate 12/31/2011 1/2/2012 3 12/27/2011 0.025001580% Computing the accrued interest The accrued interest as of the new issue date (1/3/2012) for a $100 par value is: AI AI AI Computing the Projected Cash Flows The following table presents the future interest payment dates and the number of days between them. Table 3—Payment Dates Dates Days between dates Dated Date: = T −1 Issue Date: T 0 T 0 T −1 1st Interest Date: T 1 T 1 T 0 2nd Interest Date: T 2 T 2 T 1 3rd Interest Date: T 3 T 3 T 2 4th Interest Date: T 4 T 4 T 3 5th Interest Date: T 5 T 5 T 4 6th Interest Date: T 6 T 6 T 5 7th Interest Date: T 7 T 7 T 6 8th Interest & Maturity Dates: T 8 T 8 T 7 Let a i r s and A i a i T i T i −1 { i = 8} a i T i −1 T i i a i s r a 1 A i T i i T i T i −1 T i -1 T i { i = 8} A 1 and A 8 Let B i r m i T i −1 B i T i −1 T i i B i m r B 3 The following table shows the projected daily accrued interests for $100 par value ( a i A i B i Table 4—Projected Cash Flows and Compound Factors i a i A i B i 1 0.002847227 0.250555976 1.002505559 2 0.002847227 0.259097657 1.002590976 3 0.002847227 0.261944884 1.002619448 4 0.002847227 0.261944884 1.002619448 5 0.002847227 0.256250430 1.002562504 6 0.002847227 0.259097657 1.002590976 7 0.002847227 0.261944884 1.002619448 8 0.002847227 100.261944884 1.002619448 Computing the price The price with accrued interest is computed as follows: V. Computation of Adjusted Values and Payment Amounts for Stripped Inflation-Protected Interest Components Note: Valuing an interest component stripped from an inflation-protected security at its adjusted value enables this interest component to be interchangeable (fungible) with other interest components that have the same maturity date, regardless of the underlying inflation-protected security from which the interest components were stripped. The adjusted value provides for fungibility of these various interest components when buying, selling, or transferring them or when reconstituting an inflation-protected security. Definitions: c = C/100 = the regular annual interest rate, payable semiannually, e.g., .03625 (the decimal equivalent of a 3 5/8 Par = par amount of the security to be stripped Ref CPI IssueDate Ref CPI Date AV = adjusted value of the interest component PA = payment amount at maturity by Treasury Formulas: AV = Par(C/2)(100/Ref CPI IssueDate PA = AV(Ref CPI Date Example: A 10-year inflation-protected note paying 3 7/8 IssueDate Date Definitions: c = .03875 Par = $1,000,000 Ref CPI IssueDate Ref CPI Date Resolution: For a par amount of $1 million, the adjusted value of each stripped interest component was $1,000,000(.03875/2)(100/164.00000), or $11,814.02 (no intermediate rounding). For an interest component that matured on January 15, 2000, the payment amount was $11,814.02 (168.24516/100), or $19,876.52 (no intermediate rounding). VI. Computation of Purchase Price, Discount Rate, and Investment Rate (Coupon-Equivalent Yield) for Treasury Bills A. Conversion of the discount rate to a purchase price for Treasury bills of all maturities: Formula: P = 100 (1 − dr / 360). Where: d = discount rate, in decimals. r = number of days remaining to maturity. P = price per 100 (dollars). Example: For a bill issued November 24, 1989, due February 22, 1990, at a discount rate of 7.610%, solve for price per 100 (P). Definitions: d = .07610. r = 90 (November 24, 1989 to February 22, 1990). Resolution: P = 100 (1 − dr / 360). (1) P = 100 [1 − (.07610)(90) / 360]. (2) P = 100 (1 − .019025). (3) P = 100 (.980975). (4) P = 98.097500. Note: Purchase prices per $100 are rounded to six decimal places, using normal rounding procedures. B. Computation of purchase prices and discount amounts based on price per $100, for Treasury bills of all maturities: 1. To determine the purchase price of any bill, divide the par amount by 100 and multiply the resulting quotient by the price per $100. Example: To compute the purchase price of a $10,000 13-week bill sold at a price of $98.098000 per $100, divide the par amount ($10,000) by 100 to obtain the multiple (100). That multiple times 98.098000 results in a purchase price of $9,809.80. 2. To determine the discount amount for any bill, subtract the purchase price from the par amount of the bill. Example: For a $10,000 bill with a purchase price of $9,809.80, the discount amount would be $190.20, or $10,000 − $9,809.80. C. Conversion of prices to discount rates for Treasury bills of all maturities: Formula: Where: P = price per 100 (dollars). d = discount rate. r = number of days remaining to maturity. Example: For a 26-week bill issued December 30, 1982, due June 30, 1983, with a price of $95.934567, solve for the discount rate (d). Definitions: P = 95.934567. r = 182 (December 30, 1982, to June 30, 1983). Resolution: (2) d = [.04065433 × 1.978021978]. (3) d = .080415158. (4) d = 8.042%. Note: Prior to April 18, 1983, we sold all bills in price-basis auctions, in which discount rates calculated from prices were rounded to three places, using normal rounding procedures. Since that time, we have sold bills only on a discount rate basis. D. Calculation of investment rate (coupon-equivalent yield) for Treasury bills: 1. For bills of not more than one half-year to maturity: Formula: Where: i = investment rate, in decimals. P = price per 100 (dollars). r = number of days remaining to maturity. y = number of days in year following the issue date; normally 365, but if the period from the issue date to the same date 1 year ahead contains February 29, then y is 366. (e.g., 2020 is a leap year. Suppose the issue date for a 26-week bill is February 28, 2019. The date 1 year ahead is February 28, 2020. That 1-year period from the issue date of the bill does not contain “February 29,” therefore y = 365. Now suppose the issue date of a 26-week bill is March 1, 2019. The date 1 year ahead is March 1, 2020. That 1-year period from the issue date of the bill contains “February 29,” therefore y = 366.) Example: For a cash management bill issued June 1, 1990, due June 21, 1990, with a price of $99.559444 (computed from a discount rate of 7.930%), solve for the investment rate (i). Definitions: P = 99.559444. r = 20 (June 1, 1990, to June 21, 1990). y = 365. Resolution: (2) i = [.004425 × 18.25]. (3) i = .080756. (4) i = 8.076%. 2. For bills of more than one half-year to maturity: Formula: P [1 + (r − y/2)(i/y)] (1 + i/2) = 100. This formula must be solved by using the quadratic equation, which is: ax 2 Therefore, rewriting the bill formula in the quadratic equation form gives: and solving for “i” produces: Where: i = investment rate in decimals. b = r/y. a = (r/2y) − .25. c = (P−100)/P. P = price per 100 (dollars). r = number of days remaining to maturity. y = number of days in year following the issue date; normally 365, but if the period from the issue date to the same date 1 year ahead contains February 29, then y is 366. (e.g., 2020 is a leap year. Suppose the issue date for a 26-week bill is February 28, 2019. The date 1 year ahead is February 28, 2020. That 1-year period from the issue date of the bill does not contain “February 29,” therefore y = 365. Now suppose the issue date of a 26-week bill is March 1, 2019. The date 1 year ahead is March 1, 2020. That 1-year period from the issue date of the bill contains “February 29,” therefore y = 366.) Example: For a 52-week bill issued June 7, 1990, due June 6, 1991, with a price of $92.265000 (computed from a discount rate of 7.65%), solve for the investment rate (i). Definitions: r = 364 (June 7, 1990, to June 6, 1991). y = 365. P = 92.265000. b = 364 / 365, or .997260274. a = (364 / 730) − .25, or .248630137. c = (92.265 − 100) / 92.265, or −.083834607. Resolution: (3) i = (−.997260274 + 1.038221216) / .497260274. (4) i = .040960942 / .497260274. (5) i = .082373244 or (6) i = 8.237%. [69 FR 45202, July 28, 2004, as amended at 69 FR 52967, Aug. 30, 2004; 69 FR 53622, Sept. 2, 2004; 73 FR 14939, Mar. 20, 2008; 78 FR 46428, 46430, July 31, 2013; 78 FR 50335, Aug. 19, 2013; 78 FR 52857, Aug. 27, 2013; 78 FR 59228-59230, Sept. 26, 2013; 81 FR 43070, July 1, 2016; 87 FR 40440, July 7, 2022] Appendix C to Part 356—Investment Considerations I. Inflation-Protected Securities A. Principal and Interest Variability An investment in securities with principal or interest determined by reference to an inflation index involves factors not associated with an investment in a non-indexed security. Such factors include the possibility that: • The inflation index may be subject to significant changes, • changes in the index may or may not correlate to changes in interest rates generally or with changes in other indices, • the resulting interest may be greater or less than that payable on other securities of similar maturities, and • in the event of sustained deflation, the amount of the semiannual interest payments, the inflation-adjusted principal of the security, and the value of stripped components will decrease. However, if at maturity the inflation-adjusted principal is less than a security's par amount, we will pay an additional amount so that the additional amount plus the inflation-adjusted principal equals the par amount. Regardless of whether or not we pay such an additional amount, we will always base interest payments on the inflation-adjusted principal as of the interest payment date. If a security has been stripped, we will pay any such additional amount at maturity to holders of principal components only. (See § 356.30.) B. Trading in the Secondary Market The Treasury securities market is the largest and most liquid securities market in the world. The market for Treasury inflation-protected securities, however, may not be as active or liquid as the market for Treasury non-indexed securities. In addition, Treasury inflation-protected securities may not be as widely traded or as well understood as Treasury non-indexed securities. Lesser liquidity and fewer market participants may result in larger spreads between bid and asked prices for inflation-protected securities than the bid-asked spreads for non-indexed securities with the same time to maturity. Larger bid-asked spreads normally result in higher transaction costs and/or lower overall returns. The liquidity of an inflation-protected security may be enhanced over time as we issue additional amounts or more entities participate in the market. C. Tax Considerations Treasury inflation-protected securities and the stripped interest and principal components of these securities are subject to specific tax rules provided by Treasury regulations issued under sections 1275(d) and 1286 of the Internal Revenue Code of 1986, as amended. D. Indexing Issues While the Consumer Price Index (“CPI”) measures changes in prices for goods and services, movements in the CPI that have occurred in the past do not necessarily indicate changes that may occur in the future. The calculation of the index ratio incorporates an approximate three-month lag, which may have an impact on the trading price of the securities, particularly during periods of significant, rapid changes in the index. The CPI is reported by the Bureau of Labor Statistics, a bureau within the Department of Labor. The Bureau of Labor Statistics operates independently of Treasury and, therefore, we have no control over the determination, calculation, or publication of the index. For a discussion of how we will apply the CPI in various situations, see appendix B, section I, paragraph B of this part. In addition, for a discussion of actions that we would take in the event the CPI is: discontinued; in the judgment of the Secretary, fundamentally altered in a manner materially adverse to the interests of an investor in the security; or, in the judgment of the Secretary, altered by legislation or Executive Order in a manner materially adverse to the interests of an investor in the security, see appendix B, section I, paragraph B.4 of this part. II. Floating Rate Notes A. Interest Variability An investment in securities with interest determined by reference to a 13-week Treasury bill index involves risks not associated with an investment in a fixed interest rate security. Such risks include the possibility that: • Changes in the index may or may not correlate to changes in interest rates generally or with changes in other indexes; • any given interest payment may be more or less than the amount paid on prior interest payment dates; • the resulting interest payments may be greater or less than those payable on other securities of similar maturities, and • in the event of sustained falling interest rates, the amount of the quarterly interest payments will decrease. B. Trading in the Secondary Market The Treasury securities market is the largest and most liquid securities market in the world. The market for Treasury floating rate notes, however, may not be as active or liquid as the market for Treasury non-indexed securities or Treasury inflation-protected securities. In addition, Treasury floating rate notes may not be as widely traded or as well understood as these other types of Treasury marketable securities. Prices for floating rate notes may not fluctuate in reaction to interest rate movements in the same manner as other Treasury securities. Lesser liquidity and fewer market participants may result in larger spreads between bid and asked prices for Treasury floating rate notes than the bid-asked spreads for other Treasury marketable securities with the same time to maturity. Larger bid-asked spreads normally result in higher transaction costs and/or lower overall returns. The liquidity of a Treasury floating rate note may be enhanced over time as we issue additional amounts or more entities participate in the market. C. Tax Considerations Treasury floating rate notes are subject to specific tax rules provided by Treasury regulations issued under section 1275(d) of the Internal Revenue Code of 1986, as amended. D. Indexing Issues The Bureau of the Fiscal Service publishes the High Rate immediately following a 13-week bill auction as part of the auction results. The 13-week bill is generally auctioned once per week. Treasury retains the flexibility to increase or decrease the frequency of 13-week bill auctions, which would affect the frequency of index rate resets. The High Rate is subject to various interest rate and market environments over which Treasury has no control. For a discussion of actions that Treasury would take in the event auctions of 13-week bills are discontinued or delayed, see appendix B, section I, paragraph C.4 of this part. [69 FR 45202, July 28, 2004, as amended at 78 FR 46428, 46444, July 31, 2013] Appendix D to Part 356—Description of the Indexes I. Consumer Price Index The Consumer Price Index (“CPI”) for purposes of inflation-protected securities is the non-seasonally adjusted U.S. City Average All Items Consumer Price Index for All Urban Consumers. It is published monthly by the Bureau of Labor Statistics (BLS), a bureau within the Department of Labor. The CPI is a measure of the average change in consumer prices over time in a fixed market basket of goods and services. This market basket includes food, clothing, shelter, fuels, transportation, charges for doctors' and dentists' services, and drugs. In calculating the index, price changes for the various items are averaged together with weights that represent their importance in the spending of urban households in the United States. The BLS periodically updates the contents of the market basket of goods and services, and the weights assigned to the various items, to take into account changes in consumer expenditure patterns. The CPI is expressed in relative terms in relation to a time base reference period for which the level is set at 100. For example, if the CPI for the 1982-84 reference period is 100.0, an increase of 16.5 percent from that period would be shown as 116.5. The CPI for a particular month is released and published during the following month. From time to time, the CPI is rebased to a more recent base reference period. We provide the base reference period for a particular inflation-protected security on the auction announcement for that security. Further details about the CPI may be obtained by contacting the BLS. II. Floating Rate Note Index The floating rate note index is the 13-week Treasury bill auction High Rate (stop out rate), and converted to the simple-interest money market yield computed on an actual/360 basis. [69 FR 45202, July 28, 2004, as amended at 78 FR 46444, July 31, 2013]

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