# Price Calculation for Securities with an Initial Non-Interest Paying Period: Rule G-33

The Board has adopted a method for calculating the price of securities for which there are no scheduled interest payments for an initial period, generally for several years, after which periodic interest payments are scheduled. These securities, known by such names as "Growth and Income Securities," and "Capital Appreciation/Future Income Securities," function essentially as "zero coupon" securities for a period of time after issuance, accruing interest which is payable only upon redemption. On a certain date after issuance ("the interest commencement date"), the securities begin to accrue interest for semi-annual payment.

In March 1986, the Board published for comment a proposed method of calculating price from yield for such securities.[1] The Board received five comments on the proposed method, four expressing support for the method and one expressing no opinion. The commentators generally noted that the proposed method appeared to be accurate and could be used on bond calculators commonly available in the industry. The Board has adopted the proposed method of calculation, set forth below, as an interpretation of rule G-33 on calculations.

The general formula for calculating the price of securities with periodic interest payments is contained in rule G-33(b)(i)(B)(2). For securities with periodic payments, but with an initial non-interest paying period, this formula also is used.[2] For settlement dates occurring prior to the interest commencement date the price is computed by means of the following two-step process. First, a hypothetical price of the securities at the interest commencement date is calculated using the interest commencement date as the hypothetical settlement date,[3] the interest rate ("R" in the formula) for the securities during the interest payment period and the yield ("Y" in the formula) at which the securities are sold. This hypothetical price is computed to not less than six decimal places, and then is used as the redemption value ("RV" in the formula) in a second calculation using the G-33(b)(i)(B)(2) formula, with the interest commencement date as the redemption date, the actual settlement date for the transaction as the settlement date, and a value of zero for R, the interest rate. The resultant price, using the formula in G-33(b)(i)(B)(2), is the correct price of the securities.[4]

The price of such securities for settlement dates occurring after the interest commencement date, of course, should be calculated as for any other securities with periodic interest payments.[5]

[1] *MSRB Reports*, Vol. 6, No. 2 (March 1986) at 13.

[2] This interpretation is not meant to apply to securities which have a long first coupon period, but which otherwise are periodic interest paying securities.

[3] For settlement dates less than 6 months to the hypothetical redemption date, the formula in rule G-33(b)(ii)(B)(1) should be used in lieu of the formula in rule G-33(b)(ii)(B)(2).

[4] Rule G-12(c)(v)(I) and G-15(a)(i)(I) [currently codified at rule G-15(a)(i)(A)(5)(c)] require that securities be priced to the lowest of price to call, price-to-par option, or price to maturity. Thus, the redemption date used for this calculation method should be the date of an "in whole" refunding call if this would result in a lower dollar price than a computation to maturity.

[5] The formula in G-33(b)(i)(B)(1) should be used for calculations in which settlement date is 6 months or less to redemption date.