Part VI — 0919 Publ 5271 (PDF)

Example of Calculation of Rebate Amount and Yield Restriction Analysis

The following is an example to demonstrate the application of basic concepts of the yield restriction and rebate requirements.

Facts: $49,000,000 variable yield bond issue with an issue date of January 1, 1994. The bond issue’s first interim computation date is January 1, 1999. ⁶⁶ The bond yield calculated for the first computation period is 7.00%.

In this example, the issuer received $49,000,000 in gross proceeds from the sale of bonds, and on the issue date applied $41,000,000 to purchase a U.S. Treasury note investment with an annual coupon yield of 7.53% and $8,000,000 to purchase a U.S. Treasury money fund investment bearing an annual interest rate of 4.97%. ⁶⁷ In this example, receipts from investments, unless reinvested, are disbursed immediately for the governmental purpose of the bonds.

The investment transactions used in this example are categorized as either payments or receipts. The general types of investment transactions, and their treatment, appear in the following chart. Within a typical computation of the rebate amount (or yield reduction payment), payments are represented by a negative number (monies going out) and receipts by a positive number (monies coming in).

*These are only used as adjustments if the par value of an investment is used to represent the purchase, maturity or sale of an investment.

**Excluded from payments for purposes of computing yield reduction payments.

66 See the discussion of computation dates in Part IV.

67 For ease of illustration, all transactions (purchases and sales) of the note and the fund are at par and interest payments on the fund only occur on dates when there are purchases or sales. Transaction totals are rounded to whole dollar amounts.

The accounting entries for payments and receipts on the note investment are shown in Table 1. The note purchase is shown as a $41,000,000 payment on January 1, 1994. The semiannual interest payments received on the note on each January 1 and July 1 are reflected as receipts. Sales of portions of the note occur periodically on January 1, 1995, September 1, 1995, and March 1, 1996, and are also reflected as receipts.

Table 1

U.S. Treasury Note 7.530%

Sell Receipt (+)

Interest Receipt (+)

Investment Balance

Date

Buy Payment (-)

01/01/94 (41,000,000) 41,000,000

02/01/94 41,000,000

05/01/94 41,000,000

07/01/94 1,543,650 41,000,000

01/01/95 1,780,000 1,543,650 39,220,000

07/01/95 1,476,633 39,220,000

09/01/95 18,275,000 231,844 20,945,000

01/01/96 788,579 20,945,000

03/01/96 20,945,000 259,971 0

(41,000,000) 41,000,000 5,844,328

Table 2 illustrates the accounting entries for payments and receipts on the fund investment. The purchase of the initial investment in the fund is shown as an $8,000,000 payment on January 1, 1994. Purchases of subsequent investments in the fund (representing immediate reinvestment in the fund of all receipts from interest earnings on the note and the fund on each date) are reflected as additional payments on July 1, 1994, July 1, 1995, and January 1, 1996. The periodic interest payments received on the fund are reflected as receipts. Sales of portions of the fund occur on February 1, 1994, May 1, 1994, January 1, 1995, September 1, 1995, and March 1, 1996, which are also reflected as receipts.

Table 2

U.S. Treasury Money Fund 4.970%

Sell Receipt (+)

Interest Receipt (+)

Investment Balance

Date

Buy Payment (-)

01/01/94 (8,000,000) 8,000,000

02/01/94 2,966,230 33,770 5,033,770

05/01/94 4,938,996 61,004 94,774

07/01/94 (1,544,437) 787 1,639,212

01/01/95 1,635,279 41,071 3,932

07/01/95 (1,476,730) 97 1,480,662

09/01/95 1,480,655 12,500 7

01/01/96 (788,579) 0 788,586

03/01/96 788,586 6,443 0

(11,809,746) 11,809,746 155,672

Table 3 combines the amounts of payments and receipts for each date from Table 1 and Table 2 to summarize the payments and receipts included in the computation of rebate amount and the computation of yield on investment. The total payments column represents the sum of payments for purchases of the note and the fund, represented as negative amounts. The total receipts column represents the sum of receipts from investment earnings on and sales of the note and the fund, represented as positive amounts. The net payments and receipts column is the sum of the payments and receipts columns.

Table 3

Total Total Net Payments Date Payments (-) Receipts (+) and Receipts

01/01/94 (49,000,000) 0 (49,000,000)

02/01/94 0 3,000,000 3,000,000

05/01/94 0 5,000,000 5,000,000

07/01/94 (1,544,437) 1,544,437 0

01/01/95 0 5,000,000 5,000,000

07/01/95 (1,476,730) 1,476,730 0

09/01/95 0 20,000,000 20,000,000

01/01/96 (788,579) 788,579 0

03/01/96 0 22,000,000 22,000,000

(52,809,746) 58,809,746 6,000,000

Generally, on dates when investments mature or are sold, or interest earnings are received, a receipt is included in the calculation of rebate amount. On dates when investments roll over or are purchased, or interest earnings are reinvested, a payment is included in the calculation of rebate amount. The payments and receipts on a corresponding date offset each other and the daily net total is included in the calculation of rebate amount.

Rebate Amount Calculation

Table 4 illustrates the calculation of rebate amount for the January 1, 1999, computation date based on the net payments and receipts column from Table 3 and the permitted computation credit on the last day of each bond year during which there are amounts allocated to gross

proceeds of an issue subject to the rebate requirement. The rebate amount for the computation date is calculated as the sum of the future values of each payment, receipt and computation credit ⁶⁸ as of the computation date using the bond yield (7.00% per year) as the rate of return in the future value computation. The rebate amount as of January 1, 1999, is $452,432.

68 Prior to 2007, the amount of the computation credit available under Treas. Reg. Section 1.148-3(d)(1)(iv) was $1,000. See also footnote 58 for more information on the increase in the computation credit.

Table 4

Date

Net Payments and Receipts

Future Value at Bond Yield

01/01/94 (49,000,000) (69,119,339)

02/01/94 3,000,000 4,207,602

05/01/94 5,000,000 6,893,079

07/01/94 0 0

01/01/95 5,000,000 6,584,045

01/01/95 (1,000) (1,317)

07/01/95 0 0

09/01/95 20,000,000 25,155,464

01/01/96 0 0

01/01/96 (1,000) (1,229)

03/01/96 22,000,000 26,735,275

01/01/97 (1,000) (1,148)

452,432

Table 4 demonstrates that the rebate amount is $452,432 as of the January 1, 1999, computation date. The issuer must submit a rebate payment of at least 90% of this amount within 60 days of this interim computation date by filing Form 8038-T and including the required payment. If January 1, 1999 was the final computation date, the issuer must submit 100% of the rebate amount.

Yield Restriction Analysis

An issuer determines whether it has complied with the yield restriction requirements by comparing the yield on investment with the maximum yield that is not materially higher than the yield on the bond issue. The issuer should include all unconditionally payable receipts and all unconditionally payable payments.

Computation of Yield Reduction Payments

For certain investments, an issuer can make yield reduction payments (including rebate payments) to the U.S. Treasury that reduce the yield on the investments for the yield restriction

requirements. For an eligible investment class, an issuer must pay the amount that will result in the yield on that class not being materially higher than the bond yield.

The example below assumes that the bond issue is entitled to the general 30-day temporary period and the general 1/8th of 1% materially higher yield limit.

Table 5 shows the payments for and receipts from investments in the note and the fund. The amounts entered for January 31, 1994 (the first day after the end of the general 30-day temporary period) are the values of the investments as of that date for the note and the fund, originally purchased on January 1, 1994. As permitted under the arbitrage requirements, the issuer values the note at present value and the fund at fair market value (essentially par plus accrued interest). The yield restriction requirements provide for certain temporary periods during which yield restriction does not apply. Consequently, the initial temporary period is not included in the determination of yield on investment. The result is that instead of the calculation starting on the issue date, it starts when the temporary period ends.

Table 5

Date

Value Payment (-)

U.S. Treasury Note 7.530% U.S. Treasury Money Fund 4.970%

Sell Receipt (+)

Interest Receipt (+)

Value/Buy Payment (-)

Sell Receipt (+)

Interest Receipt (+)

01/01/94 N/A N/A

01/31/94 (41,245,085) (8,032,681)

02/01/94 2,966,230 33,770

05/01/94 4,938,996 61,004

07/01/94 1,543,650 (1,544,437) 787

01/01/95 1,780,000 1,543,650 1,635,279 41,071

07/01/95 1,476,633 (1,476,730) 97

09/01/95 18,275,000 231,844 1,480,655 12,500

01/01/96 788,579 (788,579) 0

03/01/96 20,945,000 259,971 788,586 6,443

(41,245,085) 41,000,000 5,844,328 (11,842,427) 11,809,746 155,672

Table 6 summarizes the payments and receipts from Table 5 included in the computation of yield on investment. The total payments column represents the sum of payments from the value of investments (as of January 31, 1994) and purchases of the fund. The total receipts column represents the sum of receipts from investment earnings on and sales of the note and the fund.

Under the yield restriction requirements, the yield on investments cannot be materially higher than the yield on the bonds. The yield on an investment allocated to an issue is the discount rate that, when used in computing the present value as of the date the investment is first allocated to the issue of all unconditionally payable receipts from the investment, produces an amount equal to the present value of all unconditionally payable payments for the investment. When the net receipts and payments in Table 6 are present valued to January 31, 1994, that discount rate (which is the yield on investment) is 7.451%, exceeds the materially higher yield limit of 7.125%.

Table 6

Total Receipts (+)

Net Payments and Receipts

Date

Total Payments (-)

01/01/94 0

01/31/94 (49,277,766) 0 (49,277,766)

02/01/94 0 3,000,000 3,000,000

05/01/94 0 5,000,000 5,000,000

07/01/94 (1,544,437) 1,544,437 0

01/01/95 0 5,000,000 5,000,000

07/01/95 (1,476,730) 1,476,730 0

09/01/95 0 20,000,000 20,000,000

01/01/96 (788,579) 788,579 0

03/01/96 0 22,000,000 22,000,000

(53,087,512) 58,809,746 5,722,234

Table 7 illustrates a method of calculating the excess arbitrage earnings equaling the amount

of a yield reduction payment necessary to reduce the yield on investment to the maximum permitted yield of 7.125%, which is not materially higher than the bond yield. The yield reduction payment is calculated using the sum of the future values of each payment and each receipt as of the relevant computation date (January 1, 1999) using the bond yield adjusted to the materially higher yield (7.125% per year) as the interest rate in the future value computation.

Table 7

Net Payments Future Value to Date and Receipts Yield Restriction Limit

01/01/94 0 0

01/31/94 (49,277,766) (69,538,765)

02/01/94 3,000,000 4,232,654

05/01/94 5,000,000 6,932,027

07/01/94 0 0

01/01/95 5,000,000 6,615,919

07/01/95 0 0

09/01/95 20,000,000 25,256,907

01/01/96 0 0

03/01/96 22,000,000 26,826,890

5,722,234 325,632

Table 7 demonstrates that the yield on investments exceeds the bond yield increased to the materially higher limit by $325,632, which, unless reduced, would cause the bonds to be arbitrage bonds. In this example, the issuer can make a yield reduction payment because this is a variable yield bond. The yield reduction payment necessary to reduce the yield on investment to the allowable materially higher limit (that is, 7.125%) is $325,632. The issuer must submit a yield reduction payment within 60 days of the interim computation date by filing Form 8038-T together with the required payment, but need not submit a payment more than once every five years.

In this example, the issuer’s arbitrage liability to the U.S. Treasury, as of the January 1, 1999 computation date, would include a yield reduction payment of $325,632 and rebate of $126,800 ($452,432 minus $325,632), because the yield reduction payment is treated as a payment in

the determination of rebate amount under Treas. Reg. Section 1.148-3(d)(1)(v). The issuer would report this arbitrage liability and submit payment using Form 8038-T. Because January 1, 1999 is an interim computation date, the issuer need only make a payment equal to at least 90% of the rebate amount as of that date to satisfy the rebate requirements. ⁶⁹ For the final computation date, an issuer must pay 100% of the rebate amount.

69 Treas. Reg. Section 1.148-3(f)(1).