(i) Facts.
On January 1, 1994, City A issues a fixed yield issue and invests all the sale proceeds of the issue ($49 million). There are no other gross proceeds. The issue has a yield of 7.0000 percent per year compounded semiannually (computed on a 30 day month360 day year basis). City A receives amounts from the investment and immediately expends them for the governmental purpose of the issue as follows:
Date Amount
____ ______
2194 $3,000,000
5194 5,000,000
1195 5,000,000
9195 20,000,000
3196 22,000,000
(ii) First computation date.
(A) City A chooses January 1, 1999, as its first computation date. This date is the latest date that may be used to compute the first required rebate installment payment. The rebate amount as of this date is computed by determining the future value of the receipts and the payments for the investment. The compounding interval is each 6-month (or shorter) period and the 30 day month360 day year basis is used because these conventions were used to compute yield on the issue. The future value of these amounts, plus the computation credit, as of January 1, 1999, is:
Date Receipts (Payments) FV (7.0000 percent)
____ ___________________ ___________________
1194 ($49,000,000) ($69,119,339)
2194 3,000,000 4,207,602
5194 5,000,000 6,893,079
1195 5,000,000 6,584,045
1195 (1,000) (1,317)
9195 20,000,000 25,155,464
1196 (1,000) (1,229)
3196 22,000,000 26,735,275
1197 (1,000) (1,148)
Rebate amount
(10199) $452,432
(B) City A pays 90 percent of the rebate amount ($407,189) to the United States within 60 days of January 1, 1999.
(iii) Second computation date.
(A) On the next required computation date, January 1, 2004, the future value of the payments and receipts is:
Date Receipts (Payments) FV (7.0000 percent)
____ ___________________ ___________________
1199 $452,432 $638,200
Rebate amount
(10104) $638,200
(B) As of this computation date, the future value of the payment treated as made on January 1, 1999, is $574,380, which equals at least 90 percent of the rebate amount as of this computation date ($638,200 x 0.9), and thus no additional rebate payment is due as of this date.
(iv) Final computation date.
(A) On January 1, 2009, City A redeems all the bonds, and thus this date is the final computation date. The future value of the receipts and payments as of this date is:
Date Receipts (Payments) FV (7.0000 percent)
____ ___________________ ___________________
1104 $638,200 $900,244
1109 (1,000) (1,000)
Rebate amount
(10109) $899,244
(B) As of this computation date, the future value of the payment made on January 1, 1999, is $810,220 and thus an additional rebate payment of $89,024 is due. This payment reflects the future value of the 10 percent unpaid portion, and thus would not be owed had the issuer paid the full rebate amount as of any prior computation date.