THE SHORT ANSWER
An arbitrage rebate liability is calculated by compounding every receipt and every payment on an issue's nonpurpose investments to the computation date at the bond yield and taking the excess of receipts over payments. A computation credit for each bond year with rebate-subject gross proceeds is treated as a payment, installments must reach 90 percent at least every five years, and the balance is due within 60 days of the final computation date.
An arbitrage rebate liability is calculated by taking the future value of every receipt on an issue's nonpurpose investments, subtracting the future value of every payment on them, compounding both sides at the bond yield to a computation date, and treating the computation credit for each bond year with rebate-subject gross proceeds as a payment on the ledger.
The rule that produces the number is section 148(f) of the Internal Revenue Code as implemented by Treasury Regulation §1.148-3, and the requirement it enforces is the arbitrage rebate requirement described in the guide to the federal arbitrage rules.
The calculation matters even for a portfolio that respects its yield limits: IRS Publication 5271 (which states it is not formal guidance) notes that bonds are tested under both the yield restriction rules of section 148(a) and the rebate rules of section 148(f), and that the yield restriction rules may allow an issuer to earn arbitrage the rebate rules then require it to pay to the United States.
How does the future-value method work?
The rebate amount is the excess of the future value, as of the computation date, of all receipts on the issue's nonpurpose investments over the future value, as of that date, of all payments on them, with both sides compounded at the bond yield (26 U.S.C. 148(f)(2); Treas. Reg. §1.148-3(b)-(c)).
Under the economic accrual method in §1.148-3, those future values use the same compounding interval and conventions as the bond yield, so a ledger for an issue whose yield compounds semiannually compounds semiannually too.
Gains and losses on the disposition of a nonpurpose investment count in the computation as well (26 U.S.C. 148(f)(4)(A)(i)).
Treasury Regulation §1.148-3(d)(1)-(2) fills in the two sides of the ledger, and the table below sorts the items the regulation includes.
| Side of the ledger | Items the regulation includes |
|---|---|
| Payments, §1.148-3(d)(1) | Amounts paid to buy nonpurpose investments, the value of investments first allocated to the issue, the computation credit, and yield reduction payments |
| Receipts, §1.148-3(d)(2) | Earnings, return of principal, and the value of investments still held at the end of a computation period |
The instructions for Form 8038-T warn that "any cash flow representation to the contrary may result in the understatement of rebate amount," which is a caution against representing an issue's cash flows any other way.
Both sides of the ledger are measured as of a computation date, and Treasury Regulation §1.148-3(e)(1) lets a fixed-yield issue treat any date as a computation date while requiring a variable-yield issue, after the first required payment date, to use consistently either the end of each bond year or the end of each fifth bond year.
The final computation date is the date the issue is discharged, and for an issue retired within 3 years it need not fall before 8 months after the issue date, or during a period when a spending exception is expected to apply (Treas. Reg. §1.148-3(e)(2)).
What is the computation credit?
A computation credit is a dollar amount treated as a payment, taken on the last day of each bond year in which the issue has rebate-subject gross proceeds and on the final maturity date (Treas. Reg. §1.148-3(d)(1)(iv), (d)(4)).
The credit was $1,000 before 2007 and $1,400 for bond years ending in 2007, and for bond years ending after 2007 the regulation directs to an inflation-adjusted amount determined under §1.148-3(d)(4), computed with the section 1(f)(3) adjustment from a 2006 base year and rounded to the nearest $10.
IRS Publication 5271 notes that the indexed credit applies to bonds sold on or after October 17, 2016, and optionally to earlier bonds for bond years ending on or after July 18, 2016.
The dollar amount for any later bond year is the figure determined under §1.148-3(d)(4), not the 2007 number.
Once the rebate amount is set, it converts into payments on a schedule: the first rebate installment must relate to a computation date no later than 5 years after the issue date, each later installment to a date no later than 5 years after the previous one, and each installment must bring cumulative payments, measured at future value, to at least 90 percent of the rebate amount as of that date (26 U.S.C. 148(f)(3); Treas. Reg. §1.148-3(f)(1)).
At the final computation date the issuer pays enough to bring cumulative payments to 100 percent of the rebate amount, and every rebate payment is due no later than 60 days after the computation date it relates to, though a payment made within that window may be treated as paid on the computation date itself (Treas. Reg. §1.148-3(f)(2), (g)).
The payments are made on Form 8038-T, one form per issue, which carries arbitrage rebate, yield reduction payments, the penalty in lieu of rebate, and late-payment penalties and interest, and the Form 8038-T guide covers the filing.
Which gross proceeds enter the computation?
Every payment on the issue's nonpurpose investments and every receipt from them enters the ledger, and the paragraphs below state the exceptions and elections that section 148(f)(4) and the regulations under it provide.
Earnings on a bona fide debt service fund are not taken into account when gross earnings on the fund for the bond year are under $100,000, a dollar limit that is not indexed and that does not apply to non-private-activity issues with an average maturity of at least 5 years and fixed interest rates (26 U.S.C. 148(f)(4)(A)(ii)).
The 6-month spending exception treats an issue as meeting the rebate requirement when its gross proceeds, as specially defined, are spent on the governmental purpose within 6 months of the issue date, with rebate paid on amounts not required to be spent, and earnings on a reasonably required reserve fund remain subject to rebate under it (148(f)(4)(B); Treas. Reg. §1.148-7(c)).
The 18-month exception requires spending at least 15 percent of gross proceeds within 6 months, 60 percent within 12 months and 100 percent within 18 months, with rebate paid on the amounts not required to be spent and all gross proceeds qualifying for the 3-year capital project temporary period (Treas. Reg. §1.148-7(d)(1), a regulation-level exception that is unavailable if any portion of the issue uses the 2-year exception).
For a construction issue, available construction proceeds are treated as meeting the rebate requirement when at least 10 percent is spent within 6 months, 45 percent within 1 year, 75 percent within 18 months and 100 percent within 2 years, with reasonable retainage of up to 5 percent allowed until 3 years (148(f)(4)(C)(ii); Treas. Reg. §1.148-7(e)(1), (e)(2)).
In place of rebate on available construction proceeds, the issuer of a construction issue may elect on or before the issue date, irrevocably, to pay a penalty of 1.5 percent of the underexpended proceeds for each 6-month spending period that misses that schedule, filed on Form 8038-T (148(f)(4)(C)(vii); Treas. Reg. §1.148-7(k)), and whether to make that election is a determination for bond counsel and tax counsel.
The small issuer exception treats rebate as met for an issue of a governmental unit with general taxing powers when no bond is a private activity bond, 95 percent or more of net proceeds go to the unit's local governmental activities, and the unit reasonably expects to issue no more than $5,000,000 of tax-exempt governmental bonds in the calendar year, an amount that increases by the lesser of $10,000,000 or the bonds attributable to public school facility construction, to as much as $15 million where no more than $5 million of proceeds finances non-school purposes (26 U.S.C. 148(f)(4)(D)(i), (vii); Form 8038-T instructions), with the dollar amounts fixed in the statute rather than indexed.
The spending exceptions guide compares those routes, and each exception keeps its own conditions in the 6-month, 18-month, 2-year construction and small issuer guides.
Worked example: the future-value method with numbers
For illustration, say an issuer closes a $20 million issue, invests the proceeds in a nonpurpose investment that pays 5 percent annually while the bond yield is 4 percent, and receives $1 million of earnings at the end of each of the next three years, with the $20 million of principal and the third year's earnings paid at the end of year three.
The issue is retired at the end of year three, that date is the final computation date, and every cash flow is compounded to it at the 4 percent bond yield.
| Date | Payment | Receipt | Years compounded at 4 percent | Future value |
|---|---|---|---|---|
| Issue date | $20,000,000 | 3 | $22,497,280 | |
| End of year 1 | $1,000,000 | 2 | $1,081,600 | |
| End of year 2 | $1,000,000 | 1 | $1,040,000 | |
| End of year 3 | $21,000,000 | 0 | $21,000,000 |
The future value of payments is $22,497,280, the future value of receipts is $1,081,600 plus $1,040,000 plus $21,000,000, or $23,121,600, and the rebate amount is the $624,320 difference.
The illustration leaves the computation credit out of the arithmetic because for bond years ending after 2007 the credit is an inflation-adjusted figure, and in an actual computation a credit would be entered on the payments side for each of the three bond years, reducing the amount.
If the issue had instead run five years, the first installment's computation date could fall no later than 5 years after the issue date, and the installment would have to bring cumulative payments, at future value, to at least 90 percent of the rebate amount as of that date (26 U.S.C. 148(f)(3); Treas. Reg. §1.148-3(f)(1)).
An actual computation also follows the bond yield's own day-count and compounding conventions under the economic accrual method of §1.148-3(b)-(c).
When should an issuer hire a rebate analyst?
An issuer that does not run the ledger in house buys this work: assembling every receipt and payment on the nonpurpose investments, applying the bond yield conventions, tracking computation dates and computation credits, and producing the amounts behind Form 8038-T.
The financing team guide covers who is on a municipal bond financing team.
GFOA recommends formal written post-issuance compliance policies and notes that governments may outsource tasks such as arbitrage rebate while keeping ultimate responsibility for ensuring the compliance procedures are met, and it recommends listing each issue's key documents (the tax certificate, escrow documents and indenture) at closing and identifying which records to keep and for how long.
The stakes are set by the same rules, because a failure to pay the correct rebate on time makes the bonds arbitrage bonds unless the failure was not due to willful neglect and the issuer promptly pays a penalty of 50 percent of the amount for governmental and qualified 501(c)(3) bonds, or 100 percent for other bonds, plus interest at the section 6621 underpayment rate (26 U.S.C. 148(f)(7); Treas. Reg. §1.148-3(h)).
That penalty is automatically waived if the missed amount plus interest is paid within 180 days after discovery of the failure, unless the Commissioner determines the failure was due to willful neglect or the issue is under examination during the specified window, so the outcome turns on facts a computation schedule cannot control.
Errors run in both directions, and an issuer that overpaid claims a refund on Form 8038-R no later than 2 years after the final computation date, with an overpayment under $5,000 generally not recoverable before that date (Treas. Reg. §1.148-3(i)).
The calculation consumes an investment's cash flows, and the terms that produce those cash flows are what mGIC examines as an independent, SEC-registered municipal advisor and Bidding Agent paid by the winning provider rather than the issuer, which is why a free, no-obligation reinvestment review can review the terms of an existing investment.
Which exceptions and computation dates an issue may use, and whether a completed computation is correct, are conclusions for bond counsel and tax counsel.
Frequently asked questions
Does the rebate computation compound at the bond yield or at the rate the investment pays?
At the bond yield. Treasury Regulation §1.148-3(b)-(c) compounds both sides of the ledger to the computation date at the bond yield, and the economic accrual method uses the same compounding interval and conventions as the bond yield.
Do gains and losses on selling a nonpurpose investment count in the computation?
Yes. Section 148(f)(4)(A)(i) counts gains and losses on the disposition of nonpurpose investments, so a sale before the computation date changes the ledger.
How much is the computation credit for the current bond year?
The credit was $1,000 before 2007 and $1,400 for bond years ending in 2007. For bond years ending after 2007 it is the inflation-adjusted amount determined under Treas. Reg. §1.148-3(d)(4), which uses the section 1(f)(3) adjustment from a 2006 base year rounded to the nearest $10, with the amount determined for each bond year.
Do the computation date rules differ for variable-yield issues?
Yes. A fixed-yield issue may treat any date as a computation date, while a variable-yield issue must, after the first required payment date, consistently use either the end of each bond year or the end of each fifth bond year (Treas. Reg. §1.148-3(e)(1)).
What happens to the calculation if an investment pays out on a different schedule than expected?
The ledger follows the actual receipts and payments, including the value of investments still held at the end of a computation period (Treas. Reg. §1.148-3(d)(2)). The Form 8038-T instructions warn that any cash flow representation to the contrary may result in the understatement of the rebate amount.
Sources
This page is general educational information about municipal finance and federal and state rules as of the date shown. It is not legal, tax or investment advice, and it is not a recommendation about any particular investment. Product availability, legality and suitability depend on the issuer, jurisdiction, governing documents and transaction-specific facts. Final legal and tax determinations remain with the issuer's bond counsel, tax counsel and other advisors.
