This is a consolidated appeal from four summary judgments of the United States Court of Federal Claims. See Olson v. United States, 37 Fed.Cl. 727 (1997); Cahoon v. United States, No. 95-97T (Fed. Cl. Jan. 20, 1998); Gaus v. United States, No. 95-296T (Fed.Cl. Jan. 20, 1998); Lutter v. United States, No. 95-269T (Fed.Cl. Jan. 20, 1998). The taxpayers in all four suits sought refunds of taxes, interest, and penalties that resulted from their use of carrybacks and carryforwards in their joint tax returns of certain investment tax credits subsequently disallowed at the partnership level. The taxpayers argued that the taxes, interest, and penalties were improperly assessed simply because the Internal Revenue Service (the “IRS”) did not first provide the taxpayers with notices of deficiency. The Court of Federal Claims granted partial summary judgment to the government with respect to the refund claim in the Olson case, holding that the taxes and corresponding penalties and interest were validly assessed without a prior notice of deficiency. The court subsequently dismissed the tax refund claims in the other three cases, which had been stayed pending the judgment in Olson. The appeal was submitted for our decision following oral argument on December 7, 1998. Because we agree with the Court of Federal Claims that the taxes, penalties, and interest assessed here resulted from mere computational adjustments, i.e., those requiring no uniquely partner-level determinations, notices of deficiency were not required for their assessment and we therefore affirm.
BACKGROUND
The Olson appeal
In 1983, plaintiff-appellant Stephen S. Olson became a limited partner in Solar Energy Savers, Ltd. III (“Solar”). According to the appellants, Solar was set up *1313as a tax shelter for investments and was engaged in the leasing of energy-saving units. Olson acquired his partnership interest by contributing $22,000 in exchange for a 5.66% interest in partnership profits and a 5.71% interest in partnership capital. On April 18, 1984, Solar filed a Form 1065 (“U.S. Partnership Return of Income”) with the IRS for the taxable year 1983. Solar’s return reported an ordinary loss of $10,042 as well as a qualified investment of $3,208,240 in property eligible for the regular investment tax credit and the business energy investment tax credit. The return included a Schedule K-l (“Partner’s Share of Income, Credits, Deductions, etc.”) for Stephen Olson. The Schedule K-l reported that Stephen Olson’s distributive share of Solar’s ordinary loss was $568 and that his distributive share of the partnership’s qualified investment in property eligible for the regular and business energy investment tax credits was $181,495.
Stephen Olson and his wife Henrietta jointly filed a Form 1040 (“U.S. Individual Income Tax Return”), also for the taxable year 1983. In accordance with Stephen Olson’s distributive share of Solar’s ordinary loss, on their Schedule E (“Supplemental Income Schedule”) the Olsons reported a net loss of $568. On their Form 3468 (“Computation of Investment Credit”), the Olsons reported a tentative regular investment tax credit of $14,519.60 and a tentative business energy investment tax credit of $27,224.25, which were again attributable to Stephen Olson’s distributive share of Solar’s qualified investment in property eligible for those tax credits. Based upon these tentative claims, the Ol-sons’ regular investment tax credit was more than sufficient to eliminate their tax liability for 1983. Accordingly, the Olsons reported an allowed regular investment tax credit of $12,904.58 (to ehminate their 1983 tax liability of the same amount reported on their Form 1040) and an allowed business energy investment tax credit of zero.
Following this, the Olsons carried back their unused portion of the regular investment tax credit of $1,615.02 and their entirely unused business energy investment tax credit of $27,224.25 to eliminate their tax liabilities for the taxable years 1980, 1981, and 1982. To obtain refunds for these years, the Olsons filed a Form 1045 (“Application for Tentative Refund”) on March 14, 1984. The Olsons’ attachment to their Form 1045 showed an available carryforward to 1984 of $10,266.19 of the unused tax credits. On April 16, 1984, the IRS issued refunds to the Olsons for the three carryback years of approximately the amounts requested.
On May 6, 1985, the Olsons filed their Form 1040 joint income tax return for the taxable year 1984. On Schedule E of the return, the Olsons reported a net loss of $3,637, representing Stephen Olson’s distributive share of Solar’s ordinary loss for 1984. On their Form 3468 for the taxable year 1984, the Olsons reported a carryfor-ward of unused investment tax credits from 1983 of $10,266.19 and a total tentative investment credit of $10,513.63 (comprising the 1983 carryforward plus a current year investment credit of $247.44). Again, the Olsons’ tax credits were more than sufficient to eliminate their tax liability for the taxable year 1984. Accordingly, their Form 3468 reported an allowed credit of $7,008, which exactly offset the income tax liability of the same amount reported on the Olsons’ Form 1040. The record does not indicate whether the remaining credit of just over $3,500 was ever claimed by the Olsons.
By letter dated November 27, 1985, the IRS advised Stephen Olson that it was commencing a partnership-level examination of Solar. This examination was conducted and, as both parties agreed in the Court of Federal Claims, made timely by Solar and the IRS executing a Form 872-O (“Special Consent to Extend the Time to Assess Tax Attributable to Items of Partnership”). On November 16, 1989, the Olsons executed Parts I and II of Form 870-L(AD) (“Settlement Agreement for Partnership Adjustments and Affected *1314Items”) relating to the taxable year 1983 and the same two parts of the same form relating to the taxable year 1984.
Under the terms of Part I (“Offer of Settlement of Partnership Items”) of the Form 870-L(AD), the Olsons offered to enter into a settlement agreement “with respect to the determination of partnership items of the partnership for the year shown on the attached schedule of adjustments.” The schedule of adjustments attached to the Form 870-L(AD) for the taxable year 1984 contained no adjustments. The schedule for the taxable year 1983, however, reflected (1) a total allowable partnership loss of $137,090 for 1983 (instead of the loss of $10,042 reported on the Form 1065); and (2) disallowance of the partnership regular investment tax credit basis and the partnership business energy investment tax credit basis in the amount of $3,208,240. Part I of the Form 870-L(AD) also contained several other significant provisions. For instance, by executing Part I, the Olsons agreed they would “waive the restrictions on the assessment and collection of any deficiency attributable to partnership items ... provided in [Internal Revenue Code] section 6225(A),” that the treatment of partnership items under the settlement agreement would “not be reopened in the absence of fraud, malfeasance, or misrepresentation of fact,” and that “no claim for refund or credit based on any change in the treatment of partnership items may be filed or prosecuted.”
In Part II (“Offer of Settlement of Penalties”) of Form 870-L(AD), the Olsons offered to enter into a settlement agreement regarding penalties and interest attributable to the adjustment of partnership items. Under the proposed terms of Part II, the Olsons agreed “to penalties (additions to tax) and interest under section 6621(c) of the Internal Revenue Code, as shown on the attached schedule of adjustments.” With respect to penalties and interest, the schedule of adjustments provided that interest would apply to the Ol-sons’ underpayment pursuant to I.R.C. § 6621(c), and that a penalty would be assessed pursuant to I.R.C. § 6659 at a rate of 20%. Like Part I, Part II proposed that the treatment of penalties and interest would not be reopened absent fraud, malfeasance, or misrepresentation, and that “no claim for refund or credit based upon any change in the treatment of the penalties, including interest under section 6621(c) may be filed or prosecuted.”
Both Parts I and II required acceptance by the IRS Commissioner for the terms of the Olsons’ settlement offer to have any force or effect. Both Parts relating to both taxable years of 1983 and 1984 were duly accepted by the Commissioner on February 23, 1990.
On April 20, 1990, the IRS mailed to the Olsons a Form 4549-A (“Income Tax Examination Changes”), explaining how the adjustments to Solar’s 1983 partnership-level tax treatment affected their personal tax liability for the taxable years 1983 and 1984. The Form 4549-A for the taxable year 1983 reflected, inter aha, that the Olsons’ share of Solar’s disallowed tax credit bases resulted in a deficiency of $7,110 and a penalty of $1,442, plus applicable interest under I.R.C. § 6621(c). The taxes, penalty, and interest for the taxable year 1983 were paid in full by the Olsons and they have made no claim that they are entitled to a refund of those amounts.
With respect to the taxable year 1984, as a result of the IRS’s disallowance of their basis in Solar’s 1983 tax credits, a portion of which the Olsons had carried over to the 1984 return, the Form 4549-A reflected a deficiency of $6,275 and a penalty of $1,255, plus applicable interest.
Also on April 20,1990, the IRS mailed to the Olsons a second Form 4549-A explaining how the adjustments to Solar’s 1983 tax credit bases affected their personal tax liability for the taxable years 1980, 1981, and 1982. As a result of the IRS’s disal-lowance of the Olsons’ carrybacks of their unused shares of Solar’s tax credits from 1983, the Form reflected underpayments of $9,065 for 1980, $6,461 for 1981, and *1315$3,147 for 1982, together with a 20% penalty and applicable interest for each year.
On various dates between May 21 and June 18, 1990, the IRS assessed an aggregate total of $60,177.98 in taxes, penalties, and interest against the Olsons covering the years 1980, 1981, 1982, and 1984. The Olsons paid those amounts in full between May 25 and June 26,1990.
On May 28, 1992, the IRS received from the Olsons a Form 1040X (“Amended U.S. Individual Income Tax Return”) and a Form 843 (“Claim for Refund and Request for Abatement”) for the four above-mentioned taxable years. The forms requested full refunds for the amounts the Olsons had been assessed and paid. The IRS denied these requests for refunds by letter dated July 24,1992.
On July 24, 1994, the Olsons filed a complaint in the Court of Federal Claims seeking a refund of the taxes, interest, and penalties for 1980, 1981, 1982, and 1984. The Olsons asserted, inter alia, that the assessments were invalid because the Commissioner had not issued notices of deficiency prior to making those assessments. Approximately two years later, the parties filed cross-motions for summary judgment. On April 18, 1997, the Court of Federal Claims issued a decision granting partial summary judgment to the government. See Olson v. United States, No. 94-474T (Fed.Cl. Apr. 18, 1997). Judgment was entered on November 21, 1997, and the Olsons’ motion for relief from the judgment was denied on April 24, 1998.
The Court of Federal Claims held that the IRS was not required to issue notices of deficiency with regard to the amounts of tax at issue because these amounts were mere “computational adjustments” to which the deficiency procedures did not apply. Id., 37 Fed.Cl. at 737. It reasoned that under the Tax Equity and Fiscal Responsibility Act of 1982 (“TEFRA”), Pub.L. No. 97-248, 96 Stat. 324, 648-71 (1982), codified at I.R.C. §§ 6221-34, other than for a calculation error for which a taxpayer may bring a refund action, individual partners may not attack the underlying partnership-level determination that led to their computational adjustment. See id. at 734-35. Accordingly, because there is no partner-specific ground upon which to challenge the computational adjustment, the court explained that TEFRA obviates any requirement that the IRS issue a notice of deficiency to the individual partner before assessing additional tax pursuant to such an adjustment. See id. Given that notices of deficiency are not required under TEFRA when applying a computational partnership-level determination to a partner’s tax return for the same taxable year, the court reasoned that notices of deficiency should not be required for carryback or carryforward years either because the assessments are again merely computational adjustments. See id. at 734-36. The court also pointed out that, because the Olsons admitted that the tax credit they claimed over five years was invalid, it would “make[ ] no sense” to permit the IRS to collect the wrongfully withheld taxes in only one of the five years. Id. at 736. With regard to the penalties,1 the court concluded that notices of deficiency are generally required under I.R.C. § 6213(a). See id. at 737. However, the court reasoned that by executing the Form 870-L(AD) waiver, the Olsons not only waived their right to deficiency notices for the taxable year 1983, but also all years for which the disallowance of Solar’s partnership-level tax credits resulted in an underpayment of tax by the Ol-sons. See id. at 737-38.
Accordingly, the court granted the government’s motion for partial summary judgment, holding that the tax, penalty and interest assessments were validly as*1316sessed against the Olsons for the years in question despite the lack of notices of deficiency. See id. at 738. The Olsons appeal from both the grant of partial summary judgment and the denial of their motion for relief from the judgment.
The Cahoon, Gaus, and Lutter appeals
The Cahoons, Gauses, and Lutters each filed complaints seeking refunds for the taxable years 1980 and 1981. Along with each complaint was submitted a notice of related cases, stating that each case “involve[d] the same legal question” as Olson as to:
whether or not tax deficiencies resulting from adjustments to carrybacks to tax years ... resulting from adjustments to partnership items of a partnership subject to Internal Revenue Code Sections 6221-6232 (“TEFRA”) can be assessed as a computational adjustment without issuing a statutory Notice of Deficiency ... or whether a Notice of Deficiency is required because the adjustment is to an affected item requiring a partner level determination.
On June 15, 1995, the Court of Federal Claims issued orders suspending the three cases pending its decision in Olson. After issuance of the Olson summary judgment decision, the court issued orders stating that it was satisfied that Olson indeed disposed of the issues involved and thereafter entered judgment for the United States in all three cases.
This court consolidated the appeals in Olson and these three cases by order dated May 8,1998.
DISCUSSION
On appeal the taxpayers argue solely that the Court of Federal Claims erred because, without notices of deficiency, the tax, interest and penalties were improperly assessed and should therefore have been refunded. In particular, the taxpayers argue that Solar, as a partnership, was not permitted to claim any form of tax credit; they contend that only certain individual partners might be eligible to claim such tax credits. Thus, the argument goes, because some individual factual determination is apparently required to ascertain whether a partner is entitled to a tax credit, a notice of deficiency is required for any such assessment.
Under the Internal Revenue Code (the “Code”), a partnership is required to file an annual information return, but is not a taxable entity for federal income tax purposes. See I.R.C. §§ 701, 6031. Rather, the individual partners are responsible for reporting their distributive shares of the partnership’s income, loss, deductions, and credits on their individual tax returns, and then paying whatever allocable amount is due. See id. § 702.
Prior to the 1982 enactment of TEFRA, there was no administrative or judicial mechanism for making adjustments to the tax treatment of partnership items at the partnership level. Instead, adjustments had to be determined in separate proceedings involving each individual partner. If a partnership had numerous partners located throughout the country, there were often wasteful, duplicative expenditures of administrative and judicial resources, as well as inconsistency of results. See Transpac Drilling Venture, 1983-63 v. United States, 16 F.3d 383, 387 (Fed.Cir. 1994). Consequently, TEFRA was enacted in order that one proceeding would determine how partnership items would be reported on all partners’ individual returns. TEFRA thus requires partners, on their individual tax returns, to treat partnership items consistently with the item’s treatment on the partnership information return. See I.R.C. § 6222(a).
Under TEFRA, “the tax treatment of any partnership item ... shall be determined at the partnership level.” Id. § 6221. Section 6231(a)(3) of the Code authorizes the Secretary of the Treasury to prescribe which items constitute “partnership items” on the basis of “such items [being] more appropriately determined at the partnership level than at the partner level.” “Partnership items,” as defined by regulation, include items of gain, loss, de*1317duction, or credit claimed by the partnership. See Treas. Reg. § 310.6231(a)(3)-1(a). Likewise a “nonpartnership item” is one “which is (or is treated as) not a partnership item.” I.R.C. § 6231(a)(4).
Every partner has the right to participate in the IRS’s examination of the partnership’s information return. See id. § 6224(a). A partner may waive this right, however, and opt out of partnership-level proceedings by entering into a binding settlement agreement with the IRS. See id. §§ 6224(b), (c). By settling with the IRS, the settling partner’s “partnership items” become “non-partnership items.” See id. § 6231(b)(1)(C). Upon completion of the partnership-level proceedings, the IRS is required to mail to the tax matters partner and each notice partner a copy of the resulting final partnership administrative adjustment. See id. § 6223(a)(2). The tax matters partner then has ninety days to contest this adjustment by filing a petition for readjustment in the Tax Court, a district court, or the Court of Federal Claims. See id. § 6226(b). If a partner chooses not to opt out of the partnership-level proceeding, no assessment for a deficiency can be made until the later of 150 days after the final adjustment being mailed to the tax matters partner or the Tax Court making a final decision. See id. §§ 6225(a)(1), (2). Once an assessment is made, however, a participating partner generally may not bring a suit for a refund that is “attributable to partnership items.” Id. § 7422(h).
Under the non-partnership “standard” deficiency procedures of the Code, the IRS may not assess additional tax without first mailing a notice of deficiency to a taxpayer whose taxes have not been paid in full. See id. §§ 6211-16. Following this, the taxpayer may file a petition for redetermi-nation in the Tax Court, thereby, at least temporarily, preventing the IRS from assessing the tax. However, because a partner has the right to participate in the partnership-level proceeding and is bound thereby unless he or she has opted out by settlement, no notice of deficiency to a partner is necessary prior to the assessment of additional taxes that he or she owes resulting from the determinations in the partnership-level proceeding. Rather, the right to a hearing prior to an assessment of taxes that a notice of deficiency ordinarily provides is instead secured by granting every partner the right to participate in the partnership-level proceeding. In addition, every notice partner is informed of the administrative adjustments resulting from disallowance of tax credits.
Consequently, whether a notice of deficiency is required quite logically depends solely upon whether an item is classified as a “partnership item” or a “non-partnership item.” Tax adjustments derivative of “partnership items” require no notice of deficiency to partners. Tax adjustments derived from “non-partnership items,” however, require such a notice of deficiency.
Tax adjustments based upon an “overpayment attributable to a partnership item (or an affected item)” are not subject to the “standard” deficiency procedures and do not require a notice of deficiency. Id. § 6230(d)(6). An “affected item” is defined as “any item to the extent such item is affected by a partnership item.” Id. § 6231(a)(5). There are two types of affected items. The first involves a “computational adjustment,” that is, a “change in the tax liability of a partner which properly reflects the treatment under [TEFRA] of a partnership item.” Id. § 6231(a)(6). Here, “properly” can only mean “with mathematical accuracy.” Such “mere computational” affected items are not subject to the “standard” deficiency procedures and thus do not require notices of deficiency before making an assessment against the taxpayer. See Woody v. Commissioner, 95 T.C. 193, 202, 1990 WL 121140 (1990). The second type of affected item is one requiring a factual determination (other than a mere computation) at the partner level, such as a determination of negligence by that partner. For such items, a notice of deficiency is required. See N.C.F. Energy Partners v. Commis*1318sioner, 89 T.C. 741, 744, 1987 WL 45298 (1987).
We agree with the Court of Federal Claims that the assessments disputed here were mere “computational adjustments” requiring no non-computational, factual determinations at the partner level and thus were not subject to the Code’s standard deficiency procedures. By executing Form 870-L(AD) and entering into a settlement agreement with the IRS, the taxpayers conceded that they had no entitlement to either the regular investment tax credits or the business energy investment tax credits that they had formerly claimed. Because the tax credits claimed in 1983 were, by the taxpayers’ own admission, subject to disallowance, then, by definition, there can be no carrybacks or carryforwards from 1983 that could be claimed for the earlier and later years, for there was no valid credit to be applied to any year.
We are not persuaded that any form of non-computational determination was required to determine the amount of taxes, interest, and penalties to be assessed for these earlier and later years. As an initial matter, the regulations set forth that interest is to be included as a computational adjustment,2 see Temp. Treas. Reg. § 301.6231(a)(6)-1T(b), and the taxpayers expressly waived any right to a notice of deficiency with respect to penalties by executing Part II of the Form 870-L(AD). With respect to the taxes, the assessment appears to be a prime example of a mere computational adjustment because it apparently entailed nothing more than reviewing the taxpayers’ returns for the years in question, striking out the tax credits that had been improperly claimed, and re-summing the remaining figures. Although the taxpayers alleged that the appropriate amounts to be used to calculate the adjustments would not be ascertainable without certain additional information, including the sources of certain amounts already on the returns, this does not alter our analysis. That the IRS has to ask the taxpayer for a pertinent figure or for the source of a figure does not make the adjustment non-computational. Indeed, despite the fact that the IRS may need assistance as to the derivation of certain figures on the tax returns, no individualized factual determination takes place as to the correctness of the originally declared figures or any other factual matter such as the state of mind of the taxpayer upon filing. The critical question of fact — that is, the amount of tax credits improperly claimed as carrybacks and carryforwards — has already been resolved and stipulated to in a settlement agreement among the parties. The application of that stipulated fact to the tax returns in question requires only computational action. Further, it would surely undercut TEFRA’s goal of promoting a single, streamlined partnership-level determination that is binding on all participating partners, if we were to agree with the taxpayers that the application of a settled (here, conceded) partnership-level determination to an individual partner’s returns necessarily must involve unique factual determinations that are not merely computational.
In their briefing and at oral argument the taxpayers offered a number of hypothetical situations in which they alleged that partner-level, non-computational determinations would be required to assess taxes resulting from disallowed tax credits because different partners would be able to claim different amounts of tax credits. The situations alleged include, for instance, where different partners had different degrees of knowledge as to whether the transaction creating the disallowed tax credit was a sham, where different partners had different bases in their partnership interests, and where only certain partners were “at risk” by personally assuming or guaranteeing the debt arising from the partnership’s purchase of the *1319property that was the subject of the disallowed tax credit. We cannot properly express any view as to whether any of these hypothetical situations require non-computational determinations that would subject the assessment to the standard deficiency procedures — although we note that at oral argument the government conceded that, if an “at risk” determination were necessary, a notice of deficiency would be required. These expressly hypothetical situations are simply not present in the facts of this appeal and it is not our role to offer advisory opinions on hypothetical cases or controversies. See Muskrat v. United States, 219 U.S. 346, 361-62, 31 S.Ct. 250, 55 L.Ed. 246 (1911). The taxpayers argue that an “at risk” determination is always necessary because it must always be determined if a particular partner is, in fact, at risk. We find no merit in this position. No colorable allegation has been made here that any of these taxpayers’ deductions were in fact limited by the “at risk” rules of Section 465 of the Code and it cannot fall upon the government to prove the nonexistence of facts not even alleged. We thus do not agree with the taxpayers that a partner-level, non-computational “at risk” determination will always be necessary before an assessment can be made or that any such determination was necessary here.
CONCLUSION
The taxes, interest, and penalties assessed by the IRS resulted simply from computational adjustments arising from the disallowance of certain tax credits, to which the parties stipulated in their settlement agreement. Accordingly, no notices of deficiency were required and the judgments of the Court of Federal Claims are therefore
AFFIRMED.
. The Court of Federal Claims's April opinion stated that, absent a waiver, a notice of deficiency is required to assess interest under I.R.C. § 6621(c). See Olson, 37 Fed.Cl. 727, 737 (1997). On May 7, 1997, however, the court granted the government’s motion to delete the part of the opinion making that assertion. See Olson, No. 94-474T (Fed.Cl. May 7, 1997).
. No doubt, that is why the Court of Federal Claims vacated that part of its decision of April 21, 1997, to the contrary. See note 1, ante.