BOWMAN, Circuit Judge.

IES Industries, Inc., appeals from the judgment of the District Court awarding federal tax refunds to IES, but in an amount far less than IES seeks. We affirm.

I.

This tax refund case is before us for the second time. In the first appeal, IES challenged the District Court's decision that the Internal Revenue Service (IRS) had properly characterized a series of securities trades in which IES had engaged as sham transactions for tax purposes. We reversed and remanded. IES Indus., Inc. v. United States, 253 F.3d 350 (8th Cir. 2001). We affirmed on the IRS's cross appeal of the decision to award IES a tax refund related to the assessment of environmental cleanup costs, and that issue is not before us in this second appeal. For the interested reader, the facts regarding the refunds are set out in detail in our first opinion. We will repeat them here only as necessary to explain our decision today.

In 1991 and 1992, IES engaged in the purchase and sale of American Depository Receipts, or ADRs. As a result of the somewhat complicated transactions, IES, among other things, recognized capital losses and sought to offset capital gains earned in 1989 and 1990; claimed a foreign tax credit; and deducted other expenses in connection with the trades. IES also reported gross dividend income of nearly $90.8 million. After an audit, the IRS declared the ADR trades to be sham transactions, without economic substance. The IRS disallowed the capital losses and capital-loss carrybacks, as well as the foreign tax credit. Moreover, the IRS eliminated the reported foreign dividends from IES's income, just as it "disallowed all [other] results of [IES's] ADR trades." Brief of Appellee at 19. IES paid the taxes and filed a refund suit in the District Court. That court agreed with the IRS's conclusion that the ADR trades were sham transactions. On appeal, we determined that the ADR trades did not lack business purpose or economic substance, that is, that they were not shams, and remanded "for further action consistent with" our opinion. IES Indus., Inc., 253 F.3d at 356.

After remand, on December 14, 2001, IES and the IRS filed a joint report concerning the final judgment. They agreed that IES should have judgment (1) for a refund of $26,033.00 plus interest for tax year 1989 and (2) for a refund of $25,976,839.00 plus interest for tax year 1990. The parties were unable to agree to judgment for tax year 1992. On January 15, 2002, the IRS filed a motion to amend its answer to conform to the evidence, which IES opposed. The IRS believed it should be able to add to its answer the affirmative defenses of offset and equitable recoupment, to set off refunds owed to IES for tax years 1989, 1990, and 1992 because IES owed additional taxes for 1991 and 1992 for the foreign (ADR) dividends paid to the company in those years. The IRS asserted that it was entitled to those equitable defenses notwithstanding that the applicable statute of limitations would preclude the IRS from assessing and collecting any taxes for years 1991 and 1992.

The District Court granted the IRS's motion to amend, allowed the defenses, and entered judgment for IES in an amount almost $13.9 million less than the amount of IES's overpayment plus interest. Specifically, the court held that the IRS could "properly seek an offset of the $4,615,405 1992 refund based upon the inclusion of the previously removed $46.1 million of 1992 dividend income," completely eliminating the claimed refund for that year. Order of July 22, 2002, at 4. The court also ordered that the IRS "shall be permitted to equitably recoup the 1991 and 1992 tax underpayments from the 1989 and 1990 tax overpayments resulting from reversing the IRS adjustments in this matter." Id. at 6. IES appeals.

II.

For its first issue on appeal, IES claims that the District Court's decision is contrary to the mandate of this Court. We disagree. Nowhere in our opinion did we address the issues of offset and equitable recoupment as they may relate to taxes owed on IES's foreign dividend income. We said nothing at all about equitable recoupment, and our only comment on offset was in a footnote, where we noted the IRS's argument that it mistakenly allowed "IES to claim deductions for interest, commissions, and one-half of the foreign income tax withheld [relating to the ADR trades], and sought an offset against any overpayment of taxes by IES (that is, refunds due IES)." IES Indus., Inc., 253 F.3d at 353 n. 3. We said our holding — that the ADR trades had economic substance for tax purposes — resolved the offset issue, but we did not address offset or equitable recoupment in connection with the ADR dividends that the IRS eliminated from income when it audited IES's 1991 and 1992 tax returns, declared the ADR trades to be shams, and redetermined IES's tax liability for those years.

We did acknowledge the foreign dividends that resulted from the ADR trades in our opinion, but specifically to note that those dividends were income, that is, taxable, to IES. See, e.g., id. at 352 ("IES retained the dividends, which were ordinary income to the company. . . ."), 354 ("[T]he entire amount of the ADR dividends was income to IES. . . ."). The ultimate taxability of the dividends specifically, after we resolved the tax status of the ADR trades generally, was not on the Court's radar screen because it was not a question that needed to be answered in order to decide the appeal. We remanded "for further proceedings," never indicating, as IES suggests, how or in what amount judgment should be granted for IES on the ADR trades. Id. at 359. We did not remand for entry of judgment in the amount IES sought to have refunded, and so the issue was not, as IES contends, "settled on appeal." Reply Brief of Appellant at 7. There is no law of the case set out in our first opinion regarding the actual amount of the judgment to be entered on remand.

We reject IES's attempt to read between the lines of our opinion so as to interpret what we said to the company's advantage. The text of the opinion makes clear what we subjectively know: this Court did not intend to decide, and we did not decide, any question relating to any taxes IES may owe on the foreign dividends that the IRS originally excluded. We hold that the District Court's decisions to allow the amendment sought by the IRS and to allow the defenses were not in violation of our mandate.

III.

We next consider IES's argument that the District Court abused its discretion when it granted the IRS's motion made under Federal Rule of Civil Procedure 15 to amend its answer. See Clark v. Martinez, 295 F.3d 809, 815 (8th Cir. 2002) (standard of review). Under Rule 15(b), an issue not raised in the pleadings, but tried by express or implied consent of the parties, " shall be treated" as having been raised in the pleadings. Fed.R.Civ.P. 15(b) (emphasis added). Thus, "[s]uch amendment of the pleadings as may be necessary to cause them to conform to the evidence and to raise these issues may be made upon motion of any party at any time, even after judgment." Id. (emphasis added).

A.

According to IES, the District Court erred on remand in granting the motion to amend because the IRS had expressly waived its right to assert the affirmative defenses of offset and equitable recoupment by the time the government sought to amend its answer. IES did not mention this "express waiver" theory in its opposition to the government's motion to amend, which is probably why the District Court does not refer to it in its order granting the motion. Nevertheless, we will assume (without deciding) that IES's contention that the IRS's failure to assert its offset and recoupment defenses earlier put the District Court on notice of a waiver issue, that the District Court considered waiver when granting the motion, and that the issue is therefore properly before this Court on appeal.

The first waiver, according to IES, is found in a footnote in the government's memorandum in support of its partial summary judgment motion filed in the District Court before the first appeal. In that note, the IRS stated that the return of the ADR dividends to IES's income for tax years 1991 and 1992, should IES be entitled to its claimed capital-loss carrybacks, was not an issue on summary judgment. That was true. It would be a distortion of the IRS's position to read that one sentence in a footnote in its summary judgment memorandum to constitute a knowing and intelligent relinquishment of its right to raise the defenses of offset and equitable recoupment at some point later in the litigation, when the dividend income might become an issue. The government did raise the defenses, by seeking to amend its answer, when those defenses became an issue in the case after it lost on appeal. Cf. Buder v. United States, 7 F.3d 1382, 1386 (8th Cir. 1993) (holding that offset defense was waived when it was not raised until ten days before the trial date, and "the Government never pleaded or amended its complaint to include the setoff defense").

The other proof of waiver to which IES points presents a closer call. As we explained above, in the joint report filed with the District Court six months after our opinion was issued and one month before the IRS filed its motion to amend, the IRS agreed with IES as to the refund amounts due IES for tax years 1989 and 1990-amounts that did not reflect any reductions for taxes IES owed on ADR dividend income for tax years 1991 and 1992. (As we have said, the parties did not agree as to the amount of judgment to be entered for tax year 1992, so this basis for waiver cannot apply to the offset defense.) The agreement is problematic for the IRS's equitable recoupment defense because the joint report filed in the District Court purports to "advise the Court with respect to the entry of a final judgment" of the amounts owed to IES for tax and interest. Parties' Report Concerning Entry of Judgment (Dec. 14, 2001). Nevertheless, we cannot say that the District Court erred in disregarding the joint report when deciding to grant the IRS's motion to amend because we do not believe the joint report constituted a knowing and intelligent relinquishment of the IRS's right to assert an equitable recoupment defense. The report is not a stipulation to judgment in an amount certain; it only gives figures to be used "with respect to the entry" of judgment. We will not assume the government considered possible reductions to the refunds due IES and knowingly waived the defenses that would result in such reductions.

To the extent the issue of waiver was before the District Court, we cannot say that the court erred in failing to hold that the IRS waived its right to amend its answer to assert the defenses of offset and equitable recoupment.

B.

Next IES argues that a Rule 15(b) amendment should not have been permitted because the company did not consent, expressly or impliedly, to trial of the issue in the initial proceeding, as required by the language of the rule. IES's argument is not persuasive.

Throughout the proceedings in the District Court, IES took the position — indeed, it insisted — that 100% of the ADR foreign dividends was income to the company. IES had initially reported all of the dividend income to the IRS, and the parties stipulated to those amounts, totaling nearly $90.8 million. We think it somewhat disingenuous of IES to suggest that it was somehow surprised to learn, as the result of a "last-minute ambush," Brief of Appellant at 40, that the government, in seeking to amend its answer on remand, would rely on IES's consistent contention regarding the taxability of 100% of the dividends in order to recover taxes that IES had admitted it owed on the dividends. There is no suggestion here that the evidence before the District Court does not support the defenses raised in the amended answer. See Gray v. Bicknell, 86 F.3d 1472, 1481 (8th Cir. 1996) (finding no abuse of discretion in denial of Rule 15(b) motion to amend complaint where "the claims [the appellant] sought to add lacked substance"). In fact, with the stipulation to the amount of foreign dividends paid as a result of the ADR transactions, there seems very little left to be tried. If IES did not expressly consent to trial of the issue by repeatedly contending throughout the litigation that the foreign dividends were taxable, then it surely impliedly consented. See Modern Leasing, Inc. of Iowa v. Falcon Mfg. of Cal., Inc., 888 F.2d 59, 63 (8th Cir. 1989) ("Consent may be implied when evidence relevant to an unpleaded issue has been introduced at trial without objection." (quoting St. Joe Minerals Corp. v. Occupational Safety Health Review Comm'n, 647 F.2d 840, 844 (8th Cir. 1981))). The District Court did not abuse its discretion in concluding as much.

IES further contends that "Rule 15(b)'s consent requirement is not met where evidence that is relevant to an issue purportedly tried by consent is also relevant to an issue already in the case." Brief of Appellant at 37. That is an overstatement, if not a misstatement of the law. There is no bright-line rule of the sort IES suggests. It is axiomatic that evidence bearing on both claims and the defenses to those claims may well overlap in a given case. Such an inevitability does not foreclose amendment under Rule 15(b).

C.

IES also takes issue with the District Court's finding, in granting the motion to amend, that IES would not be prejudiced by the amendment, a finding that IES claims is not relevant when deciding such a motion. But the cases cited by IES in support of this argument stand for the proposition that a lack of prejudice to the non-moving party, standing alone, may not be a sufficient basis for granting the motion. Those cases do not suggest that prejudice or the lack thereof should be wholly disregarded when deciding a Rule 15 motion. Cf. Coohey v. United States, 172 F.3d 1060, 1064 n. 8 (8th Cir. 1999) (explaining that failure to plead equitable recoupment did not preclude its being raised even "on appeal where the evidence supports that defense" and noting that the taxpayers "suffered no prejudice").

IES claims that, in any event, the company — and the judicial system itself — suffered actual prejudice from the piecemeal nature of the litigation in this case and that the District Court therefore abused its discretion in granting the motion to amend. But this litigation has not been "piecemeal" as a result of the District Court's decision to grant the motion to amend. In reality, we do not think the litigation has been piecemeal at all, and to the extent it has been, it is the result of our first decision reversing and remanding the case, not the District Court's decision to allow the IRS to amend its answer. Because the District Court originally decided that the ADR trades were sham transactions, the court probably would not have addressed the IRS's defenses in the initial proceedings even if they had been raised. Likewise, those defenses would not have been issues in the first appeal. Even if raised in the government's initial answer, offset and equitable recoupment would not have been considered by the District Court until remand, precisely when the government's motion to amend made the defenses an issue. It was not necessary to prolong the litigation — to reopen discovery or to put on new evidence — for the court to decide the merits of the IRS's defenses because all that remained were questions of law, the parties having stipulated to the amount of the foreign dividends paid on the ADR trades. Further, IES had "ample opportunity to respond" to the defenses. Id. We hold that IES was not prejudiced by the District Court's decision to grant the motion to amend.

D.

In sum, given the deferential standard of review of district court decisions to grant Rule 15 amendments, we cannot say that the District Court in this case erred in allowing the IRS to amend its answer. That is not to say we would have decided the motion as did the District Court. The taxability of 100% of the dividend income from the ADR trades, if the IRS's determination that they were sham transactions did not hold up, was readily apparent when IES first sought a refund. Nevertheless, even after we held that the trades were not sham transactions — in part because, as we explicitly said in our opinion, 100% of the foreign dividend income was taxable to IES — the IRS sat on its rights. Counsel for the government even joined in submitting to the District Court on remand an agreement as to refunds due IES, which agreement did not take account of the available defenses finally asserted a month later. The defenses of offset and equitable recoupment should in no way have been novel to counsel for the IRS, of all people. Had we been in the District Court's shoes, we may well have decided the issue differently. But we are not tasked with a de novo review of the decision to grant the motion to amend, and we cannot say the court abused its discretion in deciding as it did.

IV.

We turn now to IES's challenge to the merits of the District Court's decision to allow the government's defense of equitable recoupment. We review findings of fact for clear error and conclusions of law de novo. Townsend Indus., Inc. v. United States, 342 F.3d 890, 891 (8th Cir. 2003).

As the Supreme Court has explained, a statute of limitations that forecloses a long look-back in tax cases "is an almost indispensable element of fairness as well as of practical administration of an income tax policy," to the benefit at times of both the taxpayer and the government. Rothensies v. Elec. Storage Battery Co., 329 U.S. 296, 301, 67 S.Ct. 271, 91 L.Ed. 296 (1946); see also id. at 302, 67 S.Ct. 271 ("As statutes of limitation are applied in the field of taxation, the taxpayer sometimes gets advantages and at other times the Government gets them."). Even a "just claim" must be pursued, or it will be lost. Id. at 301, 67 S.Ct. 271.

But the doctrine of equitable recoupment in federal tax jurisprudence allows a court in limited situations to disregard a statute of limitations in order to further "the public interest that no one should be permitted to avoid his just share of the tax burden except by positive command of law." Stone v. White, 301 U.S. 532, 537, 57 S.Ct. 851, 81 L.Ed. 1265 (1937). In the seminal case on the doctrine, the Supreme Court said, "[R]ecoupment is in the nature of a defense arising out of some feature of the transaction upon which the plaintiff's action is grounded." Bull v. United States, 295 U.S. 247, 262, 55 S.Ct. 695, 79 L.Ed. 1421 (1935). As distinguished from offset, equitable recoupment allows the IRS to set off a refund due a taxpayer for one tax year by an underpayment from a different year, but only in the circumstances described by the Court. The purposes of limitations statutes in federal tax litigation caution against a broad application of equitable recoupment, so the doctrine may be successfully invoked only in narrowly defined cases. Rothensies, 329 U.S. at 301-02, 67 S.Ct. 271. "[A] party litigating a tax claim in a timely proceeding may, in that proceeding, seek recoupment of a related, and inconsistent, but now time-barred tax claim relating to the same transaction." United States v. Dalm, 494 U.S. 596, 608, 110 S.Ct. 1361, 108 L.Ed.2d 548 (1990).

At issue here is the "single transaction, item, or taxable event" requirement. Id. at 605 n. 5, 110 S.Ct. 1361 (citing Rothensies, 329 U.S. at 299-300, 67 S.Ct. 271). The defense does not permit "one transaction to be offset against another," but will allow a single "transaction which is made the subject of suit by a plaintiff to be examined in all its aspects, and judgment to be rendered that does justice in view of the one transaction as a whole." Rothensies, 329 U.S. at 299, 67 S.Ct. 271. IES argues that the government's claim for equitable recoupment must fail because this case involves not a single transaction but three: purchase of the ADRs, payment of the foreign dividends, and sale of the ADRs. The District Court acknowledged the single transaction argument but did not address it.

It is tempting to declare that the inconsistent tax claims — refunds for capital-loss carrybacks and taxes owed on all of the foreign dividends — were related to different transactions. After all, the taxability of the dividends seems to be independent of the capital loss resulting from IES's sale of the ADRs, since the dividends would have been paid even if IES, after receiving the dividends, had not sold the ADRs. But having carefully considered the question, we conclude otherwise. Each ADR trade in its entirety — purchase, payment of dividends, sale — was treated by IES (and the company that sold the idea to IES) as a single transaction. In order for us to determine, in our first opinion in this case, that the trades were not sham transactions, and to conclude instead that they had business purpose and economic substance, we considered each trade as a whole, just as IES asked us to. IES purchased the ADRs for market price plus 85% of the expected dividend. After the dividend was paid to IES, it sold the ADRs for only market price, which resulted in the capital losses. It is inconceivable that IES would have agreed to sell at a loss (which would trigger one tax treatment) but for its anticipated receipt of the foreign dividends (which would trigger the second tax treatment). Indeed, the amount of the purchase price/sale price — that is, the amount of the loss — was calculated before the ADRs were purchased based on the amount IES expected to collect in dividends. In these circumstances, we must hold that the ADR trades were a single transaction.

As IES has made the trades the subject of suit, the doctrine of equitable recoupment gives the courts authority to examine them "in all . . . aspects." Id. Having done so, we conclude that the judgment of the District Court "does justice in view of the one transaction as a whole." Id. The judgment is affirmed.