
    CEMENT DIVISION, NATIONAL GYPSUM COMPANY, Reed and Brown, Incorporated, New York Marine Managers, Incorporated, et al., PlaintiffsAppellees, v. CITY OF MILWAUKEE, Defendant-Appellant.
    No. 97-1349.
    United States Court of Appeals, Seventh Circuit.
    Argued Sept. 16, 1997.
    Decided May 28, 1998.
    
      Harney B. Stover (argued), Davis & Kuelthau, Milwaukee, WI, for Plaintiffs-Appellees.
    Rudolph M. Konrad (argued), Office of the City Attorney, Milwaukee, WI, for Defendanh-Appellant.
    Before CUDAHY, FLAUM, and MANTON, Circuit Judges.
   CUDAHY, Circuit Judge.

On December 4, 1992 (the settlement date), the defendant paid the plaintiffs $1,677,541.86 (the settlement amount) to settle, in part, a lawsuit. The suit involved the defendant’s liability for the sinking of a ship owned by one of the plaintiffs and insured by the others. The settlement left open only the extent of the defendant’s liability for prejudgment interest on the judgment. There was a difference of opinion whether prejudgment interest should be awarded at all, but that has been straightened out. See City of Milwaukee v. Cement Div., National Gypsum Co., 515 U.S. 189, 115 S.Ct. 2091, 132 L.Ed.2d 148 (1995), aff'g 31 F.3d 581 (7th Cir.1994). Now the question is simply how much prejudgment interest the defendant must pay.

I.

The district court for the Eastern District of Wisconsin awarded the plaintiffs prejudgment interest on the settlement amount at “the prime rate for the period from the date of the injury (December 24, 1979) through the date of the entry of judgment, which will occur on January 31, 1997, compounded annually.” 950 F.Supp. 904, 912 (E.D.Wis.1996). The bottom line: $6,497,641 in prejudgment interest. The City had advocated the use of its own borrowing rate (a municipal rate) rather than the prime rate. This approach would have reduced the award significantly. In selecting the prime rate over a lower municipal rate, the district court was guided by the Supreme Court’s reasoning in affirming this court’s earlier decision that these plaintiffs were entitled to prejudgment interest. According to the Supreme Court, the purpose of awarding prejudgment interest is to make the plaintiff whole: “The essential rationale for awarding prejudgment interest is to ensure that the injured party is fully compensated for its loss.” 515 U.S. at 195, 115 S.Ct. 2091 (footnote omitted). The district court concluded that an award based on a rate applicable to municipal debt would not fully compensate the plaintiffs, because their cost of funds was higher. In fact National Gypsum’s cost of funds exceeded the prime rate, but the district court considered the prime rate appropriate because of the City’s favorable credit rating—which was presumably superior to the plaintiffs’.

The district court also rejected the City’s argument that the size of the prejudgment interest award should be adjusted to account for the fact that it would be taxed when paid rather than as it accrued. The City contended that failing to adjust for the timing of tax liability would produce an award in excess of the amount the plaintiffs could have realized by investing the settlement amount at the time of the injury. According to the City, the plaintiffs’ annual earnings on such an investment would have been subject to income tax each year, so that only the after-tax yield could have been compounded. The City proposed that the court assume that the award of prejudgment interest would be taxed as a lump sum when paid, and set the award at an amount which, after such lump-sum taxation, would equal the amount the plaintiffs would have realized by investing the settlement amount at the time of injury and paying tax on interest as it accrued.

The district court thought that in principle the City’s proposed tax adjustment “would result in a more accurate calculation.” 950 F.Supp. at 910. But it considered the proposal impracticable. Because the record did not contain the plaintiffs’ net income or other staples of tax accounting, it did not permit calculation of what the plaintiffs’ tax liability actually would have been, if any, with respect to accrued interest on the settlement amount for each of the 17 odd taxable years at issue. The district court also noted that the defendant cited no legal authority in support of the proposition that an award of prejudgment interest should be discounted to account for the deferral of taxes, save for an academic commentary which itself cites no legal authority in support of this adjustment, see Michael S. Knoll, A Primer on Prejudgment Interest, 75 Tex.L.Rev. 293, 335-42 (1996).

Finally, the district court sided with the plaintiffs on whether they were entitled to interest on the unpaid balance of the judgment over the interval from the settlement date to the entry of judgment on the award of prejudgment interest on January 31, 1997 (the 1997 judgment date). In the plaintiffs’ brief to the district court, they proposed that postjudgment interest be awarded from the settlement date until the City paid the prejudgment interest award. In its brief, the City pointed out that, as of the settlement date, there was no judgment awarding prejudgment interest, and argued that post-judgment interest on the prejudgment interest could only run from the 1997 judgment date. In their reply brief, the plaintiffs countered that the City’s position implied that, if the postjudgment period had not commenced for the prejudgment interest award, then the plaintiffs were still entitled to prejudgment interest on the award of prejudgment interest from the settlement date through the 1997 judgment date. The district court viewed the parties’ arguments as a dispute over the dividing line between prejudgment and postjudgment interest, which could be resolved by determining the date post-judgment interest on the prejudgment interest award should begin. On the grounds that the prejudgment interest award would not be “ ‘ascertained’ in any meaningful way,” see Kaiser Aluminum & Chem. Corp. v. Bonjomo, 494 U.S. 827, 836, 110 S.Ct. 1570, 108 L.Ed.2d 842 (1990), until the 1997 judgment date, the district court concluded that postjudgment interest would run from the 1997 judgment date, with prejudgment interest accruing until that point. Since the prime rate was well above the statutory post-judgment interest rate over the period, the use of the prejudgment rate over this period would result in a significantly higher award.

II.

Unlike postjudgment interest, there is no statutory rate of prejudgment interest, see Gorenstein Enters, v. Quality Care-U.S.A., Inc., 874 F.2d 431, 436 (7th Cir.1989), and the amount of prejudgment interest required to properly compensate the victim can vary depending on the particular circumstances of the case. Accordingly, we entrusted the details of the calculation to the discretion of the district court, see 31 F.3d at 587, and our review is limited to whether the district court has reasonably applied the appropriate federal common law principles-including the guidance provided by our previous opinion. See United States v. Taylor; 487 U.S. 326, 336, 108 S.Ct. 2413, 101 L.Ed.2d 297 (1988); Cook v. Niedert, 142 F.3d 1004, 1011 (7th Cir.1998). In our opinion remanding for determination of prejudgment interest, we indicated that “the best starting point is to award interest at the market rate, which means an average of the prime rate for the years in question.” 31 F.3d at 587 (emphasis added). We suggested that the district court “consider'the City’s status as a municipality ... as a guide to setting the interest rate” in accordance with the City’s creditworthiness. Id. We did not, however, mandate that the district court use a municipal rate.

The City maintains that the district court abused its discretion by not using a municipal rate. Specifically, Milwaukee advocates calculating prejudgment interest “at the rate that [Milwaukee] would pay to borrow the amount of the original judgment with a simple, floating rate bond that was payable in full on the [1997] judgment date with no payments made prior to that date.” Knoll, supra, at 321. The City’s arguments, however, really only address whether the use of a municipal rate was permissible, not whether it was mandatory. Our cases have consistently indicated, as did our opinion remanding, that the district.court has the discretion not to engage in the kind of “refined rate-setting,” In re Oil Spill by the Amoco Cadiz Off the Coast of France on Mar. 16, 1978, 954 F.2d 1279, 1332 (7th Cir.1992) (per curiam), advocated by Milwaukee, and to “use the prime rate for fixing prejudgment interest where there is no statutory interest rate,” Gorenstein, 874 F.2d at 436. The City does not challenge this principle; it simply ignores it. Even if we construed the City’s position as an implicit challenge to this principle, the City does no more than argue that use of the prime rate yields an imprecise estimate. But we have encouraged the use of the prime rate despite recognizing that it “may miss the mark for any particular party,” Amoco Cadiz, 954 F.2d at 1332. Further, although in this ease the prime rate exceeds the interest rate charged by the City’s voluntary creditors, the plaintiffs were not voluntary creditors. Therefore here a municipal rate is at best “the minimum appropriate rate for prejudgment interest, because the involuntary creditors] might have charged more to make a loan.” Id. at 1331 (emphasis added). There must certainly be an upper, as well as a lower, bound to the district court’s discretion, but our previous opinion indicated that both the prime rate and a municipal rate would fall within an acceptable range. The district court did consider using a municipal rate, but rejected it based on the evidence before it, on the grounds that it would not provide full compensation to the plaintiffs. Since the district court reasonably weighed the evidence in accordance with the applicable principles, its selection of the prime rate was not an abuse of discretion.

III.

On the issue of adjusting for tax deferral, the City also has failed to reconcile its challenge to the principle that the district court is not required to engage in refined rate setting. The district court’s refusal to consider tax deferral was a reasonable decision in light .of the inadequacy of the record. The City does not dispute the district court’s conclusion that the record was inadequate for this purpose. On appeal, the City suggests that it was the plaintiffs’ responsibility to introduce evidence proving that the tax liability would have been less than the City’s estimates; otherwise, the district court should have assumed that the subrogor plaintiff, National Gypsum, was subject to tax at the maximum corporate rate. But this argument was not made to the district court, despite the fact that the academic study the City relied on advocated the use of the maximum tax rate only as a default rule “that the court can deviate from ... by using explicit information from the parties about their tax status and tax rates.” The record contains no indication that the City attempted to obtain information about National Gypsum’s tax attributes over the relevant period. Under these circumstances, the district court decision was clearly not an abuse of discretion.

IV.

The City contends that the district court had no authority to award additional prejudgment interest after the payment of the settlement amount on the settlement date. Compounding interest past the settlement date, the City declares, results in “prejudgment interest on prejudgment interest,” Br. of Def.-Appellant 46, which would have the perverse effect of “compounding the interest twice,” id. at 48.

The City does not deny that compound interest must be awarded through the 1997 judgment date in order to fully compensate the plaintiffs. No rational investor would voluntarily buy a zero-coupon bond that only guaranteed repayment of the issue price at maturity and allowed the issuer an option to pay the balance (representing the accrued interest at maturity), with no additional interest, at an unspecified time in the future. But the City, after extolling the rich insights provided by economic principles in determining the proper prejudgment -rate, now maintains that even if economic logic indicates that the plaintiffs are entitled to interest through the 1997 judgment date, that result is impermissible because it is not expressly sanctioned either by statute or under the common law.

The City correctly notes that no statute resolves this issue. We turn, therefore, to the City’s spin on the common law. First, the City points out that in Devex Corp. v. General Motors Corp., 749 F.2d 1020, 1026 (3d Cir.1984), the Third Circuit concluded that “awarding interest on postjudgment interest would amount to the compounding of interest,” and was consequently unacceptable. Postjudgment interest, however, is governed by a federal statute, 28 U.S.C. § 1961; “prejudgment interest is governed by federal common law, and the courts are free to adopt a more discriminating approach.” Gorenstein, 874 F.2d at 437; see also 515 U.S. at 194, 115 S.Ct. 2091. It is, of course, settled in the case law that compounding of prejudgment interest is acceptable. See Amoco Cadiz, 954 F.2d at 1337; see also Knoll, supra, at 307-08. When prejudgment interest is compounded annually, after the first year annual interest is determined by multiplying the sum of the original damages and the interest accrued in previous years by the prevailing interest rate. Thus even the total award of interest through the settlement date must include “interest on interest” as well as interest on the settlement amount. In the case of prejudgment interest, if the compounding of prejudgment interest is acceptable, it follows by definition that “interest on interest” must be permissible.

Next, the City claims that Cherokee Nation v. United States, 270 U.S. 476, 490, 46 S.Ct. 428, 70 L.Ed. 694 (1926), established that unpaid interest is not damages. That conclusion, however, was confined “to interest against the United States” in a contract dispute. Id. And the holding of Royal In demnity Co. v. United States, 313 U.S. 289, 295, 61 S.Ct. 995, 85 L.Ed. 1361 (1941), is not that “interest on interest is not an appropriate measure of damages for the delayed payment of interest alone,” Br. of Def.-Appellant 48; actually, the Supreme Court rejected a lower court decision that had denied the recovery of interest “as damages for delayed payment of a contractual obligation to the United States.” 313 U.S. at 296, 61 S.Ct. 995.

Finally, the City observes that in Brooklyn Savings Bank v. O’Neil, 324 U.S. 697, 715, 65 S.Ct. 895, 89 L.Ed. 1296 (1945), the Supreme Court did not allow interest on damages recovered under § 16(b) of the Fair Labor Standards Act of 1938 (FLSA), 29 U.S.C. § 216(b) (1938). Section 16 of the FLSA specifies the penalties imposed on employers that fail to pay minimum wages, required overtime wage rates and so on. It provides that employees deprived of the minimum wage are entitled to the “amount of their unpaid minimum wage ... and ... an additional equal amount as liquidated damages.” 29 U.S.C. § 216(b). In O’Neil, the Supreme Court concluded that Congress intended the matching liquidated damages to compensate employees for the delayed payment of their wages; therefore, interest on the damages would be redundant. 324 U.S. at 715, 65 S.Ct. 895. The City does not identify the source of any comparable redundancy here, and there is none.

We think the relevant common law is this: “Prejudgment interest ... is part of the actual damages sought to be recovered.” Monessen Southwestern By. Co. v. Morgan, 486 U.S. 330, 335, 108 S.Ct. 1837, 100 L.Ed.2d 349 (1988); see also United States v. American Commercial Barge Line. Co., 988 F.2d 860, 864 (8th Cir.1993). The Supreme Court has already explained in this case that prejudgment interest constitutes “compensati[on] ‘for the loss of use of money due as damages from the time the claim accrues until judgment is entered,’ ” 515 U.S. at 196, 115 S.Ct. 2091 (quoting West Virginia v. United States, 479 U.S. 305, 310-11 n. 2, 107 S.Ct. 702, 93 L.Ed.2d 639 (1987)) (emphasis added). This refutes the City’s suggestion that prejudgment interest accrues only in conjunction with the settlement amount.

We also note that the City’s argument does not turn on the fact that the settlement amount was paid on the settlement date, when a partial judgment was entered. Therefore the City’s position would imply that the date of the payment of the settlement amount should have ended the accrual of prejudgment interest on the balance owed to the plaintiffs even if that payment had occurred before any judgment had been entered. (It is of course undisputed that interest on the settlement amount ceased to accrue when the settlement amount was paid.) But the City has cited no authority that attributes any relevance to the date of payment of the original amount of the loss. In fact, the very name “prejudgment” interest strongly suggests that the relevant date is a judgment date.

We conclude that prejudgment interest must continue to accrue on any unpaid damages until the 1997 judgment date. Prejudgment interest was not determined until the 1997 judgment date, and therefore damages were not determined until then. It follows that the district court was correct to identify the 1997 judgment date as the date of the relevant entry of judgment for the purpose of the prejudgment interest award.

The judgment of the district court is Affirmed. 
      
      . Under either party's proposed methodology, the prejudgment interest was calculated according to a formula (in some cases with certain adjustments) S [(1+r1980)(1+r1981) ... (1+r1992)—1], where S represents the settlement amount, and represents the value of the chosen interest rate series during year i. Under this procedure, the settlement amount is compounded annually at the value of the chosen interest rate series during each year of the interval from the injury date to the settlement date. As explained below, the district court extended the compounding through January 1997. The calculations proposed by the City would have resulted in an award between $1,664,898.35 and $2,579,111.60.
     
      
      . In the City’s view, the district court lacked a quality almost as essential in modem times as judicial temperament—respect for economic principles. See Br. of Def.-Appellant 25. The district court purportedly failed to grasp that the plaintiffs’ claim was an asset the value of which was determined by the City's borrowing rate. So if the plaintiffs had no other creditors, for example (a convenient simplification), they supposedly could have borrowed an amount equal to the settlement amount at the City’s borrowing rate. See Knoll, supra, at 315; see also James Patell et al., Accumulating Damages in Litigation: The Role of Uncertainty and Interest Rates, 11 J. Legal Stud. 341, 342 (1982). That is because the plaintiffs, with no other creditors and an investment in the City, would be forced to default only if the City defaulted; the claim would be, in effect', the lender’s collateral. Therefore a lender’s loan of the settlement amount to the plaintiffs should have the same value as the plaintiffs’ claim. The City’s analysis does not adequately address the contingent nature of a legal claim, however. See Patell et al., supra, at 363-64. Because the success of the plaintiffs’ suit was uncertain at the time of the injury, the plaintiffs' involuntary investment in the Cily was a risky one. That risky investment would not have allowed the plaintiffs to borrow the full settlement amount at a municipal rate even if they had no other creditors.
      Perhaps we should ignore the risk associated with litigating the City's liability for the settlement amount. See Knoll, supra, at 311 n. 98. But that would still leave the risk associated with the uncertainty of the award of prejudgment interest, a risk amply demonstrated by the course of this phase of the litigation. Even after conceding its liability for damages, the City contended that the plaintiffs were not entitled to any prejudgment interest. See 515 U.S. at 192-94, 115 S.Ct. 2091. Assuming that the City took this position reasonably and in good faith as late as 1992, it is hard to see why in 1979 a lender to the plaintiffs would have considered a loan in the full settlement amount to be equivalent to an investment in the City of the same amount: the lump-sum interest the plaintiffs would owe that lender at maturity would not be fully collateralized. Further, at the time of the injury, a potential lender to the plaintiffs might have expected them to receive at most only simple prejudgment interest, see 1 Dobbs Law of Remedies § 3.6(4) (2d ed.,1993); Br. of Def.-Appellant 37. For these reasons, the value of the claim (and thus the plaintiffs’ collateral for a, loan) at the time of the injury would be less, perhaps .a great deal less, than the settlement amount. So even if the plaintiffs’ entitlement to the settlement amount were undisputed, the plaintiffs would have had to pay a significant premium over the City’s borrowing rate in order to borrow the full settlement amount. The City’s contention that only a "gross misunderstanding of ... economic principles” explains the district court’s selection of the prime rate seems itself to be based on an incomplete appreciation of economics.
     
      
      . The district court apparently thought that our suggestion to consider the use of a municipal rate had to be qualified in light of the Supreme Court's opinion in this case. See 950 F.Supp. at 909. Because the district court was obviously correct to attempt to compensate the plaintiffs in full, we express no view whether the Supreme Court’s opinion narrowed the range of acceptable interest rates established by our precedents, including our prior opinion in this case.
     
      
      . This statement appeared in a preliminary version of Knoll, supra, dated August 24, 1995, at 39-40, submitted to the district court by the City. It does not appear in the published article. Cf Roman L. Weil, Compensation for the Passage of Time, in Litigation Services Handbook (Roman L. Weil et al. eds., 2d ed. 1995) 37 • 6 ("Most corporations have available tax-planning strategies (as well as timing differences) that enable them to pay income tax at a rate lower than the marginal [tax] rate ...."); id at 37 • 7 (concluding that proper tax rate to be used in accounting for income taxation is not necessarily statutory rate and that appropriate rate "seems an issue of fact for the court ... to decide").
     
      
      . The City's argument that interest on a loan to the City by the plaintiffs would have been taxed as it accrued is based on § 1272 of the Internal Revenue Code, 26 U.S.C. § 1272; see also 26 U.S.C. §§ 1271, 1273-1275.. See generally David C. Garlock et al.. Federal Income Taxation of Debt Instruments (3d ed.1998). But that provision was not added to the tax code until 1984, see Pub.L. 98-369, § 41(a), 98 Stat. 533. Before 1982 the accrual of unpaid interest applied generally only in the case of corporate bonds, see 26 U.S.C. § 1232(a)(2) (1976 & Supp. V 1981) (revised 1982, repealed 1984), not government bonds. So if at the time of the injury the plaintiffs had bought a zero-coupon taxable City bond maturing on the 1997 judgment date, the bond would not have been subject to § 1272, which was not applied retroactively to debt issued before July 2, 1982. Therefore, in the case of a taxpayer using the cash method of tax accounting (taxed on income when received), the accrued interest would have been taxed as ordinary income upon its lump-sum payment at maturity. See 26 U.S.C. § 1271(c)(2)(A). We express no view whether the subrogor plaintiff National Gypsum, as a corporation presumably using the accrual method of tax accounting, see 26 U.S.C. § 448(a)(1) (mandating accrual tax accounting by most large corporations beginning 1987); Knight-Ridder Newspapers, Inc. v. United States, 743 F.2d 781, 788-89 (11th Cir.1984) (illustrating that accrual tax accounting generally would apply to large corporations before 1987), could have been taxed on accrued original issue discount anyway. See United States v. Midland-Ross Corp., 381 U.S. 54, 58 n. 4, 85 S.Ct. 1308, 14 L.Ed.2d 214 (1965); Dixon v. United States, 381 U.S. 68, 70 n. 1, 85 S.Ct. 1301, 14 L.Ed.2d 223 (1965); 26 C.F.R. § 1.446-2 (applicable to debt instruments issued on or after April 4, 1994); Henry de Kosmian, Original Issue Discount, 22 Tax Lawyer 339, 344-47 (1969).
     