PER CURIAM.
This case involves a long-running (six years and counting) insurance-coverage dispute between the City of Sterling Heights, Michigan, and one of its insurance carriers, United National Insurance. The case arises out of lawsuits filed by Hillside Productions against the City based on alleged misconduct by city officials, and the question at hand primarily concerns United’s liability for a portion of a settlement of the lawsuit between the City and Hillside. We affirm in part, reverse in part and remand for additional proceedings.
I.
In 1999, Hillside obtained a lease for a portion of Freedom Hill Park, with the goal of developing an entertainment venue at an amphitheater located in the park. The City initially encouraged Hillside’s development of Freedom Hill, telling Hillside that it would exempt the company from several site-permit requirements. When Hillside refused the City’s demands to pay for police and other services, however, the City changed course, requiring Hillside to apply for a special-approved-land-use permit (SALU). Hillside complied, and the City approved the SALU in February 2001.
Relations between Hillside and the City worsened after this incident. Beginning in April 2001, City officials cited Hillside for building-permit, noise and other violations. In August 2001, after receiving complaints from area residents, the City determined that Freedom Hill was a nuisance based on its violations of noise and other ordinances. At roughly the same time, the City Manager, Steve Duchane, allegedly began to hinder Hillside’s operations in several ways, issuing citations, sending squads of police to concerts to harass patrons and staff, refusing to issue building permits and alcohol licenses and interfering with a possible construction deal that may have been worth $200 million.
The state-court lawsuit.
Hillside challenged the City’s actions in a state-court lawsuit. In addition to seeking declaratory and injunctive relief on the ground that the SALU exempted Hillside from the City’s restrictions, Hillside sought $14 million in damages — the value of its investment in the facility up to that point. Hillside (1) alleged that the City’s actions deprived it of the benefit of the SALU, violating its due-process and contract rights, and (2) brought business-libel and slander claims against the City and Du-chane based on a number of disparaging statements Duchane made to the press and others in 2001.
The federal-court lawsuit.
While the state-court lawsuit moved along, Hillside filed a second suit against the City and Duchane, this one in federal court. Based on essentially the same facts as the state-court suit, Hillside claimed that the City violated its due-process and equal-protection rights by depriving it of the benefit of the SALU and selectively enforcing its ordinances.
The City responded by revoking Hillside’s SALU based on a series of alleged violations of municipal ordinances. The federal court ordered the City to restore the SALU and to refrain from interfering with it or Hillside anymore. In October 2003, the court granted partial summary judgment for Hillside as to liability, finding that the City had violated Hillside’s procedural and substantive due-process
rights but that a jury question remained on the equal-protection claim.
Facing litigation in two different courthouses, the City turned to its insurers for help. Between 1999 and 2003, the relevant times of these allegations, the City held insurance policies from three companies: United National, General Star Indemnity and Specialty National. General Star provided city-and-officials coverage from September 2000 to September 2002. Specialty National provided public-entity commercial-general-liability coverage and public-officials coverage from September 2002 to September 2003. And United provided $20 million of occurrence-based comprehensive general-liability coverage from September 1999 to September 2002.
The federal-court coverage dispute.
By July 2003, none of the insurers was willing to participate in the lawsuits or commit to indemnifying the City’s losses, prompting the City to file this coverage lawsuit in federal court. Alleging breach of the insurance contracts, the complaint sought a declaratory judgment clarifying each insurer’s obligations.
The court ruled that United (unlike the other two insurers) did not have a duty to defend the City in the Hillside lawsuits but owed a duty only to indemnify the City’s losses. The court also concluded that aside from the defamation claims — which United conceded were covered by its policy — none of Hillside’s claims fell within United’s coverage.
The City, meanwhile, was in the midst of negotiating a settlement with Hillside. Though invited along with the other insurers to take part in the negotiations, United declined to participate. The City pressed ahead on its own and reached a comprehensive settlement agreement with Hillside in March 2004. The settlement resolved all of Hillside’s pending claims in the state and federal suits in exchange for $31 million and other in-kind benefits. The agreement said nothing about how the settlement should be allocated among the state and federal claims. The City funded the settlement primarily by issuing $25 million in judgment bonds.
After finalizing the settlement, the City amended its complaint to add a claim against all three insurers for breach of the implied covenant of good faith and fair dealing in handling the settlement. In January 2006, the district court, standing by its prior ruling, held that the United policy covered Hillside’s defamation claims but not the other state or federal claims.
In June 2006, the City settled its coverage claims with General Star and Specialty National. General Star agreed to pay $10.25 million, and Specialty National agreed to pay $8.5 million. The coverage lawsuit against United continued, however. In attempting to determine the portion of the settlement attributable to the defamation claims, the court applied a “time on the risk” formula, finding United liable for one third of the $31 million settlement, or $10.33 million. All told, the court placed United on the hook for $14.6 million, which included not just the liability loss but also the defense costs, consequential damages and prejudgment interest.
II.
United challenges the district court’s method of calculating United’s share of the $31 million settlement between the City and Hillside. Although United’s policies covered only the defamation claims, the settlement encompassed all of Hillside’s claims against the City, including several constitutional and contract claims. Yet because the $31 million settlement did not divide up liability for the claims, it fell to the district court to allocate part of the settlement to United.
The court rejected both parties’ all-or-nothing approaches to the problem. It did not buy the City’s argument that United was liable for all of the $31 million (really $12.25 million given the other two insurers’ settlement with the City). United’s policy, it is true, required United to indemnify the City for “all sums which the [City] is legally obligated to pay” due to a judgment or settlement. JA 638. But that clause applies only to covered claims, according to Michigan law, which all agree governs this case.
See Wolverine World Wide, Inc. v. Liberty Mut. Ins. Co.,
No. 260330, 2007 WL 705981, at *2 (Mich.Ct.App. Mar. 8, 2007);
cf. Doiu Coming Cory. v. Cont’l Cas. Co.,
No. 200143, 1999 WL 33435067, at *6-8 (Mich.Ct.App. Oct. 12, 1999) (holding insurer liable for all claims settled by insured under a similar “all sums” provision where all of the claims were covered by the policy).
The court also rejected United’s contention that it owed nothing because the City had failed to apportion the settlement among covered (defamation) and uncovered claims. The harms resulting from the City’s actions, including Duchane’s statements, the court held, were “indivisible,” making a fine-grained allocation of damages “impossible.” JA 1200-01.
Attempting to respect the Michigan Supreme Court’s admonition “to fairly allocate the risk” rather than insist on “strict standard[s] of proof,”
Gelman Seis., Inc. v. Fid. & Cas. Co. of N.Y.,
456 Mich. 305, 572 N.W.2d 617, 626 (1998),
amended on other grounds sub. nom. Arco Indus. Corp. v. Am. Motorists Ins. Co.,
456 Mich. 1230, 576 N.W.2d 168 (Mich.1998),
and overruled on other grounds by Wilkie v. Auto-Owners Ins. Co.,
469 Mich. 41, 664 N.W.2d 776 (2003), the court chose a middle path: It employed the “time on the risk” formula that Michigan and other courts have used to apportion liability among multiple insurers when they provide coverage for the same risk over time.
See, e.g., Arco Indus. Corp. v. Am. Motorists Ins. Co.,
232 Mich.App. 146, 594 N.W.2d 61, 68 (1998),
aff'd by an equally divided court,
462 Mich. 896, 617 N.W.2d 330 (Mich.2000);
Wolverine World Wide,
2007 WL 705981, at *3-4. Under that approach, each insurer’s share of the settlement is equal to a straightforward fraction: The numerator is the amount of time the insurer provided relevant coverage, and the denominator is the total amount of time covering the loss.
See Arco,
594 N.W.2d. at 68. Here, Hillside’s allegations covered September 2000 to September 2003. During the first two of those three years, United and General Star provided coverage, and in the third year only Specialty National provided coverage. That made United liable for one third of the total $31 million settlement, or $10.33 million.
Acknowledging that a time-on-the-risk formula makes sense as a way to apportion liability among insurers who cover the same risk over time, United objects that the approach does not draw distinctions between covered (defamation) and uncovered claims. The formula, as United sees it, assigns the insurance company liability for a share of the settlement that does not necessarily bear any logical relation to the loss caused by the defamation. Instead of treating Hillside’s claims as an homogenous whole, United argues that the district court should have required the City to prove the part of the settlement allocable to the defamation claims.
We disagree. United fails to come to grips with the “indivisible” nature of the damages covered by the settlement, as the district court correctly recognized. JA 1200. While Hillside alleged a number of discrete acts and captioned them under a variety of legal labels, the evidence presented to the district court showed that
they all “harmed [Hillside’s] business and business reputation.”
Id.
All of the alleged misconduct resulted “in depleted attendance, fewer shows, lower revenues, less quality bookings, less sponsorship, more debt and more expenses,” and there simply is “no feasible way to separate” the effects of Duchane’s defamatory statements from the effect of the City’s other acts. JA 1200-01. To require the City to prove the portion of the settlement attributable to the defamation claims, the district court reasoned, is to require it to “do the impossible.” JA 1201.
United fails to point to anything in the record that undermines this conclusion. It argues instead that Hillside’s defamation claims were weak and, standing alone, could have been, indeed should have been, settled for far less than $10.38 million. But that sidesteps the central issue: Unless the evidence makes it possible to separate out the effect of the defamation from the effect of the City’s other acts, it makes no difference whether Hillside’s claims were strong, weak or somewhere in between. Because we have no way of knowing whether Duchane’s defamatory statements caused
all
of the damage reflected in the $31 million settlement, let alone one third of that amount, we cannot say that United was forced to pay more than it should have.
Not so, United rejoins: We need not try to sort out the harm to Hillside’s business and reputation that stemmed from Du-chane’s statements, as opposed to the City’s other acts, because the defamation claims likely were barred by governmental immunity. The defamation claims thus had little if any value regardless of the harmful effect of Duchane’s statements, and consequently those claims could not reasonably represent more than a sliver of the total settlement amount.
The problem for United is that the time to raise that argument was during the City’s settlement negotiations with Hillside, not in litigation after the fact. Despite repeated invitations to participate, United chose to stay on the sidelines throughout the negotiations, neither presenting its arguments about the defamation claims’ value nor ensuring that the agreement included an allocation for the defamation claims. That United owed the City no duty of defense in the litigation does not mean it had no duty to look after
its own
interests in determining how the settlement should be allocated, if indeed it could have been allocated. United does not argue that the City unreasonably settled the litigation,
see, e.g., Trim v. Clark Equip. Co.,
87 Mich.App. 270, 274 N.W.2d 33, 36-37 (1978), and thus cannot say that the settlement itself was flawed. And because it chose not to participate in the settlement, even after being kept informed about it, United has only itself to blame for the lack of apportionment in the settlement.
Presented with evidence showing that the harm from the defamation and the City’s other actions were inexorably intertwined, the district court saw no alternative — and neither do we — to allocating liability based on time on the risk. Requiring an insurer to indemnify a portion of a settlement that may reflect more than the value of the claims the insurer pledged to cover, to be sure, creates a risk that an insured will leverage coverage for one claim into indemnity for uncovered losses. But United offered no alternative method to estimate the value of the defamation claims aside from a full-blown trial — an eventuality that not only would defeat the purpose of settlement but also would place an insurmountable burden of proof on the insured when damages are “indivisible.” In place of a possibility that an insured would obtain
reimbursement for harms outside its policy, United would substitute a certainty that an insured would recover nothing whenever damages cannot be meaningfully divided. The Michigan Supreme Court, we believe, would not endorse such a rule.
It bears adding that the time-on-the-risk formula, like all estimates, contains risks of imprecision. In this appeal, United features one such risk — that it is being held responsible for a third of a settlement when the covered claim (defamation) may not have been one of Hillside’s strongest claims. But the formula contains another risk of imprecision, one that may have helped United: that all of the City’s actions (and the risk of liability triggered by them) are treated equally over the three-year period. But of course it is not necessarily true that the liability-triggering actions are evenly spread out over the coverage period, and it would not appear to have been true here. Many of Hillside’s most serious allegations cover the first two years of the coverage period, the same two years covered by United’s policy, and yet the time-on-the-risk allocation treated the liability covered by the third year the same as the first two. When indivisible damages force a court to make estimates of liability, as this case illustrates, a party is as apt to be a rough-justice winner in some respects as a rough-justice loser in others. We reject United’s challenge to the district court’s allocation of the underlying damages.
III.
United and the City, through its cross-appeal, challenge several other orders issued by the district court in the wake of its allocation decision.
A.
United first argues that the district court gave the City a double recovery when it awarded consequential damages (for the costs of issuing, and paying interest on, judgment bonds for the $31 million settlement)
and
prejudgment interest (on the $10.33 million actual-damages award and the consequential-damages award).
We disagree. On top of actual damages, a court may award consequential damages to a claimant to account for additional costs that arise naturally from a breach and that were reasonably foreseeable by the parties at the time they entered the contract.
Lawrence v. Will Darrah & Assocs., Inc.,
445 Mich. 1, 516 N.W.2d 43, 48-49 (1994). The costs the City incurred to issue and maintain the judgment bonds meet that standard: United and the City reasonably could have foreseen that the City would have had to borrow money to pay a liability that United refused to pay.
See Sullivan Indus., Inc. v. Double Seal Glass Co.,
192 Mich.App. 333, 480 N.W.2d 623, 633 (1991).
The district court also correctly awarded prejudgment interest, which is based “on the entire amount of the money judgment,” Mich. Comp. Laws § 600.6013(8). A “money judgment” includes any judgment that “orders the payment of a sum of money, as distinguished from an order directing an act to be done or property to be restored or transferred.”
People ex rel. Wayne County Prosecutor v. $176,598 U.S. Currency,
465 Mich. 382, 633 N.W.2d 367, 369 (2001). Courts must award prejudgment interest “in all cases to which the statute applies.”
Everett v. Nickola,
234 MichApp. 632, 599 N.W.2d 732, 735 (1999).
The City’s “money judgment” properly includes the actual-damages and consequential-damages awards. Both orders directed United to pay a sum of money, and the Michigan interest statute by its
terms gave the City a right to prejudgment interest on both.
Nor does this award create an unfair windfall. Consequential damages and prejudgment interest compensate plaintiffs for different forms of loss: Consequential damages reimburse parties for the additional, reasonably foreseeable costs they incur as a result of a breach of contract,
see Lawrence,
516 N.W.2d at 48, while prejudgment interest—besides offsetting the costs of litigation and encouraging settlement,
see Old Orchard by the Bay Assocs. v. Hamilton Mut. Ins. Co.,
434 Mich. 244, 454 N.W.2d 73, 76 (1990),
overruled on other grounds by Holloway Constr. Co. v. Oakland County Bd. of County Road Comm’rs,
450 Mich. 608, 543 N.W.2d 923 (1996)—compensates plaintiffs for the “delays in recovering money damages,”
Yaldo v. North Pointe Ins. Co.,
457 Mich. 341, 578 N.W.2d 274, 278 (1998). By awarding both, the district court compensated the City for (1) the additional costs it incurred as a direct result of United’s breach and (2) the loss of the use of those funds while the City was seeking indemnification. All in all, that is a complete recovery, not a duplicative one.
B.
United and the City spar over whether the district court set the right dates for starting prejudgment interest and consequential damages. The district court correctly ran prejudgment interest from the date the City filed its complaint against United. The Michigan interest statute states that “interest on a money judgment recovered in a civil action is calculated ... from the date of filing the complaint.” Mich. Comp. Laws § 600.6013(8);
see also Ayar v. Foodland Distrib.,
472 Mich. 713, 698 N.W.2d 875, 877 (2005). United has no answer to, and does not try to answer, this statutory directive.
The court’s consequential-damage accrual date is another matter. The court identified January 27, 2006—the date on which it determined that United’s policy covered Hillside’s defamation claims—as the date from which consequential damages should be calculated. Yet, by their nature, consequential damages begin to accrue when the contract is breached, not when liability is determined.
See Lawrence,
516 N.W.2d at 47; 24 Richard A. Lord,
Williston on Contracts
§ 66:57 (4th ed.1990). United breached its insurance contracts with the City well before January 27, 2006.
United’s policies required it to indemnify the City for “all sums which the [City was] legally obligated to pay by reason of the liability ... assumed by the [City] under contract or agreement” for covered losses. JA 638. That duty attached when the City notified United of the settlement agreement,
see Koski v. Allstate Ins. Co.,
456 Mich. 439, 572 N.W.2d 636, 639-40 (1998); 16
Williston on Contracts
§ 49:109, and United was in breach when it refused to fulfill that duty by indemnifying the City,
see also
Mich. Comp. Laws § 500.2006. On remand, the district court should recalculate consequential damages as accruing when United breached its insurance contract with the City, not when the court later confirmed that failure.
C.
United also argues that, because the covered loss—the defamation claims—involved conduct that occurred over two policy periods, the City had to satisfy
two
$100,000 self-insured retentions. The district court held that United waived this argument, and we agree.
Insurers may waive insurance-contract conditions by failing to give reasonable notice to the insured that it is invoking them or reserving the right to do so.
See Kirschner v. Process Design Assocs., Inc.,
459 Mich. 587, 592 N.W.2d 707, 709-710 (1999). “It is well settled that a course of affirmative conduct, particularly coupled with oral or written representations, can amount to waiver.”
Quality Prods. & Concepts Co. v. Nagel Precision, Inc.,
469 Mich. 362, 666 N.W.2d 251, 261 (2003). The City bears the burden of establishing waiver by clear and convincing evidence.
Id.
at 258-59.
As early as February 2002, United was on notice that Hillside’s defamation claims implicated two policy periods, because the second amended complaint filed in the state-court lawsuit that month mentions defamatory statements occurring in two separate policy periods. Yet United not only remained silent about the possibility that the City would owe two self-insured retentions; it affirmatively told the City in letters dated April 1, 2003, and May 5, 2003, that the City “is liable for a single $100,000 [self-insured retention].” JA173.
That concession, we realize, did not arise in this precise context. United was telling the City that, even though some of the claims in the state and federal lawsuits were covered by two separate
sections
of the policy, the City was liable only for one self-insured retention. United was not, in other words, specifically disclaiming that it could hold the City liable for an additional self-insured retention because the covered conduct spanned two policy
periods.
But even though United did not expressly disclaim the argument, it did not raise the point when one reasonably would have expected it to. The April 2003 and May 2003 letters discussed the self-insured retentions the City would be responsible for and the defamation claims Hillside alleged in the second amended complaint. Neither one told the City that it would be responsible for two self-insured retentions; both letters, indeed, told the City that it would be responsible for just one. The first time United mentioned the possibility that the City might.be liable for two self-insured retentions was in November 2005, and even then it did so only in a footnote in its reply brief to the City’s motion for summary judgment. Such a cursory reference—coming nearly three and a half years after Hillside filed its second amended complaint in the state-court action and a year and a half after the settlement— does not make up for years of silence. The district court correctly found that this argument was waived.
D.
In challenging the district court’s allocation of defense costs, United argues that, because it had a separate agreement with Specialty National and General Star addressing these costs, the court should have enforced that agreement rather than separately allocate defense costs on its own. But this
other
agreement cannot trump United’s contractual duty to indemnify
the City
for its costs in defending covered claims. If, as it turns out, the court made United pay more defense costs than its allocation agreement with the two co-insurers required, United is free to seek contribution from Specialty National or General Star, or both.
See, e.g., Frankenmuth Mut. Ins. Co. v. Cont’l Ins. Co.,
450 Mich. 429, 537 N.W.2d 879, 885-86 (1995). Either way, the salient point is that United’s right of contribution against these other insurers does not alter its obligation to pay the City’s defense costs.
United separately argues that this duty should be limited to the defense costs
that the City submitted to United through a third-party administrator. United’s policies required the City to use a third-party administrator when seeking reimbursement of defense costs, and the City concedes that it did not comply with this requirement in seeking coverage for many of these costs. But, as the district court found, United cannot take shelter in this requirement because it waived the condition.
Through a “course of affirmative conduct,” as we have shown, insurers may waive a policy condition, particularly when that conduct is “coupled with oral or written representations,” showing that the insurer knowingly waived enforcement of the term.
Quality Prods. & Concepts Co.,
666 N.W.2d at 258, 261. That is just what happened here. At some point before November 2003, United told the City’s counsel to “maintain separate billings for the State and Federal suits and to provide copies of only the State suit invoices to United National, as United National’s coverage for the Federal suit has been exhausted.” JA 2286. Having told the City not to submit bills for defense costs associated with Hillside’s federal lawsuit, United cannot now blame the City for failing to abide by the third-party-administrator requirement with respect to those costs. No doubt, some of the defense costs that the City did not submit to a third-party administrator may relate to Hillside’s state lawsuit. But, as the district court concluded, the state- and federal-lawsuit defense costs are indivisible, and United at any rate points to no evidence showing that the City sought defense costs for the state-court action that it failed to submit to a third-party administrator. The district court did not commit reversible error in rejecting United’s argument.
E.
The City filed a motion to strike United’s opening brief, arguing that it raises several arguments United did not present below and that it relies on documents that the district court struck from the record. In resolving this appeal, we have disregarded any arguments United did not raise below and any facts not in the record, making it unnecessary to grant United’s motion.
See, e.g., Simmons v. Middle Term. State Univ.,
No. 95-6111, 1997 WL 400105, at *1 (6th Cir. July 11, 1997).
IV.
For these reasons, we affirm in part, reverse in part and remand for further proceedings.