
    INTERNATIONAL MARINE, L.L.C.; International Offshore Services, L.L.C., Plaintiffs-Appellants v. FDT, L.L.C., formerly known as Delta Towing, L.L.C., Defendant-Appellee.
    No. 14-31192.
    United States Court of Appeals, Fifth Circuit.
    Aug. 10, 2015.
    
      Harry Joseph Philips, Jr., Taylor, Porter, Brooks & Phillips, L.L.P., Baton Rouge, LA, James Daniel Dasso, Foley & 
      Lardner, L.L.P., Chicago, IL, for Plaintiff-Appellant.
    David Sinnott Bland, Beau Earle Leblanc, Esq., Bland & Partners, P.L.L.C., New Orleans, LA, for DefendanL-Appellee.
    Before HIGGINBOTHAM, DENNIS, and HAYNES, Circuit Judges.
   PER CURIAM:

International Marine, L.L.C., and International Offshore Services, L.L.C. (collectively, “International”) appeal the district court’s October 14, 2014, Judgment (“2014 Judgment”), which adjudged International liable for thirty-three breaches of a Vessel Sales Agreement (“the Agreement”) and assessed liquidated damages of $8.25 million, plus prejudgment interest at the rate of 5.5% per annum. For the reasons that follow, we AFFIRM in part, VACATE in part, and REMAND for further proceedings.

I. Background

In 2006, International purchased two tugboats (the TEAM and SKIPPER) from Delta Towing, L.L.C. (“Delta”) for $4 million, ostensibly for use in internal operations. International’s president, Stephen Williams, and counsel, Peter Rouse, negotiated for several months preceding the sale with the treasurer of Delta’s parent company, Darren Vorst. Delta is in the business of chartering tugboats in the Gulf of Mexico and was concerned about competition from International. Therefore, even though the tugboats were “cold stacked,” or not in use and not likely to be used anytime soon, Delta hesitated to sell the tugboats. Delta thus insisted on including a noncompete clause in Paragraph 11F of the Agreement, which imposed certain pre-charter and post-charter obligations. In particular, Paragraph 11F prohibited International from chartering the tugboats to third parties without first giving Delta advance notice and a right of first refusal on any proposed charter. If Delta accepted the charter, it would operate the charter and pay International 90% of the fee, or charter hire. If Delta did not accept the charter within a reasonable amount of time, International could operate the charter, but would be required to remit 10% of the charter hire to Delta within fifteen days of receiving payment.

The parties negotiated a liquidated damages provision, Paragraph 11G, which would apply $250,000 in liquidated damages to any breach of the noncompete clause. In relevant part, Paragraphs 11F and 11G of the Agreement state:

Paragraph 11F (“Noncompete Clause”):
Notwithstanding the foregoing, in the event [International] or its affiliated companies wish to Charter Out either or both of the Vessels in the Covered Trade during all or part of the Covered Term, [International] shall be obligated to time charter the applicable Vessels to [Delta] for [Delta] to enter into Charters Out with customers acceptable to [Delta].... [C]harter hire payable to [International] by [Delta] shall be an amount equal to 90% of the gross charter hire actually received by [Delta] from the [charters of the Vessels] and shall be due and payable to [International] within fifteen (15) days after receipt of such charter hire by [Delta]. If [Delta] is unable to secure Charters Out for the Vessels within a reasonable time of the Vessels becoming available, [International] may Charter Out either or both of the Vessels at fair market rates directly to Customer Charterers for use in the Covered Trade during all or part of the Covered term, but [International] shall pay to [Delta] as compensation therefore an amount equal to 10% of the gross charter hire actually received by [International] ... [which] shall be due and payable to [Delta] within fifteen (15) days after receipt of such charter hire by [International]. The charter hire rate charged and duration of all Charters Out shall be reasonably agreeable to both [International] and [Delta].

Paragraph 11G (“Liquidated Damages Clause”):

The consideration for the provisions in paragraph 11F and this paragraph 11G is that the above Purchase Price is below the fair market price of the Vessels at the time of the sale and other good and valuable consideration the receipt and sufficiency of which is hereby acknowledged and confessed. In the event [International] ... violates any of the covenants and agreements in paragraph 11F, [International] shall pay to [Delta] as liquidated damages, and not as a penalty ... the sum of Two Hundred Fifty Thousand and no/100 Dollars ($250,000.00) per incident or occurrence.... All liquidated damages shall be payable within 30 days of notice of the violation. It is understood that the resultant damages of any such breach ... would be difficult to ascertain with certainty but that the amount stipulated herein is a good faith reasonable estimate of the damages [Delta] would suffer.

International purchased the tugboats and, beginning in September 2006, chartered them out to third parties while awaiting completion of barges on which it "intended to use the tugboats internally. In September and October 2006, International sent emails informing Delta’s Chief Operating Officer, Barry Matherne, and Delta’s Assistant Operations Manager, Ricky Guy, that the TEAM and SKIPPER were available for charter. Delta did not respond with a request to charter the tugboats, then or later. Instead, Guy responded that International should not “pass up any work,” but should “let [him] know a start time” and “rate.” Guy testified that from September 2006 until early 2007, he received periodic post-charter' emails from International that described the start time, duration, and rate for the first five charters International undertook. Once it received payment, International remitted the 10% fee to Delta for charters it conducted in 2006, although it sometimes paid late or incompletely. Delta accepted these payments. International ultimately requested that Delta allow it to pay a 5% commission on charters, rather than the 10% fee, and Delta refused. Soon after that, from January 2007 onward, International ceased notifying Delta about new charters undertaken by the tugboats and ceased submitting the 10% payments.

In 2008, Delta twice requested to audit International’s books and records under the Agreement, suspecting that International was not notifying Delta or paying as required. International initially failed to respond, but on November 20, 2008, International sent a $52,293.33 payment to Delta, without documentation of what the payment represented. Delta did not accept the check; instead, Delta performed a comprehensive audit of International in early 2009. On February 20, 2009, International submitted another payment of $37,657, claiming its internal audit had revealed further money due. Delta again ■ refused to accept the check and sent International a letter on February 20, 2009, claiming International breached the Agreement thirty-six times and demanding that International pay liquidated damages. International rejected Delta’s demand and filed suit in 2010 seeking a declaration that International had not breached the Agreement and that the Liquidated Damages Clause was an unenforceable penalty. Delta' answered and counterclaimed for $9,000,000 in liquidated damages, plus prejudgment interest.

On cross motions for summary judgment, the district court concluded that the Liquidated Damages Clause was valid and enforceable. On International’s motion for reconsideration, the court again held that the Liquidated Damages Clause was enforceable and certified the enforceability question to this court on a Federal Rule of Civil Procedure 54(b) Judgment (“2013 Judgment”). Reviewing the 2013 Judgment on appeal, a panel of this court held International had failed to prove that the Liquidated Damages Clause was an unenforceable penalty, as the Liquidated Damages Clause was formed from the parties’ reasonable attempts to anticipate damages that would be difficult to quantify in advance. See Int’l Marine, L.L.C. v. Delta Towing, L.L.C. (International Marine I), 704 F.3d 350, 355-56 (5th Cir.2013).

The case proceeded to a bench trial on the issues of breach and damages. After the trial, the district court issued Findings of Fact and Conclusions of Láw, determining that International breached the Agreement’s pre- and post-charter obligations thirty-three times. It awarded Delta $250,000 in liquidated damages for each breach, for a total of $8.25 million, plus prejudgment interest at 5.5% per annum starting thirty days after February 20, 2009. On October 14, 2014, the district court issued its 2014 Judgment. It separated the issues of breach and damages from issues of attorney’s fees and costs and third-party liability that remained pending before the district court. International timely appealed the 2014 Judgment to this court, and the issues of breach and damages are now before us.

II. Discussion

On appeal from a bench trial, we review findings of fact for clear error and legal issues de novo. See One Beacon Ins. Co. v. Crowley Marine Servs., Inc., 648 F.3d 258, 262 (5th Cir.2011). Interpreting the terms of a maritime contract is an issue of law that we review de novo. Id. Finally, we review for clear error “the district court’s factual findings as to whether the parties fulfilled their duties under the [Agreement].” See Ergon-W. Va., Inc. v. Dynegy Mktg. & Trade, 706 F.3d 419, 424 (5th Cir.2013); cf. Automated Med. Labs., Inc. v. Armour Pharm. Co., 629 F.2d 1118, 1123-24 (5th Cir.1980).

Appealing from the 2014 Judgment, International claims the district court erred by: (1) misinterpreting International’s obligations under the Noncompete Clause of the Agreement, because properly interpreted, International complied with that Clause; (2) failing to conclude that the “extreme case” doctrine bars the award of liquidated damages because Delta suffered no actual damages; (3) improperly awarding liquidated damages for payments made by International to Delta that were solely late or for less than the agreed amount; (4) inflating the number of “incidents or occurrences” under the Agreement and thus over-counting the number of times International breached the Agreement; and (5) improperly awarding prejudgment interest on the liquidated damages award. In addition to defending the district court’s determinations, Delta argues that many of International’s arguments are foreclosed by the law of the case doctrine due to their resolution on the interlocutory appeal in International Marine I.

“Under the law of the case doctrine, an issue of fact or law decided on appeal may not be reexamined either by the district court on remand or by the appellate court on a subsequent appeal.” United States v. Matthews, 312 F.3d 652, 657 (5th Cir.2002) (citation and internal quotation marks omitted). “The law of the case doctrine applies to matters decided on interlocutory appeals,” Gene & Gene, L.L.C. v. BioPay, L.L.C., 624 F.3d 698, 702 (5th Cir.2010) (citation omitted), and “applies regardless of whether the issue was decided explicitly or by necessary implication,” Crowe v. Smith, 261 F.3d 558, 562 (5th Cir.2001). Delta raised law-of-the-case arguments on nearly every issue before us, which we address as we consider each issue raised by International.

A. Breach of the Agreement

International first argues the district court misinterpreted the Agreement, and that International was not obligated to give Delta advance notice or a right of first refusal before each charter of the tugboats. We conclude that the district court correctly interpreted the Agreement in accordance with binding law of the case. Under this interpretation, the Noncompete Clause of the Agreement requires International to consult with Delta before chartering out the TEAM or SKIPPER to third parties and to give Delta a right of first refusal. See Int’l Marine I, 704 F.3d at 352. The Noncompete Clause additionally imposes post-charter obligations requiring International to pay Delta a 10% fee within fifteen days of a charter hire’s payment.

1. Number of Breaches

The district court explicitly found that International entered into thirty-three separate time charters with third parties by the Agreement’s terms, each of which constituted a breach of the Agreement. International does not contest that it failed to notify Delta in advance of almost all of the charters, nor that it failed to pay the 10% fees due to Delta for every breach found by the district court, whether it wholly failed to pay the fees in advance of Delta’s audit or simply failed to pay the fees on time or in the correct amount. Instead, International asserts that the district court over-counted the number of breaches by counting each invoice International issued as a separate time charter and breach. Contrary to the district court’s findings, International contends that it sometimes issued multiple invoices for singular charters. Therefore, it argues that each invoice should not count as an “incident or occurrence,” or separate breach, under the contract.

The district court did not clearly err in parsing how many times International chartered out the vessels in breach of the Agreement, sometimes equating singular invoices with singular charters and sometimes aggregating multiple invoices into just one charter and one breach. Although International contests several of the charters counted by the district court as séparate breaches, it provided no direct evidence that those specific invoices represented only one charter. Evidence from the bench trial supports the distinct court’s determinations. Accordingly, we find no clear error in the district court’s conclusion that Delta breached the Agreement thirty-three times. See Ergon, 706 F.3d at 424.

2. Course of Conduct

International argues that the course of conduct between International and Delta proves the Agreement did not require International to give Delta advance notice and a right of first refusal. This course of conduct involved Ricky Guy’s email to International and International’s unchallenged practice, from September 2006 until early 2007, of informing Delta about the details of charters after they occurred. Accordingly, this court must determine the import, if any, of the parties’ conduct while International communicated with Delta about charters of the TEAM and SKIPPER from September 2006 until early 2007. This period of communication coincides with the first five breaches of the Agreement. As we addressed earlier, the fact that the Agreement required International to provide advance notice and a right of first refusal was determined by the panel in International Marine I and binds this court. 704 F.3d at 352. In International Marine I, the panel found that the Noncompete Clause and pre-char-ter obligations were pivotal to the Agreement, but did not explicitly determine whether the Agreement required International to “notify Delta and give it the option of operating charters itself’ before each charter, or only one time at the beginning of the chartering process. Id,

We review the interpretation of a maritime contract de novo. One Beacon, 648 F.3d at 262; see also Int’l Marine I, 704 F.3d at 354. When interpreting a maritime contract, general principles of contract law apply from federal admiralty law, rather than from state law. See Har-Win, Inc. v. Consol. Grain & Barge Co., 794 F.2d 985, 986-87 (5th Cir.1986); Int’l Marine I, 704 F.3d at 354. Federal maritime law “stems from the maritime jurisprudence of the federal courts, and is an amalgam of traditional common law rules, modifications of those rules, and newly created rules drawn from state and federal sources.” One Beacon, 648 F.3d at 262 (citations and internal quotation marks omitted). “Applying federal law in the contract context includes looking to ‘principles of general contract law that can be found in treatises or restatements of the law.” Univ. of Tex. Sys. v. United States, 759 F.3d 437, 443 (5th Cir.2014) (quoting Franconia Assocs. v. United States, 536 U.S. 129, 141-42, 122 S.Ct. 1993, 153 L.Ed.2d 132 (2002)), cert. denied, — U.S. -, 135 S.Ct. 1894, 191 L.Ed.2d 763 (2015).

Under federal maritime law, “a court may not look beyond the written language of [a contract] to determine the intent of the parties unless the disputed contract provision is ambiguous.” Corbitt v. Diamond M. Drilling Co., 654 F.2d 329, 332-33 (5th Cir. Unit A Aug.1981). The district court concluded that the Noncompete and Liquidated Damages Clauses are unambiguous. It interpreted the Noncom-pete Clause to require that Delta receive advance notification and the option of first refusal before -each charter and determined that any violation of the Noncom-pete Clause triggered an award of liquidated damages.

We conclude that the Noncompete Clause unambiguously required International to consult with Delta about each individual charter in advance. As the panel in International Marine I implicitly concluded, preventing and anticipating harm from competition formed the core purposes behind the Noncompete and Liquidated Damages Clauses. Int’l Marine I, 704 F.3d at 352, 355-56. Many of the provisions meant to protect Delta from competition would be ineffective if the Agreement did not require International to consult with Delta before each individual charter. For example, the parties could not easily determine whether Delta would be able to secure’ charters out for ■ the tugboats within a reasonable time of their availability if Delta was not apprised of the tugboats’ availability. Neither could the parties easily come to, a “reasonable] agree[ment]” about “[t]he charter hire rate charged and duration of all Charters Out” if they did not consult before each charter or have a larger, overarching agreement. If Delta was not informed in advance of each proposed charter, Delta could not prevent International from endearing itself and its tugboat crew to one of Delta’s customers or potential customers. By contrast, if Delta was informed in advance, it could head off this competition by exercising its right to operate the charter itself.

According to the plain language of the Agreement and the binding import attributed to it by a prior panel of this court, International was required to give advance notice and the option of first refusal to Delta before each charter. See generally Int’l Marine I, 704 F.3d at 355-56 (holding the most important damage anticipated from a breach of the Noncompete Clause “was Delta’s inability to prevent competition, leading to the potential loss of customers, business opportunities and market share due to International’s failure to notify Delta of its intent to compete”). Therefore, we need not assess the- extrinsic conduct of the parties to attempt to determine the meaning they attributed to these provisions. See Corbitt, 654 F.2d at 332-33.

However, the course of conduct between the parties makes liquidated damages inapplicable to the first five breaches of the agreement. International paid Delta late or in an incomplete amount for each of these breaches and emailed Delta details about each charter only after the fact. Yet, Delta accepted each check and correspondence and did not provide International with notice that International had breached the contract or that it would enforce the Liquidated Damages Clause for the late or incomplete payments. Restatement (SECOND) OF CONTRACTS § 278 & cmt. a & illus. 1 (1981) (“If an obligee accepts in satisfaction of the obligor’s duty a performance offered by the obligor that differs from what is due, the duty is discharged.”); see also id. cmt. c & illus. 3 (“[P]art performance by an obligor of a duty that is liquidated and undisputed is not consideration for a discharge of that duty in full, even if the obligee so accepts it.” (emphasis added)). This contrasts with Delta’s conduct for the other twenty-eight breaches. In mid-January 2007, International stopped informing Delta about charters, and the district court found that in February 2007, International falsely represented to Delta that it had chartered neither tugboat during early January. In November 2008, Delta did not accept the check when International attempted to submit late payment of the 10% fees it had failed to pay Delta since January 2007. Neither did Delta accept the second check International sent for overdue payments in February 2009.

Accordingly the parties’ course of conduct shows that liquidated damages cannot result from International’s first five breaches. The parties corresponded about these charters via email and Delta accepted the nonconforming payments. From this, we know the extent of the damage Delta suffered from each of these breaches — namely, the amount of the 10% fee Delta failed to receive when it was due. See generally Restatement (Seoond) of Contracts § 278 cmt. a & illus. 1 (1981) (noting that if an obligor chooses to accept “a performance that differs from what is due,” “the obligor is discharged in accordance with the terms of the offer”); see also id. cmt. c & illus. 3. As explained below, liquidated damages cannot issue when we can measure the extent of damages Delta suffered from these first five breaches using interest.

B. Liquidated Damages for Late or Incomplete Payments

The district court awarded liquidated damages for each breach of the Non-compete Clause’s requirements. International argues the district court erred when it granted Delta liquidated damages for breaches that it contends involved only late or incomplete payments, because liquidated damages generally may not be assessed for defaulting on an obligation to pay money. See generally 11 Joseph M. Perillo, Corbin on Contracts § 58.13 at 477-82 & n.l (rev. ed.2005) (collecting cases).

For over a century, courts have refused to award liquidated damages for contractual breaches solely involving default on payment obligations. See generally Wrenn v. Univ. Land Co., 65 Or. 482, 133 P. 627, 629 (1913). This follows logically from the fact that the damage caused by late or incomplete payment may be easily measured and remedied through an award of interest, meaning that any higher liquidated damages award would likely be punitive. See, e.g., Checkers Eight Ltd. P’ship v. Hawkins, 241 F.3d 558, 562 (7th Cir.2001) (interpreting Illinois law, holding that liquidated damages of $150,000 assessed for late installment payments were “unreasonable and excessive,” especially since interest rates could estimate the actual damage incurred); Semico, Inc. v. Pipefitters Local No. 195, 538 S.W.2d 273, 274 (Tex.Civ. App. — Beaumont 1976, writ refused n.r.e.) (holding a clause imposing liquidated damages of 15% per month on overdue labor union fees was an unenforceable penalty (quoting 5 Arthur L. Corbin, Corbin on Contracts § 1065 at 373 (1964))).

As applied to the first five breaches, the Liquidated Damages Clause would impose an unreasonable penalty, because due to the parties’ conduct, we know the extent of damages Delta suffered from each of these breaches. Therefore, we VACATE the district court’s order insofar as it granted $1.25 million in liquidated damages for International’s first five breaches of the Agreement. This reduces the total liquidated damages award from $8.25 million to $7 million. However, on remand, Delta should be awarded interest on the amount of the payments International failed to timely make related to its first five breaches, accruing for each payment from the date on which the payment became overdue until final judgment on October 14, 2014. See Probo II London v. Isla Santay MV, 92 F.3d 361, 363 (5th Cir.1996) (observing that courts award prejudgment interest in admiralty beginning on the date on which the claim accrues and extending until the date of judgment).

C. Extreme Case

International argues that the district court erred by assessing liquidated damages for each breach of the Agreement, because the “extreme case” doctrine should apply to preclude an assessment of liquidated damages in these circumstances. Delta contends that the panel in International Marine I foreclosed the application of the “extreme case” doctrine here, providing binding law of the case. This court has not explicitly adopted the “extreme case” doctrine and need not address whether to do so here because we agree with Delta that this argument is governed by law of the case. See Matthews, 312 F.3d at 657.

In International Marine I, both parties briefed the “extreme case” issue, and a different panel of this court determined that the record contained insufficient-evidence for the court to determine whether the “extreme case” doctrine applied. Int'l Marine I, 704 F.3d at 356 n. 6 (citation omitted); of. Massman Constr. Co. v. City Council of Greenville, Miss., 147 F.2d 925, 927 (5th Cir.1945) (refusing to award liquidated damages that were to accrue for delay in the completion .of a bridge because sufficient evidence showed “[t]here were no losses caused to the City by the delay ... [;] the bridge was completed in its entirety 30 or more days before there was a road to the bridge on the Arkansas side”). The panel ultimately found that the Liquidated Damages Clause reasonably estimated damages that would be difficult to anticipate and did not operate as an unenforceable penalty. Int’l Marine I, 704 F.3d at 355-56. This conclusion is binding law of the case absent any “substantially different” evidence presented at the bench trial. See Matthews, 312 F.3d at 657 (noting the law of the case doctrine does not apply if “[t]he evidence at a subsequent trial is substantially different”). The evidence presented before the district court at the bench trial was substantially the same as the evidence presented before the International Marine I panel; therefore, the decision in International Marine I binds us to decline to determine whether the “extreme case” doctrine applies here.

D. Prejudgment Interest

The district court awarded prejudgment interest at a rate of 5.5% per annum on $8.25 million in liquidated damages in accordance with the traditional hospitality to prejudgment interest in maritime cases. See Reeled Tubing, Inc. v. M/V Chad G, 794 F.2d 1026, 1028 (5th Cir.1986) (“[Ajwarding prejudgment interest is the rule rather than the exception_”). Prejudgment interest on the liquidated damages award began to accrue thirty days after February 20, 2009, because the Agreement specified that liquidated damages would be payable thirty days after notice of breach. Delta notified International on February 20, 2009, that it believed International had breached the Agreement and owed liquidated damages. International argues that the district court erroneously awarded prejudgment interest on the liquidated damages award because this court’s case law does not support awarding prejudgment interest for awards of liquidated damages, only for awards of actual damages. Cf. Montelongo v. Meese, 803 F.2d 1341, 1354 (5th Cir.1986).

This court has not held that prejudgment interest is barred on all liquidated damages awards, and Montelongo is distinguishable. See id. In Montelongo, statutory liquidated damages were awarded partially as a penalty. Id. at 1350 (holding that liquidated damages under the Farm Labor Contractor Registration Act (“FLORA”) were partially created as a penalty, and therefore, prejudgment interest was not appropriate). In Calderon v. Presidio Valley Farmers Association, this court held that Montelongo does not preclude district courts from acting within their discretion to award prejudgment interest on statutory, liquidated damages awards that are meant to approximate actual damages. 863 F.2d 384, 392-93 (5th Cir.1989) (finding “no bar to an award of prejudgment interest on actual damages based on FLORA”).

International Marine I established that the Liquidated Damages Clause is enforceable as a reasonable forecast of damages and that International did not sustain “its burden to prove that the [Liquidated Damages] Provision was a penalty.” 704 F.3d at 355-56. Accordingly, we hold that the district court acted within its discretion in awarding prejudgment interest under Montelongo, Calderon, and the maritime presumption favoring prejudgment interest. See e.g., Reeled Tubing, 794 F.2d at 1028.

III. Conclusion

Except for the first five breaches of the Agreement, we AFFIRM the district court’s 2014 Judgment and Findings and Conclusions in all respects. For International’s first five breaches, involving a quantifiable amount of damages from late payment or underpayment, we conclude that liquidated damages cannot apply.

Accordingly, we VACATE the liquidated damages awarded for the first five breaches of the agreement, reducing the total liquidated damages award to $7 million, plus prejudgment interest of 5.5% per an-num, beginning thirty days after February 20, 2009, and terminating on October 14, 2014, and REMAND for entry of a judgment consistent with this opinion. Upon remand, the district court should award the same prejudgment interest on the amounts International failed to pay Delta in its first five breaches, except interest on these breaches shall run from the date on which each payment was overdue and terminate on October 14,2014. 
      
       Pursuant to 5th Cir. R. 47.5, the court has determined that this opinion should not be published and is not precedent except under the limited circumstances set forth in 5th Cir. R. 47.5.4.
     
      
      . Although International emailed Delta to report charters through early 2007 as it received payments, the last charters it reported occurred in November and December of 2006.
     
      
      . The case was reassigned after the original district judge retired, and International filed a motion for reconsideration based in part on the changed deposition testimony of Math-erne, Delta’s Assistant Operations Manager. The court did not reconsider the order granting Delta summary judgment except to analyze the effect of Matherne’s new testimony.
     
      
      . International Marine I interpreted the precise obligations imposed by the Agreement, and the intent behind those obligations, to determine whether The Liquidated Damages Clause was a reasonable, enforceable provision. See generally In re Felt, 255 F.3d 220, 225-26 (5th Cir.2001) ("[T]hough not expressly addressed in an initial appeal, those matters that were fully briefed to the appellate court and were necessary predicates to dle ability to address the issue or issues specifically discussed are deemed to have been decided tacidy or implicitly, and their disposition is law of the case.”). Thus, when International Marine I found that "[International] was first obligated to notify Delta and give [Delta] the option of operating charters itself” before chartering out the tugboats, Int’l Marine I, 704 F.3d at 352, that decision bound the district court and now binds this court.
     
      
      .International contests breaches for which United Tugs leased the SKIPPER from 11 a.m. on June 15, 2007, through 10:30 p.m. on June 16, 2007, continuously, for three separate time periods, Each incident was denoted by a unique job number and invoice. International offers no evidence to prove that these three trips were a single charter, and we find no clear error in the district court’s conclusion that these were each separate charters. International also attempts to aggregate Smith Marine's charters of the SKIPPER from 4:30 a.m, on December 31, 2006, until January 8, 2007, plus a charter on January 10, 2007. International does not explain why distinct job numbers and invoices were issued for each time period of this job or why that does not suggest these were separate, hourly charters. Also, nothing supports International's claim that Smith Marine's charter ending on January 8 actually continued on January 10, despite the gap, because the crew "took a day off." Finally, International argues the district court erroneously double-counted three invoices for charters that took place while United Tugs had hired “both vessels.” But Matherne testified that despite having a master charter agreement with a company, a charterer would also have individual time charter agreements for specific tasks and time periods. It is not erroneous to count separate voyages from December 5-6, 2006, December 8-18, 2006, and December 16-29, 2006, as separate time charters and breaches of the Agreement.
     
      
      . Delta argues it is law of the case that International breached the Agreement twenty-seven times. See, e.g., Int’l Marine I, 704 F.3d at 356 n. 6. We need not decide this issue because we find no clear error in the district court's conclusion, básed on the evidence submitted at the bench trial, that International breached the Agreement thirty-three times.
     
      
      . There is no dispute that International failed to pay Delta the 10% fee on time or in the correct amount for these first five instances. These constitute breaches of the Agreement in any case.
     
      
      . Delta contends that law of the case governs this issue, but the panel in International Marine I did not decide this issue. International Marine I resulted from the appeal of the district court’s 2013 Federal Rule of Civil Procedure 54(b) Judgment and addressed the certified issue of whether the Liquidated Damages Clause was enforceable on its face. Int’l Marine I, 704 F.3d at 351, 353, 356. The record indicates the parties, district court, and panel in International Marine I understood that the issues of breach and damages remained pending before the district court and were not before this court in International Marine I. Accordingly, the issue of whether Delta accepted International's deficient performance for the first five breaches and the propriety of awarding liquidated damages for those breaches was not decided by the panel in International Marine I. Cf. Gochicoa v. Johnson, 238 F.3d 278, 291-92 (5th Cir.2000); Liberty Mut. Ins. Co. v. Gunderson, 387 F. App’x 480, 484-85 (5th Cir.2010) (unpublished); Fed.R.Civ.P. 54(b).
     
      
      . See also Fellows v. Nat’l Can Co., 257 F. 970, 971-72 (6th Cir.1919); Bilz v. Powell, 50 Colo. 482, 117 P. 344, 345-46 (1911); Condon v. Kemper, 47 Kan. 126, 27 P. 829, 831 (1891).
     
      
      . The "extreme case” doctrine posits that a liquidated damages clause "fixing a substantial sum as damages is unenforceable” as a penalty "[i]f, to take an extreme case, it is clear that no loss at all has occurred.” Restatement (Second) of Contracts § 356 cmt. b (1981). To illustrate an "extreme case” involving a clear lack of loss, the Restatement includes the following example: a liquidated damages clause fixed damages at $1000 per day for each day’s delay in completing a race track; the race track’s completion was delayed by 10 days, but the permit for opening the race track was delayed for one month; thus, the delay in construction did not delay the race track’s opening and caused no loss. Id. at cmt. b. illus. 4.
     
      
      . Because the first breach arose from an incomplete payment, the interest on that payment will instead begin to accrue from the date on which the payment became overdue and will continue to accrue until October 14, 2014. See Probo II, 92 F.3d at 363.
     
      
      . Neither party disputes the rate of prejudgment interest awarded (5.5% per annum) or that the prejudgment interest awarded began 30 days from February 20, 2009. As such, the parties abandoned any arguments that prejudgment interest should- be awarded in a different rate or from a different date. See Webb, 89 F.3d at 257 n. 2.
     