AMERICAN MILLING COMPANY; UN Limited; HB Marine, Inc., corporations; American Milling LP, a limited partnership, For Exoneration From, or Limitation of, liability, Plaintiffs/Appellees, John O. Johnson, Befendant/Appellee v. TRUSTEE OF the DISTRIBUTION TRUST, formerly known as President Casino, Inc.; Essex Insurance Company, Claimants/Appellants, 623 F.3d 570

COLLOTON, Circuit Judge. The Admiral, a casino ship belonging to President Casino, Inc. (“President Casino”), was damaged by a barge that broke loose from a towboat owned by American Milling Co., UN Ltd., HB Marine, Inc., and American Milling LP (collectively, “American Milling”). In a prior appeal, this court addressed the parties’ liability from the incident, as well as American Milling’s right to limit its liability. See In re American Milling Co., 409 F.3d 1005 (8th Cir.2005).

This appeal concerns President Casino’s claim against American Milling for certain promotional and wage expenses allegedly caused by-the allision. The district court, sitting without a jury, denied recovery of those expenses. We affirm. I. On April 4, 1998, the towboat MW Anne Holly was traveling north on the Mississippi River when its tow of fourteen barges allided with the Eads Bridge near St. Louis, Missouri. The impact caused the tow to break apart, leaving several barges to float uncontrolled downstream.

One of the loosed barges allided with The Admiral, a casino ship owned by President Casino and moored at the Missouri shore just downstream from the Eads Bridge. When the barge struck, The Admiral’s moorings broke loose, and the ship’s hull was damaged. Consequently, The Admiral closed for twenty-six days to undergo repairs.

Two days after the accident, the owner of the MW Anne Holly at the time, American Milling, filed a complaint in the district court seeking to limit its liability to the value of its vessel, pursuant to the Limitation of Shipowners’ Liability Act (the “Limitation Act”), 46 U.S.C.App. § 183 (current version at 46 U.S.C. § 30505). President Casino, and its subrogated insurer, Essex Insurance Company, subsequently filed claims against American Milling to recover damages.

After a first phase of litigation to resolve the issues of limitation and liability, the district court ruled that American Milling was entitled to limit its liability under the Limitation Act to $2.2 million. The court also concluded that American Milling was eighty percent at fault for the allision, and attributed the remaining twenty percent of fault to President Casino because of its failure to protect The Admiral despite past accidents where the casino boat was moored. In re American Milling Co., 270 F.Supp.2d 1068 (E.D.Mo.2003), aff'd in part, rev’d in part, 409 F.3d 1005 (8th Cir.2005).

With American Milling’s right to limitation and the parties’ liability decided, the district court proceeded to address the issue of damages. The parties stipulated to the amount of property damages, leaving in dispute President Casino’s claims for business interruption losses, certain extraordinary expenses, and wage expenses. In particular, President Casino sought to recover the profits lost during the period of The Admiral’s closure (the so-called “business interruption losses”).

President Casino also endeavored to recoup from American Milling the extra advertising and “cash coupon” promotional expenses that it allegedly incurred to attract customers after the closure. A “cash coupon” is a promotional coupon that is mailed to potential customers, who can redeem the coupon at The Admiral for chips to be used like cash in various casino games. President Casino also claimed that to mitigate potential damages from employee departures, the company continued to pay wages and tips to its hourly employees while The Admiral was closed, and that American Milling should be liable for those payments.

At trial, President Casino relied on the testimony of its Senior Vice President and Chief Financial Officer, Ralph Vaclavik, and on the report and testimony of a certified public accountant (“CPA”), Robert Traven, to support its damages claims. Vaclavik testified generally about profits lost during the closure, and he alleged that higher than normal promotional expenditures were necessary after the allision to notify customers of the casino’s reopening and to persuade them to return.

He also testified that the decision to pay employee wages and tips during the closure was reasonable in light of the uncertain duration of the closure, the likelihood that the casino’s employees would flee to competitors, and the regulatory barriers to hiring new gaming employees. On the basis of President Casino’s financial records, Traven quantified the damages from the allision, and estimated the total business interruption losses and extraordinary expenses to be $2,923,239. American Milling countered with an expert witness and CPA of its own, Peter Karutz.

In his report and testimony, Karutz disagreed with several aspects of Traven’s methodology, including how Traven measured the “ordinary” level of expenses against which any “extraordinary” expenses should be compared. Using a baseline level of expenses that was higher than that calculated by Traven, Karutz valued the disputed damages at $2,492,062. After considering the evidence, the district court determined that President Casino’s business interruption losses totaled $1,660,827, and denied recovery of the wages and tips paid during The Admiral’s closure.

The court pointed to the absence of evidence showing an exodus of employees during the closure, and concluded that the wage and tip payments were a voluntary business decision, not an action required by law. The district court also denied President Casino’s claim for extraordinary advertising and cash coupon expenses. After reducing the amount of business interruption losses by twenty percent to reflect President Casino’s fault, the court awarded the casino a total of $1,328,662, plus prejudgment interest compounded annually. II.

President Casino first challenges the district court’s decision to deny recovery of the allegedly extraordinary advertising and cash coupon expenses. We review the factual findings of the district court, sitting without a jury in admiralty, for clear error. McAllister v. United States, 348 U.S. 19, 20, 75 S.Ct. 6, 99 L.Ed. 20 (1954). This clear-error standard of review applies to the district court’s findings with respect to overhead expenses, see United States v. Capital Sand Co., 466 F.3d 655, 661 (8th Cir.2006), and lost profits. See ConAgra, Inc. v. Inland River Towing Co., 252 F.3d 979, 983 (8th Cir.2001).

We may reverse only if we are left with a definite and firm conviction that error has been committed. Anderson v. Bessemer City, 470 U.S. 564, 575, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985). President Casino contends that the district court’s denial of the advertising and cash coupon expenses was clearly erroneous, because the dispute between the witnesses at trial was not whether the casino incurred the extra expenses, but how much those expenses totaled.

President Casino’s expert, Traven, valued the above-normal advertising costs at $76,348, which he said was the difference between the amount the casino spent on advertisements in the month after the allision and the amount budgeted for that purpose. Karutz, the expert retained by American Milling, found a net increase of $43,005 by calculating the difference between the advertising expenses incurred in the two months after the allision and similar expenses from the same months in the prior year.

Given that neither expert found no extraordinary advertising expenses, President Casino suggests that the district court’s finding was unsupported by substantial evidence. The casino supplements this argument by highlighting Karutz’s statement at trial that measuring increased advertising expense after the allision appeared “reasonable.” President Casino makes a similar claim regarding cash coupon expenses, drawing on the experts’ estimates and Karutz’s testimony to conclude that the district court’s finding was clearly erroneous.

Traven calculated damages of $214,362, representing the difference between the casino’s cash coupon expenditures in the two months after the allision, May and June 1998, and the average monthly cash coupon expense in the fiscal year before the allision. Karutz estimated expenses of $149,695 by comparing the casino’s cash coupon expenses in May and June 1998 with the casino’s average monthly cash coupon expenditures from July 1998 through February 1999, after the allision.

Karutz reasoned that because cash coupon expenditures remained high long after the allision, it was appropriate to use those higher figures to establish a baseline reflecting the increase. Again, because both experts calculated some damages, President Casino argues that the district court clearly erred by awarding no damages.

President Casino also notes that when asked whether there was any extra expense related to cash coupons, Karutz responded: “Based on records we had, it appears that there is.” The difficulty with President Casino’s position is that the district court is not required to accept the opinion of either expert. “[T]he weight to be accorded expert opinion evidence is solely within the discretion of the judge sitting without a jury,” and while the judge “may not arbitrarily fail to consider such testimony, he is not bound to accept it.” Pittman v. Gilmore, 556 F.2d 1259, 1261 (5th Cir.1977); see Lukens v.

Comm’r, 945 F.2d 92, 96 (5th Cir.1991) (holding that a court “is not in any way bound by the opinions or formulas proffered by experts, and may reach a determination of value based upon its own evaluation of the evidence”); 7 J. Wigmore, Evidence § 1920, at 18-19 (J. Chadbourn rev. 1978) (stating that an expert cannot usurp the function of the trier of fact because the trier of fact can choose to reject the expert’s opinion).

The question, then, is whether the district court’s independent finding about recovery of extraordinary advertising and cash coupon expenses is clearly erroneous in light of the record as a whole. We conclude that the court’s finding is adequately supported by the evidence of record, together with a permissible adverse inference drawn from President Casino’s failure to introduce material evidence that it controlled. An inference against President Casino’s position concerning the promotional expenses was justified by company’s choice not to introduce its expense budgets for the months after the allision.

In admiralty, as at common law, “[t]he non-production of material evidence which is in the control of a party raises an inference that that evidence is unfavorable to that party.” Tupman Thurlow Co. v. S.S. Cap Castillo, 490 F.2d 302, 308 (2d Cir.1974). The district court properly could deem the casino’s budget figures material in establishing whether expenditures were greater than normal. After all, a primary purpose of a budget is to establish an expected level of expenditures.

President Casino recognized as much when it introduced its budget for the month of the allision to prove the revenues it lost during The Admiral’s closure. Curiously, however, the casino chose not to employ this same straightforward methodology for the advertising and cash coupon expenses, despite Vaclavik’s admission that he had access to the budgets for the months in which the alleged increases occurred. This selective unwillingness to introduce relevant budget figures warranted an inference that those figures were unfavorable to the casino’s advertising and cash coupon claims.

Accordingly, the district court reasonably could conclude that President Casino projected higher expenditures on promotional activities than the company actually spent after the accident, and therefore incurred no damages. This adverse inference is substantiated by evidence in the record. Karutz testified that cash coupon expenditures in the fiscal year of the accident were significantly higher than in the previous fiscal year. In October 1998, for example, six months after the allision, the casino’s cash coupon expenditures were nearly sixty times what they had been in the same month of the prior year.

For the fiscal year of the accident as whole, cash coupon expenditures increased by more than seventy percent from the previous fiscal year. Vaclavik characterized the increase as an ongoing effect of the accident, yet the casino chose to limit its claim for recovery of additional expenditures to May and June of 1998. Karutz offered an alternative explanation for the long-term rise in cash coupon expenses, attributing the increase to a change in the casino’s marketing strategy.

This explanation is consistent with the fact that cash coupon expenses were higher in March and April 1998 than in the previous year, even though the allision is not alleged to have affected expenditures in those months. Karutz accounted for President Casino’s strategic change by increasing his baseline estimate of what the casino would have spent without the accident.

Given President Casino’s failure to produce any budgets for the relevant period, however, it was not clearly erroneous for the district court to infer adversely to the casino that all of the increased cash coupon expenditures were attributable to a change in advertising strategy. There is also evidence that supports the district court’s decision on advertising expenditures. President Casino’s advertising expenditures were lower in the fiscal year of the accident than in the previous fiscal year.

Much of the decrease occurred in June through August 1998, immediately after the May 1998 increase claimed by the casino. Karutz interpreted the decrease to suggest that President Casino had reallocated a portion of its expenditures from June 1998 to May 1998, the month for which the casino sought recovery from American Milling.

Karutz also opined that given the overall decrease in advertising expenses for the year, any estimated increase resulting from the accident was “speculation.” Although he calculated an increase to counter Traven’s estimate, Karutz explained that he “wasn’t inclined to measure an increase in advertising because the current year is significantly lower than the prior year.” This conclusion, along with the lack of budget figures to verify the amount of expense reallocation that may have taken place, supports the district court’s decision to award no recovery for extraordinary advertising expenses. III.

President Casino also challenges the district court’s decision to deny recovery of the wages and tips it paid during The Admiral’s closure. The court determined that the payments were made voluntarily. We review this finding for clear error. See Fed. Barge Lines, Inc. v. Granite City Steel Div. of Nat'l Steel Corp., 809 F.2d 497, 500 (8th Cir.1987). President Casino contends that it paid $799,535 in wages and $172,169 in tips to retain its hourly employees and mitigate additional damages that would result from a staffing shortage.

It asserts that the district court, in concluding that these were voluntary payments not caused by the allision, disregarded the experts’ estimates, ignored the casino’s duty to mitigate, and improperly used hindsight to determine the reasonableness of the payments. According to the casino, the district court’s approach placed the company in a Catch-22, forcing it first to suffer the loss it sought to mitigate — i.e., losing employees and delaying reopening — before it could recover for that loss.

A party in admiralty can have a legal duty to mitigate damages, see The Baltimore, 75 U.S. 377, 387, 8 Wall. 377, 19 L.Ed. 463 (1869), and the reasonableness of its mitigation efforts should not be judged based on perfect hindsight. See The Algonquin, 70 F.2d 335, 337 (2d Cir.1934). At the same time, however, the casino owner in this case bore the burden to present sufficient evidence that the circumstances gave rise to a legal duty to pay, see Pizani v.

M/V Cotton Blossom, 669 F.2d 1084, 1088 (5th Cir.1982), because an admiralty court will not compensate a party for payments made voluntarily, or without legal obligation. See Crain Bros. v. Duquesne Slag Prods. Co., 273 F.2d 948, 953 (3d Cir.1959). The district court’s finding in this case was based on a failure of proof, not on a mistaken understanding of the law. We conclude that the finding was not clearly erroneous. President Casino relied almost exclusively on Vaclavik’s testimony to show that it had a legal duty to pay its employees while The Admiral was closed.

Vaclavik testified that although the casino had no contractual obligation to pay its hourly employees, the company was concerned that many of the nearly 1000 people staffing The Admiral — fearful of receiving no wages from President Casino — would seek work elsewhere. Vaclavik stated that he did not know how long the casino would remain closed, and worried that the departure of certain “key employees” could delay The Admiral’s reopening. He also noted that a delayed reopening was realistic given the regulated nature of the casino business.

According to Vaclavik, every casino employee had to be licensed by the Missouri Gaming Commission, and the commission “had gone to a point where they would only allow twelve people a week to apply for a license.” Vaclavik also expressed concern that finding new hourly employees would be costly, and that the departure of employees could raise the company’s “unemployment compensation rates.” Finally, Vaclavik suggested that because the employees actually reported to work during the closure, the company had a legal duty to pay them for their time.

As articulated by Vaclavik, the casino’s duty to mitigate damages rested on the likelihood of employee departures because of the closure: If a sufficient number of employees were not likely to quit, then the casino’s reopening would not be delayed, and there were no damages to mitigate.

The district court, recognizing this key point in the argument, made a specific finding that “there was no evidence before the Court demonstrating a wholesale exodus of employees from The Admiral.” This finding is supported by President Casino’s failure to introduce specific evidence to substantiate Vaclavik’s generalized assertion that “a group of people who are not getting paid ... are going to look somewhere else for a job.” Vaclavik could not identify any specific employees who did go or might have gone elsewhere during the closure.

He admitted that he did not know whether President Casino’s employees could work for a competitor casino without reapplying for a license with the Gaming Commission, a factor that would be significant in any employee’s decision to terminate employment during the temporary closure of The Admiral. President Casino also failed to establish how many employee departures could be tolerated without delaying reopening.

Surely there was some threshold number that would result in a prolonged closure, but President Casino gave no specific answer, and thereby left the court without an important piece of information in determining whether the company’s payments were necessary to mitigate damages. Similarly, even though Vaclavik suggested that the loss of a few “key employees” could delay the casino’s reopening, President Casino did not specify who were those employees or the probability of their departure.

Presumably, “key employees” earn higher wages than “regular” employees because of their skill and experience, and would have less incentive to leave the casino for “regular” work during a short-term closure. Even “regular” employees in the gaming industry, with licensing requirements functioning as a barrier to entry, could be expected to earn higher wages than their similarly skilled, unlicensed counterparts. See Morris M. Kleiner & Alan B. Krueger, The Prevalence and Effects of Occupational Licensing 5 (Nat’l Bureau of Econ.

Research, Working Paper No. 14308, 2008) (estimating that licensing requirements increase employee wages fifteen percent). The likelihood that casino employees would quit during a temporary closure presumably depends on whether comparable employment opportunities are immediately available, and there is no evidence of record to refute American Milling’s claim that the casino labor market in St. Louis was operating at full capacity at the time of the accident. President Casino also produced no evidence about how long The Admiral would be closed.

The casino was in the best position to gather estimates from those performing repairs about a likely reopening date, and the district court could reasonably infer from the absence of proof that the closure was likely to be relatively short in duration, such that employee departures would be minimal. President Casino also did not develop its contention that its unemployment compensation rates would increase because of employee departures. The record does not establish how many employees must depart before the rates would increase, or what would be the cost of such increases.

Without specific facts to support its assertion that The Admiral’s employees would leave during the temporary closure, and that reopening would be delayed or unemployment insurance costs increased as a result, President Casino’s claim to recover its wage and tip payments was too speculative to compel a favorable judgment. The district court did not clearly err in finding that President Casino was under no legal obligation to make those payments, and that American Milling was not obligated to compensate the casino for them.

President Casino argues finally that because it actually required hourly employees to report to work during the closure, the company had a legal obligation to pay those employees. The district court found “no evidence that hourly employees were mandated to continue working in this period.” But even assuming that the casino’s hourly employees were required to work during the closure, American Milling would be liable for the payments only to the extent that the allision caused the casino’s obligation. See Exxon Co., U.S.A. v. Sofec, Inc., 517 U.S. 830, 836-37, 116 S.Ct. 1813, 135 L.Ed.2d 113 (1996).

Because the district court did not clearly err in finding no such legal obligation resulting from the allision, American Milling is not liable for the wage and tip payments. The judgment of the district coxxrt is affirmed. . The Honorable Stephen N. Limbaugh, Sr., United States District Judge for the Eastern District of Missouri, now retired. . For simplicity, we refer only to President Casino when discussing appellees' claims against American Milling, and we refer to the appellees as President Casino, even though its claims are now pursued by a trustee in bankruptcy. .

While the actual amount that President Casino can recover from American Milling may not exceed the $2.2 million value of the limitation fund (plus any interest that has accrued on the fund), the total value of the damages President Casino is awarded affects the proportion of the limitation fund to which the company is entitled relative to other claimants. . President Casino claims to have used its May 1998 advertising budget figure to calculate the extraordinary advertising expenses.

Even assuming the truth of that assertion, which American Milling disputes, the budget figures were not documented in the record or provided to American Milling. Therefore, the district court properly could exclude the asserted budget figure from consideration. Tupman Thurlow Co., 490 F.2d at 308.