
    Arthur GRACE, Plaintiff-Appellant, v. CORBIS-SYGMA, f/k/a Sygma Photo News, Inc., Sygma S.A.R.L., f/k/a Sygma Paris, Corbis Corporation, Defendants-Appellees.
    Docket No. 06-0195-cv.
    United States Court of Appeals, Second Circuit.
    Argued: Oct. 30, 2006.
    Decided: May 25, 2007.
    
      Jonathan S. Abady (Ilann M. Maazel, O. Andrew F. Wilson, on the brief), Emery Celli Brinckerhoff & Abady LLP, New York, NY, for plaintiff-appellant.
    Douglas C. Fairhurst (Jeffrey L. Loop, on the brief), Dorsey & Whitney LLP, New York, NY, for defendants-appellees.
    Before: MINER, SACK, and KATZMANN, Circuit Judges.
   MINER, Circuit Judge.

Plaintiff-appellant Arthur Grace (“Grace”) appeals from a money judgment entered in his favor in the United States District Court for the Southern District of New York (Chin, J.) against defendants Corbis-Sygma, f/k/a Sygma Photo News, Inc., Sygma S.A.R.L., f/k/a Sygma Paris, and Corbis Corporation (collectively, “Syg-ma”). Alleging negligence on the part of Sygma, Grace brought this action to recover damages for the value of a large number of photographic images produced and owned by him and entrusted to Sygma as his agent and bailee. After a bench trial, the District Court entered a judgment in favor of Grace in the amount of $472,000 plus costs. Grace’s dissatisfaction with the adequacy of that award gives rise to the appeal before us.

BACKGROUND

The distinguished career of Arthur Grace as a photographer, and his arrangements with Sygma as his agent for the licensing of his photographs, are fully set forth in the thorough and detailed findings of fact made by the District Court. See Grace v. Corbis Sygma, 403 F.Supp.2d 337, 339-44 (S.D.N.Y.2005). There are no substantial objections to the District Court’s findings as to those matters, and we merely summarize them here.

Grace began his career as a photojournalist in the early 1970s as a freelance photographer for United Press International, which later hired him as a staff photographer in Europe. Id. at 339. From 1974 through 1977, Grace served as New England correspondent for The New York Times, working as an independent contractor. Id. During that period, he also shot photographs for magazines. Id. From 1978-1980, Grace served as White House photo correspondent under contract with Time Magazine. Id. He continued to work as a contract photographer for Time until 1985. Id. at 340. In 1986, he joined Newsweek as a salaried staff photographer and continued in that capacity until 1990. Id. During the 1990s, Grace shifted his attention as a news photographer principally to the photography of celebrities and celebrity events and also worked for advertising customers on a freelance basis. Id.

During his twenty-some years as a photojournalist, Grace photographed many important national and international events and figures, and most of his photographic images ended up in the Sygma archives. His worked was highly acclaimed, and its significance was described by the District Court as follows:

During the 1970s and through the 1980s, Grace was one of the leading photographers in the field of photojournalism. He captured many moments of historical significance with his “unique eye,” and his photographs had a certain quality to them that photographs of other photojournalists did not have. One of his photographs in The Neiv York Times was nominated for a Pulitzer prize. In 2003, Grace agreed to donate all his color images and many of his black and white images to the Center for American History (the “Center”) at the University of Texas. The images will be referred to as The Arthur Grace Photographic Collection and the Center will house, preserve, and maintain the collection for educational and scholarly purposes.

Id. at 340-41 (internal citations omitted).

Grace entered into an arrangement with Sygma in early 1974 whereby Sygma would act as his agent in the licensing of his photographs and Grace would receive 50% of the net sales. Id. at 341 & n. 4. Grace was assured that he would receive a monthly statement along with a check for his share of the income and that Sygma would promote Grace and seek photographic assignments for him. Id. at 341. There was no written agreement and no specific arrangement for the manner in which the photographs would be stored or returned to Grace. Sygma’s main office was in Paris, France, but it also maintained a New York City office. Id. Grace’s photographic images were licensed out of both offices. Id.

Many of the photographic images shot by Grace on assignment for Time, Newsweek, and other magazines and newspapers eventually were released to Sygma, which licensed and distributed them on behalf of Grace. Over the years, Sygma returned various photographs to Grace as requested. Included among the photographic images held by Sygma were “outtakes” — images not selected for use with stories for which they were commissioned. Id. at 342 n. 8. As licensor, Sygma provided a standard consignment form to its customers when licensing photographs. Id. at 343. The form provided for a liquidated sum of $1,500 for a lost image or transparency, but those fees often were negotiated or waived when a loss actually occurred. Id. at 343.

Sygma had no adequate means of tracking the inventory of images entrusted to it by any of the photographers it represented. Apparently, Sygma never had a system to keep track of its New York inventory and, starting in 1977, only a limited means of tracking its Paris inventory. Id. When Corbis Corporation purchased Syg-ma in 1999, it acquired the licensing rights for some forty million images, including those owned by Grace. Id. No complete inventory existed of the images retained in Sygma’s archives. Id. The Sygma images were stored with other images, whose licensing rights also were acquired by Cor-bis Corporation, and filled three large rooms of double-stacked file cabinets. Id. In a letter dated May 10, 2001, Grace notified Sygma (by then known as Corbis-Sygma) that he was terminating Sygma as his representative. Id. at 345. The letter included the following:

I expect all of my images that are now in Corbis/Sygma’s files to be returned to me no later than June 1, 2001. This includes all images from May 1972 to the present that have been archived in both New York and Paris as originals or duplicates].

Id. at 346.

Sygma made sporadic returns of Grace’s images beginning in the fall of 2001. Id. The returns continued up to the time of trial. Id. The fact that the photographs were “disorganized” and kept in a “haphazard fashion” made it impossible for Sygma to account for all of the thousands of photographs spanning a period of thirty years. Id. Sygma found some of the images by referring to a list of stories relating to photographs for which royalties were paid and matching the photographs to the stories. Id. Despite all efforts, Syg-ma simply was unable to account for and return a great number of the photographs Grace had entrusted to it as his agent and representative. During the trial, Grace claimed that 67,473 of his images were missing. Id. at 347 n. 16. The District Court found that as of December 7, 2004, Sygma had returned 33,013 original images to Grace, id. at 346, and the parties do not dispute this figure.

The District Court determined that Grace’s entrustment of his photographs to Sygma for licensing purposes as his agent was a mutual benefit bailment, that the bailment ended when Grace terminated the relationship in May 2001, and that “Sygma is presumed to have been negligent in failing to return the missing images.” Id. at 348. Accordingly, the District Court concluded as follows: “Defendants have not provided a sufficient explanation for the loss, and, indeed, the record shows that Sygma’s system of keeping track of images was ‘completely inadequate.’ Hence, defendants are liable.” Id. Sygma, having filed no cross appeal, does not disagree with these determinations nor with the damages fixed by the District Court.

In evaluating Grace’s loss, the District Court observed that Grace’s burden to prove his damages with reasonable certainty was impacted by Sygma’s wrongdoing. Id. (citing Raishevich v. Foster, 9 F.Supp.2d 415, 417 (S.D.N.Y.1998)). The Court recognized that the uniqueness and earning potential of the photographic images are essential components in the evaluation of damages. See id. Identifying the number of images as the “threshold question,” the District Court noted the difficulty in resolving this issue occasioned by the “essentially non-existent” record-keeping and stated as follows:

I conclude, however, that the number of missing images is substantially below 67,473, the number claimed by Grace, and that, more likely than not, the number is about 40,000. I reach these conclusions because some of Grace’s estimates are high (for example, there was some inadvertent double-counting); some images were undoubtedly returned to Grace over the course of the thirty years; and some of the images were not given to Sygma in the first place.... In any event, in light of my rulings below on damages, a precise number is not necessary.

Id. at 348-49 (internal citations omitted). On appeal, Grace asserts that, even assuming as accurate the District Court’s discounts for double counting, returned images, and images not given to Sygma in the first place, the number of images missing would be 43,367. Sygma advances an even higher number — 46,448. Sygma claims, however, that this figure could be reduced to reflect “the several categories of images for which, while there are no exact numbers, one can reasonably be sure Grace’s numbers did not account.” Defendants-Appellees’ Br. at 25. Grace also contests the District Court’s assertion that “a precise number is not necessary,” arguing that “the [c]ourt’s failure to accurately calculate the number of lost images ... directly resulted in a corresponding reduction in damages.” Appellant’s Br. at 57.

As to the uniqueness element essential to the valuation process, the District Court concluded that, although “Grace had a ‘unique eye’ and was one of the top photojournalists of his time, the vast majority of his images were not unique.” Id. at 349. The District Court reasoned that most of the lost images were photographs of news events covered by other photographers, that many were “out-takes” or unusable, and that “only a small percentage of any collection of photographs is placed into the licensing stream.” Id. The Court noted that Zuma, Grace’s present agent, had selected only 6% to 10% of his available images for licensing. Id.

Reviewing Grace’s earning potential as a prelude to its ultimate assessment of damages, the District Court found that Grace earned an average of $11,002.48 per year from all of his images licensed by Sygma during the thirteen-year period 1990-2002, and $5,881 per year for the ten-year period 1991-2000, with the income from celebrity photos omitted. Id. As a measure of future income, however, the District Court characterized these averages as “high” because they included revenue from images that have been returned and that remained available for licensing, as well as “low” because, in later years especially, income more likely was reduced because the lost images were not available for licensing. Id. In evaluating Grace’s earning potential, the District Court indicated that it took into consideration Grace’s outstanding reputation and experience; the fact that he had spent little time in the past fifteen years in photojournalism; the declining income stream as the stories behind the images passed into history; the possibility that interest in past events could be triggered by current events; and the significant competition between Grace’s images and those of many other successful photojournalists. Id. at 349-50.

According to the District Court, the sales of various collections of images in their entirety also entered into its final determination of damages — the sales of the Bettmann Collection for $13.5 million ($1.23 per image); the Turnley Collection for $2.3 million ($3.83 per image); and the entire Sygma Collection to Corbis for $12.5 million ($.31 per image). Id. at 350. The District Court noted that these figures were “relevant,” but “the collections are different, and, unlike here, the transactions involved willing buyers and willing sellers. Grace did not want to sell his images.” Id.

The District Court considered and rejected the industry’s liquidated damages standard of $1,500 per lost transparency delivered on consignment, observing that some courts had used this standard in cases involving unique, superior, and irreplaceable images. The court found that the per-image standard of $1,500 would lead to an “absurd result” in this case, since not all the lost images were unique and irreplaceable and the recovery for the 40,000 images ultimately found missing by the District Court would be $60 million. The District Court stated that “[w]hat a client was willing to stipulate to as compensation in the event of the loss of an image when receiving a few ‘selects’ on consignment to review under the pressure of a deadline is not relevant to a situation involving 40,000 images.” Id.

Proceeding to review Grace’s other theories of valuation, the District Court rejected the testimony of Grace’s expert, who ranked the images into three categories of values of $5,000, $2,500, and $l,500-$2,000 each. The court observed that the expert “never looked at the licensing revenue that Grace’s photographs actually earned, which clearly is a relevant consideration,” Id. at 351, and characterized his testimony as evasive, non-responsive, and nonsensical. Id. The District Court found “unreasonable” Grace’s theory that 5% of the images (assuming 66,653 images missing) were “super selects” with a value of $1,500 each; 5% were “selects” valued at $750 each; and the remaining 90% had a value of $75 each. Also rejected as unreasonable was the proposal that 10% of the 66,653 images claimed to be missing be valued at $1,500 each. As to both these last theories, the court noted that the interest earned on the resulting sums “would be more than ten times what Grace was earning a year, on average, from the licensing of all his images.” Id.

Setting forth the rationale for the award it ultimately made, the District Court

eonclude[d] that defendants’ proposal of looking at Grace’s licensing income is reasonable, but only as a starting point. At a minimum, Grace should be compensated for what he would have earned if the missing images had been available for licensing in the past and if they were available for licensing in the future. But he should be awarded something more, for the loss of the licensing income is only part of his damages. The images have a value beyond just the licensing income — Grace no longer has these images to view or hold or enjoy or otherwise do with as he wishes.

Id.

“[Tjaking into account” the foregoing rationales, the District Court awarded Grace total damages in the sum of $472,000 in accordance with the following:

First, he is awarded $8,000 a year for four-and-a-half years, or $36,000 to account for lost licensing income from July 1, 2001, when his images should have been returned, to date.
Second, he is awarded an additional $436,000 for the loss of the images, based on a value of $100 per image for 4,000 images (I conclude ten percent are “selects”) and $1 an image for the remaining 36,000 images.

Id. Although the District Court awarded costs, it explained that pre-judgment interest was included in the total damages award and that “[n]o additional award is allowed for claims for holding fees or improper deductions or any other expenses or damages.” Id.

DISCUSSION

On this appeal from a judgment entered after a bench trial, we are constrained to review the District Court’s findings of fact for clear error and its conclusions of law de novo. See Mobil Shipping & Transp. Co. v. Wonsild Liquid Carriers Ltd., 190 F.3d 64, 67 (2d Cir.1999). We also are constrained to accord de novo review in examining whether the correct legal standard was applied by the District Court. See LoPresti v. Terwilliger, 126 F.3d 34, 39 (2d Cir.1997). Since Sygma does not contest its liability as bail-ee for the negligent loss of photographic images belonging to Grace, we are confronted here only with Grace’s challenge to the methodology employed by the District Court in arriving at its award of damages and his consequent objection to the adequacy of the award. In assessing damages, we are guided by the general rule that “[t]he measure of a bailee’s liability to the bailor for ... wrongful loss of the goods is their reasonable value at the time of such loss.” 8 C.J.S. Bailments § 149.

We have stated the New York rule (applicable here) governing the valuation of lost photographic images as follows:

[T]he value of lost slides depends primarily on their uniqueness and the “plaintiffs earning potential.” Lowit v. Consolidated Edison Co., 234 A.D.2d 2, 650 N.Y.S.2d 152, 152 (1996); accord Blackman v. Michael Friedman Publ’g Group, 201 A.D.2d 328, 607 N.Y.S.2d 43, 44 (1994) (“The proper standard ... is a consideration of uniqueness of the transparencies and plaintiffs earning potential.”); see also Gasperini, 66 F.3d [427, 429 (2d Cir.1995)] (New York courts consider “(1) the uniqueness of the transparencies and (2) the earning level of the photographer”); Nierenberg v. Wursteria, Inc., 189 A.D.2d 571, 592 N.Y.S.2d 27, 28 (1993) (“uniqueness of subject matter of the slides and the earning level of the photographer”); Alen MacWeeney, Inc. v. Esquire Assocs., 176 A.D.2d 217, 574 N.Y.S.2d 340, 341 (1991) (same).

Gasperini v. Ctr. for Humanities, Inc., 149 F.3d 137, 141 (2d Cir.1998).

In Gasperini, we upheld the District Court’s determination that the jury’s ability to distinguish slides that were of “superior quality,” “unique,” and “irreplaceable” from those that were “readily replaceable and available from other sources” enabled it to assign reasonable values to the lost images accordingly. Id. (internal quotation marks and alterations omitted). The case before us is different from Gasperini and somewhat unusual in that an enormous number of images is missing, the parties are unable to agree on the number of images lost, and the incompleteness of the records available makes it impossible to identify all the images in the “unique” category. The difficulty in computing damages under these circumstances is apparent. However, in cases such as this, “in which the defendant’s wrongdoing prevented the plaintiff from demonstrating the exact measure of the damages suffered, the factfinder may make a ‘just and reasonable estimate’ of the damages caused.” Raishevich v. Foster, 247 F.3d 337, 342 n. 2 (2d Cir.2001) (quoting Bigelow v. RKO Radio Pictures, Inc., 327 U.S. 251, 264, 66 S.Ct. 574, 90 L.Ed. 652 (1946)). Therefore, although Grace had the burden of proof as to loss, “he had no obligation to offer a mathematically precise formula as to the amount of damages.” Raishevich, 247 F.3d at 343.

Despite the flexibility to be accorded in proving damages under the circumstances revealed here, we have observed that “[t]he factfinder ... may not base its award on speculation or guesswork.” Id. Relevant data must be considered, and “[w]hen damages are at some unascertainable amount below an upper limit and when the uncertainty arises from the defendant’s wrong, the upper limit will be taken as the proper amount.” Id. (internal quotation marks and citation omitted). This principle was developed in Bigelow to avoid the potential for a wrongdoer to “profit by his wrongdoing at the expense of his victim.” Bigelow, 327 U.S. at 264, 66 S.Ct. 574. Values thus may be ascertained even when establishment with precision of all of the relevant data is problematic. See, e.g., Raishevich, 247 F.3d at 343 (fixing value where 347 transparencies were seized and later destroyed while in police custody although plaintiff “provided little to no evidence indicating the uniqueness of his work”); Blackman, 607 N.Y.S.2d at 44 (fixing value of 146 lost transparencies where the “record [wa]s barren of any evidence establishing the lost transparencies’ uniqueness”).

Having the foregoing in mind, we turn to the District Court’s formulation of damages in this case. Our attention is first drawn to the number of missing images identified by the District Court: “I conclude ... that the number of missing images is substantially below 67,473, the number claimed by Grace, and that, more likely than not, the number is about 40,-000.” Grace, 403 F.Supp.2d at 348 (emphasis supplied). Supporting its finding, the District Court discounted Grace’s claim for images that were double counted, images returned to Grace, and images never given to Sygma, such as those retained in the possession of Time and Newsweek. The problem with the District Court’s finding, that Sygma lost “about 40,000” of Grace’s images, Id. (emphasis supplied), is that when the District Court calculated the ultimate damages amount it multiplied the number of lost images by a value assigned to each image. A precise number of images is therefore necessary, however inexact the method of arriving at it may be. As Grace himself points out, the court’s approximation of 40,000, rounded down from the number of lost images asserted by either party, results in a reduction of the amount of damages Grace should receive. Sygma, whose interest is in keeping the number as low as possible, asserts that the number of lost images is 46,448 at most. On appeal, Grace, although apparently adhering to the claim that 67,473 images are missing, argues that even assuming the District Court’s discounts for double counting, returned images, and images not given to Sygma in the first place, the number lost would be 43,367. In either case, the number is above the 40,000 figure which the District Court settled upon.

Compounding the District Court’s error in its finding of the number of images lost is the use of that erroneous number in awarding $100 per image for 4,000 images, said to be 10% of the total, and $1 per image “for the remaining 36,000 images.” Id. at 351. The 4,000 are designated “selects,” and it is not apparent whether the District Court intended this term to mean “unique” images or merely generic images having some value in the stock photography trade. See Alen MacWeeney, Inc., 574 N.Y.S.2d at 341 (assessing value of generic photographs of young female executive in business dress). Moreover, the District Court failed to explain the basis it employed for assigning a $100 per-image value to the “selects” and a $1 per-image value to the remaining images. Nor is it clear how the District Court came up with a “lost licensing income” figure of $8,000 per year or why it awarded $36,000 (said to be the total lost licensing income from the date that the images should have been returned to Grace) as an addition to the “face values” assigned to the lost images.

In sum, it appears to us that, in assessing damages in this case, the District Court applied an arbitrary methodology and that its award was untethered to the facts or to its own correct analysis of the applicable law. We simply are unable to identify the formula applied by the District Court. When a District Court’s explanation of methodology and subsidiary facts are inadequate, remand is indicated. See Henry v. Champlain Enters., Inc., 445 F.3d 610, 622 (2d Cir.2006) (“In the absence of a specific explanation for the district court’s findings, we are unable to determine whether this valuation, and the resulting damages award, are justified.”). We are therefore remanding this case with instructions to the District Court to develop and apply an appropriate methodology, as well as to make appropriate factual findings essential to arrive at a reasonable assessment of damages. We do so without any restrictions whatsoever upon the District Court in seeking additional data or in conducting such additional evidentiary hearings as it may deem necessary to enable it to make findings related to the evidence and germane to the formula to be applied in the ultimate assessment of damages.

To guide the District Court on remand, we suggest the following methodology, which we think would be appropriate in light of the record information. We suggest this method with the goal of ensuring that the damages calculation is both reasonable and tethered to the evidence before the court, although we recognize that this is not the only possible method that will achieve that goal. If the court is to calculate damages by assigning a value per image and multiplying that by the number of lost images, the District Court should first ascertain, as nearly as reasonably possible, the number of lost images. A good starting point would seem to entail consideration of the 46,448 number identified by Sygma and the 43,367 number that Grace concedes would be applicable if the District Court’s discounts were to be accepted. Of course, additional evidence may produce a completely different number. Certainly, the 40,000 figure adopted by the District Court is too inexact to be used for these purposes and cannot be considered “plausible in light of the record viewed in its entirety.” Zervos v. Verizon N.Y., Inc., 252 F.3d 163, 168 (2d Cir.2001) (internal quotation marks and citation omitted).

In formulating an award of damages on remand, the District Court might next consider factoring in Grace’s past annual earnings, perhaps utilizing the Bigelow principle described above. Application of this principle at this juncture requires identification of Grace’s highest earning year and the assumption that that year represented the collection’s earning capacity. The District Court may determine that this assumption takes care of the gap between “past earnings” and “earning potential.” Based upon the evidence presented of record, Grace’s highest earnings came in 1979 for Paris sales, when he earned $19,970.72 and in 1999 for New York sales, when he earned $1,288.09, for a total of $21,258.81 (reflecting conversion from francs).

The next step in this methodology would be to ascertain the percentage of lost images in order to find the earnings per year from the lost images. This would be accomplished by dividing the number of lost images by the total number of images consigned to Sygma over the years. Accepting the number of lost images put forward by Sygma (46,448) for the purpose of this example only, and adding to it 33,013, the number of non-lost images not in dispute, results in a total of 79,461 images. Dividing this hypothetical number of lost images (46,448) by the total number of images (79,461) yields 0.5845 (58%) in this example. Carrying out the methodology of this example, 58% of $21,258.81 earnings per year yields a figure of $12,330.11 earnings per year from lost images.

Although this figure may seem generous, given the District Court’s findings that Grace’s average earnings per year from all images in 1979-1989 totaled $8,475.77, without New York income, and $11,002.48 in 1990-2002, including New York income, “the wrongdoer may not object to the plaintiffs reasonable estimate of the cause of injury and of its amount, supported by the evidence, because not based on more accurate data which the wrongdoer’s misconduct has rendered unavailable.” Bigelow, 327 U.S. at 265, 66 S.Ct. 574.

We cannot tell from the record when Sygma lost the lost images, thus making it difficult to determine to what extent the past revenues from Sygma’s Grace collection are attributable to either the lost images or non-lost images. If the District Court were to determine that Sygma misplaced all of the lost images upon their arrival at Sygma, for example, then those images would presumably not have contributed at all to the past earnings generated by Sygma’s Grace collection, and the past earnings data would reflect revenue generated only by the returned images. There was no evidence before the District Court or produced by the parties, however, demonstrating that the past revenue came exclusively from the non-lost images. If Sygma did not lose the images until immediately before Grace asked Sygma to return them, then some portion of the past earnings would be attributable to the lost images, and we would be able to calculate the percentage of those earnings attributable to those images by determining how much of the entire Grace collection Sygma lost. It is likely, however, that different images were lost at different times, which is why the methodology set forth herein assumes that the lost and non-lost images produced, absent any further evidence to the contrary and on the current record before us, a proportionate share of the revenue. These findings may indeed be difficult to make in light of the state of the evidence. But we nonetheless suggest that in calculating the past earnings of the lost images using the revenues generated by the entire collection, the District Court should be aware of the possibility that those revenues were probably generated by some combination of lost and non-lost images.

Moreover, in making its own computation of annual earning potential, the District Court is free to discount the number of lost images to the extent it finds additional evidence demonstrating that some percentage of the lost images did not contribute to past revenues. A lower number in the lost-images category would of course result in a lower award overall.

Further applying the suggested methodology, the District Court would apply to the annual earnings potential a multiplier based upon the length of time that the lost images would continue to be a source of revenue. This might be the average number of years remaining on the copyrights of the lost images or some other measure based upon the input of the parties on this issue. We note that the Court in Raishe-vich applied a 30-year multiplier, though it did not indicate why it chose this length of time. Raishevich, 247 F.3d at 341. This step in the methodology assumes that past earnings reflect future earning potential. See Gasperini v. Ctr. for Humanities, 972 F.Supp. 765, 772 (S.D.N.Y.1997) (noting that “prior licensing fees collected and the prior economic experience of the photographer in connection with the slides” was one of seven elements relevant to the “earning potential” factor in a lost transparency case), vacated and remanded on other grounds, 149 F.3d 137 (2d Cir.1998); Raishevich v. Foster, 9 F.Supp.2d 415, 417 (S.D.N.Y.1998) (listing “past earnings from use of the transparencies” as one of five elements relevant to determining lost transparencies’ “earning potential”), vacated and remanded on other grounds, 247 F.3d 337 (2d Cir.2001).

The formula suggested here rests on two assumptions: first that the market value of the lost images can be determined by establishing or inferring the earnings generated by the lost images in the past, or those that they would have generated in the past. We do not disagree with the District Court that reliance on past earnings to determine the market value of the lost images may be “reasonable, but only as a starting point,” Grace, 403 F.Supp.2d at 351, though we note that some courts have relied exclusively on past earnings to determine damages awards based on projected future earnings, see, e.g., Nierenberg, 592 N.Y.S.2d at 28 (reducing damages but basing value on past licensing revenue to provide estimate of future licensing value); see also Raishevich, 9 F.Supp.2d at 421. The District Court may resolve the “past earnings”/“earning potential” gap by identifying its reliance on this assumption, or by applying the Bige-low principle we discussed earlier, or in some other fashion. As noted above, our focus here is to ensure that the damages award is reasonable and based on the evidence presented. The District Court may also see fit to expand upon the values generated by the methodology suggested here by incorporating into its damages valuation evidence of other elements of earning potential and uniqueness. See Gasperini, 149 F.3d at 141.

Our second assumption has been that the requisite uniqueness element is also reflected in past earnings. That is, to rely on this methodology alone, one must assume that past earnings reflect the ratio of unique to non-unique images in the set of images that generated the past earnings. We think this is a rational assumption given the large size of the sets of both lost and non-lost images, at least if one assumes that there is no causal connection between the unique nature of an image and whether or not it has been lost. We recognize however, that uniqueness is required under New York law to be factored into the damages calculation. We leave it to the District Court to decide whether to rely on some of the assumptions laid out in the opinion, or to find another way to incorporate uniqueness. Moreover, we note that there was some evidence of some uniqueness of some photographs. The problem here has been created by the failure of the parties, by virtue of poor record-keeping, to be more specific in regard to the uniqueness element. We also note, however, that in Blackman, 607 N.Y.S.2d at 44, as well as in Raishevich, 247 F.3d at 343, there was no evidence or implication of uniqueness. And in Nierenberg, 592 N.Y.S.2d at 28, the value of the images was based on an estimate of their licensing revenue.

In order to produce a just a reasonable estimate of value with this methodology, the Court should factor in the discounted value of the stream of future income that the images are expected to produce. See Ammar v. United States, 342 F.3d 133, 147-48 (2d Cir.2003) (remanding for recalculation of award where district court failed to discount future loss of earnings); Nestlé Holdings, Inc. v. Comm’r of Internal Revenue, 152 F.3d 83, 87-88 (2d Cir.1998) (discounting future stream of royalty payments for use of intellectual property). “[I]n computing the damages recoverable for the deprivation of future benefits, the principle of limiting the recovery to compensation requires that adequate allowance be made, according to circumstances, for the earning power of money....” Metz v. United Techs. Corp., 754 F.2d 63, 66 (2d Cir.1985) (internal quotation marks omitted). We leave the appropriate calculation to the District Court, including the assignment of the discount rate and the determination of the number of years over which to calculate the returns. See Ammar, 342 F.3d at 148 (observing that parties may adduce evidence relating to the discount rate); McCrann v. U.S. Lines, Inc., 803 F.2d 771, 773 & n. 1 (2d Cir.1986) (explaining factors to be used in setting discount rate).

Finally, we direct the District Court, after a reasoned calculation of estimated damages, discounted to present value, to assess pre-judgment interest separately in accordance with New York law. See In re Conn. Nat’l Bank, 928 F.2d 39, 42 (2d Cir.1991) (holding that district court properly applied pre-judgment interest to the total sum of discounted future payments). In its opinion, the District Court, referring to its separate awards for “select” images, “remaining” images, and lost licensing income for 4k years, stated that “[t]he above numbers take into account pre-judgment interest.” Grace, 403 F.Supp.2d at 351. Pre-judgment interest must be computed as an ascertainable amount pursuant to New York Civil Practice Law and Rules § 5001. That statute provides for the recovery of pre-judgment interest “upon a sum awarded because of a breach of performance of contract, or because of an act or omission depriving or otherwise interfering with title to, or possession or enjoyment of, property.” N.Y. C.P.L.R. § 5001(a). Sygma has deprived Grace of the possession and enjoyment of his photographic images, and Grace is entitled to pre-judgment interest. See Raishevich, 247 F.3d at 342.

CONCLUSION

We vacate the judgment of the District Court and remand the case for further proceedings consistent with the foregoing. 
      
      . There are multiple instances in the course of these calculations where the District Court may want to apply the Bigelow principle to establish a certain value. The court may determine, in its discretion, when to apply the principle — but it should apply it only once. See Raishevich, 247 F.3d at 344 (“Although the Bigelow principle should be applied, it should not be applied twice.”).
     