973 F.2d 359
HANNON ARMSTRONG & COMPANY, formerly known as Eden Hannon &Company, Plaintiff-Appellee,v.SUMITOMO TRUST & BANKING COMPANY, Defendant-Appellant.American Bankers Association, Amicus Curiae.HANNON ARMSTRONG & COMPANY, formerly known as Eden Hannon &Company, Plaintiff-Appellant,v.SUMITOMO TRUST & BANKING COMPANY, Defendant-Appellee.American Bankers Association, Amicus Curiae.
Nos. 91-2658, 91-2662.
United States Court of Appeals,Fourth Circuit.
Argued April 9, 1992.Decided Aug. 24, 1992.As Amended Oct. 5, 1992.

John Vanderstar, Covington & Burling, Washington, D.C., argued (John C. Richowsky, on the brief) for appellant.
Ralph N. Albright, Jr., Morgan, Lewis & Bockius, Washington, D.C., argued (Peter Buscemi, Thomas J. O'Brien, on the brief), for appellee.
John F. Gill, General Counsel, Michael F. Crotty, Deputy General Counsel for Litigation, American Bankers Ass'n, Washington, D.C., for amicus curiae.
Before RUSSELL, WIDENER, and HALL, Circuit Judges.
OPINION
DONALD RUSSELL, Circuit Judge:


1
Sumitomo Trust & Banking Company appeals the district court's determination on remand of the amount of the profits which the bank obtained by engaging in a certain transaction in violation of an agreement not to compete, and which the Fourth Circuit determined should therefore be placed in constructive trust for the benefit of Appellee Hannon Armstrong.   Hannon Armstrong cross-appeals.   As explained below, we affirm in part, reverse in part, and remand with instructions.

I.

2
This is an appeal of the district court's disposition on remand of our previous decision in Eden Hannon & Co. v. Sumitomo Trust and Banking Co., 914 F.2d 556 (4th Cir.1990), cert. denied, --- U.S. ----, 111 S.Ct. 1414, 113 L.Ed.2d 467 (1991).   The initial Eden Hannon action in the district court involved claims by plaintiff Eden Hannon & Company ("EHC"), now the Appellee Hannon Armstrong & Company, that defendant Sumitomo Trust & Banking Company ("Sumitomo" or "the bank") misappropriated EHC's trade secrets and breached an agreement not to compete with EHC in bidding for a type of investment vehicle offered by the Xerox Corporation.


3
In the summer of 1988, prior to the initial district court action, Sumitomo bank approached EHC, an investment analyst firm engaged in the business of valuing copying machine lease portfolios, about purchasing a portfolio of Xerox copying machine leases through EHC.   In anticipation of placing a bid on behalf of Sumitomo for the purchase of this type of investment vehicle, EHC required Sumitomo to execute a "Nondisclosure and Noncircumvention Agreement" in order to protect confidential information which EHC shared with Sumitomo as part of their negotiations.  914 F.2d at 557.   In violation of this noncompetition agreement, and after taking possession of EHC's confidential information, Sumitomo independently bid on a portfolio of Xerox copying machine leases in December of 1988, won the bid, and purchased that copier lease portfolio.  914 F.2d at 560.   EHC also engaged in the bidding for the December 1988 copier lease portfolio.   However, the Xerox Corporation ranked EHC's bid third among bids received for investment.


4
EHC sued.   While finding that Sumitomo breached the Nondisclosure and Noncircumvention Agreement, the district court struck EHC's claim for monetary damages, finding that since the Xerox Corporation ranked EHC's bid third, EHC had not proven monetary damages resulting from Sumitomo's bid with sufficient certainty, because it was most likely that the second place bidder would have otherwise won the portfolio.  Eden Hannon, 914 F.2d at 557.   EHC appealed.   This circuit affirmed the district court's finding that Sumitomo breached the agreement not to compete, but reversed the district court's refusal to award monetary damages on the breach claim.   After observing that equitable remedies are available under Virginia law1 to rectify the harm caused by violation of noncompetition agreements, and to compensate such harm where money damages are speculative, this court imposed a constructive trust in favor of EHC on Sumitomo's profits from purchasing the December 1988 Xerox copier lease portfolio.   We further directed the district court to "determine the amount of Sumitomo's profits on that portfolio, and enter an order awarding that amount to EHC."  914 F.2d at 565.   The district court's determination on remand of Sumitomo's profits on the purchase of the December 1988 Xerox copier lease portfolio is now before this court on appeal.

II.

5
The investment vehicle which Sumitomo purchased is known as a Xerox Partnership Asset Strategy ("PAS") portfolio.   An investor in a PAS portfolio purchases from the Xerox Corporation the right to receive a stream of monthly payments on a group of copying machines which Xerox has leased to its customers, plus the right to receive the sales price of the leased copiers if customers exercise an option under their leases to purchase the copiers at the end of their lease terms.   Essentially, in a PAS portfolio transaction, the Xerox Corporation initially lends its customers the sum of all the monthly rental payments which Xerox's customers are obligated to make on their lease of the copying machines.   When an investor such as Sumitomo purchases a PAS portfolio, the investor then buys Xerox's right to collect the customers' monthly payments on the financing which Xerox has extended to its copying machine customers.   In substance, a PAS investor like Sumitomo thereby assumes the role, previously held by Xerox, as lender on the financing which Xerox customers used to lease copying machines with an option to buy.   Some portion of the stream of monthly payments which a PAS investor like Sumitomo has purchased the right to collect represents a return on the investor's purchase price for the PAS portfolio, i.e., represents a return of the investor's principal;  some portion of the monthly payments represents the investor's revenues on the PAS portfolio, i.e., represents interest on the investor's principal.


6
Thus, as the district court observed on remand, an investor like Sumitomo receives monthly payments on the December 1988 PAS portfolio which are in part recovery of principal and in part interest revenue.   The interest revenue component of each monthly payment is calculated by applying the annual interest rate specified by the terms of the PAS portfolio, 10.935% per year, to Sumitomo's outstanding principal at the end of the preceding month.   Payments on the December 1988 PAS portfolio are scheduled such that Sumitomo recovers its entire principal investment, or purchase price, of $35,207,897 by July, 1992.2


7
In its memorandum opinion on remand, the district court divided its analysis of Sumitomo's profits on the December 1988 PAS portfolio into "past profits," i.e., profits Sumitomo earned on the portfolio prior to the district court's February 14, 1991, proceedings on remand, and "future profits," i.e., profits earned from the date of the remand proceedings up to the maturity of the PAS portfolio in July 1992.   We first address the past profits issue.

A.

8
In calculating past profits, the district court found that the Appellee Hannon Armstrong and Appellant Sumitomo stipulated that the interest revenue components of the monthly payments which Sumitomo had received on the portfolio from inception in December 1988 through February 14, 1991, totalled $5,186,638.3  (J.A. at 1529;  see also J.A. at 1843.)   But, while the parties agreed on the amount of pre-February 14, 1991, interest revenue, the parties disputed the amount and kind of expenses which should be deducted from the interest revenues to determine Sumitomo's past profits on the December 1988 PAS portfolio.   Sumitomo argued that the expense deductions from the $5,186,638 interest revenue figure should include a market cost of funds deduction based on the 9.735% market interest rate as of the date that Sumitomo purchased the PAS portfolio in December 1988.   In other words, to calculate profits on the PAS portfolio, Sumitomo argued, the district court should start with an interest expense rate, or "spread," based on the 10.935% interest which Sumitomo earned on the PAS portfolio minus the 9.735% market interest rate which Sumitomo claims it would have paid if the bank had borrowed on the open market the $35,207,897 which the bank used to purchase the PAS portfolio.   This "market cost of funds" approach, Sumitomo insisted, would yield only $572,881 in past interest income on the PAS portfolio's $5,186,638 in interest revenues through February 14, 1991.   Furthermore, Sumitomo contended, transactional expenses in the nature of a $131,000 fee which Sumitomo paid an agent, Mr. Gerald Sherman, to prepare and submit Sumitomo's bid to Xerox for the PAS portfolio, and $69,000 in legal fees and expenses for delivering the copying machines to Rochester, New York, should then be deducted from the $572,881 in interest income.   Sumitomo thereby argued that, after all appropriate deductions from the $5,186,638 in interest revenue, Sumitomo earned actual profits of only $372,881 on the PAS portfolio through February 14, 1991.


9
However, the district court on remand rejected Sumitomo's "market cost of funds" approach for calculating profits, and instead applied an average interest rate methodology which Eden Hannon and Company (EHC) advocated.   The district court explained the rationale for this average interest rate methodology as follows:


10
Where a bank does not specifically borrow money in order to make a specific loan or to enter a specific transaction, the bank obtains the funds for that transaction from its pool of monies which consists of several types of money such as federal funds borrowings, demand deposits, borrowings, certificates of deposits, and capital of the bank.   To arrive at an interest rate cost of the pooled monies, a bank determines its actual interest expense for each category in the pool and then divides the interest expense by the amount of funds in each category.   The resulting average interest rates for the various categories of funds in the pool are then weighted according to the size of the categories and an overall average interest rate for all the categories is produced.


11
(J.A. at 1528.)   Eden Hannon's accounting witness, Mr. John Little of Ernst & Young, testified that in a manner consistent with this rationale, and using generally accepted accounting principles ("GAAP"), he determined Sumitomo's past profits on the PAS portfolio.   Little stated that he used Sumitomo's monthly average interest rate as listed in the bank's own records, where available, and otherwise employed the average interest rate which Sumitomo listed in quarterly reports to the FDIC, to calculate over the life of the PAS portfolio the cost to the bank of funds lent to Xerox customers by Sumitomo's purchase of the portfolio.   Thus, rather than using the market rate as of the date Sumitomo purchased the PAS portfolio, 9.735%, as a constant measure of Sumitomo's cost of funds throughout the term of the portfolio, Little subtracted these monthly average interest rates from the 10.935% that Sumitomo earned on the portfolio to calculate the bank's interest income.


12
To calculate Sumitomo's net past profits on the PAS portfolio, i.e., profits through February 14, 1991, the district court adopted Little's average interest rate methodology, noting


13
Those ... interest rates were multiplied by the appropriate outstanding balance remaining on Sumitomo's Xerox investment for each month, and the resulting figures represent monthly interest expense amounts that can reasonably be assigned to Sumitomo's investment in the Xerox transaction, in the absence of any proof of actual interest expense specifically incurred on the transaction.


14
(J.A. at 1529.)   Calculated in the manner Little described, the cost of funds to Sumitomo through February 14, 1991, on the PAS portfolio was $2,182,669.   After allowing Sumitomo to deduct this cost of funds figure, and to deduct both the $131,000 fee which the bank paid for preparation of its bid and the $69,000 which Sumitomo paid in legal and transportation expenses, from $5,186,638 in interest revenues on the PAS portfolio through February 14, 1991, the district court found that Sumitomo had earned past profits on the portfolio of $2,803,969.

B.

15
The parties also disputed the proper means of determining "future profits," i.e., profits Sumitomo would earn on the PAS portfolio from the date of the February 14, 1991, remand proceedings until the maturity of the portfolio in July 1992.   The district court correctly observed that Sumitomo's future profits on the PAS portfolio would arise from two sources:  interest income from February 14, 1991, through July of 1992, and Sumitomo's right to receive the portfolio's "residual value," that is, to receive the sales revenues from copiers which Xerox customers elected to buy at the end of their lease terms.   On remand, the parties stipulated to the "residual value" of the PAS portfolio, and neither party now raises the matter on appeal.   However, the parties offered conflicting approaches for calculating future profits.


16
Appellant's witness, Mr. Hideo Amemiya, manager of Sumitomo's Structured Finance Department, testified that he calculated Sumitomo's interest income from an appropriate date near the remand hearing until the end of the transaction.   Amemiya's calculations entailed several assumptions.   First, Amemiya stated his calculations assumed that--as we have previously noted--Sumitomo recovers its entire principal investment in the PAS portfolio on a date forty-three months after December of 1988.   Second, Amemiya stated that his calculations assumed that payments of principal from January of 1991 until the recovery of all Sumitomo's principal in the forty-third month were amortized over a straight line.4  Third, Amemiya's calculations used the same method of estimating future profits as Sumitomo previously used to calculate past profits, in that Amemiya deducted the "market cost of funds" rate of 9.735%, i.e., the interest rate which Sumitomo claims it would have paid on the market to borrow $35,207,897 in order to purchase the PAS portfolio in December of 1988, from the 10.935% interest revenue which Sumitomo earned on the PAS portfolio to estimate Sumitomo's interest income on the portfolio from January 1991 until the forty-third month, July 1992.


17
Thus, Amemiya assumed that the $10,286,879 in Sumitomo's principal outstanding as of the remand proceedings on February 14, 1991, would be recovered in equal amounts until it was fully recovered in July of 1992.   Amemiya then applied the assumed 1.2% profitability spread, i.e., 10.935% interest earned minus the 9.735% interest expense rate, to the outstanding balance for each month, and summed the results to estimate that Sumitomo would achieve future profits of $102,851.5  Although the district court had rejected the very similar approach which Sumitomo offered for calculating past profits, the district court adopted Amemiya's analysis, and accordingly awarded Eden Hannon $102,851 in future profits.  (J.A. at 1531.)


18
In so doing, the district court rejected the approach which Eden Hannon offered for estimating future profits.   Eden Hannon's expert witness, Dr. Walter H.A. Vandaele, testified that he calculated the value of future profits of the PAS portfolio in the following manner.   First, Vandaele estimated that total amount of the payments remaining to be received from the PAS portfolio from the date of the remand proceeding, February 14, 1991, up to the PAS portfolio's maturity in July of 1992, was $11,178,546.   Vandaele then discounted this amount back to its net present value as of February 14, 1991, obtaining a discounted total of $10,761,935.   Subtracting from this amount the unrecovered principal on the PAS portfolio as of the date of the remand proceedings, $10,286,879, yielded a difference of $475,056.   Since a reasonable investor would therefore buy the right to receive the portfolio payments from February 14, 1991, to July 1992 for the amount of this difference, plus the amount of Sumitomo's unrecovered principal as the date of the remand proceedings--$10,286,879--Vandaele asserted that $475,056 was an accurate estimate of present value of the future profits on the PAS portfolio.   The district court found Vandaele "unpersuasive in his theory of future profits" in that his approach failed to incorporate any actual "expenses incurred by the defendant" and depended too "heavily on the choice of a correct discount rate to reduce future dollars to current dollars."  (J.A. at 1529-30.)

III.

19
Sumitomo appeals, arguing primarily that the district court erred in using the average interest rate methodology which Eden Hannon advocated to calculate pre-February 14, 1991, interest income on the PAS transaction.   Eden Hannon and Company, now known as Hannon Armstrong and Company, cross-appeals, contending that the district court erred in refusing to adopt the average interest rate methodology which it advocated to also calculate the post-February 14, 1991, interest income on the PAS transaction.   Hannon Armstrong further argues that the district court erred in allowing Sumitomo to deduct transactional expenses from profits on the PAS portfolio, and erred in refusing to award EHC prejudgment interest on Sumitomo's pre-February 14, 1991, profits on the portfolio.

A.

20
As noted above, we concluded in the first appeal of this action that "EHC is entitled to a constructive trust over Sumitomo's profits from the purchase of the December 1988 Xerox PAS portfolio.   Thus, the district court should determine the amount of Sumitomo's profits on that portfolio, and enter an order awarding that amount to EHC."  Eden Hannon & Co. v. Sumitomo Trust and Banking Co., 914 F.2d 556, 565 (4th Cir.1990), cert. denied, --- U.S. ----, 111 S.Ct. 1414, 113 L.Ed.2d 467 (1991).   This directive guides our review of the district court's determinations on remand.


21
Judge Haynsworth wrote, "A constructive trust is merely a procedural device by which a court of equity may rectify certain wrongs."  New Amsterdam Casualty Co. v. Waller, 301 F.2d 839, 842 (4th Cir.1962).   Courts have impressed equitable remedies of this kind upon wrongfully obtained profits in a variety of contexts, including breach of fiduciary obligation or breach of contract, e.g., Snepp v. United States, 444 U.S. 507, 515-16, 100 S.Ct. 763, 768-69, 62 L.Ed.2d 704 (1980), copyright infringement, see Sheldon v. Metro-Goldwyn Corp., 309 U.S. 390, 399, 60 S.Ct. 681, 683, 84 L.Ed. 825 (1940), and patent infringement, e.g., Tilghman v. Proctor, 125 U.S. 136, 146, 8 S.Ct. 894, 899, 31 L.Ed. 664 (1888).   The purpose of such equity-inspired relief is "to provide just compensation for the wrong, not to impose a penalty," and such relief is "given in accordance with the principles governing equity jurisdiction, not to inflict punishment but to prevent an unjust enrichment."  Sheldon, 309 U.S. at 399, 60 S.Ct. at 683.   Thus, as the Supreme Court observed in Sheldon, " 'The infringer is liable for actual, not for possible gains.   The profits, therefore, which he must account for, are not those which he might reasonably have made, but those which he did make, by use of the plaintiff's invention.' "  309 U.S. at 400, 60 S.Ct. at 684 (quoting Tilghman v. Proctor, 125 U.S. 136, 146, 8 S.Ct. 894, 899, 31 L.Ed. 664 (1888)).   We interpret this language to mean, consistent with our directive in Eden Hannon, 914 F.2d at 565, that a constructive trust in favor of Appellee Hannon Armstrong exists only upon the actual profits which Appellant Sumitomo bank earned on the December 1988 PAS portfolio.   Hannon Armstrong is thus entitled to a sum equal to the actual revenues which Sumitomo obtained on the PAS portfolio, minus the actual expenses which Sumitomo legitimately incurred as part of that transaction.   See Sutton v. Gulf Smokeless Coal Co., 77 F.2d 439, 441 (4th Cir.1935) (holding that where the plaintiff receives profits made by an infringer, reasonable and necessary expenses of the business are deductible from revenues to determine profits).

B.

22
Appellant Sumitomo and Appellee Hannon Armstrong agreed on remand that through February 14, 1991, Sumitomo obtained actual revenues of $5,186,638 on the PAS portfolio.   Hence, in calculating actual profits on the portfolio through February 14, 1991--the "past profits" to which the district court referred--the question here becomes one of ascertaining the actual expenses which Sumitomo incurred on the PAS portfolio transaction from the bank's purchase of the portfolio in December of 1988 to the date of the remand proceedings, February 14, 1991, so that such expenses can then be deducted from the actual revenues for the same period to arrive at an actual "past profits" figure.   The disputed expenses at issue on appeal are Sumitomo's interest expense, i.e., the bank's costs of obtaining the funds which it, in substance, lent to Xerox copier customers by purchasing the PAS portfolio,6 and transactional expenses consisting of a $131,000 fee which Sumitomo paid an agent to prepare and submit Sumitomo's bid to Xerox for the PAS portfolio, and $69,000 in legal fees and expenses for delivering copying machines to Rochester, New York.   We address each of these disputed expenses in turn.


23
As to interest expense, we find the average interest rate methodology which Appellee Eden Hannon's accounting witness, Mr. John Little of Ernst & Young, advocated on remand to be a more compelling analysis than Sumitomo's market "cost of funds" approach.   Based on a Sumitomo loan officer's determination that in December 1988 the bank would have paid 9.735% in interest were Sumitomo to then borrow $35,207,897 on the open market in order to purchase the PAS portfolio, and based on that loan officer's entry of the 9.735% figure into one of the bank's records,7 Sumitomo argues that a market "cost of funds" rate of 9.735% should be used to calculate its interest expense on the PAS portfolio.   However, the fact remains that Sumitomo never actually borrowed funds at that 9.735% interest rate to buy the PAS portfolio.   Since Sumitomo never actually borrowed at 9.735% interest the funds used to invest in the portfolio, that 9.735% rate cannot actually reflect Sumitomo's interest expense on the PAS portfolio, and the rate therefore cannot be used to determine Sumitomo's actual pre-February 14, 1991, profits.


24
In fact, Sumitomo suggests, it may be impossible to exactly ascertain the actual interest rate which the bank paid to obtain the funds loaned to the Xerox customers at the time Sumitomo entered the transaction in December 1988, because, as Sumitomo readily admits, the bank does not engage in "match funding" of loans, i.e., does not borrow specific dollars at a certain interest rate to fund a specific loan that the bank is making.  (Appellant's Br. at 9.)   In the absence of such exact information as to the cost to Sumitomo of the funds used to buy the December 1988 PAS portfolio, a court may properly use the most accurate approximation of the wrongdoer's costs in order to calculate his "actual" profits.   See Sheldon v. Metro-Goldwyn Corp., 309 U.S. 390, 403, 60 S.Ct. 681, 685, 84 L.Ed. 825 (1940) (ruling that, in determining an infringer's profits where mathematical exactness is impossible, a reasonable approximation is all that is necessary).   Further, a reasonable approximation of such costs may properly be attained with the aid of expert testimony.   See id.


25
The district court found on remand that where a bank does not borrow specific funds at a certain rate to make a specific loan, the bank obtains the funds from a pool consisting, for example, of federal funds borrowings, demand deposits, other borrowings, certificates of deposits, and the bank's capital.   To determine the average interest expense rate for using funds from this pool, the district court further found, a bank averages all the interest expense rates for each variety of money in the pool, weighting that average according to the portion of the pool that each variety comprises.   Eden Hannon's accounting witness, John Little, testified that in a fashion consistent with this practice, and using figures obtained both from Sumitomo's own monthly records and quarterly reports to the FDIC, he determined the average interest expense rate for the funds which Sumitomo used to invest in the PAS portfolio.   Upon determining this average interest expense rate, Little calculated that, through February 14, 1991, Sumitomo had incurred interest expense on the portfolio of $2,182,669.   We are persuaded that Little's methodology provides a more accurate statement of the actual costs to Sumitomo of obtaining the funds for the PAS portfolio than arbitrarily assuming that Sumitomo's true costs are somehow determined by market interests rates as of the date Sumitomo purchased the portfolio.   We therefore affirm the district court's finding on remand of Sumitomo's pre-February 14, 1991, interest expense.


26
Hannon Armstrong next disputes the district court's decision to allow Sumitomo to deduct from pre-February 14, 1991, revenues the $131,000 fee which Sumitomo paid Mr. Gerald Sherman's one-man company, Oasis, to prepare and submit the bank's bid on the PAS portfolio to the Xerox Corporation.   As Hannon Armstrong correctly notes, we observed in our previous opinion that when Sumitomo violated its agreement not to compete with EHC by bidding directly on the December 1988 PAS portfolio, Sumitomo placed the offending bid through a " 'Shell company to avoid ... damage ... to the relationship with Eden Hannon.' "  Eden Hannon & Co. v. Sumitomo Trust and Banking Co., 914 F.2d 556, 559 (4th Cir.1990), cert. denied, --- U.S. ----, 111 S.Ct. 1414, 113 L.Ed.2d 467 (1991).   We further referred to Sherman and his Oasis Company as the "stalking horse for Sumitomo" in the bank's efforts to surreptitiously place a bid on that portfolio.  Id.  Because "Sumitomo used Sherman to attempt to conceal" the bank's wrongful conduct, and because "Sherman willingly assisted" the bank's efforts, Hannon Armstrong argues, Sumitomo should not be permitted to deduct Sherman's fee from its pre-February 14, 1991, revenues on the PAS portfolio.  (Appellee's Br. at 37-38).


27
Hannon Armstrong's focus on the wrongful or willing conduct of Sumitomo and Sherman is misplaced.   This circuit stated in Sutton v. Gulf Smokeless Coal Co., "Where a complainant ... accept[s] the profits made by an infringer, reasonable and necessary expenses of the business are of course deductible, and the fact that the infringement was willful and deliberate is immaterial on that inquiry."  77 F.2d 439, 441 (4th Cir.1935).   Thus, the proper inquiry is not whether Sumitomo's breach of the agreement not to compete was wrongful, nor whether the assistance that Sherman provided to Sumitomo was willing or deliberate.   Rather, the proper inquiry is whether the $131,000 fee was "reasonable and necessary."   See id.   In view of the fact that, for the same transaction, Eden Hannon concedes that it would have charged a fee over four times larger than the $131,000 which Sumitomo paid Sherman, (J.A. at 187), any argument that the Appellee might make as to the unreasonableness of Sherman's fee lacks credibility.   We therefore affirm the district court's decision to permit Sumitomo to deduct Sherman's $131,000 fee from pre-February 14, 1991, revenues on the PAS portfolio.


28
Hannon Armstrong also appeals the district court's decision to allow Sumitomo to deduct from pre-February 14, 1991, PAS portfolio revenues a total of $69,000 in legal fees on the transaction and expenses of delivering copiers to Rochester, New York.   Hannon Armstrong argues that because Sumitomo presented no documentary evidence, e.g., invoices, canceled checks, or accounting records, of these expenses, but rather provided only oral "estimates" of such expenses at the remand proceedings, Sumitomo has failed to carry its burden of adequately proving those expenses.  (Appellee's Br. at 40.)   While it is true that Sumitomo produced no written evidence of the legal fees and delivery expenses, Hideo Amemiya, manager of Sumitomo's Structured Finance Department, testified on cross-examination that Sumitomo "had transaction costs.   We were charged legal expenses, and fees payable to [G]erry Sherman.   And delivery expense to Rochester, New York.   So, [in] all $200,0008...."  (J.A. at 1685.)   As the district court observed, Amemiya "was involved in this transaction."  (J.A. at 1677.)   Hence, while documentary evidence might have provided compelling corroboration of Amemiya's statements, his testimony at the remand proceedings was based on personal knowledge and, standing alone, is competent evidence of the transactional expenses involved in the PAS portfolio.   See, e.g., MCI Telecommunications Corp. v. Wanzer, 897 F.2d 703, 706 (4th Cir.1990) (citing Fed.R.Evid. 701).   Moreover, Mr. Hidehiko Asai, head of Sumitomo's corporate finance team, who testified on remand that he was involved in Sumitomo's discussions with Sherman in connection with the bank's bid on the December 1988 PAS portfolio, also estimated the transaction costs on the investment to be "well over $200,000."  (J.A. at 749.)   And while Hannon Armstrong now questions the adequacy of Sumitomo's proof of these expenses, EHC offered no evidence on remand which can fairly be said to have impeached or otherwise undermined Amemiya's or Asai's estimates.   On review of bench proceedings, "Federal Rule of Civil Procedure 52(a) mandates that the result reached by the district judge is not to be disturbed if there are adequate facts to support it, even though we might have preferred a determination to the contrary."  Babb v. Olney Paint Co., 764 F.2d 240, 243 (4th Cir.1985) (citing Anderson v. City of Bessemer, 470 U.S. 564, 574-75, 105 S.Ct. 1504, 1511-12, 84 L.Ed.2d 518 (1985)).   We conclude that Sumitomo presented adequate facts to support the district court's determination that the bank incurred $69,000 in legal fees and delivery expenses, and accordingly affirm the court's decision to also allow Sumitomo to deduct that amount from pre-February 14, 1991, PAS portfolio revenues.   Thereby affirming in its totality the district court's determination of Sumitomo's "past profits," or profits earned on the December 1988 PAS portfolio through February 14, 1991, we proceed to review the court's determination of "future profits," or those profits Sumitomo earned on the portfolio after February 14, 1991.

C.

29
We are persuaded that "future profits" on the PAS portfolio should now be calculated in the same manner that the district court calculated the portfolio's "past profits."   In reaching this view, we note that the method which Sumitomo's witness, Hideo Amemiya, offered for estimating future profits used the same 9.735% "market cost of funds" rate, i.e., the interest rate which Sumitomo claims it would have paid on the open market to borrow funds to purchase the December 1988 PAS portfolio, as did Sumitomo's proposed method of calculating past profits.   For the same reasons we stated in our disposition of the past profits issue, we conclude that this 9.735% "market cost of funds rate" does not accurately reflect Sumitomo's actual cost of obtaining the funds which the bank used to buy the PAS portfolio, and we therefore conclude that it was error for the district court to adopt Amemiya's approach for calculating the bank's actual future profits.


30
However, we are similarly unattracted to the approach which Eden Hannon's expert witness, Dr. Walter H.A. Vandaele, offered for estimating future profits.   Our instructions in Eden Hannon, 914 F.2d at 565, required the district court to determine Sumitomo's actual profits on the December 1988 PAS portfolio.   Even assuming, contrary to the district court's findings, that Vandaele's present value approach adequately addressed "expenses incurred by the defendant," (see J.A. at 1528), Vandaele's methods would have remained a means only of predicting, rather than calculating with the benefit of hindsight, Sumitomo's profits on the PAS portfolio after the February 14, 1991, remand proceedings.   As the district court observed, Vandaele's present value method of calculating future profits "depends heavily on the choice of a correct discount rate to reduce future dollars to current dollars."  (J.A. at 1530.)   Evidence as to the correct discount rate would probably conflict, depending on the parties' views of the types of investments which could provide a fungible alternative to the risks, returns and schedule of the future profits on the PAS portfolio.   Thus, even though a present value calculation might provide the best possible means of calculating future profits where the PAS portfolio had not yet reached maturity, we note that, unlike the district court on remand, we now have the benefit of hindsight in ascertaining post-February 14, 1991, profits on the portfolio, because those profits have now been received by Sumitomo.


31
Both the Appellant Sumitomo bank and the Appellee Hannon Armstrong suggested at varying points in the remand proceedings that an acceptable, simple means of minimizing disputes over the estimation of "future profits" would be for Sumitomo simply to forward monthly profits earned on the PAS portfolio after February 14, 1991, to Hannon Armstrong as those profits were received.   We find these suggestions prudent.   In light of our affirmance of the district court's adoption of the average interest rate methodology which Eden Hannon's accounting witness, Mr. John Little, advocated for the calculation of "past profits," i.e., those profits earned on the portfolio before February 14, 1991, it would be incongruous for the district court to employ some other means of calculating those profits earned on the portfolio after February 14, 1991.   Since these "future profits" have now been received by Sumitomo, they are, in reality, now also "past profits" which should be calculated accordingly.   We therefore vacate the district court's calculation on remand of profits earned on the PAS portfolio after February 14, 1991, and remand with instructions for the district court to calculate those "future profits" in the same manner as the court calculated profits earned on the portfolio prior to February 14, 1991.

IV.

32
Finally, Hannon Armstrong appeals the district court's refusal to award Eden Hannon any pre-judgment interest at the rate of eight percent prescribed in Va.Code Ann. § 6.1-330.54 (Michie 1950).   Under Virginia law, a district court "may provide for interest on any ... sum awarded ... and fix the period at which the interest shall commence."   Va.Code Ann. § 8.01-382 (Michie 1950).   Whether interest should be awarded pursuant to section 8.01-382, and if so, from what date, are matters within the sound discretion of the district court.   E.g., Marks v. Sanzo, 231 Va. 350, 345 S.E.2d 263, 267 (1986).   Upon remand, the district court once again reasoned that since the Xerox Corporation ranked Eden Hannon's bid for the December 1988 PAS portfolio third, Hannon Armstrong had not proven monetary damages arising from Sumitomo's breach of the agreement not to compete, because it was most likely that the second place bidder would have otherwise won the portfolio.   Thus, the court continued, no damages accrued to Eden Hannon until the Fourth Circuit in September of 1990 imposed a constructive trust upon Sumitomo's profits on the portfolio with our decision in Eden Hannon & Co. v. Sumitomo Trust and Banking Co., 914 F.2d 556 (4th Cir.1990), cert. denied, --- U.S. ----, 111 S.Ct. 1414, 113 L.Ed.2d 467 (1991).   Given the discretion which a district court may exercise in awarding or denying interest under section 8.01-382, we cannot say on the facts of this case that such an analysis is faulty.   However, we note that, by the district court's own reasoning, Hannon Armstrong may therefore still be entitled to interest on the judgment from the date we imposed the constructive trust in September 1990 until the date the judgment is received.   With due regard for the district court's discretion in ultimately awarding or denying interest pursuant to section 8.01-382, we therefore remand the interest issue for further consideration in light of these observations.

V.

33
Accordingly, we affirm the district court's determination of Sumitomo's pre-February 14, 1991, profits of the December 1988 PAS portfolio, reverse and remand with instructions the court's determination of post-February 14, 1991, profits of the portfolio, and remand the issue of interest on portfolio profits for further consideration in light of our observations here.


34
AFFIRMED IN PART, REVERSED IN PART, AND REMANDED WITH INSTRUCTIONS.



1
 At the time of the initial trial and appeal, Eden Hannon & Co. was located in Alexandria, Virginia.  914 F.2d at 557


2
 Sumitomo originally anticipated recovering its entire investment in the PAS portfolio fifty-six months after December of 1988.  (J.A. at 1679.)   However, the transaction was subsequently rescheduled such that the investment recovery date falls forty-three months after December of 1988.   Id


3
 The recovery of principal components of the monthly payments that Sumitomo had received on the portfolio through February 14, 1991, totalled $24,921,018.  (J.A. at 1843.)


4
 On direct examination, Amemiya stated that he believed there was a "50/50 percent" chance that an approach incorporating these first two assumptions would produce an accurate estimate of Sumitomo's future profits.  (J.A. at 1680.)


5
 Neither Sumitomo nor Eden Hannon suggest that this $102,851 figure was then discounted to a net present value based on then-prevailing interest rates in order to calculate a appropriate award of future profits to Eden Hannon as of the date of the remand proceeding


6
 The parties do not dispute that interest expense is properly deductible from revenues in order to calculate a wrongdoer's actual profits.   As the Third Circuit stated,
The interest on the capital which the appropriator invests in his endeavor is allowed in an effort to arrive at a realistic determination of the actual costs....  This is a practical business problem to be solved by a method as accurate as possible, and the disallowance of interest would merely distort the actualities of the money expended.
International Indus., Inc. v. Warren Petroleum Corp., 248 F.2d 696, 702 (3d Cir.1957), cert. dismissed, 355 U.S. 943, 78 S.Ct. 529, 2 L.Ed.2d 523 (1958) (citing Sutton v. Gulf Smokeless Coal Co., 77 F.2d 439 (4th Cir.1935)).


7
 Pursuant to Fed.R.App.P. 28(j), Sumitomo on July 8, 1992, offered a recent D.C. Circuit opinion, Waukesha State Bank v. National Credit Union Admin. Board, 968 F.2d 71 (D.C.Cir.1992), in support of the proposition that the records of a regulated financial institution are conclusive proof of the characteristics of that transaction, notwithstanding the efforts of another party to show that transaction had different characteristics.   Thus, Sumitomo argues, that opinion supports its position that the "market cost of funds" figure of 9.735% which Sumitomo entered in one of its internal records, a "Loan Register," is presumptively the correct cost for calculating Sumitomo's profits on the December 1988 PAS portfolio.   However, the decision in Waukesha State Bank, 968 F.2d at 72-75, involved the interpretation of the following National Credit Union Administration regulation:  "(C) Records.  (1) The account records of the insured credit union shall be conclusive as to the existence of any relationship pursuant to which the funds in the account are deposited and on which a claim for insurance is founded."  12 C.F.R. § 745.2(c)(1) (1992).   The D.C. Circuit concluded that section 745.2(c)(1) mandates that a credit union member's account records would be deemed conclusive evidence of the identity of the owners of a credit union's share certificates for purposes of determining federal insurance coverage for those owners where the credit union failed.  968 F.2d 71, 72-75 (D.C.Cir.1992).   We fail to comprehend how this interpretation of the federally-insured credit union regulation at issue in Waukesha State Bank, 968 F.2d 71, offers authority for resolution of actual profits issues presented here.   Moreover, even were we to accept Sumitomo's proffered reading of Waukesha State Bank, that reading would be no less applicable to the bank's internal records and the quarterly reports to the FDIC which Mr. John Little used to calculate the bank's average interest expense rate on the PAS transaction, and would indicate that this court should accept those records as conclusive on the issue of Sumitomo's profits on the PAS transaction


8
 $200,000 is, of course, the sum of the $131,000 fee paid to Sherman and the $69,000 in legal fees and delivery expenses


