
532 F.3d 326 (2008)
UNITED STATES of America, Plaintiff-Appellee,
v.
Kenneth N. HARVEY, Defendant-Appellant. *327
United States of America, Plaintiff-Appellee,
v.
Michael G. Kronstein, Defendant-Appellant.
Nos. 07-4310, 07-4311.
United States Court of Appeals, Fourth Circuit.
Argued: March 19, 2008.
Decided: July 14, 2008.
*330 ARGUED: Christopher M. Choate, McNabb Associates, P.C., Houston, Texas; Franklin B. Reynolds, Jr., Washington, Virginia, for Appellants. M. Kendall Day, Public Integrity Section, United States Department of Justice, Washington, D.C., for Appellee. ON BRIEF: William M. Welch, II, Chief, Public Integrity Section, United States Department of Justice, Washington, D.C., for Appellee.
*331 Before WILLIAMS, Chief Judge, WILKINSON, Circuit Judge, and IRENE M. KEELEY, United States District Judge for the Northern District of West Virginia, sitting by designation.
Affirmed in part, vacated in part, and remanded by published opinion. Judge KEELEY wrote the opinion, in which Chief Judge WILLIAMS and Judge WILKINSON joined.

OPINION
KEELEY, District Judge:
Following their convictions of two counts of honest services wire fraud and one count each of bribery, Appellants Kenneth Harvey ("Harvey") and Michael Kronstein ("Kronstein") (from time to time "Appellants"), appeal their convictions and sentences, including the trial court's orders of restitution. We affirm their convictions and sentences of incarceration. Because the district court's restitution orders were not based on findings of actual loss, however, we vacate those orders and remand for further proceedings as discussed below.

I.
Harvey, a civilian employee with U.S. Army Intelligence and Security Command ("INSCOM"), engineered the award of a noncompetitive, "sole-source" contract to Program Contract Services, Inc. ("PCS"), a closely-held corporation wholly owned and controlled by Kronstein, who had been a close friend of Harvey's for over twenty years. At trial, the government established that, in justifying the sole-source award, Harvey made numerous false statements to contracting officials at INSCOM regarding PCS's ability to handle the job. Specifically, Harvey represented to INSCOM that PCS had highly specialized personnel available to commence work immediately when, in fact, PCS lacked the minimum number of employees the contract required. He further led INSCOM to believe that no other firm was qualified to perform the contract. At trial, however, the government established that there were approximately one hundred other qualified companies in the immediate area. Based on Harvey's misleading representations, INSCOM awarded the contract to PCS in January 1999.
As the Contracting Officer Representative on the PCS contract, Harvey oversaw performance of the contract through July 1999, after which he recused himself, citing a possible conflict of interest due to a business relationship with a PCS employee named Peckham. According to the evidence at trial, however, even after recusing himself, Harvey continued to be involved in the contract by recommending modifications and "add-ons," and by approving payments to PCS.
During the first year of services, INSCOM paid PCS over $1,250,000.00. It then renewed the contract in 2000 and 2001, pursuant to a contractual renewal option. The evidence at trial was inconclusive as to what role, if any, Harvey may have played in obtaining those renewals. Ultimately, PCS received approximately $4,795,265.79 in payments from INSCOM, which were electronically wired to a PCS bank account in Front Royal, Virginia. The contract designated an eight percent profit margin for PCS.
Beginning in the fall of 1999, a series of monetary transactions occurred between businesses owned by Kronstein, including PCS and a convenience store called Foodway Supermarket, and businesses owned by Harvey, including several tobacco outlets and a franchise of the Johnny Appleseed restaurant chain. Kronstein and Harvey never exchanged money directly. Instead, they utilized employees and family *332 members as intermediaries, most frequently their wives, Karla Kronstein and Samra Harvey. At trial, the government provided specific examples of at least seven transactions in which money was funneled from PCS to Harvey's businesses, each of which was designed to obscure the money trail. This evidence supported the government's theory at trial that the payments from Kronstein to Harvey were bribes made in remuneration for the award of the PCS contract.
In one such example, on October 5, 1999, Kronstein wrote a check for $7,500 from a PCS account to Foodway Supermarket. An employee of Foodway then wrote a $7,500 check from Foodway to Samra Harvey, who deposited the check into a Johnny Appleseed account. Other examples abound. On January 5, 2000, Kronstein wrote a $15,000 check from PCS to Foodway. On the same day, a Foodway employee wrote a $5,000 check from Foodway to Samra Harvey. In still another example, on May 8, 2000, Kronstein hired a plumber to perform maintenance work at Harvey's Johnny Appleseed restaurant. Several days later, a Foodway employee wrote a check for $2,136 from Foodway to the plumber to pay for the work done at Johnny Appleseed. And, on February 17, 2001, Kronstein endorsed a check made payable to PCS in the amount of $47,005.50 over to Karla Kronstein's father. On the same day he deposited the check into his personal account, Mrs. Kronstein's father withdrew $8,578.91 from that account in the form of a cashier's check, and delivered it to Samra Harvey, who used it to pay an overdue electric bill for Johnny Appleseed.
Ultimately, the evidence at trial established that, from the fall of 1999 through the spring of 2001, a total of $43,000 was funneled from PCS to Harvey's businesses. The evidence further established that Harvey concealed these payments from INSCOM, despite requirements that he disclose them. Finally, in May 2001, Harvey resigned from INSCOM, telling his supervisors that he was taking a position with a company called AAR Cadillac. Although he worked with AAR Cadillac, in truth Harvey was actually employed by PCS. Had his supervisor at INSCOM known of Harvey's employment with PCS, he testified that he would have suspended Harvey immediately and referred the matter to INSCOM's legal department for investigation.
In April 2006, the government indicted Harvey and Kronstein on two counts of honest services wire fraud, alleging that, between November 1998 and March 2002, they aided and abetted each other in a scheme to defraud the United States and the Army in violation of 18 U.S.C. §§ 1343, 1346 and 2. The indictment further named Harvey in one count of bribery in violation of 18 U.S.C. § 201(b)(2)(A), which applies to public officials who accept bribes, and Kronstein in one count of bribery in violation of 18 U.S.C. § 201(b)(1)(A), which applies to those who bribe public officials.
At a jury trial in December 2006, the government presented evidence that Harvey and Kronstein defrauded the government by forming PCS for the sole objective of obtaining the INSCOM contract. In exchange for being awarded the contract, Kronstein funneled earnings from PCS to Harvey via various family members and employees, primarily in the form of financial assistance to Johnny Appleseed, Harvey's restaurant. While admitting that Kronstein and his wife had given Harvey money to keep the restaurant afloat, the defendants characterized those transactions as mere business loans between old friends.
Following their convictions on all counts, on March 6, 2007 the district court sentenced *333 Harvey to 72 months of incarceration and Kronstein to 70 months. It also ordered each, jointly and severally, to pay $383,621.00 in restitution to INSCOM.
Harvey and Kronstein appeal their convictions, sentences and the orders of restitution.

II.

A.
Initially, Appellants contend that the government presented insufficient evidence for a jury to convict them of honest services wire fraud and bribery. In reviewing the sufficiency of the evidence in the context of these convictions, we ask "whether, viewing the evidence in the light most favorable to the government, any rational trier of facts could have found the defendant guilty beyond a reasonable doubt." U.S. v. Tresvant, 677 F.2d 1018, 1021 (4th Cir.1982) (citing U.S. v. Shaver, 651 F.2d 236, 238 (4th Cir.1981)). We consider both circumstantial and direct evidence, and allow the government all reasonable inferences that could be drawn in its favor. Id. "Where there are conflicts in the testimony, it is for the jury and not the appellate court to weigh the evidence and judge the credibility of the witnesses." Id. at 1021-22 (citing U.S. v. Fisher, 484 F.2d 868, 869-70 (4th Cir.1973), cert. denied, 415 U.S. 924, 94 S.Ct. 1428, 39 L.Ed.2d 480 (1974)).

1.
Harvey and Kronstein were convicted under 18 U.S.C. §§ 1343 and 1346. Section 1343 provides, in relevant part:
Whoever, having devised or intending to devise any scheme or artifice to defraud, or for obtaining money or property by means of false or fraudulent pretenses, representations, or promises, transmits or causes to be transmitted by means of wire ... in interstate or foreign commerce, any writings ... for the purpose of executing such scheme or artifice, shall be fined under this title or imprisoned not more than 20 years or both.
Section 1346 clarifies that "the term `scheme or artifice to defraud' includes a scheme or artifice to deprive another of the intangible right of honest services."
The "intangible right of honest services" refers to the public's right to a government official's "honest, faithful, and disinterested services." U.S. v. Mandel, 591 F.2d 1347, 1362 (4th Cir.1979), aff'd in relevant part, 602 F.2d 653 (1979) (en banc), cert. denied, 445 U.S. 961, 100 S.Ct. 1647, 64 L.Ed.2d 236 (1980). When a government official accepts a bribe, he undermines this public right because, although the official is "outwardly purporting to be exercising independent judgment in passing on official matters," in fact, the official has been paid for his decisions and, perhaps, has not even considered the merits of the matter. Id.
Thus, in order to convict Appellants of honest services wire fraud, the government was required to prove beyond a reasonable doubt that Harvey and Kronstein engaged in (1) a scheme or artifice to defraud another of the intangible right of honest services, (2) that involved a material misrepresentation or concealment of fact, (3) undertaken with the specific intent to defraud, and (4) furthered by the use of interstate wire communications. See 18 U.S.C. §§ 1343, 1346 (2000); Neder v. U.S., 527 U.S. 1, 25, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999) (materiality of falsehood is an element of the federal wire fraud statute); U.S. v. Godwin, 272 F.3d 659, 666 (4th Cir.2001) (the government must prove specific intent to defraud).
Despite Appellants' protests to the contrary, we have no doubt that the government *334 presented sufficient evidence to establish that each was involved in a scheme or artifice to defraud, which included a material misrepresentation or concealment of fact, and that they acted with specific intent to defraud.[1]
Although Harvey and Kronstein contend that the government lacked direct evidence of a scheme to defraud, such evidence is not necessary to convict because "the specific intent to defraud ... `may be inferred from the totality of the circumstances and need not be proven by direct evidence.'" Godwin, 272 F.3d at 666 (quoting U.S. v. Ham, 998 F.2d 1247, 1254 (4th Cir.1993)). Because the government presented sufficient circumstantial evidence of a scheme to defraud, including (1) evidence of misrepresentations Harvey made to INSCOM regarding PCS' performance capabilities, (2) evidence of Harvey's ongoing involvement in the PCS contract, and (3) evidence of the subsequent money transfers from PCS to Harvey's businesses, a lack of direct evidence does not undermine the jury's verdict.
Appellants next argue that the government failed to sufficiently prove that they concealed material facts from INSCOM. Again, the evidence presented at trial amply supported such a finding. The government established that Harvey had failed to report the "gifts" from Kronstein to his employers, despite a requirement that he do so on an annual financial disclosure form. It also established that Harvey misrepresented to INSCOM his subsequent employment with PCS.
Failure to report income, including gifts, on a required financial disclosure form, and failure to report the conflict of interest associated with it, constitute significant evidence of concealment of material facts. See U.S. v. Woodward, 149 F.3d 46, 62 (1st Cir.1998) ("[N]ondisclosure of a conflict of interest is a second way in which a public official can steal his honest services."); U.S. v. Espy, 23 F.Supp.2d 1, 6 (D.D.C.1998) ("[A] public official who solicited gifts from entities over which he held decision-making discretion and later concealed receipt of those gifts, exhibited elements of dishonesty sufficient to support a charge he breached a fiduciary duty owed to the United States and its citizens.").
Finally, although Appellants contend that they lacked specific intent to defraud, "a bribery-like, corrupt intent to influence official action necessarily is an intent to deprive the public of an official's honest services." Woodward, 149 F.3d at 55. Because the government presented sufficient evidence that Harvey and Kronstein not only had engaged in a scheme to defraud but also had actively concealed material facts from the government, a reasonable jury could have found that these acts were undertaken with specific intent to influence an official action, which, in turn, would indicate a specific intent to deprive the public of honest services.
We therefore affirm Appellants' convictions for honest services wire fraud. When viewed in the light most favorable to the government, sufficient evidence existed for a rational trier of fact to convict them of these crimes.

2.
Each Appellant was also convicted of one count of bribery under 18 U.S.C. § 201(b). Pursuant to that statute, a person who, directly or indirectly, corruptly gives, offers or promises anything of value *335 to a public official, with intent to influence an official act, is guilty of bribery. Id. at § 201(b)(1)(A). Similarly, any public official who, "directly or indirectly, corruptly demands, seeks, receives, accepts, or agrees to receive or accept anything of value personally or for any other person or entity, in return for being influenced in the performance of any official act" is also guilty of bribery. Id. at § 201(b)(2)(A). A "public official" includes "an officer or employee... of the United States, or any department, agency or branch of the Government thereof." Id. at § 201(a)(1). An "official act" includes "any decision or action on any question, matter, cause, suit, proceeding, or controversy, which may at any time be pending ... in such official's official capacity, or in such official's place of trust or profit." Id. at § 201(a)(3).
"Not every gift, favor or contribution to a government or political official constitutes bribery. It is universally recognized that bribery occurs only if the gift is coupled with a particular criminal intent." U.S. v. Arthur, 544 F.2d 730, 734 (4th Cir.1976). The requirement of "corrupt intent," simply means "the intent to receive a specific benefit in return for the payment." U.S. v. Jennings, 160 F.3d 1006, 1013 (4th Cir.1998).
The intent to receive a "specific benefit," however, is not as limiting as it first appears; it is "sufficient that the gift is made on the condition `that the offeree act favorably to the offeror when necessary.'" Arthur, 544 F.2d at 734 (quoting U.S. v. Isaacs, 493 F.2d 1124, 1145 (7th Cir.1974)). Thus,
[t]his requirement of criminal intent would, of course, be satisfied if the jury were to find a `course of conduct of favors and gifts flowing' to a public official in exchange for a pattern of official actions favorable to the donor even though no particular gift or favor is directly connected to any particular official act.
Id. (quoting U.S. v. Baggett, 481 F.2d 114, 115 (4th Cir.1973), cert. denied, 414 U.S. 1116, 94 S.Ct. 850, 38 L.Ed.2d 744 (1973)).
The only contested issue here is whether Harvey and Kronstein acted with corrupt intent in their dealings. Because the alleged money transfers all took place after Harvey helped engineer the contract award to PCS, Appellants strenuously contend that no bribe can be inferred. We have previously observed, however, that "[b]ribes often are paid before the fact, but `it is only logical that in certain situations the bribe will not actually be conveyed until the act is done.'" Jennings, 160 F.3d at 1014 (quoting U.S. v. Campbell, 684 F.2d 141, 148 (D.C.Cir.1982)). Thus, Appellants' reliance on the timing of the alleged bribes is misplaced.
As the government has argued, the same evidence that supported the charges of honest services wire fraud also supported the bribery convictions. "Corrupt intent" can be inferred from the circumstances surrounding the award of the contract to PCS and the payments from Kronstein to Harvey's businesses. Thus, there is no question that a rational trier of fact could have found that the evidence at trial established a course of conduct in which Harvey, a public official, engaged in a series of official acts in exchange for a series of payments that Kronstein made through third parties for Harvey's benefit, and that each undertook such actions with corrupt intent. Accordingly, we affirm Appellants' convictions for bribery.

B.
Although they failed to object at trial, Appellants now assert that the district court made several antagonistic comments in the presence of the jury that *336 prejudiced them and the outcome of their cases. In circumstances of alleged judicial interference, "we may not intervene unless the `judge's comments were so prejudicial as to deny [the defendants] an opportunity for a fair and impartial trial.'" Godwin, 272 F.3d at 673 (alteration in original) (quoting U.S. v. Gastiaburo, 16 F.3d 582, 589-90 (4th Cir.1994)). Moreover, where, as here, a defendant fails to timely object to the alleged interference, we only review such claims for plain error. Id. (citing U.S. v. Castner, 50 F.3d 1267, 1272 (4th Cir. 1995)). After a thorough review of the transcript, we cannot conclude that any of the district court's comments rise to such a level.
Appellants concede that the statements of the trial judge they consider most prejudicial actually were made outside the presence of the jury. The remaining comments, concerning the length of the testimony of a particular witness and the admissibility of another witness's statements, do not constitute plain error because "`[a] judge's ordinary efforts at courtroom administration  even a stern and short-tempered judge's ordinary efforts at courtroom administration  remain immune' and do not establish bias or partiality." Castner, 50 F.3d at 1274 (quoting Liteky v. U.S., 510 U.S. 540, 555-56, 114 S.Ct. 1147, 127 L.Ed.2d 474 (1994)). Here, the trial judge was merely acting on his "crucial duty to ensure `that the facts are properly developed and that their bearing upon the question at issue are clearly understood by the jury.'" Id. at 1272 (quoting U.S. v. Seeright, 978 F.2d 842, 847 (4th Cir.1992)).
We further note that any influence the trial judge's comments may have had on the jury was neutralized by the court's instruction to the jury at the beginning of the trial, and repeated again at the close of trial, that "[n]othing the Court may say or do during the course of the trial is intended to indicate or should be taken by you as indicating what your verdict should be." We therefore decline to find that any comments made by the trial judge in the jury's presence were infected by plain error.

C.
Having disposed of Appellants' arguments about their convictions, we turn next to their claims that the district court incorrectly applied the Sentencing Guidelines to their cases. The district court calculated a total offense level 27 and criminal history category I for each defendant, which resulted in an advisory sentencing range of 70 to 87 months of incarceration for each of them. Harvey received a sentence of incarceration of 72 months while Kronstein received a sentence of 70 months. Each now contends that the district court erred in applying (1) a two-level enhancement for more than one bribe pursuant to the U.S. Sentencing Guidelines Manual ("U.S.S.G.") § 2C1.1(b)(1), (2) a four-level enhancement for role in the offense pursuant to U.S.S.G. § 3B1.1, and (3) a nine-level enhancement for amount of loss pursuant to U.S.S.G. § 2C1.1(b)(2)(A).
Pursuant to Gall v. U.S., ___ U.S. ___, 128 S.Ct. 586, 590, 169 L.Ed.2d 445 (2007), we review the sentences imposed by the district court under a deferential abuse of discretion standard. Initially, we "ensure that the district court committed no significant procedural error, such as ... improperly calculating ... the Guidelines range." U.S. v. Osborne, 514 F.3d 377, 387 (4th Cir.2008) (quoting Gall, 128 S.Ct. at 590). "In assessing whether a sentencing court properly applied the Guidelines, `we review the court's factual findings for clear error and its legal conclusions de novo.'" Id. (quoting U.S. v. Allen, 446 F.3d 522, 527 (4th Cir.2006)). Clear error occurs "when, `although there is evidence to support it, the reviewing *337 court on the entire evidence is left with the definite and firm conviction that a mistake has been committed.'" In re Mosko, 515 F.3d 319, 324 (4th Cir.2008) (quoting U.S. v. U.S. Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 92 L.Ed. 746 (1948)). With these principles in mind, we consider each of the alleged sentencing errors in turn.

1.
Under U.S.S.G. § 2C1.1(a), the base offense level for bribery is 10.[2] Section 2C1.1(b)(1) provides that "[i]f the offense involved more than one bribe or extortion, increase by two levels." The district court, therefore, straightforwardly applied a two-level increase to each defendant's base offense level.
Harvey and Kronstein each claim that because the jury made no specific findings about which payments were bribes and which may have been legitimate gifts or loans, the court clearly erred in finding that more than one bribe existed. To the extent this argument raises a question of law, specifically whether the district court impermissibly made factual findings regarding the number of bribes, it is well-settled that a sentencing judge may, indeed frequently must, make findings of fact in order to appropriately calculate the advisory guideline range, and may do so as long as such findings are supported by a preponderance of the evidence. E.g. U.S. v. Battle, 499 F.3d 315, 322-23 (4th Cir. 2007) ("When applying the Guidelines in an advisory manner, the district court can make factual findings using the preponderance of the evidence standard."). We therefore review the factual findings of the district court regarding the application of this enhancement for clear error. See Osborne, 514 F.3d at 387.
In considering whether to apply this enhancement, the district court found that the benefits provided in exchange for the bribes included the issuance of the PCS contract, the subsequent add-ons to that contract, and the payments authorized by Harvey. In return, Harvey received numerous payments from Kronstein as well as employment with PCS. In making these findings, the court cited the testimony and evidence at trial, and noted that significant circumstantial evidence supported its conclusions.
Because the district court considered that Harvey had undertaken multiple acts for Kronstein's benefit, and that Kronstein had made multiple payments to Harvey in return, it did not clearly err in finding, by a preponderance of the evidence, that this case involved multiple bribes.

2.
Pursuant to U.S.S.G. § 3B1.1(a), the district court also enhanced each defendant's guideline calculation by four levels based on their roles as leaders or organizers in the offense. Under § 3B1.1(a), a court may increase a defendant's offense level by four if the defendant "was an organizer or leader of a criminal activity that involved five or more participants or was otherwise extensive." Harvey and Kronstein dispute this enhancement, arguing they were not leaders or organizers because they exercised no authority over any other participant in the scheme. Failing that, they claim the criminal activity involved fewer than five participants.
*338 Because Appellants are challenging the factual findings the district court made in applying this enhancement, we again review for clear error, and again find none. As an initial matter, we note that Appellants' focus on whether there were fewer than five participants is misplaced; the district court clearly based its decision to apply the enhancement on the fact that the criminal activity was "otherwise extensive." The Application Note to U.S.S.G. § 3B1.1 explains that, in determining if a criminal activity is "otherwise extensive," all persons involved during the course of the entire offense are to be considered, including outsiders who provided unwitting services and thus do not qualify as "participants." U.S.S.G. § 3B1.1 cmt. n. 3 (2000). "Participants" are persons involved in the criminal activity who are criminally responsible, not innocent bystanders used in the furtherance of the illegal activity. Id. at cmt. n. 1. The district court specifically noted that Harvey and Kronstein used a number of persons, both knowing and unknowing, in their scheme, including family members and various employees of their businesses. Based on this, we cannot say that the district court plainly erred in finding that the criminal activity was sufficiently "otherwise extensive."
The remaining question, whether Harvey and Kronstein were "organizers or leaders" in the criminal activity, requires a determination of whether they were organizers, leaders, managers, or supervisors of one or more other "participants." Id. at § 3B1.1(a). In this case, the district court specifically found that Samra Harvey and Karla Kronstein, both of whom testified at trial, were participants in the criminal activity, and that Harvey and Kronstein were their organizers, leaders, managers or supervisors. Accordingly, we affirm the district court's four-level enhancement for role in the offense.

3.
Appellants also challenge the district court's application of a nine-level enhancement pursuant to U.S.S.G. § 2C1.1(b)(2)(A) for the amount of loss suffered by the government as a result of their offense. The sentencing guideline governing this enhancement provides:
If the value of the payment, the benefit received or to be received in return for the payment, or the loss to the government from the offense, whichever is greatest, exceeded $2,000, increase by the corresponding number of levels from the table in § 2F1.1 (Fraud and Deceit).
U.S.S.G. § 2C1.1(b)(2)(A) (2000). In this case, the district court calculated the total loss as $383,621.00, an amount equivalent to the eight percent profit margin in PCS's contract with INSCOM. This amount equates to a nine-level increase on the table found at U.S.S.G. § 2F1.1.
At sentencing, Appellants argued that there was no actual loss because PCS had adequately performed its obligations to INSCOM under the contract and the government presented no evidence at trial indicating that the profit PCS earned was unreasonable for this type of contract. The government, however, contended that INSCOM had suffered an actual loss because PCS had not met certain contractual expectations.
Pursuant to the plain language of U.S.S.G. § 2C1.1(b)(2)(A), a finding of either actual loss or the amount of the benefit received may support such enhancement. The Application Note accompanying U.S.S.G. § 2C1.1 states:
"Loss" ... includes both actual and intended loss. The value of "the benefit received or to be received" means the net value of such benefit. Examples:... (2) A $150,000 contract on which $20,000 profit was made was awarded in *339 return for a bribe; the value of the benefit received is $20,000. Do not deduct the value of the bribe itself in computing the value of the benefit received or to be received. In the above example[ ], therefore, the value of the benefit received would be the same regardless of the value of the bribe.
Id. at § 2C1.1 cmt. n. 2.
The facts here mirror the example in this Application Note. Kronstein bribed Harvey in exchange for obtaining a contract with INSCOM for PCS; the profit PCS made on that contract, $383,621.00, is therefore the "value of the benefit received." To the extent that the district court mischaracterized its findings about loss as "actual loss," rather than the value of the benefit received, such error is clearly harmless and did not affect Appellants' substantive rights. We therefore affirm the district court's nine-level enhancement for this specific offense characteristic.

D.
Lastly, Appellants claim that the district court's restitution order directing them to pay, jointly and severally, $383,621.00 to INSCOM was erroneous because (1) no actual loss to the government could be calculated in this case; (2) the court failed to take into account the factors set forth in 18 U.S.C. § 3663(b), and failed to "key its findings" to these factors; and (3) the court imposed a payment schedule without taking into account their finances and ability to pay pursuant to 18 U.S.C. § 3664(f)(2). We review the trial court's restitution orders for abuse of discretion. See U.S. v. Vinyard, 266 F.3d 320, 325 (4th Cir.2001).
The district court ordered Appellants to pay restitution pursuant to 18 U.S.C. § 3663, the Victim and Witness Protection Act ("VWPA"), which permits, but does not require, a court to order restitution when there is an identifiable victim. This section differs from 18 U.S.C. § 3663A, the Mandatory Victim Restitution Act ("MVRA"), which requires a court to order restitution when a victim has been identified and the count of conviction falls into one of four categories of cases, none of which is applicable here.
Both the VWPA and the MVRA direct that any order of restitution made under either statute be issued and enforced in accordance with 18 U.S.C. § 3664, which sets forth procedures for calculating and ordering restitution. Thus, once a court determines that restitution is appropriate, whether under either the VWPA or the MVRA, § 3664(f)(1)(A) provides that "the court shall order restitution to each victim in the full amount of each victim's losses as determined by the court and without consideration of the economic circumstances of the defendant." (emphasis added).
We and other circuits have interpreted this language to require that an order of restitution be based on "actual loss," rather than "intended loss." See U.S. v. Adams, 19 Fed.Appx. 33 (4th Cir. 2001) (unpublished) (citing U.S. v. Messner, 107 F.3d 1448, 1455 (10th Cir.1997)); U.S. v. Barnes, 1997 WL 337454, at *4 (4th Cir. June 19, 1997) (unpublished); U.S. v. Innarelli, 524 F.3d 286, 294-95 (1st Cir. 2008); U.S. v. Boccagna, 450 F.3d 107, 119 (2d Cir.2006); U.S. v. Beydoun, 469 F.3d 102, 108 (5th Cir.2006); U.S. v. Quillen, 335 F.3d 219, 226 (3d Cir.2003); U.S. v. Menza, 137 F.3d 533, 538 (7th Cir.1998). The government bears the burden of proving actual loss by a preponderance of the evidence. 18 U.S.C. § 3664(e); U.S. v. Ubakanma, 215 F.3d 421, 428 (4th Cir. 2000).
We agree with Appellants that the government failed to present sufficient evidence *340 of actual loss at either trial or sentencing. Rather, it relied on testimony indicating that PCS had failed to comply with certain aspects of its contract, for example, failing to hire the contractually required number of employees, and employing individuals who lacked the requisite level of security clearance called for in the contract.
While these violations may have seriously impaired PCS's performance of the contract, they do not establish the amount of loss INSCOM actually suffered. For example, the government offered no facts evincing either how INSCOM was injured by these contractual failures or, if so, in what amount. Indeed, at trial, during the defense's cross-examination of two INSCOM officials, those officials admitted that they had no complaints about PCS's performance of the contract.
Because there was no evidence of actual loss, to calculate restitution the district court looked to the measure of loss under U.S.S.G. § 2C1.1, specifically the eight percent profit margin earned by PCS pursuant to its contract. In ordering that amount in restitution, the court stated:
I think 8% is actually a conservative figure ... the government was just ripped off terribly. I mean, they had  I mean, the contract called for 11 people. And I think five to six was the most they ever had. And they didn't have the security clearances, as I recall, that they should have had.
Notably, testimony at trial had indicated that eight percent is a standard profit margin for this type of contract.
Pursuant to 18 U.S.C. § 3664, we must determine whether the eight percent paid to PCS as profit under the contract may properly be used as a proxy for actual loss. While we have not previously specifically addressed whether gain can be used as an approximation of actual loss for the purpose of ordering restitution, two of our sister circuits have held that a defendant's gain cannot be used as a proxy for actual loss.
In United States v. Chalupnik, 514 F.3d 748 (8th Cir.2008), a case arising under the MVRA,[3] the Eighth Circuit stated:
[T]he amount of restitution that may be awarded is limited to the victim's provable actual loss, even if more punitive remedies would be available in a civil action. Thus, while the fact that a defendant profited from the crime without causing actual loss to an identifiable victim may be an appropriate reason to increase his punishment, Petruk and the plain language of the MVRA confirm that punishment of a federal criminal defendant must be imposed by means of criminal penalties  fines, criminal forfeitures, and imprisonment. Restitution to MVRA victims `must be based on the amount of loss actually caused by the defendant's offense.'

Id. at 754 (quoting U.S. v. Petruk, 484 F.3d 1035, 1036 (8th Cir.2007)) (emphasis added).
The Tenth Circuit has also concluded that a defendant's gain in undertaking criminal activity is not an appropriate estimate of loss for purposes of calculating the amount of restitution. In United States v. Galloway, 509 F.3d 1246 (10th Cir.2007), a case also arising under the MVRA, the *341 Tenth Circuit vacated and remanded the trial court's restitution order, observing:
It is well settled that a restitution order must be based on actual loss. As we explained in Quarrell, although gain may be used to determine a defendant's offense level under the Guidelines (if it more closely reflects actual harm than actual loss does), it is not an appropriate estimate of loss when determining the amount of restitution under § 5E1.1 or the MVRA.

Galloway, 509 F.3d at 1253-54 (citing U.S. v. Quarrell, 310 F.3d 664, 679-80 (10th Cir.2002)) (emphasis added).
Here, the district court erroneously used gain to approximate the amount of actual loss. While we agree that INSCOM can and should be considered a victim in this case, any order of restitution nevertheless must be based on sufficient evidence of the amount of actual loss incurred as a result of the fraudulently obtained contract. Profit gained by the defendants may not be used in its stead.
Notably, the probation officers who prepared the Appellants' pre-sentence investigation reports predicted this legal dilemma. In responding to the government's objection to their decision not to recommend restitution, the officers wrote:
The probation office concurs the government can and should be considered a victim if an offense results in financial harm. In determining whether there is restitution in this case, the probation office considered that PCS provided "suspect" services, however the services provided from 1999 through 2001 were as required by contract. The profit margin for the contract awarded PCS was calculated at 8% which provided an estimated profit of $383,621.26. The government agrees that PCS fulfilled at least some of the services paid for under the contract, and does not contend that the contract was not needed and simply manufactured by Harvey and Kronstein. Understanding there were issues with the performance of PCS, it would be difficult at best to calculate a percentage of restitution based on which services were acceptable and which were not.

(emphasis added).
We do not doubt the district court's finding that Harvey and Kronstein "ripped off" the government and profited unjustly. Because it failed to make appropriate findings as to the actual loss incurred by the government, however, the district court abused its discretion in ordering Appellants to pay $383,621.26 in restitution to INSCOM. We therefore vacate the district court's restitution orders and remand the case so that it may determine whether the amount of actual loss can be calculated. If so, the district court is free to decide whether, in light of the statutory dictates of 18 U.S.C. §§ 3663 and 3664, new restitution orders should issue and in what amount and form.

III.
For the foregoing reasons, the judgment of the district court is affirmed in part, vacated in part, and remanded.
AFFIRMED IN PART, VACATED IN PART, AND REMANDED
NOTES
[1]  The use of interstate wire communications in connection with the alleged scheme was not disputed.
[2]  The district court properly calculated the guideline range using the 2000 edition of the Sentencing Guidelines Manual, the edition in effect on the date the crime ended, which provides a lower base offense level (10 as opposed to 12 or 14) than does the 2006 edition, which was in effect on the date of sentencing. See Elliott v. U.S., 332 F.3d 753, 767 n. 12 (4th Cir.2003).
[3]  The fact that Chalupnik arose under the MVRA does not undercut its relevance to this issue. As noted above, 18 U.S.C. § 3664, which is widely interpreted as requiring that an order of restitution be based on actual loss, governs restitution orders under both the VWPA and the MVRA. See 18 U.S.C. §§ 3663(d), 3663A(d); U.S. v. Adams, 19 Fed. Appx. 33 (4th Cir.2001) (unpublished).
