After a 10-day trial, a jury convicted defendants Craig Near and Genziko, Inc. of wire fraud and filing false claims against the United States. These convictions stemmed from misuse of grant money Near and Genziko received from the National Science Foundation (NSF) and the National Aeronautics and Space Administration (NASA). Both defendants appeal their convictions. They contend that there was insufficient evidence supporting those convictions, statements by the government and the district court’s jury instructions constructively amended the indictment charging them, and statements and evidence from the government served to lower the burden of proof they faced. For its part, the government cross-appeals the defendants’ sentences. After careful review and with the benefit of oral argument, we affirm the defendants’ convictions and sentences.
I. BACKGROUND
Near and Genziko were charged with seven1 counts of committing wire fraud, in violation of 18 U.S.C. § 1343, and three counts of filing false claims against the United States, in violation of 18 U.S.C. § 287.2 A jury convicted both defendants on all seven wire fraud counts and two of the three false claims counts. Near was sentenced to four months’ imprisonment followed by one year of supervised release. Genziko was sentenced to five years’ probation and fined $5,000. Neither defendant was ordered to pay restitution.
A. Near and Genziko
Near founded Genziko in 2004 to research and develop products based on piezoelectric materials, which generate energy from vibrations or movement. Near had worked with these materials for nearly twenty years before he founded the company, Genziko was a one-man operation with Near as its only paid employee. Despite its small size, the company managed to win grants and contracts from government agencies, including NSF and NASA.
B. SBIR Program and Grants
Genziko applied for and received an NSF grant and a NASA contract under the Small Business Innovation Research (SBIR) program. The SBIR program was established by Congress to direct a portion of federal research funding to small businesses to help them develop innovative products that could be successfully commercialized. See Small Business Innovation Development Act of 1982, Pub. L. No. 97-219, 96 Stat. 217, Near, Genziko, and some subcontractors legitimately performed research under these grants, but the government alleged that Near submitted false budgets to obtain the grants. We will discuss each grant in turn.
1. NSF Grant
In response to NSF’s public solicitation for SBIR proposals, Near submitted a proposal for Genziko to develop a “High Performance Vibration Energy Harvester” that would eliminate the need for battery *594recharging, replacement, and disposal in industrial and transportation applications. The solicitation to which Near responded listed several award conditions, including complying with a separate document containing NSF’s general grant conditions and complying with the budget the grantee submitted to NSF,
Genziko proposed a budget just shy of $100,000, broken down into different expense categories. Am NSF employee followed up and requested more detailed budget information for Genziko’s proposal to receive further consideration. Near complied, sending a detailed budget that listed himself, an unnamed student technician, and two named individuals, including a professor from the Georgia Institute of Technology (“Georgia Tech”), as employees for the project. The detailed budget also included a lease payment to Georgia Tech for a lab that was to be used for some of the necessary research and development. At trial, Dr. Benaiah Schrag, an SBIR program director at NSF, testified that NSF expected companies to follow their proposed budgets and contact NSF for approval of any changes.
NSF approved the proposal and awarded Genziko an SBIR grant. NSF paid Gen-ziko two-thirds of the grant amount up front with the remainder to be paid when the company submitted its final report. Schrag testified that the final reports were the only thing NSF expected to receive as a result of SBIR grants. Although Genziko performed some of the anticipated research and development, the company did not follow its proposed budget. NSF Office of the Inspector General (OIG) Special Agent Brian Hess testified that he examined Genziko’s records and bank accounts and found no evidence that Genziko had paid the expenses outlined above. Indeed, Hess related that when he interviewed Near as part of OIG’s investigation, Near stated that he never paid any employees but himself.
In Genziko’s final report, Near certified that to best of his knowledge the work for which he was requesting payment was performed in accordance with the award terms and conditions. Schrag testified that the agency viewed this certification as confirming that money was spent according to the proposed budget. After receiving Gen-ziko’s final report, NSF .wired the final third of the grant from the U.S. Treasury to Genziko’s account.
2. NASA Contract
Near submitted a proposal to NASA’s SBIR program for Genziko to develop a “Frequency-Steerable Acoustic Transducer.” In layman’s terms, this device would function as something like an ultrasound to detect leaks or changes inside structures. Genziko was approved for and received a six-month NASA SBIR contract to develop the idea. After completing that contract, Near applied for a second one, which is the subject of most of the charges in this case. This second, multi-year contract was a continuation of the first contract and relied on the same proposal.
Genziko proposed a budget of just under $600,000 over two years for the second contract. The budget listed payments to an unnamed engineer, an unnamed technician, and two named consultants that were to be paid in the contract’s first year. NASA contracting officer Julie Delgado testified at trial that she followed up requesting more detail, and Near responded that Timothy Meyer would serve as the engineer and Chris Brooks as the technician.
Genziko was awarded the second contract. The contract specified that Genziko would be paid in installments after submitting quarterly interim reports of its progress. Genziko’s proposal was also expressly incorporated by reference into the terms *595of the contract. A NASA contracting officer testified at trial that the budget included in the proposal was part of the contract.
Genziko submitted the required quarterly interim reports and received its installment payments under the contract. NASA OIG Special Agent Lee Gibson and a NASA accountant testified to five wire transfers of NASA contract money from the U.S. Treasury to three different Genzi-ko bank accounts over the course of the contract. According to Gibson, Near spent money from all three Genziko accounts on personal expenses.
As part of the seventh report, which Near filed well into the contract’s second year, Near certified that Genziko’s performance had complied with the contract’s terms and conditions. Yet Genziko did not spend the contract money as specified in its proposal. Brooks, for example, testified that he was never paid (and never expected to receive any payment) for some technical help he provided Near on the project. Hess, the NSP OIG agent, testified that, after examining Genziko’s records, he found no evidence of payments to Brooks, Meyer, or the two consultants. In addition, the University of Toledo (“UT”) entered into a contract with Genziko to act as a subcontractor on the NASA contract. A UT accountant testified that although UT faculty and students performed nearly $300,000 worth of work on the subcontract, Genziko paid UT only about $70,000.
C. The Trial3
A grand jury indicted the defendants, and the case proceeded to trial. Genziko was unrepresented at trial. During its opening statement, the government showed slides that Near had viewed at a presentation for NSF grantees given by Dr. Montgomery Fisher, a lawyer and investigator with NSF’s OIG. The slides stated in large letters “Don’t lie” and “Don’t steal” and warned viewers that if they lied or stole they would be investigated and prosecuted. Presentation of Montgomery Fisher (Doc. 190-65 at 9-12).4 When Fisher testified, the government again displayed these slides for the jury.
At the conclusion of the government’s case, Near made a motion for a judgment of acquittal, which the court denied. Near did not renew this motion at the close of his own case.
The district court instructed the jury on all counts using the Eleventh Circuit’s pattern instructions. It added that the jury had to decide whether the government had proven the defendants guilty of the crimes charged in the indictment, clarifying that stealing was not a crime charged in the indictment, nor was using money derived from federal grants for personal expenses.
The jury convicted the defendants on all counts but one.
D. Sentencing
Over the course of two days during the sentencing hearing, the district court heard testimony, from Gibson for the government and forensic accountant Jean-Pascal Gingras for the defense, on the issue of how much monetary loss was attributable to the defendants. Ultimately, the court concluded that the government agencies got the full benefit of their bargains, so they could not show any loss. In the alternative, the court concluded that the value of the services provided by Near, Genziko, and Genziko’s subcontractors was greater than any loss to the government *596and could be used to offset that loss, resulting in no net loss. The court declined to order any restitution, finding that there were no victims who had sustained a loss.
⅜ ‡ ⅜
The defendants appealed their convictions. The government cross-appealed, challenging the defendants’ sentences.
II. DISCUSSION
The defendants raise three challenges on appeal. First, they challenge the sufficiency of the evidence supporting their convictions. Second, they argue that statements the government made to the jury about the crimes’ elements and the instructions given by the district court constructively amended the indictment charging them. Third, they argue that the series of slides introduced by the government and read by a government witness, along with statements about lying and stealing by the government during the government’s opening and closing, lowered the burden of proof by suggesting to the jury that it could convict the defendants of simple lying and stealing. We reject these arguments and affirm the defendants’ convictions. First, the government produced sufficient evidence such that the defendants’ convictions did not amount to a manifest miscarriage of justice. Second, looking at the full context of the trial, we disagree that the indictments were constructively amended. Third, even assuming the district court erred in admitting the challenged evidence, that error was harmless in light of the court’s curative instructions.
The government appeals the defendants’ sentences. It contends that the district court erred in calculating a loss amount of zero for the defendants’ crimes because in making its calculation the court should have applied a special rule relating to government benefits. The government also argues that the district court erred in offsetting any loss with the value of services provided by Near, Genziko, and Genziko’s subcontractors. After reviewing the record, we are not convinced that the district court’s factual findings about loss were clearly erroneous. Nor did the district court err in offsetting any losses by the value of services provided under the grants. Given these conclusions, we need not decide whether the government benefits rule applies because it would have no impact on the defendants’ sentences. Finally, the government urges us to overturn the district court’s decision not to order any restitution. On the record before us, however, the district court did not abuse its discretion in declining to order restitution. We therefore affirm the defendants’ sentences.
A. Sufficiency of the Evidence
The defendants challenge the sufficiency of the evidence supporting each of their convictions. We generally review the evidence supporting a defendant’s convictions de novo, drawing all reasonable inferences in favor of the verdict. United States v. Perez, 443 F.3d 772, 774 (11th Cir. 2006). But Near failed to preserve his challenge by renewing his Rule 29 motion for acquittal at the close of the evidence, so we will reverse for insufficient -evidence only where necessary to prevent a manifest miscarriage of justice. United States v. Fries, 726 F.3d 1286, 1291 (11th Cir. 2013). Genziko made no motions at trial, so we review the sufficiency of the evidence supporting its convictions under the same manifest miscarriage of justice standard. “This standard requires us to find either that the record is devoid of evidence of an essential element of the crime or that the evidence on a key element of the offense is so tenuous that a conviction would be shocking.” Id. (internal quotation marks *597omitted). After carefully reviewing the evidence, we conclude that neither Near nor Genziko has met this high standard.
1. Wire Fraud
To convict the defendants of wire fraud in violation of 18 U.S.C. § 1343, the government must prove beyond a reasonable doubt that they (1) participated in a scheme or artifice to defraud; (2) with the intent to defraud; and (3) used, or caused the use of, interstate wire transmissions for the purpose of executing the scheme or artifice to defraud. United States v. Martin, 803 F.3d 581, 588 (11th Cir. 2015). The defendants argue that the government produced insufficient evidence to satisfy the third prong.
Sufficient evidence established that the defendants made the seven transmissions at issue for the purpose of executing the scheme with which they were charged. “A transmission is for the purpose of executing the [charged] scheme if it is incident to an essential part of the scheme.” United States v. Evans, 473 F.3d 1115, 1118 (11th Cir. 2006) (internal quotation marks omitted). Here, the defendants were charged with “knowingly and willfully devising] and intending] to devise a scheme and artifice to defraud the United States, and to obtain money and property by means of materially false and fraudulent pretenses, representations, and promises.” Indictment ¶ 1 (Doc. 9).
Six of the transmissions were wire transfers of the proceeds of the defendants’ scheme. Gibson and a NASA accountant testified that five of the charged transmissions were wire transfers of NASA grant money from the U.S. Treasury to three Genziko bank accounts.5 An NSF grant officer testified that a sixth charged transmission was a wire transfer of NSF grant money from the U.S. Treasury to one of these Genziko accounts. These six bank transfers plainly were essential to the defendants’ scheme to obtain money — they were that money.
The seventh wire transmission was an April 23, 2014 email Near sent on behalf of Genziko to Delgado, the NASA contracting officer. Delgado had emailed Near the day before, asking for information about how NASA money allocated in Near’s project budget to pay an engineer and a technician had been spent. She requested this information to dose out NASA’s contract with Genziko and process final payments to the company. Near replied by naming two employees who purportedly had worked as an engineer and a technician on the project. Genziko received its final two payments from NASA within a month of Near’s email. Yet Gibson testified that neither of the individuals Near named had received any money from Genziko. Taken together, the evidence supports the jury’s verdict that Near sent the email for the purpose of defrauding the United States in order to obtain money.
The defendants contend that these seven wire transmissions cannot have been for the purpose of executing the scheme with which they were charged because each transmission was sent after that scheme had concluded. Generally, a wire transmission sent after a scheme has reached fruition cannot be for the purpose of executing the scheme. See Evans, 473 F.3d at 1118—19. The defendants argue that these post-award transmissions could not have been for the purpose of executing their scheme because they took place well after the scheme came to fruition. That is, the de*598fendants argue that the charged scheme was “limited to misrepresentations in the proposals,” so “once the proposals were accepted and the awards made, the scheme had reached fruition.” Near’s Appellant’s Br. 47-48 (internal quotation marks omitted). But this argument ignores that the indictment charged the defendants with a broader scheme to defraud the United States “to obtain money and property by means of materially false and fraudulent pretenses, representations, and promises.” Indictment ¶ 1 (Doc, 9). Considering the full charge, sufficient evidence supported the six wire fraud counts based on wire transfers and the seventh count based on Near’s email. We therefore affirm both defendants’ convictions for seven counts of wire fraud.
2. False Claims
Sufficient evidence also supported the defendants’ convictions on two counts of presenting false claims to the United States. To obtain a conviction under the false claims statute, 18 U.S.C. § 287, the government must prove beyond a reasonable doubt that (1) the defendant presented a claim against the United States to an agency or department thereof; (2) such claim was false, fictitious, or fraudulent; and (3) the defendant knew that the claim was false, fictitious, or fraudulent. United States v. Hesser, 800 F.3d 1310, 1320 (11th Cir. 2015). The first. false claims count alleged that the defendants falsely certified that they performed work in accordance with the terms and conditions of Genziko’s NSF award to receive payment from the NSF. The second false claims count alleged a similar false certification relating to the terms and conditions of one of Genziko’s NASA contracts. The defendants insist that the proposed budgets did not form part of the terms and conditions of their awards, so they did not present any false claims to the United States when Near signed those certifications.
a. NSF Grant
Near submitted to NSF a final report of the work Genziko completed under its NSF grant. When submitting that report, Near had to certify on behalf of Genziko that “to the best of [his] knowledge the work for which payment is hereby requested was performed in accordance with the award terms and conditions.” NSF Final Report (Doc. 190-28 at 32). The government argued that this certification was false because Genziko did not comply with the budget it proposed when seeking the grant. Specifically, the government offered evidence that after submitting the grant proposal, an NSF program director contacted Near requesting more detail about Genziko’s proposed budget. The program director stated that he needed the information in order for Genziko’s proposal to receive further consideration. Near responded by providing a more detailed budget proposal that listed payments to two named individuals, an unnamed student technician, and Georgia Tech. Hess testified that he examined Genziko’s records and found no evidence that Genziko had paid any of these expenses.
The defendants make several arguments about why the more detailed budget listing those four expenses was not part of the terms and conditions with which Near had certified compliance. But the government offered enough evidence that the award terms and conditions included the detailed budget to persuade us that there has been no manifest miscarriage of justice.
Schrag testified that NSF expected companies to follow their proposed budgets, that the agency viewed the final report certification as confirming that money was spent according to the proposed budget, and that companies were required *599to contact NSF for approval of any changes. These expectations were supported by program documents. The solicitation for NSF SBIR grant proposals required proposals to include “[detailed documentation of budget line items.” SBIR Phase I Solicitation 11 (Doc. 190-26 at 11). The solicitation also specified that SBIR “award conditions” included “the budget, which indicates the amounts, by categories of expense, on which NSF has based its support.” Id. at 16. And the SBIR Grant General Conditions document stated that “[p]ayment of the grant amount is conditioned upon the Grantee’s ... compliance with the award terms and conditions.” NSF SBIR Phase Grant General Conditions 4 (Doc. 190-28 at 7). Moreover, the SBIR program director who requested more detailed budget information after Genziko submitted its proposal made clear that he needed the additional information “[i]n order [for Genziko’s proposal] to receive further consideration.” Email from Craig Near to Murali Nair, NSF Program Director (Sept. 25, 2008) (Doc. 190-28 at 63). Taken together, the evidence that the defendants knowingly' made a false certification regarding their compliance with the NSF grant terms and conditions was not “so tenuous that a conviction would be shocking.” Fries, 725 F.3d at 1291 (internal quotation marks omitted).
b. NASA Contract
Genziko was required to submit quarterly reports on the status of the work it performed pursuant to its NASA contracts as a condition of receiving payment. As part of the Seventh Quarterly Interim Report for Genziko’s NASA contract, which was filed well into the project’s second year, Near certified that during the performance of contract, “[tjerms and conditions set forth in this contract have not been altered, except [sic] approved in writing by the Contracting Officer.” Seventh Q. Interim Rep, Certification (Doc. 190-39 at 67). The government argued that this certification was false because Genziko had not paid the expenses listed in its budget. The government placed into evidence Genziko’s budget proposal, which listed payments to an unnamed engineer, an unnamed technician, and two named consultants that were to be made in the contract’s first year. Delgado testified Near informed her that Meyer was the engineer and Brooks was the technician. But Brooks testified that he was never paid (and never expected to receive any payment) for some technical help he provided Near. Hess testified that when he interviewed Near, Near stated that he never paid any employees but himself. Hess also testified that, after examining Genziko’s records, he found no evidence of payments to Brooks, Meyer, or the two named consultants.
The defendants argue that because the terms and conditions of Genziko’s NASA contract did not include a specific timeline for paying employees, the possibility of payment remained open, meaning the certification was not false. But the government introduced evidence that these payments were budgeted for the contract’s first year, which concluded nine months before Near certified his compliance with the contract.
Sufficient evidence supported the government’s argument. The cover page of the NASA contract that Near signed on Genziko’s behalf specified that the contract would be governed by several documents including “this award/contract” and “such provisions, representations, certifications, and specifications, as are attached or incorporated by reference herein.” NASA Contract (Doc. 190-43 at 19). Within that contract, a term provided that Genziko’s proposal was “hereby incorporated into *600this contract by reference.” Id. (Doc. 190-59 at 31). A NASA contracting officer also testified that the budget proposal itself was part of the contract. That proposal listed specific amounts of money to be paid to an engineer, a technician, and the consultants under the column “Year One,” meaning during the first year of the contract. Genziko NASA Budget (Doc. 190-42 at 145). Given this evidence, we cannot say that the defendants’ convictions represented a manifest miscarriage of justice.
B. Constructive Amendment of the Indictment
The defendants argue that the district court and government constructively amended the indictment charging them. “A constructive amendment occurs when the essential elements of the offense contained in the indictment are altered to broaden the possible bases for conviction beyond what is contained in the indictment.” United States v. Castro, 89 F.3d 1443, 1452-53 (11th Cir. 1996) (internal quotation marks omitted). “The indictment may be amended as a result of erroneous jury instructions or a prosecutor’s statements.” Id. at 1453. “In evaluating whether the indictment was constructively amended, we review the district court’s jury instructions and the prosecutor’s summation ⅛ context’ to determine whether an expansion of the indictment occurred either literally or in effect.” Id. at 1450. Because the defendants did not raise this objection at trial, we ' review for plain error. See United States v. Dortch, 696 F.3d 1104, 1112 (11th Cir. 2012). We find no error here, much less that the error was plain.
1. Wire Fraud
One of the elements of wire fraud is that the defendant acted with knowledge when he devised or participated in a scheme to defraud another. Langford v. Rite Aid of Ala., Inc., 231 F.3d 1308, 1312 (11th Cir. 2000). The indictment in this case, however, charged that Near and Genziko “did knowingly and willfully devise and intend to devise a scheme and artifice to defraud the United States,” thus adding a willfulness requirement. Indictment ¶9 (Doc. 9) (emphasis added). Knowledge and willfulness are distinct: A defendant “acts knowingly if he acts with knowledge of the facts that constitute the offense,” but acting willfully requires that he “act[ ] with knowledge that his conduct was unlawful.” United States v. Clay, 832 F.3d 1259, 1301 (11th Cir. 2016) (internal quotation marks omitted), cert. denied sub nom. Farha v. United States, — U.S. —, 137 S.Ct. 1814, 197 L.Ed.2d 758 (2017). The government mentioned neither requirement in its closing argument, instead focusing on the separate specific intent element of the wire fraud statute by stating that the government “ha[d] to prove and ha[d] proved that [Near] had [the] intent to defraud.” Trial Tr. June 18, 2015 (Doc. 252 at 14-15). The district court then instructed the jury using the Eleventh Circuit pattern wire fraud instruction, which does not include willfulness. See Eleventh Cir. Pattern Jury Instr. 51, Criminal (2010). The defendants contend that the government’s failure to mention willfulness combined with the court’s omission of willfulness from the jury instructions constructively amended the indictment charging them by dropping the willfulness requirement.
We disagree. “[I]n context,” the government and district court’s failure to mention willfulness did not constructively alter the indictment. Castro, 89 F.3d at 1450. The court instructed the jury that it had to decide whether the government had proved the defendants guilty “of the crimes charged in the indictment.” Trial Tr. June 18, 2015 (Doc. 252 at 59) (emphasis added). The jury had that indictment, *601which included the willfulness element, in its possession in the jury room. The court also defined the term willfully, albeit in the context of a different charge. Given this context, the indictment here was not constructively amended.
The defendants rely on United States v. Cancelliere, 69 F.3d 1116 (11th Cir. 1995), a case in which we overturned a defendant’s conviction where his indictment charged that he “knowingly and willfully” laundered money. Id. at 1119. At the close of evidence in Cancelliere, the government moved to strike “willfulness,” which was not a statutory element of the offense, from the indictment. Id. The district court granted the motion, and we reversed because in so doing the district court had constructively amended the indictment. Id. at 1121-22. Although Cancelliere appears very similar to the present case, there are two important differences. First, the district court in Can-celliere physically redacted the word “willfully” from the indictment, so the jury could not have considered the element in its deliberations. Second, as we recognized in United States v. Mozie, 752 F.3d 1271 (11th Cir. 2014), the defendant in Cancelliere “rested his ‘whole defense’ on disproving the mental state that was stricken” after trial by the district court. Id. at 1284-85 (quoting Cancelliere, 69 F.3d at 1122). Here, by contrast, Genziko presented no defense, and Near’s defense did not focus on his lack of willfulness in having devised a scheme to defraud the United States. Near points out that he elicited testimony from a witness that the witness did not believe Near willfully misrepresented anything. And Near notes that he specifically argued in closing that “he didn’t willfully misrepresent anything.” Trial Tr. June 18, 2015 (Doc. 252 at 28). But one line of testimony and one mention of willfulness in a closing argument are insufficient to conclude that Near rested his defense wholly on a lack of willfulness. Thus, we hold that the defendants’ wire fraud indictment was not constructively amended.
2. False Claims
One of the elements of the crime of filing false claims is that the defendant knew that the claim he filed was false, fictitious, or fraudulent. Hesser, 800 F.3d at 1320. This Court has never decided whether a false claim must also have been material, United States v. White, 27 F.3d 1531, 1534-35 (11th Cir. 1994), but our Circuit’s false claims pattern jury instruction requires the jury to find that “the claim was based on a false or fraudulent material fact.” See Eleventh Cir. Pattern Jury Instr, 11.2, Criminal (2010). Neither our case law nor our jury instructions, however, require the government to prove that the defendant knew that the false claim he filed was material. Nevertheless, the indictment in this case charged that Near and Genziko made claims “which they knew to be materially false, fictitious, and fraudulent.” Indictment ¶ 14 (Doc. 9) (emphasis added). The pattern instruction the district court gave did not tie knowledge to materiality.6 The defendants contend that these instructions constructively amended the indictment.
As with the wire fraud counts, we are unconvinced. The court instructed the jury to decide whether the government had proved the defendants guilty of the crimes as charged, the jury had the indictment *602during its deliberations, and the court defined both knowledge and materiality (the latter, again, in the context of a different charge). Cancelliere does not compel a different outcome for the same reasons we discussed above. Although Near identifies one witness who gave testimony relevant to Near’s knowledge of his false claims’ materiality, Near did not even mention this lack of knowledge in closing. He argued instead that his misrepresentations were not material at all. Given this context, the court’s use of the pattern jury instruction did not effect a constructive amendment to the indictment. See Castro, 89 F.3d at 1450.
C. Trial Objections
The defendants argue that the government impermissibly lowered the burden of proof via testimony and exhibits admitted at trial. Specifically, they argue that the government should not have been allowed to introduce Fisher’s slide presentation because it equated simple lying and stealing with guilt under the charged statutes. For the same reason, the defendants object to Fisher’s reading of the slides to the jury, the government’s preview of the slides during its opening argument, and the government’s reference to lying and stealing during its closing argument. We review the admission of evidence over the defendant’s objection for an abuse of discretion. United States v. Joseph, 709 F.3d 1082, 1093 (11th Cir. 2013). An abuse of discretion in the admission of evidence requires reversal unless we find it harmless beyond a reasonable doubt. United States v. Turner, 474 F.3d 1265, 1275 (11th Cir. 2007).
Assuming the district court abused its discretion, we conclude that any error was harmless. The district court’s jury instructions ameliorated any harm the slides, testimony, and arguments might have caused. With regard to stealing, the court instructed the jury that “[i]t [was] not a crime as charged in the indictment nor an element of any charged crime to use money derived from federal grants or contracts for personal expenses.” Trial Tr. June 18, 2015 (Doc. 252 at 69). With regard to lying, the court gave two separate instructions that lies had to be material in order to be criminal under the wire fraud and false claims statutes. “Few tenets are more fundamental to our jury trial system than the presumption that juries obey the court’s instructions.” United States v. Stone, 9 F.3d 934, 938 (11th Cir. 1993). Given this presumption and the court’s clear instructions that simple lying and stealing were not enough to convict the defendants, any errors the district court committed in allowing Fisher’s slides, Fisher’s testimony, or the government’s arguments were harmless.
D. Sentencing
The government cross-appeals two of the district court’s sentencing rulings. First, it challenges the court’s determination that the special rule for government benefits established by the Sentencing Guidelines was inapplicable. Second, the government contends that the district court erred in declining to award restitution to the defendants’ victims. After careful review, we find no error.
1. Loss Calculation
The district court determined that there was no loss to the government in this case because NSF and NASA got what they bargained for. The government argues that the district court should have applied the “Special Rule” for government benefits spelled out in Application Note 3(F)(ii) to the fraud guideline, which properly would have recognized the government’s loss amount. See U.S.S.G. § 2B1.1 cmt. n.3(F)(ii). This Court reviews a district *603court’s interpretation of the Sentencing Guidelines de novo, its factual findings for clear error, and its application of those factual findings to the Guidelines de novo. United States v. Doe, 661 F.3d 550, 565 (11th Cir. 2011); United States v. Jordi, 418 F.3d 1212, 1214 (11th Cir. 2005). We will find clear error only if we are “left with a definite and firm conviction that a mistake has been committed.” United States v. Crawford, 407 F.3d 1174, 1177 (11th Cir. 2005) (internal quotation marks omitted).
The Government Benefits Rule provides that in cases involving certain government benefits programs, the loss amount used to determine a defendant’s sentence should be the entire amount (1) obtained by unintended recipients or (2) diverted to unintended uses. U.S.S.G. § 2B1.1 cmt. n.3(F)(ii). The district court considered the government’s argument that this rule applied to the defendants but found that even if it might apply, Genziko and Near were not unintended recipients. This finding was not clearly erroneous. There was ample testimony that the purpose of the SBIR program was to help small businesses commercialize technology products, and the evidence established that Genziko was such a small business.
Regardless, the government argues that Near diverted money to unintended uses, which also falls under the Government Benefits Rule. We need not decide whether the government is correct, however, because the result would be the same whether the Government Benefits Rule applied or not. The district court found that the value of Near’s labor — along with labor, equipment, and materials provided by Georgia Tech and UT — was worth more than any loss suffered by the government. Applying a different subsection of the same Application Note that establishes the Government Benefits Rule, the court credited the fair market value of the services Genziko and its subcontractors performed pursuant to the grants against the loss amount, resulting in a loss of zero. U.S.S.G. § 2B1.1 cmt. n.3(E). After reviewing the record, which includes extensive testimony by a forensic accountant for the defendants, we are not persuaded that the district court’s finding about the value of Near and Genziko’s services was clearly erroneous.
The government insists, however, that losses under the Government Benefits Rule are not subject to credits against them. It cites United States v. Maxwell, 579 F.3d 1282 (11th Cir. 2009), in which this Court declined to credit the value of services provided by an unintended recipient against losses under the Government Benefits Rule. See id. at 1306 (“[T]he appropriate amount of loss here should have been the entire value of the [] contracts that were diverted to the unintended recipient.”). The government is correct that Maxwell declined to offset losses under the Government Benefits Rule, but Maxwell involved funds received by an unintended recipient. Id. It makes sense that such losses could not be offset by the value of services provided because those services should never have been provided by that recipient in the first place.
But Maxwell does not speak to whether the value of services provided by an intended recipient can be credited against losses caused by that recipient’s unintended use of funds. We are persuaded that such losses can be offset by the value of service provided. “Money is fungible,” Sabri v. United States, 541 U.S. 600, 606, 124 S.Ct. 1941, 158 L.Ed.2d 891 (2004), so it makes sense to consider as a whole the money received and the money expended by Genziko. Moreover, as the Third Circuit noted when considering this question, there is textual support in the Guidelines *604for crediting the value of services against losses under the Government Benefits Rule. See United States v. Nagle, 803 F.3d 167, 182 (3d Cir. 2015). “[T]he drafters of’ the Application Note containing both the Government Benefits Rule and the provision for offsetting losses “knew how to indicate that no credits would be permitted.” Id. A different subsection of that same note, “which governs certain types of misrepresentation schemes, specifically states that ‘loss shall, include the amount paid for the property, services or goods transferred, rendered, or misrepresented, with no credit provided for the value of those items or services,’” Id. (quoting U.S.S.G. § 2B1.1 cmt. n.3(F)(v)). “Had the Sentencing Commission intended to preclude crediting services rendered against loss” under the Government Benefits Rule, the Third Circuit concluded, “it would have used similar language.” Id.
We find no error in the district court’s conclusion that the government suffered no loss. We therefore affirm Near’s sentence of four months’ imprisonment and Genziko’s sentence of five years’ probation and a $5,000 fine.
2. Restitution
The government also argues that the district court erred in refusing to order restitution. The Mandatory Victim Restitution Act (MVRA) requires district courts to order restitution if the defendant is convicted of a covered offense “in which an identifiable victim or victims has suffered a pecuniary loss.” 18 U.S.C. § 3663A(a)(l), (c)(1)(A) and (B). Wire fraud is a covered offense. 18 U.S.C. § 3663A(c)(1)(A)(ii); United States v. Dickerson, 370 F.3d 1330, 1335-36 (11th Cir. 2004). “We review de novo the legality of an order of restitution, but review for abuse of discretion the determination of the restitution value of lost or destroyed property. We review for clear error factual findings underlying the restitution order.” United States v. Robertson, 493 F.3d 1322, 1330 (11th Cir. 2007) (internal quotation marks and citations omitted).
Here, the district court explained that it ordered no restitution because it did not believe that any actual victim sustained an actual loss. The government, by contrast, identifies seven victims that it contends suffered loss: NSF, NASA, two Georgia Tech professors, Georgia Tech, UT, and Mound Laser and Photonics Center, Inc. The MVRA defines the term “victim” expansively. See United States v. Speakman, 594 F.3d 1165, 1169-70 (10th Cir. 2010). Victims are entitled to restitution if they are “directly and proximately harmed as a result of the commission of an offense” covered under the MVRA. 18 U.S.C. § 3663A(a)(2). The government has the burden of showing that “the conduct underlying the offense of conviction” was the “but for” cause of the victims’ harm and that “the causal connection between the conduct and the loss is not too attenuated (either factually or temporally).” Robertson, 493 F.3d at 1334 (internal quotation marks omitted).
As explained above, we agree with the district court’s finding that neither NSF nor NASA suffered monetary harm, so the agencies are not entitled to restitution. And our review of the record does not persuade us that the district court clearly erred in declining to order restitution to the other alleged victims because the connection between the defendants’ offense conduct and the victims’ losses was too attenuated. See id. at 1334 (“[P]roximate cause is a factual finding we review for clear error.”). As the district court explained, the non-agency victims’ losses were not directly caused by the defendants obtaining the grants and grant money. Indeed, these victims hoped to benefit from *605the grants. The fact that the victims never were paid — like many to whom the defendants owed debts — is too attenuated a connection to satisfy the government’s burden of demonstrating a causal connection between the defendants’ conduct and the loss in question. We therefore affirm the district court’s decision to order no restitution.
III. CONCLUSION
For the foregoing reasons, we AFFIRM the defendants’ convictions and sentences.
. The indictment charged the defendants with eight counts of wire fraud, but the government dismissed one of these counts before trial.
. The indictment charged that each defendant was responsible for each count both as a principal and as an aider and abettor.
. We include here only the facts essential to resolving the issues on appeal.
. References to "Doc.” refer to the numbered docket entries in the district court record of the case.
. Gibson also testified that Near spent money from all three Genziko accounts, so he indisputably had access to those funds.
. The defendants contend that the government failed to mention the scienter element of materiality in closing. This is true, but the government did not mention scienter at all, nor did the government purport to lay out the elements it was required to prove. The government’s closing argument did not, therefore, constructively amend the indictment.