O'SCANNLAIN, Circuit Judge:

Oren appeals from his jury verdict convictions of one count of wire fraud and one count of false statement within the jurisdiction of a federal agency. He also appeals from the district court's sentencing order. We affirm the convictions, but we vacate part of his sentence.

I

In 1978, Oren bought 811 acres of undeveloped land in Agoura, California. This property is adjacent to the Santa Monica Mountains National Recreation Area.

In 1982, Oren was approached by a representative from the Trust for Public Lands ("TPL") about selling his land. TPL is a non-profit organization that helps the United States Forest Service, the National Park Service, and other government agencies acquire undeveloped land for public parks. TPL aids these government agencies by either buying the land that an agency wishes to obtain or securing an option on such land, while the agency seeks public funding for the acquisition. In this case, the National Park Service desired Oren's land as an addition to the Santa Monica Mountains National Recreation Area, but had not yet secured funding. TPL therefore hoped to buy Oren's land for later resale to the National Park Service when public funds became available.

In 1983, TPL and Oren agreed to an option on 200 acres of his land. The option agreement set a purchase price of $5 million; the option was to expire on September 30, 1984.

To be able to resell the land to the National Park Service, TPL had to obtain an appraisal of the market value of the land. TPL therefore hired Steve Whittlesey to appraise not only the 200 acres that the July 1983 option agreement covered, but also an additional 136 acres in which TPL had become interested. In August 1984, Whittlesey presented a collective appraisal value of $5.8 million for both the 200 acres under option and the other 136 acres.

Oren was displeased with the low appraisal value and threatened to terminate the sale. TPL thereupon hired another appraiser, Thomas Erickson. In addition, in September 1984, TPL and Oren amended their option agreement. The amended option agreement included the additional 136 acres that TPL wanted and fixed the purchase price for the entire parcel of 336 acres at $7.5 million. The amended option agreement extended the period for exercise to November 15, 1984. This time period was a tight one because an appraisal normally takes six months. However, Oren insisted on the November 15th date because, he said, he had another offer on the land.

In fact, Oren had no other offer. When TPL pressed Oren to forward the offer to the appraiser so that a higher evaluation might result, Oren and two business associates created a false offer letter. The false document purported to be a detailed offer from Union Pacific to purchase all of Oren's 811 acres and contained a subsidiary offer of $9.3 million for the 336 acres TPL wanted. Partially relying on the fabricated Union Pacific offer, on October 3, 1984, Erickson presented TPL and Oren with an appraisal of $8.4 million. Erickson's appraisal referred to the terms of the false Union Pacific offer.

On October 10, 1984, TPL sent a copy of the Erickson appraisal to the National Park Service. Later, the National Park Service requested a copy of the false offer itself; Erickson supplied the letter, but deleted the name of the purported offeror (Union Pacific). Erickson made this deletion in order to comply with Oren's request for confidentiality.

On November 15, 1984, TPL exercised its option to purchase the 336 acres for $7.5 million. Two months later, TPL resold the land to the National Park Service for $8 million.

In 1986, a grand jury indicted Oren on two counts: (1) wire fraud and (2) making a false statement within the jurisdiction of the National Park Service. At trial, the district court excluded evidence relating to the value of the property, Oren's belief as to that value, and the National Park Service's reliance on Oren's false offer letter. Later, the district court instructed the jury that the excluded evidence was irrelevant. At the government's request, the district court instructed the jury that the government must prove that Oren could reasonably foresee that the false statements were within the jurisdiction of the United States. In July 1987, the jury convicted Oren on both counts.

Prior to sentencing, Oren offered to the National Park Service, as an unrestricted gift, twenty acres of his property. When restitution in the amount of $272,000, plus interest, was made a part of his sentence, Oren attempted to have this gift applied in fulfillment of that portion of his sentence. The district court refused Oren's request because it found that Oren's gift was merely an expression of remorse. As of the date of this case's submission on appeal, the Park Service had not yet decided whether to accept the gift.

II

We first consider Oren's conviction of wire fraud under 18 U.S.C. § 1343. Oren contends that the district court erred in excluding three types of evidence and in giving certain jury instructions. "[W]e review decisions regarding the relevance of evidence for abuse of discretion." United States v. Kessi, 868 F.2d 1097, 1107 (9th Cir. 1989). We reject each contention.

A

First, Oren contends that the government must "show that the defendant actually caused a monetary or property loss to be guilty of mail fraud." Appellant's Opening Brief at 29. For this contention he invokes only the United States Supreme Court decision in McNally v. United States, 483 U.S. 350, 107 S.Ct. 2875, 97 L.Ed.2d 292 (1987). As Oren reads it, McNally requires "an actual loss, not just a plan or scheme" to defraud. Appellant's Opening Brief at 33. In short, Oren contends that, after McNally, the mail and wire fraud statutes punish only successful schemes.

We cannot agree with this reading of McNally. The contribution of McNally to mail fraud jurisprudence (if it may be so called) was to establish that there was no property right, for purposes of these statutes, in "honest and impartial government." McNally, 483 U.S. at 355, 107 S.Ct. at 2879. The Court found such "an interest too ethereal in itself to fall within the protection of the mail fraud statute. . . ." Carpenter v. United States, 484 U.S. 19, 25, 108 S.Ct. 316, 320, 98 L.Ed.2d 275 (1987). There is nothing in McNally to support Oren's argument that the case requires "an actual loss, not just a plan or scheme." See United States v. Utz, 886 F.2d 1148, 1149-50 (9th Cir. 1989) (specifically rejecting a reading of McNally which provided that "a scheme to defraud must succeed before it can form the basis of a mail fraud prosecution").

Because Oren's reading of McNally cannot stand, so, too, falls his argument that wire fraud requires a government showing that the defendant caused an actual loss of money or property. This argument therefore cannot serve as a basis for his contention that the district court erred in excluding evidence of the property's value.

Oren presents a second, more problematic, argument that the district court erred in excluding evidence of the property's value. He contends that the evidence was relevant because, even if the government did not have to show that he caused actual loss, it at least had to show that he intended to cause actual loss. He derives this notion from the phrase "intending to devise any scheme or artifice to defraud" in the wire fraud statute. 18 U.S.C. § 1343. In Oren's view, "to defraud" is "to cause injury from the loss of property or money for less than fair market value." Appellant's Opening Brief at 29 (emphasis added). Without evidence of the property's value, the argument concludes, it cannot be known whether Oren intended that TPL pay more than fair market value for the property or, in other words, whether he intended that TPL be defrauded. In short, Oren argues that if he had been allowed to, and able to, establish that TPL paid no more than fair market value for the property, this would have precluded any conclusion that TPL was defrauded.

If we could agree with Oren's contention that "to defraud" is only "to cause injury from the loss of property or money for less than fair market value," we would also share his view that the excluded evidence of value was relevant. But we see it otherwise.

"To defraud," as used in the mail and wire fraud statutes, has a broader meaning. Twice in the past several years, the Supreme Court has undertaken to explain it for us. See McNally v. United States, 483 U.S. 350, 107 S.Ct. 2875, 97 L.Ed.2d 292 (1987); Carpenter v. United States, 484 U.S. 19, 108 S.Ct. 316, 98 L.Ed.2d 275 (1987). In Carpenter, the Court summarized its teachings on the meaning of "to defraud" as used in the mail and wire fraud statutes:

Sections 1341 and 1343 reach any scheme to deprive another of money or property by means of false or fraudulent pretenses, representations, or promises. As we observed last Term in McNally, the words "to defraud" in the mail fraud statute have the "common understanding" of "wronging one in his property rights by dishonest methods or schemes, and usually signify the deprivation of something of value by trick, deceit, chicane or overreaching."

Id. at 27, 108 S.Ct. at 321 (quoting McNally, 483 U.S. at 358, 107 S.Ct. at 2880) (quotation omitted). This can leave no doubt that "to defraud" has a more encompassing meaning than Oren's "to cause someone to receive less than fair market value" (our phrasing) for an item. As the above Supreme Court statement shows, one defrauds another when he causes him to be "deprive[d] . . . of property by means of false . . . representations. . . ."

Oren's conduct unquestionably falls within this meaning of "to defraud." Knowing that TPL would not buy the property without an appraisal that reached certain conclusions, he intentionally made a false representation to TPL's appraiser. The appraisal partially relied on Oren's false representations. Relying on the appraisal itself, TPL gave Oren money in exchange for his property. Money, of course, is property. TPL was thereby "deprive[d] . . . of property by means of false . . . representations . . . ."

We therefore reject Oren's second argument that evidence of the property's value was relevant to whether TPL was defrauded. Even if the property here was worth what TPL paid for it, TPL was nonetheless defrauded. The actual value of Oren's land was therefore irrelevant.

B

Oren raises a second challenge to the district court's exclusion of evidence. Specifically, he argues that the district court erred in excluding evidence of Oren's belief in the value of the property. We find no error here.

Oren contends that if he actually believed that the property was worth the $9.3 million that he falsely represented Union Pacific as being willing to pay, then he could not have intended to defraud TPL. In his view, an honest good-faith belief in the land's value negates an intent to defraud. Thus, the argument concludes, the district court acted improperly in excluding evidence as to Oren's belief of value.

We are unpersuaded by this argument. Oren's guilt or innocence of the crime charged is entirely independent of and unrelated to his belief of the property's value. Oren was charged in count one of violating the wire fraud statute by doing the following: falsely representing that he had a competing $9.3 million offer on his property and intending to induce, by this false statement, TPL to buy his property. It therefore would have been a defense for Oren to argue that, at the time he submitted the false offer letter to Erickson, he really believed that a $9.3 million offer from Union Pacific was pending on his property and that the letter was genuine. Cf. United States v. Benny, 786 F.2d 1410, 1417 (9th Cir.) ("While an honest, goodfaith belief in the truth of the misrepresentations may negate intent to defraud, a good-faith belief that the victim will be repaid and will sustain no loss is no defense at all."), cert. denied, 479 U.S. 1017, 107 S.Ct. 668, 93 L.Ed.2d 720 (1986). Oren never so argued; he has conceded from the beginning of this prosecution that there was no offer from Union Pacific and that the letter was false. Because he has conceded that he intentionally created a false statement, it was no defense here for him to argue that he genuinely believed that the property was worth what the government paid for it.

We conclude that the district court did not abuse its discretion in excluding evidence of Oren's belief as to the property's value. Oren's contention, in effect, that he intended that the buyer of his property get a bargain was irrelevant to the crimes charged.

C

Finally, Oren contends that the district court erred by excluding evidence relating to the National Park Service's reliance on the false offer letter. We reject this contention.

Oren concedes, as he must, that reliance is not a necessary element of the wire fraud offense. See United States v. Halbert, 712 F.2d 388, 390 (9th Cir. 1983), cert. denied, 465 U.S. 1005, 104 S.Ct. 997, 79 L.Ed.2d 230 (1984). He argues instead that the district court should have admitted it as relevant to Oren's intent to defraud. He further views this evidence as relevant to the question of whether his misrepresentations were material.

We note first that the district court admitted most of the evidence that Oren sought to introduce as to the National Park Service's purported lack of reliance on Oren's misrepresentations. For instance, the court allowed defense counsel to cross-examine Park Service employee Jack McDonald about his alleged lack of reliance on the copy of the offer letter that appraiser Erickson provided to him. In fact, Oren does not challenge the government's contention that the only evidence as to reliance that the court excluded was evidence that the National Park Service was desperate to buy Oren's property and would have done so at any price.

We think that the district court did not abuse its discretion in excluding this evidence of lack of reliance. The evidence was irrelevant to the question of whether Oren intended to defraud. As discussed at length above, the necessary intent was to cause someone to part with his property by means of a false representation. Given these predicates of a wire fraud offense, we can see neither how the excluded evidence could have supported a defense to the charge nor, particularly, how evidence of the Park Service's desperation was relevant to Oren's intent.

We therefore reject Oren's argument that the district court acted improperly in excluding evidence of the National Park Service's lack of reliance on Oren's misrepresentations.

III

We next turn to Oren's conviction for making a false statement within the jurisdiction of the National Park Service. Oren raises three challenges to this conviction under 18 U.S.C. § 1001. We consider and reject each of these challenges.

A

First, Oren contends that count two of his indictment was insufficient because it failed to allege expressly the materiality of his false statements. We review de novo the sufficiency of the indictment. See United States v. Normandeau, 800 F.2d 953, 958 (9th Cir. 1986). We disagree with Oren's contention.

Materiality is an essential element of a conviction for false statements under section 1001. United States v. Facchini, 874 F.2d 638, 641 (9th Cir. 1989) (en banc). An indictment's failure, however, to allege materiality will not necessarily render the indictment insufficient. Indeed, "[i]t is well settled, at least in this circuit, that an indictment need not allege the materiality of a false representation if the facts advanced by the pleader warrant the inference of materiality." Dear Wing Jung v. United States, 312 F.2d 73, 75 (9th Cir. 1962) (emphasis added); see also United States v. McGough, 510 F.2d 598, 602 (5th Cir. 1975) ("If the facts alleged in the indictment warrant an inference that the false statement is material, the indictment is not fatally insufficient for its failure to allege materiality in haec verba.").

Count two of Oren's indictment clearly met this standard of sufficiency. It does not explicitly mention materiality. It does, however, allege that Oren made a false statement about having an offer for his land in excess of $7.5 million; that this statement was within the jurisdiction of the Park Service, which was considering acquiring the land via TPL; that the Park Service would purchase the land only if it had an appraisal; and that Oren gave his false statement to TPL's appraiser. Surely these allegations "warrant the inference of materiality" of Oren's false statement.

We therefore reject Oren's claim that his indictment was insufficient.

B

Second, Oren argues that the district court erred when it found that Oren's false offer letter was within the Park Service's jurisdiction for purposes of 18 U.S.C. § 1001. Because it determined a question of law, we review de novo this finding of the district court. See United States v. Gonzalez-Mares, 752 F.2d 1485, 1492-93 (9th Cir.), cert. denied, 473 U.S. 913, 105 S.Ct. 3540, 87 L.Ed.2d 663 (1985); United States v. Moreno-Pulido, 695 F.2d 1141, 1143 (9th Cir. 1983). We agree with the district court's determination and reject Oren's argument.

To be a crime under section 1001, a false statement must be made in a "matter within the jurisdiction of a department or agency of the United States." 18 U.S.C. § 1001; see also Facchini, 874 F.2d at 641. For purposes of section 1001, Congress intended that the term "jurisdiction" "should not be given a narrow or technical meaning." United States v. Rodgers, 466 U.S. 475, 480, 104 S.Ct. 1942, 1946, 80 L.Ed.2d 492 (1984) (quotation omitted); see also id. at 484, 104 S.Ct. at 1948. An agency has "jurisdiction" under this statute "when it has the power to exercise authority in a particular situation." Id. at 479, 104 S.Ct. at 1946. "Understood in this way, the phrase `within the jurisdiction' merely differentiates the official, authorized functions of an agency or department from matters peripheral to the business of that body." Id. For this "jurisdiction" element to be satisfied, there is no requirement that the false statement be made directly to the federal agency. Facchini, 874 F.2d at 641. It is, however, necessary under section 1001 that "the false statement involve a matter within federal agency jurisdiction at the time it was made." United States v. Green, 745 F.2d 1205, 1210 (9th Cir.) (emphasis added), cert. denied, 474 U.S. 925, 106 S.Ct. 259, 88 L.Ed.2d 266 (1985).

Oren contends that "the false statement need not be made directly to the government agency if, and only if, there is a pre-existing contractual relationship or regulatory control between the private entity to which the false statement is made and the government agency." Appellant's Opening Brief at 38. For this proposition, he cites United States v. Wolf, 645 F.2d 23, 25 (10th Cir. 1981). Without agreeing that this is an accurate reading of Wolf, we think that the Supreme Court has clearly indicated that "jurisdiction" in section 1001 has a broader meaning than that advanced by Oren. See Rodgers, 466 U.S. at 479, 104 S.Ct. at 1946.

Oren also argues that, at the time he submitted the false offer letter to TPL's second appraiser in the fall of 1984, the matter was not within the Park Service's jurisdiction. We cannot agree.

At the time that Oren made his false statement, the Park Service had the power to acquire his property. The National Park Service is part of the Department of the Interior. 16 U.S.C. § 1 (1988). Its purposes include the regulation and promotion of national parks. Id. At the time of Oren's false statement, the Secretary of the Interior was responsible for managing, through the Park Service, the Santa Monica Mountains National Recreation Area and for acquiring additional land within this Recreation Area. See 16 U.S.C. § 460kk(b), (r) (1982). Congress had authorized the appropriation of funds for such acquisitions. 16 U.S.C. § 460kk(r). Most importantly, Oren's property was within the Recreation Area.

It is thus clear that, when they were made in 1984, Oren's statements concerned a situation in which the Park Service "ha[d] the power to exercise authority." Rodgers, 466 U.S. at 479, 104 S.Ct. at 1946. Moreover, given the statutory scheme detailed above, acquisition of land such as Oren's must be considered an "official, authorized function" of the Park Service and not a "matter peripheral to [its] business." Id. Oren's statement therefore concerned a "matter within the jurisdiction of a department or agency of the United States." 18 U.S.C. § 1001.

Thus, we reject Oren's argument that the district court erred in this context.

C

Oren raises a third challenge relating to his conviction under section 1001. He contends that the district court erred in refusing to instruct the jury that the government must prove that Oren intentionally caused submission of the letter to the Park Service. We review de novo the district court's determination that intentional causation of submission is not required under section 1001. See Moreno-Pulido, 695 F.2d at 1143. We find for two reasons that the district court did not err here.

First, if Oren is correct that the government had to prove that he intentionally caused submission of his false statement to the Park Service, then the government would effectively have to show that Oren actually knew that his statement would be so submitted. Yet section 1001 does not require such actual knowledge. United States v. Yermian, 468 U.S. 63, 74-75, 104 S.Ct. 2936, 2942, 82 L.Ed.2d 53 (1984) (stating that in enacting section 1001 Congress exercised its "power to impose criminal sanctions for deliberately false statements submitted to a federal agency, regardless of whether the person who made such statements actually knew that they were being submitted to the Federal Government") (emphasis added). Oren's argument thus runs afoul of Yermian.

Second, we have earlier held in this context that the government need not prove any jurisdictional knowledge. Green, 745 F.2d at 1209 ("We are persuaded that no mental state is required with respect to federal involvement in order to establish a violation of section 1001."). We note that in this case the district court instructed the jury that it had to find whether it was reasonably foreseeable by Oren that his statement was within the Park Service's jurisdiction. Under Green, this required the government to prove more than was necessary. This could scarcely have harmed Oren.

In short, we reject Oren's argument that the district court erred in refusing to instruct the jury that the government had to prove that Oren intentionally caused submission of the letter to the Park Service.

IV

We last confront Oren's sentence for the two crimes of which he was properly convicted. Oren contends that the district court erred when it refused to allow him to offset the court's restitution order of $272,000 by the value of twenty acres of land which he had offered to the Park Service as a gift. We agree with Oren.

Congress has provided a statutory scheme whereby a federal court, in sentencing a convicted criminal, "may order . . . that the defendant make restitution to any victim of the offense." 18 U.S.C. § 3579(a)(1) (1982). The district court has discretion under this scheme to make such an order. United States v. Kenney, 789 F.2d 783 (9th Cir.), cert. denied, 479 U.S. 990, 107 S.Ct. 586, 93 L.Ed.2d 588 (1986). Its discretion, however, is not unbounded; Congress has specified that, except under circumstances irrelevant here, "the court shall not impose restitution with respect to a loss for which the victim has received or is to receive compensation." 18 U.S.C. § 3579(e)(1).

Restitution having been ordered here, our role is to determine "[w]hether section 3579 authorizes restitution under the circumstances of this case. . . ." United States v. Spinney, 795 F.2d 1410, 1416 (9th Cir. 1986). We conclude that section 3579 authorizes restitution only to the extent that the Park Service's loss exceeds the value of any gift of Oren's land which it accepts.

We are unimpressed by the government's argument that Oren's gift should not be used to offset the restitution ordered because "the gift was not intended as restitution when made." Appellee's Brief at 44. Oren's intention at the time he offered the gift is irrelevant; rather, the crucial inquiry is whether, if accepted, the gift would result in the Park Service's having received compensation for its loss. See 18 U.S.C. § 3579(e)(1). The gift clearly would result in at least partial compensation; in fact, to judge by the district court's comments at sentencing, the land that Oren seeks to give would more than compensate the Park Service for any loss intended to be satisfied by the restitution order. Compare Reporter's Transcript, Sept. 14, 1987 at 42 (court noted that, depending on estimates believed, land Oren offered was worth somewhere from $350,000 to $460,000) with id. at 64 (court fixed restitution "in the sum of $272,000" plus interest). The government fails to understand that in determining whether a victim has been compensated for its loss, one looks to what the victim has received, not to what the giver has intended. Oren's subjective intention cannot alter the pertinent economic fact.

Equally unpersuasive is the government's contention that, by ordering restitution offset by the value of any land offered to and accepted by the Park Service, we permit Oren to determine the form of compensation. Oren determines nothing here; the Park Service determines whether or not to accept the gift. If it does accept the land, the Park Service receives restitution to the extent that the gift has compensated it for its loss; otherwise, section 3579(e)(1) would be violated. If the Service does not accept the land or if he withdraws his offer, Oren must pay restitution in the amount previously ordered by the court.

In short, the restitution portion of the sentence is vacated and this case remanded to the district court for redetermination of restitution consistent with this opinion; the remainder of Oren's sentence is affirmed.

AFFIRMED IN PART AND VACATED IN PART.