On July 2, 1986, defendant-appellant Ralph A. Eckhardt, a promoter of tax shelters, was charged under a ten-count indictment with wire fraud, 18 U.S.C. § 1343, mail fraud, 18 U.S.C. § 1341, perjury, 18 U.S.C. § 1621, and submitting false statements to the government, 18 U.S.C. § 1001. Eckhardt initially pled not guilty and sought to dismiss the indictment on the grounds that (1) the indictment was time-barred, (2) the delay in bringing the criminal charges against him violated his due process rights under the fifth amendment, and (3) he had been granted “equitable immunity” from prosecution. The district court rejected all three arguments and denied his motion to dismiss.

On March 2, 1987, Eckhardt pled guilty to four counts of the indictment ^[1] pursuant to a written conditional plea agreement. Under the plea agreement, Eckhardt reserved the right to appeal from the trial court’s order denying his earlier motion to dismiss the indictment. He now appeals from that order of the district court, raising the same three arguments on appeal. Eckhardt also raises the argument for the first time on appeal ^[2] that the indictment does not state a cognizable charge of wire-fraud under the standard announced by the Supreme Court in McNally v. United States, — U.S. -, 107 S.Ct. 2875, 97 L.Ed.2d 292 (1987). We affirm the judgment of the district court and find further that Count I of the indictment does sufficiently allege the offense of wire fraud under McNally.

I. Background

Many tax shelter schemes perpetrate a fraud on the government by inducing tax[*992] payer-investors to claim tax deductions to which they are not legitimately entitled. The tax shelters promoted by Ralph Eck-hardt, however, perpetrated an additional fraud on the taxpayer-investors themselves. Eckhardt represented to taxpayer-investors that they could obtain favorable tax treatment by investing in breeding cattle herds which he would purchase and manage on their behalf. The taxpayer-investor was required to make only a small, or in some cases no, down payment. According to Eckhardt, the balance of the investment would be financed by loans taken out in the names of the investors and secured by the herds of cattle. The taxpayer-investor was also required during the first two years to pay Eckhardt an annual maintenance fee for managing the herd. Taxpayer-investors were told that they could deduct the business expenses and depreciation associated with the cattle-breeding operation on their tax returns.

Eckhardt did, in fact, take out loans in the names of the investors, but the proceeds of these loans were not used to purchase cattle; they were used to purchase certificates of deposit in Eckhardt’s name. The loans, in turn, were secured by the certificates of deposit, not by cattle. Eck-hardt perpetuated his fraud by sending investors false annual “Income and Expense Statements” purporting to represent the financial status of the taxpayers’ investment in the herds of cattle. The taxpayer-investors thereafter filed a series of false federal income tax returns on the basis of the information provided by Eckhardt in these statements.

Eckhardt’s fraud was discovered in the course of an Internal Revenue Service (“IRS”) investigation of two of the taxpayer-investors, Dr. Morton Rosen and Dr. Robert Wheeler. In December 1979, the IRS disallowed farm losses and investment credits claimed by Drs. Rosen and Wheeler on their 1975, 1976, and 1977 income tax returns. Drs. Rosen and Wheeler then petitioned the United States Tax Court challenging the IRS disallowance.

On August 2, 1982, Eckhardt was subpoenaed in the Rosen and Wheeler Tax Court proceedings to produce documents and appear for a deposition regarding the tax shelter investment program. Prior to the taking of his deposition, Eckhardt agreed to meet with Rosen and Wheeler’s attorney, Alan Segal, and with IRS staff attorneys Stephen Morrow and David Baier on August 24, 1982 in State Center, Iowa to show them the cattle Eckhardt had allegedly purchased for Drs. Rosen and Wheeler.

Eckhardt then sought to purchase cattle for delivery in time for his meeting with the attorneys. He arranged for one herd of cattle to be delivered on or about August 11, 1982. On or about August 20, 1982, Eckhardt placed a collect telephone call from State Center, Iowa to Attorney Segal in Chicago and rescheduled their cattle-viewing visit for August 31, 1982, so that he would have an opportunity to purchase a second herd of cattle prior to their meeting. About the same time, he mailed a letter to Drs. Rosen and Wheeler informing them that the meeting had been postponed. He then ordered a second herd of cattle which was delivered on August 27, 1982. At the cattle viewing on August 31, Eckhardt told Attorneys Morrow and Segal that the cattle on the farm were the herds of cattle he had purchased for Drs. Rosen and Wheeler in 1974, 1975, and 1976.

Eckhardt was deposed on September 21, 1982. During that deposition, Eckhardt made the following false statements: (1) that the cattle shown to the attorneys on August 31, 1982 were the property of Drs. Wheeler and Rosen and that the cattle had been moved from two separate pastures which Eckhardt was renting, (2) that the records he provided to Drs. Wheeler and Rosen represented accurate inventories of their respective herds of cattle, (3) that monies borrowed in Dr. Rosen’s name from Decatur County State Bank in 1975 and 1976 were applied as a down payment on herds allegedly purchased for Dr. Rosen in 1974 and 1976, (4) that a representative of the Decatur County State Bank had been sent to count the number of cattle because the loan was partially secured by the herd, and (5) that the proceeds of Dr. Rosen’s loan were paid to American Land and Cat-[*993] tie Industries, one of the companies Eck-hardt allegedly used to purchase cattle. In fact, there were no herds of cattle purchased on behalf of Dr. Rosen and the proceeds of the Decatur County State Bank loan were used to purchase certificates of deposit in Eckhardt’s name.

On September 27, 1982, Eckhardt submitted false documents to the IRS, entitled “Wheeler Tally Sheets” and “Rosen Tally Sheets,” which purported to be accountings for cattle purchases and sales made on behalf of Drs. Wheeler and Rosen.

On November 19, 1982, Eckhardt testified before the Tax Court in the Wheeler and Rosen proceedings. Eckhardt falsely testified before the court that the loan from Decatur County State Bank was used to purchase cattle for Dr. Rosen’s 1974 and 1976 herds.

In December 1982, IRS Attorney Morrow learned that the cattle he had viewed on August 31, 1982 had been purchased by Eckhardt on August 11 and August 25, 1982, and that the cattle had been repossessed from Eckhardt on October 1, 1982. A criminal investigation of Eckhardt was then initiated and an indictment was returned on July 2, 1986 charging him with wire and mail fraud, perjury, and submitting false statements to the government. Eckhardt sought to have the indictment dismissed, and the district court denied Eckhardt’s motion on November 12, 1986.

Subsequently, in his conditional plea agreement, Eckhardt pled guilty to counts one, three, five and six of the indictment. Under count one, which charged him with wire fraud, Eckhardt admitted to misappropriating loans obtained in the names of his tax scheme investors to purchase certificates of deposit for himself. He also admitted to mailing false “statements of income and expenses” to his investors, and to furthering his tax scheme by calling Rosen and Wheeler’s attorney to postpone the showing of cattle. Under count three, Eck-hardt pled guilty to committing perjury during his deposition, which was taken for Rosen and Wheeler’s Tax Court proceedings. Under count five, Eckhardt admitted that to further his scheme he submitted material false documents to the IRS. These documents, entitled the “Wheeler Tally Sheets” and the “Rosen Tally Sheets,” were later submitted to the Tax Court. Finally, under count six, Eckhardt pled guilty to perjury for falsely testifying in the Tax Court proceedings that he used the loans to purchase cattle.

II. Discussion

A. Statute of Limitations

The first ground upon which Eckhardt sought to dismiss the indictment in the district court was that the indictment returned on July 2, 1986 was time-barred. Eckhardt argues that the applicable five-year limitations period for non-capital offenses, see 18 U.S.C. § 3282, began to run from the date the underlying cattle tax shelter scheme was “completed.” According to Eckhardt, the scheme was completed no later than 1979, when the last “purchase of cattle” by the taxpayer-investors from the defendant was effected. Thus, he claims that all charges arising out of this scheme do not fall within the period prescribed by the statute.

We reject Eckhardt’s construction of the statute of limitations. First, it is well-settled that the statute of limitations for wire fraud and mail fraud does not begin running with the completion of the fraud scheme; rather, it runs from the date of the charged call or mailing in furtherance of the scheme. See United States v. Read, 658 F.2d 1225, 1240 (7th Cir.1981); Fournier v. United States, 58 F.2d 3, 6 (7th Cir.1932). It is therefore irrelevant when the fraud scheme itself ended, so long as the charged call or mailing took place within the statutory period.

The telephone call charged in Eckhardt’s indictment was the call he made to Attorney Segal on August 20, 1982 postponing the cattle-viewing meeting. The charged mailing was the mailing of letters to Drs. Rosen and Wheeler on August 21, 1982. Thus, the statute of limitations with respect to the telephone call did not run until August 20,1987, and did not run with respect to the mailing until August 21,[*994] 1987 — more than one year after the indictment was returned.

Eckhardt attempts to circumvent the rule which applies the limitations period from the date of the call or mailing by arguing that the charged call and mailing were not in furtherance of the underlying fraud scheme. Because, in his view, the scheme was completed no later than 1979, Eck-hardt argues that any call or mailing occurring after that date could not have been in furtherance of the scheme.

As the government points out, this is not merely a limitations challenge, but a challenge to the sufficiency of the indictment. Eckhardt is essentially arguing that the indictment fails to allege sufficiently an essential element of the offenses of wire fraud and mail fraud — that the use of the wires or mail was “for the purpose of executing” the underlying fraud scheme. See 18 U.S.C. §§ 1341 and 1343.

We find Eckhardt’s argument without merit. The indictment plainly alleges that the call and mailing were made “for the purpose of executing” an underlying fraud scheme. Moreover, the fact that Eckhardt had already obtained the taxpayer-investors’ money at the time he made the telephone call and mailing is not fatal. The Supreme Court and this Circuit have held that even mailings and calls which occur after the defendant has obtained the victims’ money are in furtherance of the scheme if they facilitate concealment or postpone investigation of the scheme. See United States v. Lane, 474 U.S. 438, 106 S.Ct. 725, 88 L.Ed.2d 814 (1986); United States v. Sampson, 371 U.S. 75, 83 S.Ct. 173, 9 L.Ed.2d 136 (1962); United States v. Rauhoff, 525 F.2d 1170, 1176 (7th Cir.1975); SEC v. Holschuh, 694 F.2d 130, 143-44 & n. 24 (7th Cir.1982) (quoting United States v. Reidel, 126 F.2d 81, 83 (7th Cir.1942)).

The charges of perjury and making false statements were wholly independent of the underlying fraud scheme, such that the limitations period began to run on the dates that those charged crimes occurred. Toussie v. United States, 397 U.S. 112, 115, 90 S.Ct. 858, 860, 25 L.Ed.2d 156 (1970). Thus, the date that the scheme was completed is irrelevant for purposes of limitations analysis.

Counts three and six of the indictment charge Eckhardt with committing perjury on September 21, 1982 and November 19, 1982, respectively. Counts five, nine, and ten charge Eckhardt with submitting false statements to the government on September 27, 1982 and September 7, 1984. Accordingly, the peijury and false statement counts were also timely filed.

The district court properly found that each count of the indictment charged Eck-hardt with unlawful conduct committed within the five-year period preceding July 2, 1986, the date the indictment was returned.

B. Pre-Indictment Delay

The second ground on which Eckhardt challenged his indictment in the district court, as well as on appeal, is that the delay between the government’s learning of his involvement in the tax shelter and the date of his indictment violated his due process rights under the fifth amendment.

We agree with the district court that this claim must fail in light of Eckhardt’s failure to sustain his burden of proving actual prejudice resulting from the delay. A pre-indictment delay does not rise to the level of a due process violation unless the delay causes actual and substantial prejudice to the defendant’s fair trial rights. See United States v. Perry, 815 F.2d 1100, 1103 (7th Cir.1987); United States v. Watkins, 709 F.2d 475, 479 (7th Cir.1983). It is the defendant’s burden to prove that he was prejudiced by the delay. See United States v. Williams, 738 F.2d 172, 175 (7th Cir.1984).

Eckhardt alleges first that he was prejudiced by the mere passage of time. This argument is based on the premise that the period of delay amounted to nine years. In Eckhardt’s view, the delay commenced in 1977 when “the government either knew or should have known of defendant’s involvement in the cattle tax shelter.” The government argues conversely that the pe[*995] riod of delay totaled less than four years, beginning in December 1982 when the government first learned that the tax shelter scheme was a fraud, i.e., that there was no tax shelter and that defendant had not purchased or managed any cattle for Drs. Rosen and Wheeler. Regardless of the length of the delay, Eckhardt still bears the burden of proving that the delay prejudiced him. “The mere passage of time is not enough” to constitute substantial prejudice. Perry, 815 F.2d at 1103.

Eckhardt also alleges that he was prejudiced by the delay because his accountant, Edward Krochmal, was unavailable to testify on his behalf. Krochmal apparently died sometime before July 2, 1986, although Eckhardt does not state exactly when. Eckhardt states only that Krochmal was familiar with defendant’s tax shelter program and that “his testimony would have been probative.” The defendant does not specifically describe the substance of Krochmal’s testimony nor does he indicate how Krochmal’s testimony would have advanced his defense. He also does not show that Krochmal would have been available if the indictment had been returned sooner.

The death of a witness alone is not sufficient to establish prejudice. See United States v. Lovasco, 431 U.S. 783, 789, 97 S.Ct. 2044, 2048, 52 L.Ed.2d 752 (1977); United States v. Solomon, 688 F.2d 1171, 1179 (7th Cir.1982). See also United States v. Hollins, 811 F.2d 384, 387-88 (7th Cir.1987). Where, as here, the defendant has failed to explain the substance and relevance of the witness’ testimony, the court cannot reach a finding of actual and substantial prejudice. See Williams, 738 F.2d at 175; United States v. Antonino, 830 F.2d 798, 804-05 (7th Cir.1987) (noting , that the showing of actual prejudice must be “concrete, not speculative”).

Eckhardt’s final argument is that he was prejudiced by pre-indictment delay because he would have invoked his fifth amendment privilege against self-incrimination in the Tax Court proceedings if criminal charges had been made against him at that time. We dismiss this argument as speculative and note that Eckhardt was represented by competent counsel in the Tax Court and was free to exercise his fifth amendment privilege if he chose to, even in the absence of criminal charges against him.

Because defendant has failed to meet his burden of showing that the alleged pre-in-dictment delay caused him actual and substantial prejudice, his claim under the fifth amendment is without merit. We must defer to the government’s prosecutorial decision in the absence of such a showing. See Perry, 815 F.2d at 1104-05.

C. Equitable Immunity

The final ground raised by Eckhardt in support of his motion to dismiss the indictment in the trial court was that he was entitled to rely on a grant of “equitable immunity” in testifying before the Tax Court. Eckhardt points to a statement made by IRS counsel Morrow in the Tax Court agreeing with Eckhardt’s counsel that no investigation of Eckhardt was “in the works” or planned for the future. He further points to the Tax Court’s statement that “any testimony given here will be strictly for the purpose of this case and not for any other purpose.” These statements taken together, he argues, constitute a grant of “equitable immunity from prosecution.”

This circuit has neither accepted nor rejected the doctrine of equitable immunity. We need not decide here, however, whether to adopt the doctrine and to apply it in Eckhardt’s case. At the time that he testified in the Tax Court, Eckhardt had already testified as to the same matters in deposition without any grant of immunity. He testified in his deposition, as well as in the Tax Court, that the loan obtained from Decatur County State Bank in Dr. Rosen’s name was used to purchase cattle on behalf of Dr. Rosen. The government was therefore free to use this testimony in pursuing its investigation and indictment of Eckhardt.

We also note that the only charge in the indictment directly based on Eckhardt’s testimony in the Tax Court was the perjury charge. Even a grant of immunity will not preclude the use of defendant’s testimony[*996] in a subsequent prosecution for perjury. See United States v. Apfelbaum, 445 U.S. 115, 131, 100 S.Ct. 948, 957, 63 L.Ed.2d 250 (1980); United States v. Watkins, 505 F.2d 545 (7th Cir.1974).

We therefore affirm the district court’s finding that Eckhardt is not entitled to rely on equitable immunity.

D. Sufficiency of Wire Fraud Charge Under McNally

Eckhardt raises for the first time on appeal the argument that the wire fraud count of the indictment was legally insufficient under the rule recently announced by the Supreme Court in McNally v. United States, — U.S. -, 107 S.Ct. 2875, 97 L.Ed.2d 292 (1987), and applied by this court in United States v. Gimbel, 830 F.2d 621 (7th Cir.1987). ^[3]

In McNally, the Supreme Court held that the mail fraud statute is “limited in scope to the protection of property rights,” and that it does not proscribe schemes to defraud individuals or entities of intangible rights. — U.S. at -, 107 S.Ct. at 2881. Thus a proper charge under the mail fraud statute must allege that the defendant used the mails in furtherance of a scheme to deprive an individual or entity of money or property.

This court first applied the McNally rule in Gimbel and found that a scheme which concealed information from the Treasury Department did not deprive the Department of “money or property,” even though the Department might have assessed a tax deficiency had the information been disclosed. 830 F.2d at 627. We therefore concluded that an indictment for mail fraud based on such a scheme did not state an offense under the mail fraud statute. Id. We also held that the McNally standard applied to prosecutions under the wire fraud statute and struck down an indictment for wire fraud based on the same underlying scheme. Id.

In the instant case, Eckhardt argues that Count I of the indictment does not state an offense for wire fraud because it does not allege that the telephone call made by Eck-hardt to postpone the cattle-viewing defrauded the government of money or property.

The indictment charges that Eckhardt devised a fraud scheme with the following objectives:

A. To defraud the United States by impeding and impairing, obstructing and defeating the lawful functions of the Internal Revenue Service in the ascertainment computation, assessment and collection of the revenue, to wit, income taxes, of taxpayer-investors in American Land and Cattle Industries, Triple E. Cattle Co. and Iowa Cattle Co.;

B. To defraud the United States Tax Court of its right to conduct its proceedings free of trickery, deceit, false documents, perjury and fraud;

C. To defraud the taxpayer-investors in American Land and Cattle Industries, Triple E. Cattle Co. and Iowa Cattle Co. of their right to truthful representations and reports from their agent, RALPH A. ECKHARDT, with respect to any inventory, expenses, depreciation, income and loans relating to their investments in cattle breeding herds purchased from the Cattle Companies of defendant RALPH A. ECKHARDT, for use in support of claimed adjustments on the income tax returns of the taxpayer-investors to be filed with the Internal Revenue Service; and

D. To obtain money and property by false and fraudulent representations and pretenses, well knowing said representations and pretenses were false when made.

We find that although three objectives of the fraud scheme alleged in Count I of the indictment are insufficient to state a claim for wire fraud under McNally, the fourth objective does include the requisite element —a scheme to defraud an individual or entity of money or property.

Paragraph A charges Eckhardt simply with interfering with the IRS’s proper[*997] ascertainment and collection of income taxes. It does not specifically allege that he deprived the government of revenue. As we noted in Gimbel, it is not sufficient to allege conduct which could have resulted in the government’s failure to collect revenue owed to it. 830 F.2d at 627. The connection between the charged conduct and the loss of revenue here is too tenuous and speculative to constitute an actual deprivation of money or property.

Paragraph B charges Eckhardt with defrauding the United States Tax Court of its right to conduct its proceedings free of fraud. This is clearly an “intangible right,” the deprivation of which is insufficient to constitute an offense under McNally.

Under Paragraph C, Eckhardt is charged with defrauding taxpayer-investors “of their right to truthful representations and reports.” Again, the object of the fraud alleged here is a deprivation of intangible rights.

Paragraph D, however, satisfies the McNally standard by alleging that a fourth object of Eckhardt’s scheme was to “obtain money and property by false and fraudulent representations.” Although Paragraph D does not specify from whom Eckhardt sought to obtain money and property, the allegation logically refers to Eckhardt’s appropriation of the taxpayer-investors’ down payments and loan proceeds by means of false representations that he would purchase and maintain cattle on their behalf. The failure of the indictment to allege an underlying scheme to defraud the government of money or property is not fatal because it does allege a scheme to defraud the investors of money or property.

Where a fraud scheme involves multiple objectives, some of which are insufficient to state an offense under McNally, the remaining charge or charges will be deemed sufficient to state the offense if they are “easily separable” from the charges deemed insufficient. See United States v. Cooke, 833 F.2d 109 (7th Cir.1987). In such a case, those allegations which are insufficient to state an offense are mere surplusage, and do not taint the remainder of the indictment. See United States v. Miller, 471 U.S. 130, 136-37, 105 S.Ct. 1811, 85 L.Ed.2d 99 (1985); Cooke, 833 F.2d at 110.

We find that Eckhardt’s scheme to defraud investors of their tangible property rights by converting the proceeds of their loans into personal certificates of deposit is “easily separable” from the scheme to deprive the government of its intangible rights to compute income taxes without obstruction, and to conduct court proceedings free from fraud and perjury. Count I of the indictment therefore is sufficient to state an offense under the wire fraud statute on the basis of Paragraph 9D alone. ^[4]

We have determined that the sole charge in Count I which survives defendant’s McNally challenge is the charge that Eck-hardt used the wires for the purpose of executing a fraud, the object of which was to deprive investors of their money and property. We must now look at the specific admissions made by Eckhardt in his plea agreement to determine whether he, in fact, confessed to conduct which is consistent with the portion of the indictment deemed sufficient under McNally.

Paragraph 8(d) of the plea agreement signed by Eckhardt states that Eckhardt used the proceeds of loans taken out in the names of Drs. Wheeler and Rosen to purchase certificates of deposit in his own name rather than to purchase cattle, as he had represented to the investors. This conduct is consistent with the charge that Eckhardt deprived the investors of money and property by means of false representations.

Paragraph 8(i) of the plea agreement states that Eckhardt placed a collect call to Attorney Segal on August 20, 1982 to postpone the cattle-viewing meeting until August 31, 1982, when both herds of newly-purchased cattle would be available for showing, and that this telephone call was[*998] “in furtherance of the scheme.” This conduct is consistent with the charge that Eck-hardt used the wires for purposes of executing his scheme to defraud the investors of money and property.

We are therefore satisfied that Eckhardt has pled guilty to a charge of wire fraud which is sufficient under the McNally standard.

III. Conclusion

The district court properly found that Eckhardt’s indictment was not time-barred, that his due process rights were not violated by any delay in bringing the indictment, and that he was not granted equitable immunity from prosecution at the time he testified in the Tax Court. Moreover, we find that Count I of the indictment states a cognizable charge of wire fraud under McNally. Accordingly, the judgment of the district court is

Affirmed.