Defendants-appellants Fruehauf Corporation, William E. Grace, and Robert Rowan were indicted for conspiring, in violation of 18 U.S.C. § 371, to defraud the United States by obstructing the lawful governmental functions of the Internal Revenue Service, to attempt to have appellant Frue-hauf Corporation evade illegally the payment of federal excise taxes, and to aid or assist in the preparation and presentation of materially false and fraudulent excise tax returns for the appellant Fruehauf. Following a lengthy trial without a jury, the district judge, found that appellants were guilty as charged. Appellant Frue-hauf Corporation was sentenced to pay a $10,000 fine. Appellants Grace and Rowan were each sentenced to serve a prison term of six months and one day (the one day was suspended), followed by a two year period of unsupervised probation, and to pay a $10,000 fine. Appellants perfected this appeal. We affirm.
I
District Judge Thomas P. Thornton entered 142 findings of fact in his opinion 1 to support his conclusion that appellants were guilty as charged of having engaged in a conspiracy in violation of 18 U.S.C. § 371.2 After examining the voluminous record in this case, we conclude that Judge Thornton’s findings of fact were supported by substantial evidence and were not clearly erroneous.3 The following statement of *1042facts is based on the findings made by Judge Thornton.
The Indictment: The Parties and the Excise Tax Provisions Involved
The corporation indicted in the present case, appellant Fruehauf, is a very large and well-known manufacturer of trailers. Appellants Grace and Rowan were top executives of the Fruehauf Corporation. During the period of the alleged conspiracy, appellant Grace served as vice-president (1955-57), executive vice-president (1957-58), president (1958-65), and chief executive officer (1959-65), and appellant Rowan held the positions of controller (1955-64), vice-president (1962-64), and vice-president, finance (1964-65).
Named in the indictment along with appellant Fruehauf Corporation and appellant-executives Grace and Rowan were two other Fruehauf executives, unindicted co-conspirators Kenneth A. Morris and Robert M. Chawner. From 1951 through 1965, Morris was the manager of appellant Fruehauf’s Tax Department. In that position, Morris was responsible to appellant Rowan for the correct reporting of appellant Fruehauf’s taxes. From 1955 to 1964, Chawner was appellant Fruehauf’s assistant controller, and from 1962 to 1964, he was the controller of the Fruehauf Division of the appellant Fruehauf Corporation.
Section 4061 of the Internal Revenue Code of 1954, 26 U.S.C. § 4061, imposes a tax on the sale of motor vehicles and parts (including trailers) by the manufacturer.4 The tax is computed by applying the tax rate established in § 4061 to the motor vehicle or part “price.” That “price” is defined in § 4216(a) of the Internal Revenue Code of 1954, 26 U.S.C. § 4216(a), as the price for which the article is sold;-5 how*1043ever, § 4216(b), as amended effective January 1, 1959, provides for a constructive sales price that enables a manufacturer which sells at both retail and wholesale to compute the excise tax on all sales based upon the highest price for which the motor vehicle or part is sold at wholesale.6
Appellant Fruehauf Corporation sold 94% of its trailers at retail and the remaining 6% at wholesale. By virtue of § 4216(b) and of a private ruling obtained by appellant Frue-hauf in 1949, appellant Fruehauf used its wholesale price as the base for excise tax computations on all sales.7 Just prior to the beginning of the conspiracy, in December, 1956, distributors of appellant Fruehauf Corporation paid 61.75% of the list price for the trailers, a discount of 38.25%.
Section 6416(c) of the Internal Revenue Code of 1954, 26 U.S.C. § 6416(c), provides for tax credits that reduce the excise tax liability of a manufacturer.8 A tax credit is given when a finished taxable article sold by the manufacturer includes parts that have previously been subjected to a separate excise tax. Hence, excise tax credits are given when trailers are sold with tires upon which an excise tax, in this case imposed by § 4071 of the Internal Revenue Code of 1954, 26 U.S.C. § 4071, has been previously levied. Appellant Fruehauf Corporation took such credits on the tires that were placed on their trailers.
Appellant Fruehauf Corporation could thus reduce its excise tax liability by (1) reducing the price at which the trailers were sold at wholesale to distributors and (2) increasing the price paid for tires that were to equip the trailers. If, however, Fruehauf Corporation were to cut its excise *1044tax liability simply by reducing its wholesale trailer prices and increasing the prices paid for tires, the net income total would be reduced more by the decreased gross income and increased tire expense than increased by the excise tax savings.
The indictment in the present case, brought November 9, 1970, alleged that appellants conspired to obtain by two fraudulent schemes the best of two worlds, excise tax savings and income unaffected by reduced wholesale trailer prices and increased tire payments. The first scheme, which involved a supplemental billing plan, sought to reduce the excise tax base without reducing gross income. The second scheme was directed at generating excessive excise tax credits by computing the tire tax credit on invoice prices without adjustment for rebates. As overt acts charged to have been committed to further the conspiracy, the indictment alleged the filing of quarterly manufacturers excise tax returns for 37 consecutive quarters, beginning in the final quarter of 1956 and extending through the last quarter of 1965, returns which understated the excise tax liability of appellant Fruehauf Corporation in the amount of $12,344,587.31.
The Supplemental Billings Scheme
1. The Meeting in Washington, D.C.: Approval of the Supplemental Billing System.
On December 13, 1956, appellant Rowan and co-conspirator Morris met with appellant Fruehauf’s Washington, D.C. counsel, Raymond Cushwa, of the law firm of Davies, Richberg, Tydings & Landa, and with W. K. Engel, of the accounting firm of Touche, Niven, Bailey & Smart. The purpose of the meeting was to obtain Cushwa’s and Engel’s approval of a “supplemental charge plan” that had originally been drafted by co-conspirator Chawner. The supplemental charge plan would break out of the price of a trailer charges for certain “extra” services allegedly rendered to appellant Fruehauf’s distributors and would bill for those services separately. At the same time, the discount to distributors would be increased, and by lowering the wholesale price of the trailer, appellant Fruehauf’s excise tax liability would also be reduced because the excise tax base for both retail and wholesale sales was computed on the wholesale price.
Engel, in an inter-office memorandum written five days after the meeting, summarized the proposal presented on behalf of appellant Fruehauf by appellant Rowan and co-conspirator Morris.
Fruehauf performs certain services for its wholesale customers which it does not perform for its retail customers. In the past the charges for these extras has been included in the invoice price to distributors and consequently in the excise tax base. Fruehauf has concluded that the charges for these extra services should be made separately and not included in the invoice price of the trailers in order to make the invoice price of trailers to distributors comparable to that to retailers. It is anticipated that the extra charges to be billed separately to distributors would approximate the $260 reduction in selling price due to the proposed additional discount so that the total received per trailer from distributors would be what it is at present. The advantage would be in obtaining a lower wholesale base on which excise tax would have to be paid and thus a saving in excise tax of about $26 per trailer on both wholesale and retail sales.
The extra charges to distributors which Fruehauf has proposed are as follows:
EXPENSE EXPENSE
PER
BASIS FOR CHARGE UNIT
Advertising National advertising
charge — total units sold $ 34.00
General sales Executive sales expense
expense per unit sold 58.00
Interest 4% of average balance of equipment accounts receivable which are at present carried by Fruehauf until units are sold by dis-
tributors 164.00
Sales engi-Estimated 5.00
neering
*1045EXPENSE EXPENSE
PER BASIS FOR CHARGE UNIT
Sales man- Estimated 2.00 uals, technical bulletins, etc.
Legal and ac- Estimated 5.00 counting services _
$268.00
(Government Exhibit 16).
Cushwa and Engel approved this proposal, stating to appellant Rowan and co-conspirator Morris that it was generally in accord with the law governing manufacturers excise tax, but conditioned their approval on the observance of certain procedures. First, it would be necessary to be able to demonstrate that a particular distributor actually received the service for which the distributor was charged. Second, the proposed charges would need to be based upon the cost of the services performed; the amounts charged in a specific case had to equal or be less than the value of the services actually performed. Third, records would have to be maintained showing the services rendered for each distributor and for each of the categories of supplemental fees charged. Cushwa and Engel told appellant Rowan and co-conspirator Morris that a flat charge to a distributor for some service never received, even though billed separately, was part of the selling price of the trailer and would have to be included in the excise tax base. Appellant Rowan and co-conspirator Morris were thus put on notice that appellant Fruehauf’s counsel approved the supplemental charge plan on the conditions that records would be maintained which would demonstrate that the supplemental charges were for extra services actually performed and that the value of the services rendered equalled or exceeded the amounts charged.9
2. Implementation and Control of the Supplemental Billing System.
Following the December 13, 1956, meeting in Washington, D.C., appellant Rowan personally called all of appellant Fruehauf’s distributors in order to inform them about the implementation of the supplemental charge plan. The plan increased the discount to distributors to 42% off the list price. Along with this increased discount, however, the distributors received from appellant Fruehauf supplemental billings for amounts designated on the special invoices as “advertising,” “management consulting fees,” and “interest.”
These monthly supplemental charges to distributors were posted as credit entries to Fruehauf’s advertising, general administrative, and interest earned accounts. Distributors were advised by appellant Fruehauf that the supplemental charges should be *1046posted on the distributors’ books as selling or administrative expenses and not as part of the trailer costs so that appellant Frue-hauf’s billing system would not be misinterpreted by the Internal Revenue Service. As an additional precaution, the invoices for the supplemental charges were mailed to distributors in envelopes marked “personal and confidential.” Co-conspirator Chawner told F. S. Newman, manager of appellant Fruehauf’s Sales Department, that the supplemental billing practice should be kept on a confidential basis so that appellant Frue-hauf’s tax position would not be endangered.
This concern was legitimate. The supplemental charge plan as implemented was designed so that the total of the supplemental billings to each distributor equalled the 3.75% increase in the discount extended to distributors at the time of the institution of the supplemental charge plan.10
Appellant Fruehauf’s home office billing department monitored the supplemental charge plan by means of “Distributor Analysis of Price Adjustment” work sheets, which were used to reconcile the supplemental billing figures against the increase in the discount to the distributors. A running account of the amounts by which total supplemental billings exceeded or fell short of the increase in discount was kept by means of a credit or debit entry under a column entitled “Adjustment Due Customer.” Appellant Fruehauf kept distributors informed as to the status of this running account in monthly “Status of Excise Tax Savings” reports.
Moreover, it was impossible for a distributor to avoid full payment of the supplemental charges. Trailer sales to distributors were made on open account with thirty or ninety day terms. The monthly supplemental charge for interest was computed at the rate of 4%% per annum on the month-end balance of each distributor’s open receivables account. No adjustment was made if payment was received by Fruehauf within the thirty or ninety day terms of the trailer invoices. The monthly supplemental charge for advertising and management consulting were computed by subtracting the interest charge from the “net selling price adjustment” (which was 3.75% of the list price when the additional discount given to the distributors was 3.75% of the list price) and then allocating the remainder to advertising and management consulting. If, however, a distributor would return a trailer to appellant Fruehauf Corporation, the supplemental billings were proportionately cancelled; if there were no trailer sales to a distributor, there were no supplemental billings. Appellant Fruehauf Corporation could thus receive roughly the same payment from distributors as they would have without the supplemental billings plan, but had a lowered wholesale price as its excise tax base, which meant reduced excise taxes on the trailers sold to all customers.
3. Amounts in the Supplemental Billings Increase.
Despite the fact that the supplemental billing system had been approved by counsel only on the conditions that records be maintained to show that the supplemental charges were for actual services rendered and that the value of the services equalled or exceeded the amounts charged, by July, 1957, only nine months after the effective *1047date of the supplemental charge plan,11 the charges for advertising and management consulting fees had risen to amounts vastly in excess of the amounts that appellant Rowan and co-conspirator Morris had represented to the attorney Cushwa as the proper charges for the extra services allegedly rendered to the distributors. In 1957, the distributor Motor Truck Equipment Company was charged $147.34 per unit for advertising, an increase from $34 in December, 1956. In November, 1957, Berman Sales Company was charged $124.91 per unit for advertising, also increased from $34 in December, 1956.12
Because the charges for advertising, management consulting, and interest were vastly overstated, appellant Fruehauf’s budget was being distorted. This distortion was rectified in August, 1957, when the supplemental charges were taken out of the expense and income account postings and thereafter posted as reductions to the cost account applicable to new trailers.
In July, 1958, an internal Fruehauf study was made, which demonstrated that the average supplemental charges to each distributor under the categories “advertising” and “management consulting” were in excess of the amounts conditionally approved by the attorney Cushwa at the December, 1956, meeting in Washington, D.C. Consequently, in the autumn of 1958, co-conspirator Morris expressed concern to appellant Rowan that the records maintained by appellant Fruehauf Corporation were not sufficient to substantiate the supplemental charges for services being rendered to distributors. Nevertheless, appellant Rowan, who was responsible for appellant Frue-hauf’s record keeping, did not cause Frue-hauf Corporation to maintain records to demonstrate that a certain distributor actually had received the service for which it was charged or that the value of the service in a specific case equalled or exceeded the amounts charged.
It was during this initial period of swelling supplemental charges that appellant Grace became aware of and educated himself about the supplemental billing system. In fact, in a letter dated October 11, 1957, to Christopher Hammond, President of Great Dane Trailers, appellant Grace boasted “The excise tax problem is one which I believe no one has gone into any deeper and come up with more ways to save money than yours truly.” Also in 1960, appellant Grace was aware of a Fruehauf memorandum titled “The Excise Tax Story,” which described the supplemental billing procedures and indicated that Fruehauf had saved $921,324 in excise taxes in 1959 as a result of the supplemental charge plan.
4. Treasury Regulation 330.1-l(b) and Appellant Fruehauf’s Response.
On December 16,1958, the Internal Revenue Service published in the Federal Register, Treasury Regulations on Manufacturers Excise Tax. T.D. 6340, 1959-1 Cum.Bul. 694, Regulation 330.1-l(b) provided:
Any charge which is required by a manufacturer, producer, or importer to be paid as a condition of sale of a taxable article and which is not attributable to an expense falling within one of the exclusions provided in Section 3441(a), is includible in the sale price upon which the tax is based. It is immaterial for this purpose that the charge may be paid to someone other than the manufacturer, producer, or importer, or that it may be separately billed to the purchaser as one earmarked for expenses incurred or to be incurred in his behalf, as for example, for advertising at the national or local level, for a demonstration or display of the article, for a sales promotion program, or otherwise. *1048As a result of the promulgation of this regulation, appellant Fruehauf did not eliminate its supplemental billing for advertising and include that cost in the wholesale price. Rather, appellant Fruehauf changed in its supplemental charges the billing designation “advertising” to “printed matter, catalogues, etc.” Co-conspirator Morris testified at trial that the printed matter charge was based on the $7 per unit sales engineering and sales manual expenses in the plan presented to Cushwa and Engel in December, 1956; apparently no study was made to justify the new printed matter charge. The printed matter charge was in effect from January, 1959, through December, 1964.
5. Excise Tax Audit 1958-59; Indiana Gross Income Tax Incident.
Internal Revenue Service Agent Francis J. Rochefort conducted an excise tax audit of appellant Fruehauf Corporation from the fall of 1958 to November, 1959. On December 5, 1958, co-conspirator Morris conferred with the attorney Cushwa concerning the audit and the excise tax procedures followed by appellant Fruehauf. Fruehauf Corporation did not want a close scrutiny of the supplemental billing system. Co-conspirator Morris told Cushwa that the invoices for the supplemental billings were being kept in a completely separate file from the trailer invoices so that it would only be remotely possible that the examination would turn up the billings.
During the course of the audit Revenue Agent Rochefort asserted that Fruehauf had erroneously excluded from its excise tax base an Indiana gross income tax included in the invoice price of the trailers sold at wholesale to three distributors, Warner-Fruehauf Trailer Company, Motor Truck Equipment Company, and Berman Sales Company. Appellant Fruehauf responded by proposing a compromise with the Internal Revenue Service. Fruehauf offered to refund the amounts collected from the three distributors.
On August 28,1959, the Internal Revenue Service accepted the Fruehauf proposal and agreed that if the refunds were made, no tax deficiency would be asserted. Credit memoranda, prepared by co-conspirator Chawner and personally approved by appellant Rowan, were issued to the Warner-Fruehauf Trailer Company, the Motor Truck Equipment Company, and the Ber-man Sales Company. In the next monthly billing to the three distributors, however, the same amounts that had been credited to their accounts pursuant to the compromise between appellant Fruehauf Corporation and the Internal Revenue Service were re-billed to them as extra charges, in addition to the normal monthly supplemental charges, under the designation “printed matter, catalogues, etc.”
6. The Hobbs Trailer Company Installation Charge and the Appellant Frue-hauf Handling Charge for Retail Sales.
In 1955, appellant Fruehauf Corporation acquired Hobbs Trailer Company. Examination by Fruehauf of the excise tax procedure of Hobbs as to its installation charge triggered an inquiry into the possible exclusion from the excise tax base of a $50 Fruehauf charge for handling.
On November 15, 1955, the attorney Cushwa wrote to co-conspirator Morris. Cushwa advised that the costs incurred in putting the trailer in perfect condition for delivery were not excludable from the excise tax base. On December 12, 1955, Cush-wa again wrote to co-conspirator Morris, advising Morris that he had consulted with a Mr. Dodge of the Internal Revenue Service. Cushwa stated that the opinion of Mr. Dodge was that if a handling charge was included in the sales price, the charge was includable in the excise tax base and that only if a separate charge for installation had been made to the customer could the charge be excluded from the excise tax base.
In a memorandum dated December 14, 1955, addressed to appellant Rowan, co-conspirator Morris compared the Hobbs method of computing tax on a new trailer sale with the method used by appellant Fruehauf Corporation. Co-conspirator Morris showed *1049that appellant Fruehauf would have paid a greater tax than Hobbs on the same transaction; however, Hobbs had an installation charge included in its sales price that was excluded from its excise tax base. Co-conspirator Morris stated that Hobbs was in error to exclude the installation charge from the excise tax base.
On December 5, 1958, Cushwa advised co-conspirator Morris that the handling charge to retail customers need not be included in the excise tax base so long as the charge was not made to distributors. Cush-wa and co-conspirator Morris reviewed trailer invoices, which indicated that a handling charge was being made to distributors. It was decided to discontinue the practice of charging distributors for a handling charge.
On March 6, 1959, appellants Rowan and Grace and co-conspirator Morris discussed the excise tax aspect of Fruehauf’s handling charge. Appellant Grace stated that it was his impression that Hobbs Trailer Company, before it had been acquired by Fruehauf Corporation, had obtained a ruling from the Internal Revenue Service to the effect that a “get ready” charge could be included in the list price of the trailers but excluded from the excise tax base. Co-conspirator Morris subsequently obtained the Hobbs ruling, which was in fact a District Director’s letter. That letter approved the exclusion of an installation charge from the excise tax base when the installation charge varied from sale to sale depending upon the cost of labor and parts.
At an April 13, 1959, meeting, appellant Rowan and co-conspirator Morris represented to Cushwa that appellant Fruehauf’s handling charge in connection with retail sales was exactly the same as the installation charge of Hobbs Trailer Company. Accepting the representation of appellant Rowan and co-conspirator Morris, Cushwa advised that appellant Fruehauf Corporation could use the Hobbs method of including the handling charge in the retail price but excluding that amount from the list price for the calculation of the excise tax base.
Fruehauf’s handling charge, however, was not the same as the Hobbs installation charge. Fruehauf’s handling charge for retail sales was not limited to installation but covered such diverse items as repairing minor manufacturing defects, replacing defective light bulbs, repairing scratches, lubricating the wheels, washing the tires, and hitching the trailer to the customer’s tractor. Appellant Fruehauf always charged $50 for these services, without regard to the actual costs incurred. Furthermore, appellant Rowan and co-conspirator Morris were aware that the District Director’s letter to Hobbs, which upheld the exclusion from the excise tax base of an installation charge included in the retail price, conflicted with the advice that Mr. Dodge of the Internal Revenue Service had given Cushwa about Fruehauf’s handling charge. Revenue Agent Rochefort did not represent to appellant Fruehauf that the exclusion of a handling charge from appellant Fruehauf’s excise tax base was proper.
In November, 1959, the Hobbs method was instituted through the issuance of new Fruehauf sales manuals. The implementation of the Hobbs method resulted in Frue-hauf maintaining a double set of equipment invoices with respect to each trailer sold to a distributor. One copy showed figures in accord with the information sent to the distributors, the list price less a distributor discount, which was the method of computation consistent with representations made by' Fruehauf to the Internal Revenue Service concerning sales to distributors. The other copy showed an $83 reduction in the list price of the trailer prior to the application of the distributor discount, which was in accord with the figures used by Fruehauf in recording the transaction for its own books and which reflected the exclusion of the handling charge from the excise tax base.
7. Further Increases in the Supplemental Charges and the Distributor Discount.
Along with the issuance of new Fruehauf sales manuals in November, 1959, the distributor discount was increased from 42% *1050off the list price to 45%, and total supple- ' mental charges increased from 3.75% of the list price to 5%. The supplemental billings maintained the same designations as before the increase; interest was increased from 4V2% to 6% per annum on the open receivables account balance due from each distributor. Co-conspirator Chawner recommended this increase in supplemental billings, and appellant Rowan approved the increase, even though there were no studies made by appellant Fruehauf to support the increase in supplemental charges. At this time, distributors again were cautioned to record supplemental charges as expenses rather than as a part of trailer cost.
Effective September 1, 1961, appellant Fruehauf, with the specific approval of appellant Grace, again increased the discount to distributors from 45% off the list price to 50% off, plus $50 per unit. With this rate of discount, Fruehauf Corporation was selling certain models of its trailers to distributors virtually at cost; in developing list prices, appellant Fruehauf’s rule of thumb was that cost was 50% of the list price.
This September, 1961, increase in the distributor discount was motivated by excise tax savings considerations. In a memorandum dated February 13, 1962, appellant Grace advised R. N. Biggers, the vice-president of Fruehauf Corporation in charge of the Hobbs Division, that the reason for the “fooling around we have done with Federal Excise Tax” was that “Fruehauf will pick up some $20,000 per month by a 50 percent discount with a 5 percent charge-back than they would if they had stayed at 45 percent and charged back 5 percent.”
8. The Warranty Allowance.
The September, 1961, increase in the distributor discount to 50% off the list price included the warranty allowance that prior to September, 1961, had been indicated specifically on the face of each distributor equipment invoice. The change was quite significant.
At the December 13, 1956, meeting in Washington, D.C., Cushwa, Engel, appellant Rowan, and co-conspirator Morris discussed not only the'proposed supplemental charge plan but also the effect on the excise tax base of a $40 warranty allowance given to Fruehauf’s distributors. In 1956, appellant Fruehauf Corporation had reduced the wholesale price by $40, with the understanding that the distributors would bear the expense of performance under the routine warranty, but in accordance with advice received from the attorney Cushwa and the Internal Revenue Service, had been adding back this warranty allowance into the excise tax base for retail sales. At the Washington, D.C. meeting, Cushwa again advised appellant Rowan and co-conspirator Morris that the warranty allowance would still have to be included in the excise tax base in computing excise taxes on retail sales.
After that meeting, Cushwa sought to verify his advice by conferring with Mr. Dodge of the Internal Revenue Service and by requesting the Internal Revenue Service to issue a ruling on the question. Both the advice of Mr. Dodge and the formal ruling of the Internal Revenue Service indicated that a warranty charge to retail purchasers must be included in the excise tax base in computing the tax on retail sales, despite a warranty allowance given at wholesale. As to distributor sales, the Internal Revenue Service refused to take a position in the absence of the copies of the agreements in which the distributors agreed to assume the warranty costs. Until September, 1961, the procedure was thus to treat retail and wholesale sales differently in terms of the excise tax treatment of the warranty. The warranty allowance to distributors was excluded from the excise tax base on distributor sales, but it was added back to the excise tax base on retail sales.
Effective September 1, 1961, the price to distributors was decreased from 45% off the list price to 50% off plus $50 per unit. Concealed in the increased discount at wholesale was the warranty allowance that had previously appeared as a separate deduction on each distributor equipment invoice. The warranty charge to retail purchasers was thus effectively eliminated *1051from the excise tax base attributable to retail sales, contrary to the ruling of the Internal Revenue Service.
Co-conspirator Morris, in an October 25, 1961, letter to Cushwa falsely stated that after September 1, 1961, there was “no allowance to the distributor for warranty expense.” In fact, there was still a warranty allowance. It was concealed in the additional discount so that the warranty allowance could be excluded from the excise tax base for retail sales as well as wholesale sales. Appellant Grace told one distributor that appellant Fruehauf “changed the name from warranty to something else in order to help out a little on the tax problem.”
9. Appellant Fruehauf’s Make-Ready Allowance to Distributors.
In his October 25, 1961, letter to Cushwa, co-conspirator Morris wrote that appellant Fruehauf Corporation was extending a $50 make-ready allowance to its distributors to cover the expenses of adjusting the customer’s coupler, of any necessary rework, and of any other delivery preparation, expenses which were being incurred in connection with the sale of each trailer. Beginning January 1, 1962, the $50 allowance to distributors was recovered by increasing the supplemental charge to distributors by $50 per unit. The make-ready charge was thus shifted from the wholesale price to the supplemental billings. This additional $50 per unit supplemental charge was not separately designated on the monthly supplemental charge invoices.
Before this procedure of extending the make-ready allowance and recouping that allowance in the supplemental billings was instituted, co-conspirator Morris expressed a reluctance to appellant Rowan as to putting into effect the procedure. Co-conspirator Morris did not believe the $50 exclusion from the distributors’ price, with subsequent recovery of the allowance through supplemental charges, to be proper. When at one time co-conspirator Morris and appellant Rowan were discussing the matter, appellant Rowan received a telephone call from appellant Grace, who asked to speak to co-conspirator Morris. Appellant Grace told co-conspirator Morris that he wanted to hear co-conspirator Morris tell appellant Rowan to go ahead with the make-ready allowance from price and recovery in supplemental charges. Despite the misgivings that co-conspirator Morris had concerning this matter, Morris, holding the telephone in a way that would carry his voice to appellant Grace, told appellant Rowan to go ahead with the make-ready charge.
In February and March, 1962, co-conspirator Chawner told distributors that the $50 per unit increase in supplemental charges for handling was strictly fictional for the purpose of saving $5 in excise tax.13 Despite the obvious addition of a $50 per unit charge on the supplemental billings, appellant Rowan told attorney Milton J. Mehl that there had been no change in the procedure or amount of supplemental billings.
10. The Supplemental Charges For the Southern Railway Trailers.
In March and April of 1964, distributor Warner-Fruehauf purchased a number of trailers from appellant Fruehauf and then leased those trailers to Southern Railway. At Warner-Fruehauf’s request, appellant Fruehauf cancelled the supplemental charges for “printed matter” and “management consulting” that had been issued at the time of the sale of the trailers to Warner-Fruehauf. New charge invoices were prepared for the same amount as had been billed under the designations “printed matter” and “management consulting,” but the charges were for special engineering research, stress analysis, and design cost work *1052allegedly performed from January 1, 1964, through June 30, 1964. No records were maintained by appellant Fruehauf, however, as to these services described as special engineering research, stress analysis, and design cost.
11. Supplemental Charges Come Under Internal Revenue Service Scrutiny; Fruehauf’s Response.
By 1964, when Internal Revenue Service agents were questioning appellant Frue-hauf’s supplemental charge plan, the amounts charged in the supplemental billings had really grown to excessive proportions. In September, 1964, the supplemental charges to Hobbs Trailer Company were in excess of $366 per unit for printed matter and in excess of $733 per unit for management consulting fees. In October, 1964, Hobbs was charged $473 per unit for printed matter and $946 per unit for management consulting fees. (Government Exhibit 22.) These figures for September and October were within a few cents of equall-ing 5% of the trailer price.
On September 18, 1964, co-conspirator Morris told Revenue Agent Kiefer that the denomination of billings for services to distributors made no difference to the Frue-hauf Corporation and that the supplemental charge for interest was “not really interest but an amount billed to show the distributor what he could owe as interest.” On October 16, 1964, co-conspirator Morris admitted to Revenue Agent Kiefer that there were no records to substantiate the supplemental charges.
On December 29, 1964, co-conspirator Morris wrote a memorandum to appellant Rowan, recommending that Fruehauf Corporation consider the revision of its method of computing the federal excise tax on its sales. In the memorandum, co-conspirator Morris first reviewed the structure of the supplemental charge plan, noting that the supplemental billings were at 5% of the list price, and then indicated that federal agents would be contending that the supplemental charges were components of the wholesale price and hence includable in the excise tax base. Morris stated that most of the items billed as supplemental charges were “doubtful at best” and that “upon negotiation we will be fortunate . to sustain our position on two of the five (percentage) points.” Morris advised that the alternatives were: (1) that the supplemental billings be eliminated, (2) that the supplemental billings be based on specific charges rendered (which according to the original advice of attorney Cushwa was necessary to counsel’s approval of the plan), (3) that the supplemental billings be included in the wholesale price, and (4) that computation of the excise tax be done according to the “retail method.” 14
Effective January 1, 1965, the Fruehauf supplemental charge plan designations were changed from “printed matter,” “management consulting,” and “interest” to “finance,” “teletype,” and “interest.” These new charges were posted on appellant Fruehauf Corporation’s books, like the old charges, as recovery of costs applicable to new trailers. The supplemental charge for “teletype” was an allocation of Fruehauf’s total expenses of operating its teletype system, over and above that amount already recouped through monthly teletype “rental” charges to each distributor. The supplemental charge for “finance” was a proration of the total operating expenses of the Fruehauf Finance Company, a separately incorporated but wholly owned subsidiary of appellant Fruehauf Corporation. The supplemental “interest” charge was equal to 9% per annum on the month-end balances of each distributor’s equipment account and parts and services account. These billing designations continued in effect through February 8, 1966, the date of the filing of the quarterly manufacturers excise tax returns for the fourth calendar quarter of 1965, the last overt act listed in the indictment.
In recorded testimony taken in 1967 by the Internal Revenue Service, appellant Rowan admitted that the cost of rendering *1053services to appellant Fruehauf’s distributors was an unsegregated portion of the cost of operating several of appellant Fruehauf’s departments and was considered by appellant Fruehauf in developing its selling prices and profit margins. At trial, co-conspirator Morris testified that he had no knowledge of any studies that justified the increases in and modifications of the supplemental billings.
The Tire Tax Credit Scheme
Tire manufacturers publish price lists, known as OEM (original equipment-manufacturer) price lists. During the period of the conspiracy charged in the indictment, appellant Fruehauf Corporation, as a large volume purchaser of tires, was able to negotiate contracts for the purchase of tires at prices substantially below the OEM price level. Appellant Fruehauf executives referred to such prices as “confidential” prices. Appellant Grace, on behalf of appellant Fruehauf participated in the contract negotiations with tire companies, and he had the final authority in approving the contracts.
At the request of appellant Fruehauf, the tire manufacturers billed Fruehauf on the basis of OEM prices, rather than on the basis of the negotiated “confidential” prices. The difference between the invoice price, stated at the OEM level, and the lower “confidential” price was rebated to appellant Fruehauf by means of monthly checks or credit memoranda. Fruehauf executives, including appellants Grace and Rowan, were aware of the amount of the rebate to which Fruehauf was entitled before the actual receipt of the checks or credit memoranda from the tire manufacturer. Nevertheless, the tire tax credit claimed against Fruehauf’s excise tax liability was computed from schedules prepared by co-conspirator Morris based, not on the confidential prices, but on the OEM prices without regard to the rebates.15
In March, 1958, co-conspirator Morris and appellant Rowan discussed Fruehauf’s computation of the tire tax credit. Co-conspirator Morris initially took the position that the credits should be based on the lower contract price, taking into account the rebates; however, after co-conspirator Morris and appellant Rowan together studied the statute and the regulations, they concluded •that the “purchase price” of the tires, on which the tax credit was to be computed, could be construed as the invoice price, regardless of whether rebates were received. Co-conspirator Morris and appellant Rowan did not seek the advice of Cushwa or in-house counsel to verify their conclusion. Rather, co-conspirator Morris made telephone calls to various automobile companies to determine on what basis they computed tire tax credits.
In 1964, when appellant Fruehauf’s method of claiming tire tax credits came under the scrutiny of the Internal Revenue Service, co-conspirator Morris and appellant Rowan were less than forthright about their March, 1958, meeting concerning the tire tax credit. On November 23, 1964, appellant Rowan falsely represented to Revenue Agent Kiefer that the tire tax credit was computed on the OEM price, rather than on the negotiated “confidential” price, as the result of oversight.16 On *1054August 4, 1965, co-conspirator Morris falsely represented to Revenue Agent Kiefer that he had not been aware until the end of 1964 that appellant Fruehauf received rebates on tire purchases.
Through December 31, 1964, appellant Fruehauf Corporation claimed tire tax credits based on the OEM tire prices. Effective January 1, 1965, however, appellant Frue-hauf Corporation did change its practice of claiming tire tax credits so that the credit would be based on the negotiated “confidential” price rather than the invoiced OEM price.
The District Judge’s Final Findings After reviewing this evidence, the district judge determined that appellant Fruehauf Corporation, through the use of two schemes that utilized deceptive invoicing procedures, had evaded a substantial part of its excise tax liability during the period beginning with the filing of the manufacturers excise tax return for the final quarter of 1956 and ending with the filing of the manufacturers excise tax return for the final quarter of 1965. First, the supplemental charges were not properly excluded from the excise tax base in the computations for the excise tax returns because (1) the charge for interest was not really for interest, (2) the charge for printed matter was a continuation of the charge for national advertising and hence includable in the price of the trailer, (3) the charge for management consulting fees was required to be included in the price of the trailer, (4) the 1965 supplemental charges for teletype and finance were part of appellant Fruehauf’s costs of doing business and thus required to be included in the taxable price of the trailer, (5) the warranty allowance was not ex-cludable from the price of the trailer and hence the excise tax base had to reflect a warranty charge, and (6) the additional $50 per unit allowance to distributors, which was given effective January 1, 1962, and which was recouped in the supplemental billings, was a fictitious item, instituted solely for the purpose of evading excise taxes. Second, appellant Fruehauf overstated its tire tax credits in the period from October 1,1956, through December 31,1964, thereby understating its excise tax liability, because such credits were claimed on the basis of the invoice prices, which stated the prices at OEM levels, rather than on the lower true purchase price that took rebates into account.
The district judge further determined that the deceptive invoicing procedures were instituted and utilized to reduce the excise tax base and to increase the amount of excise tax credits by the willful and unlawful conspiracy of appellants Fruehauf Corporation, Grace, and Rowan and unin-dicted co-conspirators Morris and Chawner, a conspiracy that commenced no later than December 12, 1956, and that extended through February 8, 1966. Appellants Fruehauf Corporation, Grace, and Rowan were thus found guilty of conspiring in violation of 18 U.S.C. § 371, (1) to defraud the United States by impeding, impairing, obstructing, and defeating the lawful governmental functions of the Internal Revenue Service in the assessment and collection of federal manufacturers excise taxes, (2) to attempt to evade and defeat, contrary to 26 U.S.C. § 7201, the payment of federal excise taxes' due and owing to the United States by Fruehauf Corporation for the period from October 1, 1956, through December 31, 1965, and (3) to aid or assist in the preparation and presentation, contrary to 26 U.S.C. § 7206, of materially false and fraudulent excise tax returns for the Frue-hauf Corporation for all calendar quarters in the period from October 1, 1956, through December 31, 1965. The district judge also found that the quarterly manufacturers excise tax returns for the fourth calendar quarter of 1964 and the four calendar quarters of 1965 in particular had substantially
*1055understated the excise tax liability of appellant Fruehauf.
After the entry of the district judge’s findings of fact, appellants moved for a new trial. The district judge issued an opinion in which he denied appellants’ motion. Judgment was then entered against appellants. Appellants now appeal to this Court.
II
In urging reversal of their convictions, appellants first argue that appellee United States failed to prove the offense charged in the indictment. According to appellants, the conspiracy of which the district judge found appellants guilty was altogether different from the conspiracy alleged in the indictment.17 The indictment charged that distributors were billed by appellant Frue-hauf for services that were never rendered and that the supplemental billings containing the charges were concealed from the Internal Revenue Service.18 The district judge found that, as had been charged in the indictment, appellants had employed deceptive invoicing procedures to conceal the supplemental billings, but in apparent contrast to the indictment, found that appellants had billed distributors under the supplemental charge plan for amounts that should have been included in the wholesale price and hence in the excise tax base. Appellants point out that the conspiracy found by the district judge, unlike that alleged in the indictment, did not involve fictitious charges for services that were never rendered.
The law upon which appellants premise this argument is the law of amendment and .variance, which the Supreme Court laid out in three decisions. In Ex Parte Bain, 121 U.S. 1, 7 S.Ct. 781, 30 L.Ed. 849 (1887), the Supreme Court held that the fifth amendment grand jury requirement forbade the United States from formally amending an indictment as to its charging terms and that any such formal amendments constituted reversible error per se. In Berger v. United States, 295 U.S. 78, 55 S.Ct. 629, 79 L.Ed. 1314 (1935), the Supreme Court was confronted with a variance between the particulars alleged in the indictment and the proof at trial; after noting that the interests of fair notice and freedom from double jeopardy were involved in such cases, the Court held that a variance would be harmless error if not prejudicial to the defendant. In Stirone v. United States, 361 U.S. 212, 80 S.Ct. 270, 4 L.Ed.2d 252 (1960), the Supreme Court held that certain variances, those created when the proof presented at trial was of a different or an additional crime than the one alleged in the indictment, amounted to “constructive amendments” and were subject to the reversible per se rule of formal amendments.
*1056This Court and other courts of appeal have thus distinguished between amendments, formal and constructive, which are considered reversible per se, and variances, which are reversible error only if prejudicial to the defendant. Watson v. Jago, 558 F.2d 330 (6th Cir. 1977); United States v. DeCavalcante, 440 F.2d 1264 (3d Cir. 1971); United States v. Silverman, 430 F.2d 106 (2d Cir. 1970); Gaither v. United States, 134 U.S.App.D.C. 154, 413 F.2d 1061 (D.C. Cir. 1969). Also, this Court and other courts of appeal have recognized the following distinction between amendments and variances.
An amendment of the indictment occurs when the charging terms of the indictment are altered, either literally or in effect, by prosecutor or court after the grand jury has last passed upon them. A variance occurs when the charging terms of the indictment are left unaltered, but the evidence offered at trial proves facts materially different from those alleged in the indictment.
Watson v. Jago, supra, 558 F.2d at 334; Gaither v. United States, supra, 134 U.S.App.D.C. at 164, 413 F.2d at 1071; United States v. Pelose, 538 F.2d 41, 45 n.8 (2d Cir. 1976); United States v. Somers, 496 F.2d 723, 743 n.38 (3d Cir.), cert. denied, 419 U.S. 832, 95 S.Ct. 56, 42 L.Ed.2d 58 (1974); United States v. Bursten, 453 F.2d 605, 607 (5th Cir. 1971), cert. denied, 409 U.S. 843, 93 S.Ct. 44, 34 L.Ed.2d 83 (1972).
In the present case, we are not confronted with a formal amendment of the indictment. There has been no literal alteration of the indictment, and appellants do not contend otherwise.
Nor do we have a constructive amendment. The present case is distinguishable from Stirone v. United States, supra, 361 U.S. 212, 80 S.Ct. 270, 4 L.Ed.2d 252, and from a constructive amendment case in this Circuit, Watson v. Jago, supra, 558 F.2d 330. In Stirone v. United States, supra, the defendant was charged with a Hobbs Act violation for interfering with sand shipments into Pennsylvania, but the defendant’s conviction was based not only on the Hobbs Act violation charged in the indictment but also on another Hobbs Act violation, the interference of steel shipments moving from Pennsylvania into interstate commerce. In Watson v. Jago, supra, a state defendant was charged with premeditated murder, but at trial the defendant was tried for both premeditated murder and felony-murder, which under Ohio law were separate offenses.19 See Cole v. Arkansas, 333 U.S. 196, 68 S.Ct. 514, 92 L.Ed. 644 (1948); United States v. Swarthout, 420 F.2d 831 (6th Cir. 1970). By contrast, in the present case, appellants were convicted of conspiracy to defraud the United States, to evade payment of excise taxes, and to aid or assist in the preparation and presentation of materially false excise tax returns, the crime which was charged in the indictment;20 the conviction was based *1057on the supplemental billing system and inflated tire tax credits, particulars of the crime also alleged in the indictment.21 Appellants were not confronted with a prosecution for an additional or different crime. Appellants could plead double jeopardy to another conspiracy prosecution for evasion of taxes based on the facts of the supplemental billing system and inflated tire tax credits. Contained in the indictment was the information required to be there to give appellants fair notice and to insure that the indictment formed the basis of the convictions. See Watson v. Jago, supra, 558 F.2d at 339 and n.7; Russell v. United States, 369 U.S. 749, 769-70, 82 S.Ct. 1038, 8 L.Ed.2d 240 (1962).
Appellants’ argument must therefore rest upon a variance between the particulars alleged in the indictment and the proof at trial. The considerations governing variances have been stated before by this Court.
A variance is not to be regarded as material where it is not of a character which could have misled the defendant at the trial, Berger v. United States, 295 U.S. 78, 82, 55 S.Ct. 629, 79 L.Ed. 1314; or where it involves no element of surprise prejudicial to the efforts of the defendant to prepare his defense, United States v. Ragen, 314 U.S. 513, 526, 62 S.Ct. 374, 86 L.Ed. 383, rehearing denied, 315 U.S. 826, 62 S.Ct. 620, 86 L.Ed. 1222; or where it does not affect substantial rights. Rule 52(a), F.R. of Crim.P.; cf. United States v. Haskins, 345 F.2d 111, 114 (C.A.6). “Whether or not a variance is prejudicial is a judgment that must be made on the facts of each case.” United States v. Russano, 257 F.2d 712, 715 (C.A.2).
United States v. Mills, 366 F.2d 512, 514 (6th Cir. 1966); United States v. Goble, 512 F.2d 458, 466 (6th Cir.), cert. denied sub nom. Shad v. United States, 423 U.S. 914, 96 S.Ct. 220, 46 L.Ed.2d 143 (1975). See United States v. Crowder, 346 F.2d 1, 3 (6th Cir. 1964), cert. denied, 382 U.S. 909, 86 S.Ct. 249, 15 L.Ed.2d 161 (1965).
In urging that appellants’ convictions be affirmed, appellee United States denies that there was a variance. The United States takes the position that the indictment fairly embraced four theories that the Government contends that the proof at trial supported; (1) that no “extra” services were rendered to distributors that were not *1058rendered to retail purchasers; (2) that the supplemental billings were not for any such “extra” services that may have been rendered; (3) that any “extra” services rendered did not remotely approach in value the amounts billed as supplemental charges; and (4) that the billings for the “extra” services were required to be included in the taxable price of the trailers that appellant Fruehauf sold (the “condition of sale” theory).
Under the authority of United States v. Ragen, 314 U.S. 513, 62 S.Ct. 374, 86 L.Ed. 383 (1942), the first three of these theories were fairly embraced in the indictment. The appellants’ argument — that because the indictment charges “no services” the Government must prove that no services were rendered — was rejected by the Supreme Court in Ragen. In that case, the Supreme Court reviewed a conviction for conspiracy to evade corporate income taxes. The alleged conspiracy involved the deduction from reported corporate taxable income disbursements to corporate shareholders labelled as “commissions.” In a manner similar to the indictment in the present case, the Ragen indictment charged that “no services” were rendered to support the commissions. At trial, the judge instructed the jury with a charge calling for a determination of whether the “commissions” were intentionally made to include amounts that should have been treated as dividends (which would assume that some undefined amount of services could have been rendered). Like the appellants in the present case, the Ragen respondents made a variance argument. The Supreme Court held that there was not a fatal variance.
The respondents also urge that there was a fatal variance between the indictment and the proof, in that the indictment alleges that the commission payments were actually dividends in their entirety, whereas the evidence indicates that some services were performed. The fifth count of the indictment does refer to “all of the moneys . . . paid . by virtue of the . .. so-called ‘Employment Contracts’ ” as “in truth and in fact, distributions of profits and dividends.” But the gravamen of the charge is distribution of dividends in the guise of commissions, and the respondents cannot fairly claim that they were not adequately apprised of the nature of the offense. Any variance which existed, at most a matter of the extent of the alleged tax evasion, involves no elements of surprise prejudicial to the respondents’ efforts to prepare their defense.
United States v. Ragen, supra, 314 U.S. at 526, 62 S.Ct. at 379.22
The Ragen decision is not authority, however, for dismissing the variance question as to the fourth Government theory, the “condition of sale” theory, and it is that theory about which appellants particularly complain.23 Nevertheless, our analysis of *1059applicable law leads us to conclude that there was not a fatal variance between the facts alleged in the indictment and the condition of sale theory.
The gist of Subpart (11) of the indictment is the allegation that appellants conspired to manipulate the wholesale price of trailers in order to establish a reduced excise tax base and to recapture the amounts otherwise lost by the lower price through the supplemental billings.
THE GRAND JURY CHARGES that, in addition, it was a part of the conspiracy:
(11) that the invoiced price to the wholesalers would be reduced by an arbitrary percentage to establish a false lower Excise Tax base, and that a substantial amount would be recouped in the form of supplemental billings for these non-existent services (emphasis supplied).
One method of manipulating the wholesale price would be the exclusion of charges required to be included in the wholesale price.
Furthermore, appellants cannot claim that they were misled or surprised when the United States included the condition of sale theory as one of the prosecution’s theories. Appellants, after being served the indictment, filed a motion for a bill of particulars. In that motion, appellants requested the following information.
(10)(b) State whether the government will contend at trial that none of the “services” referred to herein were rendered. If the answer to the preceding is in the negative, describe those “services” that the government will concede were in fact rendered.
(c) State whether the government will contend at trial that even if the “services” referred to herein were rendered, the amounts billed for them are not legally excludable from the excise tax base applicable to wholesale sales. Joint Appendix at 34. The Government’s Response to appellants’ motion properly informed appellants that they would be facing a number of prosecution theories, including the condition of sale theory.
(10)(b) The Government will contend the Fruehauf Corporation rendered no ex-cludable services to its wholesale distributors, nor will it concede that any services were rendered.
(10)(c) The Government will contend that if any services were rendered, the charges therefore were not properly ex-cludable from the excise tax base.
Joint Appendix at 50. Appellants read the indictment to include the possibility that the United States would contend that even if services were rendered to distributors, the charges were still required to be included in the wholesale price and hence in the excise tax base.
Ill
Appellants’ second main argument on appeal is that the appellant Fruehauf excise tax returns were prepared according to applicable law. In appellants’ view, the exclusion of the supplemental charges from the wholesale price (and hence the excise tax base) and the computation of the tire tax credits with invoice prices without regard to pre-arranged rebates was proper. Of course, the conclusion would follow that appellants would not be guilty of the criminal conspiracy charged in the indictment.
We believe, however, that it was clear that the supplemental billing plan did not operate in accordance with applicable law and that the computation of the tire tax credits based on the invoiced OEM price without regard to pre-arranged rebates was improper. Appellants did engage in the conspiracy charged in the indictment and did not innocently miscalculate the amount of taxes owed under a complex excise tax law.
*1060The Supplemental Billings
1. The Exclusion of “Supplemental” Charges from the Excise Tax Base.
Appellants contend that charges for articles not listed in § 4061(a) of the Internal Revenue Code of 1954, 26 U.S.C. § 4061(a),24 are not subject to the manufacturers excise tax. According to appellants, § 4061(a) imposes a tax on sales by manufacturers of certain articles, including truck trailer and semitrailer bodies and chassis, and not on services rendered contemporaneously with the sale. As support for this proposition, appellants attempt to compare this situation with that when a taxable article and a nontaxable article are sold by a manufacturer as a unit and the manufacturers excise tax applies to that portion of the sales price that is properly allocable to the taxable article. Macey's Jewelry Corp. v. United States, 387 F.2d 70 (5th Cir. 1967); Revenue Ruling 60-259,1960-2 C.B. 318. Appellants add that § 4216(a) of the Internal Revenue Code of 1954, 26 U.S.C. § 4216(a), specifically excludes transportation, delivery, insurance, installation, or other charge.
Appellants do not accurately state the law. The price used by the computation of the excise tax in § 4061(a) is defined in § 4216(a),25 and it is not strictly limited to manufacturing costs. Rather, the taxable price essentially excludes no expense incurred by the manufacturer in connection with the article taxable under § 4061(a) prior to the shipment of the article. Even packaging cost is included. Fitch Co. v. United States, 323 U.S. 582, 65 S.Ct. 409, 89 L.Ed. 472 (1945); Waterman-Bic Pen Corp. v. United States, 332 F.2d 711 (2d Cir. 1964); United States v. Stowe-Woodward, Inc., 306 F.2d 678 (1st Cir. 1962), cert. denied, 371 U.S. 949, 83 S.Ct. 503, 9 L.Ed.2d 498 (1963). See Hunt Foods and Industries, Inc. v. United States, 436 F.2d 443, 193 Ct.Cl. 759 (1971). In addition, § 4216(a) by its terms does not permit the exclusion of a transportation, delivery, insurance, installation, or other charge unless such a charge is not incident to placing the article in condition ready for shipment and unless the amounts so excluded are established to the satisfaction of the Secretary of the Treasury.
Appellants cite Fitch Co. v. United States, 323 U.S. 582, 65 S.Ct. 409, 89 L.Ed. 472 (1945), as authority for their position that services are not intended to be covered by the manufacturers excise tax, but appellants misread the case. In Fitch, the Supreme Court held that advertising and selling expenses were to be included in the taxable price of the manufacturer’s product because all such pre-shipment charges were to be included in the excise tax base.
Congress sought in the Revenue Act of 1932 to use the manufacturer’s or wholesaler’s selling price, rather than the retail price, as the measure of the excise taxes imposed by § 603. 75 Cong.Rec. 11383, 11657. Section 619(a) was designed to lay down specific rules for determining this selling price, especially in relation to costs incurred after the article itself had been manufactured. It provides for the use of the manufacturer’s or producer’s f. o. b. price at the factory or place of production. In essence, all manufacturing and other charges incurred prior to the actual shipment of an article and reflected separately or otherwise in the f. o. b. wholesale price are to be included in the sale price underlying the tax, while all charges incurred subsequent thereto are to be excluded. Hence any additional charge which a purchaser would not be required to pay if he accepted delivery of the article at the factory or place of production may be so excluded. See H.Rep.No.708 (72d Cong., 1st Sess.) p. 37; S.Rep.No.665, Part 3 (72d Cong., 1st Sess.) p. 3; H.Conf.Rep.No.1492 (72d Cong., 1st Sess.) p. 22.
*1061Advertising and selling expenses incurred by a manufacturer such as petitioner clearly fall within the class of charges which Congress intended to be included in the tax base. Regardless of whether we consider such expenses technically as manufacturing costs, it is obvious that they are incurred prior to the actual shipment of articles to wholesale purchasers and that they enter into the composition of the wholesale selling price. Even if the purchaser accepts delivery at the factory, he pays for the advertising and selling expenses. Thus they must be included in the taxable sales price.
323 U.S. at 584-85, 65 S.Ct. at 411. The same provisions that the Supreme Court interpreted were reenacted in full in the Internal Revenue Code of 1954, and the Fitch case is the governing Supreme Court authority in interpreting § 4216(a). United States v. Stowe-Woodward, supra, 306 F.2d 678; Hunt Foods and Industries, Inc. v. United States, supra, 436 F.2d 443, 193 Ct.Cl. 759; General Motors v. United States, 339 F.2d 648, 652, 168 Ct.Cl. 301 (1964).
The cases of United States v. Stowe-Woodward, Inc., supra, 306 F.2d 678, and Hunt Foods and Industries, Inc. v. United States, supra, 436 F.2d 443, illustrate the Fitch principle. In both cases, it was held that presale transportation charges, which fell within the literal terms of the language in § 4216(a) conditionally providing for the exclusion of transportation and delivery charges, were required to be included in the taxable price. The courts in both cases cited Ayer Co. v. United States, 38 F.Supp. 284, 289, 93 Ct.Cl. 386 (1941), for the “added value” test and found that the transportation charge added to the attractiveness of the manufacturers product and therefore put value into the taxable articles.
This review of the relevant judicial authority on § 4216(a) should make clear that the Government’s prosecution of appellants did not rest on administrative interpretation, which appellants vigorously argued and which appellee United States just as strongly denied. According to appellants, the regulations supporting the prosecution, Regulations 31626 and 330,27 were repealed, Regulations 316 on October 8, 1958, and Regulations 330 on February 7, 1963. Appellants argue that in view of the doubtful efficacy of these regulations, they could not have formed the necessary intent to violate the provisions of the regulations. According to appellee United States, these regulations were never repealed but were not necessary to the legal underpinning of the conspiracy case.
Because we agree with the United States that the prosecution against appellants could proceed without the regulations in question, we do not reach the question as to whether they were repealed. See United States v. Stowe-Woodward, Inc., supra, 306 F.2d at 682. Examination of the exclusion of the particular supplemental charges will further demonstrate how the Government’s prosecution did not rest upon the regulations. We do observe here, however, that the importance of the regulations lies in the fact that they embody an administrative interpretation of the statute consistent with the judicial interpretation,28 and appellants *1062concede that the regulations were in effect during a portion of the period of the alleged conspiracy.
2. The Exclusion of the Supplemental Interest Charges.
Appellants contend that a charge for interest is not includable in the taxable price of an article, citing Macey’s Jewelry Corp. v. United States, 387 F.2d 70 (5th Cir. 1967), and thus conclude that the amounts charged as interest in the supplemental billings were properly excludable from the taxable price of the trailers. Appellee United States does not contest the statement that a bona fide charge for interest is excludable from the taxable price. The United States does dispute appellant’s broad reading of the Macey’s Jewelry case and argues further that the district court was not clearly erroneous in finding that the supplemental interest charges were not really interest charges.
We agree with the United States. In Macey’s Jewelry, the Fifth Circuit held “that an extra charge for goods sold on credit may be a true finance charge not within the price for which the goods are sold.” 387 F.2d at 71. In so holding, the court in Macey’s Jewelry quoted, 387 F.2d at 72, the following passage from Berman’s Jewelry Store, Inc. v. United States, 198 F.2d 675, 678 (4th Cir. 1952).
There can be, of course, such a thing as a “finance charge” or “carrying charge” on installment sales and they are not unusual. And where such a charge is confined to and is truly representative of the added expense imposed upon the vendor by installment selling (as distinguished from cash sales) it is not to be included in the tax base. Such a charge may properly include lawful interest on the deferred portion of the purchase price, the cost of the book-keeping necessary to keep the records of such sales, and any other expense directly attributable to the fact that payment is to' be made in installments instead of cash.
It should be noted that the Macey’s Jewelry and Berman’s Jewelry decisions do not stand for the proposition that any interest charge is excludable. Both cases dealt with finance charges on credit sales. The Court in Macey’s Jewelry reversed the trial court’s grant of summary judgment in favor of the Government and ordered that the taxpayer company be given an opportunity to prove at trial that its finance charge was bona fide. In Berman’s Jewelry, a finance charge was included in the taxable price.
In the present case, the district court found that the supplemental interest charge was not really for interest. When the supplemental charge plan was proposed, the interest charge was intended to cover the cost of equipment accounts receivable balance carried by appellant Fruehauf until the units were sold by distributors; however, the evidence did not disclose the existence of a deferred or installment payment plan between appellant Fruehauf and its distributors. The sales were made on open account, and payment was not due until the expiration of the thirty or ninety day period stated on the invoice. The “interest” charge was computed by applying the prevailing interest rate to the distributor’s month ending equipment account receivable balance, regardless of whether the account was current. Distributors were charged “interest” without regard to whether payment was due.
Macey’s Jewelry is distinguishable in another regard. That decision could not justify tax evasion. As was stated in Berman’s Jewelry, supra, 198 F.2d at 678:
*1063. [I]t is obvious that in fixing the amount which a customer is to pay on a credit sale a merchant cannot arbitrarily name any amount that he chooses as a “finance charge” or “carrying charge” and thereby exclude it from the tax base. This would open unlimited opportunities for evasion of tax.
In the present case, when the supplemental charge plan was instituted, amounts received by appellant Fruehauf in payment for the interest charges were posted to an interest income account. In August, 1957, this practice was changed because of the distortion to the corporate budget, and thereafter interest income was charged as reductions to the cost account applicable to new trailers, indicating that the interest charge lacked substance. Even more revealing, the interest charge was manipulated for the ends of the supplemental charge plan. In November, 1959, when the supplemental billings were increased from 3.5% to 5% of the list price, the interest charge was increased from 4y2% to 6% per annum on the open equipment receivable account balance due from each distributor. In January, 1965, when two of the designations of the supplemental billings were changed to “teletype” and “finance,” the interest charge was increased to 9% per annum on the month-end balances of each distributor’s equipment account and parts and services account. In September, 1964, co-conspirator Morris accurately admitted to a revenue agent that the supplemental charge for interest was not really for interest. The district court was thus not clearly erroneous in finding that the supplemental interest charge was not really an interest charge.
3. The Exclusion of Supplemental Charges for Advertising, Printed Matter, Management Consulting, and Teletype.
As with the supplemental interest charges, appellants contend that the supplemental charges for advertising, printed matter, and teletype were excludable from the taxable price. Appellants state that the Internal Revenue Service has authorized exclusions from the excise tax base for advertising charges (primarily for local advertising) 29 and for expenses incurred in helping distributors sell at retail, and it is true that at the time that the supplemental charge plan was approved by the attorney Cushwa and the accountant Engel, the Internal Revenue Service was issuing private letter rulings allowing for the exclusion from the excise tax base of charges for retailing expenses and (despite Fitch) for advertising. Appellants also state that four of their witnesses testified to the rendition of services charged to distributors.
A necessary assumption of appellants’ argument is that the charges in the supplemental billings were actually for whatever services that were rendered. The evidence shows otherwise. The supplemental billings were at least excessive, were always a function of the trailer sales price, and were not documented by the kind of records that the Internal Revenue Service would require to establish that the charges for the services were properly excludable from the price upon which the excise tax was computed.
The approval of the supplemental charge plan by the attorney Cushwa and the accountant Engel was conditioned on the value of the services in a specific case equall-ing or exceeding the amounts charged and on the keeping of records that would demonstrate that the distributor actually received the services for which it was charged. When this conditional approval was given, the charges were represented to be $34 per unit for national advertising and $70 per unit for management consulting fees.
The supplemental charge plan that was first put into operation did not really incorporate the procedures that counsel advised to be necessary to avoid problems with the Internal Revenue Service. Distributors were charged the amounts approved by counsel, and the supplemental charges were *1064posted on the corporate books in a proper fashion. Supplemental charges for advertising and management consulting fees were posted to expense accounts, and supplemental interest charges were posted to an interest income account. However, the supplemental charges were from the beginning a function of the sales price and not of services rendered. The “Distributor Analysis of Price Adjustment” work sheets and the method of computing the charges for advertising and management consulting fees (subtracting the interest charge from the increase in discount to distributors given along with the implementation of the supplemental charge plan and allocating the remainder between the two charges) insured that the supplemental billings would not be based on the value of services performed but on the sales price. Distributors were thus unable to avoid the supplemental charges, regardless of whether services were performed, when they purchased trailers. If distributors returned trailers, the billings would be cancelled proportionately; if distributors did not purchase trailers, no supplemental billings were issued. Of course, because the supplemental billings were a function of the sales price, they would increase corresponding to the increases in the list price of the trailers.
Within a short period of time after the institution of the supplemental charge plan, the charges did in fact increase. In June, 1957, the distributor Motor Truck Equipment Company was charged $147.34 per unit for national advertising. In November, 1957, the distributor Berman Sales Company was charged $124.91 per unit for advertising.
As a result of these increases in the supplemental charges, the credits for the charges on appellant Fruehauf’s books were distorting the budgets of appellant Frue-hauf’s departments. Of course, it would be impossible for appellant Fruehauf’s method of accounting to distort the budgets if there were in fact expenses matching the amounts charged to distributors in the supplemental billings. In August, 1957, the postings to expense and interest income accounts were reversed, and thereafter the supplemental charges were posted as adjustments to the price of new trailers. In effect, the supplemental charges were treated as part of the trailer costs. This accounting treatment was inconsistent with the original theory of the supplemental billings, that distributors were billed for services not related to trailer production.
This change in the accounting treatment of supplemental billings indicated that the supplemental charge plan was operating in an unjustifiable manner. So did the lack of record keeping. In the autumn of 1958, appellant Rowan was warned by co-conspirator Morris that sufficient records were not being kept, but appellant Rowan took no action to correct the situation. This situation prevailed throughout the life of the supplemental charge plan. In October, 1964, during the course of the Internal Revenue Service audit of Fruehauf’s excise tax returns, co-conspirator Morris admitted to Revenue Agent Kiefer that there were no records to substantiate the supplemental charges as costs to be separated from the trailer expenses.
It is not clear, however, that any records could have justified the amounts charged in the supplemental billings. In July, 1958, an internal Fruehauf study demonstrated that the charges were far in excess of the amounts discussed with the attorney Cush-wa and the accountant Engel in December, 1956. The charges were not decreased but were instead increased, in November, 1959, from a total of 3.75% of the list price of the trailers to a total of 5%. The charges were continued at that percentage through 1964, by which time the supplemental charges were way out of line with the original amounts approved by Cushwa and Engel and were unrelated to the value of whatever services were being performed. In September, 1964, the distributor Hobbs Trailer Company was charged over $366 per unit for printed matter and over $733 per unit for management consulting fees. In October, 1964, charges to Hobbs were $473 per unit for printed matter and $946 for management consulting fees.
*1065The fact that the supplemental charges had grown to excessive amounts and had little, if any, relationship to the value of services rendered to distributors was further demonstrated by the manner in which the supplemental billings were manipulated. In December, 1958, Regulations 330 were published. Regulation 330.1-l(b) provided that charges for advertising could not be excluded from the excise tax base, reversing the policy that the Internal Revenue Service had been following in previous years when issuing private letter rulings. Appellant Fruehauf’s reaction to this regulation, which would disallow its exclusion of national advertising from the taxable price of trailers, was to change the billing designation of advertising to printed matter.According to co-conspirator Morris, the change was made without any new study being made to determine whether there was enough printed matter furnished to Frue-hauf distributors to justify the charge. Of course, the charge for printed matter was a continuation of the charge for national advertising.
The Indiana gross income tax and Southern Railway transactions were even more blatant manipulations of the supplemental billing system. The Indiana gross income tax incident occurred in the autumn of 1958, when the Internal Revenue Service was auditing appellant Fruehauf’s excise tax returns. During the course of the audit, the examining agent found that appellant Fruehauf had been improperly excluding from the excise tax base a tax on gross income levied by the State of Indiana, which was included in the price of trailers sold to certain wholesale distributors. Appellant Fruehauf proposed a compromise whereby the Internal Revenue Service would not assert a tax deficiency if appellant Fruehauf would refund to distributors the amounts collected as Indiana gross income tax, and the Internal Revenue Service agreed to the proposal. The three affected distributors, Warner-Fruehauf, Berman Sales, and Motor Truck Equipment, were issued credit memoranda in the amounts collected as Indiana gross income tax. In the next month’s supplemental billings, however, the same amounts were added to that month’s regular billings. Thus, the amounts credited to the distributors’ accounts under the compromise with the Internal Revenue Service were recouped through the supplemental billings. In this case, the supplemental billing system provided the mechanism by which appellant Fruehauf could renege on its agreement with the Internal Revenue Service.
The Southern Railway incident occurred in 1964. The distributor Warner-Fruehauf purchased from appellant Fruehauf a number of trailers which were in turn leased to Southern Railway. The sale of the trailers was accompanied by the regular monthly supplemental charges. At the request of Warner-Fruehauf, however, credit memo-randa were issued by Fruehauf cancelling the regular supplemental charges in connection with the Southern Railway trailers and new charge invoices were prepared and submitted in the identical amounts, only describing the purported services as special engineering research, stress analysis, and design cost, performed from January 1, 1964, through June 30, 1964. No records were maintained to substantiate that these services were rendered.
Finally, there was the 1965 revision of the supplemental charge plan. Co-eonspirator Morris, worried about the Internal Revenue Service excise tax audit, authored a memorandum in December, 1964, to appellant Rowan, recommending that appellant Fruehauf consider revising its method of computing the manufacturers excise tax because of the dubious validity of the exclusion of the supplemental charges from the price upon which the excise tax was computed. Appellant Fruehauf did revise its supplemental charge plan but not in a way that would bring the plan into accord with the law. Instead, the supplemental charges were maintained under the new designations “finance” and “teletype” in replacement of the charges for “printed matter” and “management consulting.” These supplemental charges, although under new designations, continued to be posted to the Fruehauf books as adjustments to the price *1066of new trailers and to be a function of the list price of trailers. The teletype charge was for running Fruehauf’s teletype system, over and above the rental fee already charged, and the finance charge was for operating Fruehauf’s own finance company. Of course, the charges for teletype and finance as instituted in the supplemental charge plan were for costs of appellant Fruehauf doing business, the selling of trailers, and were not excludable from the price upon which the excise tax was computed. In addition, the 1965 revision’ dramatized how different the actual supplemental charge plan was from that proposed to Cushwa and Engel in December, 1956.
In light of this evidence, the district judge correctly found that the supplemental charges for advertising, printed matter, management consulting fees, teletype, and finance were required to be included in the price upon which the excise tax was computed; in reality, the supplemental charges constituted a portion of appellant Frue-hauf’s real price for the trailers. Co-conspirator Morris and appellant Rowan admitted as much. In September, 1964, Morris told Revenue Agent Kiefer that the denomination of the billings to distributors made no difference to appellant Fruehauf. In recorded testimony taken in 1967 by the Internal Revenue Service, appellant Rowan admitted that the costs of rendering services to appellant Fruehauf’s distributors constituted an unsegregated portion of the costs of operating several of Fruehauf’s departments and were considered by appellant Fruehauf in developing its selling prices and profit margins. In short, there was no basis for separating out the costs of the services billed in the supplemental charge plan from the costs of producing the trailers. The true price of trailers covered the costs billed for separately in the supplemental charge plan; the price upon which the excise tax was to be computed could not therefore exclude those costs.
4. The Exclusion of Handling, Installation, Make-Ready, and Delivery Charges.
Appellants contend that charges for installation, make-ready, delivery, and handling services are excludable from the excise tax base pursuant to § 4216(a). Appellee United States replies that not all such charges billed as handling or make-ready are excludable, arguing that many of these charges are charges incident to placing the article in condition, packed ready for shipment, and hence includable in the taxable price under § 4216(a) and Fitch. Appellee United States cites Lionberger v. United States, 371 F.2d 831, 842, 178 Ct.Cl. 151, cert. denied, 389 U.S. 844, 88 S.Ct. 91, 19 L.Ed.2d 110 (1967), in which it was held that a trailer manufacturer’s charges, such as “hitching the trailers, connecting tail lights, inspection, minor repair, washing, wheel greasing * * * tire care and replacement” were outside the intended scope of the exclusions enumerated in § 4216(a).
Appellee United States presents the better legal analysis. The Revenue Rulings, private letter rulings, and Technical Advice Memoranda issued by the Internal Revenue Service in this area and relied upon by appellants as supporting their position have permitted the exclusion of handling, installation, make-ready, and delivery charges after shipment to a particular customer begins, a position consistent with Fitch.
There is, however, a question of when such shipment begins. Appellants suggest it is at the inspection area of the manufacturing plant, but that can hardly be true in every case. That there is a question, though, does explain the district judge’s treatment of appellant Fruehauf’s adoption of the Hobbs method of including a handling charge in the price to retail customers but excluding that amount from the list price for the calculation of the excise tax base, an action that was questionable in view of the fact that the Fruehauf handling charge was not like the Hobbs handling charge and the fact that the Internal Revenue Service had advised that the Fruehauf handling charge was not excludable. The Fruehauf handling charge was in fact more a standard charge for putting the trailers into perfect condition ready for shipment than the Hobbs charge, which varied from sale to sale depending on the services per*1067formed. The district judge noted that the Internal Revenue Service did not approve the exclusion and that appellant Fruehauf kept a double set of invoices with respect to trailers sold to distributors in order to hide the exclusion from the Internal Revenue Service, but did not explicitly find that the exclusion was improper.
By contrast, the district judge did find that the $50 per unit make-ready allowance to distributors, which was recognized in the supplemental charges from January 1,1962, through December, 1964, was a fictitious item, established for the sole purpose of evading excise tax due with respect to trailers sold by appellant Fruehauf, and the district court had ample evidence on which to base that finding. Regardless of any technical questions with respect to handling charges, such a fictional charge cannot be justified. The institution of that charge was further proof that appellants engaged in the conspiracy charged in the indictment.
5. The Exclusion of the Warranty Allowance.
Effective September 1, 1961, the increase in distributor discount included the warranty allowance that had previously been stated on the invoices separately; by this change, appellant Fruehauf excluded the warranty allowance from the excise tax base for all sales. Appellants contend that the district judge erroneously found that the warranty allowance extended to distributors was not excludable from the taxable price of the trailer.30 Appellee United States replies that under the authority of Chrysler Corp. v. United States, 300 F.2d 154 (6th Cir. 1962), aff’g 190 F.Supp. 412 (E.D.Mich.1960), appellant Fruehauf’s warranty allowance was not a permissible exclusion from the excise tax base.
The Chrysler Corp. case does state the relevant law in this Circuit. In Chrysler Corp., the manufacturer hired its distributors to satisfy the manufacturer’s warranty obligations to ultimate customers. Warranty expenses were held not to constitute price readjustments under § 6416 of the Internal Revenue Code of 1954, 26 U.S.C. § 6416, because the sales price was for an article free of defects and the warranty expenses were thus spent for correcting defects so that the manufacturer’s part of the bargain to deliver a sound article would be satisfied. See General Motors Corp., Frigidaire Div. v. United States, 147 F.Supp. 739, 142 Ct.Cl. 878 (1957).
In the present case, implicit in certain of the district judge’s findings was the finding that distributors were given a warranty allowance in return for the distributors performing warranty services on appellant Fruehauf’s behalf,31 and thus under the Chrysler Corp. case the warranty allowance to appellant Fruehauf’s distributors could not be excluded from the taxable price of the trailers.32 Although appellants claim that the district judge based his finding that the warranty allowance was not ex-cludable on the ground that appellant Frue-hauf could not contract away any warranty obligations, it is clear that the evidence supported the implicitly stated finding that distributors performed warranty services on Fruehauf’s behalf.
The Tire Tax Credits
Appellants contend that the practice of computing tire tax credits on the basis of invoice prices stated according to the OEM *1068price lists, without reflecting any adjustment for pre-arranged rebates to Fruehauf, was arguably proper and that appellants could not therefore be prosecuted for following such a procedure. Appellants seek support in the fact that the “purchase price” of the tires, upon which the tire tax credit is to be computed, is not defined in the Internal Revenue Code. According to appellants, without such a statutory definition, their practice was not unreasonable.
We are not impressed with this argument. The incidence of federal taxation has always depended upon the substance of transactions, Commissioner of Internal Revenue v. Court Holding Co., 324 U.S. 331, 334, 65 S.Ct. 707, 89 L.Ed. 981 (1945), Owens v. Commissioner of Internal Revenue, 568 F.2d 1233 (6th Cir. 1977), and in the present case, the purchase price was unquestionably the negotiated “confidential” price. The evidence clearly established that appellant Fruehauf negotiated prices with tire companies that were below the OEM prices, that appellant Fruehauf requested that it be billed for the tires according to the OEM price lists rather than according to the negotiated prices, and that Fruehauf received monthly rebates equal to the difference between the negotiated and OEM prices. To suggest that such a procedure could raise a question of law as to the “purchase price” of tires for the purpose of the manufacturers excise tax law is simply disingenuous, and it is not unfair to say that appellant Rowan and co-conspirator Morris were aware of the complete lack of justification for the procedure followed by appellant Fruehauf in claiming tire tax credits. In 1964, during the course of the Internal Revenue Service audit, both men feigned ignorance when questioned about the practice of computing tire tax credits on the basis of invoice prices without adjustments for prearranged rebates.
Nor does a 1925 Solicitor’s Memorandum help appellants. S.M. 2706, IV — 1 Cum.Bull. 315 (1925). In the situation treated by the Solicitor’s Memorandum, rebates were given by the manufacturer to the purchaser, in accordance with trade practice, based upon a sharp post-sale decline in the market price of tires. The amount of the rebate was not known at the time of the purchase. In fact, it was not known whether there would be a rebate at all. The Solicitor’s Memorandum concluded that the original contract between the parties stated the “purchase price” and that the excise tax was to be computed on that price.
In contrast, the evidence in the present case showed that there was but one negotiated price, the “confidential” price. The rebate was in no way dependent upon subsequent events, but existed only because appellant Fruehauf had requested billing at the OEM price in order to compute tire tax credits on a higher price. That appellant Fruehauf could not legally follow such a practice can hardly be questioned. If appellant Fruehauf’s practice could be instituted, then companies in appellant Frue-hauf’s position could wipe out its excise tax liability by simply negotiating prices for tires high enough to create enough tax credits, with the understanding that a fixed portion of the “price” would be returned by the tire companies in rebates.
IV
Appellants contend that their convictions cannot be affirmed because they relied in good faith upon the advice of counsel and hence a basic element of the offense was not proved. According to appellants, it is well settled that proof that one acted on the advice of counsel negates criminal intent if the legal advisor is competent, if full disclosure of all known pertinent facts is made to counsel, and if there is a good faith attempt to follow the advice given.
Appellee United States does not quarrel with appellants’, statement of the general legal principle with respect to reliance on the advice of counsel. .What the United States does dispute is the assertion that appellants did in fact act in good faith reliance upon the advice of counsel.
We believe that the record clearly shows that appellants did not rely in good faith on the advice of counsel. Appellants did not *1069follow the advice of the attorney Cushwa and the accountant Engel concerning the supplemental charge plan. Cushwa and Engel limited their approval of the plan on the conditions that appellant Fruehauf be able to demonstrate that a particular distributor actually received the service for which the distributor was charged, that the value of the services performed in a specific case equal or exceed the amount charged, and that records be maintained showing the services rendered for each distributor and for each of the categories of supplemental fees charged. Cushwa and Engel warned that a flat charge to a distributor for some service never rendered, even though billed separately, was part of the selling price of the trailer and would have to be included in the excise tax base. As Parts I and III of this opinion reveal, appellants did not heed this counsel and incorporate into the supplemental charge plan the procedures advised by counsel to be necessary to justify breaking out the supplemental charges from the price of the trailer. The plan that was instituted bore little resemblance to the plan to which counsel gave a conditional blessing. Instead, the supplemental billings operated as a function of the trailer price and thus fell within the scope of Cushwa’s and Engel’s warning concerning flat charges to distributors.
Nor did appellants rely in good faith on counsel’s advice as to the computation of tire tax credits based on the invoiced OEM price without regard to pre-arranged rebates. At first, appellants did not even inform counsel. When co-conspirator Morris and appellant Rowan discussed the tire tax credit in March, 1958, they did not seek the advice of counsel. Instead, automobile companies were called and asked how they computed tire tax credits. After counsel was informed in December, 1958, the attorney Cushwa advised appellant Fruehauf that its method of computing tire tax credits was highly questionable and that the company should recognize the potential liability.33 As with the supplemental charge plan, appellants ignored Cushwa’s advice until the 1964 Internal Revenue Service excise tax audit forced appellants to change this practice.
Finally, appellants were not always honest with their counsel. When appellants sought counsel’s approval of the exclusion of a handling charge made to retail customers in April, 1959, appellant Rowan and co-conspirator Morris falsely represented to Cushwa that the Fruehauf handling charge was the same as the installation charge of Hobbs Trailer Company. In October, 1961, shortly after the institution of the September, 1961, increase in discount to distributors, co-conspirator Morris told Cushwa that there was no allowance to distributors for warranty expense, even though the warranty allowance was in fact concealed in the increase in discount.
V
Appellants contend that the indictment in the present case was time-barred. According to appellants, the conspiracy to aid or assist in the preparation and presentation of materially false and fraudulent excise tax returns in violation of 26 U.S.C. § 7206(2) was subject to the three-year limitation period of 26 U.S.C. § 6531,34 and the *1070conspiracy to defraud the United States was subject to the general five-year statute, 18 U.S.C. § 3282.35
Appellants’ argument is without merit. The applicable statute of limitations to the conspiracy to attempt to evade or defeat the payment of taxes in violation of 26 U.S.C. § 7201 is the six-year period stated for 26 U.S.C. § 6531(8), Braverman v. United States, 317 U.S. 49, 55, 63 S.Ct. 99, 87 L.Ed. 23 (1942), and as to that portion of the indictment, there was no bar.
A conspiracy to defraud the United States is also subject to the six-year period of 26 U.S.C. § 6531 because of the plain meaning of the terms of subsection (1) of that statute, United States v. Lowder, 492 F.2d 953 (4th Cir.), cert. denied, 419 U.S. 1092, 95 S.Ct. 685, 42 L.Ed.2d 685 (1974), but even under the five-year statute that appellants would apply, the charge was not time-barred. The last overt act alleged in the indictment was the filing of the manufacturers excise tax return for the final calendar quarter of 1965, which occurred February 8, 1966. The present indictment was returned November 9, 1970, less than five years after the last overt act in the indictment.
A conspiracy to violate 26 U.S.C. § 7206(2) is subject either to the six-year period of § 6531 or to the general five-year statute, 18 U.S.C. § 3282. As was stated in Braverman v. United States, supra, 317 U.S. at 54, 63 S.Ct. at 102, “A conspiracy is not the commission of the crime which it contemplates, and neither violates nor ‘arises under’ the statute whose violation is its object.” The three-year period stated in § 6531 covers offenses that arise under the revenue laws, excepting those enumerated as falling within the six-year period. Thus, the three-year portion of the statute cannot apply to conspiracy cases such as this one. The six-year period, however, is not by its terms strictly limited to offenses that arise under the revenue laws. Subsections (1) and (8) apply the six-year period of limitations to conspiracies to defraud the United States and to evade taxes. In the present case, those subsections determine the limitations period for the portions of the indictment alleging the conspiracy to defraud the United States and to evade taxes. Subsection (3) of § 6531 covers the substantive offense of violating 26 U.S.C. § 7206(2) but does not expressly cover the conspiracy to violate § 7206(2); however, it would be sensible to interpret § 6531 to extend subsection (3) to cover the conspiracy offense as well. But if § 6531(3) does not cover a conspiracy to violate § 7206(2), the general five-year statute does. In either event, the conspiracy to violate § 7206(2) was not time-barred.
VI
Appellants contend that their convictions must be vacated for errors of pleading and proof: (1) the indictment failed to allege willfulness as to the object offenses of the conspiracy and (2) the proof failed to show that a tax was due and owing. Appellee United States replies that appellants are improperly trying to treat the charged conspiracy as substantive revenue offenses and denies that there were any errors of pleading and proof in this conspiracy prosecution.
*1071We agree with the United States. Appellants’ contentions here are at odds with the principle that the crime of conspiracy to commit an offense is an entirely separate crime from the commission of the object offense itself. Pinkerton v. United States, 328 U.S. 640, 643, 66 S.Ct. 1180, 90 L.Ed. 1489 (1946); United States v. Rabinowich, 238 U.S. 78, 86, 35 S.Ct. 682, 59 L.Ed. 1211 (1915).
In Wong Tai v. United States, 273 U.S. 77, 81, 47 S.Ct. 300, 301, 71 L.Ed. 545 (1927), the Supreme Court treated the question of what precision in pleading object offenses was required in a conspiracy indictment.
It is well settled that in an indictment for conspiring to commit an offense — in which the conspiracy is the gist of the crime — it is not necessary to allege with technical precision all the elements essential to the commission of the offense which is the object of the conspiracy, Williamson v. United States, 207 U.S. 425, 447, 28 S.Ct. 163, 52 L.Ed. 278, or to state such object with the detail which would be required in an indictment for committing the substantive offense, Thornton v. United States, 271 U.S. 414, 423, 46 S.Ct. 585, 70 L.Ed. 1013; Jelke v. United States (C.C.A. 5 Cir.), 255 F. 264, 275; Anderson v. United States (C.C.A. 8 Cir.), 260 F. 557, 558; Wolf v. United States (C.C.A. 7 Cir.), 283 F. 885, 886; Goldberg v. United States (C.C.A. 8 Cir.), 277 F. 211, 213. In charging such a conspiracy “certainty to a common intent, sufficient to identify the offense which the defendants conspired to commit, is all that is necessary.” Williamson v. United States, supra, 207 U.S. 447, 28 S.Ct. 163; Goldberg v. United States, supra, 213.
See United States v. Branan, 457 F.2d 1062, 1063-65 (6th Cir. 1972); United States v. Mixon, 374 F.2d 20, 22 (6th Cir. 1967); Davis v. United States, 253 F.2d 24, 25 (6th Cir. 1958). The indictment in the present case identified the object offenses, referring appellants to the specific statutory sections involved, and for the purpose of an indictment charging a conspiracy offense, that was sufficient. Davis v. United States, supra, 253 F.2d at 25. Moreover, the indictment in the present case charged that appellants “then and there well knew” that Fruehauf’s excise tax liability was understated, which is a statement that appellants did have a willful state of mind with respect to the tax evasion and false returns object offenses of the conspiracy.36 In Wong Tai, the Supreme Court upheld an indictment that used the term “well knowing” in connection with the object offense of the conspiracy.
As for the alleged failure to prove that a tax was due and owing, the short answer to appellants’ contention is that such proof was not necessary. The gist of the crime of conspiracy is the agreement to commit an illegal act, not the accomplishment of the illegal act. United States v. Rabinowich, supra, 238 U.S. at 87-89, 35 S.Ct. 682.
Contrary to appellants’ statements, the Supreme Court cases of Sansone v. United States, 380 U.S. 343, 85 S.Ct. 1004, 13 L.Ed.2d 882 (1965), Lawn v. United States, *1072355 U.S. 339, 78 S.Ct. 311, 2 L.Ed.2d 321 (1959), and Spies v. United States, 317 U.S. 492, 63 S.Ct. 364, 87 L.Ed. 418 (1943), do not stand for the proposition that there can be no conspiracy to attempt to evade a tax that is not due and owing. The Sansone and Spies decisions are strictly substantive tax evasion cases that do not even discuss the question of conspiracy. The Lawn decision, when treating the conspiracy aspect of the case, does not require the showing of a tax deficiency.
Nor are Ingram v. United States, 360 U.S. 672 (1959), and United States v. Andrews, 347 F.2d 207 (6th Cir.), cert. denied, 382 U.S. 956, 86 S.Ct. 431, 15 L.Ed.2d 360 (1965), of any assistance to appellants’ case.37 In Ingram v. United States, supra, the Supreme Court held that in a gambling tax conspiracy case, the defendants had to know they were liable for federal taxes by reason of the gambling operations. In United States v. Andrews, supra, this Court stated that “convictions for conspiracy to evade federal gambling tax laws cannot be sustained absent proof 1) that defendants were parties to an agreement to defeat or evade the taxes, or 2) that defendants had knowledge that the taxes were due and were not being paid, plus conduct in furtherance of a plan to evade them” (emphasis supplied).
Even if it were necessary in this conspiracy case for the United States to plead and prove that taxes were due and owing (and it is not), the Government carried that burden. The indictment charged and the district judge found that appellant Fruehauf had substantially understated its excise tax liability in its returns during the period of the conspiracy as a result of the supplemental charge plan and excessive tire tax credits. The district judge also found that there were taxes owing for each of the last five calendar quarters listed in the indictment, the last quarter of 1964 and the four quarters of 1965. Appellants’ contention that against these deficiencies they are entitled to set off certain overpayments, resulting from the tax paid on nontaxable refrigeration units, in order to defeat criminal liability is ridiculous.
VII
Appellants raise a number of arguments in support of their contention that they were denied a fair trial. None of the arguments, however, have any merit. The district judge did not engage in any improper ex parte communications with Government counsel or witnesses. The district judge did not err in refusing to grant an evidentiary hearing concerning the grand jury’s possible knowledge of Regulations 316 and 330. Appellants’ claims concerning the “Surrey letter” are frivolous. The findings of fact entered by the district judge fully complied with the requirements of Rule 23(c) of the Federal Rules of Criminal Procedure. See B. F. Goodrich Co. v. Rubber Latex Products, Inc., 400 F.2d 401, 402 (6th Cir. 1968); Deal v. Cincinnati Board of Education, 369 F.2d 55, 63-64 (6th Cir. 1966), cert. denied, 387 U.S. 847, 88 S.Ct. 39, 19 L.Ed.2d 114 (1967); United States v. Peterson, 338 F.2d 595, 598 (7th Cir. 1964), cert. denied, 380 U.S. 911, 85 S.Ct. 896, 13 L.Ed.2d 798 (1965). Finally, the district judge did not err in his rulings-' on the admissibility of evidence.
The judgments of conviction are affirmed.
. District Judge Thornton’s opinion has been reported unofficially. United States v. Fruehauf Corporation, et al., 75-2 U.S.Tax Cas. 16,207, 36 Am.Fed.Tax R.2d 75-5979 (E.D. Mich. July 17, 1975).
. 18 U.S.C. § 371 provides:
If two or more persons conspire either to commit any offense against the United States, or to defraud the United States, or any agency thereof in any manner or for any purpose, and one or more of such persons do any act to effect the object of the conspiracy, each shall be fined not more than $10,000 or imprisoned not more than five years, or both.
If, however, the offense, the commission of which is the object of the conspiracy, is a misdemeanor only, the punishment for such conspiracy shall not exceed the maximum punishment provided for such misdemeanor.
. Appellants argue that the district judge’s findings are clearly erroneous even when the evidence is viewed in the light most favorable to the United States. Appellants complain that the district judge did not consider their evidence, and they refer this Court to the evidence in the record that supports their version of the facts.
While appellants correctly acknowledge that this Court reviews the findings of the district judge under the “clearly erroneous” standard and must consider the evidence in the light, most favorable to the United States as to the specific findings made by the district judge, the arguments pressed by appellants on this issue fail to recognize that a district judge’s finding *1042of fact is not clearly erroneous simply because there is evidence in the record that might support a different finding. Our review of the evidence leads us to conclude that all the findings of fact were supported by substantial evidence. In fact, this was not a close case. For a few examples that illustrate the lack of merit to appellants’ attack on the district judge’s findings of fact, see footnotes 9, 10, 13, 15, and 16.
. As originally enacted in 1954, 26 U.S.C. § 4061(a) provided:
(a) Automobiles. — There is hereby imposed upon the following articles (including in each case parts or accessories therefor sold on or in connection therewith or with the sale thereof) sold by the manufacturer, producer, or importer a tax equivalent to the specified percent of the price for which so sold:
(1) Articles taxable at 8 percent, except that on and after April 1, 1955, the rate shall be 5 percent—
Automobile truck chassis.
Automobile truck bodies.
Automobile bus chassis.
Automobile bus bodies.
Truck and bus trailer and semitrailer chassis. Truck and bus trailer and semitrailer bodies. Tractors of the kind chiefly used for highway transportation in combination with a trailer or semitrailer.
A sale of an automobile, truck, bus, truck or bus trailer or semitrailer shall, for the purposes of this paragraph, be considered to be a sale of the chassis and of the body.
(2) Articles taxable at 10 percent except that on and after April 1, 1955, the rate shall be 7 percent—
Automobile chassis and bodies other than those taxable under paragraph (1).
Chassis and bodies for trailers and semitrailers (other than house trailers) suitable for use in connection with passenger automobiles.
Motorcycles.
A sale of an automobile, trailer, or semitrailer shall, for the purposes of this paragraph, be considered to be a sale of the chassis and of the body.
(b) Parts and accessories. — There is hereby imposed upon parts or accessories (other than tires and inner tubes and other than automobile radio and television receiving sets) for any of the articles enumerated in subsection (a) sold by the manufacturer, producer, or importer a tax equivalent to 8 percent of the price for which so sold, except that on and after April 1, 1955, the rate shall be 5 percent.
. 26 U.S.C. § 4216(a) provides:
(a) Containers, packing and transportation charges. — In determining, for the purposes of this chapter, the price for which an article is sold, there shall be included any charge for coverings and containers of whatever nature, and any charge incident to placing the article in condition packed ready for shipment, but there shall be excluded the amount of tax imposed by this chapter, whether or not stated as a separate charge. A transportation, delivery, insurance, installation, or other charge (not required by the foregoing sentence to be included) shall be excluded from the price only if the amount *1043thereof is established to the satisfaction of the Secretary or his delegate in accordance with the regulations.
. 26 U.S.C. § 4216(b)(1), as amended effective January 1, 1959, provides:
(b) Constructive sale price—
(1) In general. — If an article is—
(A) sold at retail,
(B) sold on consignment, or
(C) sold (otherwise than through an arm’s length transaction) at less than the fair market price,
the tax under this chapter shall (if based on the price for which the article is sold) be computed on. the price for which such articles are sold, in the ordinary course of trade, by manufacturers or producers thereof, as determined by the Secretary or his delegate. In the case of an article sold at retail, the computation under the preceding sentence shall be on whichever of the following prices is the lower: (i) the price for which such article is sold, or (ii) the highest price for which such articles are sold to wholesale distributors, in the ordinary course of trade, by manufacturers or producers thereof, as determined by the Secretary or his delegate. This paragraph shall not apply if paragraph (2) applies.
. Prior to the amendment of 26 U.S.C. § 4216(b) in 1959, appellant Fruehauf had the benefit of a private letter ruling issued to it by the Treasury Department, dated December 29, 1949, stating that the excise tax was to be based on the discounted price at which sales were made at wholesale to independent distributors. Except for the question of the excise tax treatment of a warranty allowance to distributors, there was no issue at trial as to appellant Fruehaufs entitlement throughout the period of the alleged conspiracy to compute its excise tax on all sales based on the wholesale price, even though over 90% of its sales were at retail.
. 26 U.S.C. § 6416(c) provides:
(c) Credit for tax paid on tires or inner tubes. —If tires or inner tubes on which tax has been paid under chapter 32 are sold on or in connection with, or with the sale of, another article taxable under chapter 32, there shall (under regulations prescribed by the Secretary or his delegate) be credited (without interest) against the tax imposed on the sale of such other article, an amount determined by multiplying the applicable percentage rate of tax for such other article by—
(1) the purchase price (less, in the case of tires, the part of such price attributable to the metal rim or rim base), if such tires or inner tubes were taxable under section 4071 (relating to tax on tires and inner tubes); or
(2) if such tires or inner tubes were taxable under section 4218 (relating to use by manufacturer, producer, or importer), the price (less, in the case of tires, the part of such price attributable to the metal rim or rim base) at which such or similar tires or inner tubes are sold, in the ordinary course of trade, by manufacturers, producers, or importers thereof, as determined by the Secretary or his delegate.
The credit provided by this subsection shall be allowable only in respect of the first sale on or in connection with, or with the sale of, another article on the sale of which tax is imposed under chapter 32.
. District Court Finding No. 23 states:
Messrs. Rowan, Morris and Chawner were aware that Cushwa’s approval of the exclusion of the supplemental charges from Frue-hauf’s constructive tax base was predicated upon the maintenance of records which would demonstrate that the charges were for actual extra services performed, and that the value of the services in a specific case eq-ualled or exceeded the amounts charged (GX 2, Q. and A. 186-188; Tr., V. 5, pp. 526-527).
Appellants contend that testimony taken from the attorney Cushwa in a deposition and read into the record during the cross-examination of co-conspirator Morris showed that the supplemental charges for services to distributors did not have to be limited to the actual costs incurred by appellant Fruehauf so long as the charges were reasonable and that the charges were excludable from the excise tax base, notwithstanding the lack of records, because it was the existence of the services and not the records that justified the exclusion.
The problem with this argument is that it ignores the evidence supporting the district judge’s finding. The memorandum written by Engel, admitted into evidence as Government Exhibit 16, stresses that the approval given to the supplemental charge plan, given at the December 13, 1956, meeting in Washington, D.C., by Cushwa and Engel, was conditioned on the limiting of supplemental charges to the value of the services and on the maintenance of records to substantiate the rendition of services. In addition, the testimony of co-conspirator Morris at trial and of appellant Rowan in an interview with the Internal Revenue Service in 1967 was that there was an understanding at Frue-hauf that records would have to be maintained to substantiate the services that were billed in the supplemental charge plan. Without the records, appellant Fruehauf would not be able to prove that the charges for the services could be properly segregated from the billing for the cost of the trailers and there would not be a safeguard against tax evasion.
. District Court Finding No. 38 states:
As designed and implemented, the monthly supplemental billing to each distributor eq-ualled, in total, the 3.75 percent increase in discount (GX 22; GX 3, Q. and A. 394).
The evidence relied upon by appellants in contending that this finding of fact was clearly erroneous only supports the finding. Appellants note that appellant Rowan testified that it was agreed with distributors that a condition of separately billing them for the services under the supplemental charge plan was that such supplemental charges would not exceed 3.75% of the list price of new trailers invoiced to them. Conveniently overlooked by appellants is the fact that the limitation on the total supplemental charges to each distributor was equal to the increase in the distributor discount that was instituted along with the supplemental billings. Appellants also ignore the evidence of the “Distributor Analysis of Price Adjustment” work sheets, introduced into evidence as Government Exhibit 22.
. When the supplemental charges were instituted, they were applied retroactively to October 1, 1956.
. The district judge found that in July, 1957, one distributor was charged in excess of $600 per unit for national advertising. The finding is not clearly erroneous because it is substantiated in Government Exhibit 22, but this Court’s statement of facts points to other figures taken from Government Exhibit 22 in order to present a more accurate indication of the level of supplemental charges in the summer and autumn of 1957.
. District Court Finding No. 96 states:
In February and March 1962 co-conspirator Chawner advised distributors that the $50 per unit increase in the supplemental charges for handling was strictly fictional for the purpose of saving $5 in excise tax (GX 115-118).
Appellants argue that co-conspirator Chawner never advised distributors that the increase in the supplemental charges was fictional and that a reading of Government Exhibits 115 through 118 demonstrates the error. Those exhibits, however, clearly speak for themselves and fully support the district judge’s finding.
. Government Exhibit 155.
. District Court Finding No. 104 states:
The “tire tax credit” claimed against Frue-hauf’s excise tax liability was computed from schedules prepared by co-conspirator Morris based on the O.E.M. prices, without regard to rebates received (Tr., V. 9, 1017, and V. 24, p. 2800; GX 43).
Appellants complain that the testimony of co-conspirator Morris indicates that a Virginia Ruesman prepared the schedules to which the district judge referred in his finding and that Virginia Ruesman was not instructed by co-conspirator Morris concerning the schedules. Appellants’ reference to a subordinate of co-conspirator Morris is disingenuous. Moreover, the testimony of co-conspirator Morris and Revenue Agent Kiefer clearly indicates that Fruehauf s Tax Department, headed by co-conspirator Morris, prepared the schedules.
. District Court Finding No. 115 states:
On November 23, 1964 Mr. Rowan stated to Revenue Agent Kiefer that the tire tax credit was computed on the O.E.M. price rather than the negotiated price as the result of an oversight (Tr., V. 24, pp. 2793-2794).
Appellants contend that a review of the evidence would show that appellant Rowan never *1054made the statement attributed to him in the finding. In the testimony of Revenue Agent Kiefer, however, Kiefer testified that he asked appellant Rowan why he had not advised co-conspirator Morris and his Tax Department concerning the tire rebates. At the time, co-conspirator Morris was claiming ignorance about the rebates. Appellant Rowan told Revenue Agent Kiefer that it must have been overlooked.
. Treated in Part III will be the issues raised by appellants and appellee United States as to the tire tax credit, the relevancy of certain regulations, and the evidence of the conspiracy, issues which were briefed in connection with the variance argument but which can be better handled in Part III.
. Indictment Subparts (10), (11), and (12) state:
(10) that defendant ROWAN and co-conspirator Morris sought approval of independent attorneys and accountants to lower the wholesale price tax base by representing to them that the defendant FRUEHAUF CORPORATION performed “extra services” for wholesalers which it did not perform for other FRUEHAUF customers, and that the charges for these “extra services” were included in the invoiced prices to the wholesalers, thus allegedly overstating the wholesale tax price base; whereas it was well known that FRUEHAUF never had nor did it intend to furnish any of these “extra services” to the wholesalers.
THE GRAND JURY CHARGES that, in addition, it was a part of the conspiracy:
(11) that the invoiced price to the wholesalers would be reduced by an arbitrary percentage to establish a false lower Excise Tax base, and that a substantial amount would then be recouped in the form of supplemental billings for these nonexistent services.
(12) that elaborate accounting and invoicing procedures were set up by ROWAN, Chawner and Morris for the benefit of defendant FRUEHAUF CORPORATION wherein the charges for these false services were concealed in such a manner as to escape detection upon an Internal Revenue Service audit. .
. Watson v. Jago, 558 F.2d 330 (6th Cir. 1977), was before this Court on appeal of the denial by a federal district court of the defendant’s petition for a writ of habeas corpus. We held that the defendant was entitled to the issuance of the writ, conditioned on the State’s right to retry the defendant, because as a consequence of the constructive amendment to the indictment, the defendant was deprived of his right to fair notice of the criminal charges to be brought against him, which was guaranteed to him by the Fourteenth Amendment.
. Indictment Subparts (1), (2), and (3) state: Vio: Section 371, Title 18, United States Code (Conspiracy) THE GRAND JURY CHARGES:
COUNT ONE
That on or about October 1, 1956, the exact date being unknown to the Grand Jury, and continuously thereafter up to and including February 8, 1966, in the Eastern District of Michigan and in other judicial districts of the United States, the FRUEHAUF CORPORATION (known prior to May 2, 1963, as the Fruehauf Trailer Company), and WILLIAM E. GRACE and ROBERT ROWAN, defendants, and Robert M. Chawner (now deceased), and Kenneth A. Morris, co-conspirators but not defendants, wilfully and unlawfully conspired with each other, and with other persons unknown to the Grand Jury, to:
(1) defraud the United States by impeding, impairing, obstructing and defeating the lawful governmental functions of the Internal Revenue Service (IRS) of the Treasury Department of the United States in the ascertainment, computation, assessment, and *1057collection of $12,344,587.31 in Federal Manufacturer’s Excise Taxes;
(2) attempt to evade and defeat (contrary to Section 7201, Title 26, United States Code), the payment of $12,344,587.31 in Federal Excise Taxes to be due and owing and due and owing to the United States by the FRUEHAUF CORPORATION for the period October 1, 1956, through December 31, 1965;
(3) aid or assist in, and procure, counsel and advise the preparation and presentation (in violation of Section 7206(2), Title 26, United States Code), of materially false and fraudulent Excise Tax Returns (IRS Form 720) for the defendant FRUEHAUF CORPORATION for all calendar quarter years beginning October 1, 1956, and ending December 31, 1965, the returns understating the amount of Excise Tax payable by FRUE-HAUF CORPORATION totaling $12,344,-587.31.
. See footnote 18 for the indictment particulars with respect to the supplemental charge plan. Indictment Subparts (13) and (14) -alleged the particulars concerning the excessive tire tax credits.
(13) that on behalf of defendant FRUE-HAUF CORPORATION, defendant WILLIAM E. GRACE and other FRUEHAUF CORPORATION employees and the agents negotiated with various tire manufacturers for a precise and confidential contract price for tires used on FRUEHAUF products, but that these tire manufacturers were required by defendant GRACE to invoice FRUEHAUF CORPORATION at higher original equipment manufacturer (O.E.M.) prices followed up with a cash rebate from the tire manufacturer to FRUEHAUF CORPORATION for the difference between the higher O.E.M. invoiced price and the actual lower confidential contract price;
(14) that defendant FRUEHAUF CORPORATION, acting through its officers: defendants GRACE and ROWAN, and co-conspirator Morris, would knowingly and wilfully claim a Manufacturer’s Excise Tax credit based upon the higher O.E.M. invoiced price rather than the lower confidential contract price, thus substantially overstating the credit and substantially understating the Manufacturer’s Excise liability owed and owing by FRUEHAUF CORPORATION to the United States.
. Appellants contend in their reply brief that United States v. Ragen, 314 U.S. 513, 62 S.Ct. 374, 86 L.Ed. 383 (1942), is irrelevant in the absence of a district court finding that the distributors were billed for services never received. The Supreme Court rejected this argument in Ragen, supra, 314 U.S. at 524-25, 62 S.Ct. 374.
The respondents, however, raise a further objection going not to the propriety of such a submission as a matter of law, but to the insufficiency of the evidence upon which the jury could have found an answer to the question submitted. They contend that the record discloses that the recipients of commissions performed some services; that the record fails to show that the services disclosed were the only services rendered; that there was no direct testimony as to the total amount of services rendered or the reasonable value thereof; and that, therefore, the jury had no rational basis upon which to conclude that the sums deducted as “commissions” were more than a reasonable allowance for compensation for the services rendered. We must reject this contention.
. It would be inaccurate to say, as appellants seem to do, that the district judge relied solely on the condition of sale theory. The district judge found that the 1962 $50 per unit make-ready allowance to distributors (recouped in the supplemental billings) was fictional. District Court Finding No. 132. The district judge found that the amounts charged as interest were not really for interest. District Court Finding No. 133. The district judge made findings concerning the Southern Railway and Indiana gross income tax incidents, in which the supplemental charges appeared patently fic*1059tional. District Court Findings Nos. 74-77, 109-12. In addition, it should be observed that the district judge, in finding that certain charges were required to be included in the taxable price of the trailers, was not therefore concluding that the charge was actually for the service or that the value of the service equalled the amount charged in the supplemental billing. See Part III of this opinion.
. See footnote 4.
. See footnote 5. The term “other charge” in the statute was interpreted by the Supreme Court in Fitch Co. v. United States, 323 U.S. 582, 65 S.Ct. 409, 89 L.Ed. 472 (1945), to mean charges similar in nature to transportation, delivery, insurance, or installation charges.
. Regulation § 316.12 provides:
Exclusion of charges for transportation, delivery, etc., generally. — Charges for transportation, delivery, insurance, installation, and other charges actually incurred in connection with the delivery of an article to a purchaser pursuant to a bona fide sale, are to be excluded in computing the tax.
No other additional charge may be excluded in computing the tax unless it can -be shown by adequate records to the satisfaction of the Commissioner that such charge properly is not to be included ^is a manufacturing or selling expense, or is in no way incidental to placing the article in condition packed ready for shipment.
. For Regulation § 330.1-l(b), see Part I of this opinion.
. Appellants deny that Regulations 316 and 330 constituted an administrative recognition of the Fitch case, but appellants’ arguments are quite unimpressive on this point. First, appellants quote language in a reversed district court case, Stowe-Woodward, Inc. v. United States, 200 F.Supp. 855 (D.Mass.1961), rev’d, 306 F.2d 678 (1st Cir. 1962), cert. denied, 371 U.S. 949 (1963). The quoted language is sup*1062posed to inform us that the Government did not in the Stowe-Woodward case recognize Fitch as creating a flat rule including all pre-shipment expenses in the taxable price, but all that the quoted language indicates is that the Government would not rule out including in the taxable price certain postshipment but presale expenses. The Government won on appeal in the First Circuit, which relied upon Fitch in deciding the case. Second, appellants reproduce one Internal Revenue Service memorandum concerning T.D. 6340 and the exclusion of cooperative advertising charges from the excise tax base. Appellants note that Fitch is not quoted in the memorandum. We believe, however, that this memorandum is not much support for appellants’ position.
. 26 U.S.C. § 4216(f), enacted to be effective January 1, 1961, provides for the exclusion of local advertising charges from the sale price ■ definition in 26 U.S.C. § 4216(a).
. Appellants contend that the warranty allowance question was not properly in the case because it was not included in the indictment. While it is true that the warranty issue is not specifically addressed in the indictment, the indictment does refer to the arbitrary, false reduction of the wholesale price by appellants, an allegation that would include this warranty allowance question. Furthermore, our review of appellants’ Motion for a Bill of Particulars and the Government’s Response does not reveal to us that the Government failed to disclose the question or that the question was removed from the case by any Government response.
. District Court Findings 25, 31, and 126.
. The price readjustment provisions of 26 U.S.C. § 6416(b) and the definition of price provisions of 26 U.S.C. § 4216(a) are to be read in pari materia. Waterman-Bic Pen Corp. v. United States, 332 F.2d 711, 714 (2d Cir. 1964).
. Government Exhibits 83, 103, and 104.
. 26 U.S.C. § 6531 provides in pertinent part: No person shall be prosecuted, tried, or punished for any of the various offenses arising under the internal revenue laws unless the indictment is found or the information instituted within 3 years next after the commission of the offense, except that the period of limitation shall be 6 years—
(1) for offenses involving the defrauding or attempting to defraud the United States or any agency thereof, whether by conspiracy or not, and in any manner;
(2) for the offense of willfully attempting in any manner to evade or defeat any tax or the payment thereof;
(3) for the offense of willfully aiding or assisting in, or procuring, counseling, or advising, the preparation or presentation under, or in connection with any matter arising under, the internal revenue laws, of a false or fraudulent return, affidavit, claim, or document (whether or not such falsity or fraud is with the knowledge or consent of the person authorized or required to present such return, affidavit, claim, or document);
*1070(4) for the offense of willfully failing to pay any tax, or make any return (other than a return required under authority of part III of subchapter A of chapter 61) at the time or times required by law or regulations;
(5) for offenses described in sections 7206(1) and 7207 (relating to false statements and fraudulent documents);
(6) for the offense described in section 7212(a) (relating to intimidation of officers and employees of the United States);
(7) for offenses described in section 7214(a) committed by officers and employees of the United States; and
(8) for offenses arising under section 371 of Title 18 of the United States Code, where the object of the conspiracy is to attempt in any manner to evade or defeat any tax or the payment thereof.
. 18 U.S.C. § 3282 provides:
Except as otherwise expressly provided by law, no person shall be prosecuted, tried; or punished for any offense, not capital, unless the indictment is found or the information is instituted within five years next after such offense shall have been committed.
. The “overt acts” section of the indictment makes this allegation.
OVERT ACTS
THE GRAND JURY FURTHER CHARGES: That on or about 30 days after the close of each quarter year shown in Column 1 below, at the office of the District Director of Internal Revenue for the Internal Revenue District of Michigan, in Detroit, Michigan, and in furtherance of, in the execution of and for the purpose of carrying into effect the object, design and purpose of the conspiracy, the defendant FRUEHAUF CORPORATION by and through its officers: defendants GRACE and ROWAN, and co-conspirator Morris, and other corporate employees and agents unknown to the Grand Jury, filed quarterly Manufacturer’s Excise Tax Returns (IRS form 720) purporting to show an Excise Tax liability of defendant FRUEHAUF CORPORATION (Column 2), when in fact the defendants GRACE and ROWAN and co-conspirator Morris then and there well knew that the purported Excise Tax liability was substantially understated (Column 3), and that the true and correct Excise Tax liability for each quarter year was that shown in Column 4; the conspiracy being a violation of Section 371, Title 18, United States Code.
. Appellants also cite United States v. DeNiro, 392 F.2d 753 (6th Cir.), cert. denied, 393 U.S. 826, 89 S.Ct. 89, 21 L.Ed.2d 97 (1968), but that case only in passing discusses the need for knowledge of tax liability to sustain a tax conspiracy conviction and is no support for the broad propositions of law that appellants press to this Court.