United States Gypsum Company (USG) and United States Gypsum Export Company (Export), a wholly owned subsidiary of USG, brought actions for refund of income taxes. Some of taxpayers’ claims were established. The only issues before us on appeal relate to offsets claimed by the government on account of reallocations of income under 26 U.S.C. § 482 between USG and Export and between USG and another subsidiary, Panama Gypsum Company, Inc. (PG). The decision of the district court *447is reported at 304 F.Supp. 627 (N.D.Ill., 1969), and we shall avoid unnecessary-repetition.
The Shipping Issue.
PG provided shipping service to USG, its parent corporation, during a number of years, including 1954, 1955, 1957 and 1958, the years in question. The government claims that the compensation paid by USG to PG was excessive. 26 U.S.C. § 482, in part, authorizes the Secretary or his delegate to allocate gross income, deductions, etc., between a parent and subsidiary if he determines that such allocation is necessary in order clearly to reflect their respective incomes.
As stated in the government’s brief: “If, upon examination, it is determined that the dealings between the corporations under common control do not approximate what would have taken place between uncontrolled corporations dealing at arm’s length, a reallocation of income is required under Section 482 to clearly reflect the income of the separate taxable entities involved.”
The district court found “that the rates set, though they may have been relatively high and were not actually negotiated at arm’s length but arbitrarily set, were reasonably- within the range of what would have been charged for similar services in an independent transaction between unrelated parties under similar circumstances. Even with its well informed hindsight, the government has presented no persuasive evidence that the rates were unreasonable.” The court found that the resulting income should not be reallocated, (p. 635)
PG and USG entered into long term contracts of affreightment, under which PG charged USG a freight rate per ton for carriage of gypsum rock from ports near the sources to ports serving USG’s plants. The rate was computed by taking the cost of time chartering a ship, of a type suitable for the purpose and then available on the market for charter, adding expenses which a charterer on a time-charter basis would have to bear (fuel, port charges, and administrative burden), dividing this total cost of a round trip by the number of tons the prototype ship could carry, and adding 25 cents per ton for unloading (15 cents per ton beginning in 1955).
The ships actually used were larger and faster than the prototype and the expenses of operation lower. They were specially built so as to meet certain problems peculiar to the port at the Canadian source of supply, and, except for the King, carried equipment which, when used with equipment at the ports of destination, made the ships self-unloading. No closely comparable ships were available. The agreed rate per ton was not adjusted to reflect the greater efficiency of the specially built ships, and unless some other adverse factor were to operate, the rate would be very advantageous to PG. On the other hand PG was exposed to the risk that USG would not need enough rock to keep the ships busy and that loss would result from idleness if alternative uses could not be found.
It turned out in fact that the ships were kept busy and PG enjoyed a high profit at the per ton rates under these contracts. The real question is whether people dealing at arm’s length would have deemed the advantageous rate per ton a reasonable, though not directly related, offset for PG’s assuming the risk of slack usage.
The choice of this approach was described by Mr. Rembert, Executive Vice President of USG. Mr. Bardelmaier, the expert called by USG, testified that the Rembert approach was fair and reasonable, although he considered the 25 cents per ton for unloading unrealistically low, and therefore favorable to USG as shipper. He made comparisons of the agreed rate with rates constructed on other bases, including the rates he thought he would have charged if he had been an independent ship owner offering to perform the same service. In each comparison he found the agreed rate reasonably in line or lower.
*448Mr. Kerwin, the government’s expert, stated his opinion that a long term time charter would have been the only practical form of agreement under the circumstances. Under such a charter, USG would have assumed any risk of underemployment of the ships. Proceeding on this basis, and with knowledge of the actual use of PG’s ships during the years in question, Kerwin computed USG’s transportation costs (1) “based on the actual voyage expenses, plus the minimum vessel expense which an owner would have accepted’’ and (2) “based on the actual voyage expenses, plus the maximum amount which a shipper would have reasonably paid.” He included amounts which he deemed appropriate for the owner’s profit and depreciation. The results were very substantially below the amounts paid by USG to PG during the respective years.
On cross-examination, it was developed that Mr. Kerwin’s figures did not represent a projection of a long term contract as of the time of contracting. “Q. * " * You have taken the costs and pulled them back into a time charter, have you not ?” A. “Yes.”
“Q. You didn’t do like Mr. Bardelmaier did and put himself in our place in 1947 and again in 1954 and try to project rates for a long-term contract? You did not approach it that way?”
“A. This was not my approach.”
Thus Mr. Kerwin’s analysis was open to the interpretation that it was, in effect, a retroactive renegotiation of the agreement for the purpose of limiting the ship owner to a reasonable profit rather than a reconstruction of bargaining over an agreement to cover future conduct.
We might well speculate that if parties under similar circumstances had been dealing at arm’s length, and had acquired the experience from 1948 to 1954, they might, by 1954 and later years, have worked out a deal which would have cost the shipper less and returned to the ship owner a lower, yet still reasonable, profit. Nevertheless, we are unable to say, on this record, that the finding of the district court that the shipping charges were those which would have been arrived at by dealings at arm’s length was clearly erroneous.
Whether the district court addressed itself to precisely the proper issue is not free from doubt. The problem arises because the district court was, in effect, reviewing an ex parte administrative decision to allocate, and many decisions refer to the power to allocate as discretionary, stating that an allocation between taxable entities under common control is to be upheld in court unless the court finds the allocation is unreasonable, arbitrary, or capricious.1
We note that the Treasury Regulations, 26 CFR § 1.482 have recognized close restrictions upon the breadth of discretion which might reasonably have been read into the statute. Under those provisions the key question is whether the terms of transactions under consideration are such as would have been arrived at in independent transactions with or between unrelated parties under similar circumstances, considering all relevant facts. This key question is factual in nature, and such nature tends to narrow any difference between an issue whether a price was equivalent to an arm’s length price and an issue whether an administrator’s ex parte decision that it was not an arm’s length price is unreasonable, arbitrary, or capricious.
*449Our recent decision in Baldwin-Lima-Hamilton2 implies that the question of what terms would have been arrived at in arm’s length dealing is a question of fact to be resolved by the court, for when it appeared that some allocation was appropriate, but the allocation made by the Commissioner was erroneous, we remanded the case with instructions that the court determine the proper allocation.
Bearing in mind that the district court expressly found the government’s evidence unpersuasive, and that the government has not really addressed argument to the distinction above suggested, we treat the district court’s finding as equivalent to a finding that the administrative decision that the charges were not arm’s length charges was unreasonable, arbitrary, and capricious, and deem the finding not clearly erroneous.
The issue as to USG’s payments to PG for transportation is before us on the government’s appeal. With respect to this issue, the judgment will be affirmed.
Prices of goods sold to Export.
In 1954, USG organized Export as a Western Hemisphere trade corporation in order to take advantage of favorable tax provisions. 3 Export purchased finished products including felt, paper, and building materials from USG and resold them in Canada, Mexico, South and Central America and the West Indies. The great bulk of its sales were to Canadian Gypsum Company, another subsidiary of USG. It employed only two salesmen and they worked in Latin America and the Caribbean.
USG’s price to Export amounted to cost plus depreciation plus 3%%. It seems clear that Export performed only a minimal service in the distribution of these products, yet its markup on sales to Canadian was 77% in 1957, 72% in 1958, and on sales to non-controlled buyers 47% and 56%. The opinion of the government’s expert was “that under no circumstances that I could consider reasonable could an arm’s length pricing possibly have resulted in the allocation of profits that actually occurred.” The experts called by USG did not testify that the prices charged would have been arrived at by independent parties dealing at arm’s length. At best for taxpayers, one of the experts indicated that USG’s small markup over cost “could produce a reasonable profit to USG.”
It appears from the opinion of the district court, 304 F.Supp. at pp. 644, 645, that consideration of the evidence virtually persuaded the district court that USG’s prices to Export were substantially lower than the prices which would have been arrived at by unrelated parties dealing at arm’s length. Certain decisions, listed in the opinion, however, led the district court to find that “the distribution of income between USG and Export was not unreasonable and clearly reflects the income of both taxpayers.” We do not consider the cited cases helpful in deciding whether, as a matter of fact, USG’s prices to Export were the same as would have been reached in arm’s length dealing. Insofar as these eases support a proposition that there may be “reasonable” prices, different from those which would have been reached in arm’s length dealing, which will result in clearly reflecting the income of controlled taxpayers, we respectfully decline to follow them. We approve the district court’s statements indicating that the USG prices were not arm’s length prices, and conclude that the ultimate finding was clearly erroneous. A fortiori, the administrative decision to allocate could not be said to be unreasonable, arbitrary, or capricious.
For 1957 and 1958, the District Director at Chicago notified USG that he had allocated all Export’s taxable income to USG.4 USG argues that although the *450district director was a delegate of the Secretary, he failed to include sufficient information why the allocation was necessary to prevent evasion or clearly to reflect income. Moreover, noting that in defending the action for refund, the government attorneys have claimed less than complete allocation, USG contends that the only allocation made by a proper officer had been conceded to be arbitrary and the court had no basis for considering the partial allocations for which the government attorneys did contend.
We think USG’s approach is more formalistic than is soundly required under the circumstances, even though the allocation which the district court was asked to recognize was based upon theories which would not support the allocation made by the proper officer. These are refund actions in which the taxpayer must not only show the commissioner’s error in the tax demanded and paid, but also the correct amount of the tax owed and the resulting overpayment.5 We have held that where a district court has found grounds for allocation but that the allocation made is improper, it may proceed to determine a correct one.6 We think that particularly in refund suits, where wide latitude for equitable set-off is permitted the government, even minimal formal action by a delegate of the Secretary ought to be recognized as foundation for considering an otherwise meritorious case for allocation necessary clearly to reflect income.
The issue as to USG’s prices for sales for finished products to Export is before us on the government’s appeal. With respect to this issue, the judgments will be reversed.
Export’s income from purchase and sale of gypsum rock.
(It delights government counsel to dub this the “falling rock issue.” The aptness of the phrase will be evident, particularly from the opinion of the district court.)
Prior to 1955, USG purchased gypsum rock from Canadian and other subsidiaries. In 1955, for tax reasons, USG arranged that Export purchase the gypsum rock and resell it to USG. The profit derived by Export would be income of a Western Hemisphere trade corporation, and a tax advantage would result. In order to avoid Canadian taxation on income of Export, it was agreed that ownership and possession of the rock would pass to Export when the rock came across the dock at the Canadian port in the process of loading a vessel, and in order to preserve the United States tax advantage title would pass from Export to USG as each piece of rock came to rest in the vessel, or possibly as late as when the vessel became fully loaded. USG paid Export 50 cents per ton plus costs and administrative overhead.
The district court decided that Export’s holding of the title while the rock fell from the dock to a vessel, although formalized by contracts for purchase and sale, and with a purely theoretical risk that USG might not buy all that Export purchased, did not constitute active conduct of a trade or business. Hence, the income therefrom could not be counted toward qualifying Export as a Western Hemisphere trade corporation.
The district court also decided that in any event, in order clearly to reflect income, Export’s income ascribed to its momentary ownership of the gypsum rock must be allocated to USG. We affirm the latter holding, and it appears that if such income be thus allocated, it is unnecessary to consider the first conclusion of the district court.
The details of the matter are set forth in the opinion of the district court, 304 F.Supp. at pp. 636 to 644. We agree that the nominal participation of Export in the process of bringing the raw mate*451rial to the processing plants is so wholly without real substance that the activity of USG rather than Export must be deemed to have generated the income,
Income is to be taxed to the one who earns it.7 It is at least arguable that, aside from the allocation under 26 U.S.C. § 482, USG’s payment to Export of 50 cents per ton was an attempt to transfer liability for a tax on income by a donation of the income to another.
Taxpayers assert, in substance, that the fact that the parties were motivated by tax considerations in framing the transactions does not make the transactions sham. We agree with that proposition, so stated, but, on the other hand, a transaction which is fake or sham is not relieved of that character by the fact that the parties were motivated by tax considerations in formulating it. The fact that a taxpayer may properly arrange its affairs to minimize taxation does not give it license to create purposeless entities or to engage in transactions with subsidiaries which independent parties would not dream of concluding.
This court has held that Western Hemisphere trade corporations are not immune from § 482.8
The issue as to Export’s income from purchase and sale of gypsum rock is before us on taxpayers’ appeal, and in that respect, the judgments will be affirmed.
Insofar as the judgments appealed from rejected allocation on account of the shipping rates paid to PG by USG and upheld allocation of Export’s income derived from purchase and sale of gypsum rock, they are affirmed. Insofar as they rejected allocation of Export’s income on account of the prices at which USG sold finished products to Export, they are reversed. The causes are remanded for further proceedings, to determine the proper allocation on account of such prices, to determine whether, taking the determinations in these actions into consideration, Export qualifies as a Western Hemisphere trade corporation, and to adjust the judgments for refund accordingly.
. E. g., Charles Town, Inc. v. Commissioner of Internal Revenue, 372 F.2d 415, 422 (4th Cir., 1967) ; Hall v. Commissioner of Internal Revenue, 294 F.2d 82, 87 (5th Cir., 1961) ; Spicer Theatre, Inc. v. Commissioner of Internal Revenue, 346 F.2d 704, 706 (6th Cir., 1965) ; Baldwin-Lima-Hamilton Corporation v. United States, 435 F.2d 182, 185 (7th Cir., 1970) ; Oil Base, Inc. v. Commissioner of Internal Revenue, 362 F.2d 212, 214 (9th Cir., 1966) ; Young & Rubicam, Inc. v. United States, 410 F.2d 1233, 1244, 187 Ct.Cl. 635 (1969).
. Supra, footnote 1.
. 26 U.S.C. §§ 921, 922.
. No allocation of Export’s income was made under § 482 for 1955, and the government has not appealed the decision as to that year.
. Eli Lilly and Company v. United States, 372 F.2d 990, 178 Ct.Cl. 666 (1967).
. Baldwin-Lima-Hamilton Corporation v. United States, supra, footnote 1.
. Helvering v. Horst, 311 U.S. 112, 119, 61 S.Ct. 144, 85 L.Ed. 75 (1940).
. Baldwin-Lima-Hamitton, supra, footnote 1, 435 F.2d p. 185.