DYER, Senior Circuit Judge:
Three sets of taxpayers 1 seek review of tax court decisions denying their petitions for redetermination of deficiencies with respect to losses claimed on investments in computer equipment leasing activities. The tax court concluded that a portion of the claimed losses under long-term installment partial recourse notes used to purchase equipment were in substance nonre-course obligations and subject to a loss-limiting arrangement. The amount of the allowed deductions was limited to the amounts for which the investors were “at risk” within the meaning of the Internal [1086]*1086Revenue Code, 26 U.S.C. § 465.2 In each case, the tax court determined that the taxpayers were liable for the increased interest rate provided for under section 6621(c)(3),3 applicable in a tax motivated transaction, for the loss disallowed by reason of section 465(a). We affirm.
Computer Sale/Leaseback Transactions
As the facts have been set out in great detail in the tax court’s opinions4, we need only briefly summarize them here. The taxpayers in these cases entered into sale/leaseback transactions in the form of agreements by the taxpayers to purchase computer equipment from a company named Elmco, Inc. or its wholly-owned subsidiary CTC. By agreements, the taxpayers acquired Elmco’s leases, and leased the equipment back to the party from whom it was purchased by Elmco. The purchase price to each investor consisted of a partial cash payment, a recourse purchase money equity note, and an installment note stated to be partially recourse and partially nonre-course. The original owners, referred to as third-party lessors, had purchased the equipment, leased it to end-users, and then sold the equipment to Elmco and entered into a leasing arrangement with Elmco, CTC or the investor/taxpayers.5 The third-party lessor was indebted to a bank for the purchase price of the equipment, and the bank had a first lien on the equipment. When Elmco purchased the equipment from the third-party lessor subject to end-user leases and the bank lien, its purchase money note was nonrecourse.
Elmco leased the equipment back to the third-party lessor for rental payments equal to or in excess of its payments due to the third-party lessor. When Elmco sold the “package” to an investor, it assigned its rights under the lease, including the receipt of rent, to the investor. The documents contain a guarantee by the third-party lessor of its subsidiary’s rent obligations. Elmco indemnified the taxpayers for any material breach of its representations or obligations set forth in the agreement. Pursuant to a written or oral agreement, no part of the rent payments were actually made to anyone by the third-party lessor, except the amount in excess of the nonrecourse note payments due to the third-party lessor by Elmco. These note payments were in the exact amount as the partial recourse note payments due from the investor to Elmco. The third-party lessor credited the rent amount to the investor, credited the investor's note to Elmco with the amount due on it, and credited its note from Elmco with an equal amount. Periodically, the excess, if any, of the rentals over the note payments was paid by the third-party lessor to Elmco and transferred by Elmco to the investor. Obligations due to each party in this circular arrangement were credited as bookkeeping entries. It would be unnecessary for the third-party lessors to make any payment at all, as the transfers were made on the books of a designated depository or agent. The circular arrangement brought back to the third-party lessor its own rental payments applied against the nonrecourse note of Elm-co.
Amendment to Answer to Assert “At Risk” Theory
As an initial procedural issue,6 ap[1087]*1087pellants contend that the tax court abused its discretion by permitting the government to amend its answer in each case [except Cohen ] to set forth the theory that the appellants were not “at risk” within the meaning of 26 U.S.C. § 465,7 inserting a new issue into these cases prior to trial. The motion to amend was granted three days prior to the commencement of the trial.
Rule 41(a) of the Rules of Practice and Procedure of the United States Tax Court8 provides that “leave [to amend] shall be given freely when justice so requires”. Appellants argue that the late date that the Motion for Leave to File Amendment to Answer was granted resulted in prejudice and injury. The government argues that appellants have failed to demonstrate prejudice, as the facts relevant to the “at risk” issue were the same facts relevant to the other issues raised in the notices of deficiency.9 We agree. ■ The determination of whether justice requires an amendment is within the sound discretion of the trial court. Foman v. Davis, 371 U.S. 178, 182, 83 S.Ct. 227, 230, 9 L.Ed.2d 222 (1962); Gregory v. Mitchell, 634 F.2d 199, 203 (5th Cir.1981).10 The tax court did not abuse its discretion in allowing the amendments to the answers, where the amendments were proposed over 30 days prior to the trial date and reflected in content the stated issues broadly covered by the deficiency notices.
Not At Risk Under Section 465(h)(4)
The fundamental issue is to what extent the investors were at risk pursuant to section 465 with respect to the long-term installment notes. Their claimed losses are allowed to the extent that the taxpayers were at risk on their investments. The tax court analyzed whether, in fact, considering all the documents signed by the parties in the cases, Elmco would have any right to collect the “recourse” part of the installment notes from the investors. The tax court determined that if the third-party les-
926 F.2d—25 [1088]*1088sor defaulted on its rental payments, that the investors were not the party of last resort, since the third-party lessor would in effect merely cease paying itself. Elmco’s indebtedness would be discharged since its notes to the third-party lessor were nonre-course, and it would therefore be unrealistic to believe that Elmco would make any attempt to collect on the investors’ notes to it. The court found unconvincing the testimony of Elmco’s principal officer, Mr. Meadows, that he would have compelled appellants to pay the stated recourse portion of the note. He “believed [he would collect] because it would be a windfall for [Elmco], in effect.” There is no clear error in the lower court’s credibility determination. Henson v. Commissioner, 887 F.2d 1520, 1526 (11th Cir.1989) (citing Marsellus v. Commissioner, 544 F.2d 883, 886 (5th Cir.1977)).
Appellants contend that there was no arrangement which protected the taxpayers against loss.
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DYER, Senior Circuit Judge:
Three sets of taxpayers 1 seek review of tax court decisions denying their petitions for redetermination of deficiencies with respect to losses claimed on investments in computer equipment leasing activities. The tax court concluded that a portion of the claimed losses under long-term installment partial recourse notes used to purchase equipment were in substance nonre-course obligations and subject to a loss-limiting arrangement. The amount of the allowed deductions was limited to the amounts for which the investors were “at risk” within the meaning of the Internal [1086]*1086Revenue Code, 26 U.S.C. § 465.2 In each case, the tax court determined that the taxpayers were liable for the increased interest rate provided for under section 6621(c)(3),3 applicable in a tax motivated transaction, for the loss disallowed by reason of section 465(a). We affirm.
Computer Sale/Leaseback Transactions
As the facts have been set out in great detail in the tax court’s opinions4, we need only briefly summarize them here. The taxpayers in these cases entered into sale/leaseback transactions in the form of agreements by the taxpayers to purchase computer equipment from a company named Elmco, Inc. or its wholly-owned subsidiary CTC. By agreements, the taxpayers acquired Elmco’s leases, and leased the equipment back to the party from whom it was purchased by Elmco. The purchase price to each investor consisted of a partial cash payment, a recourse purchase money equity note, and an installment note stated to be partially recourse and partially nonre-course. The original owners, referred to as third-party lessors, had purchased the equipment, leased it to end-users, and then sold the equipment to Elmco and entered into a leasing arrangement with Elmco, CTC or the investor/taxpayers.5 The third-party lessor was indebted to a bank for the purchase price of the equipment, and the bank had a first lien on the equipment. When Elmco purchased the equipment from the third-party lessor subject to end-user leases and the bank lien, its purchase money note was nonrecourse.
Elmco leased the equipment back to the third-party lessor for rental payments equal to or in excess of its payments due to the third-party lessor. When Elmco sold the “package” to an investor, it assigned its rights under the lease, including the receipt of rent, to the investor. The documents contain a guarantee by the third-party lessor of its subsidiary’s rent obligations. Elmco indemnified the taxpayers for any material breach of its representations or obligations set forth in the agreement. Pursuant to a written or oral agreement, no part of the rent payments were actually made to anyone by the third-party lessor, except the amount in excess of the nonrecourse note payments due to the third-party lessor by Elmco. These note payments were in the exact amount as the partial recourse note payments due from the investor to Elmco. The third-party lessor credited the rent amount to the investor, credited the investor's note to Elmco with the amount due on it, and credited its note from Elmco with an equal amount. Periodically, the excess, if any, of the rentals over the note payments was paid by the third-party lessor to Elmco and transferred by Elmco to the investor. Obligations due to each party in this circular arrangement were credited as bookkeeping entries. It would be unnecessary for the third-party lessors to make any payment at all, as the transfers were made on the books of a designated depository or agent. The circular arrangement brought back to the third-party lessor its own rental payments applied against the nonrecourse note of Elm-co.
Amendment to Answer to Assert “At Risk” Theory
As an initial procedural issue,6 ap[1087]*1087pellants contend that the tax court abused its discretion by permitting the government to amend its answer in each case [except Cohen ] to set forth the theory that the appellants were not “at risk” within the meaning of 26 U.S.C. § 465,7 inserting a new issue into these cases prior to trial. The motion to amend was granted three days prior to the commencement of the trial.
Rule 41(a) of the Rules of Practice and Procedure of the United States Tax Court8 provides that “leave [to amend] shall be given freely when justice so requires”. Appellants argue that the late date that the Motion for Leave to File Amendment to Answer was granted resulted in prejudice and injury. The government argues that appellants have failed to demonstrate prejudice, as the facts relevant to the “at risk” issue were the same facts relevant to the other issues raised in the notices of deficiency.9 We agree. ■ The determination of whether justice requires an amendment is within the sound discretion of the trial court. Foman v. Davis, 371 U.S. 178, 182, 83 S.Ct. 227, 230, 9 L.Ed.2d 222 (1962); Gregory v. Mitchell, 634 F.2d 199, 203 (5th Cir.1981).10 The tax court did not abuse its discretion in allowing the amendments to the answers, where the amendments were proposed over 30 days prior to the trial date and reflected in content the stated issues broadly covered by the deficiency notices.
Not At Risk Under Section 465(h)(4)
The fundamental issue is to what extent the investors were at risk pursuant to section 465 with respect to the long-term installment notes. Their claimed losses are allowed to the extent that the taxpayers were at risk on their investments. The tax court analyzed whether, in fact, considering all the documents signed by the parties in the cases, Elmco would have any right to collect the “recourse” part of the installment notes from the investors. The tax court determined that if the third-party les-
926 F.2d—25 [1088]*1088sor defaulted on its rental payments, that the investors were not the party of last resort, since the third-party lessor would in effect merely cease paying itself. Elmco’s indebtedness would be discharged since its notes to the third-party lessor were nonre-course, and it would therefore be unrealistic to believe that Elmco would make any attempt to collect on the investors’ notes to it. The court found unconvincing the testimony of Elmco’s principal officer, Mr. Meadows, that he would have compelled appellants to pay the stated recourse portion of the note. He “believed [he would collect] because it would be a windfall for [Elmco], in effect.” There is no clear error in the lower court’s credibility determination. Henson v. Commissioner, 887 F.2d 1520, 1526 (11th Cir.1989) (citing Marsellus v. Commissioner, 544 F.2d 883, 886 (5th Cir.1977)).
Appellants contend that there was no arrangement which protected the taxpayers against loss. They argue that there was no offsetting arrangement, that neither the guarantee by the parent company third-party lessor of its subsidiary’s rent obligation, nor the indemnification clause in the purchase agreement which provides that Elmco will indemnify the taxpayer against any loss which the taxpayer may incur by reason of any material breach by Elmco of any of its representations or obligations set forth in the agreement, constitutes a loss-limiting arrangement. They further argue that it is not the labels such as “guarantee” which must control, Levy v. Commissioner, 91 T.C. 838, 869 (1988), and that the court must look to the substance of the transaction, Thomock v. Commissioner, 94 T.C. 439 (1990).
Primary weight must be given to the factual findings of the tax court judge. Commissioner v. Scottish American Inv. Co., 323 U.S. 119, 125, 65 S.Ct. 169, 172, 89 L.Ed. 113 (1944), cited in, Turner v. Commissioner, 812 F.2d 650, 654 (11th Cir.1987). “Where there are two permissible views of the evidence, the tax court’s choice between them cannot be clearly erroneous.” Piggly Wiggly Southern, Inc. v. Commissioner, 803 F.2d 1572, 1576 (11th Cir.1986). Accordingly, we hold that the tax court properly determined the effect of the guarantee and indemnity terms of the agreements.
A significant feature of the tax court’s analysis was that, in substance, under the circular nature of the transaction, the investors had merely assumed Elmco's non-recourse liability to the third-party lessors. Equally significant were the terms incorporated into the documents setting forth the third-party lessors’ guarantees of performance and Elmco’s indemnities.
We view the transactions in accordance with economic reality.11 The taxpayers were not at risk with respect to personal liability and a loss-limiting arrangement in the circular sale/leaseback transactions with guarantees of rent, indemnities for default and an underlying nonrecourse obligation connecting the taxpayers’ obligee Elmco to the taxpayers’ lessees. The stated recourse liabilities of the taxpayers were not realistically subject to collection after a discharge of the nonrecourse note. The chain of “payments” could either continue as bookkeeping entries or cease, and there would be no actual circumstance upon which a demand for a payment would be made. See American Principals Leasing Corp. v. United States, 904 F.2d 477, 483 (9th Cir.1990) (affirming Baldwin v. United States based on circular nature of obligations subject to analysis of no realistic possibility of economic loss).12
[1089]*1089Our resolution of the applicability of section 465(b)(4) to these cases makes consideration of the government’s position under section 465(b)(3) unnecessary. The tax court incorporated its consideration of that position, which asserted the conception of Elmco as a straw man, to determine that the investors had merely assumed Elmco’s nonrecourse liability to the third-party lessors, as part of the court’s conclusion based on the “other similar arrangement” exception under section 465(b)(4).
Not At Risk Under Section 465(b)(2)
The Cohen case presents a separate issue where appellants contend that the tax court’s conclusion that they were not personally liable and, thus, not at risk, blurs the distinction between sections 465(b)(2) [personal liability] and 465(b)(4) [exceptions to at risk].13 The distinction for purposes of analysis is that after it is determined under section 465(b)(2) that a debtor appears to be ultimately liable on an investment obligation, a determination is made under section 465(b)(4) as to whether the debtor is protected against that ultimate liability by means of “nonrecourse financing, guarantees, stop loss agreements, or other similar arrangements.” See Melvin v. Commissioner, 88 T.C. 63 (1987), aff'd, 894 F.2d 1072 (9th Cir.1990).
Appellants also rely, in part, on the fact that the Commissioner conceded in its tax court reply brief in this case “that the petitioners were not protected against loss through guarantees, stop loss agreements, or other similar arrangements,” i.e., items under section 465(b)(4). Upon this “unequivocal” concession, appellants contend that section 465(b)(4) cannot serve as a basis for the tax court’s decision. However, no concession was made by the Commissioner with respect to “nonrecourse financing”, the remaining exception which is listed in section 465(b)(4).
Appellants’ argument is based on statutory interpretation and asserted improper analysis14. The tax court’s rulings on the interpretation and application of the statute are conclusions of law subject to de novo review. Estate of Caporella v. Commissioner, 817 F.2d 706 (11th Cir.1987). We are convinced that an examination of exceptions under section 465(b)(4) follows logically from the issue of personal liability, and is proper in these circumstances.15 The tax court, by stripping away the trappings of the “partial recourse” notes which lacked actual substance, and by considering the documents as a whole, correctly concluded that these investors were not personally liable. We find that the transaction was structured on paper to give the appearance of creating personal liability, while the substance and the economic realities surrounding the transaction through the agreement terms and relationships of the parties “effectively immunized [Cohen] from any realistic possibility of suffering an economic loss” other than the down payment. See Moser v. Commissioner, 914 F.2d 1040, 1049 (9th Cir.1990).
[1090]*1090The government may assert the applicability of the correct section in support of the tax court’s judgment. A case may be affirmed on any ground, whether relied upon, or even considered, by the court below. United States v. Arthur Young & Co., 465 U.S. 805, 814 n. 12, 104 S.Ct. 1495, 1501 n. 12, 79 L.Ed.2d 826 (1984). See also Dandridge v. Williams, 397 U.S. 471, 475 n. 6, 90 S.Ct. 1153, 1156 n. 6, 25 L.Ed.2d 491 (1970); Helvering v. Gowran, 302 U.S. 238, 245, 58 S.Ct. 154, 157, 82 L.Ed. 224 (1937). Furthermore, the asserted concession regarding inapplicability of certain statutory exceptions, if considered a mistake of law by the government in its pretrial submission, may be corrected. The doctrine of equitable estop-pel is not a bar to the correction by the Commissioner of a mistake of law. Dixon v. United States, 381 U.S. 68, 72-73, 85 S.Ct. 1301, 1304, 14 L.Ed.2d 223 (1965); Automobile Club v. Commissioner, 353 U.S. 180, 183, 77 S.Ct. 707, 709, 1 L.Ed.2d 746 (1957); Dickman v. Commissioner, 690 F.2d 812, 818 (11th Cir.1982), aff'd, 465 U.S. 330, 104 S.Ct. 1086, 79 L.Ed.2d 343 (1984) (quoting Crown v. Commissioner, 67 T.C. 1060, 1070 (1977) (dissent), aff'd, 585 F.2d 234 (7th Cir.1978)); Estate of Vitt v. United States, 706 F.2d 871, 874 (8th Cir.1983). See Metropolitan Life Ins. Co. v. United States, 874 F.2d 1234 (8th Cir.1989), where the government was permitted to argue the inapplicability of 26 U.S.C. § 6324 on appeal even though its trial counsel had conceded the applicability of this section. The result in allowing the government to assert the applicability of section 465(b)(4) on appeal would not be inconsistent with substantial justice, id. at 1235, as the factual record developed by appellants below would not have required any additions or modifications in presentation if subjected to the alternate “at risk” theory now argued.
Additional Interest for Tax Motivated Transactions
Section 6621(c)(1) imposed at the relevant times to these cases additional interest on substantial underpayments of tax attributable to tax motivated transactions.16 For the purposes of this subsection, losses disallowed by reason of section 465(a) are included in the meaning of a tax motivated transaction. 26 U.S.C. § 6621(c)(3)(A)(ii). Because we affirm the tax court’s finding that the Young, Diaz, and Cohen investors were not at risk on a portion of their recourse notes, the tax court correctly determined that the investors’ tax liability is subject to the imposition of additional interest pursuant to section 6621(c).
CONCLUSION
For the reasons stated above, the tax court’s decisions are AFFIRMED.