In this tax case, 79 T.C. 456, we decide the tax consequences arising out of the transfer of mortgages and a promissory-note from an ex-husband of the taxpayer, where the transfer occurred when the ex-husband was in arrears in alimony payments. We affirm.
Facts
Dorothy Olster and her husband executed a property settlement and custody agreement (original agreement) dated April 6, 1972, providing that petitioner would re*1170ceive $2,500 per month alimony for life. Upon remarriage, however, petitioner would only be entitled to a lump sum amount equal to two years’ alimony, or $60,000. On April 11, 1972, Olster and her husband were divorced; the final judgment incorporated by reference the original agreement. Over the next few years, 01-ster’s ex-husband experienced severe financial difficulties. By June 10, 1976, he was in substantial arrears in his alimony payments.
On June 10, 1976, Olster and her ex-husband executed a “Stipulation for Modification of Agreements and Lump-Sum Settlement Agreement” (modification agreement) designed to alleviate the harshness of the alimony obligations of the ex-husband under the original agreement and to guarantee a more realistic income flow to petitioner.1 Pursuant to paragraph 2(A) of the modification agreement, the ex-husband transferred to Olster mortgages with a face value of $87,243.18. Of the six mortgages transferred, three were wrap-around mortgages.2 The modification agreement also provided that the ex-husband would continue to pay the first mortgages underlying the three wrap-around mortgages. If the ex-husband failed to make the payments, Olster would have been entitled under the modification agreement to the dif*1171ference between the first mortgage payments owed and the amount due Olster under the wrap-around mortgages. In addition to the mortgages, Olster received a $25,000 promissory note payable one year after execution of the modification agreement. This note was secured by a mortgage on a parcel of land owned by the ex-husband located in Dade County, Florida.
Olster filed a 1976 individual tax return in which she excluded the value of the mortgages. In 1980, the Internal Revenue Service issued a notice of deficiency in the amount of $26,796.62.3 In July, 1980, Olster filed suit in the tax court seeking a redetermination of this deficiency. The issues before the tax court were (1) whether the mortgages were in settlement of the ex-husband’s past as well as future alimony obligations or solely in settlement of future alimony obligations; (2) if the value of the mortgages were in satisfaction of past alimony obligations and are includable in gross income, whether such value is to be measured by the amount of alimony arrearages or the fair market value of the mortgages transferred; (3) what is the value of the alimony arrearages; and (4) what is the fair market value of the mortgages Olster received. The tax court held that the transfer of the mortgages was in consideration for the release of the ex-husband’s past alimony obligations and determined that the fair market value of the mortgages, $36,183.24, was includable in Olster’s gross income for 1976. Pursuant to 26 U.S.C.A. § 7482(a) (West Supp.1984), Olster brings this appeal.
Issues
On this appeal, we must consider four main issues: (A) whether the tax court’s finding that the transferred mortgages were intended as satisfaction of past, present, and future alimony obligations was clearly erroneous; (B) whether the tax court erred as a matter of law in determining that a mortgage transferred without the underlying note has value; (C) whether the tax court erred as a matter of law in determining that the value of the mortgages to be included in gross income was the fair market value of the mortgages, and not the amount of cash received in payment on the mortgage debt during the 1976 tax year; and (D) whether the government has a duty to determine a tax deficiency by the method most favorable to Olster.
Discussion
A. Whether the mortgages were satisfaction for past as well as future alimony obligations.
Olster argues that paragraph 3 of the modification agreement identifies the release of the right to future alimony payments as the exclusive consideration for the transfer of the mortgages and the promissory note. The government contends that paragraphs 2 and 3 must be read together, and when read together, support the interpretation that past alimony payments were also consideration for a receipt of the mortgages and the promissory note.
Under 26 U.S.C.A. § 71(a)(1) (West 1984), Olster is required to include in gross income “periodic payments” made pursuant to a decree of divorce by her ex-spouse.4 Alimony payments received on time are taxed in the year of receipt. The tax consequences of delinquent alimony payments, however, are determined based on the intent of the parties. If the payment is made to satisfy back alimony, it *1172retains the character of the original payments for which it is substituted. Holloway v. United States, 428 F.2d 140, 143 (9th Cir.1970); Davis v. Commissioner, 41 T.C. 815, 820 (1964); Holahan v. Commissioner of Internal Revenue, 21 T.C. 451, 463 (1954), aff'd, 222 F.2d 82 (2d Cir.1955). Lump sum payments made solely in consideration for the wife’s release of her husband from future alimony obligations, are not taxable to the wife under section 71(a): these payments are not “periodic payments” within the meaning of section 71(c)(2).5 See Sechrest v. United States, 490 F.2d 102, 104 (4th Cir.1974); Commissioner of Internal Revenue v. Senter, 242 F.2d 400, 403 (4th Cir.1957), aff'g 25 T.C. 1204 (1956).
The law on the tax' consequences of lump-sum payments in satisfaction of a mixture of alimony arrearages and future alimony obligations is unsettled. In Holloway v. United States, the Ninth Circuit held that where a lump sum payment is made to satisfy a taxpayer’s obligation to pay past, present, and future alimony, and the “nub” of the payment is for alimony arrearages, the payment is treated for tax purposes as alimony to the extent of such arrearages. Holloway, 428 F.2d at 143. While Holloway deals with deductions of lump sum payments and does not clarify its meaning of “nub,” we think the proper approach is to treat these payments as satisfaction of unpaid alimony to the extent of such alimony unless there is an amount specifically allocated to the satisfaction of future alimony obligations and the allocation conforms to the substance of the transaction.
While Olster does not dispute this principle, she does argue that the modification agreement, in paragraph 3, specifically allocated the lump sum settlement to future alimony obligations. In her view, she received no consideration for the release of the right to past alimony obligations. 01-ster’s contentions are without merit. Past and future alimony obligations were intended by the parties as consideration for the lump sum settlement. Both parties were benefited by such a bargain: Olster received a guaranteed flow of income while relieving her ex-husband of the obligation to pay past as well as future alimony payments. The conclusion that such benefit was the intent of the modification agreement is further supported by two other observations: (1) in prefatory language, the agreement provides that “covenants and conditions” of the agreement are “mutual,” suggesting mutual obligations and benefits; and (2) the alimony arrearages of $44,800 substantially exceed the value of the transferred mortgages, $36,183.24, suggesting that the mortgages were to satisfy the alimony debt. See Holloway, 428 F.2d at 143. We hold, therefore, that the transferred mortgages and the promissory note were in satisfaction of the ex-husband’s past, present, and future alimony obligations, and as such, the value of the mortgages and the promissory note are includable in petitioner’s gross income as periodic payments under 26 U.S.C.A. § 71(a)(1).
B. Transfer of the mortgages without the note.
Petitioner argues that mortgages transferred without the underlying note *1173have no value. This contention is made for the first time on appeal. “The law is clear that, absent special circumstances, defenses not presented and for which proof is not offered in the trial court cannot be raised for the first time on appeal.” Newton v. Pennington, 718 F.2d 1015, 1018 (11th Cir. 1983) (citing Johnson v. Smith, 696 F.2d 1334, 1338 (11th Cir.1983) (citations omitted)). Petitioner makes no claim of the existence of special circumstances. See, e.g., Fehlhaber v. Fehlhaber, 681 F.2d 1015 (5th Cir. Unit B 1982) (an issue not preserved for appeal will not be reviewed unless it is a purely legal one and the error is so obvious that a failure to review would be a miscarriage of justice). Accordingly, we will not review this issue.
C. Valuation of mortgages and promissory note.
Olster contends that the mortgages have a value equal to the amount of cash actually received in 1976, $13,055.62. Olster received, under the modification agreement, six mortgages with a face value of $87,-243.6 The tax court found that the mortgages had value.7 We agree.
On the specific question of valuation, various estimates of actual value in relation to face value were received by the tax court. Olster’s ex-husband estimated that the mortgages were worth approximately 50-cents on the dollar. The government estimated that the fair market value of the mortgages was also 50% of their face value. Neither party, however, provided any basis for this calculation. Olster provided evidence that the value of the mortgages was substantially impaired at the time of transfer.8 The tax court found that the wrap around mortgages were worth 40% of their face value at the time of the transfer and the other mortgages were worth 45% of their face value at that time. The value transferred in the form of the mortgages, therefore, totalled $36,183.24. This finding is not clearly erroneous.
The government contends that the fair market value of the promissory note at the time of transfer was $25,000. The evidence does not support that contention. The $25,000 note was payable in full within one year from the date of transfer at a rate of 6%. The note was secured by a parcel of land, already encumbered by substantial *1174senior mortgages and unsuitable for commercial development.9 As has been established, Olster’s ex-husband was experiencing financial difficulties in the period before and after the execution of the modification agreement. In fact, Olster’s ex-husband failed to make the note payment when it became due in 1977, and no evidence exists in the record that he has made any payments on this note. We agree with the tax court, therefore, that the promissory note was virtually worthless when transferred. Accordingly, the tax court’s finding that the promissory note had no value was not clearly erroneous.
The fair market value of the property transferred pursuant to the modification agreement was $36,183.24. This value was transferred in satisfaction of past, present, and future alimony obligations of Olster’s ex-husband under the original agreement. Because the value of the transferred mortgages is less than the value of the alimony arrearages, the amount taxable to petitioner is this lesser amount.10
D. Government’s duty to calculate taxpayer’s deficiency by the most favorable method.
Olster contends that the government has a duty to compute her tax deficiency using the most favorable method to her. Without citing any authority, Olster implies that this duty arises from the issuance of the notice of deficiency three years after the 1976 tax return was filed, four days before expiration of the statute of limitations. This question is of first impression in the context of the computation of a tax deficiency.
It is undisputed that the government has a strong interest in maintaining the validity of its tax assessments. The compelling nature of this interest, however, does not mean that the government is entitled to “calculate its assessment in any manner its agents choose.” Thomas v. U.S., 531 F.2d 746, 749 (5th Cir.1976). Absent a finding that the computational methods used, and therefore the assessment, was arbitrary and without foundation, the tax deficiency is presumptively correct. Sailor v. U.S., 343 F.Supp. 1279, 1280 (W.D.Ky.1971). The taxpayer has the burden of proving that the computational method used is arbitrary and without foundation. Mersel v. United States, 420 F.2d 517 (5th Cir.1970).
Olster’s contention that the government has a duty to compute her tax deficiency by the most favorable method is without merit. In Sailor v. US., 343 F.Supp. 1279, taxpayer questioned the assessment determined by the taxing authorities pursuant to the record requirements for wagers, 26 U.S.C.A. § 4403, and the authority to prepare returns for those failing to make a return, 26 U.S.C.A. § 6020. There, the court explained:
It is obvious that where a taxpayer keeps no records and files no returns disclosing his income, no method can be devised which can produce an exact result. Accordingly, the law does not require such exactitude. It is sufficient if the method employed produces a result which is substantially correct. All taxpayers, including the one here involved, by failure to keep records of their income assume the hazard that they may be called upon to pay a tax based upon an income which cannot be determined to a certainty.
Sailor, 343 F.Supp. at 1280-81. This is not a failure to keep a record case. It is obvious, however, that as in Sailor, Olster has done little to come forward with informa*1175tion casting doubt on the Commissioner’s assessment. Cf. U.S. v. Firtel, 446 F.2d 1005, 1007 (5th Cir.1971). She has had ample opportunity to challenge the government’s choice of computational method. See 26 U.S.C.A. Rule 155(b) (West Supp. 1984).11 She has declined to challenge this method through prescribed procedures and has chosen this court as the forum for addressing the validity of the government’s computational method. We hold that the proper forum for challenging the government’s choice of computational method is in a rule 155 proceeding, not for the first time on appeal. We also hold that no duty exists on the government to compute a tax deficiency using the method most favorable to a taxpayer.
Conclusion
In sum, we hold that the tax court properly determined that the consideration paid by Olster’s ex-husband was in satisfaction of his past, present, and future alimony obligations; that where a mixture of such obligations exists and no clear basis is established for allocating between them, the payments are to be considered as satisfaction of unpaid and accrued alimony to the extent of such alimony; that the total alimony arrearages as of June 10, 1976, the time the modification agreement was entered into, was $44,800; that the fair market value of the property Olster received pursuant to the modification agreement was $36,183.24; and that this amount is includable in petitioner’s gross income for the 1976 taxable year. Accordingly, the tax court is affirmed.
AFFIRMED
. The modification agreement provides, in pertinent part:
NOW THEREFORE, in consideration of the mutual covenants and conditions herein contained, and other good and valuable considerations, it is mutually covenanted and agreed between Evan Olster and Dorothy Olster as follows:
1. The parties agree that paragraph 9 of the agreement of 6 April 1972 be deleted, rendered null and void, and of no further force and effect.
2. In consideration of and for Wife having released the Husband from his obligation to provide future alimony to her pursuant to paragraph 9 of the agreement of 6 April 1972, the Husband agrees to pay as a lump sum settlement of his obligation to pay future alimony pursuant to paragraph 9 of the agreement of 6 April 1972 the following:
A. Husband will forthwith cause the mortgages receivable set forth on Schedule "A" hereof to be assigned to the Wife and the Husband shall personally endorse the mortgages and mortgage notes with recourse so that in the event that any of the mortgages become in default, the Husband shall be personally obligated to pay to the Wife any deficiency which results from said default.
B. The Husband shall execute and deliver to the Wife a promissory note in the sum of $25,000.00 bearing interest at the rate of 6% per annum and payable within one year from date hereof.
3. In consideration of and for the lump sum settlement of future alimony payments under paragraph 9 of the agreement of 6 April 1972 as hereinabove provided in paragraph 2, the Wife hereby agrees to remise, release, and forever discharge the Husband from any obligation to pay to her any past due alimony presently due her under paragraph 9 of the agreement of 6 April 1972, as of the date of this agreement.
7. In connection with the promissory note which the Husband will deliver to the Wife by reason of paragraph 2 hereinabove, the parties agree that the the [sic] payment of that promissory note will be secured by a mortgage on the following described property:
The North quarter of Section 13, Township 55 South, Range 38 located in Dade County Florida.
which said mortgage will be inferior only to mortgages, liens, encumbrances and conditions of record. Husband owns the fee simple title to said property as trustee and will cause a mortgage in due form to be executed and delivered to the satisfaction of the Wife's attorneys.
It is further provided, that the mortgage referred to in this paragraph shall also be security for any default with respect to the mortgages receivable being assigned in connection with paragraph 2A hereof. However, upon the default of a mortgage under paragraph 2A, the Husband shall first have the right to substitute any such defaulted mortgage receivable with another mortgage or mortgages of equal value to the then principal balance of any such defaulted mortgage or mortgages, subject to the Wife’s right of reasonable rejection of any proposed mortgage or mortgages for such substitution.
. A wrap-around mortgage is a second mortgage which exists in addition to a first or other mortgages. The wrap-around mortgagor’s only obligation is that of paying the wrap-around mortgage. The wrap-around mortgagee has the obligation to make payments on the first mortgage. Should the wrap-around mortgagee fail to make such payments, the wrap-around mortgagor can do so and offset such payments against the obligation owed to the wrap-around mortgagee. See, e.g., ICM Realty v. Cabot, Cabot & Forbes Land Trust, 378 F.Supp. 918, 923 n. 6 (S.D.N.Y. 1974).
. This deficiency was based on the Internal Revenue Service’s determination that the mortgages had a value of $60,000 and were includable in petitioner’s 1976 tax return.
. Title 26 U.S.C.A. § 71(a)(1) provides:
(1) Decree of divorce or separate maintenance. — If a wife is divorced or legally separated from her husband under a decree of divorce or of separate maintenance, the wife’s gross income includes periodic payments (whether or not made at regular intervals) received after such decree in discharge of (or attributable to property transferred, in trust or otherwise, in discharge of) a legal obligation which, because of the marital or family relationship, is imposed on or incurred by the husband under the decree or under a written instrument incident to such divorce or separation.
. Title 26 U.S.C.A. § 71(c) provides:
(c) Principal sum paid in installments.—
(1) General rule. — For purposes of subsection (a), installment payments discharging a part of an obligation the principal sum of which is, either in terms of money or property, specified in the decree, instrument, or agreement shall not be treated as periodic payments.
(2) Where period for payment is more than 10 years. — If, by the terms of the decree, instrument, or agreement, the principal sum referred to in paragraph (1) is to be paid or may be paid over a period ending more than 10 years from the date of such decree, instrument, or agreement, then (notwithstanding paragraph (1)) the installment payments shall be treated as periodic payments for purposes of subsection (a), but (in the case of any one taxable year of the wife) only to the extent of 10 percent of the principal sum. For purposes of the preceding sentence, the part of any principal sum which is allocable to a period after the taxable year of the wife in which it is received shall be treated as an installment payment for the taxable year in which it is received.
. At trial, petitioner stated that she did not receive a seventh mortgage, the Bass mortgage. The tax court found that the Bass mortgage was not received.
. Petitioner contends that the mortgages received were mere executory contracts, absent receipt of the underlying notes. This issue was raised for the first time on appeal, see discussion of issue B, supra, and for that reason is not reviewable by us. Nonetheless, it is indisputable that one objective of the modification agreement was to guarantee petitioner an income flow. The tax court, for example, found such a guarantee in the financing of the wrap-around mortgages.
As we understand the evidence, Mr. Olster financed the original purchase of these three pieces of property by mortgages payable to the sellers of the property. Subsequently, he sold the properties to third parties, who in turn financed their purchases by mortgages payable to Mr. Olster. If payments on the first mortgages ceased, the original sellers would have the right to foreclose on the underlying properties, and by their actions reduce or negate the obligation of the second buyers (the third parties) to continue paying on the wrap-around mortgages. Once the wrap-around mortgages were transferred to petitioner, she had full right to receive the monies paid by the second purchaser. This amount would be received free and clear so long as Mr. Olster continued making payments on the original mortgage. If however, such payments ceased, petitioner would protect her rights to receive the payments on the second mortgages by making the payments owed by Mr. Olster on the first mortgages. Alternatively, the second purchasers could protect their interest in the properties by making the underlying mortgage payments and offsetting such payments against their own mortgage payments to Mrs. Olster. Thus, in either case, Mrs. Olster would receive only the excess of the payments under the second mortgage over the payments under the first mortgage. [Emphasis added.]
. Petitioner testified that the mortgages could not be valued at face value and in fact were worth much less. In regard to these mortgage payments, she stated: "Some of them bounced. Some of them didn’t pay for several months. A lot of them still do that. Some had to be foreclosed. I mean, I had real problems with them.”
. The land was encumbered by a $1,500,000 pledge to Walter E. Heller and Company, a first mortgage to Elvida Corporation, and a tax lien of approximately $115,000.
. The exact amount of the arrearages was in dispute at trial. Olster, by an affidavit executed December 15, 1978, estimated the arrearages to be $60,000 as of June 10, 1976. At trial, however, Olster testified that the arrearages were more accurately $44,800. The latter figure was based on periodic recordings of payments actually received under the original agreement. The record is devoid of a more accurate estimate of the arrearages as of June 10, 1976. Accordingly, the tax court’s finding was not clearly erroneous.
. Title 26 U.S.C.A. Rule 155(b) provides, in pertinent part:
(b) Procedure in absence of agreement. If, however, the parties are not in agreement as to the amount of the deficiency, liability, or overpayment to be entered as the decision in accordance with the findings and conclusions of the Court, either of them may file with the Court a computation of the deficiency, liability, or overpayment believed by him to be in accordance with the Court’s findings and conclusions. The Clerk will serve upon the opposite party a notice of such filing accompanied by a copy of such computation. If the opposite party fails to file objection, accompanied or preceded by an alternative computation, on or before a date specified in the Clerk’s notice, the court may enter decision in accordance with the computation already submitted. If in accordance with this Rule computations are submitted by the parties which differ as to the amount to be entered as the decision of the Court, the parties may, at the Court’s discretion, be afforded an opportunity to be heard in argument thereon and the Court will determine the correct deficiency, liability, or overpayment and will enter its decision accordingly.