882 F.2d 820
64 A.F.T.R.2d 89-5418, 89-2 USTC  P 9488
Bruce A. and Marianne S. PRABEL, Appellants,v.COMMISSIONER OF INTERNAL REVENUE, Appellee.
No. 89-1265.
United States Court of Appeals,Third Circuit.
Argued July 25, 1989.Decided Aug. 18, 1989.Rehearing and Rehearing In Banc DeniedSept. 13, 1989.

Robert D. Whoriskey (argued), Curtis, Mallet-Prevost, Colt & Mosle, New York City, and John A. Craig, Hawthorne, N.Y., for appellants (Marilyn K. Freedman and Judith D. Szokol, Curtis, Mallet-Provost, Colt & Mosle, of counsel).
Shirley D. Peterson, Asst. Atty. Gen., Gary R. Allen, Chief Appellate Section, David English Carmack, and Mary Frances Clark (argued), Attys. Tax Div. Dept. of Justice, Washington, D.C., for appellee.
Before GIBBONS, Chief Judge, and HUTCHINSON, Circuit Judge, and WOLIN, District Judge*
OPINION OF THE COURT
GIBBONS, Chief Judge:


1
Bruce and Marianne Prabel appeal from an adverse decision by the United States Tax Court.  The Prabels owned an interest in a partnership which had calculated its interest expense for a long-term loan using the Rule of 78 method.  The Commissioner of Internal Revenue determined that this method did not clearly reflect the actual interest expense.  The Commissioner required that the interest expense be calculated under the economic accrual method and issued a notice of deficiency.  The Tax Court found that the Commissioner did not abuse his discretion under 26 U.S.C. Sec. 446(b) and upheld the deficiency.  We will affirm the Tax Court decision.

I. BACKGROUND

2
Bruce and Marianne Prabel, residents of Chadds Ford, Pennsylvania, are cash basis taxpayers who timely filed joint federal income tax returns for 1981 and 1982.  On or about October 20, 1980, Bruce Prabel became a limited partner in Quincy Associates, Ltd., acquiring a 3.7485 percent share.  In late 1980, Quincy Associates purchased a shopping center from First Delaware Equity Corp.  (FDEC) for $2,471,000.  The shopping center was located in Quincy, Florida.  The purchase price was payable by a cash downpayment of $192,000 and the balance of $2,279,000 by a nonrecourse, 23-year, 20-month purchase-money note.  The note was issued in the total amount of $7,268,249, reflecting the $2,279,000 deferred purchase price and $4,989,249 of stated, precomputed interest.  In effect, the note is issued at a discount.  The discount substitutes for or is the equivalent of interest.  According to the terms of the note, the discount is written off, or interest accrues, in accordance with the Rule of 78's method.  The note matures on December 31, 2003, and is secured by a mortgage and security agreement issued by Quincy Associates.


3
The terms of the transaction including the terms of the note were the result of dealings between related entities and were not the result of arms-length negotiations.


4
The payment schedule for the note is set forth infra and includes a comparison to economic accrual of the interest expense.  During the first 13 years, interest expense under the Rule of 78's amortization substantially exceeds actual cash payments.  This is negative amortization.  The accrued but unpaid interest is carried over to subsequent years.  However, interest does not accrue on unpaid interest owed.  There is no compounding of interest for the entire term of the loan.


5
Pursuant to the terms of the note, Quincy Associates had the right, at its discretion, to prepay in whole or in part the outstanding principal of the note.  In the event of a prepayment, Quincy was required to pay all unpaid and accrued interest thereon.  The note provides:


6
Regular monthly payments will be allocated first to the Interest Element and then to the Principal Element in accordance with the "Rule of 78."


7
* * *


8
* * *


9
Mortgagor shall have the right to prepay this Note in whole, at any time that First Mortgage or Subsequent First Mortgage may be prepaid, by paying to mortgagee the sum of:  (i) the then outstanding principal balance of this Note;  (ii) all unpaid and accrued interest on this Note;  (iii) and the amount of any prepayment charge or penalty due on the First Mortgage and/or Subsequent First Mortgage.


10
* * *


11
* * *


12
On prepayment of this Note in whole, the Mortgagor will receive a credit for the unearned portion of the Interest Element determined in accordance with the "Rule of 78."


13
(A. 166, 169-70).


14
For federal income tax purposes, Quincy Associates reports its income on an accrual basis.  Quincy Associates determined its annual interest expense for this loan by taking the total precomputed interest (discount) and allocating it to annual accounting periods according to the Rule of 78.


15
Following an examination of Quincy Associates' tax returns for 1980, 1981 and 1982, the Commissioner determined that the Rule of 78 method of computing interest expense did not clearly reflect income and that Quincy Associates must recompute interest under the economic accrual method.1   See 26 U.S.C. Sec. 446(b).  The partnership's alleged excessive accrual for 1980 was adjusted by way of a section 481 adjustment reflected in deficiencies issued with respect to 1981.


16
As a result of these adjustments, the Commissioner determined deficiencies in the Prabel's tax liabilities for 1981 and 1982 based on their distributive share of the partnership loss claimed on their tax returns.  For 1981, the Commissioner determined a deficiency in the amount of $2,986.00 and for 1982, he determined a deficiency of $1,870.28.


17
The Prabels filed a petition with the Tax Court.  Both parties moved for summary judgment.  The Tax Court held that the Rule of 78 method used to compute interest expense distorted partnership income and that it was within the Secretary's discretion under Sec. 446(b) to require recomputation of interest pursuant to the economic accrual method.  We shall affirm the tax court's decision.

II. DISCUSSION

18
The Internal Revenue Code, 26 U.S.C. Sec. 446(b), gives the Commissioner the power to disallow any accounting method which does not clearly reflect income and requires that the taxpayer's income be computed under such method which in the opinion of the Commissioner does clearly reflect income.2   In the present case, the Commissioner determined that Quincy Associates' use of the Rule of 78 to compute interest expense distorted the partnerships' reported income and that its income must instead be computed by economic accrual.  The Commissioner has broad discretion both to determine whether an accounting method clearly reflects income and to choose an accounting method which does clearly reflect income.  See Thor Power Tool Co. v. Commissioner, 439 U.S. 522, 532-33, 99 S.Ct. 773, 780-81, 58 L.Ed.2d 785 (1979);  Commissioner v. Hansen, 360 U.S. 446, 467, 79 S.Ct. 1270, 1281, 3 L.Ed.2d 1360 (1959);  Ferrill v. Commissioner, 684 F.2d 261, 264 (3d Cir.1982).  In the present context, we hold that the Commissioner has not committed an abuse of discretion.  Furthermore, we reject taxpayer's argument that entry of summary judgment was improper.  There is no material issue of fact precluding summary judgment.


19
The economic accrual method of calculating interest expense is set forth in Revenue Ruling 83-84, 1983-1 C.B. 97.  It is merely a traditional present value analysis of the cost of borrowing.  See W. Meigs & R. Meigs, Financial Accounting 488-91 (4th ed.1983);  T. Maness, Introduction to Corporate Finance 154-56 (1988).  The concept of present value, like interest, is based upon the time value of money.  If a debt instrument is issued at face amount, has a stated interest rate, and requires periodic payments which cover accrued interest, the cost of borrowing is fairly easy to determine.  For example a one-year note for $1,000, for which $1,000 was received, which pays 12% annual interest has an effective cost of borrowing of 12%.  At the end of the one-year term, the borrower will be required to repay $1,120.  The cost of borrowing or effective interest rate equals the stated interest rate.


20
However, suppose the one-year $1,000 note has no stated interest rate.  The note merely pays $1,000 at the end of the one-year term.  Assuming a sale, the purchaser will not pay $1,000 today for the note.  The note will be purchased for less than $1,000.  The difference between the face amount and the purchase price is an original issue discount.  Assuming that the note is acquired for $909, the purchaser will effectively receive $91 in interest when the note is paid off, or approximately a 10% return.  Another way of stating this is that assuming an implicit rate of return of 10%, $909 is the present value of a debt instrument paying $1,000 in one year.  If we had only been told that the note had been acquired for $909 and that it would pay $1,000 in one year, we could have used present value analysis to determine that the implicit interest rate is approximately 10%.


21
In the previous two examples, determining the cost of borrowing is fairly simple.  However, when notes have below market stated interest rate, issue at a discount and provide that interest is not compounded on interest owed but not paid, then the determination of the cost of borrowing becomes more complex.  At a certain discount factor, the present value of cash outlays equals the present value of cash receipts.  See Introduction to Corporate Finance at 129-32.  The interest rate corresponding to this discount factor in the present value table3 is the real or effective cost of borrowing, the implicit interest rate.


22
Determining the real or effective interest rate and interest expense is the essence of the economic accrual method.  Revenue Rule 83-84 describes it as follows:


23
The amount of interest attributed to the use of money for a period between payments is determined by applying the "effective rate of interest" on the loan to the "unpaid balance" of the loan for that period.  The unpaid balance of a loan is the amount borrowed plus interest earned minus amounts paid.  The effective rate of interest is a measure of the cost of credit, expressed as a yearly rate, that relates the amount and timing of values received to the amount and timing of payments made, and is thus a reflection of the cost of the amount borrowed for the time it is actually available.  See Conf.  Rep. No. 97-760, 97th Cong., 2d Sess. 553 (1982), 1982-2 C.B. 600, 637;  S.Rep. No. 97-494 (Vol. 1), 97th Cong., 2d Sess. 209 (1982);  Supplement I to Regulation Z issued by the Federal Reserve System, 12 CFR Sections 226.6 and 226.40 (1979).  Therefore, the effective rate of interest, which is a uniform rate over the term of the loan and is based on the amount of the loan and the repayment schedule provided in the loan agreement, when applied to the unpaid balance of the indebtedness for a given period, will produce the true cost of that indebtedness for that period.  That cost is referred to as the economic accrual of interest for that period.


24
Rev.Rul. 83-84, 1983-1 C.B. 97, 98.  Revenue Ruling 83-84 provides that even though a loan agreement provides that interest shall be earned in accordance with Rule of 78, no deduction for interest will be allowed for any year in excess of the economic accrual of interest.  The Internal Revenue Code, 26 U.S.C. Sec. 7805, which authorizes the issuance of rules and regulations by the Commissioner, also grants the Commissioner the discretion to apply them retroactively.4


25
Interest is defined as the amount charged for the use or forbearance of money.  See Old Colony R.R. Co. v. Commissioner, 284 U.S. 552, 52 S.Ct. 211, 76 L.Ed. 484 (1932).  Economic accrual, or present value analysis, is in general the most precise measure of the cost of borrowing or effective interest.  When a note is not issued at a discount or premium and the stated (market) rate of interest is compounded periodically, the effective rate of interest may equal the stated rate.  Also, other more simple accounting methods such as straight-line amortization may so closely approximate the real cost of borrowing that they are permissible.


26
Quincy Associates attempted to use the Rule of 78 method for computing annual interest expense.  The Rule of 78 is also referred to as the sum of the years digits.  It is a method of allocating the total interest due over the course of a loan to the respective periods.  The total interest for the loan is multiplied by a fraction, the numerator of which is the number of periods remaining on such indebtedness and the denominator is the sum of the periods' digits for the term of the indebtedness.  It is called the Rule of 78 method because a twelve period loan, for which the sum of the digits equals 78, is often used to demonstrate how it works.  The Tax Court used the following explanation:


27
The rule of 78's is based on the idea of a 12-month loan repayable in equal installments.  If the borrower takes out a $1200 loan, he has the use of 12 $100 bills the first month.  11 $100 bills the second month, 10 the third month, and only one the last month.  During the full 12 months, he therefore has the use of 78 $100 bills (12 plus 11 plus 10 * * * plus 1).  The number 78 becomes the denominator of the fraction, while the numerator depends upon when the prepayment takes place.  If prepayment is made at the 7th installment, 57/78 of the total finance charge [is regarded as having] been earned by the creditor (the numerator is the sum of 12, 11, 10, 9, 8, and 7).  * * *  this would amount to 57/78 of $211.68 [the total interest due on the loan], or approximately $155.  Therefore, [the debtor's] rebate due on August 1 would be approximately $57.  [1 J. Fonseca, Handling Consumer Credit Cases, sec. 3:7, at 101 (3d ed.1986).  Fn. ref. omitted].


28
Prabel v. Commissioner, 91 T.C. 1101, 1105 (1980).  Where a loan has more than 12 periods, the sum of the years digits is greater than 78.


29
Quincy Associates' note stated that the total precomputed interest owed over the term of the loan was $4,989,249.  The note also stated that payments would be allocated to accrued interest determined under the Rule of 78 and next to principal.  In the event of prepayment of the whole note, Quincy Associates was to receive a credit for the unearned portion of the interest element of the note determined in accordance with the Rule of 78.  The present situation is the equivalent of a note issued at a discount where the note calls for Rule of 78 amortization of the discount for purposes of interest expense and a credit upon prepayment of the note for any unamortized discount.


30
This Court may not interfere with the Commissioner's audit adjustments under Sec. 446(b) unless they are "clearly unlawful," or "plainly arbitrary."    Thor Power Tool Co. v. Commissioner, 439 U.S. 522, 532-33, 99 S.Ct. 773, 781, 58 L.Ed.2d 785 (1979).  As will be demonstrated, the adjustments are neither of the above.  The note requires the following annual payments:


31
Year                Payments
1980               $ 133,000
1981                 385,000
1982                 379,000
1983                 362,000
1984 through 2003    206,000
                   ---------


32
An additional balloon payment of $1,889,249 is due upon maturity in the year 2003 to pay off the principal balance of the note.  The following schedule provides the annual accrual under the different methods:


33
Year     Annual     Rule of 78's    Economic    Difference
        Payments    Amortization    Accrual      Between
           *          of Pre-          of       Rule of 78
                      computed      Interest       and
                      Interest                   Economic
                                                 Accrual
1980     $ 71,402                    $ 71,402      $ 43,964       $ 27,438
1981      385,000                     417,604       249,847        167,757
1982      379,000                     399,078       233,415        165,663
1983      362,000                     380,552       216,349        164,203
1984      206,000                     362,026       207,659        154,367
1985      206,000                     343,500       207,866  **    135,634
1986      206,000                     324,976       208,098        116,878
1987      206,000                     306,448       208,358         98,090
1988      206,000                     287,924       208,651         79,278
1989      206,000                     269,396       208,981         60,415
1990      206,000                     250,872       209,351         41,521
1991      206,000                     232,345       209,768         22,577
1992      206,000                     213,820       210,236          3,584
1993      206,000                     195,293       210,763        (15,470    )
1994      206,000                     176,766       211,354        (34,586    )
1995      206,000                     158,241       212,020        (53,779    )
1996      206,000                     139,716       212,768        (73,052    )
1997      206,000                     121,190       213,609        (92,419    )
1998      206,000                     102,664       214,555       (111,891    )
1999      206,000                      84,139       215,618       (131,479    )
2000      206,000                      65,612       216,813       (151,201    )
2001      206,000                      47,087       218,156       (171,069    )
2002      206,000                      28,560       219,667       (191,107    )
2003      206,000                         ***        10,036        221,366  (2-
                                                                              1
                                                                              1
                                                                              ,
                                                                              3
                                                                              3
                                                                              0
-------------------------------------------------------------------------------
TOTAL  $5,185,213      $4,989,249  $4,989,249       0


34
*  The total payments due in 1981 through 1992 are allocated solely to


35
interest, and the excess interest accruals result in negative


36
amortization of accrued interest that is charged to the payments due


37
in the 11 subsequent years.  Thus, even though the Rule of 78's accrual


38
of interest in years 1993 through 2003 is less than the payments due,


39
in years 1993 through 2001 the entire payments due still are to be


40
allocated or credited to the negatively amortized interest from the


41
earlier years.


42
**  In years 1985 through 2003, interest accruals under the economic-accrual


43
method increase from year to year due to the negative amortization of


44
interest that also occurs under this method.


45
***  On maturity of the note in 2003, an additional balloon payment of


46
$1,889,249 is due in order to pay off the principal balance of the


47
note.


48
We fundamentally disagree with the taxpayers' position that the Rule of 78 accrual represents economic reality and clearly reflects income.  For example, from 1981 to 1982, the Rule of 78 method results in negative amortization.  Interest accrued exceeds interest paid.  Yet no interest is accrued on this unpaid amount.  Furthermore, the principal owed remains the same from 1981 to 1982 and yet interest expense goes down.  In other words, the effective interest rate decreases from 1981 to 1982.  This is not economic reality.  From 1981 to 1992, the amount of interest accrued annually exceeds the annual payments.  While interest is owed and unpaid, further interest does not accrue on this unpaid amount.  There is no compounding of interest.  Throughout the course of the loan, the annual interest expense decreases according to the Rule of 78.  Thus, from 1981 to 1992, while the total amount owed (principal plus unpaid but accrued interest) is increasing, the interest expense is decreasing.  Again, this is not economic reality.  By way of contrast, the economic accrual method applies the effective interest rate to the total amount owed consistently among periods.


49
The taxpayer argues that economic accrual was not a permissible method of accounting for tax years 1981 and 1982.  Section 446(c) lists permissible methods by which the taxpayer may calculate taxable income.  The second method listed is accrual.  The taxpayer argues that the economic accrual method is not an accrual method because it disregards the all events test.  Treasury Regulation 26 C.F.R. Sec. 1.446-1(c)(ii) provides:


50
(ii) Accrual method.  Generally, under an accrual method, income is to be included for the taxable year when all the events have occurred which fix the right to receive such income and the amount thereof can be determined with reasonable accuracy.  Under such a method, deductions are allowable for the taxable year in which all the events have occurred which establish the fact of the liability giving rise to such deduction and the amount thereof can be determined with reasonable accuracy.  The method used by the taxpayer in determining when income is to be accounted for will be acceptable if it accords with generally accepted accounting principles, is consistently used by the taxpayer from year to year, and is consistent with the Income Tax Regulations.  For example, under an accrual method, a taxpayer engaged in manufacturing may account for the sale of an item when the item is shipped, when the item is delivered, when the item is accepted, or when title to the item passes to the purchaser, whether or not billed, depending upon the method regularly employed in keeping the taxpayer's books;  however, see Sec. 1.451-5 relating to advance payments.  The determination of when an item is shipped, delivered or accepted, or when title passes, does not depend upon when any other item in the contract is shipped, delivered or accepted, or when title passes.


51
The taxpayer argues that the all events test requires that interest be computed in accordance with the parties' agreement.  In the present case, the note calls for amortization of precomputed interest in accordance with the Rule of 78.  However, the agreement is between related parties and the Rule of 78 does not reflect economic reality.  Conversely, economic accrual precisely reflects the cost of borrowing per period.  Economic accrual complies with the all events test.  It is a traditional accrual method within the meaning of section 446(c).


52
Taxpayers point out that in the event of prepayment, a credit against the interest element of the note is determined in accordance with the Rule of 78.  This does not change the economic reality of the cost of borrowing for the term of the loan or the years in dispute.  Prepayment is an event which did not happen in 1981 or 1982 and under the all events test does not affect the interest computation for those years.  Moreover, prepayment is an event solely within the control of the taxpayers.  In economic reality, the difference between the interest element in the event of prepayment and the economic accrual interest owed should be considered a prepayment penalty.


53
The Internal Revenue Code, 26 U.S.C. Sec. 441, requires that income be computed on an annual basis.  See Security Flour Mills Co. v. Commissioner, 321 U.S. 281, 64 S.Ct. 596, 88 L.Ed. 725 (1944);  Burnett v. Sanford & Brooks Co., 282 U.S. 359, 51 S.Ct. 150, 75 L.Ed. 383 (1931).  The taxpayers argue that by considering the whole term of the loan, the Tax Court violated the annual accounting principle found in Sec. 441.  The taxpayers argue that for the years in question, 1981 and 1982, the amount of interest accrued under the Rule of 78 method was not significantly greater than the payments made.  The taxpayers' argument ignores the fact that interest expense is the amount charged for the use or forbearance of money, not the total amount repaid on an obligation.  See Old Colony Railroad Co. v. Commissioner, 284 U.S. 552, 52 S.Ct. 211, 76 L.Ed. 484 (1932).  In reality, a significant portion of those payments should be applied to principal.  Moreover, it was not improper for either the Commissioner or the Tax Court to determine the economic reality of the transactions occurring in the relevant annual accounting periods by reference to the whole term of the note.  Taxpayers ask this court to miss the forest for the trees.


54
In summary, the Commissioner did not abuse his discretion in determining that the Rule of 78 method of computing interest expense failed to clearly reflect income.  He, furthermore, did not commit an abuse of discretion in determining that the economic accrual method of computing interest does clearly reflect income.  There are no unresolved issues of fact material to our determination.  We, therefore, affirm the Tax Court's grant of summary judgment in favor of the Commissioner.



*
 Honorable Alfred M. Wolin, United States District Judge for the District of New Jersey, sitting by designation


1
 Mulholland v. United States, 16 Cl. Ct. 252 (1989) is a related case.  See Appellant's Brief, Ex.  B. Kenneth and Catherine Mulholland owned an interest in Quincy Associates, Ltd. for the years 1981 and 1982.  The Mulhollands brought suit for a refund of federal taxes as recomputed by the Commissioner using the economic accrual method.  The three count complaint provided:  (i) the Commissioner erroneously determined that Quincy was not entitled to deduct interest expenses calculated pursuant to the Rule of 78's method of accounting to the extent that such method resulted in claimed interest expense in excess of that which would be computed under the economic accrual method, Revenue Ruling 83-84, 1983-1 C.B. 97; alternatively, (ii) the Commissioner abused his discretion under 26 U.S.C. Sec. 7805(b):  (a) in failing to apply the rationale of Rev. Rul. 83-84 on a prospective only basis to loans and notes entered into on or after June 6, 1983, and (b) in exempting short-term consumer loans from its mandate;  alternatively, (iii) the Commissioner erred in refusing to allow Quincy to utilize the procedures outlined in Revenue Procedure 84-28, 1984-1 C.B. 475, for changing from the Rule of 78 method to economic accrual
The parties made cross-motions for partial summary judgment as to counts II & III.  The parties stipulated that count I is not currently before the court because of a material issue of fact.  As to count II, the court found no abuse of discretion in the Commissioner's decision retroactively applying Rev. Rule 83-84, see 26 U.S.C. Sec. 7805.  As to count III, the court found that there was a material issue of fact as to the application of Rev. Proc. 84-28, Sec. 3.08:  the parties disputed whether the issue of Quincy Associates' interest calculations had been raised and was pending before the Service on or before April 2, 1984.  The court did not grant partial summary judgment as to count III.
In another similar but unrelated case, the Tax Court upheld the Commissioner's discretion under section 446(b) to disallow interest deductions in excess of economic accrual when the taxpayer has used the Rule of 78 method.  See Levy v. Commissioner, 92 TC, No. 92, CCH Dec. 45,808 (1989).


2
 Sec. 446.   General rule for methods of accounting
(a) General rule.--Taxable income shall be computed under the method of accounting on the basis of which the taxpayer regularly computes his income in keeping his books.
(b) Exceptions.--If no method of accounting has been regularly used by the taxpayer, or if the method used does not clearly reflect income, the computation of taxable income shall be made under such method as, in the opinion of the Secretary, does clearly reflect income.
(c) Permissible methods.--Subject to the provisions of subsections (a) and (b), a taxpayer may compute taxable income under any of the following methods of accounting--
(1) the cash receipts and disbursements method;
(2) an accrual method;
(3) any other method permitted by this chapter;  or
(4) any combination of the foregoing methods permitted under regulations prescribed by the Secretary....
26 U.S.C. Sec. 446.


3
 A present value table provides discount factors for various interest rates by period


4
 The Tax Court determined that the Commissioner did not abuse his discretion in retroactively applying Revenue Rule 83-84 to the years in question.  On appeal, taxpayers do not challenge the retroactive application as an abuse of discretion


