This appeal involves a dispute between taxpayer and the government over the proper method of accounting for the cost of taxpayer's inventory.

Bangor Punta Operations, Inc., the taxpayer, is a Wisconsin manufacturer of diverse types of engines for many different industries. Because it uses the accrual system of accounting, taxpayer employs inventories in determining its annual net income. The method chosen to allocate production costs between inventory and current or "periodic" expenses is important, because those costs assigned to inventory are not deducted from gross income until the respective goods are sold. Thus, if the production costs allotted to inventory are too low, currect expenses are overstated and net income is a lower figure than a more accurate accounting system would produce.

There are three components of inventory costs; two of them, direct labor and direct materials, are not at issue in this case. The third, indirect manufacturing expenses or "burden," is the source of the controversy.

During the period in question, the fiscal years ending July 31, 1953, through July 31, 1958, taxpayer employed the "practical capacity" method of allocating burden between inventory and current expenses. The aim of the practical capacity method is to identify that portion of indirect manufacturing expenses attributable to "idle capacity;" in other words, to ascertain the cost of running a factory at less than its "normal" or "practical" capacity. The theory is that only those burden expenses directly relating to goods produced should be charged to inventory, that otherwise an item produced when the factory is operating at low capacity will be improperly inflated by "idle capacity" expenses and will be valued higher than an item produced at full capacity.

The practical capacity method is implemented in two steps, first by estimating the practical capacity of a plant or department. Practical capacity is maximum capacity, usually based on a 5-day, 8-hour shift, reduced by factors of downtime such as setup, lost time, cleanup, engineering changes, parts conversion and training. A "burden rate" is then established by dividing the estimated indirect manufacturing expenses at practical capacity by the number of labor hours or machine hours at practical capacity.

The second step comes at the end of the accounting period, when the burden rate is multiplied by the number of man-hours and machine-hours actually attained (actual earned hours) during the period. This amount is charged to inventory. If there is any excess of actual expense over the calculated amount, it is deducted as a current expense since it represents "idle capacity" cost. This excess is called "unabsorbed burden."

The following is an illstration of the practical capacity method, taken from one of taxpayer's charts:

Anticipated production stated in earned hours 10,000

Normal burden rate ($20,000/10,000) = $2/hour

Burden charged to inventory ($2x9,000) = $18,000

Unabsorbed burden ($19,000-$18,000) = $1,000

During the years in question, taxpayer deducted the following amounts of unabsorbed burden from its gross income:

1953    $1,593,906
1954     2,231,674
1955     1,568,916
1956       990,007
1957     2,113,078
1958     2,440,070
Total  $10,937,651

The government disallowed these deductions because of alleged errors in the use of the practical capacity method and adjusted taxpayer's accounts for costs of goods sold and ending inventory so that the full amount of burden was charged to inventory. The taxpayer sued for refund of some $400,000 in excess profits tax. The district judge upheld the government and the taxpayer appealed.

* The standard used by the Internal Revenue Service in inventory accounting is a method "conforming as nearly as may be to the best accounting practice in the trade or business and as most clearly reflecting the income." 26 U.S.C. Sec. 471 (1967). Cost of inventory must include "indirect expenses incident to and necessary for the production of the particular article." 26 C.F.R. Sec. 1.471-3(c). The government's theory of the case is that taxpayer's misapplication of the practical capacity method invalidates it as a "best accounting practice" and prevents taxpayer's accounts from "clearly reflecting the income." The government challenged a number of taxpayer's practices in applying the practical capacity method; the district court found evidence to support several of the challenges.

A. The first of taxpayer's errors occurred in the 1953-1956 computations of the burden rates for four categories of indirect expenses called the "fixed-four." Indirect expenses are the costs of operating some 60 support departments. These costs are allocated to the production departments through 12 allocation pools. The fixed-four pools, floor space area, machine cost, factory equipment cost, and tools, jigs and factory cost, consist of primarily fixed expenses. These expenses theoretically should not vary greatly according to production levels.

The district court used the following figures to illustrate taxpayer's mistake:

Hours           1952 Budget  1952 Actual  1953 Actual
Regular                 100          100          100
Overtime                              80
Total                   100          180          100
Fixed expenses         $100         $100          100
Burden rate         $1/hour

At the end of 1952 a new burden rate was computed as follows:

Anticipated production stated in earned hours 180

Rather than retaining the previous estimate of normal production hours, taxpayer in 1953 recalculated burden rates for the fixed-four by estimating the next year's production as the higher of the normal hours (100) or the actual production of the previous year (180). This computation violated the theory of the practical capacity method because it used overtime hours to increase the anticipated hours of production beyond a normal 40-hour week. Meanwhile, anticipated expense remained at the 40-hourweek level. As a result, the burden rate dropped after each year of over-capacity production.

The consequence of this error is shown when the unabsorbed burden for 1953 is computed:

The company would then deduct 44 percent of its fixed-four expenses as the cost of "idle capacity" in a year when production equaled the original estimate of full practical capacity. The district court characterized this application of the practical capacity method as "nonsense;" we agree.

The illustration parallels the actual experience of the taxpayer, which had an enormous amount of overtime in 1952 plus a second shift of 35 men. Production dropped substantially in the next four years, but the burden rate continued to include anticipated production based on the exceptional number of hours recorded in 1952. A taxpayer abuses the practical capacity method and understates its income if it deducts as a current expense the purported cost of "idle capacity," which turns out to be the cost of not operating on a heavy overtime schedule.

B. Further distortion in taxpayer's application of the practical capacity method occurred when the 1954 burden rates were revised. An unidentified employee of taxpayer increased the burden rate for each department by 20 cents per hour. There is nothing in the record to show the basis for this increase except speculation about accelerated depreciation and higher labor costs.

Assuming an increase in burden rates could be justified without a study and analysis of cost factors, a percentage increase would have caused less distortion in taxpayer's inventory than did the 20cent across-the-board increase. The 20cent raise resulted in high percentage increases in departments with relatively low burden rates, such as the assembly departments, and in low percentage increases in high-burden departments such as the machine shops.

C. Taxpayer's burden rates were substantially revised in 1956; the erroneous practices outlined above were corrected. In computing rates for its "other indirect" expenses, however, taxpayer made another critical mistake. These other indirect expenses are the eight allocation pools besides the fixed-four. They are primarily variable expenses and should be substantially absorbed under the practical capacity method since their amount varies with volume of production.

Taxpayer estimates its anticipated other indirect expenses for 1956 by using the actual totals for 1955. These totals were in most cases revised slightly upward. But they did not approach a reasonable estimate for expenses at practical capacity because the plant in 1955 was operating at about 70 percent of practical capacity. The burden rate was then figured by dividing the understated anticipated expenses by the normal hours; the result was a much lower burden rate than correct usage of the practical capacity method would have produced.

The district court used the following illustration to show the effect of this error:

1955 figures
--------------------------------------
  Anticipated production
    (normal standard hours)               25,000
  Actual earned hours
    (70% of 25,000)                       17,500
  Indirect expenses
    Fixed-four                           $50,000
    Other (variable)                    $100,000
                                        --------
    Total                               $150,000
Correct method for 1956 burden rate
--------------------------------------
  Actual fixed-four expenses             $50,000
  Normal standard hours                   25,000
  Burden rate for fixed-four
    ($50,000 / 25,000)                            $2.00/hour
  Actual other indirect expenses        $100,000
  Actual earned hours                     17,500
  Burden rate for other indirect
    expenses ($100,000 / 17,500)                  $5.70/hour
                                                  ----------
Burden rate for indirect expenses                 $7.70/hour
Taxpayer's method for 1956 burden rate
--------------------------------------
  Total indirect expenses               $150,000
  Normal standard hours                   25,000
  Burden rate for indirect
    expenses ($150,000 / 25,000)                  $6.00/hour
The difference in unabsorbed burden is then computed:
                     Correct                    Taxpayer's
                     Method                       method
                     ------------               -----------
Total indirect
  expenses                            $150,000                 $150,000
Actual earned hours  17,500                     17,500
Burden rate          X $7.70                    X $6.00
                     ------------               -----------
Absorbed burden                       $134,750                 $105,000
                                   -----------               ----------
Unabsorbed burden                     $ 15,250                 $ 45,000
Difference                                                   --$ 15,250
                                                             ----------
                                                               $ 29,750

When the burden rate for other indirect expenses is derived correctly, the unabsorbed burden almost exactly represents the cost of idle capacity for fixed expenses. Experience conforms to the theory of the practical capacity method. But under taxpayer's method, almost twice as much burden is unabsorbed; it cannot be labeled idle acpacity.

The district court cited other errors, mostly errors of omission, that further interfered with the accuracy of taxpayer's accounting system; it is unnecessary to review them since we have already concluded that taxpayer's system did not reflect income accurately and was not a "best accounting practice."

Taxpayer argues that its erroneous practices had no material effect on its reported income. The basis of its argument is a chart purporting to show that the company absorbed more burden than theoretically required in most years. But this chart was designed using the erroneously high figures for production capacity described in part A above. We are satisfied that the record provides ample support for the district court's conclusion that taxpayer's practices materially distorted its income.

Taxpayer next contends that the government's substitution of the full-absorption method of accounting for inventory was improper. Taxpayer's contention depends on its assertion that the method it used accurately reflected income, which assertion we have rejected. When the method used by taxpayer is unacceptable, "the computation of taxable income shall be made under such method as, in the opinion of the Secretary or his delegate, does clearly reflect income." 26 U.S.C. Sec. 446 (1967).

Under this statute, plaintiff in a suit for refund has the heavy burden of proving that the government's assessment is arbitrary or an abuse of discretion. Lucas v. Kansas City Structural Steel Co., 281 U.S. 264, 50 S. Ct. 263, 74 L. Ed. 848 (1930); Commissioner of Internal Revenue v. Joseph E. Seagram & Sons, Inc., 394 F.2d 738 (2d Cir. 1968); F. & D. Rentals, Inc. v. Commissioner of Internal Revenue, 365 F.2d 34 (7th Cir. 1966), cert. denied, 385 U.S. 1004, 87 S. Ct. 707, 17 L. Ed. 2d 543 (1967).

Furthermore, the taxpayer must produce evidence from which another and proper calculation can be made before it is entitled to any refund. Compton v. United States, 334 F.2d 212 (4th Cir. 1964); United States v. Pfister, 205 F.2d 538 (8th Cir. 1953); Roybark v. United States, 104 F. Supp. 759 (S.D.Calif. 1952), aff'd, 218 F.2d 164 (9th Cir. 1954). We agree with the district court that the taxpayer here failed to provide the kind of evidence that would allow a recalculation of its inventory cost under a correct application of the practical capacity method. Under these circumstances, substitution of the full-absorption method is appropriate. Photo-Sonics, Inc. v. Commissioner of Internal Revenue, 42 T.C. 926 (1964), aff'd, 357 F.2d 656 (9th Cir. 1966); Frank G. Wikstrom & Sons, Inc. v. Commissioner of Internal Revenue, 20 T.C. 359 (1953).

In regard to the government's computation of inventory cost, taxpayer raises one objection for the first time on appeal. It complains that the government has charged to inventory items of depreciation, taxes and losses that are deductible from gross income under 26 U.S.C. Secs. 164, 165 and 167 (1967). Taxpayer cites All-Steel Equipment, Inc. v. Commissioner of Internal Revenue, 54 T.C. 1749 (1970), in which similar items were not charged to inventory under the full-absorption method.1

We believe this case falls under United States v. Tyrrell, 329 F.2d 341 (7th Cir. 1964). In Tyrrell this court held that only an exceptional case should be reopened to consider recomputations urged for the first time on appeal. Sections 164, 165 and 167 have been part of the Internal Revenue Code at least since 1954; they were available as a basis for objection during the entire ten-year pendency of this case in the district court. All-Steel's deduction of those items was not a startling development. Even if it had been, the opinion in All-Steel was published several months before the district judge's opinion was issued without its being called to his attention. This is not the extraordinary case that merits a recalculation of the government's assessment.

Having decided taxpayer was not entitled to a refund because of its misapplication of the practical capacity method, the district court proceeded to consider a contention first raised by the government in its posttrial brief. This argument, which was not presented in the pleadings, in the pretrial briefs nor during the taking of evidence,2 is that the practical capacity method-even used correctly-is not appropriate for valuing taxpayer's inventory. The district judge accepted the government's reasoning, that the complex and ever-shifting nature of taxpayer's manufacturing operations made inaccuracy in computation of practical capacity inevitable.

Because neither party addressed itself to this issue during the trial, there is no testimony directed to the question whether taxpayer's operations precluded use of the practical capacity method. While there is evidence of taxpayer's variances in production levels, there is no evidence that the theory of practical capacity requires steady production to function accurately. The tardy emergence of this issue and the lack of support in the record for the government's position oblige us to reject this holding of the district court.

Resolution of this issue did not affect the outcome of the case; in fact, the holding was so irrelevant to the issues at trial as to constitute an advisory opinion on a hypothetical question. We believe the taxpayer should not be precluded from showing in future years that proper application of the practical capacity method will result in a reasonably accurate division of inventory costs and periodic expenses. This is especially so in light of the government's recent steps seemingly in the direction of officially approving use of the practical capacity method to allocate fixed burden costs.3

The district court's order dismissing the complaint is affirmed as modified in part II.