*546 Decision will be entered under Rule 155.
SUPPLEMENTAL MEMORANDUM OPINION
These cases were originally assigned to Special Trial Judge Hu S. Vandervort pursuant to section*547 7456(d) (redesignated section 7443A(b) by the Tax Reform Act of 1986, Pub. L. 99-514 section 1556, 100 Stat. 2755), and Rules 180, 181, and 183. 1 On September 22, 1987, the Court filed its opinion in these cases (T.C. Memo 1987-479">T.C. Memo 1987-479) and provided decisions would be entered under Rule 155. The parties were unable to agree to the correct tax liability. The cases were subsequently assigned to Special Trial Judge Carleton D. Powell pursuant to section 7443A for hearing under Rule 155. The Court agrees with and adopts the opinion of the Special Trial Judge, which is set forth below.
SUPPLEMENTAL MEMORANDUM OPINION OF THE SPECIAL TRIAL JUDGE
POWELL, Special Trial Judge: At issue in these cases is the fair market value of timber eligible for treatment under section 631(a) for taxable years 1974 to 1977. Petitioner, an Oregon corporation engaged in logging and related activities, harvested the timber in Oregon, Louisiana, and Arkansas. For convenience, references to Louisiana*548 timber will include timber harvested in both Louisiana and Arkansas.
Section 631(a) provides that a taxpayer may elect to treat the cutting of timber as though it were a hypothetical sale or exchange of that timber and, therefore, a taxable event. Prior to the enactment of section 631(a), the entire gain realized from timber cut by a taxpayer was taxed as ordinary gain. Consequently, a taxpayer electing section 631(a) converts what would otherwise be ordinary income into capital gain on the cutting of eligible timber.
The capital gain or loss under section 631 (a) is an amount equal to the fair market value of the timber as of the first day of the taxable year in which the timber is cut, less the taxpayer's adjusted basis for depletion of the timber. The resulting gain or loss qualifies for section 1231 capital gain or ordinary loss treatment, provided the required holding period is met.
To determine the fair market value of the timber as of the first day of the tax year in which the timber*549 was cut, we resolved various issues in our original opinion and articulated guidelines for the parties to follow. We held, in part, that the best indicator of fair market value for purposes of section 631 (a) is the comparable sales method of valuation. Under this method, values from contemporary sales of comparable timber in the same geographical area are obtained. From the sales of the comparable timber, we sought to derive a formula to determine the fair market value of the eligible timber.
A majority of the comparable sales were multiple-year contracts to cut timber. They did not require the purchaser to pay cash on the bid date, but required payment in the future when the timber was cut. In Louisiana, the contracts were generally three years in length, while in Oregon the contract period ran up to five years. We held that bids on long-term (i.e., greater than twelve months) contracts were to be discounted to reflect current cash value (present value). Having decided that some discount is necessary to value the comparable government timber sales, we discussed the Hammon, Jensen*550 and Wallen (HJW) theory as a solution to arrive at the most accurate comparable values. We recognized, however, that adjustments were necessary to allow the HJW theory to conform comparable sales to timber valuations of petitioner.
With respect to the Louisiana timber, we found that it grew at a rate of 7 percent annually. Therefore, an adjustment was necessary to account for the growth that took place between the cruise date, which takes place approximately 6 to 9 months before the bid date, and the valuation date. Further, we held that the fair market value was to be determined by the statistical high bid for purposes of standing timber.
Rather than stating a fair market value of the timber, we entered the decision under Rule 155 and left the calculation to the parties. Under Rule 155, parties are required to submit "computations pursuant to the Court's determination of the issues, showing the correct amount of the deficiency * * * to be entered as the decision." The starting point for the computation is the statutory notice of deficiency from which the parties compute the redetermined*551 deficiency based upon matters agreed by the parties or ruled upon by the Court. The Home Group, Inc. v. Commissioner,91 T.C. 265">91 T.C. 265, 269 (1988).
Due to unresolved differences in determining the 1974 to 1977 timber values, the parties failed to submit agreed tax calculations for the Court's approval. The parties were not in agreement as to the correct methodology for calculating either the Oregon or Louisiana timber values.
PRELIMINARY MATTERS
Many of the problems encountered by the parties in their Rule 155 conputation concerning the Oregon timber issues arise from the fact that the Court, in its prior opinion, only described the method the parties were to use in computing the value of the comparable timber but did not set forth the algebraic formula that would accomplish the desired result. In order to eliminate confusion on this point, we now set forth the algebraic formula to be used by the parties.
As we stated in our previous opinion, we began with the standard formula for determining the present value of a single future payment:
CE = FP/(1+i)<t>
Where
CE = the cash equivalency (i.e., present value) of a payment to be received in the future
FP*552 = the payment to be received in the future
i = the monthly discount rate (as determined in our prior opinion to be 0.66667% per month, i.e., 8% per year/12 months per year)
t = the period of time (measured in months) in which the payment is to be received.
We then modified the formula "to apply to the facts of this case." Willamette Industries, Inc. v. Commissioner,54 T.C.M. (CCH) 616">54 T.C.M. 616, 631, P-H Memo T.C. par. 87,479 at 2576.
The initial modifications reflect the fact that payment for the timber was made in a series of payments over time rather than in a single payment:
CE = SIGMA<T>[t=1] (FP/(1+i)<t>)
Where
T = contract length in number of months.
The next modification is the one about which the parties disagree. We stated that "[f]urther modification is required to account for the fact that no interest is incurred on payments made within the first 12 months of the contract." 54 T.C.M. (CCH) 616">54 T.C.M. 616, 631, P-H Memo T.C. par. 87,479 at 2576. This statement reflects the agreement of the parties and means that amounts received within 12 months of the bid date are not to be discounted. It does not mean, as petitioner contends, that amounts paid*553 after the twelfth month are to be discounted back to the first day of the thirteenth month. We cannot accept petitioner's contention because it is inconsistent with the underlying rationale of discounting payments in order to determine their present value on the bid date. Failing to discount payments back to the bid date would unnecessarily distort and inflate the cash equivalency values. Therefore, all payments received after the twelfth month shall be discounted back to the bid date. Thus, the equation becomes
CE = SIGMA<12>[t=1] FP [t] + SIGMA<t>[t=13] (FP [t]/(1+i)<t>)
The payment to be received in the future (FP<t>) is equal to the price per unit for that species during that time period (Q<t>). By substituting P<2>Q<t> for FP<t>, we allow the volume harvested in each month to vary over the length of the contract. Thus, the formula becomes:
CE[s] = SIGMA<12>[t=i] P[s]Q[t] + SIGMA<t>[t=13] P[s]Q[t]/(1+i)<t>)
WHERE
CE[s] = the cash equivalency (i.e., present value) in dollars for species S
P[s] = indicated bid price in dollars per thousand board feet for species S
Q[t] = harvest volume in month t in thousand board feet of species*554 S
The cash equivalency of the contract is then the sum of the cash equivalency for each species.
Having clarified the formula the parties are to use in valuing the comparable timber, we now turn to the specific differences the parties have.
OREGON TIMBER ISSUES
1. Application of Discount to Private Sales
Respondent takes the position that a discount should be applied to all Oregon long-term timber sales contracts, regardless of the nature or the terms and conditions of those sales. Petitioner argues that a discount should be applied to United States Forest Service (USFS) and Bureau of Land Management (BLM) sales only. Petitioner further argues that if a discount is to be applied to private sales, then the actual terms of each of those contracts should be taken into account.
When we discussed the approach to be taken with respect to the present value discounting, we concluded with the following parenthetical instruction: "(Unless of course, such contracts have their own stated interest rate or cutting schedules. If such is the case, then the HJW theory can be adjusted and applied to reflect the specifications outlined in the contract.)" 54 T.C.M. (CCH) 616">54 T.C.M. 616, 632, P-H Memo T.C. par. 87,479 at 2577.*555
Since the private contracts require an interest payment on all deferred payments, they take into account time value of money considerations. However, some of the private contracts contain stated interest below the 8 percent rate we selected in our prior opinion. Respondent's approach to discounting these contracts by using a discount factor equal to the interest rate differential (i.e., 8 percent minus the stated interest rate) is overly simplistic. When we selected the 8 percent rate we only did so in response to the fact that the public contracts contained no stated interest. The 8 percent rate was used as an approximation of a weighted average of relevant interest rates for the years in question. Where a contract, such as the private sale contract, contains stated interest we assume that the stated interest rate represents the appropriate rate of interest at which to discount payments inasmuch as the buyer and seller are better aware of the economics surrounding that particular contract and have factored the relevant risk elements into the stated interest rate. Therefore, there is no need to actually discount a private contract containing its own payment schedule and stated*556 rate of interest because, assuming it is the result of arm's length bargaining, the private contract stated rate of interest would closely approximate the true cost of money adjusted for contract-specific risk. This method follows more closely the language of section 1.631-1(d)(2), Income Tax Regs., as cited in our original opinion, which requires timber eligible for treatment under section 631 to be valued in "light of the most reliable and accurate information available with reference to the condition of the property."
This is also the more practical approach to valuation under the comparable sales method because the Court does not have to second guess interest rates and because it reflects the reality of a true comparable sale. Moreover, if we take respondent's position to tis logical conclusion, the Court would be required to discount at a rate of 8 percent even those private contracts with a stated interest rate of greater than 8 percent.
2. Discount Period
The parties agree that all payments made on contracts lasting less than one year and all payments*557 made during the first twelve months on long-term contracts should not be discounted. This is more of a rule of convenience than a reflection of economic theory since the amount of discount during the first twelve months is minimal.
The parties, however, dispute the reference date to which to discount payments made after the first twelve months on long-term contracts. Petitioner contends that this stream of payments should be discounted back to the end of the twelfth month. Respondent argues that the stream of payments should be discounted to the bid date.
We hold that all payments received after the first twelve months are to be discounted back to the bid date. The purpose of our previous opinion was to determine the fair market value of the subject timber on the bid date by reference to the sales price of comparable timber. Since the purchaser of the comparable timber typically did not pay the total sales price of the timber on the bid date but rather paid for the timber over a period of time, the Court had to make allowances for the time value of money (i.e., the payments had to be discounted). In doing so, the Court discussed the discounting theories advanced by the parties, *558 particularly the HJW theory. The Court modified the HJW theory, as discussed supra page 6, "to apply to the facts of this case." In doing so, the Court decided that payments received after the first twelve months are to be discounted back to the bid date.
3. Application of Discount to Bid Prices
Respindent takes the position that the discount formula should be applied to the indicated market value (IMV), not to bid prices. IMV is a term used, in various forms, by many of the appraisers in these cases. In each instance, the IMV indicates a dollar amount that has resulted from adjusting bid prices for quality differences, logging costs, and other costs.
We hold that the discount formula is to be applied to the bid price, rather than to any form of adjusted price. The fundamental purpose of discounting is to make adjustments to payments to be made in the future. The purchaser of a long-term timber sale contract is obligated to pay the bid price, not the IMV, at a date sometime in the future.
4. Logging Road Costs
We ruled in our original opinion that the value of standing timber does not include the cost of constructing roads. We directed the parties to use the Cascade*559 Appraisal Services (CAS) data base of comparable sales (i.e., the average indicated values) as the starting point in the Rule 155 computation. Respondent argues that road construction costs must be subtracted from CAS' average indicated values to accurately reflect the Court's ruling that the value of standing timber does not include the cost of constructing roads. Petitioner argues that the subtraction of the road construction costs is improper.
In deriving its average indicated value for USFS comparable sales, CAS started with the so-called high bid, which includes road construction costs. It then subtracted from the high bid the road credits for merchantable and per acre material. This net figure is the so-called stat high bid. CAS' second step in deriving the average indicated value was to make a quality adjustment. CAS' final step, and the one which creates the dispute, was the logging cost adjustment. The logging cost adjustment included, inter alia, the addition of the costs of constructing roads to the indicated value.
The first step CAS took in making the logging cost adjustment was to determine the logging costs of the USFS comparable sale. The total logging cost*560 of the USFS comparable was then compared to the total logging cost for a specific subject area. Where the total logging costs of the USFS comparable timber exceeded the total logging costs for the subject timber, CAS increased the indicated market value of the subject timber by the difference.
Thus, CAS added in the cost of constructing roads to derive the total logging costs of the USFS comparable timber but did not include the cost of constructing roads to derive the total logging cost of the subject timber. Therefore, even if the USFS comparable and subject total logging costs were identical, CAS would still make a positive logging cost adjustment thereby increasing the indicated market value of the subject timber in an amount equal to the costs of constructing roads on the USFS comparable timber. This violate the Court's prior opinion.
We will adopt the solution proposed by respindent. The indicated market value of each subject timber sale should be reduced by the road construction costs reflected in the logging cost data portion of CAS' data analysis sheets. This puts both the USFS comparable and the subject timber on the same footing. This solution produces a value for*561 the standing timber itself without the enhanced value attributable to the existence of the roads and so complies with our holding on this issue.
5. Use of Material Not in the Record
To determine the private sales data available for applying the discount formula, we need to rule on the appropriate use of material not in the record. It appears that most of the pertinent data is in the record. As to the data that is not in the record, there is no reason the parties cannot enter in to a stipulation or agreement as to data in the parties' workpapers for the purposes of the Rule 155 computation and the Court directs that this be done.
6. Discount Rate
The discount formula used an 8-percent annual rate of interest at which to discount and to compute the present value of future payments under long-term cutting contracts. Petitioner contends that the annual rate of interest should be reduced to 4.16-percent to reflect the effect of a 48 percent corporate income tax deduction.
We hold that the 8 percent annual rate of interest shall apply without adjustment for income taxes. In our prior opinion, we adopted the discount formula using the 8 percent annual rate of interest. Even*562 if petitioner's argument were timely made, we decline to amend our decision because, although a 4.16 percent discount rate may be appropriate to determine a corporation's after-tax cost of an asset, it is inappropriate to use a tax-adjusted interest rate in order to determine fair market value.
LOUISIANA TIMBER ISSUES
1. Southern Pine Growth Factor
In our previous opinion, we indicated that the USFS timber in Louisiana was generally cruised six to nine months prior to the actual sale date, and that an adjustment must be made for the growth taking place during that period. Respondent has proposed that the parties use 7-1/2 months as the appropriate period for adjustment, as a compromise between six and nine months. Petitioner has indicated that it is willing to accept this compromise. We hold that this is a fair time period for adjustment.
2. Southern Cut-out Schedule
Petitioner suggests that 25 percent of the timber should be deemed cut in the first year, 25 percent deemed cut in the second year, and 50 percent deemed cut in the third year of three-year timber contracts. Respondent has agreed with that position. We hold that the parties should adopt this cut-out*563 schedule. Furthermore, for contracts of more than three years or less than three years, comparable sales will be deemed to have been cut 50 percent ratably during the first two-thirds of the contract term and 50 percent ratably in the final one-third of the contract term.
3. Application of Growth to Hardwoods
Petitioner argues that the Louisiana growth factor should not apply to hardwood saw timber. Petitioner argues that this adjustment for growth to hardwood is not necessary since the parties agreed on hardwood values for three of the five periods. Respondent does not dispute the agreed-upon hardwood values for the years 1975, 1976, and 1977. Respondent, however, submits that the hardwood values should be adjusted on the same basis as the pine values for the disputed periods.
It is well known that hardwoods, such as oak, hickory, hard maple, sweetgum, ash, walnut, and yellow poplar, on average grow more slowly than softwoods, such as yellow pine, cypress, and red cedar. See, e.g., Rasson, et al., "Forest Resources of Louisiana," Resource Bulletin SO-130, United States Department of Agriculture Forest Service Experimental Station, New Orleans, Louisiana (1988); Gedney, *564 et al., "Timber Resource Statistics for Non-Federal Forest Land in West CentralOregon," Resource Bulletin PNW-RB-143, United States Department of Agriculture Forest Service, Pacific Northwest Research Station, Portland, Oregon (1987). We hold that for the disputed period the growth factor the parties will use for the Louisiana hardwood will be an amount equal to two-thirds of the growth rate for the Louisiana softwood (as discussed in 1. Southern Pine Growth Factor, supra page 14) for that period.
4. Southern Purchaser Road Credits
For the valuation of subject Forest Service timber, we ruled in our original opinion that the timber should be valued without road credits and that the appropriate sales price of the Forest Service comparable figures is to be the bid price without road credits. We held that the road credit issue was pertinent only to Forest Service timber in Oregon. Respondent invites us to reconsider and to hold that road credits should be applied to the subject Louisiana timber as well as the Oregon timber. We decline.
5. Continental Can Timber
During the years in question, petitioner cut a significant volume of timber on land owned by Continental*565 Can Company (CCC). One of the issues resolved in our prior opinion was whether to value the timber purchased from CCC using USFS sales. After considering a variety of factors, we found that the value of CCC timber was "at least equal to the value" of USFS timber. Accordingly, we found that USFS sales could be used to value the CCC timber.
Respondent contends that CCC timber must be valued using a combination of USFS sales and other, less valuable, private sales. In doing so respondent does not dispute our finding that CCC timber was at least equal in value to USFS timber. Petitioner asserts that only USFS sales can be used to value the CCC timber, and that private sales should be ignored. Having already found that the USFS timber is an adequate measure of the value of the CCC timber, we see no reason to cloud the issue by introducing the value of private timber. USFS sales will be used exclusively in valuing the CCC timber.
To reflect the foregoing,
Decision will be entered under Rule 155.
Footnotes
1. All section references are to the Internal Revenue Code as in effect for the years in issue, unless otherwise noted. All Rule references are to the Tax Court Rules of Practice and Procedure.↩