*1129OPINION.
Green:The sole assignment of error set out in petitioner’s petition is that the deductions allowed by the Commissioner for the two years in question, on account of depletion of the petitioner’s interests in several ore properties, are not reasonable allowances as contemplated by section 234(a) (9) of the Revenue Act of 1918. The determination of the deductions to which the petitioner is entitled, as a matter of statutory right, on account of depletion of its interests in certain ore properties, must be made through the use of three factors: (1) Estimated ore reserves in place in the mines at March 1, 1913; (2) March 1,1913, value of those reserves; and (3) tonnage sold by the several lessees during the years in question. By dividing the second factor by the first, a unit rate of depletion is obtained which, when multiplied by the third factor, will produce a result representing the proper annual depletion allowance. The Commissioner and the petitioner are in agreement as to the figures repre-*1130seating the first and third factors, but disagree as to the March 1, 1913, value of the ore reserves and of the petitioner’s interests therein at that date. Consequently, the issue presented by this appeal must be decided accordingly as we find that the March 1, 1913, value fixed by the Commissioner is correct or incorrect.
In the determination of the value, at any basic date, of ore. properties, in the case of a lessor, the most common and generally accepted method of making such a valuation is what is known as the present-value method. This method contemplates that the total expected income to be derived from the extraction and/or sale of ores by operating lessees will be received by the lessor in equal annual installments over the estimated life of the property. Where the programs of production of the operating lessees contemplate a material variation in the annual production and sale of ores from a uniform scale over the life of the property, then the method must be modified so as to give effect to actual conditions. The March 1, 1913, value of the petitioner’s interests in several ore properties fixed by the Commissioner was determined in principle in accordance with the present-value method, and gives effect to the variations in annual production which must result through the carrying out by the lessees of their programs of production. However, the petitioner contends that in the application of the present-value method the Commissioner has fallen into error in several respects and hence his valuation is erroneous.
We have set out in our findings of fact how the Commissioner reached his determination as to the March 1, 1913, values of the interests of this petitioner in certain ore properties. For the sake of clarity we illustrate below his determination as to the value of a single mine, described in the several exhibits as Tract No. 1, Lot No. 3, NE14 of NW% and Lot No. 4, NWy4 of NW%, Section 6, Township 57, Eange 20:
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*1131The classification of the estimated ore reserves at March 1, 1913, according to open pit, milling, and underground, was made in accordance with the method to be used in their extraction. Open pit ore, being the top layer, is removed by steam shovel; milling ore is mined and broken down by hand methods and then taken out by steam shovels; while underground ore is broken down into cone-shaped openings, drawn out at the bottom of the cone through chutes, loaded into cars underground, trammed to the shaft and hoisted to the surface. With respect to some of the mines, the operating lessees’ programs of ore production ostensibly provided for the deferment of operations in respect of milling and underground ores until the open pit ores had been entirely exhausted. With respect to certain other mines, milling and underground operations overlapped open pit operations, and in still further instances the three operations were to be carried on simultaneously. The active life in years is the operating lessee’s estimate of the time necessary to exhaust each class of ore, while the deferred life in years represents the operating lessee’s estimate of the number of years before extraction of each class of ore will commence. The discount factors computed on the basis of a risk rate of 6 per cent are those prescribed by Hoskold’s tables for ascertaining the present worth of $1 accumulated over a period of years, assuming that the income will be received in equal annual installments. The deferred factor computed on the basis of 6 per cent compound interest is used to reduce the present worth of royalties at the date the petitioner will begin to receive them to their present worth at March 1, 1913.
The petitioner points out what it believes to be two fundamental errors in the Commissioner’s method of computing the March 1,1913, value of its ore properties, as follows:
(1) The valuation of each mine is based upon a classification of ores according to the process of extraction to be employed by the operating lessees; and
(2) Ores which will be extracted and sold simultaneously have been assigned different values though the lease agreements provide the same royalty payment in respect of every ton of ore extracted.
With respect to the first allegation of error, the petitioner contends that a valuation based upon a classification of ores according to the process of extraction must necessarily be erroneous, since the leases make no distinction in the value of the ore, but, on the other hand, irrespective of the process of extraction employed, it is entitled to receive the same royalty for every ton of ore extracted and sold. With respect to the second allegation of error, the illustration heretofore set out shows precisely the ground upon which it is predicated. It will be noted therefrom that, during the last eleven years of the life of the mine, open pit, milling, and underground operations will *1132be carried on simultaneously. It would appear from this illustration, at first glance, that the Commissioner has assigned a March 1, 1913, value to each ton of open-pit ore mined during the last eleven years of 10.824 cents ($1,375,211-4-12,105,110) and a value, at the same date, to each ton of milling or underground ore mined during the same period, of 6.103 cents ($224,019.55-4-3,670,570). This is a circumstance which the petitioner can not understand, since under the terms of its lease it is entitled to the same royalty on every ton of ore mined whatever the process involved. It contends that each ton of ore had an equal value at March 1,1913.
It is apparent from its petition and all the arguments set out in its brief, that the petitioner is laboring under a misapprehension as to just what is the basis of the Commissioner’s valuation. The petitioner has assumed that the Commissioner has valued each class of ore separately according to the process of extraction employed. But this is not a correct assumption. The Commissioner has made reference in his valuation schedules to the three classes of ore simply as a matter of convenience and for the purpose of readily identifying certain items in those schedules relating to production with the same items as they appear in the operating lessee’s programs of production. For instance, reverting again to the illustration, the classification of the ore reserves into three classes is of no importance whatever and the Commissioner’s valuation is not in the least affected by it. The important thing in this respect is that, according to the operating lessee’s program of production, 12,705,110 tons of ore will be extracted during twenty-eight years by the open pit process, an annual production by this process during the life of the mine, of 453,753-26/28 tons, and that during the last eleven years 3,670,750 tons of ore will be extracted by the milling and underground processes, an annual production by the latter process during the last eleven years of 333,704-6/11 tons. But all of this simply indicates that, irrespective of the processes of extraction involved, during the first seventeen years of the life of this mine the annual production by the operating lessee will be 453,753-26/28 tons, while the production for the last eleven years of the life of the mine will be 787,458 tons.
The March 1,1913, value of the petitioner’s interests in certain ore properties may, in the absence of evidence of a more satisfactory basis, be computed upon the present worth at that date of the expected future royalties. To determine the present worth of those royalties at the basic date, March 1, 1913, necessitates a determination of the rate at which those royalties will be received by the petitioner, and this, in the last analysis, must depend upon the estimated rate of extraction according to the operating lessee’s program of production. Having determined the rate at which the ores will be extracted and the royalties received, appropriate discount factors must be applied to those expected royalties to reduce them to their present worth at *1133the basic date. In the illustration the expected minimum annual production over the life of the mine will be 453,753-26/28 tons, hence, on a 25 cent royalty basis, the expected annual minimum royalties over the same period will be $113,438.25, or a total for the period of $3,176,271. To ascertain the present worth of these minimum royalties at March 1,1913, necessitates the application of a single discount factor, predicated upon a fair risk rate and the length of the period over which the income will accumulate. From the eighteenth to the twenty-eighth year there will be an additional annual production over the minimum of 333,704-6/11 tons, yielding additional royalties to the petitioner during this period of $83,426 per annum, a total for the period of $917,687.50; but the petitioner will not begin to receive these additional royalties until the beginning of the eighteenth year, hence, the application of the single discount factor referred to above, to these additional royalties, will only serve to reduce them to their present worth at the beginning of the eighteenth year, so that a further discount rate, representing the present worth of $1 at a fair rate of compound interest for seventeen years, must be applied to reduce the royalties to their present worth at March 1, 1913. The sum of the present worths at March 1, 1913, of the minimum and additional royalties is the March 1, 1913, value of the lessor’s equity in the ore in this mine. The following illustrates the working out of this method of valuation:
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*1134Estimated expense 3% of gross royalties:
Present worth at March 1, 1913, of net minimum royalties, 6% and 4%. ($3,176,271.00 — $96,288.13) X.446356_$1,375,215.19
Present worth at March 1, 1913, of additional royalties 3rd to 28th yr. 6% and 4%— ($6.50 — $0.20) X.465820X.88999644_ 2.61
Present worth at March 1, 1913, of additional royalties 18th to 28th yr. 6% and 4%= ($917,687.50 — $27,530.63) X.677672X .37136442_ 224, 019.75
Present worth at March 1, 1913, of lessor’s equity in the mine_ 1, 599,237. 55
Present worth at March 1,1913, of petitioner’s one-third interest- 533, 079.18
The method adopted by the Commissioner is but a short cut which arrives at the same result. Under the method outlined above, as well as the Commissioner’s method, each ton of ore in the mine, irrespective of the process of extraction to be employed, has the same valué at March 1, 1918, ascertained by dividing the value of the lessor’s equity by the total ore reserves.
All that has previously been said with respect to the one mine used in the illustration applies with equal force to all the ore properties we have under consideration.
The petitioner contends that the only proper method of valuing its interests in these ore properties at March 1, 1913, is to assume that the ores contained in each mine will be extracted by the operating-lessees in equal amounts over the maximum life of the mine, and that the royalties will be received in equal installments. The petitioner considers the maximum life of the mine as the number of years of active operations necessary to exhaust all the ores plus the number of years of deferment of operations. With this contention we are forced to disagree. With respect to all the mines, except those covered by leases Nos. 4, 7, and 8, the operating lessees had, at March 1, 1913, laid down programs of operation and production. With respect to several of the mines these programs called for a deferment of all operations for a period in some instances running as long as eight years. In the case of some mines the programs provided for a considerable production in the early years with a much lessened output in later years, while the converse was provided for in the case of still other mines. In the valuation of these ore properties as of March 1, 1913, we see no good, reason to disregard the operating lessees’ programs of production which later developments have shown to have been reasonably correct.
The petitioner contends that in computing the values of the ores in the mines covered by leases Nos. 4, 7, and 8, the Commissioner should have used a risk rate of 6 per cent in lieu of 8 per cent for the purpose of ascertaining the present worth at March 1, 1913, of expected future royalties in excess of the minimum royalty payments provided for in the lease agreements. As pointed out in our *1135findings of fact, the operating lessees under these three lease agreements had at March 1, 1913, no definite programs of operation. During the taxable years in question no ore was produced from the mines covered by leases Nos. 7 and 8, the lessees under these leases making only the minimum royalty payments provided in the lease agreements; and this appears to be true with respect to the mines covered by lease No. 4, although the record is not entirely clear in that respect. At March 1,1913, it was highly speculative as to when the petitioner would begin to receive under these three leases royalties in excess of the minimum royalty payments provided in the lease agreements, and the same situation appears to have still existed eight years later. Under such circumstances, we approve the Commissioner’s action in adopting a risk rate of 8 per cent in valuing the mines covered by leases Nos. 4, 7, and 8.
Judgment will be entered for the Commissioner.