ROBERTS, J.

Respondent is the owner of the Sheraton-Johnson Hotel in Rapid City, Pennington County. The 1956 assessment fixed the value of the land at $59,985, the structure at $813,485, and the personal property at $77,470. The city and county boards of equalization denied petitions for reductions and the owner appealed to the circuit court. Following a trial de novo the circuit court *556 reduced the assessed value of the structure to $566,383, and confirmed the assessed value of the personal property as made by the assessor. There appears to have been no controversy concerning the assessment of the land. The city and county have appealed from the judgment of the circuit court.

Appellants contend that the evidence is insufficient to justify the finding of the court that the assessed value of the hotel structure for 1956 was in excess of its true and full value in money and that the court erred in granting the reduction. Their contentions more specifically are (1) that the complaining taxpayer did not overcome the presumption that the assessor’s valuation was correct and not excessive; (2) that the sale price of the property nine years prior to the assessment did not furnish a substantial basis for evalution; and (3) that the assessor ascertains the valuation of property for taxation purposes in Pennington County by analyzing replacement costs, comparative sales, and capitalization of inc'ome which is a generally accepted method of evaluating property and that from the evidence the court should have found that such a formula was fairly and impartially applied in 1956 to the hotel structure.

The standard of valuation prescribed by statute at the time of the assessment here in question was that “All property shall be assessed at its true and full value in money. In determining the true and full value of real and personal property the assessor shall not adopt a lower or different standard of value because the same is to serve as a basis of taxation, nor shall he adopt as a criterion of value the price for which the property would sell at an auction or at a forced sale, or in the aggregate with all the property in the town or district; but he shall value each article or description of property by itself and at such a sum or price as he believes the same to be fairly worth in money.” SDC 57.0334. “True and full value”, as defined in SDC 57.0301, means “the usual cash selling price at the place where the property to which the term is applied shall be at the time of the assessment.” The statute in other words provides for an assessment at the price that property would bring to its owner if it were offered for *557 sale on an open market under conditions in which neither buyer nor seller could take advantage of the exigencies of the other. See Tidball v. Miller, 72 S.D. 243, 32 N.W.2d 683. The Constitution (Art. XI, § 2) requires not only that “taxes shall be uniform on all property of the same class”, but that the “valuation of property for taxation purposes shall never exceed the actual value thereof.”

As we have stated there is no claim of discrimination in valuation between the the hotel property and similar property in the same taxing district and that reduction was necessary to effect uniformity. However, if the hotel property was assessed in excess of its actual value, respondent taxpayer was entitled to a reduction notwithstanding there was no discrimination in valuation and assessment. In re Jepsen’s Appeal, 76 S.D. 421, 80 N.W.2d 76 and cases cited.

An appeal to the circuit court from the action of the county board of equalization in refusing to reduce the assessed valuation of property is tried de novo and the circuit court does not merely have power to determine whether the action of the board of equalization was without jurisdiction or arbitrary, but to determine anew what is the actual value of the property and to reduce the assessment if the same is in excess of actual value. Williams v. Stanley County Board of Equalization, 69 S.D. 118, 7 N.W.2d 148; In re Robinson, 73 S.D. 580, 46 N.W.2d 908; Appeal of Margulies, 75 S.D. 36, 58 N.W.2d 620.

Appellants place much stress on the presumption that the assessor’s valuation is correct. This is an application of the general rule that in the absence of proof to the contrary courts will presume that public officers have properly discharged the duties of their offices, Adamson v. Minnehaha County, 67 S.D. 423, 293 N.W. 542; State ex rel. Gosch v. Lemler, 77 S.D. 23, 84 N.W.2d 418. We have held that the presumption had no application where the assessing authorities made no investigation of their own, but accepted valuations made by professional appraisers. In re Jepsen’s Appeal, supra. The presumption, however, like other presumptions does not take the place of evidence. It disappears when evidence is introduced from which facts may be found. *558 Peters v. Lohr, 24 S.D. 605, 124 N.W. 853; McKiver v. Theo. Hamm Brewing Co., 67 S.D. 613, 297 N.W. 445. The burden of proof in other words is on the complaining taxpayer to prove that an assessment is excessive. Appellants relying principally upon Bennett v. Board of Review, 234 Iowa 800, 13 N.W.2d 351 and LeDioyt v. County of Keith, 161 Neb. 615, 74 N.W.2d 455, contend that the assessing authority’s valuation is reviewable only for arbitrariness or failure to follow standards prescribed by law and not for mere errors of judgment. The Constitution as above stated prohibits an assessment of property for purposes of taxation in excess of its actual value. The purport of the decisions of this court cited above with respect to an appeal from a board of equalization to the circuit court is that the court exercises an independent judicial judgment where valuation in excess of actual value is claimed.

The city assessor based the value of the hotel structure upon replacement costs less depreciation. The assessor prepared a tabulation which was received in evidence as Exhibit 4. It shows that the structure was classified as a fireproof building having a cubical content of 1,173,264 feet; that the basic replacement cost of $962,076 was arrived at by multiplying the cubical content by the replacement figure of 82^ per cubic foot; that various increments were added to the basic cost such as terrazzo tile floors, revolving entrance doors, elevators, cut stone facing and ceramic tile in the lobby; and that the total of these amounts, less a deduction of $970 for each room having a connecting bath, represents' a replacement cost of $1,078,938. The hotel was erected in 1927, but because of remodeling in 1938, 1947 and 1955 the effective age in the opinion of the assessor was reduced to 19 years. Allowing for 17%% depreciation, the exhibit indicates a value in 1956 of $890,125. This amount as returned by the assessor was reduced to $813,485 by reason of a percentage reduction by the State Board of Equalization on a class of structures in Rapid City which included hotels. The assessor testified:

“Our manual * * * was set up in 1952 * * *. There has not been a great deal of variation since 1952 * * *.

*559 “Q. Now, the 82‡ a cubic foot — how did you arrive at that 82‡ cost? A. In 1952, the city com- . mission employed a nationally-known appraisal firm to draw up and create this manual * *.

“Q. And what rate of depreciation per year did you allow? A. This is taken under what we know as Table D-3, scale of depreciation applying to brick or stone, solid or veneer, or poured concrete. It is a graded scale, starting out at one per cent a year. That gets lesser as the building gets older.

“Q. In other words, you computed the number of years of depreciation at 19? A. That’s right. * * * This is the table (Exhibit A) inserted in the manual by the appraisal firm which I mentioned that did this appraisal work in 1952. * * *

“Q. And this rate of depreciation, as applied to this building, then, did not take into account an actual examination of the building or any of these factors of obsolescence which I have just asked you about? A. The assessment — the original appraisal in 1952 consisted of a thorough examination to arrive at these many variations which I have shown. And any obsolescence factors which you have mentioned were not considered to have any particular bearing on the actual worth of the building.”

An appraiser employed by the firm engaged by defendant city to make the appraisal of all taxable property in 1952 within the city gave testimony in support of the valuation fixed by the assessor and approved by the local boards of equalization. He testified in detail and arrived at substantially the same valuation by analyzing data on replacement costs less depreciation and obsolescence, comparative sales of hotels listed in a national survey, and income or profits produced in the operation of the hotel.

Evidence was received of the sale in August, 1947, of ninety-five per cent of the issued and outstanding capital stock of the corporation owning the hotel property and *560 business for $630,711. The purchase included not only the real estate, but also the furniture and furnishings, foods and beverages, accounts receivable and cash on hand. A balance sheet listing assets and liabilities attached to the contract of sale appears in the record. The amount of the sale price attributable to both building site and hotel structure did not exceed $480,000.

A witness who had been associated with hotel operations for thirty-six years and familiar with the building here involved and with values of hotel properties testified as to the physical condition of the hotel, type of construction, depreciation and obsolescence, earnings from the property and other elements affecting its value. He fixed the value of the hotel structure in 1956 at $450,000.

A witness who had for several years been employed as an appraiser to determine valuations for purposes of sale negotiations, mergers and taxation fixed the value of the hotel structure at the time of the assessment in question at $43'97760: -He was not in disagreement with the assessor in his calculations of replacement costs of 82 ‡ per cubic foot. He claimed, however, that the cubical content of the hotel structure as determined by the assessor was excessive in the amount of 78,102 feet. He purported to value the structure primarily on replacement costs less physical and functional depreciation. He testified to the poor design of the building and the impaired c'ondition of the hardware, floor in the lobby, elevators, heating plant and plumbing. The eleventh story was an observatory when originally constructed and the tenth story was a solarium. The witness asserted that these areas are not suitable for hotel use and are difficult to maintain and that much of their construction dost cannot be reflected in the value of the property for purposes of taxation.

A single sale of property as appellants contend citing decisions from other jurisdictions does not ordinarily determine true and full value of a property as there may be economic conditions of a temporary nature and other factors which prevent the same from being a true measure of value. There is no reason to believe nor is there anything in the record to indicate that the trial court gave *561 undue weight to the sale price of the hotel property. The findings of fact indicate the contrary.

In assessing property, the statutory standard of “true and full value” must be adhered to. This as we have indicated is commonly construed to mean the amount a willing purchaser will pay a willing seller in an open market. If there is no market for property subject to taxation, it nonetheless must be assessed at its “true and full value.” Tidball v. Miller, supra. If the market value method cannot be followed, the assessor in the performance of the duty that the law has imposed upon him must use such pertinent factors as replacement costs less proper deductions and income from the property in determining true and full value. De Luz Homes, Inc. v. County of San Diego, 45 Cal.2d 546, 290 P.2d 544; Underwood Typewriter Co. v. City of Hartford, 99 Conn. 329, 122 A. 91; Essex Co. v. City of Lawrence, 214 Mass. 79, 100 N.E. 1016. Among the factors to be considered in the instant case were the age of the hotel structure, its condition and its replacement cost less depreciation and obsolescence. The computation process used by the assessor in determining the replacement cost less depreciation is outlined above and need not be detailed with greater particularity at this point except to state that it was based upon the manual prepared by the appraisal firm and represented with the exception of deduction for rooms having connecting baths a theoretical present cost of reproducing the hotel structure. See Lampe Market Co. v. Alliance Ins. Co., 71 S.D. 120, 22 N.W.2d 427. Such form of depreciation is the loss, not restored by current maintenance, resulting from wear and tear, decay and age. Another form of depreciation is obsolescence or a functional capital loss or diminution of economic usefulness due to “changes in the art, shifting of business centers, loss of trade, inadequacy * * * and other things * * *, apart from physical deterioration * * *.” United States Cartridge Co. v. United States, 284 U.S. 511, 52 S.Ct. 243, 245, 76 L.Ed. 431; Lindheimer v. Illinois Tel. Co, 292 U.S. 151, 54 S.Ct. 658, 78 L.Ed. 1182; Fidelity Union Trust Co. v. McGraw, 138 N.J.Eq. 415, 48 A.2d 279. These *562 elements of depreciation are interrelated and combine to produce a diminution in value.

It clearly appears that beyond physical deterioration there was in the instant case a further loss in value because of functional depreciation or obsolescence and that the assessing and equalizing authorities failed to give reasonable consideration to the diminution in value caused by this pertinent factor and that the formula by which they calculated depreciation produced an excessive assessment. The statutory standard for determining true and full value permits evidence of all relevant factors and does not authorize assessing authorities to fix an assessment within a specific formula. Any method used for the determination of replacement cost less depreciation must be sufficiently flexible to meet the circumstances of each particular case and to reflect actual value.

We conclude that the true and full value of the property fixed by the trial court is sustained by the evidence.

The judgment is therefore affirmed.

HANSON, P. J., and SMITH and RENTTO, JJ., concur.