
95 N.W.2d 61 (1959)
167 Neb. 875
In re the assessed valuation, Bert E. MATZKE and Marian L. Matzke, husband and wife, Appellants,
v.
BOARD OF EQUALIZATION OF MADISON COUNTY, Nebraska, Appellee.
No. 34511.
Supreme Court of Nebraska.
February 20, 1959.
*62 Daniel D. Jewell, Norfolk, for appellants.
Eugene C. McFadden, Vincent J. Kirby, Norfolk, for appellee.
Heard before SIMMONS, C. J., and CARTER, MESSMORE, YEAGER, CHAPPELL, WENKE and BOSLAUGH, JJ.
CARTER, Justice.
This is an appeal from a judgment of the district court for Madison County affirming the actual valuation placed on appellants' property in the amount of $28,685.
The appellants Matzke are the owners of the property involved in this litigation, the legal description of which is correctly described in the pleadings. The property is located within the corporate limits of the city of Norfolk at the intersection of South Third Street and Northwestern Avenue. The property is located in a business area approximately 1 mile and 3 blocks south of the main business district of Norfolk, which area has deteriorated because of economic factors to such an extent that it is described as having the appearance of a ghost town. The building occupies the full width of the land at the front. It is 143 feet long, and is 45 feet wide for 49 feet and 35 feet wide the balance of its length. The building is a two-story building with a basement. Its exterior walls were constructed with brick. The interior walls, floors, and roof were wood construction. The building contains 33 sleeping rooms, a lobby, 8 baths, 25 lavatories, a sink, and a water heater. The *63 building is heated with steam from a boiler fueled with a coal stoker. The main part of the building was constructed in 1911 and the remaining part in 1914.
The building was constructed as a hotel and used as such for many years. In April 1954, the Matzkes purchased the property and its contents for $20,000. The purchase price was on a basis of $13,000 for the building and the land, and $7,000 for personal property in it. The Matzkes continued to operate the property as a hotel until December 3, 1956, when it was converted into a nursing home. It has a capacity to care for 41 patients. On March 1, 1957, there were 10 patients in the home, the most that had occupied the nursing home to that date. When the case was tried in January 1958, there were 35 patients in the home. The gross income from occupants of the home was in excess of $3,500 per month when the case was tried. In addition to the Matzkes, 11 persons work at the home. The Matzkes made improvements on the building in excess of $3,000. Matzke testified that the market value of the property on March 1, 1957, was $15,504.35.
The evidence of appellee is substantially as follows: By a fixed formula the replacement cost of the building was determined to be $94,881. The building was depreciated 52 percent of its replacement cost on account of its age, the building being approximately 43 years old. The physical value of the building was determined to be $45,542. A functional depreciation of 40 percent was taken off on account of the location of the property and the irregularity of its occupancy, leaving a valuation of $27,325. To this was added the value of the real estate in the amount of $1,360, thus fixing the actual value at $28,685.
The case will be tried de novo in this court as an equitable proceeding. The burden of proof is upon the taxpayer to establish his contention that his property has been valued in an amount greater than its actual value, or that his property has not been fairly and proportionately equalized with all other property, resulting in a discriminatory assessment. Appeal of Newman (Newman v. County of Dawson), 167 Neb. 666, 94 N.W.2d 47.
The evidence of the plaintiffs is sufficient standing alone, to sustain a finding that the property involved had an actual value of $15,500 on March 1, 1957. The question for determination is the sufficiency of the evidence of the county board of equalization to sustain an actual value of $28,685 as determined by it.
The evidence of the county board of equalization is that the actual value of the property was determined by a formula which was uniformly and impartially applied. By this formula the replacement cost of the building was fixed at $94,881. The building was 43 years old. The evidence is that the useful life of the building was 50 years. Any use in excess of 50 years is dependent upon its care and the extent of the repairs made upon it. There is no evidence in this record as to the upkeep of the building over the years. The evidence indicates that the building had run down considerably during the years it was unprofitably operated as a hotel. In its calculations the county board of equalization allowed a physical depreciation of 52 percent on account of age. There is no showing in the record to explain or justify a physical depreciation of only 52 percent on a 43-year-old building with a useful expectancy of 50 years. The physical depreciation of the building by 52 percent was the result of arbitrary action by the county board of equalization. LeDioyt v. County of Keith, 161 Neb. 615, 74 N.W.2d 455; Appeal of Newman (Newman v. County of Dawson), supra. The only basis in the record on which the building could be depreciated on account of age produces a depreciated value, under the formula employed, which would result in an actual value less than $15,500, *64 the actual value established by the plaintiffs.
In Appeal of Newman (Newman v. County of Dawson), supra, we approved a formula for determining the value of tangible property for taxation purposes where it was shown to comply substantially with section 77-112, R.S.Supp., 1955, and had been uniformly and impartially applied. But where the formula applied requires the use of an arbitrary figure to arrive at a result, the result is as arbitrary as the figure itself. In the instant case the county board of equalization allowed a physical depreciation of 52 percent on the building because of its age. Since the building was 43 years of age with a use expectancy of 50 years, the physical depreciation of 52 percent is not shown to have any reasonable relation to the depreciation of the reproduction cost on account of age. We realize, of course, that a building which has completed its use expectancy may be of considerable actual value. Reproduction cost less depreciation is but one element of the statutory formula for determining actual value. But the physical depreciation of a building on account of age may not be exclusively asserted in the evidence on the basis of its age as compared with its use expectancy, and then allowed on an arbitrary basis not shown by the evidence to have any relation to its age or the depreciation resulting therefrom. A formula for determining the value of tangible property for taxation purposes must tend to produce the result required by section 77-112, R.S. Supp., 1955, when applied uniformly and impartially. Where it appears that an arbitrary basis is used which is not uniformly applied to all tangible property the result is an arbitrary one. It will not sustain a valuation for tax purposes.
We conclude that the actual value of the property fixed by the county board of equalization is the result of arbitrary action and is not sustained by the evidence. We find that the evidence sustains a valuation of $15,500. The judgment of the district court is reversed and the cause remanded with directions to enter a decree fixing the actual value of plaintiffs' property in the amount of $15,500.
Reversed and remanded with directions.
