
586 A.2d 1153 (1991)
Albert and Janet BREAULT
v.
TOWN OF JERICHO.
No. 88-172.
Supreme Court of Vermont.
January 11, 1991.
*1154 Kolvoord, Overton & Wilson, Essex Junction, for defendant-appellant.
Before ALLEN, C.J., and PECK, GIBSON, DOOLEY and MORSE, JJ.
DOOLEY, Justice.
The Town of Jericho appeals from a decision of the State Board of Appraisers (Board) reducing the listed value of taxpayers' residence in Jericho because of "economic obsolescence." We affirm.
Taxpayers' property is located on one acre of land on a paved road. The Town listers had appraised the land at $27,049 and the house at $70,250. Upon the taxpayers' appeal to the board of civil authority (BCA), the value of the improvements was increased, bringing the total valuation to $98,700. Taxpayers appealed to the Board, which at first found an even higher total valuation than the BCA, but arrived at a final total listed value of $92,900 after reducing its own initial figure by thirteen percent for physical depreciation and eight percent for "economic obsolescence,"[*] and then reducing the product by an additional ten percent, which it found to be the Town equalization ratio.
The Town does not contest the physical depreciation figure or the equalization ratio. The only issue on appeal is the Town's objection to the reduction for "economic obsolescence." This term refers to loss from the upper limit of value due to "factors external to the property." International Ass'n of Assessing Officers, Property Assessment Valuation 171 (1977). The Vermont State Appraisal Manual prepared by the Vermont Department of Taxes defines it as "[a]ny outside influence that would adversely affect the value of the subject property," such as an "adjacent gas station, shop or any undesirable type of use." Division of Property Valuation and Review, Agency of Administration, Vermont State Appraisal Manual GI-10 (1980).
*1155 The reduction for economic obsolescence was based on taxpayers' testimony that their well suffers from salt contamination from the nearby Town salt shed and that the Town landfill is visible from their property. The representative of the Town testified that no property in the Town was adjusted for economic obsolescence because it is a "clean town." The Board found that "the proximity of the subject to both the Town landfill and the Town salt shed constitutes an impairment in the desirability of the Breault house because of its location. Therefore, in the opinion of the Board, this situation warrants the application of a locational obsolescence factor to the subject." The Board went on to note that it had no evidence of the effect of this factor on the sale price of properties with similar negative environmental influences. It concluded, however, that an 8% factor was appropriate.
The Town argues first that the finding that the landfill is visible from taxpayers' property is not supported by the evidence. The taxpayers testified that it was visible before the Board, and there was no contrary evidence. Where warranted by the evidence, the Board's finding must stand. Sondergeld v. Town of Hubbardton, 150 Vt. 565, 571, 556 A.2d 64, 68 (1988). While the Town is correct that the Board did not find that noise or odors from the landfill reached taxpayers' property, the Board did not purport to make such finding.
The Board's choice of the eight percent figure for economic obsolescence is more problematical. The Board was faced with a situation where a recognized adjustment to value was necessary and the Town had failed totally to make that adjustment. However, there was no evidence from comparable properties showing the impact of the locational factors on fair market value. Indeed it is unlikely that such evidence would exist since the locational factors are unique to each property affected.
Both the Town and the taxpayers offered comparables, and these showed a range of values for similar properties. The Town offered evidence of three comparable properties, sold near the date of listing, in support of its listed value. Taxpayers introduced an appraisal report, valuing their property (house and land) at $80,000 as of approximately one year earlier. They also submitted evidence of the listed values of three comparable properties.
The Board accepted that the location of taxpayers' house devalued it, approximating that devaluation at eight percent. The Board also accepted the comparables offered by the Town and stated: "This data would support a value for the subject of $109,700 without the application of a locational factor; with the application of ... depreciation, a FMV of $103,200 is attained." In support of its method, the Board found: "The neighborhoods of these comparables are more desirable than Brown Trace Road [where taxpayers property is located]." The listed value obtained by the Board lies within the range of the evidence and is higher than the listed value of each of the comparables offered by the taxpayers.
The evidence presented by both the taxpayers and the Town was abundant and the Board's evaluation of the competing presentations was fully explained, unlike the myriad of cases that have come before this Court in which there has been little or no explanation of why or how the Board arrived at its decision. See id. at 570, 556 A.2d at 67 (surveying cases where Board's decision was unsupported by adequate findings). The missing piece, if there is one, is the absence of evidence of why the locational factors cause an adjustment of precisely eight percent, as found by the Board.
We do not believe that this missing piece is fatal to the Board's conclusion. We have said that once the Board shows that it has considered the evidence before it and has explained the reasons for its result, its decision enjoys a presumption of validity. Id. at 571, 556 A.2d at 68. It is not necessary for an administrative body or a trial court exercising discretion to explain the precise mathematics that led to a particular decision involving a sum of money. See Coty v. Ramsey Assocs., 149 Vt. 451, 461, 546 A.2d 196, 203 (1988) (where exact *1156 computation of tort damages is difficult, award will stand unless "grossly excessive"); Stamper v. University Apartments, Inc., 147 Vt. 552, 556, 522 A.2d 227, 229 (1986) (disability benefits upheld where testimony "reasonably supports" the percentage of disability). Once the Board has shown some basis in evidence for its valuation, the appellant bears the burden of demonstrating that the exercise of discretion was clearly erroneous. See, e.g., In re Green Mountain Power Corp., 138 Vt. 213, 215, 414 A.2d 1159, 1161 (1980); Pantasote Co. v. City of Passaic, 100 N.J. 408, 413, 495 A.2d 1308, 1310 (1985). If the decision is within the range of rationality, it must be affirmed. Department of Taxes v. Tri-State Industrial Laundries, Inc., 138 Vt. 292, 294, 415 A.2d 216, 218 (1980).
Although we have not had occasion to apply these principles to a case exactly like this one, there are numerous precedents from other courts on point. These decisions affirm property tax valuation conclusions that fall within the range of the evidence before them, with or without a precise mathematical breakdown. For example, in North American Philips Lighting Corp. v. Board of Assessors, 392 Mass. 296, 465 N.E.2d 782 (1984), the taxpayer challenged the state appellate tax board's determination of the rental income value of the subject property. Although the board had rejected the assessors' methodology and adopted that of the taxpayer, it still considered the assessors' evidence. The court disagreed with the taxpayer's claim of error, stating:
Here Norelco's [taxpayer's] witness himself presented the board with comparable average square foot values ranging from a low of $1.06 to a high of $2.09. The board was not required to agree with the conclusion of Norelco's witness as to which value in this range was appropriate. The board's decision to adopt $1.90 per square foot is a proper exercise of its discretion in this area of expertise. Accordingly, even if we agree that the board had to disregard all evidence presented by the assessors' witness after rejecting the multi-tenant approach to determine the rental value of the assessed property, the board's decision is supported by the record.

Id. at 300, 465 N.E.2d at 785-86 (emphasis added). See also Foxboro Associates v. Board of Assessors, 385 Mass. 679, 689, 433 N.E.2d 890, 897 (1982) (in the absence of specific evidence of the degree of deterioration of the property or the appropriate adjustment factor for obsolescence, factor chosen by board was within its discretion). In Federal Reserve Bank of Minneapolis v. County of Hennepin, 372 N.W.2d 699 (Minn.1985), the taxpayer placed obsolescence at $20,000,000, while the assessor's figure was $11,000,000. The court affirmed the tax court's decision, which found a market value different from that of either party but did not detail its calculations, stating:
Apparently, the relator's expert regards the unique design and quality materials, such as the granite used in the office tower and plaza, as "superadequacies" which add to the cost of reproduction while adding nothing to market value. The tax court found the assessor's allowance for obsolescence, a matter of peculiarly subjective judgment, the more persuasive. We cannot say the tax court's acceptance of the assessor's position on obsolescence was clearly erroneous. Nor does the tax court's declination to adopt the exact market values proposed by either of the expert appraisers constitute error. The value opinions of experts are merely advisoryevidence to be considered with the other evidence in the caseand the finder of fact is not concluded by them.
Id. at 701-02 (emphasis added).
In choosing an economic obsolescence factor, the Board acted within its expertise, the range of the evidence, and the discretion we must accord to it.
Affirmed.
NOTES
[*]  The actual figures show that the Board applied depreciation factors that are a smaller percentage of the fair market value than the percentage figures specified by the Board. It appears that the discrepancy can be explained if we apply the percentage depreciation figures solely to the value of the house. Thus, it is possible that the adjustment was actually too small and the value should be lower. However, any mistake benefited the Town and is harmless to the Town's appeal.
