delivered the opinion of the court.
This appeal involves the assessment of C. & N. W. Railway property for the tax year 1968. The State Board of Equalization employed Justin H. Haynes & Company, a firm of professional appraisers, to appraise, for determining the true value for tax purposes, all railroads operating in Wyoming for the tax years 1967 and 1968. Insofar as this case is concerned, although it is profusely discussed and an extensive showing was made before the board, no attack has been made upon evaluation for the year 1967. The value of all these railroad properties was determined for the tax year 1968 by applying a flat reduction of 3.9 percent; or stated conversely, placing an evaluation of 96.1 percent of the valuation as determined for the year 1967 to arrive at the valuation for the year 1968. Appellant objects strenuously to the determination of this tax value for this year, contending that the 3.9 percent reduction is discriminatory and unfair. It is admitted by the board that the figure of 3.9 percent is based upon a computation involving the Union Pacific Railroad.
Appellees seek to sustain this action and justify the result by contending that no single approach or formula for the determination of railroad value can be applied to this appellant because of the wide variance in result if any one of the standard approaches were applied to appellant (or for that matter to any other railroad in Wyoming except Union Pacific) ;1 that to avoid this consequence the board determined in 1967 that the best way to arrive at the true value was to first determine the replacement cost- — less physical and functional loss — and reduce the same by economic loss as indicated by the stock and debt and capitalized earnings approach. According to appellees, the exact amount of economic loss in each case was the result of exercise of the appraisers’ judgment from their examination and consideration of the sharply varying results of the stock and debt and capitalized earnings approaches.
The first step in the 1968 appraisal was the obtaining of reports submitted by the railroads to both the board and their stockholders and other information deemed necessary. This data indicated no significant change in physical property and, hence, no change in replacement costs. The replacement cost, stock and debt, and capitalized earnings approaches to valuation were all again calculated and examined in 1968 for the various railroads. These various approaches to value in 1968 again yielded, as they did in 1967, a similar result for the Union Pacific property and wide variations with regard to all other Wyoming railroads. In the opinion of the appraisers since there had been no significant changes in physical property any difference in value from 1967 to 1968 would consist solely of economic gain or loss to railroad property generally, and they concluded that the economic loss for the one-year period 1967 to 1968 indicated for Union Pacific property was a valid and reliable measure of one-year economic loss of all railroad property in Wyoming. The record indicates that if there was sole reliance upon that formula used to determine the proper reduction for the Union Pacific and it was applied to the C. & N. W. it would have resulted in a reduction in excess of 36 percent. It may well be suggested when we *191consider the basis of this tax as being ad valorem that in the absence of some substantial change of the physical plant and property this result would be ridiculous.
Appellants herein protested the allowance of the 3.9 percent reduction and after hearing on this protest the board found as follows:
“That after investigation and analysis of the factors of stock and debt, capitalized earnings and replacement cost less depreciation (depreciation for physical, functional and economic loss, as established by the appraisal as of January 1, 1967) for all operating railroads in the State of Wyoming, it was determined by Justin H. Haynes & Co--that the best indication of economic change from the January 1, 1967, value, which equally affected all operating railroads, was demonstrated by the computation of stock and debt and capitalized earnings applied to replacement cost less depreciation found in the Union Pacific Railroad valuation in which all three factors were approximately equal and that the resultant 3.9% decline in value was applicable to all operating railroads in Wyoming.”
In its review the district court found the method was correct and did not discriminate against appellant; the board acted upon necessary and proper information; the findings of fact were supported by competent and substantial evidence; and the board did not act capriciously or arbitrarily, or abuse its discretion.
It appears that the material question presented to this court is whether the board from the record had a proper basis for the application of the 3.9 percent reduction as applied to this appellant. The answer lies in the record.
The principal witnesses for the State were Ainsworth, an employee of the board, and Leet, representing Justin H. Haynes & Company. It is their testimony upon which this determination rests and which must be examined.
Ainsworth states this reduction of 3.9 percent as it affects appellant was based upon an analysis made of stock and debt and capitalized earnings value and the physical depreciation value. No explanation thereof or the results of such analysis, particularly as applied to this appellant, were ever submitted. The work sheets appearing in evidence do not reveal the basis of any reduction insofar as it affects appellant nor the correlation between examination of the appellant’s reports and the proposed reduction, and we can find nothing appearing in these sheets which would have permitted the board to determine why this figure was a proper reduction for C. & N. W. Ainsworth also testified the board was advised that the factors of physical value, capitalized earnings, and stock and debt value were all considered in arriving at this figure as applied to appellant, but the details of this advice are not set out; that no formula was used; that C. & N. W. figures were not closely enough related to be indicative of value. The 3.9 percent figure was applied as a matter of Leet’s appraisal judgment. Ainsworth worked under the supervision of Leet and with him.
Because the Ainsworth opinion and work are dependent almost entirely upon Leet, his testimony is of particular importance. After considerable testimony as to the method used in preparing the 1967 appraisal, which is used as a basis for the 1967 tax valuation, Leet explained that in the case of Union Pacific all indexes of value lead to this final conclusion. He stated it was a so-called “textbook case.” He testified that he arrived at a reduction of 3.9 percent for this appellant after an analysis of all the indexes of value; that as a matter of equity this reduction was applied to other railroads as reflecting a change in value from the previous year; and that the same work was done in 1968 as in 1967. His testimony does show that upon a comparative basis the C. & N. W. value was very low for assessment purposes. It is to be noted the 1967 appraisal showed appellant’s property exclusive of land to be 14.5 percent of replacement cost as contrasted to Union Pacific’s 38.63 percent. He testi*192fied that in updating this appraisal he exercised judgment in not slavishly following a formula. A great deal of his testimony and his cross-examination was directed to the 1967 evaluation, which was not under attack.
Leet’s testimony further states the same material was analyzed for all railroads for that year but that the 3.9 percent was ascertained from Union Pacific calculations; that the records of C. & N. W. were examined but no calculations were ever worked out in detail; that after examination of all the same material of the other railroads it was determined to use the figure obtained from analysis of the Union Pacific. We find no explanation of the basis for this determination. The basis of this reduction was calculated on an exhibit which shows such calculations for Union Pacific but no other railroad. It was then lifted and applied to C. & N. W. The 1967 appraisal allowed for an economic loss of 45 percent to Union Pacific and 74 percent for the appellant. Leet testified that the additional loss of 3.9 percent was applicable in his judgment to maintain equalization, primarily a matter of economic loss due to other considerations, and defined economic loss as a loss in value due to physical and functional economic factors affecting property in Wyoming.
The testimony and opinions of these experts upon which the finding of the board rests must be examined in light of the rule that such findings must be supported by substantial evidence in the record.2
The basis of the board’s action is clearly set out in the findings as being the determination of Justin H. Haynes & Company. There is no suggestion by the appel-lees of application of their own expertise or special knowledge. This necessitates focusing our attention on the testimony of these experts. A rather general statement of the rule is that the record must show sufficient facts upon which the judgment and opinion of the expert were based.3 A witness who asserts an opinion of the value of property not supported by facts is not competent, and an expert’s opinion is not substantial evidence unless he can give a satisfactory explanation of how he arrived at his opinion.4 The expert, if relying upon a formula, should state his reasons for its adoption and its component factors and assumptions.5 The opinion of the expert cannot be inferred from the conclusion nor is it proof of existence of factors necessary to support it.6 Nowhere in this, record is there any evidence as to the manner in which the data supplied for the year 1968 was applied in determining the evaluation for C. & N. W. The general statement that this information was considered does not suffice in the absence of some explanation of its applicability and just how it was applied. Leet, upon whom the board relied in its finding, does not have any work sheets reflecting the process or calculations he used to determine the propriety of this reduction as applied to appellant. The thrust of his testimony suggests the 3.9 percent reduction was recommended for the purpose of equalization *193as required by our law.7 The finding of the board, however, bases this reduction upon economic change affecting all railroads. There is no evidence in the record as to general economic change in these railroads or any railroad other than the Union Pacific, and apparently all recognized formulas used for appraisal demonstrate a similar result insofar as that railroad is concerned. The fact this produces a greatly dissimilar result as to appellant and other railroads makes application of this same reduction to all Wyoming railroads suspect.8 The finding of the board as set out above is, as this court has heretofore described it, an ultimate fact and must be supported by findings of basic facts.9
The remainder of the findings do not affect or explain the adoption of the finding that this change equally affected all operating railroads. The findings that there was no change in the physical property and that application of the stock and debt and capitalized earnings method would result in a value less than the value of operating lands owned by C. & N. W. in this state are important but these are negative findings which may demonstrate the impropriety of the use of the formula which was applied to the Union Pacific but certainly do not demonstrate the propriety of the application of this flat reduction to the appellant. The finding of the board “That use of the allocations for railroad operating property which fluctuate from 45.71% to 29.07% in one year would result in an unwarranted change in value of the properties in Wyoming which physically remained substantially the same” is a finding of the same character.
It is our view, then, that appel-lees herein did not have substantial evidence before them upon which they could have properly arrived at the conclusion “that the best indication of economic change from the January 1, 1967, value, which equally affected all operating railroads” (emphasis supplied) as appearing in the findings and which was based upon the formula applied to the Union Pacific. We have heretofore recognized the rule that the finding of basic facts will not be implied from the finding of ultimate facts,10 and it is upon this ultimate fact that the board bases its decision.
This case and the record herein are certainly demonstrative of the fact that courts must rely upon expertise and information of state boards specializing in such matters, and this court must never substitute its judgment therefor. We also recognize that the state board in this case is composed of honest, dedicated, and conscientious public servants who have honestly and diligently attempted to arrive at a fair valuation for C. & N. W. However, the legislature has enjoined upon that board and exacted from them a requirement that its decisions be based upon substantial evidence. This court has the duty to examine this record and to determine whether there be such substantial evidence, which we find lacking in this case insofar as it applies to the flat valuation reduction of 3.9 percent. *194Stated in most elemental and simple terms, this reduction is based upon a formula admittedly inapplicable to C. & N. W.
The judgment of the trial court is therefore reversed with instructions that its judgment and order be vacated and that the order of the board be set aside and the proceedings remanded to the board for further consideration and rehearing to determine the propriety of the reduction herein allowed and to determine if the 3.9 percent figure properly represents the economic loss suffered by appellant. If the same be determined not to be applicable the board is instructed to determine the proper percentage of reduction which should be applied to this appellant.
Reversed with instructions.
. Pour approaches to appraisal of value of railroad property are: (1) original cost less depreciation; (2) replacement cost new less physical and functional loss ; (3) stock and debt; (4) capitalized earnings. The first approach is limited to near new property and under the circumstances present in the instant situation was not used. In 1967 the second, third, and fourth approaches were tried for all entire railroad operating systems in the state, with widely divergent results for each railroad except in the case of Union Pacific where all separate approaches yielded the same or nearly the same value.
. Section 9-276.32 (c), W.S.1957, 1971 Cum.Supp.; Monahan v. Board of Trustees of Elementary School District No. 9, County of Eremont, AVyo., 486 P.2d 235, 237; Pan American Petroleum Corporation v. Wyoming Oil and Gas Conservation Commission, Wyo., 446 P.2d 550, 555.
. Downs v. Longfellow Corporation, Okl., 351 P.2d 999, 1004; 32 O.J.S. Evidence § 546(63), p. 267.
. United States v. Certain Land Located at 400 Lee Street, Montgomery, Alabama, D.C.N.D., 214 F.Supp. 148, 150-151; Arkansas State Highway Commission v. Stanley, 234 Ark. 428, 353 S.W.2d 173, 175, 4 A.L.R.3d 749; State Highway Commission v. Byars, 221 Ark. 845, 256 S.W.2d 738, 741-742; Board of Regents of University and State Colleges of Arizona v. Cannon, 86 Ariz. 176, 342 P.2d 207, 209.
. Standard Oil Company of California v. Moore, 9 Cir., 251 F.2d 188, 221, certiorari denied 356 U.S. 975, 78 S.Ct. 1139, 2 L.Ed.2d 1148.
. Arkin Construction Company v. Simpkins, Fla., 99 So.2d 557, 561.
. Sections 10 and 11, Art. 15, Wyo.Const.; § 39-26(a), W.S.1957.
. The witness explained why the stock and debt method was inapplicable to the then C. B. & Q. R. R. because of peculiar market conditions engendered by the fact that stock was closely held.
. Pan American Petroleum Corporation v. Wyoming Oil and Gas Conservation Commission, supra.
.Pan American Petroleum Corporation v. Wyoming Oil and Gas Conservation Commission, supra; Fallon v. Wyoming State Board of Medical Examiners, Wyo., 441 P.2d 322, 327, rehearing denied 443 P.2d 135.