
78 Cal.Rptr.2d 58 (1998)
66 Cal.App.4th 384
AMERICAN SHEDS, INC., et al., Plaintiffs and Appellants,
v.
COUNTY OF LOS ANGELES, Defendant and Respondent.
No. B111513.
Court of Appeal, Second District, Division Two.
August 11, 1998.
*59 Rodi, Pollock, Pettker, Galbraith & Cahill, John D. Cahill and Cris K. O'Neall, Los Angeles, for Plaintiffs and Appellants.
De Witt W. Clinton, County Counsel, and Albert Ramseyer, Deputy County Counsel, for Defendant and Respondent.
FUKUTO, Acting Presiding Justice.
American Sheds, Inc. (ASI), and its parent corporation Browning-Ferris Services, Inc. (BFI; collectively plaintiffs), appeal from a judgment after court trial in an action for refund of real property taxes paid to defendant County of Los Angeles (county). The taxes were levied on a 302-acre landfill property in the cities of Azusa and Irwindale (the property), which ASI acquired in 1987 together with ownership of the corporation that operates the landfill, Azusa Land Reclamation Company (ALR).
Plaintiffs' fundamental contention is that in assessing the market value of the property, the county's assessment appeals board (board) improperly included the value of certain related intangibles of the landfill business, namely, its operating permits and "business enterprise" value. Plaintiffs also contend that certain factors of the board's value determination are not supported by substantial evidence. We conclude that the judgment approving the board's method of valuation must be affirmed.


*60 FACTS
In 1987, ASI acquired the property, and the stock of ALR, for a consideration of $60.3 million, together with agreed additional payments to the seller of 10 percent of the "gate revenues" from the property. Those payments were to become payable upon the occurrence of one of two contingencies, which ultimately did not materialize. Among the most significant of ALR's assets were an assortment of governmental permits authorizing the landfill operation, principally the operating permit issued by the county's Department of Health Services and waste discharge requirements issued by the regional water quality board. After the transfer of ownership, ALR sought enlargement of the discharge requirements, for expansion of the landfill use, but in 1991 the administrative proceedings culminated in restriction of the landfill to deposit of inert waste at the original site, a situation of "Virtua[l] shutdown.'" (Main San Gabriel Basin Watermaster v. State Water Resources Control Bd. (1993) 12 Cal.App.4th 1371, 1378, fn. 4, 16 Cal.Rptr.2d 288 [rejecting challenge to administrative decision].)
ASI's purchase of the property triggered reassessment. The county assessor initially appraised the property at $60 million for the base year of 1987. Subsequent assessments through 1990 reflected this value. Beginning in 1991, when ALR's permits were restricted, the assessment was reduced by about 90 percent, under Revenue and Taxation Code section 51, subdivision (a)(2), which provides that taxable value shall take into account factors "causing a decline in value." Contending that all of these valuations should have been substantially lower, ASI sought reduction from the board.
Before the board, the parties agreed that the income method of value determination was appropriate for the property. That method involves capitalizing, or reducing to present value, the future income attributable to a property. (See Bret Harte Inn, Inc. v. City and County of San Francisco (1976) 16 Cal.3d 14, 24, 127 Cal.Rptr. 154, 544 P.2d 1354 (Bret Harte); Freeport-McMoran Resource Partners v. County of Lake (1993) 12 Cal.App.4th 634, 642, 16 Cal.Rptr.2d 428.) The parties differed, however, regarding the specific method for attributing or projecting income. The county's proposed approach took into account the entire projected income realizable through the landfill business, less expenses and a return to management. ASI tendered the "royalty method," under which the income to be considered would be a percentage rent, or royalty, such as would be paid to the owner by an independent lesseeoperator of the property.
A principal issue was the treatment to be given to intangible rights associated with the property and the landfill operation, particularly the permits. As discussed below, such intangibles are not directly subject to real property tax. On the other hand, the presence of intangible features may enhance the value of real property, which may be determined by assuming their presence. For example, in explaining one of his opinions of value, ASI's principal appraiser testified that "there is an enhancement to the real property by virtue of the franchise which the company has to operate a landfill on that real property." The royalty valuation method, advanced by ASI, was meant to isolate the income attributable to the property itself, and thereby yield a value exclusive of intangibles.
In its decision, the board adopted the royalty approach to determining income, as ASI had advocated. However, to determine and capitalize income, the board employed royalty and discount rates that were respectively greater and less than those ASI had proposed as appropriate.[1] Applying these factors to a projection of operator income, the board determined the taxable value of the property for the 1987-1993 tax years to be as follows: 1987 and 1988, $61 million; 1989, $62,220,000; 1990, $63,464,400; 1991, following restriction of the permits, $5.5 million; 1992, $6.2 million; 1993, $6.9 million.
*61 Having paid the taxes, plaintiffs filed a claim for refund and then this case. Plaintiffs contended that in valuing the property the board had "improperly included the value of non-taxable intangible franchises, permits and licenses," that the royalty and discount rates were not supported by substantial evidence, and that the board had incorrectly attributed to the property's value ASI's entire purchase price, for the property and for ALR and its permits and licenses. These contentions intermeshed: in plaintiffs' view, the calculation rates had produced a valuation equal to the cost of both the land and the intangibles, thus subsuming and effectively taxing those non-taxable elements.
Upon review of the administrative record and the parties' arguments, the trial court ruled in favor of the county. In its statement of decision, the court found speculative the contention that the board had applied the royalty method "with a design to come as near as possible to the property's nominal sales price." The court further held that the board had not unlawfully included the intangibles in its valuation. Finally, the court found that the board's royalty and discount rates were reasonable in view of the evidence.
Plaintiffs' contentions on this appeal essentially mirror those below. Substantively, plaintiffs contend that the board's valuation improperly included the permits and other intangibles associated with the landfill, and that the royalty and discount rates utilized were not grounded in substantial evidence. In addition, plaintiffs pose an initial issue regarding the scope of the trial court's review.

DISCUSSION

1. Scope of Review.
Plaintiffs initially contend that the trial court applied an incorrect scope of review to the board's decision. We conclude that the court's analysis on this score was free of prejudicial error.
The scope of judicial review of tax assessment valuations was explained in Bret Harte, supra, 16 Cal.3d at p. 23, 127 Cal.Rptr. 154, 544 P.2d 1354, as follows: "If the plaintiff claims only that the assessor and the [board] erroneously applied a valid method of determining full cash value, the decision of the board is equivalent to the determination of a trial court, and the trial court in turn may review only the record presented to the board. [Citations.] The trial court may overturn the board's decision only when no substantial evidence supports it...." [Citations.] On the other hand, when the taxpayer challenges the validity of the valuation method itself, the trial judge is faced with a question of law. [Citations.] That question... is whether the challenged method of valuation is arbitrary, in excess of discretion, or in violation of the standards prescribed by law."
Plaintiffs contended below that their claim that the board had improperly included intangibles in its valuation represented a challenge to the validity of the valuation method, requiring review as a question of law under the above rules. The trial court initially agreed, and ruled that plaintiffs accordingly would not be limited to the administrative record but could introduce additional evidence on the question. Subsequently, however, the court reversed itself, noting that the board had employed a valuation method (royalty income) which not only was recognized but indeed had been propounded by ASI itself. The court concluded that the board's decision did not on its face reflect improper inclusion of intangibles in the valuation, and thus the case raised only "a claim of error in applying the correct calculation method." The court restated and adhered to this ruling in its statement of decision.
Plaintiffs again urge that the issue of intangibles should have been considered as a question of law, but we essentially agree with the trial court's conclusion, and also find the issue academic as an appellate matter. In the first place, it is clear that the actual valuation method employedthe royalty income methodnot only was legally recognized but also was adopted at ASI's own suggestion. To that extent, the method was valid as a matter of law, and plaintiffs were estopped from urging otherwise. Second, the claim that this method was applied improperly, to the permits and other intangible *62 matters in addition to the property, addresses not the board's selection of a methodology but rather its application.
In disagreement, plaintiffs cite a number of cases in which assessing authorities' treatment of intangibles was held to give rise a challenge to the valuation method, presenting a question of law, (GTE Sprint Communications Corp. v. County of Alameda (1994) 26 Cal.App.4th 992, 1001, 32 Cal.Rptr.2d 882; Service America Corp. v. County of San Diego (1993) 15 Cal.App.4th 1232, 1235, 19 Cal.Rptr.2d 165 (Service America); County of Orange v. Orange County Assessment Appeals Bd. (1993) 13 Cal.App.4th 524, 529, 16 Cal.Rptr.2d 695; County of Stanislaus v. Assessment Appeals Bd. (1989) 213 Cal. App.3d 1445, 1450, 262 Cal.Rptr. 439 (Stanislaus).) Several of these cases frankly observe that characterization of the issue presents a subtle if not semantic question. (GTE, supra, 26 Cal.App.4th at p. 1001, 32 Cal.Rptr.2d 882 ["Sometimes it is difficult to distinguish between the two types of challenges."]; County of Orange, supra, 13 Cal. App.4th at p. 530, fn. 6, 16 Cal.Rptr.2d 695 ["We ... recogniz[e] there is often a fine line between a challenge to an application of a valuation method and a challenge to the method itself."].)
The cited cases are otherwise distinguishable. In each, the assessing authority had plainly adopted a position concerning the inclusion or exclusion of intangibles, which could be tested as a matter of law against pertinent authority. That is not so in the present case, in which plaintiffs' claim that intangibles were improperly "subsumed" depends on circumstantial evidence, including the numerical components of the valuation formula and the values ultimately yielded.[2] Hence, although a legally unwarranted assessment of intangibles would constitute error as a matter of law, the instant claim that there was such error requires analysis and construction of the evidentiary record.
In any event, the trial court ultimately did measure the intangibles issue against the rules of law regarding the proper effect of intangibles on real property valuation and taxation, and we will do the same. The significance of plaintiffs' scope of review contention therefore: boils down to the trial court's disallowance of additional evidence beyond the administrative record. But plaintiffs have failed to demonstrate prejudice from that ruling. Plaintiffs summarily describe their proposed evidence, essentially concerning the nature and proper valuation of intangibles, chiefly the operating permit. Much of that subject matter appears in the briefs. Plaintiffs have made no showing that a more favorable result would have obtained had their proffered evidence been admitted, and for this reason too their scope of review contention cannot command reversal. (E.g., Evid.Code, § 354.)

2. Treatment of Intangibles.
We consider next the principal contention that the board's valuation of the property improperly subsumed with it the value of intangible assets, primarily ALR's permits to operate the landfill, but also the related "business enterprise" of the landfill. We conclude that plaintiffs have failed to establish error in this respect.[3]
The leading decision regarding property tax consideration of intangibles associated with real property is Roehm v. County of Orange (1948) 32 Cal.2d 280, 196 P.2d 550 (Roehm) (per Traynor, J.). Roehm held that a liquor license, being an intangible asset, did not constitute taxable personal property, under constitutional and statutory provisions. However, the court explained, "Intangible values ... that cannot be separately taxed as property may be reflected in the valuation of taxable property. Thus, in determining the value of property, assessing authorities may take into consideration earnings derived therefrom, which may depend upon the possession of intangible *63 rights and privileges that are not themselves regarded as a separate class of taxable property." (Id. at p. 285, 196 P.2d 550, italics added.) In short, in a real property case, intangibles associated with the realty, such as zoning, permits, and licenses, are not real property and may not be taxed as such. However, insofar as such intangibles affect the real property's value, for example by enabling its profitable use, they may properly contribute to an assessment of fair market value.
These concepts are reflected in Revenue and Taxation Code sections 110 and 212, as amended in 1995.[4] Section 212, subdivision (c) provides that "Intangible assets and rights are exempt from taxation," and that they "shall not enhance or be reflected in the value of taxable property," except that "[t]axable property may be assessed and valued by assuming the presence of intangible assets or rights necessary to put the taxable property to beneficial or productive use." Section 110, subdivision (d)(1) provides, on the one hand, that "The value of intangible assets and rights relating to the going concern value of a business using taxable property shall not enhance or be reflected in the value of the taxable property." But section 110, subdivision (e) then restates the language last quoted from section 212, subdivision (c). Moreover, subdivision (f) of section 110 provides that for purposes of determining the taxable value of real property, "intangible attributes of real property shall be reflected in the value of the real property. These intangible attributes of real property include zoning, location and other such attributes that relate directly to the real property involved."[5]
A useful explanation of the rules embraced in these statutes appears in a September 15, 1995, letter to the Secretary of the Senate by Senator Ken Maddy, author of the amendments. According to Senator Maddy, "The bill provides that the intangible assets and rights relating to the going concern ... are not to be reflected in the value of property. However, under subdivision (e) of Section 110... as added by the bill, property may be valued assuming the existence of intangible assets necessary to put the property to productive use.... For example, under the terms of the bill, an assessor could not use a liquor license to enhance the value of taxable property. However, the assessor may assume the presence of a license so that a bar's taxable property may be taxed as a bar and not at salvage value (i.e., as a warehouse)."
Instructive illustration also appears in Stanislaus, supra, 213 Cal.App.3d 1445, 262 Cal.Rptr. 439. At issue there was the proper assessment and tax treatment of a cable television operator's municipal franchise. The court held that the possessory interests granted by the franchise (e.g., use of public rights of way) were taxable real property, but that the right to conduct a cable business pursuant to the franchise was an intangible, which was not taxable. However, the court concluded, "that the intangible right to do business is not assessable for ad valorem tax purposes . .. does not mean the value of [the company's] intangible rights may not be considered in assessing the value of the possessory interests." (Id. at p. 1454, 262 Cal.Rptr. 439.) After discussing Roehm, supra, 32 Cal.2d 280, 196 P.2d 550, and cases following it, the court held that the assessor should consider the intangibles insofar as they contributed to the property's beneficial use, and that in so doing the assessor could impute an amount of income derivable by reason of the intangible right to do business. (Stanislaus, supra, at pp. 1455-1456, 262 Cal.Rptr. 439.)
In the present case, as the trial court properly observed, the board's valuation decision did not on its face violate these *64 rules by including the permits in the property. Indeed, the purpose of the board's (and ASI's) royalty valuation method was to "capture," or impute to the property, only a percentage of the income realizable from the landfill, corresponding to the value of the property to its owner, when leased for landfill use to an operator. Plaintiffs assert, however, that if incorrect rates are used in such a royalty calculation, the practical effect is to subsume income, and hence value, attributable to nontaxable intangibles. We consider below whether the board's rates were intrinsically valid. Plaintiffs presently contend that certain other components of the board's decision establish, circumstantially, that the board wrongly included the value of the permits and other intangibles in reaching its valuations.
Plaintiffs primarily contend that the fact that the board found a base year value of $61 million, roughly equal to the $60.3 million ASI had paid not only for the land but also for the assets of ALR including the permits, yields "[t]he inescapable conclusion" that the board fully included those intangibles with the property. The trial court found this argument speculative, and we agree that it is nowise dispositive. First, as the court noted, ASI paid substantial additional consideration for the purchase, namely the agreement to pay the seller 10 percent of receipts. ASI counters that the contingencies to payment under the agreement never materialized, and it apparently was terminated in 1991. But that does not mean that the agreement was valueless when it was made, four years before, just as the conditioning of the permits in 1991 does not mean that the property's value was de minimis in 1987. Indeed, the contingent additional payments for which ASI obligated itself appear to have roughly equalled 50 percent of the hypothetical royalty payments on which the board based the value of the property.[6]
Nor is the board's appraisal figure vitiated by the fact that plaintiffs' contractual allocation of the purchase price, and their title insurance coverage and appraisals, minimized the value of the property as compared with the business assets. These allocations largely reflected plaintiffs' own construction of the values, and at least one of them was specifically made for federal tax purposes.
Plaintiffs also point to the board's 90 percent diminishment of value as of 1991, in recognition of the restriction of the permits. Plaintiffs assert that this response confirms that the board included the permits as a principal component of the property and its value. But that does not necessarily follow. The reassessment is also consistent with treating the intangibles as nontaxable, while recognizing the impact of their presence or absence on the beneficial use of the property, and consequently the amount of income it could yield in either case. (Cf. Stanislaus, supra, 213 Cal.App.3d at pp. 1454-1456, 262 Cal.Rptr. 439.)
In sum, plaintiffs' circumstantial evidence does not establish that the board improperly utilized or included for valuation the intangibles of the permits and related business enterprise. Plaintiffs finally contend, however, that such error is manifest from the board's decisional findings. This contention too is unsubstantiated. The board's decision largely explained its application of the royalty method of valuation. The only reference to intangibles question was a statement that "We agree with and adopt the argument and conclusion reached by assessor's counsel as to the `non assessable intangible property issue.'" That reference appears to relate to a similarly titled page of proposed findings and conclusions by the assessor, which the board included (along with ASI's parallel proposals) with its decision.
The most significant of these proposed findings is that the "[o]perating permits are site specific and under California law, their contributory value to real property may be assessed." This statement accords with *65 Roehm, supra, 32 Cal.2d 280, 196 P.2d 550, Stanislaus, supra, 213 Cal.App.3d 1445, 262 Cal.Rptr. 439, Revenue and Taxation Code section 110, subdivision (e), and Senator Maddy's explanation of it, all of which acknowledge that the presence of intangibles associated with property may be assumed and considered in valuing it at beneficial use. Plaintiffs stress that the permits were issued to ALR and are not a form of real property. But we do not read the reference to "site specific" as contradicting that. The permits are "operator specific," because they were granted to ALR. But they authorize operations at this specific property, and contain terms and conditions about how that property must be arranged, maintained, and utilized. The proposed finding recognizes this, and refers to the practical connection between the permits and the property, and vice versa.
The proposed findings go on to state that the landfill was the "primary asset" ASI purchased, and to list certain intangible aspects of the land and the general environment for landfills which contribute to "the site's value." These statements do not evince any impermissible treatment of the permits. The final proposed finding recites, "In contemplation of the foregoing, and after considering all of the evidence, ... we reject the contention that [ASI's] purchase price imputed value to non-assessable intangibles." This Statement too fails to confirm an improper view of the intangibles; it appears to refer to the evidentiary issue of ASI's allocation of the purchase price.
We therefore are not persuaded that the board improperly treated the intangibles associated with the property. The board permissibly considered the permits in appraising the property at beneficial and productive use. The board conducted that appraisal by capitalizing the income attributable to the property by means of the royalty method, to avoid including income that represented the fruits of the intangibles alone rather than the property itself. It remains to consider whether the elements of the royalty income determination were flawed.

3. Royalty and Discount Rates.
Plaintiffs' final contention is that the trial court erred in approving the royalty and discount rates employed by the board. There is no dispute that the scope of review for these issues was and remains substantial evidence. This means that the board's decision may be reversed "only when no substantial evidence supports it, in which case the actions of the board are deemed so arbitrary as to constitute a deprivation of property without due process." (Bret Harte, supra, 16 Cal.3d at p. 23, 127 Cal.Rptr. 154, 544 P.2d 1354.) In this connection, "`" ... `substantial evidence' should be construed to confer finality upon an administrative decision on the facts when, upon an examination of the entire record, the evidence, including the inferences therefrom, is found to be such that a reasonable [person], acting reasonably, might have reached the decision...." [Citation.]'" (Dennis v. County of Santa Clara, supra, 215 Cal.App.3d at p. 1027, 263 Cal.Rptr. 887.)
Plaintiffs first challenge the board's use of a 20 percent royalty rate, i.e., the percentage of income a hypothetical operator of the landfill would pay the owner. They contend that this rate was greater than the evidence supported. We do not agree. The board heard evidence of a variety of actual landfill royalty rates, representing different locations and regions, different times of negotiation, and various types of properties and parties. Plaintiffs' principal appraiser reported 11 contract rates ranging from 5 percent to 20 percent, with a market average, in his opinion, of 15 percent. The assessor added a 30 percent arrangement in Glendale, which plaintiffs' appraiser characterized as atypical because of its age and parties. According to the two sides' conflicting testimony, another Southern California landfill carried either a 25 percent rate or a "split rate" of 10 and 17.5 percent. Finally, plaintiffs' second appraisal expert generally reported rates of 20 to 30 percent during the 1970s, but stated that they had since fallen.
The board's 20 percent royalty rate was within the range of these figures. The board further based its selection on a number of characteristics of the landfill that were perceived as making it desirable, such *66 as its flat, urban location, freeway access, and the scarcity of desirable sites in Los Angeles County. Plaintiffs criticize these elements as not being unique to this landfill, but that charge does not render them irrelevant. In light of all the evidence, the board's assigned royalty rate cannot be characterized, as plaintiffs claim, as one that "no reasonable man would have selected."
The discount rate is the rate used to capitalize projected income by reducing it to present value. It reflects the rate of return an investor would seek to achieve from the property, which in turn includes a factor for the risk inherent in the investment. The board arrived at a rate of 12 percent. Plaintiffs had urged rates of 33 percent, or 18-20.6 percent. The primary reason for the discrepancy was that plaintiffs' rates attributed risk rates not of a landfill property owner but of a waste disposal business, such as BFI itself. In the words of one of their studies, plaintiffs' assumptions "[r]ecogniz[ed] a virtually parallel level of risk for the rental and business income." Similarly, the assessor's proposed discount rate, of 17-18 percent, also derived from considering ownership and operation together, just as the assessor had proposed that the board capitalize all of the net operational income, rather than a royalty.
The board rejected these approaches, and sought to isolate a discount rate that would reflect the risk level of an owner-lessor. Both of plaintiffs' appraisers acknowledged (one of them in a report regarding another landfill) that a prudent lessor could be shielded from the principal risk of environmental litigation by contracting for the operatorlessee to assume responsibility for it. The board accordingly added a risk factor of 2 percent to a 10 percent real estate "debt rate," a more conservative type of investment rate that it viewed appropriate for a longterm lease. In his report mentioned above, plaintiffs' appraiser had also used a 10 percent rate.
Plaintiffs do not challenge the board's rationale of using a discount rate suited to a lessor-owner. They contend, however, that the composite 12 percent rate lacks substantial evidentiary basis, because there was no direct evidence endorsing that rate, or its two components. That is not so. The assessor advanced a 10.25 percent debt rate in reaching its own composite rate, and plaintiffs' appraisers both applied discount rates of 10 percent and 12 percent, in a prior appraisal report and study respectively.
Moreover, direct evidence of the specific rate was not indispensable to justify it. The board's decision that the discount rates proposed for the property and its operation taken together were unrealistically high pointed inexorably to a rate below 17 percent. Under a governing regulation, the board was authorized and directed to develop the discount rate from debt and equity capital rates appropriate to California money markets, and to exercise judgment and discretion in doing so. (Cal.Code Regs., tit. 18, § 9, subd. (g)(2).)[7] In light of the foregoing factors, the board's discount rate and its components were sufficiently, substantially supported.

DISPOSITION
The judgment is affirmed.
NOTT and ZEBROWSKI, JJ., concur.
NOTES
[1]  A higher royalty rate imputes a higher amount of income, while a lower discount rate produces a greater present value for that income.
[2]  As plaintiffs' counsel argued to the trial court, "It's the result that creates the intangible issue."
[3]  Our conclusions with regard to the permits will also apply to the enterprise factor, an intangible which represents the income-producing capacity of the operator's business skill arid practices Plaintiffs themselves have largely treated the enterprise factor as derivative of the permitting.
[4]  Although these amendments postdated the tax years and administrative proceeding at issue, both sides have cited them as reflecting preexisting law, which they appear to do.
[5]  Plaintiffs also cite subdivision (d)(3) of section 110, which provides that "The exclusive nature of a concession, franchise, or similar agreement... is an intangible asset that shall not enhance the value of taxable property, including real property." The present case, however, does not involve any such agreements. That distinction also applies to a case on which plaintiffs heavily rely, Service America, supra, 15 Cal.App.4th 1232, 19 Cal.Rptr.2d 165. That decision held it improper to have valued income and rents attributable to a stadium concessionaire's exclusive rights (as well as income that reflected its business acumen and goodwill).
[6]  Plaintiffs cite Dennis v. County of Santa Clara (1989) 215 Cal.App.3d 1019, 263 Cal.Rptr. 887 for the proposition that a sales price is prima facie evidence of fair market value. The case actually holds that to be true with respect to an arm's length, open market sale, not influenced by exigency, with the proviso that the probative value of such a sale may be displaced by a variety of factors, including the influence of tax and other business considerations. (Id. at p. 1028, 263 Cal.Rptr. 887.)
[7]  In other contexts, prevailing interest rates have been held subject to judicial notice. (Gamer v. duPont Glare Forgan, Inc. (1976) 65 Cal.App.3d 280, 290, 135 Cal.Rptr. 230.)
