MACY, Justice.

Appellant Amax Coal West, Inc. appealed to the district court from the findings of fact, conclusions of law, and order which had been issued by Appellee Wyoming State Board of Equalization. The district court certified the case to the Wyoming Supreme Court pursuant to W.R.A.P. 12.09(b).

We affirm the State Board of Equalization's decision.

Issues

Amax presents several issues in its appeal:

A. Whether the Order of the Board must be set aside because it is contrary to the standards in the Wyoming Administrative Procedure Act, Wyo.Stat[.] § 16-3-114(c) and otherwise not in accordance with law.

B. Whether the State Board denied Amax due process and the right to a full and fair contested case hearing by excluding key documents and testimony on the rate of return issues.

C. Whether critical findings of fact and conclusions o[f] law on the rate of return issues must be set aside because they are unsupported by substantial evidence in the record of this proceeding.

D. Whether the entire audit should be set aside because there was no attempt on the part of the Department of Revenue or the Board to determine fair cash market value.

E. Whether the auditors acted contrary to law by exceeding their authority under Section 14 of the Board's Rules.

F. Whether the auditors and the Department failed to collect necessary facts and acted arbitrarily by limiting their review of the valuation formula and the rate of return issues.

G. Whether the original assessment for 1986 production constituted fair cash market value and should be affirmed.

H. Whether the fixed rate of return approved by the Board is a hypothetical cost that is improper in a valuation methodology and must be set aside.

I. Whether the Board erred when it denied Amax a credit for return on post-mine mouth transportation equipment investment.

J. Whether Amax was denied due process in the presentation of its offer of proof when the Hearing Officer precluded Amax's witnesses from testifying.

Facts

Amax operated the Belle Ayr and Eagle Butte surface coal mines located in Campbell County. The Department of Audit commenced an audit in 1990 of the valuation of Amax's coal production from the two mines for the years 1985 through 1989. Only the audit results for the 1986 and 1987 production years are at issue in this appeal. Appellee Wyoming Department of Revenue used a net-back valuation formula to determine the value of Wyoming coal which had been sold away from the mouths of the mines for the 1986 and 1987 production years. Amax Coal Company v. Wyoming State Board of Equalization, 819 P.2d 825 (Wyo. 1991), contains a description of the net-back valuation formula. 819 P.2d at 827 n. 4. After the audit had been completed, the Department of Revenue issued a notice to Amax in which it assessed additional severance taxes and increased the taxable value of Amax's coal production for ad valorem tax purposes.

Amax disagreed with the Department of Revenue's conclusions and appealed to the State Board of Equalization. During the contested case hearing, Amax sought to introduce evidence to prove (1) that the standard industry rate of return on and of its investment which was used by the Department of Revenue in the net-back valuation formula should have been examined by the auditors and (2) that Amax's actual rate of return on and of its investment should have been used instead of the standard rate of return. The State Board of Equalization ruled that the evidence was irrelevant to the issues which were being presented at the hearing and refused to allow its admission; however, the Board allowed Amax to present a written offer of proof with regard to the excluded evidence.

Following the hearing, the State Board of Equalization issued its findings of fact, conclusions of law, and order in which it affirmed some of the Department of Revenue's assessments and increases in the taxable value. The State Board of Equalization specifically found that the Department of Revenue had erroneously allowed in-pit transportation costs to be deducted in Amax's original 1986 valuation. The State Board of Equalization also denied Amax's request for a deduction for its post-mine-mouth-transportation-equipment investment.

Amax appealed to the district court, and that court certified the case to this Court pursuant to W.R.A.P. 12.09(b).

Discussion

When we are reviewing cases which have been certified to us pursuant to W.R.A.P. 12.09(b), we apply the appellate standards which are applicable to the reviewing court of the first instance. Hepp v. State ex rel. Wyoming Workers' Compensation Division, 881 P.2d 1076, 1077 (Wyo. 1994).

We review an administrative agency's findings of fact under the substantial evidence standard:

"Our task is to examine the entire record to determine if substantial evidence exists to support the hearing examiner's findings. We will not substitute our judgment for that of the hearing examiner if his decision is supported by substantial evidence. Substantial evidence is relevant evidence which a reasonable mind might accept in support of the agency's conclusions."

Romero v. Davy McKee Corporation, 854 P.2d 59, 61 (Wyo. 1993) (citing Farman v. State ex rel. Wyoming Workers' Compensation Division, 841 P.2d 99, 102 (Wyo. 1992)).

Bearden v. State ex rel. Wyoming Workers' Compensation Division, 868 P.2d 268, 269 (Wyo. 1994). We do not, however, defer to an agency's conclusions of law. "Instead, if the `correct rule of law has not been invoked and correctly applied, . . . the agency's errors are to be corrected.'" Thunder Basin Coal Company v. Study, 866 P.2d 1288, 1291 (Wyo. 1994) (quoting Devous v. Wyoming State Board of Medical Examiners, 845 P.2d 408, 414 (Wyo. 1993)).

Amax maintains that the original valuation represented the fair cash market value of its production and that the Department of Revenue "abandoned the concept of [fair cash market value]" when, as a result of the audit, it determined the adjusted valuation.

The Wyoming Constitution mandates that all coal mines shall be taxed uniformly on the value of their gross product. WYO. CONST. art. 15, §§ 3 11. Article 15, Section 10 of the Wyoming Constitution vests the State Board of Equalization with authority to perform taxation functions for the state. See Amax Coal Company, 819 P.2d at 826 n. 1. At the time that the coal production was originally valued, WYO. STAT. § 39-2-202(a) (1985) required the State Board of Equalization to value the gross product of all mines at the fair cash market value of the product where produced after the mining process had been completed. See Enron Oil Gas Company v. Department of Revenue and Taxation, State of Wyoming, 820 P.2d 977, 980 (Wyo. 1991).

The Wyoming Constitution's valuation requirement when emplaced by relevant statutes requires that mineral production be valued at the "mouth of the mine" for purposes of calculating ad valorem and severance taxes.

Amax Coal Company, 819 P.2d at 827.

The State Board of Equalization's rules provided that recognized appraisal techniques must be used to determine the fair cash market value of a mineral when the mineral is sold away from the mouth of the mine. RULES AND REGULATIONS, WYOMING STATE BOARD OF EQUALIZATION ch. XXI, § 9(c) (1986). All factors which pertain to value must be taken into account in determining whether the valuation represents the fair cash market value of the product. Hillard v. Big Horn Coal Company, 549 P.2d 293, 298-99 (Wyo. 1976); see also RULES AND REGULATIONS, supra at § 10(d). In valuing mineral production,

[t]he Board has general statutory authority to prescribe a system or systems for establishing the uniform valuation of all properties. In performing its constitutional and statutory functions the Board may arrive at different valuations for different properties, but the method or system used by the Board must lead to a fair value, and the properties must be assessed at a uniform rate.

549 P.2d at 294 (citations omitted).

The Department of Revenue used the net-back valuation formula as the appraisal technique when it determined the fair cash market value of the coal which had been sold away from the mouths of the mines for the 1986 and 1987 production years. Neither the Department of Revenue nor the Department of Audit changed the net-back valuation formula during the audit. Amax seeks to challenge two components of the net-back valuation formula: (1) the use of a standard rate of return instead of Amax's actual rate of return and (2) the denial of a deduction on its post-mine-mouth-transportation-equipment investment.

Amax had the right to dispute the components of the net-back valuation formula; however, it waived that right when it elected not to challenge the original assessments. See Amax Coal Company v. Wyoming State Board of Equalization, 819 P.2d 834, 836-37 (Wyo. 1991); Hillard, 549 P.2d at 296-97. In 1986 and 1987, WYO. STAT. § 39-2-201(d) (1985) provided:

(d) Following determination of the taxable value of property subject to subsection (a) of this section, the board shall notify the taxpayer of the value assessed by mail. The person assessed may file written objections to the assessment within fifteen (15) days following receipt of notice and appear before the board at a time specified by the board.

The Board's rules reiterated the fifteen-day deadline. RULES AND REGULATIONS, supra at § 12(a). Additionally, Amax could have applied for a refund of any excess taxes it had paid pursuant to WYO. STAT. § 39-6-304(g) (1985) (repealed 1988):

(g) Any excess tax found to have been paid, whether as the result of overpayment, an appeal or an erroneous assessment shall be refunded to the person paying the tax. All applications for refunds shall be made within two (2) years from the payment of the erroneous tax.

A party waives any future objection to a ruling on an issue when that party fails to contest that issue on appeal. See Triton Coal Company v. Husman, Inc., 846 P.2d 664, 668 (Wyo. 1993). Waiver is "`the intentional relinquishment of a known right and must be manifest in some unequivocal manner.'" Jackson State Bank v. Homar, 837 P.2d 1081, 1086 (Wyo. 1992) (quoting Baldwin v. Dube, 751 P.2d 388, 392 (Wyo. 1988)).

Amax knowingly and voluntarily waived its right to contest the components of the net-back valuation formula when it failed to appeal from the original assessments. At the contested case hearing, witnesses for Amax testified that the net-back valuation formula is a recognized appraisal technique, and they admitted that Amax had voluntarily elected not to appeal from the original assessments. Amax's intention to relinquish its right to contest the components of the valuation formula is also illustrated by its failure to apply for a refund under the provisions of § 39-6-304(g). Amax acquiesced to the net-back valuation formula by failing to appeal from the original assessments and, thereby, conceded that the net-back valuation formula resulted in a fair-cash-market-value determination.

The audit revealed a mathematical error which resulted in the additional assessments being made. Amax reported two different numbers for its transportation costs for 1986: (1) its transportation costs from the face of the coal to the point of first crushing and (2) its transportation costs from the top of the ramp to the point of first crushing. The Department of Revenue allowed Amax to have a deduction for its total transportation costs from the coal face to the point of first crushing in the original assessments. Following the audit, the Department of Revenue concluded that the deduction for in-pit transportation costs was improper and issued an assessment notice to correct the error.

Amax argues that the Department of Revenue exercised its "appraisal judgment" to reach a fair-cash-market-value determination in the original assessments. Amax submits that the Department of Revenue allowed it to deduct its in-pit transportation costs in exchange for (1) the department using the standard rate of return instead of Amax's actual rate of return and (2) the department's failure to grant any return to Amax on its post-mine-mouth-transportation-equipment investment. The State Board of Equalization rejected Amax's "offset" argument, and so do we.

The Department of Revenue did not have authority to allow Amax to have a deduction for its in-pit transportation costs. The Department of Revenue is required to apply the applicable statutes and regulations. Fullmer v. Wyoming Employment Security Commission, 858 P.2d 1122, 1124 (Wyo. 1993) (citing Jackson v. State ex rel. Wyoming Workers' Compensation Division, 786 P.2d 874, 878 (Wyo. 1990)). In the words of the State Board of Equalization's order, the Department of Revenue did not have the "`flexibility' to ignore the law and rules on authorized deductions."

The mouth of the mine was the proper point of valuation for Amax's coal production. The State Board of Equalization's rules defined "mouth of the mine" as being "the place or point at which a mineral, except oil or gas, is brought to the surface of the ground after the mining is completed." RULES AND REGULATIONS, supra at § 4(h). The parties agree that the "top of the ramp" is considered to be the mouth of a surface coal mine.

Concerning transportation and processing costs, the State Board of Equalization's rules provided:

(b) The Division shall consider whether the sales price includes the value of processing or transportation to market or both added after the mineral has passed beyond the mouth of the mine or wellhead.

(i) If the selling price includes such value, the Division shall deduct such value from the selling price to determine the fair cash market value of the mineral. . . .

. . . .

(e) The fair cash market value of a mineral shall not include direct and indirect costs attributable to processing or transportation to market.

RULES AND REGULATIONS, supra at § 10.

Under the relevant constitutional, statutory, and regulatory provisions, a taxpayer was entitled to have a deduction for post-mine mouth transportation costs, but in-pit transportation costs were part of the value of the mineral which was subject to assessment. The Department of Revenue erred when it originally allowed Amax to have a deduction for its in-pit transportation costs, and it properly corrected that error by issuing the additional assessment after the audit had been completed. See Wyoming State Tax Commission v. BHP Petroleum Company Inc., 856 P.2d 428, 435-39 (Wyo. 1993). The adjusted assessment, therefore, reflected the fair cash market value of Amax's coal.

Amax contends that the Department of Audit exceeded the scope of its authority as "granted by Section 14 of the Rules which limited the auditors' role to verification of filed data." The State Board of Equalization ruled that the Department of Audit properly exercised its audit authority "as provided by law to examine returns, verify reported information, and determine whether taxable value for the years under audit was correctly calculated." We agree with the State Board of Equalization's determination.

WYO. STAT. § 39-1-304(a)(xiv) (1994) directs the State Board of Equalization to:

(xiv) Carefully examine into all cases wherein it is alleged that property subject to taxation has not been assessed or has been fraudulently, improperly, or unequally assessed, or the law in any manner evaded or violated, and cause to be instituted proceedings which will remedy improper or negligent administration of the tax laws of the state[.]

This Court construed § 39-1-304(a)(xiv) in BHP Petroleum Company Inc. In that case, we stated: "This section provides for revaluation when it directs the State Board of Equalization to discover errors or unequally assessed taxes and remedy those errors." 856 P.2d at 435-36.

The State Board of Equalization's rules and regulations set forth an audit procedure which helps the Board fulfill the directive contained in § 39-1-304(a)(xiv). RULES AND REGULATIONS, supra at § 14. The State Board of Equalization's rules provided in pertinent part:

(a) Financial data and other information prescribed by these rules and contained in reporting forms required to be filed with the Division is subject to audit examination by the Department. The purpose of such audit is to:

(i) Verify the accuracy of the financial data submitted by the taxpayer or operator as well as to determine whether such financial data is in accordance with generally accepted accounting principles; and

(ii) Verify the accuracy of all other data or information contained in the required reporting forms.

RULES AND REGULATIONS, supra at § 14(a). The rules also provided that, after the auditing process had been completed, the Department of Revenue was required to "determine whether the taxable value of mineral production for the year or years under audit [was] correct and make any appropriate adjustments to the taxable value." RULES AND REGULATIONS, supra at § 14(f)(ii). The Department of Revenue was then required to compute the taxpayer's severance tax liability and give notice to the taxpayer of any deficiency or overpayment. RULES AND REGULATIONS, supra at § 14(f)(iii). When we construe the relevant statutory and regulatory provisions together, it is apparent that the Department of Audit had the authority to conduct the audit and that the Department of Revenue and the State Board of Equalization had the responsibility to correct any errors which were encountered during that audit.

Amax also argues that the Department of Audit violated generally accepted audit standards when it failed to contact an "appraisal specialist" in the course of the audit. With regard to this issue, the State Board of Equalization stated:

We disagree with [Amax] concerning the significance of the role of "specialists." There is no evidence indicating the employees involved with the initial valuation of [Amax's] production were "specialists" when compared with the individuals involved in the audit and redetermination.

We agree with the State Board of Equalization. The mistakes which were discovered and corrected as a result of the audit were simple mathematical errors which could be and, indeed, were found by the auditors without them having to exercise any appraisal judgment in the process. It was not necessary for the auditors to contact appraisal specialists in this audit.

Amax argues that the State Board of Equalization denied Amax due process of law when the board excluded evidence of the standard and actual rates of return. We disagree. Since Amax had waived its right to object to the Department of Revenue's use of a standard rate of return instead of Amax's actual rate of return, any evidence on that issue was irrelevant to the issues properly before the State Board of Equalization at the contested case proceeding. WYO. STAT. § 16-3-108 (1990) directs administrative agencies to exclude irrelevant evidence from contested case hearings. The evidence offered by Amax was irrelevant because it did not have "any tendency to make the existence of any fact that [was] of consequence to the determination of the action more probable or less probable than it would be without the evidence." W.R.E. 401 (emphasis added).

As a related issue, Amax contends that the State Board of Equalization erred by requiring it to present its excluded evidence in a written offer of proof instead of allowing it to present its excluded evidence in an offer of proof through oral testimony. A party has the right to make an offer of proof about evidence which is excluded from a proceeding. See Contreras By and Through Contreras v. Carbon County School District # 1, 843 P.2d 589, 595 (Wyo. 1992); Vanover v. Vanover, 77 Wyo. 55, 67, 307 P.2d 117 (1957). Section 16-3-108(a) provides in pertinent part: "[I]f the interests of the parties will not be prejudiced substantially[,] testimony may be received in written form subject to the right of cross-examination." Amax has failed to show how it was substantially prejudiced by the State Board of Equalization requiring it to present its offer of proof in writing instead of through oral testimony.

Amax argues that the record did not contain any evidence which would support the State Board of Equalization's findings of fact and conclusions of law with regard to the origins of the standard industry rate of return used in the net-back valuation formula. Since Amax waived its right to challenge the standard rate of return by failing to appeal from the original assessments, those findings and conclusions were gratuitous and were not essential to the State Board of Equalization's decision. "[A]n agency's action is arbitrary and capricious and must be reversed if any essential finding is not supported by substantial evidence." Majority of Working Interest Owners in Buck Draw Field Area v. Wyoming Oil and Gas Conservation Commission, 721 P.2d 1070, 1079 (Wyo. 1986) (emphasis added). The fact that Amax waived its right to challenge the standard rate of return is dispositive; therefore, we do not need to address whether the State Board of Equalization's alternative findings on the origins of the standard rate of return were supported by substantial evidence. 721 P.2d at 1079 n. 7.

Conclusion

The State Board of Equalization did not commit any reversible error. Its findings of fact, conclusions of law, and order are, therefore,

Affirmed.