
53 P.3d 646 (2001)
BAINBRIDGE, INC.; Village Homes of Colorado, Inc., a Colorado corporation; Tradition Concepts, Inc., a Colorado corporation; The Genesee Co./Castle Pines, Inc., a Colorado corporation; High View Homes, LLC, a Colorado limited liability company; South Platte Company, LLC, a Colorado limited liability company; April Corporation, a Colorado corporation; Forest Glen, Inc., a Colorado corporation; Larsen Homes, Ltd., a Colorado corporation; LHL I, Ltd., a Colorado corporation; LHL II, Ltd., a Colorado corporation; and Sattler Homes, Inc., a Colorado corporation, Plaintiffs-Appellants,
v.
The BOARD OF COUNTY COMMISSIONERS OF The COUNTY OF DOUGLAS, STATE OF COLORADO, Defendant-Appellee.
No. 00CA1435.
Colorado Court of Appeals, Div. III.
August 30, 2001.
Rehearing Denied October 11, 2001.
Certiorari Denied September 3, 2002.[*]
Otten, Johnson, Robinson, Neff & Ragonetti, P.C., Thomas J. Ragonetti, Brad W. Schacht, David P. Hutchinson, Denver, CO, for Plaintiffs-Appellants.
J. Mark Hannen, Office of the County Attorney, Castle Rock, CO; Mulliken, Gleason, Weiner, Whitney & Jolivet, P.C., Edward A. Gleason, Murray I. Weiner, Colorado Springs, CO, for Defendant-Appellee.
*647 Opinion by Judge MARQUEZ.
In this dispute about building permit fees, plaintiffs, Bainbridge, Inc.; Village Homes of Colorado, Inc.; Tradition Concepts, Inc.; The Genesee Co./Castle Pines, Inc.; High View Homes, LLC; South Platte Company, LLC; April Corporation; Forest Glen, Inc.; Larsen Homes, Ltd.; LHL I, Ltd.; LHL II, Ltd.; and Sattler Homes, Inc., appeal the trial court's judgment on remand in favor of defendant, the Board of County Commissioners of Douglas County, Colorado. We affirm.
After adopting the 1991 Uniform Building Code, Douglas County imposed upon plaintiffs *648 the code's recommended building permit fees. It did so pursuant to legislative authority, §§ 30-28-114 and 30-28-205(1), C.R.S. 2000, that permits counties to fix a reasonable schedule of fees for the issuance of building permits.
Plaintiffs filed a complaint asserting that these permit fees were illegal because the county building department's revenue exceeded its direct costs. The trial court ruled in the county's favor, concluding that the General Assembly did not intend §§ 30-28-114 and 30-28-205(1) to limit the schedule of fees authorized by those sections to only the direct costs of operating the building department.
Plaintiffs appealed, asserting that, unless the fees collected approximate the direct costs of operating the building department, the fees constituted an unlawful tax in violation of the Colo. Const. art. X, § 3, which mandates uniform property taxation.
In Bainbridge, Inc. v. Board of County Commissioners, 964 P.2d 575 (Colo.App. 1998), a division of this court held that: (1) the county's indirect costs of running its building department, including services by other county offices, such as the county manager, the county attorney's office, and other various divisions of the county government, may be calculated in determining the present operational cost and future expansion of the building department, but (2) the fees would constitute unlawful taxes in violation of the Colorado Constitution if they did not generally approximate the overall costs, direct and indirect, of operating the building department. The division remanded the case to the trial court for findings of fact whether the fees charged were approximately required to offset the direct and indirect costs of operating the building department. Bainbridge, Inc. v. Board of County Commissioners, supra, 964 P.2d at 577.
On remand, the district court held an evidentiary hearing limited to that issue. In its June 15, 2000, order, the trial court ruled in favor of the county, finding that the building fees charged by the county were approximately required to offset the direct and indirect costs of operating the building department. Plaintiffs appeal only the provisions of this order relating to costs allocated from the county commissioners, county manager, and county attorney, and the engineering and planning departments.

I. Burden of Proof
At the outset, we address plaintiffs' contention that the trial court erred in determining that they were required to prove their case beyond a reasonable doubt, instead of by a preponderance of the evidence. We disagree.
The district court found that plaintiffs were, in effect, attempting to have the county's resolution ruled unconstitutional. The court thus decided that the burden was beyond a reasonable doubt. See Loup-Miller Construction Co. v. City & County of Denver, 676 P.2d 1170, 1174 (Colo.1984)(the burden is upon the party attacking a legislative act to establish its unconstitutionality beyond a reasonable doubt).
In its June 2000 order, however, the court twice noted that, whether the standard was beyond a reasonable doubt or by a preponderance of the evidence, plaintiffs had failed to overcome the presumption of constitutionality that attaches to a legislative act of the board. The court stated that "even if the burden of proof is by a preponderance of the evidence, this Court's findings do not change."
Consequently, even if the trial court erred in applying the beyond a reasonable doubt standard, any such error was harmless because the court explicitly stated that plaintiffs would lose under either standard. See Poudre Valley Rural Electric Ass'n v. City of Loveland, 807 P.2d 547, 557 (Colo.1991)(judgment entered by the trial court will not be reversed for alleged errors unless those errors are shown to prejudice the substantial rights of the complaining party).

II. Indirect Costs
Plaintiffs contend that the trial court erred on remand in its application of controlling law by concluding that general governmental expenses relating to growth management are recoverable through permit fees charged as indirect costs. We disagree.
*649 Section 30-28-114 states, in pertinent part, that the board of county commissioners "may also fix a reasonable schedule of fees for the issuance of [building] permits." Section 30-28-205(1), C.R.S.2000, states, in pertinent part, that the "board of county commissioners shall fix a reasonable schedule of fees for the issuance of building permits by [the] county building inspector."
Unlike a tax, a special fee is not designed to raise revenues to defray the general expenses of government, but rather is a charge upon persons or property for the purpose of defraying the cost of a particular governmental service. The amount of a special fee must be reasonably related to the overall cost of the service. Bloom v. City of Fort Collins, 784 P.2d 304, 308 (Colo.1989).
Because the setting of rates and fees is a legislative function that involves many questions of judgment and discretion, an appellate court will not set aside the methodology chosen by the ratemaking authority unless it is inherently unsound. Krupp v. Breckenridge Sanitation District, 19 P.3d 687, 694 (Colo.2001).
A determination of reasonableness is a question of fact for the trial court. See American Water Development, Inc. v. City of Alamosa, 874 P.2d 352, 386 (Colo.1994)(reasonableness of attorney fees).
At the remand hearing here, the parties offered conflicting expert testimony on how to determine the building department's indirect costs. We review the trial court's resolution of that conflicting evidence under a highly deferential standard. Determinations of the credibility of witnesses and the weight to be afforded the evidence are issues committed to the sound discretion of the trial court as the trier of fact. Tiger v. Anderson, 976 P.2d 308, 310-11 (Colo.App.1998). Its findings must be accepted on review unless they are so clearly erroneous as not to find support in the record. C.R.C.P. 52; M.D.C./Wood, Inc. v. Mortimer, 866 P.2d 1380, 1384 (Colo.1994).
In its June 2000 order, the district court found in favor of the county. After considering all of the evidence, the court specifically found:
[T]he method for determining indirect costs of the building department as determined by [the county's expert] was both reasonable and appropriate. The fees generated by the building department generally approximate the overall costs of operating the building department. The Court finds the evidence establishes that the fees charged were approximately required to offset the direct and indirect costs of operating the building department.
Ample evidence exists in the record to support the trial court's findings, and we will not disturb them on review. In particular, the trial court's determination that the county's expert was more credible than plaintiffs' expert is well supported, and we will not second-guess it. See M.D.C./Wood, Inc. v. Mortimer, supra.

A. The County's Expert
The indirect costs of the building department were determined through a study performed in 1994 and updated in 1999 by the county's expert, its budget manager. This expert described the mission of the building department as issuing building permits and doing building inspections, plan checks, and reinspections.
Significantly, for a period of four to six months, the expert spent approximately one-half of her time analyzing building department costs. She focused on determining who within the county interacted with the building department and provided it services. She interviewed representatives from various branches of the county government and spoke with all the elected officials and department directors and managers in the county to determine "what their interaction was with the building department" and what percentage of their work focused on growth issues. She described growth as "new construction" and stated that anything that ended up with new people moving into the county was growth.
The expert's study determined the extent to which services rendered by other departments conferred a benefit upon the building department and then allocated certain costs *650 of those departments to the building department. The expert determined that the indirect costs of the building department fell into thirteen categories, including, as relevant here (1) county commissioners/manager/attorney (CCMA), (2) engineering growth management (engineering), and (3) planning/community (planning).
Those three categories, which plaintiffs challenge on appeal, coincidentally account for the largest cost allocations.
The expert's analysis of the CCMA category involved review of a representative sample of the CCMA's weekly scheduled meetings for a six-month period and determination of which meetings related to growth management. She determined that seventy-five percent of the CCMA's time went to growth and new construction. She then allocated half of that amount to the building department and half to the planning department, which contains the building department.
Her analysis of the planning department was based upon research into the portion of the planning department's work that was driven by growth. The expert determined that portion to be eighty percent, based upon her research and communication with the department director. She then multiplied the department's costs by eighty percent and allocated that amount to the building department. Because the building department is part of the planning department, it is not unreasonable to conclude that certain planning department services were conferred upon the building department.
The engineering department analysis involved a determination of what the department was working on and what portion of that work was related to growth. Based upon her research and communication with the department, the expert determined that seventy percent of its work was growth related. She then multiplied its costs by seventy percent and allocated that amount to the building department.
In support of the conclusion by the county's expert, another witness for the county, a Colorado certified public accountant and former chairman of the American Institute of Certified Public Accountants, reviewed the work performed by both parties' experts and described the county's expert's approach as "appropriate," "professional," and "reasonable."

B. Plaintiffs' Expert
Plaintiffs' expert, a certified public accountant, opined that the cost allocation method of the county's expert, in the three contested categories, was not rationally related to the benefit received. He presented five alternative means of analyzing the costs of the building department. All five of plaintiffs' alternatives allocated significantly fewer costs to the building department than the county's theory did.
However, in Alternative I, contrary to the holding in Bainbridge, plaintiffs' expert did not allocate any indirect costs to the building department. In Alternative II, the expert allocated to the building department only limited departmental expenditures from the other departments. In Alternative III, the expert allocated to the building department an amount based on personnel services from the other departments. Alternative IV replicated the county expert's initial report verbatim. The only change plaintiffs' expert made was to omit two categories of indirect costs: CCMA and planning. Finally, the expert's Alternative V was the same as the county expert's, except that it allocated only 3.8 percent of the three disputed categories' costs to the building department. This was based upon the percentage of FTEs (full-time equivalent employees) in the building department, compared to all FTEs in the county.
Further, plaintiffs' expert spent far less time on his analysis than did the county's expert; instead, he copied large portions of her work and then modified it. He did not interview the director of planning, the county engineer, the county commissioners, the county manager, the county attorney, or the head of the building department. Nor did he investigate the working relationship between the engineering and building departments. He did nothing to determine how the county commissioners spent their time. In contrast, the county's expert did all these things.
*651 Additionally, because the studies were performed before the Bainbridge opinion issued, Alternatives I-IV failed to include indirect costs that the division in Bainbridge determined to be allowable.
Because of these and other deficiencies in plaintiffs' expert's opinion, the trial court found that the county's expert's analysis carried more weight.
As the trial court noted, the county presented a "detailed and time consuming analysis," performed by its expert and budget manager, "before any litigation began." This analysis was "not prepared for any purpose of litigation or even in anticipation of litigation."
In our view, the trial court correctly concluded that the county's evidence demonstrated that use of growth management as a component of indirect cost analysis was reasonable and appropriate. See Krupp v. Breckenridge Sanitation District, supra. The evidence demonstrated that growth has driven the costs of the building department. Further, the evidence supports the finding that the fees charged by the building department were approximately required to offset the direct and indirect costs of operating that department. Mathematical exactitude is not required. Krupp v. Breckenridge Sanitation District, supra, 19 P.3d at 694; Westrac, Inc. v. Walker Field, 812 P.2d 714, 717 (Colo.App. 1991).
We reject plaintiffs' contention that, without the improper allocation of growth costs to the building department, the only conclusion supported by the record is that revenues from permit fees grossly exceed the total costs, including direct and indirect costs, of issuing the permits.
Plaintiffs' counsel conceded at oral argument before this court that growth causes greater activity in the building department. However, plaintiffs have not articulated which particular aspects of this growth should not be allocated to the building department. We also note that the county's expert did not allocate one hundred percent of the costs of growth to the building department. For example, after interviewing officials from the sheriff's and assessor's offices, she did not allocate any growth costs from those departments. Nor did the county's expert allocate all of the CCMA's growth costs to the building department. Instead, after determining that seventy-five percent of the department's time went to growth and new construction, she allocated only fifty percent of that component to the building department.
Thus, we conclude that it was permissible for part of the growth costs to be allocated to the building department as indirect costs. See Bainbridge, Inc. v. Board of County Commissioners, supra, 964 P.2d at 577 (allowing consideration of indirect, "`overall costs' required to operate [the] department").

III. OMB A-87
Plaintiffs also contend a federal Office of Management and Budget document (OMB A-87) should have controlled the allocation of costs to the building department. We are not persuaded.
Three witnesses for the county testified that the OMB A-87 plan pertained to federal grants and had no application to the cost allocation issue before the trial court on remand. This testimony was sufficient to support the trial court's conclusion that the evidence was clear that costs that may be very appropriate for cost allocation never make it onto the OMB A-87 because of the federal guidelines.
Accordingly, ample evidence in the record supports the trial court's findings, and we will not overturn them. See M.D.C./Wood, Inc. v. Mortimer, supra.
Accordingly, the judgment is affirmed.
Judge JONES and Judge DAILEY concur.
NOTES
[*]  Justice KOURLIS would grant as to the following issues:

Whether the respondent, though the imposition of building permit fees, may defray the general governmental expenses of growth by labeling such expenses as "indirect costs" of the building division.
Whether the respondent, though its imposition of building permit fees, mat recover expenses that are not caused, directly or indirectly, by the issuance of building permits.
Whether the court of appeals erred in its application of the "inherently unsound" standard by endorsing a methodology for setting building permit fees that is based on the value of construction rather than on the costs of issuing building permits.
Whether the "inherently unsound" standard applies to the Country's methodology for calculating indirect costs of issuing building permits, and if so, whether a methodology designed to measure the cost impact of growth rather than the cost impact of issuing building permits is inherently unsound.
