OPINION

VOROS, Judge:

¶ 1 This case involves a dispute over a cost-plus contract to build two high-end custom homes on adjacent lots. When the builder, Big H Construction, Inc., filed a mechanics' lien on one of the homes, the owners, Charles F. Hale and Beverly I. Hale, sued Big H and its president, T. Dwayne Horsley, for breach of contract and related claims. Big H counterclaimed for nonpayment of a ten percent builder's fee. After a bench trial, the trial court awarded Big H $172,100 plus attorney fees and costs. The Hales moved unsuccessfully for a new trial and to amend the findings pursuant to rules 52(b) and 59 of the Utah Rules of Civil Procedure. The Hales appeal. We affirm.

BACKGROUND1

¶ 2 In February 2003, the Hales hired Big H to construct two custom homes on adjacent lots known as Lots 45 and 46. The parties agreed that Big H would construct the homes on a cost-plus basis with the Hales covering all reasonable costs (the Costs) plus a builder's fee equal to ten percent of the Costs. The project involved forty-seven separate subcontractors and suppliers, some of whom the Hales contracted with and paid directly over the course of construction.

¶ 3 Two of Dwayne Horsley's family members worked on the project in some capacity with Big H or the Hales or both. David Horsley, Dwayne's father and a licensed real estate agent, prepared Real Estate Purchase Contracts (REPCs) for the Hales' purchase of the Lots from the developer and their purchase of the homes from Big H. James Horsley, Dwayne's brother, negotiated the purchase of Lots 45 and 46 on the Hales' behalf and worked as a site foreman.

¶ 4 The Hales executed an REPC for the purchase of Lots 45 and 46 from Triple Crown Estates on February 25, 2003. The REPC provided for a three percent commission to the developer's agent. David Horsley was listed as the Hales' agent, but the REPC did not provide for a commission to him. That same day, the Hales executed two separate REPCs for the Lot 45 and Lot 46 homes, with Big H listed as seller. The REPCs listed no agents for either buyers (the Hales) or sellers (Big H) and mentioned no sales commissions.

¶ 5 By late 2004, Big H had largely completed construction on the Lot 45 home. However, the parties' working relationship had deteriorated. When the Hales refused to pay anything further, Big H left the project. Approximately three months later, Big H filed a mechanics' lien on the Lot 45 home in the amount of $165,000. Big H claimed this sum approximated its builder's fee. The Hales sued. Big H counterclaimed for breach of contract and foreclosure of its mechanics' lien.

¶ 6 At trial, Big H offered into evidence voluminous documentation, including stacks of invoices from dozens of vendors documenting expenses and copies of cancelled checks from the Hales documenting payments. The invoices for both homes totaled more than $2.7 million. Dwayne Horsley testified about the Costs and payments that he tracked on a spreadsheet over the course of the project; Big H's expert witness testified that the Costs were reasonable. By Big H's account, the Hales owed it roughly $172,000 (although that figure varied over the course of the litigation from $165,000 to $174,000).

¶ 7 The Hales advanced a different version of Costs incurred and payments made. They offered testimony from their accounting expert. The Hales' expert testified that he had reviewed all the records furnished by the Hales and Big H, and that the Hales had overpaid Big H by $116,994.77. His conclusion was based in part on "unsupported costs" and various alleged overpayments and underpayments. However, the trial court found much of the Hales' evidence — including their expert's testimony — unreliable, and relied instead mainly on the evidence offered by Big H. The trial court found that Costs of $1,721,000 had been incurred and paid for by the Hales on the Lot 45 home, entitling Big H to a builder's fee of $172,100.2

¶ 8 The trial court entered judgment for Big H in the amount of $172,100 for its builder's fee, $94,463 in prejudgment interest, and $342,240.84 in attorney fees and costs. It denied the Hales' subsequent motion for a new trial or to amend the court's findings of fact. The Hales timely appeal.

ISSUES AND STANDARDS OF REVIEW

¶ 9 First, the Hales contend that the trial court erred in ruling that Big H met its burden at trial because it relied on estimates rather than an actual accounting of Costs. "Whether the trial court calculated the damages award within the framework dictated by the [contract] ... is a question of law," Traco Steel Erectors, Inc. v. Comtrol, Inc., 2009 UT 81, ¶ 21, 222 P.3d 1164, which we review for correctness, see State v. Pena, 869 P.2d 932, 936 (Utah 1994), holding modified by State v. Levin, 2006 UT 50, 144 P.3d 1096. However, "an appeal from the types of properly admitted evidence upon which the trial court applies" the damages formula is "an appeal from a question of fact," Traco, 2009 UT 81, ¶ 33, 222 P.3d 1164. "In all actions tried upon the facts without a jury,... [f]indings of fact ... shall not be set aside unless clearly erroneous, and due regard shall be given to the opportunity of the trial court to judge the credibility of the witnesses." Utah R. Civ. P. 52(a). A finding is clearly erroneous "`only if the finding is without adequate evidentiary support or induced by an erroneous view of the law.'" State v. Walker, 743 P.2d 191, 193 (Utah 1987) (quoting Wright & Miller, Federal Practice & Procedure § 2585 (1971)). Therefore, we will not disturb a finding unless it is "against the clear weight of the evidence, or if [we] otherwise reach[] a definite and firm conviction that a mistake has been made." Id.

¶ 10 Second, the Hales contend that the trial court included in its calculation other "improper and unreasonable costs," including duplicate and mistaken invoices, and both overpayments and underpayments by Big H. This question involves a finding of fact that we review for clear error. See Traco, 2009 UT 81, ¶¶ 17, 33, 222 P.3d 1164.

¶ 11 Third, the Hales challenge the trial court's finding that the Hales were not entitled to an offset based on Big H's alleged failure to perform work in a good and workmanlike manner. This challenge presents a mixed question of law and fact. "It is therefore reviewed under a clearly erroneous standard for questions of fact and a correctness standard for questions of law." Tooele Assocs. Ltd. Partnership v. Tooele City Corp., 2011 UT 04, ¶ 16, 247 P.3d 371.

¶ 12 Fourth, the Hales assert that the trial court erred by including the cost of the land in its calculation of the builder's fee, arguing that doing so runs afoul of the Utah Real Estate Licensing and Practices Act, see Utah Code Ann. §§ 61-2-1 to -24 (Lexis Publishing 2000) (current version at id. §§ 61-2f-101 to -512 (LexisNexis 2011 & Supp. 2012)).3 Determining whether inclusion of the cost of the land in calculating Big H's builder's fee violates the statute is a legal question of statutory interpretation that we review for correctness. See Sachs v. Lesser, 2008 UT 87, ¶ 9, 207 P.3d 1215.

¶ 13 Fifth, the Hales challenge the finding that they are not entitled to a credit from Big H for a $30,000 payment the Hales made to James Horsley. This issue turns on whether James Horsley had authority to act on behalf of Big H, a mixed question of law and fact. See Glew v. Ohio Sav. Bank, 2007 UT 56, ¶ 19, 181 P.3d 791. We review the court's legal conclusions for correction of error, see Tooele Assocs., 2011 UT 04, ¶ 16, 247 P.3d 371, but "[w]e will not disturb the court's findings of fact unless they are clearly erroneous," Glew, 2007 UT 56, ¶ 18, 181 P.3d 791. "[I]n those instances in which the trial court's findings include inferences drawn from the evidence, we will not take issue with those inferences unless the logic upon which their extrapolation from the evidence is based is so flawed as to render the inference clearly erroneous." Id. Furthermore, because the trial court's application of the equitable doctrine of apparent authority is "extremely fact-sensitive," "we grant significant deference" to the trial court. Id. ¶ 19.

¶ 14 Finally, the Hales challenge the trial court's conclusion that neither Big H nor Dwayne Horsley violated the Utah Mechanics' Lien statute, see Utah Code Ann. § 38-1-25 (LexisNexis 2005). Whether Dwayne Horsley intentionally filed an inflated lien is a question of fact. Therefore, we review this claim for clear error. See Traco Steel Erectors, Inc. v. Comtrol, Inc., 2009 UT 81, ¶ 17, 222 P.3d 1164.

ANALYSIS

¶ 15 We note at the outset that the Hales face an uncomfortable reality on appeal: the trial court expressly determined that neither Charles Hale nor the Hales' expert was a credible witness. As to Charles Hale's credibility, the court found that "he has little or none":

The trial court was equally skeptical of the Hales' expert. It found that his Analysis and Report was "riddled with numerous flaws in the way that its figures [were] formatted, reported and analyzed." This conclusion left the court with "little or no confidence that his Analysis and Report is reliable"; consequently, the court "decline[d] generally to accept any of [the Hales' expert]'s conclusions."

¶ 16 Assessing the credibility of a witness is within the trial court's domain. See Rawlings v. Rawlings, 2010 UT 52, ¶ 45, 240 P.3d 754 ("We are keenly aware that trial courts are in the best position to make determinations about credibility and veracity."); Lamkin v. Lynch, 600 P.2d 530, 531 (Utah 1979) ("The matter of witness credibility... falls within the province of the fact-finder."). Given the trial court's credibility assessment, the Hales face an uphill battle to demonstrate on appeal that the court's findings of fact — many of which are based in significant part on witness testimony — are clearly erroneous.

I. The Trial Court Did Not Improperly Determine Costs.

A. Cost Estimates

¶ 17 The Hales contend that the trial court erred in ruling that Big H proved its mechanics' lien and breach of contract claims because the court "relied on estimates rather than complete accounting evidence."

¶ 18 The trial court considered a compilation of invoices and payment records submitted by Big H that filled two voluminous three-ring binders, one of which was dedicated to documentation of Costs and payments for the Lot 45 home. As Big H points out, it "adduced, and the trial court credited, extensive documentary evidence of every billing invoice and available payment record for every claimed Cost on which Big H's ten percent [builder's fee] was based." The trial court found that the invoices and payment records that Big H offered to substantiate its Costs "appear[ed] to be accurate reflections of the actual Costs for which Big H was billing," and that "the Hales ordered, and Big H provided, every material and service reflected in the invoices." Moreover, the trial court noted that the incomplete state of payment documentation was owing, at least in part, to the Hales' failure to keep Big H apprised of their direct payments to suppliers and subcontractors over the course of the project. Based on this evidence, the trial court arrived at its damage award of $172,100 in favor of Big H.4

¶ 19 In addition to this documentation, Big H introduced expert testimony that the Costs were reasonable. Big H's expert relied on two methods of valuation, each based in some part on estimates. One method relied on the actual invoices for Lot 45, an index of construction costs produced by R.S. Means, and the expert's own database of costs. The other method calculated value on a price-per-square-foot basis and added a fifteen percent premium to account for high-quality amenities. Based on his analysis, Big H's expert estimated that the value of the Lot 45 home was consistent with the Costs Big H asserted, and concluded, therefore, that Big H's Costs were reasonable.

¶ 20 The Hales challenge this expert testimony. "In a cost-plus contract," they maintain, "the contractor can satisfy its burden of proof only with evidence of actual expenditures and payments; estimates and averages may not be used." In support of their claim, the Hales cite cases from six other states. We need not consider foreign precedent, however, because the issue was settled by our own supreme court three years ago in Traco Steel Erectors, Inc. v. Comtrol, Inc., 2009 UT 81, 222 P.3d 1164.

¶ 21 In Traco, a general contractor hired a subcontractor for steel erection work. Under their agreement, the general contractor could recover the actual costs incurred along with reasonable overhead and profits for completing any work that the subcontractor failed to perform. See id. ¶ 5. When the subcontractor abandoned the job before completion, the general contractor completed the work using its own labor force along with that of another company, then sought to recover its costs from the subcontractor. See id. ¶ 7.

¶ 22 To account for its labor costs at trial, the general contractor introduced R.S. Means Building Construction Cost Data: 2001 Western Edition (Philip R. Waier ed., 14th ed. 2001), into evidence. This is "an index of average wages and costs for skilled structural steelworkers and equipment in the western United States" that contains typical billing rates for labor and the average cost of equipment. Traco, 2009 UT 81, ¶ 8, 222 P.3d 1164. The general contractor based its labor costs on the R.S. Means data, and the general contractor's president testified that the figure was an accurate representation of the actual costs incurred. See id. ¶¶ 9-10. The trial court awarded the general contractor damages based in part on these industry averages. See id. ¶ 11. The subcontractor argued on appeal, much as the Hales do here, that "the trial court improperly relied on the R.S. Means average and oral testimony to establish the costs . . . actually incurred to complete [the subcontractor's] steel erection work." Id. ¶ 12.

¶ 23 Our supreme court rejected this argument. It agreed that the general contractor "was obligated to prove damages as part of its prima facie case and that the subcontracts only allowed damages in the amount of costs actually incurred." Id. ¶ 23. However, it continued, "We are aware of no authority ... that restricts evidence that may be used to prove contract damages to primary documentation of actual cash outlays to workers or suppliers, or [that indicates] that failure to do so results in a failure to present a prima facie case of damages." Id. In determining damages, the court stated, "`the desired objective is to evaluate any loss suffered by the most direct, practical and accurate method that can be employed.'" Id. ¶ 24 (quoting Even Odds, Inc. v. Nielson, 22 Utah.2d 49, 448 P.2d 709, 711 (1968)). On appeal, "[t]he central inquiry is whether the evidence was sufficient; not whether it was perfect." Id.

¶ 24 Here, Big H produced extensive documentation of actual costs. It used expert testimony and evidence of industry averages to verify those costs and establish that the costs were reasonable. The Hales' challenge to Big H's use of estimates and averages is the very attempt rejected in Traco to "restrict[] evidence that may be used to prove contract damages to primary documentation of actual cash outlays to workers or suppliers," id. ¶ 23. Indeed, the Hales criticize the trial court here for relying on an index similar to that used in Traco. And while the Hales seek to distinguish Traco on the ground that one of the parties here — the Hales — is a nonbuilder, the supreme court's reasoning in Traco did not rely on the professional status of the parties. The Hales' claim is thus squarely foreclosed by Traco.

B. Damage Calculation Formula

¶ 25 The Hales' next contention is a variation of their first. They argue that by relying on expert testimony "based ... on estimates, rather than an accounting of the costs and payments," the trial court employed a "methodology to calculate damages [that] is fundamentally flawed," and thus committed an error of law. See Traco Steel Erectors, Inc. v. Comtrol, Inc., 2009 UT 81, ¶ 21, 222 P.3d 1164 ("Whether the trial court calculated the damages award within the framework dictated by the [contract] ... is a question of law.").

¶ 26 The Hales rely on this court's holding in Wasatch Oil & Gas, LLC v. Reott, 2011 UT App 152, 263 P.3d 391. The issue addressed in Wasatch Oil was what measure of damages applied where production from a gas well was interrupted, then restarted after the price of gas had risen. See id. ¶¶ 10-11. Appellants argued that the trial court should have applied a lost profits test to determine damages, and this court held that the trial court had in fact applied such a test. See id. ¶ 11. Neither the nature of the evidence relied on by the trial court nor the sufficiency of that evidence was at issue in Wasatch Oil.

¶ 27 The measure of damages, or the formula by which damages are calculated, is not at issue here. The parties agree that the contract established a cost-plus arrangement in which the Hales would pay Big H Costs plus a builder's fee equal to ten percent of those Costs. The trial court explicitly based its damages award on what the trial court found to be Costs incurred on the Lot 45 home. Specifically, the trial court found that $1,721,000 of Costs were incurred, entitling Big H to a builder's fee of $172,100-ten percent of Costs pursuant to the parties' contract. The Hales contend not that the trial court should not have applied a costs-plus-ten-percent measure of damages, but that Big H's evidence was insufficient to establish its Costs. Under Traco, Big H's evidence was not insufficient merely because Big H used estimates and averages in addition to documented costs. See Traco, 2009 UT 81, ¶¶ 23-24, 222 P.3d 1164. Wasatch Oil dictates no different result.

II. The Trial Court's Damage Calculation Is Not Clearly Erroneous.

¶ 28 Next, the Hales contend that the trial court "permitted improper and unreasonable costs" in calculating damages, including duplicate and mistaken invoices and both overpayments and underpayments by Big H to subcontractors or suppliers. According to the Hales, the trial court "improperly credited Big H twice for duplicate and mistaken invoices." These errors, the Hales maintain, are shown in the documents themselves:

(Footnotes omitted.)

¶ 29 Appellants' brief contains no further explanation or analysis. Yet the identified exhibits are not self-explanatory. For example, the C.J. Heating invoice does appear in apparently duplicate form in both Exhibits RR and SS.5 However, the record does not clearly show whether this invoice properly belongs only in Exhibit RR (and therefore was appropriately included in the Lot 45 home Costs calculation), or properly belongs only in Exhibit SS, or should have been divided between the two, or reflects identical costs incurred separately for each of the two homes. Yet the Hales offer nothing more than a bare assertion that the invoices are duplicative. With respect to the Stroud invoice, the Hales state that "Exhibit SS Item 24 lists Invoice 4601 from Stroud at $120,000, but the invoice is only $60,000." However, Invoice 4601 actually shows two "totals," one $60,000, the other $120,000. It also shows a payment of $30,000. Furthermore, as Big H notes, Invoice 1494 from Stroud, dated about six months later, also shows two "totals," one $85,954.10, and a "final total" of $59,954.10. The Hales have not explained these discrepancies or offered record support for their assertion that $60,000 is the correct total. The RT Custom Cabinet invoices are similarly unclear. The Hales assert that Invoice 1011 was double-counted. Big H concedes that the amount on Invoice 1011 should not have appeared twice on its schedule, but asserts that the apparent double billing is explained by a different document. The Hales do not address this additional document, claiming only that Big H is "mistaken." In short, we cannot agree with the Hales that these documents on their face prove that the trial court's damage calculation was fundamentally flawed and thus clearly erroneous.

¶ 30 That said, Big H concedes that "the Hales are technically correct that three of the several hundred billing invoices were not fully accurate," but notes that "the aggregate amount of the inaccuracies is $19,294.90 which, when multiplied by 10% [to calculate the builder's fee], yields a swing to the Hales of only $1,929.49." Big H asserts that the damages award of $172,100 should remain intact despite the errors because "[i]t is more than offset by the $52,493 of Big H loan advances that the Hales failed to repay." Indeed, the trial court found that "[a]ccording to Schedule 8 of [the Hales' expert]'s twice-revised cost and payment analysis, Big H was repaid only $675,205 of the $727,698 that it advanced to help assure completion of the project." After trial, the court thus declined to amend the relevant findings and reduce the damages award because of evidence showing that the Hales in fact owed Big H substantially more than the $172,100 awarded.

¶ 31 On appeal, the Hales acknowledge this finding but do not challenge it as clearly erroneous. Nor do they contend that the trial court was precluded as a matter of law from backstopping its damage calculation with this unpaid $52,493. And, perhaps more to the point, the Hales do not challenge Big H's appellate argument — though not phrased quite this way — that any errors in the court's damage calculation that aggregate less than $52,493 are necessarily harmless. The Hales thus have not demonstrated that the trial court's damage calculation requires reversal.

¶ 32 The Hales also contend that the trial court improperly included overpayments and underpayments by Big H — that is, payments made to subcontractors and suppliers for either more or less than the amount reflected in their invoices. The rationale for this argument is that when the amount actually paid is less than the invoice amount, the contractor should base its fee on the former, whereas when the amount paid is more than the invoice amount, the contractor should base its fee on the latter. Furthermore, the Hales contend that they "presented undisputed evidence that certain invoices were underpaid or overpaid. Yet, the court relied on [Big H's invoices and other documentation] without deducting the unreasonable amounts."

¶ 33 The trial court rejected the Hales' approach to overpayments and underpayments for two reasons. First, the court stated that, "[u]nder basic accounting principles, these debits and credits are netted-out to reflect the actual financial effect to the obligor and obligee, resulting in no damage to the owner." Second, the court found that the Hales' expert's presentation of the evidence cast "substantial doubt on the credibility of his decision to suddenly include the `underpayments' as a debit against Big H." Their expert's initial report did not apply underpayments as a debit against Big H. He did so, the court noted, only in reaction to a ruling of the court sixteen months later, "as a way of trying to cushion a portion of the financial swing in Big H's favor from the Court's ruling."

¶ 34 We reject the Hales' challenge for three independent reasons. First, the Hales have not borne their burden as appellants of demonstrating that the law is on their side. They cite no Utah authority, and while the foreign cases they cite deal with cost-plus contracts, they do not deal with underpayments or overpayments and thus do not support the Hales' contention. See Burdette v. Drushell, 837 So.2d 54, 62 (La.App. Cir.2002) (addressing the need to itemize costs to protect against claims for vague or inflated costs); Metropolitan Elec. Co. v. Mel-Jac Constr. Co., 576 P.2d 323, 325-26 (Okla.Civ. App.1978) (examining a claim of overcharging, not overpayment). Accordingly, the Hales have given us no reason to reject, as a matter of law, the trial court's approach.

¶ 35 Second, the Hales' "undisputed evidence that certain invoices were underpaid or overpaid" is the testimony of their expert witness. As noted above, the trial court doubted the credibility of that witness. "Upon review, we accord deference to the trial court's ability and opportunity to evaluate credibility and demeanor." State v. Goodman, 763 P.2d 786, 787 (Utah 1988); Iacono v. Hicken, 2011 UT App 377, ¶ 17, 265 P.3d 116 (explaining that appellate courts "defer to the [trial] court's determinations of the weight to be placed on each witness's testimony" because the trial court is "the arbiter of witness credibility in a bench trial" (citing Lamkin v. Lynch, 600 P.2d 530, 531 (Utah 1979))). As the Hales' counsel conceded at trial, without expert testimony "our case is over."

¶ 36 Third, the Hales have not demonstrated prejudice. As noted above, they make no effort to refute Big H's argument that any errors that do not in the aggregate exceed $52,493 are harmless.

¶ 37 In sum, the Hales have not established that the trial court's damage calculation resulted in reversible error.

III. The Hales Have Not Shown a Right to an Offset for Unfinished Items.

¶ 38 The Hales also challenge the trial court's finding that they are not entitled to an offset for items allegedly left unfinished or in need of repair. In their Complaint, the Hales alleged breach of contract by Big H for "failure to complete the Project as per the terms of the [contracts]" and "failure to complete work on the Project in a good and workmanlike manner[, which] further constitutes a substantial and material breach of the [contracts]." They argue on appeal that the trial court should have offset Big H's damage award by the value of "warranty repair work" Big H allegedly failed to provide.

¶ 39 This warranty repair work amounted to "punch list items" that were, according to the Hales, left unfinished or in need of repair when Big H left the project in late 2004. The Hales claimed that the punch list items totaled more than $73,000. They supported their claim at trial with schedules prepared by their expert and with photographic evidence of the alleged unfinished items. Their expert's schedules contained estimated values for each item claimed. The Hales contend that, because the trial court's judgment "failed to consider the cost of those repairs in its calculation, ... [its judgment] is not based on sufficient evidence." They point out that "[n]o evidence whatever exists to challenge" their expert's figures on the value of the punch list items.

¶ 40 However, the trial court ruled that the Hales were not entitled to an offset. It based this ruling on several grounds, including that Big H substantially complied with the contract and that the Hales failed to prove damages.

A. Substantial Performance

¶ 41 "To establish a breach of contract claim, a party must identify a contracted duty that the other party has breached." Tooele Assocs. Ltd. Partnership v. Tooele City, 2011 UT App 36, ¶ 2, 251 P.3d 835. The trial court concluded that the Hales did not prove that Big H breached its contractual duty to complete the homes in a good and workmanlike manner. Its conclusion was based on three key factual findings. First, based at least in part on Dwayne Horsley's testimony, the trial court found that "[Big H] repaired items made known to them and there [was] no evidence that things were left incomplete or completed improperly insofar as the items were known to them before December 1, 2004," when the Hales breached the contract and Big H left the project. Second, the trial court concluded that the parties' contract required Big H to build the homes in "`substantial compliance' with agreed-upon plans and specifications." Third, the trial court found, "based upon all the testimony, that the Hales received the two [h]omes in accordance with their plans and specifications, plus substantial upgrades and modifications that they themselves requested," and that "[a]ll of the allegedly defective and/or incomplete work items ... constitute minor punch list items."

¶ 42 The Hales argue that Dwayne Horsley's testimony, when "read in full," does not support these findings. Specifically, they argue that "he equivocated in some parts of his testimony on the subject" by testifying that he had completed the punch list items "`to [his] knowledge,'" and that he was uncertain of or disputed three items on the list. "On the other hand," the Hales point out, Charles and Beverly Hale, their son, and "both experts testified that there were items that still needed to be fixed."

¶ 43 Our role is not to second-guess the trial court's assessment of witness credibility based on the cold record on appeal. See State v. Pena, 869 P.2d 932, 936 (Utah 1994) (explaining that trial court judges are "considered to be in the best position to assess the credibility of witnesses and to derive a sense of the proceeding as a whole, something an appellate court cannot hope to garner from a cold record"), holding modified by State v. Levin, 2006 UT 50, 144 P.3d 1096; Sorenson v. Kennecott-Utah Copper Corp., 873 P.2d 1141, 1147 (Utah Ct.App.1994) (noting the "well-settled principle that an appellate court will not second-guess a trial court on issues of witness credibility"). As noted above, one of the Hales' obstacles on appeal is the trial court's assessment of the credibility of its principal witnesses, specifically, Charles Hale and the Hales' expert. Although this credibility determination undermines their warranty claim, the Hales do not discuss it on appeal. More importantly, they do not specifically challenge the trial court's findings that Big H substantially complied with the parties' contract and that the homes Big H constructed complied with the plans and specifications, including upgrades and modifications the Hales requested.

¶ 44 In sum, the Hales have not demonstrated that the trial court's findings with respect to the warranty repair work are clearly erroneous.

B. Proof of Damages

¶ 45 Proof of damages is an element of a claim for breach of contract. See Bair v. Axiom Design, LLC, 2001 UT 20, ¶ 14, 20 P.3d 388. The Hales' expert provided estimates of the cost of the repair work, and the Hales assert that "[n]o evidence whatever exists to challenge [their expert]'s figures on the cost of repairs." But the trial court found that the Hales' expert's value estimates for the allegedly unfinished or damaged items were not reliable. Inasmuch as the expert himself labeled the amounts on the punch list as "`estimates,' and acknowledged at trial that they were less accurate and precise" than other schedules the court found to be "riddled with numerous substantive flaws," the court found "little ... to credit in [the Hales' expert's estimates of the repair work]." The Hales have not challenged this credibility determination. Instead, they argue that the trial court erred by "dismiss[ing their expert's] figures as `estimates,'" because "where a breach is found, and no contrary evidence is presented, damages are to be quantified in whatever method is reasonable; mathematical precision is not required." (Emphasis added.) Even if the Hales could successfully challenge the trial court's finding that Big H substantially complied with the contract — which they have not — their argument is unavailing. The trial court found not that the Hales' evidence was insufficient because the values were estimated, but that their expert's estimates were not reliable. The Hales have not demonstrated error in this regard.

IV. The Hales Have Not Shown that the Trial Court Erred by Including the Cost of the Land in the Fee Calculation.

¶ 46 The Hales contend that the trial court erred by permitting Big H to recover profit on the cost of the land for the Lot 45 home because doing so contravenes the Utah Real Estate Licensing and Practices Act (the Act), see Utah Code Ann. §§ 61-2-1 to -24 (Lexis Publishing 2000) (current version at id. §§ 61-2f-101 to -512 (LexisNexis 2011 & Supp. 2012)). They argue that including the cost of the Lots is "improper as a matter of law because, under [the Act], only licensed agents and brokers may take commissions on the sale of real estate." According to the Hales, "[b]ecause there is no finding and no evidence that Big H or Dwayne Horsley were licensed real estate agents or brokers, neither is entitled to recover a commission on the cost of the lots."6

¶ 47 Big H responds that "the parties' course of conduct recognized that the price of the [Lots] was among the costs on which Big H's 10% fee was to be based." In other words, the portion of the builder's fee that was based on the cost of the Lots was indeed a builder's fee, not a commission on the sale of land as defined by the Act. The trial court ruled, "Neither Big H nor anyone else is claiming that the Hales owe such a commission as part of their acquisition of Lot 45 from [Triple Crown Estates]. Rather, Big H is simply claiming that the price of the land, i.e., its cost — once it has been acquired-is a `Cost' on which its agreed — upon fee is to be paid."

¶ 48 The Act generally governs who may recover commissions on the sale of real estate. See Sachs v. Lesser, 2008 UT 87, ¶¶ 11-12, 207 P.3d 1215 (discussing a later but substantively similar version of the Act). Specifically, section 61-2-18 of the Act places limits on who may file suit to recover commissions for certain actions:

Utah Code Ann. § 61-2-18(1) (Lexis Publishing 2000) (current version at id. § 61-2f-409(1) (LexisNexis 2011)). Under section 61-2-4, an act "for valuable consideration, of buying, [or] selling ... real estate for another,... requires the person performing ... the act to be licensed as a principal real estate broker, an associate real estate broker, or a real estate sales agent as set forth in this chapter." Id. § 61-2-4 (Lexis Publishing 2000) (current version at id. § 61-2f-201(2) (LexisNexis 2011)).

¶ 49 Here, Big H included the cost of Lot 45 in the Costs of the finished home built on that lot for purposes of calculating its ten percent fee. The question raised on appeal, then, is whether that portion of Big H's builder's fee was — as Big H maintains — a fee for building the home or — as the Hales maintain — a real estate sales commission. The Hales' briefing of this question consists of four sentences, one of which asserts a violation of the act, one of which asserts the uncontested fact that neither Big H nor Dwayne Horsley were licensed real estate brokers or agents, and two of which quote the statutory subsections cited above. Their reply brief adds the assertion that "[a] simple reading of the plain language of the Licensing Act makes it clear that Defendants cannot claim a commission on the cost of the lots."

¶ 50 We do not agree that the issue is so plain from the language of the statutes as to require no analysis on the facts presented here. The text of the relevant provisions does not contemplate the situation these parties find themselves in. Application of the law to the facts thus requires some connective tissue. The duty to supply it falls on the party claiming error.

¶ 51 An adequately briefed argument must "contain the contentions and reasons of the appellant with respect to the issues presented, including the grounds for reviewing any issue not preserved in the trial court, with citations to the authorities, statutes, and parts of the record relied on." Utah R.App. P. 24(a)(9). Case law applying this rule makes clear that it "`requires not just bald citation to authority but development of that authority and reasoned analysis based on that authority.'" State v. Green, 2004 UT 76, ¶ 13, 99 P.3d 820 (quoting State v. Thomas, 961 P.2d 299, 305 (Utah 1998)). Citing relevant provisions and cases without "any meaningful analysis of this authority" falls short. State v. Jaeger, 1999 UT 1, ¶ 31, 973 P.2d 404. The Hales have presented no more here. We accordingly conclude that this claim of error is inadequately briefed and we reject it on that ground.7

¶ 52 The Hales make two additional arguments on appeal for why we should reverse the trial court's ruling on this issue. First, they argue that inclusion of the land as a cost violates the Statute of Frauds in this case. The trial court rejected this argument "for the reasons set forth in Big H's written opposition [to the motion for new trial and to amend the judgment]." Among those reasons was that the Hales' claim was waived. We agree that it was.

¶ 53 Rule 8(c) of the Utah Rules of Civil Procedure requires a party to plead affirmative defenses in its responsive pleading. The rule explicitly includes the Statute of Frauds defense. See Utah R. Civ. P. 8(c). Subject to exceptions not applicable here, defenses not properly pleaded are waived. See Utah R. Civ. P. 12(h) ("A party waives all defenses and objections not presented either by motion or by answer or reply...."); City Elec. v. Dean Evans Chrysler-Plymouth, 672 P.2d 89, 90 (Utah 1983) (declining to consider a Statute of Frauds defense when the party failed to raise it at trial).

¶ 54 The Hales did not raise the Statute of Frauds until their objection to Big H's proposed findings of fact and conclusions of law and their motion for new trial-well after having answered Big H's counterclaims without pleading the Statute of Frauds as an affirmative defense, and more than five years into the case. The Hales persuasively argue that they could not have foreseen Big H's damage calculation at the pleadings stage. But they offer no explanation for withholding this defense until their post-trial motion. Accordingly, we conclude that the Hales waived this affirmative defense at trial and we decline to address it now. See City Elec., 672 P.2d at 90.

¶ 55 The Hales also argue that inclusion of the land as a Cost contravenes the Utah Mechanics' Lien statute, see Utah Code Ann. §§ 38-1-1 to -37 (LexisNexis 2005) (current version at id. §§ 38-1a-101 to -804 (LexisNexis Supp. 2012)). This argument was not preserved. To preserve an issue for appellate review, a party must raise the issue at trial in a timely, specific fashion and introduce supporting evidence or relevant legal authority in order to "put the [trial court] on notice of the asserted error" so that the trial court has an opportunity to correct it. O'Dea v. Olea, 2009 UT 46, ¶ 18, 217 P.3d 704 (citation and internal quotation marks omitted); see also Utah R.App. P. 24(a)(5)(A)-(B) (requiring appellant's brief to provide either a "citation to the record showing that the issue was preserved in the trial court" or "a statement of grounds for seeking review of an issue not preserved"). We find no mention in the record of this argument, and the Hales have not pointed us to any. Because the Hales did not raise this issue at trial, they did not preserve it. Because they did not preserve it, we decline to consider it. See Bangerter v. Poulton, 663 P.2d 100, 102 (Utah 1983) ("It is axiomatic that defenses and claims not raised by the parties in the trial cannot be considered for the first time on appeal.").

V. The Hales Have Not Shown that James Horsley Had Authority to Accept a $30,000 Payment for Big H.

¶ 56 The Hales contend that the trial court erred by not giving them credit for $30,000 they paid to James Horsley in November 2004. They argue that James Horsley had authority to accept payment on Big H's behalf, and that the Hales intended the November 2004 payment to be a payment to Big H. According to the Hales, "[i]t was both within the apparent and actual scope of James [Horsley's] authority to receive a builder's profit payment from the Hales, and the trial court erred in failing to credit that payment to the Hales."

A. Actual Authority

¶ 57 "Under agency law, an agent cannot make its principal responsible for the agent's actions unless the agent is acting pursuant to either actual or apparent authority." Zions First Nat'l Bank v. Clark Clinic Corp., 762 P.2d 1090, 1094 (Utah 1988). Actual authority may be express or implied:

Id. (citations omitted). As its name suggests, implied authority "may be implied from the words and conduct of the parties and the facts and circumstances attending the transaction in question." Id. at 1095.

¶ 58 The trial court found that James Horsley did not have actual authority to receive payments on behalf of Big H based on two findings: that James Horsley was not an officer, director, or management employee of the corporation; and that, as Dwayne Horsley testified, neither he nor Big H ever delegated this authority to James Horsley.

¶ 59 The Hales argue that both findings are clearly erroneous. They point out that both James Horsley and Dwayne Horsley testified that they had an agreement to equally divide the profit on the Hales' homes. In addition, Dwayne Horsley testified that James Horsley acted as "foreman" on the project, and James Horsley testified that he performed "project management" duties. Given this evidence, the Hales argue, "it is clearly erroneous to imply that James [Horsley] was not authorized to receive from the Hales a portion of the builder's fee."

¶ 60 We acknowledge that the trial court had before it evidence that reasonably supported both the Hales' and Big H's conflicting accounts. However, when, as here, "there is conflicting evidence, we defer to the trial court as the factfinder. The existence of conflicting evidence does not give rise to clear error as long as evidence supports the trial court's decision." Gardner v. Madsen, 949 P.2d 785, 790 (Utah Ct.App.1997) (citation omitted). We think the record adequately supports the trial court's finding that James Horsley did not have actual authority to accept payment on Big H's behalf.

¶ 61 The record lacks any evidence that James Horsley appears in Big H records maintained by the Utah Division of Corporations. Dwayne Horsley testified that James Horsley was "just a foreman basically," managing work "[o]ff and on," and that James Horsley "[n]ever" accepted payments on behalf of Big H from the Hales. In addition, at trial, James Horsley testified that he was a "representative" of Big H but that the Hales "knew all along" that he was not an employee, "other than [he] was doing a service for Big H," that he "helped out" with the Hales' project, and that he served as a foreman "in a way."

¶ 62 Furthermore, at the time that the Hales gave James Horsley the check for $30,000, there were, as the trial court described, "enormous tensions" between Dwayne and James Horsley "that had led to numerous arguments between them." James Horsley used the $30,000 — with full knowledge of the Hales — for a personal investment in a mortgage company, unrelated to Big H or the Hale project. James Horsley testified that he did not inform Big H or Dwayne Horsley when he received the check from the Hales. When asked at trial whether he had informed Dwayne, James answered, "No.... It had nothing to do with him." Thus, even if the Hales could establish that James Horsley had some kind of express authority as a "representative" or "foreman," this evidence undermines the claim that, based on "the facts and circumstances attending the transaction in question," see Zions First Nat'l Bank, 762 P.2d at 1095, James Horsley had authority to accept payment from the Hales on Big H's behalf.

¶ 63 In light of the evidence supporting the trial court's conclusion, the Hales have not demonstrated that the trial court clearly erred in concluding that James Horsley lacked actual authority to accept payment on Big H's behalf.

B. Apparent Authority

¶ 64 Apparent authority exists where the conduct of the principal causes a third party to reasonably believe that someone has authority to act on the principal's behalf, and the third party relies on this appearance of authority and will suffer loss if an agency relationship is not found. Luddington v. Bodenvest Ltd., 855 P.2d 204, 209 (Utah 1993); Posner v. Equity Title Ins. Agency, Inc., 2009 UT App 347, ¶ 18, 222 P.3d 775. "Thus, an analysis of apparent authority focuses on the acts of the principal from a third party's perspective." Posner, 2009 UT App 347, ¶ 18, 222 P.3d 775 (citation and internal quotation marks omitted).

¶ 65 The Hales contend that the trial court erred in ruling that James Horsley lacked apparent authority to receive the payment, and that "some of the factual findings supporting [that conclusion] are clearly erroneous." First, the Hales argue that Big H created an appearance that James Horsley had authority. They point out that James Horsley accepted reimbursement for $4,000 of construction expenses from the Hales on at least one prior occasion and "there is no evidence that Big H rejected or disgorged that payment," and that "James Horsley also testified that he `received a couple of checks payable to James Horsley' as reimbursement for the construction."

¶ 66 Second, the Hales argue that they reasonably believed, based on the appearance Big H created, that James Horsley had authority to receive the payment. They argue, "[T]he Hales understood that James [Horsley] was Dwayne[ Horsley]'s `partner' in Big H and that he was a representative of it." Indeed, they assert, both brothers testified that James Horsley "was a representative of Big H." The Hales point out that Big H entered into an agreement with James Horsley to divide the profits on the Hales' homes, an act on the part of Big H that made it reasonable for the Hales to believe that James Horsley had authority to accept payment for Big H.

¶ 67 Finally, the Hales argue that they relied on this appearance of authority and will suffer loss if they do not receive a credit equal to the $30,000 payment. They argue, "[I]t is undisputed that the Hales paid James [Horsley] $30,000, he has not paid it back, and the trial court did not credit [the Hales] for that payment."

¶ 68 Based on the evidence, the Hales contend that "the court's legal conclusion" that James Horsley lacked apparent authority "is in error because the factual findings do not properly consider the factors that would support a ruling of apparent authority."

¶ 69 We disagree. First, the trial court properly considered whether Big H's "acts or conduct" created an appearance that James Horsley had authority to accept payment on Big H's behalf. See Posner v. Equity Title Ins. Agency, Inc., 2009 UT App 347, ¶ 18, 222 P.3d 775 (citation and internal quotation marks omitted). The trial court found no evidence that Dwayne Horsley ever told the Hales, or otherwise led them to believe, that James Horsley had such authority. For the court to find apparent authority, "[i]t is the principal who must cause [the third party] to believe that the agent is clothed with apparent authority." City Elec. v. Dean Evans Chrysler-Plymouth, 672 P.2d 89, 90 (Utah 1983). The Hales challenge this finding largely by pointing to evidence that James Horsley — the alleged agent — accepted payments from the Hales.

¶ 70 The trial court properly considered facts relevant to the Hales' reasonable perspective (as a third party) of James Horsley's authority. The trial court found that it was "unreasonable for the Hales to have expected James [Horsley] to apply the $30,000 check to Big H's account." For example, the Hales knew that James Horsley intended to use the funds for a separate business venture that did not involve Big H. The Hales were aware that their delay in paying the builder's fee had created "enormous tensions between" Dwayne Horsley and James Horsley. Moreover, the Hales made the check payable to James Horsley without designating Big H as a joint payee or even notifying Dwayne Horsley or Big H of the payment prior to filing the lawsuit, despite the fact that, as the trial court described it, "they were in an adversarial relationship with Big H, making it incumbent upon them to clearly inform Big H of the payment." Finally, the Hales "had never, in the entire history of their ... family business, issued to an individual" — such as James Horsley — "a check intended for a business entity creditor" — such as Big H.

¶ 71 Once again, we acknowledge that the trial court had before it evidence that reasonably supported both the Hales' and Big H's conflicting accounts. However, we grant broad deference to the trial court's application of the doctrine of apparent authority to the facts of the case. Glew v. Ohio Sav. Bank, 2007 UT 56, ¶ 19, 181 P.3d 791. Where, as here, "the trial court's findings include inferences drawn from the evidence," we defer to the trial court "unless the logic upon which [its] extrapolation from the evidence is based is so flawed as to render the inference clearly erroneous." Id. ¶ 18. Here it was not. We therefore decline to disturb the trial court's ruling that the Hales are not entitled to a credit for the $30,000 payment to James Horsley.

VI. The Hales Have Not Shown that Big H Violated the Mechanics' Lien Statute.

¶ 72 The Mechanics' Lien statute imposes criminal and civil liability on "[a]ny person entitled to record or file a lien ... who intentionally causes a claim of lien against any property, which contains a greater demand than the sum due to be recorded or filed." See Utah Code Ann. § 38-1-25 (LexisNexis 2005) (current version at id. § 38-1a-308 (LexisNexis Supp. 2012)).8 A person who violates the provision "is liable to the owner of the property" for either "twice the amount by which the wrongful lien exceeds the amount actually due," or "the actual damages incurred." Id. § 38-1-25(2).

¶ 73 The Hales contend that the trial court erred in finding that neither Big H nor Dwayne Horsley is liable for damages for abuse of a lien right under the statute. To prove a claim for abuse of a lien right, the Hales must show as a threshold matter that the lien contained a "greater demand than the sum" actually owed. See id. § 38-1-25(1). They assert that the amount of the lien was excessive by the full face amount of the lien because the Hales "actually overpaid" Big H. Therefore, "it is axiomatic that the lien filed by [Big H,] ... asserting a right to an addition[al] payment in the amount of $165,000, was high by $165,000." But, according to the Hales, even if a proper accounting showed that the Hales owe Big H some amount of money, Big H is still liable under section 38-1-25(2) because the information that Horsley testified that he had relied on in preparing the lien did not establish, "or even giv[e] a reasonable forecast of, the face amount of the lien" at the time. Therefore, the Hales argue that in authorizing the lien, Dwayne Horsley and Big H "sought to cloud [the] Hales' title to Lot 45 in order to extract from them an amount more than was due, and otherwise to procure an unjustified advantage or benefit."

¶ 74 The trial court found, "Based upon a review of all invoices, ... the lien amount filed by [Dwayne Horsley on behalf of Big H] reflected less than the balance [the Hales] actually owed." Therefore, the trial court concluded that the $165,000 mechanics' lien that Big H filed against the Lot 45 home was valid. See Utah Code Ann. § 38-1-3 (LexisNexis 2005) (current version at id. § 38-1a-301 (LexisNexis Supp. 2012)) (authorizing liens "for the value of the service rendered, labor performed, or materials or equipment furnished or rented"). Because the Hales have not shown that the trial court's damages calculation was clearly erroneous, see supra Part II, they have not shown error in the court's finding that the lien was valid. Because the lien was valid, neither Big H nor its employee, Dwayne Horsley, violated Utah Code section 38-1-25(1) for abuse of a lien right. Because neither violated section 38-1-25(1), neither is liable to the Hales under section 38-1-25(2). We therefore affirm the trial court's ruling on the Hales' abuse of lien claim.

CONCLUSION

¶ 75 In sum, the Hales have not shown reversible error. The trial court did not err as a matter of law when it considered the evidence Big H provided, along with expert and lay testimony, in calculating Costs. Nor have the Hales shown that the trial court's inclusion of the cost of the land was an error of law. They have not shown that the trial court's findings were clearly erroneous regarding expenses and payments, the Hales' claim for an offset for warranty repair work, or James Horsley's lack of actual or apparent authority. Finally, they have not shown that the trial court erred in ruling that neither Dwayne Horsley nor Big H violated the mechanics' lien statute. At trial, the court considered "a sizeable mass of evidence that [it] was required to sift and weigh in aid of reaching a lawful result." See Traco Steel Erectors, Inc. v. Comtrol, Inc., 2009 UT 81, ¶ 20, 222 P.3d 1164. The trial court acted within its discretion in weighing the relative credibility of that evidence, and its rulings find sufficient factual support in the record. Accordingly, we decline the Hales' invitation to second-guess those factual findings on appeal. Affirmed.

¶ 76 WE CONCUR: WILLIAM A. THORNE JR., Judge, and STEPHEN L. ROTH, Judge.