McHugh, J.
Hampton Associates (Hampton), a Massachusetts limited partnership, owned a low-income housing complex (complex) in Northampton in fiscal years 1992, 1993, and 1994. Claiming that the Northampton board of assessors overvalued the complex for those years, Hampton appealed the valuation to the Appellate Tax Board (board). After an evidentiary hearing, the board concluded that Hampton had failed to sustain its burden of proving overvaluation and consequently found in the assessors’ favor. This appeal followed. Finding no error, we affirm.
Although the ultimate issue in the case centers on whether Hampton carried its burden of proof, resolution of that issue [111]*111implicates the special problems assessors encounter when determining the value of residential real estate on which income and income distribution have been artificially capped. That problem, in turn, flows from the nature of the complex and the financing that produced it. Before examining the evidence the parties presented to the board, therefore, we look briefly at the complex and its genesis.
The complex consists of twenty-six two-story buildings on approximately eighteen acres of land. The buildings contain a total of 207 apartments ranging in size from one to four bedrooms. Among other things, the complex has access to highways and public transportation, has its own on-site pumping station for a sanitary sewer system, and has five or six on-site managers.
In late 1972, Hampton obtained the construction funds to build the complex through participation in a program created by § 236 of the National Housing Act, 12 U.S.C. §§ 1701, 1715z-l (1970), a Federal program designed to encourage construction of low-income housing nationwide. Under the program, Hampton invested approximately $530,000 of its own funds and obtained approximately $4.7 million in construction funds from a commercial lender under a forty-year loan carrying a seven percent annual interest rate. The Department of Housing and Urban Development (HUD), which oversaw the program, agreed to pay all but one percent of the annual interest directly to the lender. In addition to the mortgage subsidy, participation in the program also meant that Hampton, its principals, and investors would not be liable for payments due under the note and mortgage in the event of a default in those payments. Finally, the program provided the investors with a number of significant tax benefits including offsets, or “shelter,” for income the investors obtained from other pursuits.1
In return for the foregoing benefits, Hampton, like other program participants, agreed to a number of restrictions designed to achieve the program’s over-all goals. For present [112]*112purposes, the most important restrictions included a limit on the amount of rent Hampton could charge for each of the apartments in the complex.2 In addition, Hampton was prohibited from prepaying the mortgage note, and thus from escaping the restrictions, for twenty years. Finally, the program limited to $31,979, or six percent of Hampton’s $530,000 original equity investment, the amount of income from operation of the complex Hampton could distribute to its investors annually.3
The record of proceedings before the board reveals that, in the mid- and late 1980’s, two changes in Federal law altered basic principles theretofore ápplicable to § 236 housing like the complex. First, in 1986, the Federal tax code was amended to restrict, among other things, the kinds of income that losses from operation of the complex could shelter.4 Indeed, insofar as the record before the board is concerned, none of the original tax benefits available to Hampton and its investors remained available by fiscal year 1992.5
Second, in 1987, Congress, concerned about the impact on [113]*113availability of low-income housing potentially resulting from substantial note prepayments, enacted the Emergency Low Income Housing Preservation Act of 1987 (ELIHPA), Pub. L. 100-242, Title II, 101 Stat. 1877 (1987). See 12 U.S.C. § 17151. That statute substantially but temporarily limited the right Hampton and other developers had to prepay their notes after twenty years and thereby shed the program’s restrictions on use of their properties. In return for the limitations, however, ELI-HPA provided the possibility of incentives, including withdrawal of some of the owner’s equity, for continued program participation. See generally Alder Terrace, Inc. v. United States, 39 Fed. Cl. 114, 116-117 & n.2 (Ct. Cl. 1997). In 1990, Congress made the temporary limits and accompanying incentives permanent by replacing ELIHPA with the Low Income Housing Preservation and Resident Homeownership Act (LIHPRHA), 12 U.S.C. §§ 4101-4147. See generally Greenbrier v. United States, 193 F.3d 1348, 1351-1353 (Fed. Cir. 1999), cert, denied, 530 U.S. 1274 (2000).
As of the first of the valuation dates here at issue, therefore, the legislation just described severely circumscribed Hampton’s ability to remove the complex from the program before maturity of the forty-year note. At the same time, Hampton’s continued participation in the program carried with it at least the prospect of certain financial incentives designed to make continued participation more attractive than it had been when the program began.6
Against that backdrop, the assessors valued the complex at $7,919,500 for fiscal year 1992 and $7,127,600 for fiscal years 1993 and 1994.7 Hampton timely filed applications for abatement with the assessors together with its petition to the board pursuant to G. L. c. 59, §§ 64, 65.
[114]*114The board held an evidentiary hearing on Hampton’s petition. At the hearing, the board heard from three witnesses: Andes, the vice president of Spear Management Company, a company Hampton had hired to manage the complex; King, the appraiser Hampton had hired; and Levitch, the appraiser the assessors had hired. Both appraisers agreed that the capitalization of income approach to valuation provided the appropriate method for determining the value of the complex on the relevant dates.8
Although both appraisers looked at similar elements of income and expense, their use of those elements differed dramatically. King determined that the net income from operation of the complex in each of the taxable years was greater than $31,979. Because the program limited the amount of Hampton’s annual withdrawal to $31,979, however, King used that amount as the net income to be capitalized.9 Using a capitalization rate of ten percent he derived, with some modifications, from treasury bills and other “safe” investments, King capitalized the “income” from the complex at $319,790. To that amount, he added $4,124,969, the unpaid principal balance of the construction mortgage, to produce a total value of $4,444,759, which he rounded to $4,500,000, for fiscal year 1992.10
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McHugh, J.
Hampton Associates (Hampton), a Massachusetts limited partnership, owned a low-income housing complex (complex) in Northampton in fiscal years 1992, 1993, and 1994. Claiming that the Northampton board of assessors overvalued the complex for those years, Hampton appealed the valuation to the Appellate Tax Board (board). After an evidentiary hearing, the board concluded that Hampton had failed to sustain its burden of proving overvaluation and consequently found in the assessors’ favor. This appeal followed. Finding no error, we affirm.
Although the ultimate issue in the case centers on whether Hampton carried its burden of proof, resolution of that issue [111]*111implicates the special problems assessors encounter when determining the value of residential real estate on which income and income distribution have been artificially capped. That problem, in turn, flows from the nature of the complex and the financing that produced it. Before examining the evidence the parties presented to the board, therefore, we look briefly at the complex and its genesis.
The complex consists of twenty-six two-story buildings on approximately eighteen acres of land. The buildings contain a total of 207 apartments ranging in size from one to four bedrooms. Among other things, the complex has access to highways and public transportation, has its own on-site pumping station for a sanitary sewer system, and has five or six on-site managers.
In late 1972, Hampton obtained the construction funds to build the complex through participation in a program created by § 236 of the National Housing Act, 12 U.S.C. §§ 1701, 1715z-l (1970), a Federal program designed to encourage construction of low-income housing nationwide. Under the program, Hampton invested approximately $530,000 of its own funds and obtained approximately $4.7 million in construction funds from a commercial lender under a forty-year loan carrying a seven percent annual interest rate. The Department of Housing and Urban Development (HUD), which oversaw the program, agreed to pay all but one percent of the annual interest directly to the lender. In addition to the mortgage subsidy, participation in the program also meant that Hampton, its principals, and investors would not be liable for payments due under the note and mortgage in the event of a default in those payments. Finally, the program provided the investors with a number of significant tax benefits including offsets, or “shelter,” for income the investors obtained from other pursuits.1
In return for the foregoing benefits, Hampton, like other program participants, agreed to a number of restrictions designed to achieve the program’s over-all goals. For present [112]*112purposes, the most important restrictions included a limit on the amount of rent Hampton could charge for each of the apartments in the complex.2 In addition, Hampton was prohibited from prepaying the mortgage note, and thus from escaping the restrictions, for twenty years. Finally, the program limited to $31,979, or six percent of Hampton’s $530,000 original equity investment, the amount of income from operation of the complex Hampton could distribute to its investors annually.3
The record of proceedings before the board reveals that, in the mid- and late 1980’s, two changes in Federal law altered basic principles theretofore ápplicable to § 236 housing like the complex. First, in 1986, the Federal tax code was amended to restrict, among other things, the kinds of income that losses from operation of the complex could shelter.4 Indeed, insofar as the record before the board is concerned, none of the original tax benefits available to Hampton and its investors remained available by fiscal year 1992.5
Second, in 1987, Congress, concerned about the impact on [113]*113availability of low-income housing potentially resulting from substantial note prepayments, enacted the Emergency Low Income Housing Preservation Act of 1987 (ELIHPA), Pub. L. 100-242, Title II, 101 Stat. 1877 (1987). See 12 U.S.C. § 17151. That statute substantially but temporarily limited the right Hampton and other developers had to prepay their notes after twenty years and thereby shed the program’s restrictions on use of their properties. In return for the limitations, however, ELI-HPA provided the possibility of incentives, including withdrawal of some of the owner’s equity, for continued program participation. See generally Alder Terrace, Inc. v. United States, 39 Fed. Cl. 114, 116-117 & n.2 (Ct. Cl. 1997). In 1990, Congress made the temporary limits and accompanying incentives permanent by replacing ELIHPA with the Low Income Housing Preservation and Resident Homeownership Act (LIHPRHA), 12 U.S.C. §§ 4101-4147. See generally Greenbrier v. United States, 193 F.3d 1348, 1351-1353 (Fed. Cir. 1999), cert, denied, 530 U.S. 1274 (2000).
As of the first of the valuation dates here at issue, therefore, the legislation just described severely circumscribed Hampton’s ability to remove the complex from the program before maturity of the forty-year note. At the same time, Hampton’s continued participation in the program carried with it at least the prospect of certain financial incentives designed to make continued participation more attractive than it had been when the program began.6
Against that backdrop, the assessors valued the complex at $7,919,500 for fiscal year 1992 and $7,127,600 for fiscal years 1993 and 1994.7 Hampton timely filed applications for abatement with the assessors together with its petition to the board pursuant to G. L. c. 59, §§ 64, 65.
[114]*114The board held an evidentiary hearing on Hampton’s petition. At the hearing, the board heard from three witnesses: Andes, the vice president of Spear Management Company, a company Hampton had hired to manage the complex; King, the appraiser Hampton had hired; and Levitch, the appraiser the assessors had hired. Both appraisers agreed that the capitalization of income approach to valuation provided the appropriate method for determining the value of the complex on the relevant dates.8
Although both appraisers looked at similar elements of income and expense, their use of those elements differed dramatically. King determined that the net income from operation of the complex in each of the taxable years was greater than $31,979. Because the program limited the amount of Hampton’s annual withdrawal to $31,979, however, King used that amount as the net income to be capitalized.9 Using a capitalization rate of ten percent he derived, with some modifications, from treasury bills and other “safe” investments, King capitalized the “income” from the complex at $319,790. To that amount, he added $4,124,969, the unpaid principal balance of the construction mortgage, to produce a total value of $4,444,759, which he rounded to $4,500,000, for fiscal year 1992.10 King added the unpaid principal balance of the mortgage to the capitalized value of the complex’s “income” on the theory that, because a potential buyer “can’t pay off the existing mortgage, [that buyer is] going to . . . pay whatever the [115]*115principal balance is on the mortgage. I don’t see any reason why they would pay anything more than that.”
In its decision, the board rejected King’s analysis concluding, among other things, that it made no sense simply to add the unpaid principal balance of the mortgage to the value derived by capitalizing the “income.” In the board’s view, the way King used the mortgage balance meant that the value of the complex actually decreased as the mortgage balance declined and Hampton’s equity in the complex increased. To the board, such a result was at war both with common sense and with recognized appraisal standards.11 Moreover, the board noted, King himself had appraised the complex at a total value of $8 million when Hampton submitted an application to HUD for withdrawal of its equity interests in the project under the LIH-PRHA program.12
The board’s rejection of King’s testimony was well within its power. The board was required to accept neither the opinions nor the calculations of any expert witness. See Assessors of Lynnfield v. New England Oyster House, Inc., 362 Mass. 696, 701-702 (1972). See also New Boston Garden Corp. v. Assessors of Boston, 383 Mass. 456, 473 (1981). Although Hampton bore the burden of proving overvaluation, Schlaiker v. Assessors of Great Barrington, 365 Mass. 243, 245 (1974); Foxboro Associates v. Assessors of Foxborough, 385 Mass. 679, 691 (1982), the board could not disbelieve the evidence Hampton proffered “without an explicit and objectively adequate reason,” New Boston Garden Corp. v. Assessors of Boston, 383 Mass. at 470-471, quoting from Jaffe, Judicial Control of Administrative Action 607 (1965). The board’s articulated reasons for rejecting King’s opinion in this case fully met both criteria.
[116]*116Without King’s opinion, nothing in Hampton’s affirmative case carried its burden. In an effort to remedy that defect, Hampton focuses on the opinion delivered by Levitch, the assessors’ appraiser.13 Hampton urges that, even if the board properly discounted the case it presented, the opinion Levitch rendered, and thus the assessors’ case, was so deeply flawed that the board was left with no substantial evidence on which to rest its ultimate decision in the assessors’ favor.
There can be little doubt about the flaws in the opinion Lev-itch presented. Unlike King, Levitch did not cap Hampton’s net income at the amount of its permitted annual distributions. Indeed, apart from considering limitations on the rent the complex could develop, Levitch gave the distribution limits under which Hampton operated no weight or consideration at all. Moreover, Levitch used a discount rate of 3.97 percent to capitalize Hampton’s net income of $304,99214 and, in so doing, to achieve a fiscal year 1992 complex value of $8,037,100.15
Central to Levitch’s opinion of value was his assessment of tax benefits Hampton received from owning the complex. In his [117]*117appraisal report, a copy of which was introduced at the hearing, Levitch said this about his 3.97 percent discount rate:
“This rate is a very low rate that on the face of it is difficult to justify. Other real estate has capitalization rates ranging from 9% to say 12%. The difference is in the consideration of the after-tax benefits. While all real estate carries with it some depreciation benefits, the low income housing has extreme tax credits attached to it.”
He repeated that thought in his testimony before the board.
The trouble is that Levitch was unable to identify — in his report, in his direct testimony, or on cross-examination — a single tax benefit actually applicable either to Hampton or, more significantly, to someone who purchased the property from Hampton. Cf. Community Dev. Co. of Gardner v. Assessors of Gardner, 377 Mass. 351, 354-356 (1979). In fact, the only evidence about tax benefits applicable to Hampton’s ownership of the complex at the relevant time was Andes’s testimony that, by fiscal year 1992, no such benefits remained. Moreover, while discussing the tax benefits upon which he based his “difficult to justify” capitalization rate, Levitch proffered an article entitled “Valuing Property Developed with Low-Income Housing Tax Credits” from the July, 1994, issue of The Appraisal Journal. But that article, introduced as an exhibit at the hearing, dealt with a Federal low-income housing program first introduced in the Budget Reform Act of 1986, years after the complex was constructed. The 1986 program’s incentives consisted entirely of tax credits,16 not subsidies, and, unlike the § 236 program, was not administered by HUD.
Chiefly for two reasons, however, the flaws in Levitch’s testimony, however large, do not invalidate the board’s decision. First of all, the board did not accept all of what Levitch said. To be sure, the board said that, unlike King, Levitch “sought to take into consideration not only the federal restrictions imposed by § 236 of the National Housing Act but also the benefits provided under the HUD agreement. Thus he sought to incorporate the factors limiting the value of the property as well [118]*118as the factors enhancing the value of the property.” Nevertheless, the board went on to say that it “did not endorse the Lev-itch analysis in its entirety but found that [Hampton’s] own valuation was flawed. More importantly, the board found that [Hampton] did not meet its burden of proving that the assessed valuation exceeded the fair cash value of the property for the years at issue.”17
Second, and more important, under the circumstances of this case substantial evidence was not required to validate the board’s decision. “[W]here as here there is no persuasive evidence on the part of the party carrying the burden of proof,[18] a conclusion that a presumptively valid assessment must stand is by its nature not such an affirmative finding as to require substantial evidence to support it.” Schlaiker v. Assessors of Great Barrington, 365 Mass. at 245 n.2. See note 13, supra. That principle is applicable not only when the assessors test the adequacy of the taxpayer’s case by declining to present any evidence when the taxpayer rests, see General Electric Co. v. Assessors of Lynn, 393 Mass. 591, 599-600 & n.4 (1984) (citing 801 Code Mass. Regs. § 1.01(7)(d)(l) (1979)); cf. Western Massachusetts Lifecare Corp. v. Assessors of Springfield, 434 Mass. 96, 101, 106-107 (2001), but also when, as in this case, the assessors present their own affirmative evidence. See Schlaiker v. Assessors of Great Barrington, 365 Mass. at 246; Foxboro Associates v. Assessors of Foxborough, 385 Mass. at 689, 691. Accordingly, even if the board had relied on Levitch’s [119]*119opinion after concluding that Hampton had not met its burden, that reliance would not invalidate its ultimate decision in the assessors’ favor.
At first blush, it may seem anomalous that the taxpayer loses when the taxpayer and the assessors present the board with equally footless cases. But that result flows from the fact that proceedings before the board, like most adversary proceedings, are designed to produce a decision, not a potentially endless quest for abstract verities. The burden of proof — here placed on the taxpayer — plays a central role in insuring that a decision in fact results.19 The board’s rejection, actual or required, of Levitch’s testimony that the assessors did not overvalue Hampton’s property is no evidence of overvaluation any more than the board’s rejection of King’s testimony that the property was overvalued is evidence that the assessors’ valuation was proper. See generally Commonwealth v. Marino, 343 Mass. 725, 728 (1962); Cohen v. Board of Registration in Pharmacy, 350 Mass. 246, 251-252 (1966); Atkinson v. Rosenthal, 33 Mass. App. Ct. 219, 224 (1992). Consequently, rejection of Levitch’s opinion of value, or flaws in the methodology he used to produce that opinion, did not, and could not, satisfy Hampton’s burden of proof. Indeed, when both King’s and Levitch’s opinions are discarded, nothing produced by the board proceedings could alter what existed when the proceedings began, i.e., the valuation the assessors had placed on the complex. In the end, therefore, that valuation remains and the decision of the board must be affirmed.
So ordered.