Botsford, J.
Two telephone companies appeal from a decision of the Appellate Tax Board (board) upholding the property tax assessments by the board of assessors of Boston (assessors) for fiscal year (FY) 2012 on certain personal property each company
owns. At issue is whether the tax assessments, which were based on a “split” tax rate structure determined in accordance with G. L. c. 40, § 56 (§ 56), constituted a disproportionate tax that, as such, violated the Constitution of the Commonwealth. More particularly, the question is whether the split tax rate structure authorized by § 56 — a rate structure that provides for taxable personal property to be taxed at a rate identical to the rate applied to commercial and industrial real property but higher than the rate that would apply if all taxable property, real and personal, were taxed at a single, uniform rate — violates the proportionality requirement of Part II, c. 1, § 1, art. 4, of the Constitution of the Commonwealth, as amended by art. 112 of the Amendments to the Constitution, as well as art. 10 of the Massachusetts Declaration of Rights. We conclude that the split tax structure authorized by § 56 and related statutes does not violate the Massachusetts Constitution. We affirm the board’s decision.
1.
Background.
a.
Procedural background.
Verizon New England Inc. (Verizon) and RCN BecoCom LLC (RCN) (collectively, taxpayers) are subject to property tax in the city of Boston on personal property consisting primarily of machinery, poles, underground conduits, wires, and pipes (§ 39 property) that they own and use for business purposes. Pursuant to G. L. c. 59, § 39, the Commissioner of Revenue (commissioner) is required on an annual basis to centrally determine and certify the valuation of this type of property owned by telephone and telegraph companies, including the taxpayers; the commissioner’s certified central valuations then become the basis for tax assessments by the assessors in each city and town where such property is located and subject to taxation, including Boston. For purposes of property tax assessments for fiscal year 2012, the commissioner centrally valued the § 39 property owned by Verizon in Boston at $215,846,800, and the § 39 property owned by RCN in Boston at
$48,444,900.
The assessors thereafter assessed a property tax for FY 2012 on Verizon’s § 39 property at the tax rate of $31.92 per thousand dollars of value for a total assessment of $6,889,829.86; they assessed a FY 2012 tax on RCN’s § 39 property at the same rate of $31.92 per thousand for a total assessment of $1,546,361.21. The taxpayers timely paid the personal property taxes thus assessed, and then timely filed abatement applications with the assessors.
The requested abatements were denied, and both taxpayers filed timely appeals with the board. On April 24, 2013, the board consolidated the taxpayers’ petitions for hearing. On October 24, 2014, the board issued its decision denying the taxpayers’ appeals, and thereafter issued findings of fact and a report. The taxpayers timely appealed to the Appeals Court, and we transferred the case on our own motion.
b.
Constitutional and statutory background.
Part II, c. 1, § 1, art. 4, of the Constitution of the Commonwealth (art. 4), as amended in 1978 by art. 112 of the Amendments (art. 112), authorizes the Legislature
“to impose and levy proportional and reasonable assessments, rates, and taxes, upon all the inhabitants of, and persons resident, and estates lying, within the said commonwealth,
except that, in addition to the powers conferred under Articles XLI and XCIX of the
Amendments,[
]
the general court may classify reed property according to its use in no more than four classes and to assess, rate and tax such property differently in the classes so established, but proportionately in the same class, and except that reasonable
exemptions may be
granted’ (emphasis supplied).
Before it was amended by art. 112, art. 4 had been consistently interpreted by this court to require that
“all taxes levied under [the taxing authority of art. 4] be ‘proportional and reasonable,’ and [art. 4] forbids their imposition upon one class of persons or property at a different rate from that which is applied to other classes, whether that discrimination is effected directly in the assessment or indirectly through arbitrary and unequal methods of valuation.”
Cheshire
v.
County Comm’rs of Berkshire,
118 Mass. 386, 389 (1875). See, e.g.,
President, Directors, & Co. of the Portland Bank v. Apthorp,
12 Mass. 252, 255 (1815);
Oliver
v.
Washington Mills,
11 Allen 268, 275 (1865);
Opinion of the Justices, 220
Mass. 613, 618-619, 621 (1915);
Opinion of the Justices,
332 Mass. 769, 778-779 (1955);
Bettigole
v.
Assessors of Springfield,
343 Mass. 223, 230-231 (1961).
In practice, however, local municipal assessors — to whom the Legislature has delegated for over two centuries the power to assess local property taxes, see
Opinion of the Justices,
378 Mass. 802, 810 & n.11 (1979) — did not follow this constitutional mandate of strict proportionality, or the statutory requirement that local assessment of property taxes be based on “a fair cash valuation of all the estate, real and personal, subject to taxation therein.” G. L. c. 59, § 38. See
Bettigole,
343 Mass. at 231-232. See also
Sudbury
v.
Commissioner of Corps. & Taxation,
366 Mass. 558, 563 (1974);
Shoppers’ World, Inc.
v.
Assessors of Framingham,
348 Mass. 366, 371-372 (1965). Rather, there was a widespread practice of employing varying percentages of fair cash values that favored residential properties at the expense of commercial and industrial properties. See
Keniston
v.
Assessors of Boston,
380 Mass. 888, 890-891 (1980);
Bettigole, supra
at 227-228. Particularly beginning in the 1960s this court more insistently declared disproportionate assessments of property illegal and also broadened remedies available to taxpayers bringing claims of disproportionate taxation. See
Sudbury, supra
at 568-569;
Shoppers’ World, Inc., supra
at 372-373;
Bettigole, supra
at 236-237;
Stone
v.
Springfield,
341 Mass. 246, 248 (1960). How
ever, in the midst of the “accelerated judicial enforcement of the [proportionate taxation and] fair cash valuation requirement, . . . there was public challenge to the concept of 100% valuation” (citation omitted),
Keniston,
380 Mass.
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Botsford, J.
Two telephone companies appeal from a decision of the Appellate Tax Board (board) upholding the property tax assessments by the board of assessors of Boston (assessors) for fiscal year (FY) 2012 on certain personal property each company
owns. At issue is whether the tax assessments, which were based on a “split” tax rate structure determined in accordance with G. L. c. 40, § 56 (§ 56), constituted a disproportionate tax that, as such, violated the Constitution of the Commonwealth. More particularly, the question is whether the split tax rate structure authorized by § 56 — a rate structure that provides for taxable personal property to be taxed at a rate identical to the rate applied to commercial and industrial real property but higher than the rate that would apply if all taxable property, real and personal, were taxed at a single, uniform rate — violates the proportionality requirement of Part II, c. 1, § 1, art. 4, of the Constitution of the Commonwealth, as amended by art. 112 of the Amendments to the Constitution, as well as art. 10 of the Massachusetts Declaration of Rights. We conclude that the split tax structure authorized by § 56 and related statutes does not violate the Massachusetts Constitution. We affirm the board’s decision.
1.
Background.
a.
Procedural background.
Verizon New England Inc. (Verizon) and RCN BecoCom LLC (RCN) (collectively, taxpayers) are subject to property tax in the city of Boston on personal property consisting primarily of machinery, poles, underground conduits, wires, and pipes (§ 39 property) that they own and use for business purposes. Pursuant to G. L. c. 59, § 39, the Commissioner of Revenue (commissioner) is required on an annual basis to centrally determine and certify the valuation of this type of property owned by telephone and telegraph companies, including the taxpayers; the commissioner’s certified central valuations then become the basis for tax assessments by the assessors in each city and town where such property is located and subject to taxation, including Boston. For purposes of property tax assessments for fiscal year 2012, the commissioner centrally valued the § 39 property owned by Verizon in Boston at $215,846,800, and the § 39 property owned by RCN in Boston at
$48,444,900.
The assessors thereafter assessed a property tax for FY 2012 on Verizon’s § 39 property at the tax rate of $31.92 per thousand dollars of value for a total assessment of $6,889,829.86; they assessed a FY 2012 tax on RCN’s § 39 property at the same rate of $31.92 per thousand for a total assessment of $1,546,361.21. The taxpayers timely paid the personal property taxes thus assessed, and then timely filed abatement applications with the assessors.
The requested abatements were denied, and both taxpayers filed timely appeals with the board. On April 24, 2013, the board consolidated the taxpayers’ petitions for hearing. On October 24, 2014, the board issued its decision denying the taxpayers’ appeals, and thereafter issued findings of fact and a report. The taxpayers timely appealed to the Appeals Court, and we transferred the case on our own motion.
b.
Constitutional and statutory background.
Part II, c. 1, § 1, art. 4, of the Constitution of the Commonwealth (art. 4), as amended in 1978 by art. 112 of the Amendments (art. 112), authorizes the Legislature
“to impose and levy proportional and reasonable assessments, rates, and taxes, upon all the inhabitants of, and persons resident, and estates lying, within the said commonwealth,
except that, in addition to the powers conferred under Articles XLI and XCIX of the
Amendments,[
]
the general court may classify reed property according to its use in no more than four classes and to assess, rate and tax such property differently in the classes so established, but proportionately in the same class, and except that reasonable
exemptions may be
granted’ (emphasis supplied).
Before it was amended by art. 112, art. 4 had been consistently interpreted by this court to require that
“all taxes levied under [the taxing authority of art. 4] be ‘proportional and reasonable,’ and [art. 4] forbids their imposition upon one class of persons or property at a different rate from that which is applied to other classes, whether that discrimination is effected directly in the assessment or indirectly through arbitrary and unequal methods of valuation.”
Cheshire
v.
County Comm’rs of Berkshire,
118 Mass. 386, 389 (1875). See, e.g.,
President, Directors, & Co. of the Portland Bank v. Apthorp,
12 Mass. 252, 255 (1815);
Oliver
v.
Washington Mills,
11 Allen 268, 275 (1865);
Opinion of the Justices, 220
Mass. 613, 618-619, 621 (1915);
Opinion of the Justices,
332 Mass. 769, 778-779 (1955);
Bettigole
v.
Assessors of Springfield,
343 Mass. 223, 230-231 (1961).
In practice, however, local municipal assessors — to whom the Legislature has delegated for over two centuries the power to assess local property taxes, see
Opinion of the Justices,
378 Mass. 802, 810 & n.11 (1979) — did not follow this constitutional mandate of strict proportionality, or the statutory requirement that local assessment of property taxes be based on “a fair cash valuation of all the estate, real and personal, subject to taxation therein.” G. L. c. 59, § 38. See
Bettigole,
343 Mass. at 231-232. See also
Sudbury
v.
Commissioner of Corps. & Taxation,
366 Mass. 558, 563 (1974);
Shoppers’ World, Inc.
v.
Assessors of Framingham,
348 Mass. 366, 371-372 (1965). Rather, there was a widespread practice of employing varying percentages of fair cash values that favored residential properties at the expense of commercial and industrial properties. See
Keniston
v.
Assessors of Boston,
380 Mass. 888, 890-891 (1980);
Bettigole, supra
at 227-228. Particularly beginning in the 1960s this court more insistently declared disproportionate assessments of property illegal and also broadened remedies available to taxpayers bringing claims of disproportionate taxation. See
Sudbury, supra
at 568-569;
Shoppers’ World, Inc., supra
at 372-373;
Bettigole, supra
at 236-237;
Stone
v.
Springfield,
341 Mass. 246, 248 (1960). How
ever, in the midst of the “accelerated judicial enforcement of the [proportionate taxation and] fair cash valuation requirement, . . . there was public challenge to the concept of 100% valuation” (citation omitted),
Keniston,
380 Mass. at 891, and in response to this public sentiment, the General Court approved in 1975 and again in 1977 the constitutional amendment embodied in art. 112; the amendment was ratified by the voters on November 7, 1978 — by a two-to-one margin.
See
Associated Indus. of Mass., Inc.
v.
Commissioner of Revenue,
378 Mass. 657, 659 (1979);
Opinion of the Justices, supra
at 804. Accord
Keniston, supra.
Article 112 empowered the Legislature to establish a property tax system that would impose “different rates of taxation on different classes of real property,”
Opinion of the Justices, supra,
and that in practical effect would resemble and legitimize the long-time local practice of establishing relatively lower property tax assessments for residential property and vacant land or open space as compared to other classes of property. See
id.
at 804-805.
Article 112 permits the Legislature to establish different classes of real property and to tax the different classes at different rates, so long as all real property within a class is taxed at the same rate. In anticipation of the ratification of art. 112, the Legislature enacted St. 1978, c. 580, which, pursuant to the authority contained in the proposed amendment, created a property tax system based on classifying real property in four classes. In 1979, following the amendment’s ratification, the Legislature considered a somewhat different classification system and submitted two questions to this court concerning the constitutionality of certain of its features.
See
Opinion of the Justices,
378 Mass. at 802, 806-815. Following receipt of our affirmative answers to its questions, the Legislature enacted new legislation, St. 1979, c. 797, to implement art. 112, establishing a property tax structure almost identical to that proposed. At the same time, the Legislature also repealed the classification provisions of St. 1978, c. 580. See St. 1979, c. 797, § 23. See also St. 1980, c. 261, § 16.
The implementing legislation set out in St. 1979, c. 797, is codified as G. L. c. 40, § 56; G. L. c. 58, § 1A; and G. L. c. 59, § 2A, and remains in effect;
the assessors here implemented the split tax structure in place in Boston for FY 2012 pursuant to these statutes.
Under them, the commissioner is required every three years to determine, within each city and town in the Commonwealth, whether the locally assessed values represent the full and fair cash valuation for each class of real property, defined in c. 59, § 2A,
and for all personal property not exempt from local taxation. See G. L. c. 40, § 56; G. L. c. 58, § 1A.
For every municipality that the commissioner determines is using full and fair cash valuation, the commissioner also ascertains a “minimum residential factor” (MRF).
See G. L. c. 40, § 56; G. L. c. 58, § 1A.
The municipality next determines “the percentages of local tax levy to be borne by each class of real property, as defined in [G. L. c. 59, § 2A], and personal property.” G. L. c. 40, § 56. To do so, the municipality first adopts a residential factor (RF) to be applied in making the determination of local levy percentages for each class of property; the RF may not be less than the MRF determined by the commissioner.
Id.
The municipality then determines the tax rate per thousand dollars of value for each class of property by dividing the share of the levy to be raised by each class by the total assessed valuation for that class, and multiplying the result by 1,000.
Id.
c.
Factual background.
Turning to this case, for FY 2012, Boston elected to adopt a split rate tax structure pursuant to
§ 56.
The city having elected to use an RF of 59.6005%, the assessors determined the following percentages of the total tax levy to be borne by each class of real property and by personal property:
Classification Levy Percentage Tax Rate Per Thousand
Residential 38.7353% $13.04
Open Space 0% $0.00
Commercial 50.9987% $31.92
Industrial 1.3352% $31.92
Personal 8.9308% $31.92
On December 12, 2011, the commissioner approved and certified Boston’s FY 2012 tax rates.
Under the FY 2012 tax rates in Boston, personal property as a whole constituted 8.9308% of the tax levy, but it accounted for 5.1033% of the total valuation of all real and personal property situated in the city; residential property made up 38.7353% of the total tax levy, but accounted for 64.9915% of the total valuation of all real and personal property located in the city. With respect to the two taxpayers in this case, Verizon’s taxable property situated in Boston for FY 2012 was approximately 0.2439% of the value of all taxable property in the city, but Verizon was required to pay 0.4269% of the total tax levy; RCN’s taxable property was approximately 0.0547% of the total taxable property, but RCN was required to pay 0.0958% of the total tax levy. At the same time, the value of Verizon’s § 39 property was approximately 4.78% of the total valuation of personal property and approximately 0.6966% of the total valuation of property in the commercial, industrial, and property (CIP) classes located in Boston for FY 2012, and the tax assessed on that property represented these exact same percentages of the total taxes levied on all personal property and all CIP property, respectively. For RCN, the value of its § 39 property was 1.07% of the total valuation of personal property and 0.156% of the total valuation of property in the CIP classes for FY 2012, and the same respective percentages of the total taxes levied on all personal property and CIP property, for that year.
2.
Discussion.
The taxpayers argue that art. 112 created a limited exception to art. 4’s overarching proportionality require -
ment, an exception that applies solely to the taxation of real property, and based on the plain language of art. 112, the tax treatment of personal property remains unchanged by art. 112. That is, the taxpayers argue that, just as was true before the ratification of art. 112, in order to conform to art. 4’s mandate that tax assessments be “proportional and reasonable,” the assessors should have imposed a tax rate on personal property that would result in owners of personal property being responsible only for their proportionate share of the tax levy, measured by the relative value of their personal property compared to the total value of all the taxable property in Boston, real and personal. On the facts of this case, that measurement would have yielded a tax rate of $18.24 per thousand dollars of value, rather than the rate of $31.92 per thousand dollars of value applied by the assessors, which is 1.75 times greater. The taxpayers contend that because the tax rate applied to their personal property in FY 2012 exceeded this permissible limit, the tax was unconstitutionally disproportionate in violation both of art. 4 and of art. 10 of the Massachusetts Declaration of Rights. We disagree.
As the board’s decision states, and the taxpayers do not dispute, the assessors determined the challenged FY 2012 tax rates and assessments in compliance with the provisions of § 56.
The taxpayers’ challenge, therefore, is that the split tax structure permitted by § 56 is unconstitutional because it imposes a disproportionate tax on owners of personal property and there is no constitutional authority to do so. The board disagreed, and its opinion sets forth the board’s reasoning in some detail, but questions of constitutional interpretation are questions of law, and we review them de novo. See
RCN-BecoCom, LLC
v.
Commissioner of Revenue,
443 Mass. 198, 201-202 (2005). See also
Geoffrey, Inc.
v.
Commissioner of Revenue,
453 Mass. 17, 22, cert. denied, 557 U.S. 920 (2009).
“We start from the premise that ‘[a] tax measure is presumed valid and is entitled to the benefit of any constitutional doubt, and the burden of proving its invalidity falls on those who challenge the measure.’ ”
WB&T Mtge. Co.
v.
Assessors of Boston,
451 Mass. 716, 721 (2008), quoting
Opinion of the Justices,
425 Mass. 1201, 1203-1204 (1997). A party challenging the validity of a tax measure must “establish[ ] its invalidity ‘beyond a rational doubt’ ”
(citation omitted).
Geoffrey, Inc.,
453 Mass. at 22.
Determining the constitutional validity of § 56 requires an examination of art. 112 and in particular, how art. 112 affected the proportionality requirement within art. 4. Our cases have defined principles that guide our analysis: “A constitutional amendment should be ‘interpreted in the light of the conditions under which it . . . [was] framed, the ends which it was designed to accomplish, the benefits which it was expected to confer, and the evils which it was hoped to remedy.’ ”
Mazzone
v.
Attorney Gen.,
432 Mass. 515, 526 (2000), quoting
Tax Comm’r
v.
Putnam,
227 Mass. 522, 524 (1917). See
Attorney Gen.
v.
Methuen,
236 Mass. 564, 573 (1921). “An amendment to the Constitution is one of the most solemn and important of instruments. It commonly is a brief and comprehensive statement of a general principle of government.... Its words should be interpreted in a sense most obvious to the common understanding at the time of its adoption, because it is proposed for public adoption and must be understood by all entitled to vote” (citation omitted).
Cohen
v.
Attorney Gen.,
357 Mass. 564, 571 (1970).
As discussed earlier in this opinion, before art. 112 was ratified, beginning early in the Nineteenth Century, see
President, Directors, & Co. of the Portland Bank,
12 Mass. at 255, and continuing, art. 4 was uniformly interpreted to forbid the imposition of taxes “upon one class of persons or property at a different rate from that which is applied to other classes, whether that discrimination [was] effected directly in the assessment or indirectly through arbitrary and unequal methods of valuation.”
Cheshire,
118 Mass. at 389. See
Bettigole,
343 Mass. at 230-232. As also discussed, because of popular dissatisfaction with the combined effect of the constitutional proportionality requirement and the statutory obligation of municipalities to assess residential property and vacant land (open space) at full and fair cash value and in the same manner as all other types of property, the Legislature in response proposed art. 112 as an amendment to art. 4. See
Associated Indus. of Mass., Inc.,
378 Mass. at 659;
Opinion of the Justices,
378 Mass. at 804.
This history reflects that the animating purpose of art. 112 was to change the meaning of proportionality in art. 4 in order to enable residential property to be treated differently from other property classes. Article 112 must be interpreted to give effect to this purpose, see, e.g.,
Mazzone,
432 Mass. at 526, and our review of the constitutionality of § 56, in turn, must consider whether the statute helps to effectuate this purpose. It does.
Section 56 — in combination with G. L. c. 58, § 1A, and G. L. c. 59, § 2A, see St. 1979, c. 797 — authorizes a city or town to adopt a split tax rate structure that enables it to tax residential and open space property at a lower effective tax rate than all other classes or types of property. At the same time, § 56 adheres to or at least supports the principle of proportionality with respect to all such other property types by treating commercial real property, industrial real property, and personal property — the CIP classes — in the exact same manner.
In contrast, the taxpayers’ interpretation of art. 112 would contradict the concept of proportionality by creating a single and separate tax rate for personal property, treating it differently from all other classes of property.
The taxpayers argue that art. 112 effected a “narrow” exception to the proportionality requirement of art. 4, one limited to real property, and they suggest that, as an exception, art. 112 must itself be construed narrowly. Their argument might have more force if it were directed at the language of a statute rather than a constitutional amendment; we have certainly stated that “[e]x-ceptions to statutory provisions are construed narrowly.” See
LeClair
v.
Norwell,
430 Mass. 328, 336 (1999). Cf.
New England Forestry Found., Inc.
v.
Assessors of Hawley,
468 Mass. 138, 148 (2014) (“Exemption statutes [here, property tax exemption stat
ute] are strictly construed . . . ”)• But a constitutional amendment “is a statement of general principles and not a specification of details.... It is to be interpreted as the Constitution of a State and not as a statute or an ordinary piece of legislation. Its words must be given a construction adapted to carry into effect its purpose.”
McDuffy
v.
Secretary of the Executive Office of Educ.,
415 Mass. 545, 559 (1993), quoting Cohen, 357 Mass. at 571. In the case of art. 112, its purpose of enabling cities and towns to tax residential property at an effective rate different from and lower than other property is clear, and because art. 112 is a constitutional amendment, we do not interpret it narrowly, despite its inclusion of the phrase, “except that.” The Legislature understood from the outset — as shown by the fact that it enacted contingent legislation to implement art. 112 before the amendment had even been ratified by the voters, see
Associated Indus.,
378 Mass. at 659, 662-663 — that art. 112 did indeed state “general principles” that would require fleshing out in implementing statutes. Section 56 is such a statute. It effectuates the overarching objective of art. 112, and does so in a manner that retains proportionality to a large extent by treating nonexempt personal property — which, as in this case, is used for business purposes
— the same as commercial and industrial real property.
We conclude that the board’s decision rejecting the taxpayers’ challenge to the constitutionality of § 56 and upholding the assessors’ denial of the requested tax abatements was correct.
3.
Conclusion.
The decision of the Appellate Tax Board is affirmed.
So ordered.