FAQs FAQs The Appraisal Institute has compiled a list of commonly asked questions about appraisers and appraisal: Q: What is an appraisal (real estate)? A: It is the process of valuation real property, usually to find market value. Q: What are appraisers? A: People who identify and provide values for real property, which can include real property, personal property, machinery and equipment, business valuation, and even appraisal review. Q: What is defined as real property? A: Real property is any property that is attached to the land, as well as the land itself. It not only includes buildings and improvements, but also rights and interests. It can be fee simple or leased fee. Q: Why would I need an appraisal? A: There are many needs for appraisals such as for litigation, managing planning, estate tax, and more. Please visit our Purpose & Use section of the website for more examples.

Plain Language Dictionary Mark Pomykacz, MAI, has compiled a plain language dictionary of appraisal terms that are commonly misunderstood. While technical and legal definitions abound in the real estate industry, there remains a gap between the highly technical expert’s understanding and the beginner’s understanding. The purpose of this dictionary is to bridge that gap, help prevent costly mistakes and to improve market performance. Mr. Pomykacz provides plain language definitions for these commonly misunderstood terms, along with real world examples and practical advice. Readers of this page are encouraged to also read the common fallacies and mistakes pages. Dictionary Table of Contents Allocation The division of an overall appraised value or sale price of a business or property among the various component assets of that business or property. Commonly, allocations are performed for taxing purposes: property taxes (allocated between land and building), transfer taxes (real property, personal property, and exempt property), and income taxes (real property of various classes, personal property of various classes, and intangibles of various classes). Allocations are also made for SEC/investor reporting, along real, personal, and intangible classifications. Debt, equity value, and other allocations are also made. See purchase price allocation and cost segregation studies. Appraisal An opinion of value, sometimes written, sometimes oral. Government agencies and banks often provide detailed definitions of appraisal that sometimes are not consistent with each other. For example, some allow appraisals to be written by unlicensed appraisers. While others require licensed and MAI designated appraisers. You get what you pay for. Appraisals cost thousands of dollars, sometimes tens of thousands of dollars, but given the value of the assets under appraisal, and given the costs associated with damage control should the asset prove to be non-performing or the appraisal prove to be noncompliant, appraisals should be viewed as at least an insurance policy. At best, appraisals should be viewed as an integral part of or essential complement to a company’s own due diligence process. Therefore, even though many brokers and accountants provide valuation opinions at low to no cost, the most prudent course of action is to obtain the services of the seasoned appraisal professional. Order a USPAP compliance report, whether it is required or not. Appraisal Report There are three narrative appraisal report formats; complete (full) narratives, summary narratives, and limited narratives, as defined by USPAP. Also, there are two types of appraisal scope of services: complete (full) analysis appraisals and restricted analysis appraisals, according to USPAP. See our USPAP pages. Even if a consultant reported that you need not comply with the USPAP requirements for an appraisal report, compliance is strongly recommended. Approaches to Value AKA: the Three Approaches to Value. See the individual sales, cost, and income approaches below. For income producing properties and businesses, when reliable income data is available, the income approach rules, and the other approaches play supporting roles. Assessed Value Established by the assessor, assessed value is often the statutorily established percentage of market value. One must apply the assessed value to market value ratio to the assessed value to determine the assessor’s opinion of market value. Many novices mistakenly believe that they are under assessed, because they confuse assessed value with market value. Band of Investment Analysis A Band of Investment Analysis is a weighted average of the elemental yield rates or of the elemental capitalization rates of investment, i.e., equity investment rates and debt investment rates. The mortgage equity and investment analysis is one of the most common analyses used to determine overall property capitalization rates. Book Value Book value is an accounting defined and derived value and need not have any relationship to market value. Market value is defined and derived by appraisers. Most often, book value does not equal market value. For some accounting purposes book value is needed. When market value is needed, do not use book value. Broker’s Opinion of Value or Broker Price Opinion (BPO) Not an appraisal. Remember that you get what you pay for. Business Appraisal The process of finding the economic value of an owner’s interest in a certain business. It is the appraisal of the combination of assets, real property, personal property, and business intangibles that make up a going concern or enterprise. Common Area Maintenance (CAM) The definitions of CAM vary widely. So be sure to obtain a through definition before you sign a lease. Also, regularly check your landlord’s calculations of CAM for under or overestimates. See our lease audit services. Capitalization The conversion of income into value. Capitalization Rate A rate, commonly a percentage between 7 percent and 12 percent, used to convert an estimation of next year’s net operating income into estimation of value. There are numerous ways to determine capitalization, including various mathematical formulas and market surveys. The higher the risk in a property, the higher the cap rate and the lower the value. Sometimes equivalent to the yield rate minus the inflation rate on the value and income. Great care must be exercised when determining capitalization rates so as not to confuse the capitalization rates with the various but not equivalent yield rates and other rates employed within the income approach to value, and to ensure that the proper kind of capitalization rate is matched with its proper income type. Cash Flow The periodic income, usually annual income, expected from an interest in real estate or a business. Also see “Income”. Consulting, Process-Oriented Consulting on issues or projects where there is no obvious or well-defined deliverable or timetable when the engagement is commenced. Consulting, Task-Oriented Consulting on issues or projects where a traditional, well-defined deliverable or timetable is targeted from the beginning of the engagement. Cost Approach One of the primary three approaches to value, the cost approach is an analysis of the cost to build a replacement property. A cost approach should consider part in soft costs, physical, functional, and external obsolescence, the cost to acquire the interests in the land, and entrepreneurial profit. Depreciation Most people understand physical depreciation, the loss in value due to aging and physical deterioration. As real estate and other assets age they often lose value. Proper appraisals not only reflect physical depreciation, but also functional and external (economic) obsolescence. Functional obsolescence (or super adequacy) is the loss in value (value measured as the cost to build) due to bad design. For example, multi-story warehouses suffer functional obsolescence, because today users prefer one story warehouses. External obsolescence refers to conditions occurring off site, that negatively value. For example, many power plants suffered external obsolescence immediately following deregulation, because their new lower or riskier income under deregulation no longer supports their cost of construction. Direct Capitalization Direct capitalization converts next year’s estimated net operating income into a value. While the math is simple to calculate, because of the limited number of inputs into the model, this approach can be less accurate than the DCF, especially when future income and values vary significantly from year to year. Discounted Cash Flow Analysis (DCF) A discounted cash flow analysis uses the mathematics of compounding and discounting to convert the cash flow expected from an investment in real estate or business into an estimation of market value. The cash flow is discounted using a yield rate, which is analogous to the internal rate or return. While difficult to construct and analyze (given the relatively large number of inputs), the approach is preferred for its accuracy. Furthermore, the technique is necessary when future income and value will vary significantly from year to year. Discount Rate The rate used to discount a cash flow in a DCF. AKA yield rate. Commonly between 8 and 15 percent for common real estate types. The higher the risk in a property, the higher the discount rate, and the lower the value. Sometimes equivalent to the capitalization rate plus the inflation rate on the value and income. External Obsolescence See Depreciation Functional Obsolescence See Depreciation Good Will An intangible business asset, such as company or product name, franchise or reputation, or a customer list that generate value above the value of the hard (real, machinery and equipment, and personal) assets and the soft (intangibles, such as contracts) assets. It’s often measured as the difference between the sum of the values of all other assets and the sale price. Gross Lease Sometimes the landlord pays the operating expenses, common area maintenance, utilities, real estate taxes, insurance, advertising, and capital repairs. Sometimes the landlord pays only some of these expenses. Sometimes the tenant pays all or nearly all of these expenses. A gross lease is one where the landlord pays the expense(s). A net lease is one where the tenant pays the expense(s). A “triple net” lease is not officially defined but is generally meant to describe a lease where the tenant pays operating expenses, utilities and taxes; however, because operating expenses is not a universally defined term and other expenses may also be included or excluded, the term, “triple net” lease, is the cause of common, and costly confusion. When renting or analyzing a lease, be sure to obtain and understand the lease’s definition of gross, net, and triple net, and do not assume your definition is the same as the landlord’s. See our lease auditing services pages for details on the related services available to our clients. Highest and Best Use That use which is typical, legal, physically practical, and yields the highest value and return. Assuming the highest and best use is critical to a market value appraisal. Assuming a particular investor’s/buyer’s use, when that use is not the typical, will result in an investment value or value in use that is different from market value. Income There are dozens of types of income and cash flow, including potential or effective gross income, net operating income before or after capital expenditures, cash flow before and after debt or taxes. They sometimes have acronyms, such as NOI, Io, EBIT, EBITDA, Im, Ie. Each is used for different purposes and are not interchangeable. Consequently, appraisers take great care to ensure they’ve calculated the right income for their analysis. Income Approach The appraisal methodology that forecasts future income and converts it into a value. There are two major types of Income Analysis: Direct Capitalization and Yield Capitalization (AKA Discounted Cash Flow). Net Lease Sometimes the landlord pays the operating expenses, common area maintenance, utilities, real estate taxes, insurance, advertising, and capital repairs. Sometimes the landlord pays only some of these expenses. Sometimes the tenant pays all or nearly all of these expenses. A gross lease is one where the landlord pays the expense(s). A net lease is one where the tenant pays the expense(s). A “triple net” lease is not officially defined but is generally meant to describe a lease where the tenant pays operating expenses, utilities, and taxes; however, because operating expenses is not a universally defined term and other expenses may also be included or excluded, the term, “triple net” lease, is the cause of common, and costly confusion. When renting or analyzing a lease, be sure to obtain and understand the lease’s definition of gross, net, and triple net, and do not assume your definition is the same as the landlord’s. See our lease auditing services pages for details on the related services available to our clients. Real Property Real property includes not only buildings but also any improvements as well as the land itself. It also includes the rights or interests to the property. Sales Comparison Approach One of three appraisal methodologies which compare a subject property’s characteristics to similar properties that were recently sold called comparables. Consideration (adjustments) is made for the differences in characteristics between the subject and these comparable properties. The adjusted indications of value are reconciled to come up with a final conclusion. Triple Net Lease Sometimes the landlord pays the operating expenses, common area maintenance, utilities, real estate taxes, insurance, advertising, and capital repairs. Sometimes the landlord pays only some of these expenses. Sometimes the tenant pays all or nearly all of these expenses. A gross lease is one where the landlord pays the expense(s). A net lease is one where the tenant pays the expense(s). A “triple net” lease is not officially defined but is generally meant to describe a lease where the tenant pays operating expenses, utilities, and taxes; however, because operating expenses is not a universally defined term and other expenses may also be included or excluded, the term, “triple net” lease, is the cause of common, and costly confusion. When renting or analyzing a lease, be sure to obtain and understand the lease’s definition of gross, net, and triple net, and do not assume your definition is the same as the landlord’s. See our lease auditing services pages for details on the related services available to our clients. Zero Cash Flow Net Leases (AKA: Net Zero Leases or Zeros) are an estate planning and investment strategy tool and are often used in conjunction with 1031 and 1033 exchanges. The strategy is to accept low annual equity cash flows in exchange for lower investment risk, a minimal down payment, higher tax write-offs, and a high reversionary/residual equity value. The estate acquires a property, with a low down payment (often less than 20%). Sometimes the investor pays with cash proceeds from a 1031 exchange, but then refinances thereby extracting equity without severe tax consequences. The acquired property has a lease with a high credit-rated tenant that calls for lease payments that merely cover the debt service. Thus, the net cash flow to the equity interest during the term of the lease is at or near zero. During the lease, the investor enjoys high tax write-offs for depreciation and the interest expense. The debt is paid off during the term of the lease, so the equity interest in the reversion (residual value after the lease expires) is high.

Business Improvement Ideas How to Improve Your Business by Managing Your Real Estate and Using Appraisal and Appraisal Consulting Services. Real estate represents one of the largest capital outlays for businesses. Even leased real estate, where rental payments exceed the market value of the fee simple real estate after seven to ten years, amounts to one of the largest operating expenses for businesses. Yet few businesses have professional staff dedicated to the management of their real estate. Consequently, all too often real estate assets are not maximizing their potential yield for their businesses. Not only does this impact corporate income and returns to shareholders, but it also consumes excessive capital, distracts staff from the business core focus, and it often negatively impacts business flexibility due to the lack of proper real estate for their core business operation. Federal Appraisal & Consulting LLC is dedicated to helping its clients maximize their profits and returns, which is more critical than ever in this ever-changing, fast paced, competitive business environment. Here are several actions that businesses can take to maximize their real estate investment yields and values. 1. Strategic Planning Develop and maintain a place for real estate in the company strategic plan. By integrating real estate into its strategic planning, companies can transform their real estate (owned or leased) from an isolated cost center into a strategic asset. Among other benefits, a strategic plan that includes real estate will help companies use space more efficiently, achieve greater flexibility in space utilization and core business operations, and reduce operating costs. While the strategic planning should be coordinated by a senior real estate professional, such as an MAI designated appraiser, overall, this is a team effort. Much of the support for strategic planning must come from numerous sources, including appraisers, consultants, accountants, attorneys, engineers, brokers, and property managers. Federal Appraisal & Consulting LLC provides numerous appraisal and consulting services to large corporations and small businesses, individuals, and their managers and fiduciaries for the purpose of real estate strategic planning. We also offer various issues solutions and management solutions that assist in the strategic planning for real estate. Follow the links above for more information. 2. Surplus Real Estate Eliminate surplus real estate. Surplus assets include un-utilized and under-utilized real estate and can be owned or leased or can even include real estate that does not maximize market share, distribution, or corporate goals. Largely overlooked in large corporations, often small companies fail to address this issue for lack of work force and other priorities. Once identified, a holding/disposition program should be implemented. The program should reflect the goals of the company strategic plan. The program will resolve the surplus through sales, leasing, gifting, conversion/development/restructuring to new uses and to other alternatives as discussed herein. The surplus real estate elimination program should be a team effort, and includes appraisers to identify surplus and set acceptable prices and yields. Federal Appraisal & Consulting LLC provides numerous appraisal and consulting services to large corporations and small businesses, individuals, and their managers and fiduciaries for the purpose of eliminating surplus real estate. We also offer various issues solutions and management solutions that assist in the strategic planning for real estate. 3. Alternatives to Simple Ownership and Simple Leases Employ special financing and transfer structures, such as sale-leasebacks or other structured lease transactions, 1031 exchanges, barter transfers, and securitization (monetization). Such structures help businesses move real estate assets off their books, cut costs and raise capital for new investment or other purposes. Federal Appraisal & Consulting LLC provides numerous appraisal and consulting services to attorneys and accountants for purposes such as deal and financial structuring. See our Accountants and our Attorneys pages. 4. Cost Reduction Strategies & Tactics 1. Review real estate operations, management, and administration. Analyze basic costs, such as contract services, staffing, janitorial, utilities, security, general maintenance, parking, electromechanical and plumbing, elevators and escalators, and preventive maintenance. Employ benchmarking and best practice studies to analyze the performance of a company real estate against its competitors. Review a company’s organization and management structure as it relates to its real estate operations. Federal Appraisal & Consulting LLC provides customized research and consulting services. See our issues solutions and management solutions and research services pages. 2. Conduct Lease Audits. Lease audits examine landlords pass through rents and expenses, such as operating expenses, CAM, real estate taxes, utilities, and insurance, and help companies identify errors and recover overcharges. Audit/analyze all major leases prior to execution and then every several years or as required by the lease. Lease audits should be conducted by an appraiser experienced with accounting records or accountant familiar with lease analysis. Lease analyses, because they are forward looking, should be conducted by appraisers. Federal Appraisal & Consulting LLC provides lease audit and analysis services. See our Lease Audit and Analysis page. 3. Actively manage property taxes. Such management ensures that companies pay no more than their fair share of real and personal property taxes. This should include an annual review of all real estate assets with market values over $3,000,000. Even leased real estate should be reviewed annually, since most leases give tenants rights to appeal assessments. The review should be conducted by an appraiser or a professional with real estate valuation and property tax experience. Federal Appraisal & Consulting LLC provides complete property tax management and appeals services. See our Property Tax and Property Tax Management pages. 4. Segregate costs. Cost segregation improve the depreciation of various elements of a real estate asset and can dramatically increase after-tax cash flows. Conduct a cost segregation study immediately after completing construction or after acquisition. The study should be written by an appraiser or engineer with accounting experience. Federal Appraisal & Consulting LLC provides complete segregation services. See our Cost Segregation page. 5. Manage income taxes. Actively seek out real estate tax savings ideas. We have listed many ideas in this article, but many others exist. Management should maintain relationships with accountants, attorneys, and other real estate professionals, such as appraisers, for the purpose of seeking tax saving ideas for their real estate. See our Tax Savings page for more information on this topic. 6. Maintain vigilance concerning environmental issues, legal issues, and development and use rights issues. Such issues require management activities off-site, often where and with whom managers are not accustomed to operating; however, proper vigilance can avoid non-compliance issues, damage to title and to marketability, and can ensure a proper holding/disposition strategy. Management should maintain relationships with various types or real estate professionals, in particular appraisers and brokers, for the purpose of maintaining information about the market that their real estate is in. This service is most likely to be provided by local professionas: appraisers, brokers, property managers, or attorneys. Federal Appraisal & Consulting LLC provides customized research and consulting services. See our issues solutions and management solutions and research services pages.

High Value Assets The Variable Tax Rate Phenomenon In Tax-Adjusted Cap Rate Formulas By Mark Pomykacz Prepared: Wednesday, July 30, 2003 Introduction It is now widely acknowledged that capitalization rates can and should be adjusted for the property tax rate, while the net income should be calculated without the property tax expense, in order to accurately estimate the market value of income producing properties for property tax assessment purposes; however, the standard property tax adjusting methods assume that the property tax rate is invariable. In fact, for high-value assets, those that represent a substantial portion of the taxing jurisdiction’s taxable base, the property tax rate is dependent on the market and assessed values of the high-value asset. Applying the standard property tax adjusting methods to high-value assets will result in over-estimated market and assessed values, but under-estimated tax rates, and municipal budget short falls [1]. This article explains this phenomenon and presents a formulaic solution that greatly improves appraisal accuracy and budgeting. The formula is easy to use and cost effective. Additionally, this article presents practical steps for employing the analysis. It is expected that the formulas and processes presented herein will be widely used in the planning, negotiation, litigation, and settlement of property tax disputes for high-value properties to the benefit of both the taxpayer and the taxing jurisdiction. The taxing jurisdiction will benefit from the avoidance of previously unexpected changes to the tax rate, allowing more accurate budget planning. Furthermore, it will permit the full capture of the taxable base. For the taxpayer, it will provide sound appraisal rationale for relief from under-estimated tax rates, which result in over-estimated assessments and over taxation. The Variable Tax Rate Phenomenon To understand why tax rates are variable and dependent in the assessment analysis process, analysts must recognize that 1) tax rates are based on assessed values, but 2) for income-generating properties, assessed values are based, in part, on tax rates. Table I Basic Tax Rate and Value Formulas [2] Tax Rate = Budget ¸ Sum of all Assessed Values in the Taxing Jurisdiction ( T = B ¸ Sall ) Assessed Value of Subject High-Value Asset = Income before Property Taxes ¸ (Capitalization Rate + Tax Rate) ( As = I ¸ (C + T) ) When the assessed value of one high-value asset is wrong, then the sum of all assessed values and the tax rate are computed wrong. When the tax rate is wrong, then the assessed value of the highvalue, income-producing assets are computed wrong. Only when both the assessed values of all high-value assets and the tax rate are correct will the assessment process work properly. Each depends on the other. This is a circular analysis, or co-dependent analysis. The assessment process often proceeds as presented in Table II, for income-generating properties. Table II Example of Assessment Process  Column/Iteration 121High-Value Asset’s Income Before TaxesI$7,500,000$3,750,0002Capitalization RateC10%10%3Assume Tax RateT12.5%12.5%4Tax Adjusted Cap Rate $60,000,000$30,000,0005Assumed Assessed Value of High-Value AssetAs$60,000,000$30,000,0006Assessed Value of High-Value AssetAs$60,000,000$30,000,0007Assessed Value of All Other AssetsS$140,000,000$140,000,0008Sum of All Assessed ValuesSall$200,000,000$170,000,000 Cross Checks   8BudgetB$5,000,000$5,000,0009Indicated Tax Rate for BudgetB2.5%2.941176%10Assumed Tax RateT2.5%2.5%11Consistency YesNo12Sum of All Assessed ValuesSall$200,000,000$170,000,00013Assumed Tax RateT2.5%2.5%14Jurisdiction RevenuesB$5,000,000$4,250,0015BudgetB$5,000,000$5,000,00016Balanced Budget YesNo17Indicated Tax rate for BudgetT2.5%2.41176%18Taxes on high-Value Asset 1,500,000882,35319Income After TaxesI$6,000,000$2,867,64720Capitalization RateC10%10%21Indicated Value of High-Value AssetAs$60,000,000$28,676,47122Assumed Assessment of High-Value AssetAs$60,000,000$30,000,00023Consistency YesNo If the budget is $5 million and the sum of all assessed values is correct, at $200 million, then the tax rate is correct at 2.5 percent (See Line 11, Column 1, Table II). If the assessed value of the high-value assets are estimated based on the 2.5 percent tax rate, then all elements of the assessment process are consistent (See Lines 11, 16 and 23, Column 1, Table II). If the value of one high-value asset should need a substantial correction, then the sum of the assessed values for the jurisdiction would be substantially impacted (See Line 8, Column 2, Table II). Consequentially, the tax rate would need to be corrected in order to maintain the budget (See Lines 11, 16 and 23, Column 2, Table II). Failure to correct the tax rate will result in failure for the revenues to meet the budget, and therefore, an improper assessment on the high-value asset. The Iteration Solution The appraiser can solve this problem using an iteration process. The appraiser estimates a corrected tax rate, calculates the assessed value of the high-value asset and the sum of all assessed values, and cross checks the conclusions with the assumptions. When the conclusions and assumptions do not match, then the appraiser attempts another estimate. The example from Table II is solved using iteration, in Table III below. Table III Example of Iteration Process  Column/Iteration 1234511 High-Value Asset’s Income Before TaxesI$ 7,500,000$3,750,000$ 3,750,000$ 3,750,000 2Capitalization RateC10.000000%10.000000%10.000000%10.000000% 3Assumed Tax RateT2.500000%2.500000%2.958978%2.959702% 4Tax Adjusted Cap Rate 12.500000%12.500000%12.958978%12.959702% 5Assumed Assessed Value of High-Value Asset As$ 60,000,000$ 30,000,000$ 28,937,468$ 28,935,850 6Assessed Value of High-Value AssetAs$ 60,000,000$ 60,000,000$ 28,937,468$ 28,935,850 7Assessed Values of All Other AssetsS$ 140,000,000$ 140,000,000$ 140,000,000$ 140,000,000 8Sum of All Assessed ValuesSall$200,000,000$ 170,000,000$ 168,937,468$ 168,935,850  Cross Checks      8BudgetB$ 5,000,000$ 5,000,000$ 5,000,000$ 5,000,000 9Indicated Tax Rate for BudgetB2.500000%2.941176%2.959675%2.959703% 10Assumed Tax RateT2.500000%2.500000%2.958978%2.959702% 11Consistency YesNoNoNo 12Sum of All Assessed ValueSall$ 200,000,000$ 170,000,000$ 168,937,468$ 168,935,850 13Assumed Tax RateT2.500000%2.500000%2.958978%2.959702% 14Jurisdiction RevenuesB$ 5,000,000$ 4,250,000$ 4,998,822$ 4,999,998 15BudgetB$ 5,000,000$ 5,000,000$ 5,000,000$ 5,000,000 16Balanced Budget YesYesNoNo 17Indicated Tax Rate for BudgetT2.500000%2.941176%2.959675%2.959703% 18Taxes on High Value Asset 1,500,000882,353856,455856,415 19Income After TaxesI$ 6,000,000$ 2,867,647$ 2,893,545$ 2,893,585 20Capitalization RateC10.000000%10.000000%10.000000%10.000000% 21Indicated Value of High-Value AssetAs$ 60,000,000$ 28,676,471$ 28,935,450$ 28,935,847 22Assumed Assessed Value of High-Value AssetAs$ 60,000,000$ 30,000,000$ 28,937,468$ 28,935,850 23Consistency YesNoNoNo  The Algebraic Solution [3] The iteration technique, while intuitive, is cumbersome. As an alternative, the appraiser may wish to employ “Value/Tax Rate Algebraic Solution”. The algebraic proof follows. Table IV Algebraic Proof Definitions Property Tax Rate = T Taxing Jurisdiction Budget = B Subject Property Net Operating Income before Property Taxes = I Subject Property Capitalization Rate = C Subject Property Assessed Value = As Sum of all Other Assessed Values = S Known Relationships Tax Rate, Budget, Assessment Base Formula T = B ¸ ( As + S ) Income Capitalization, using a Property Tax-Weighted Capitalization Rate As = I ¸ ( C + T ) Given Data Supplied by Taxing Jurisdiction: B and S Estimated by Appraiser: I and C Derivation [4] T = B ¸ ( As + S ) Substitute I ¸ ( C + T ) for As T = B ¸ [{ I ¸ ( C + T )} + S ] Transform using Algebra T = B ¸ [{ I + S ( C + T )} ¸ ( C + T )] T = { B ( C + T )} ¸ ( I + S C + S T ) T ( I + S C + S T ) = B ( C + T ) T I + T S C + S T2 = B C + B T T I + T S C + S T2 – B C – B T = 0 S T2 + T I + T S C – B T – B C = 0 S T2 + T ( I + S C – B ) – B C = 0 Use the quadratic formula to solve for T T = [ B – I – S C + {( I + S C – B )2 + 4 S B C}½ ] ¸ 2 S The Value/Tax Rate Algebraic Solution T = [ B – I – S C + {( I + S C – B )2 + 4 S B C}½ ] ¸ 2 S Cross Check Use data from Column 2, Table II; T = [ B – I – S C + {( I + S C – B )2 + 4 S B C}½ ] ¸ 2 S T = [ 5,000,000 – 3,750,000 – 140,000,000 x .10 + {( 3,750,000 + 140,000,000 x .10 – 5,000,000) 2 + 4 x 140,000,000 x 5,000,000 x .10}½ ] ¸ 2 x 140,000,000 T = 2.959703% Thus, As = I ¸ ( C + T ) As = 3,750,000 ¸ ( .10 + .02959703 ) As = 28,935,848 And T = B ¸ ( As + S ) T = 5,000,000 ¸ ( 28,935,779 + 140,000,000 ) T = 2.959703% Therefore, the assumed tax rate is consistent with the indicated tax rate and the Value/Tax Rate Algebraic Solution works! Practical Considerations Now that the theory and mathematics have been established, there remain only a few practical considerations before the appraisal community can widely deploy this new technique, the “Value/Tax Rate Algebraic Solution”. The appraiser must estimate the given inputs to be entered into the formula. The appraiser should continue to estimate the net operating income before property taxes and the capitalization rate as the appraiser has always done. New to the appraiser’s research and analysis work is the need to estimate the budget for the taxing jurisdiction and sum of the assessed values for all other properties in the jurisdiction. To complete this work, the appraiser will need to research and analyze the historical trends and future expectations within the taxing jurisdiction. Historical data will provide the customary basis for a projection of both the budget for the taxing jurisdiction and the sum of the assessed values for all other properties in the jurisdiction. Of course, adjustments to the historical trends may be needed to stabilize trends, to account for abnormal trends, or to account for anticipated changes to historical trends for inflation, structure change, and social and political activity. Interviews with the authorities at taxing jurisdiction and reviews of market-wide general economic and real estate industry market forecasts will be useful. This new research and analysis may not be mindlessly simple, but often the most basic forecasting techniques will suffice to greatly improve the accuracy of the assessment process. Furthermore, the difficulties with precisely forecasting budget and general assessed values are mitigated by recognizing the fact the between the tax rate and the assessed values, there must always be enough municipal revenue generated to support the budget, which often grows year after year, regardless of the health of the real estate market. Between the three - budgets, assessed values, and tax rates – value increases perennially, assuming all else remains constant. Assessed values oscillate up and down, but are generally up year by year, and tax rates make up the difference. Conclusion In conclusion, now that the theory and mathematics have been established, the appraiser can estimate assessed values and forecast budgets with a new and greater accuracy. Given the simplicity and the ease of use of the “Value/Tax Rate Algebraic Solution”, the appraisal community should have little difficulty adding this tool to its repertoire. The formulas and processes will need to be integrated into automated valuation models and mass appraisal systems. It is expected that the formulas and processes presented herein will be widely used in the planning, negotiation, litigation, and settlement of property tax disputes for high-value properties to the benefit of both the taxpayer and the taxing jurisdiction. The taxing jurisdiction will benefit from the avoidance of previously unexpected changes to the tax rate and budget, allowing more accurate budget planning. Furthermore, it will permit the full capture of the taxable base. For the taxpayer it will provide sound appraisal rationale for relief from under-estimated tax rates, which result in over-estimated assessments and over taxation. [1] Strictly speaking, the error with the standard formulas occurs on properties of all sizes, but the magnitude of the error is not material on smaller properties, unless the error occurs throughout a group of smaller properties. [2] This article assumes that the assessed value to market value ratio (AKA equalization rate) is 100 percent. Thus, assessed values equal market values, and the nominal tax rate equals the effective tax rate. The formula and processes proposed in this article work equally well with assessed value to market value ratios of other than 100 percent, but only after proper adjustments are made for the assessed value to market value ratio. For details on the proper adjustments for the assessed value to market value ratio, see “The Next Generation in Weighted Cap Rates”, (add link when ready), by Mark Pomykacz, MAI. [3] © 2003. The contents of this article, and specifically the Value/Tax Rate Algebraic Solution are copyrighted by Mark Pomykacz. All rights reserved. This article, and any part thereof, may not be used, copied, modified, or distributed by any means without the express written permission of Mark Pomykacz. Also, the use of the procedures and specifically the “Value/Tax Rate Algebraic Solution” are prohibited without the express written permission of Mark Pomykacz. [4] Special acknowledgement and thanks to Professor Xiaochun Rong, Rutgers University, New Brunswick, NJ, Math Department, for his assistance with the completion of the algebra.