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Property Description and Appraisal Math
Chapter 7: Property Description and Appraisal Math
This chapter delves into the critical aspects of property description and the mathematical principles underpinning accurate property valuation. It connects directly to the course description by providing the necessary tools for mastering both the cost and sales comparison approaches, enabling appraisers to confidently estimate depreciation, reproduction costs, replacement costs, and perform effective market analysis with comparable sales data.
I. Precise Property Description: The Foundation of Valuation
A cornerstone of sound appraisal practice is the ability to accurately and unambiguously describe the property under consideration. This section outlines the scientific principles behind legal descriptions, ensuring that the property being valued is uniquely identified.
A. Legal Descriptions: Defining the Parcel
A legal description is a precise identification of a property’s boundaries, distinguishing it from all other properties. Unlike street addresses, which are for convenience, legal descriptions are essential for legal and valuation purposes. The book describes three primary methods: Metes and Bounds, Rectangular Survey System, and Lot, Block, and Tract system.
- Metes and Bounds: The oldest and often most complex method.
- Principle: Defines property by sequential measurements and directions from a known Point of Beginning (POB). relies on both artificial markers (stakes) and natural monuments (rivers, trees).
- Scientific Basis: Plane geometry and trigonometry. Bearings (angles) and distances are used to trace the property’s perimeter.
- Mathematical Representation: Each boundary line is described by a bearing (e.g., North 45 degrees East) and a distance (e.g., 100 feet).
- Practical Application: Useful for irregular parcels where rectangular systems are unsuitable. Surveyors use transits and GPS to determine bearings and distances. GPS now allows high precision.
- Experiment: Simulate surveying a simple rectangular lot using a compass, measuring tape, and protractor. Calculate the area using plane geometry (Area = Length x Width) and compare it to the dimensions on a deed. Account for errors in your measurements.
- Rectangular Survey System (Government Survey System): A systematic grid based on principal meridians and base lines.
- Principle: Divides land into townships (6 miles x 6 miles) and sections (1 mile x 1 mile). Each section contains 640 acres.
- Scientific Basis: Geodesy (study of the Earth’s shape and dimensions). Accounts for the Earth’s curvature and convergence of meridians using correction lines.
- Mathematical Representation: Land is described by its location within the grid (e.g., “NW 1/4 of Section 10, Township 2 South, Range 3 East”). Calculate area based on fractions of sections. (e.g. SW1/4 of NW1/4 of SE1/4 = 40 acres)
- Practical Application: Dominant in much of the US. Simplifies land description, particularly for large areas.
- Experiment: Map a fictional township on graph paper, dividing it into sections. Calculate the acreage of various fractional sections.
- Lot, Block, and Tract System (Recorded Plat System): Relies on recorded subdivision plats.
- Principle: Land is described by lot number, block number, and the recorded plat map.
- Scientific Basis: Cartography (map-making) and surveying. ensure❓s consistent boundary descriptions through official recordation.
- Mathematical Representation: The plat map depicts all property boundaries with specified measurements.
- Practical Application: Common in urban and suburban areas where subdivisions are developed.
- Experiment: Obtain a plat map of a local subdivision. Identify a specific lot and describe its boundaries using the plat map information.
Accuracy: Modern techniques, including lasers and GPS-enabled survey equipment, have improved accuracy. Survey markers are now often set in concrete, and serve as permanent reference points.
II. Appraisal Mathematics: Quantifying Value
This section explores the mathematical tools that appraisers utilize to derive value indications.
A. Area and Volume Calculations
Accurate area and volume calculations are fundamental to both the cost and sales comparison approaches, as differences in size are a common adjustment factor. This connects directly to the course objective of enhancing valuation expertise through data collection, adjustment processes, and reconciliation of values.
- Area of a Rectangle: A = L x W (Area = Length x Width)
- Practical Application: Calculating the area of a house footprint, lot size, or a specific room.
- Experiment: Measure a room’s length and width in both feet and meters. Calculate area in square feet and square meters. Convert between the two units and compare the results. Understand propagation of error when measurements are not precise.
- Area of a Triangle: A = 0.5 x B x H (Area = 0.5 x Base x Height)
- Practical Application: Calculating the area of an irregularly shaped lot or a gable end.
- Experiment: Draw an irregular lot shape and subdivide it into rectangles and triangles. Measure the necessary dimensions and calculate the total area. Use CAD software to get a more precise area and check your calculations.
- Units and Conversions: Ensure consistent units of measurement. 1 acre = 43,560 sq ft; 1 sq yd = 9 sq ft.
- Volume of a rectangular prism (room): V = L x W x H (Volume = Length x Width x Height)
- Practical Application: Calculating the volume of a room to estimate heating/cooling requirements.
B. Percentages and Ratios:
These are essential for market analysis and adjustment procedures in the sales comparison approach.
- Percentage Calculation: Part = Percentage x Whole.
- Practical Application: Determining the percentage of the lot covered by a building, or the percentage increase in sales price over time.
- Ratio Calculation: A/B = C/D
- Practical Application: Market segmentation and analysis - if one property has a different ratio of sales price to square footage than others, it may be an outlier and should be analyzed.
C. direct capitalization❓❓ (Income Approach):
This fundamental technique for value based on projected income stream is introduced, preparing the student for the Income Approach covered later.
- Formula: V = I / R (Value = Net Operating Income / Capitalization Rate)
- Scientific Basis: The principle of anticipation, where value is based on the expected future benefits (income) discounted to their present worth. This assumes a stable income stream.
- Practical Application: Estimating the value of income-producing properties like rental houses. Determining market rates and multipliers from comparable sales is critical.
D. Financial Calculations: Time Value of Money:
Appraisers must be proficient in these. In the cost approach❓❓ they are used to deal with the value of future income and expenses, as discussed in the book, and can also be used when calculating adjustments.
- Present Value (PV) and Future Value (FV): Understand the relationship: FV = PV * (1 + i)^n, where i is the interest rate and n is the number of periods.
- Scientific Basis: Compound interest and discounting. Value depends on when the money is received.
- Practical Application: Calculating the present value of deferred payments.
E. Measures of Central Tendency and Dispersion:
This information is critical to understanding how an appraiser selects good comparables.
- Mean, Median, Mode, and Range: Calculate and interpret these measures from a set of comparable sales prices or rental rates.
- Scientific Basis: Descriptive statistics. Understanding data distribution and identifying outliers.
- Practical Application: Determining the typical market price or rent.
- Standard Deviation: Helps quantify the dispersion of data. Large deviations reduce confidence in average prices or multipliers.
III. Practical Applications and Experiments
The principles and theories discussed above must be applied.
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Legal Description Exercise: Provide students with legal descriptions using all three methods. Have them sketch the property on graph paper and calculate the approximate area.
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Comparable Sales Adjustment: Provide a detailed case study of a subject property and several comparable sales. Have students make adjustments for differences in size, location, features, and time of sale. Quantify the adjustments using market data and sensitivity analysis.
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Financial Calculator Simulation: Use a financial calculator (physical or online) to solve present value, future value, and amortization problems related to investment property. Experiment with different interest rates and time periods to understand their impact on value.
Scientific Theories and Principles
Throughout this chapter, several overarching scientific theories and principles are applied. These include:
- Systems Theory: The valuation process involves the interaction of interconnected factors (physical, economic, legal) and requires a holistic understanding.
- Information Theory: Accurate and reliable data are essential for reducing uncertainty in value estimations.
- Statistics: Descriptive statistics and regression analysis are employed to interpret market trends, analyze comparable sales data, and quantify adjustments.
- Economics: Supply and demand determine market dynamics and influence property values. Time value of money concepts are applied to discount future benefits.
By combining property description skills with these essential mathematical tools, appraisers can confidently approach the cost and sales comparison approaches to property valuation, providing reliable and data-driven opinions of value. The inclusion of practical examples and experiments will allow you, as an appraiser, to hone the necessary skill set.
Chapter Summary
Scientific Summary: property❓ Description and Appraisal Math
This chapter, “Property Description and Appraisal Math,” from the course “Mastering Property Valuation: Cost & Sales Comparison Approaches,” provides essential foundational knowledge for accurate property valuation. The chapter covers the legal descriptions of properties and the mathematical skills necessary to apply appraisal methodologies, particularly the cost and sales comparison approaches emphasized in the course description.
Key Scientific Points:
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Legal Property Descriptions: The chapter details three main systems for legally describing property:
- Metes and Bounds: A boundary-based system using reference points, courses, and distances. While crucial for older properties and irregular parcels, the chapter acknowledges its complexity and potential for error.
- Rectangular (U.S. Government) Survey System: A grid-based system referencing principal meridians, base lines, townships, and sections. This approach enables precise parcel identification across vast areas.
- Lot, Block, and Tract System: A reference to official maps that are maintained by the county, showing boundaries of subdivisions and individual lots. This is the simplest method of describing property that is in a platted subdivision.
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Essential Appraisal Mathematics: The chapter emphasizes proficiency in basic geometric calculations (area, volume) and their application to real property. Formulas are provided for calculating the area of rectangles and triangles, addressing unit conversions, and determining volumes of rectangular solids. These principles directly support the cost approach’s estimation of building costs and the sales comparison approach’s analysis of property size.
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Financial and Capitalization Concepts: The chapter introduces fundamental financial mathematics, including percentages, interest❓ calculations, and direct capitalization❓ (I=R*V). Understanding these concepts is essential for implementing the income approach and for adjusting comparable sales for differing financing terms, both critical topics in the broader course. The text also references more advanced financial concepts, for example, present/future value discounting, as well as the “Hoskold” and “Inwood” methods. While not the main focus, these are touched upon to lay the groundwork for later learning.
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Measures of Central Tendency: The chapter includes measures of central tendency (mean, median, mode, range, and standard deviation). Understanding statistics helps appraisers analyze market data and identify relevant information in order to refine their value estimates.
Conclusions and Implications:
- Foundation for Appraisal Techniques: Mastery of property description and appraisal math is fundamental to understanding and correctly applying the cost and sales comparison approaches. This skill set underpins accurate data collection, adjustment processes, and, ultimately, defensible property valuation, as highlighted in the course description.
- Accuracy and Reliability: Correct application of geometric and financial calculations improves the accuracy and reliability of value indicators derived from the cost, sales comparison, and income approaches. Errors in these calculations can lead to significant discrepancies in value estimates.
- Compliance and Reporting: Accurate property descriptions are essential for meeting legal and regulatory requirements (e.g., USPAP compliance) and for creating clear and understandable appraisal reports.
- Effective Analysis: Understanding mathematical concepts and descriptive methods facilitates effective analysis of market trends, property characteristics, and comparable sales data, enabling appraisers to make informed judgments in the reconciliation process.
Relation to Course Description:
This chapter is highly relevant to the course description’s emphasis on the cost and sales comparison approaches. It provides the necessary mathematical toolkit for:
- Cost Approach: Calculating reproduction/replacement costs, estimating depreciation, and determining site value separately, as required by the cost approach.
- Sales Comparison Approach: Making adjustments to comparable sales prices based on quantitative factors (e.g., lot size) and financial terms, ensuring an accurate reflection of the subject property’s value relative to market data.
