Property Description and Appraisal Math

Chapter 4: Property Description and Appraisal Math

Introduction

This chapter is foundational to the course “Property Appraisal Essentials: Site, Improvements, and Sales Comparison.” Accurate property descriptions and proficient appraisal mathematics are essential for conducting thorough site analysis, assessing improvement values, and performing sales comparisons, ultimately leading to reliable property value estimations. Mastering these skills is crucial for gaining a competitive edge in the real estate market❓.

I. Property Description

• Legal Description: A precise identification of real estate is paramount. A legal description is an unambiguous and legally defensible method of defining the boundaries of a property. It’s crucial for appraisal accuracy as it defines the subject of valuation. Informal descriptions like street addresses are insufficient for legal purposes.
• Significance of Legal Description: The legal description uniquely identifies the property, ensuring that the appraisal is conducted on the correct parcel of land. It also specifies the exact property rights being appraised (e.g., fee simple, leasehold).
• Relationship to Site Analysis: The legal description is the foundation for site analysis. It provides the framework for understanding the size, shape, and location of the property, all of which influence its value.

• Common Systems of Land Description: Understanding the three major systems is vital for interpreting property deeds and legal documents:

  • Metes and Bounds System:
    • The oldest system relies on reference points (monuments, natural features) and courses and distances (bearings and lengths) to define the property’s boundaries.
    • It is typically used in older areas of the country where rectangular surveys were not implemented.
    • Point of Beginning (POB): The starting point of the description. The description then follows the boundaries until returning to the POB, completing the closed loop.
    • Mathematical Concept: The accuracy of metes and bounds descriptions relies on the principles of geometry and trigonometry. Surveys use instruments like transits and GPS to measure angles and distances with precision. Errors in measurements can lead to boundary disputes. For complex parcels, surveyors use coordinate geometry (COGO) software to analyze and verify the description.

    • Practical Application: Analyzing a deed to determine the property’s area and boundary lines. Use surveying software to plot the metes and bounds description and check for closure (ensuring the description forms a closed loop).

      • Experiment: Given a metes and bounds description, use CAD or GIS software to plot the property’s boundaries. Calculate the enclosed area. Compare the calculated area with the area stated in the legal description.
        • Rectangular (U.S. Government) Survey System:
          • Established in 1785 to provide a systematic method for describing land.
          • Divides land into a grid using principal meridians (north-south lines) and base lines (east-west lines).
          • townships❓: Six-mile square units formed by range lines (north-south) and township lines (east-west). Each township contains 36 sections.
          • Sections: One-mile square units within a township, containing 640 acres. Sections are further divided into quarter sections, quarter-quarter sections, etc.
          • Correction Lines: To account for the curvature of the Earth, the grid system is adjusted periodically using correction lines (standard parallels) and guide meridians. This creates irregularities in some sections.
          • Mathematical Concept: The system relies on planar geometry. The convergence of meridians towards the poles introduces errors that are corrected using standard parallels. Calculations of areas and distances within sections and townships use formulas based on squares and rectangles.
          • Practical Application: Interpreting a property description using the rectangular survey system. Calculating the area of a parcel described as “NW 1/4 of SE 1/4 of Section 10, Township 2 North, Range 3 East.” Determine the acreage.
      • Equation: Area = 640 acres / (Divisor of 1st fraction * Divisor of 2nd fraction…). For example: 640 / (4 * 4) = 40 acres
      • Experiment: Given a rectangular survey description, locate the property on a map or plat. Calculate the dimensions and area of the parcel.
        • Lot, Block, and Tract System:
          • Used in platted subdivisions. Land is described by reference to a recorded plat map showing individual lots and blocks.
          • The plat map provides a detailed survey of the subdivision, including dimensions, easements, and other relevant information.
          • Practical Application: Locating a property on a recorded plat map. Understanding the dimensions and easements affecting the lot.
          • Experiment: Obtain a recorded plat map for a local subdivision. Analyze the map to identify lot dimensions, easements, and other relevant information.

II. Appraisal Math: Essential Concepts and Applications

• Importance of Math: Accurate calculations are essential in all appraisal approaches (sales comparison, cost, and income). Errors in calculations can significantly affect the value opinion. The course description indicates the mastery of site, improvements, and sales is essential, and the following sections enhance the course description by discussing essential math.

• Distance, Area, and Volume:

  • Distance: Measurement in one dimension (e.g., length, width, height).

  • Area: Measurement in two dimensions (e.g., square feet, acres).

    • Area of a Rectangle: A = L * W (Length * Width)

    • Area of a Triangle: A = 0.5 * B * H (0.5 * Base * Height)

      • Right Triangle: When a triangle includes a right angle, the formula, A=0.5BH, can be easily calculated to help the appraiser.
        • Volume: Measurement in three dimensions (e.g., cubic feet, cubic yards).

    • Volume of a Rectangular Prism: V = L * W * H (Length * Width * Height)

      • Units of Area: Square feet (sq ft), square yards (sq yd), acres (ac).
    • Conversion Factors:
      • 1 acre = 43,560 sq ft
      • 1 sq yd = 9 sq ft
      • Practical Application: Calculating the living❓ area of a house, the size of a lot, or the volume of concrete needed for a foundation.

    • Example: A rectangular lot is 100 ft wide and 150 ft deep. Calculate the area in square feet and acres.

      • Area = 100 ft * 150 ft = 15,000 sq ft
      • Area in acres = 15,000 sq ft / 43,560 sq ft/acre = 0.34 acres

• Percentages:

  • Essential for calculating adjustments in the sales comparison approach, capitalization rates in the income approach, and depreciation in the cost approach.
  • Formula: Part = Percentage * Whole (P = % * W)
  • Application in Appraisal: Calculating market adjustments in the sales comparison approach. For example, if a comparable sale requires a 5% downward adjustment for inferior location, calculate the adjustment amount.

  • Example: Calculate a 5% downward adjustment from an inferior location.

    • Adjustment = % * comparable amount -> .05 * amount

• Reciprocals: A reciprocal is 1 divided by a number.

  • Formula: A/B
  • Application: Used to calculate the gross rent multiplier.

• Direct Capitalization:

  • A method of estimating value based on a property’s income.

    • Formula: Value = Net Operating Income (NOI) / Capitalization Rate (Cap Rate)

    • Cap Rate = NOI/ Value

      • Understanding the relationship between income, value, and cap rate.

    • For Example: 500,000 = $30,000/.06

• Simple Interest: Calculating interest earned on investments.

  • Formula: Interest = Principal * Rate * Time (I = P * R * T)
  • Time should be expressed in the same units as the interest rate (e.g., annual rate, annual time).
  • Practical Application: Calculating the interest expense on a mortgage, or the return on an investment property.

    • Example: Calculate the interest earned on a $10,000 investment at a 5% annual interest rate for 3 years.

      • Interest = $10,000 * 0.05 * 3 = $1,500

• Measures of Central Tendency:

  • Range: Subtract the lowest value from the highest value.
  • Standard Deviation: A statistical measure of the dispersion of a set of values around the mean. Used to assess the variability of sales prices in a market area. A smaller deviation has a higher percentage of the same prices, or very similar.
  • Mean: Average
  • Median: Exact middle of values
  • Mode: most commonly seen values.

III. Financial Calculations (Beyond the Scope of this Book but Essential)

• Present Value (PV) and Future Value (FV):

  • Understanding the time value of money – a dollar today is worth more than a dollar in the future due to its potential to earn interest.
  • Present Value: PV = FV / (1 + r)^n, where r is the discount rate and n is the number of periods.
  • Future Value: FV = PV * (1 + r)^n, where r is the interest rate and n is the number of periods.
  • Understanding the concept of discounting to determine the present value of future income streams.

  • Compound Interest: Interest earned on both the principal and accumulated interest.

  • Compounding Period: The frequency with which interest is calculated and added to the principal (e.g., annually, semi-annually, quarterly, monthly).

  • Equation: A = P (1 + r/n)^(nt) where: A = the future value of the investment/loan, including interest; P = the principal investment amount (the initial deposit or loan amount); r = the annual interest rate (as a decimal); n = the number of times that interest is compounded per year; t = the number of years the money is invested or borrowed for.

  • Annuities: A series of equal payments or receipts occurring over a specified period.

  • Present Value of an Annuity: The current value of a stream of future payments, discounted at an appropriate interest rate.

IV. Practical Exercises and Examples

• Sales Comparison Approach:

  • Given a subject property and three comparable sales, calculate indicated value ranges for the subject using percentage and dollar adjustments. Discuss potential issues with large adjustments.

    • Equation: Adjusted Sale Price = Comparable Sale Price +/- Adjustments
    • Cost Approach:

  • Calculate the reproduction cost of a building, deduct depreciation, and add land value to arrive at an indicated value.

    • Equation: Property Value = Site Value + Reproduction Cost - Depreciation

  • Income Approach:

  • Calculate the value of an investment property using direct capitalization.

    • Equation: Value = Net Operating Income / Capitalization Rate

V. Conclusion

Proficiency in property description and appraisal mathematics is essential for accurate and reliable property valuations. A deep understanding of these concepts, combined with practical application, will provide you with a solid foundation for success in the property appraisal profession. The content should be accurate in its terminology and concepts and related to the Course Description and Book Content.