Property Description and Appraisal Math

Chapter 4: Property Description and Appraisal Math

This chapter bridges the gap between understanding real estate concepts and applying the quantitative methods necessary for accurate appraisal. It covers methods of legally describing property, and essential mathematical principles, laying the groundwork for complex valuation techniques.

I. PROPERTY DESCRIPTION

Accurate property description is crucial for legal identification and clear communication. Several systems exist, each with strengths and weaknesses depending on location and historical context. A clear and unambiguous property description is a fundamental element of any appraisal report.

II. METES AND BOUNDS SYSTEM

The metes and bounds system relies on physical features and measurements to define❓ property boundaries. This system is common in older areas, particularly in the eastern United States, where original land grants often used natural landmarks.

A. Reference Points
Metes and bounds descriptions always begin at a defined point of beginning (POB). This POB must be clearly identifiable and permanent. Accepted reference points include:
1. monuments❓❓: Natural (e.g., a specific large rock, ancient tree) or artificial (e.g., an iron pin, a concrete marker) landmarks. Legal precedence dictates that monuments generally prevail over distances or courses if discrepancies arise.
2. Points of Intersection: Where two roads or property lines meet. Their exact location is critical.

B. Courses and Distances

From the POB, the description proceeds, stating the course (direction) and distance of each boundary line (or “call”).
1. Course (Bearing): Expressed as an angle from North or South (whichever is closer) towards East or West. For example, “North 45 degrees East” (N 45° E) means 45 degrees east of due north. Bearings are measured in degrees, minutes, and seconds. A full circle is 360 degrees (°), each degree is divided into 60 minutes (‘), and each minute into 60 seconds (“).
2. Distance: The length of each boundary line, usually measured in feet, chains (66 feet), or rods (16.5 feet).

Example:
* Begin at an iron pin marking the southeast corner of Lot 1, Block A, of the Plat of Sunny Acres, recorded in Plat Book 10, Page 25 at the County Recorder’s Office; thence N 45° E, a distance of 100 feet to a concrete monument; thence S 45° E, a distance of 100 feet to an iron pin; thence S 45° W, a distance of 100 feet to an iron pin; thence N 45° W, a distance of 100 feet to the point of beginning.

Challenges of Metes and Bounds:
* Descriptions can be complex and difficult to interpret.
* Monuments can be moved or destroyed, leading to boundary disputes.
* Accuracy depends on the precision of the original survey.

III. RECTANGULAR (U.S. GOVERNMENT) SURVEY SYSTEM

This system, also known as the Public Land Survey System (PLSS), was developed to survey and describe land in a systematic way. It is used across much of the United States.

A. Base Line and Meridian

The system relies on a grid network based on:
1. Principal Meridian: A north-south line designated by name (e.g., the 6th Principal Meridian). There are multiple principal meridians across the US.
2. Base Line: An east-west line that intersects the Principal Meridian at a designated initial point.

B. Townships

The grid is then divided into townships.
1. Township Lines: East-west lines running parallel to the Base Line at 6-mile intervals.
2. Range Lines: North-south lines running parallel to the Principal Meridian at 6-mile intervals.
3. Township Definition: A township is a 6-mile by 6-mile square containing approximately 36 square miles. It is identified by its township number (distance north or south of the Base Line) and its range number (distance east or west of the Principal Meridian). For example, “Township 2 North, Range 3 West” (T2N, R3W) refers to the township that is two townships north of the Base Line and three ranges west of the Principal Meridian.

C. Sections

Each township is divided into 36 sections.
1. Section Size: Each section is approximately 1 mile by 1 mile (640 acres).
2. Section Numbering: Sections are numbered sequentially, starting with section 1 in the northeast corner, proceeding west to section 6, then south to section 7, and proceeding east to section 12, and so on, ending with section 36 in the southeast corner.

D. Partial Sections

Sections can be further subdivided into quarter sections (160 acres), quarter-quarter sections (40 acres), and so on. These subdivisions are described in relation to the larger section.

Example:
* The Northwest Quarter of the Southeast Quarter of Section 10, Township 2 North, Range 3 West of the 6th Principal Meridian (NW ¼ SE ¼, Sec. 10, T2N, R3W, 6th PM). This describes a 40-acre parcel.

E. Adjustments and Government Lots
Due to the curvature of the earth, the rectangular survey system isn’t perfectly rectangular. Correction lines are introduced periodically to account for these variations, leading to irregular sections and “government lots” along the north and west sides of townships.

F. Rectangular Survey System Descriptions
A complete description must include the smallest subdivision (e.g., quarter-quarter section), the section number, township number and direction, range number and direction, and the Principal Meridian. The order is generally from the specific to the general.

Advantages of the Rectangular Survey System:
* Provides a systematic and relatively simple method of land description.
* Reduces ambiguity compared to metes and bounds.

Disadvantages of the Rectangular Survey System:
* Not applicable in areas predating the system.
* Corrections for the Earth’s curvature lead to irregular sections.

G. Geodetic Survey System

The Geodetic Survey System employs sophisticated coordinate systems (latitude and longitude) and high-precision surveying techniques. It is mainly used for large-scale mapping and infrastructure projects that require extremely accurate spatial data. Reference points are permanently established using GPS and other advanced technologies.

IV. LOT, BLOCK, AND TRACT SYSTEM

This system is used in platted subdivisions, particularly in urban and suburban areas. A plat map❓ shows the division of land into lots, blocks, and streets.

1. Plat Map: A legal document recorded with the local government, depicting the subdivision.
2. Lot: An individual parcel of land within the subdivision.
3. Block: A group of lots surrounded by streets.
4. Tract: The overall area being subdivided.

Example: Lot 22, Block B, of the Willow Creek Subdivision, as recorded in Plat Book 45, Page 12 at the County Recorder’s Office.

Advantages of Lot, Block, and Tract System:
* Simple and easy to understand.
* Clear identification of property boundaries.

Disadvantages of Lot, Block, and Tract System:
* Only applicable in platted subdivisions.

V. APPRAISAL MATH

Accurate calculations are essential for all three approaches to value (cost, sales comparison, and income).

A. Distance, Area, and Volume
Understanding the relationship between these concepts is crucial.
* Distance: Measured in linear units (feet, meters, miles).
* Area: The measure of a two-dimensional surface, measured in square units (square feet❓, square meters, acres).
* Volume: The measure of a three-dimensional space, measured in cubic units (cubic feet, cubic meters).

B. Area of a Rectangle

The area (A) of a rectangle is calculated by multiplying its length (L) by its width (W):

• A = L x W

Example: A rectangular lot that is 100 feet wide and 200 feet long has an area of 20,000 square feet (100 ft x 200 ft = 20,000 sq ft).

C. Units of Area

Common units of area used in real estate:
1. Square Foot (sq ft): A square that is 1 foot by 1 foot.
2. Square Yard (sq yd): A square that is 1 yard by 1 yard. (1 sq yd = 9 sq ft)
3. Acre: A unit of land area equal to 43,560 square feet.
4. Square Mile: A square that is 1 mile by 1 mile. (1 square mile = 640 acres)

D. Converting Units

It is essential to be able to convert between different units of measurement. This involves using conversion factors.

Example: Converting square feet to acres.
1. A lot is 8❓7,120 sq ft. How many acres is that?
2. We know 1 acre = 43,560 sq ft.
3. Acres = Total sq ft / sq ft per acre
4. Acres = 87,120 sq ft / 43,560 sq ft/acre = 2 acres

E. Area of a Triangle

The area (A) of a triangle is calculated as one-half times the base (b) times the height (h):

• A = 1/2 * b * h

Example: A triangular lot has a base of 50 feet and a height of 40 feet. Its area is 1,000 square feet (0.5 * 50 ft * 40 ft = 1,000 sq ft).

F. Right Triangles

A right triangle has one angle that is 90 degrees. The side opposite the right angle is the hypotenuse (c). The Pythagorean theorem relates the sides of a right triangle:

• a² + b² = c²

Where a and b are the lengths of the two shorter sides, and c is the length of the hypotenuse. This theorem can be used to calculate unknown lengths if two sides are known.

G. Areas of Complex Figures

Complex figures can be divided into simpler shapes (rectangles, triangles) to calculate their total area. Calculate the area of each simpler shape and then sum them together.

H. Volume

The volume (V) of a rectangular solid (e.g., a room) is calculated by multiplying its length (L), width (W), and height (H):

• V = L x W x H

Example: A room that is 12 feet long, 10 feet wide, and 8 feet high has a volume of 960 cubic feet (12 ft x 10 ft x 8 ft = 960 cu ft).

I. Reciprocals
The reciprocal of a number is 1 divided by that number. Reciprocals are useful for solving equations and understanding relationships.
* Reciprocal of x = 1/x

J. Percentages

A percentage is a way of expressing a number as a fraction of 100. Percentages are used extensively in appraisal for adjustments, depreciation calculations, and capitalization rates.

1. Calculating a Percentage of a Number:
   * Value = Base x Percentage
   * Example: What is 10% of $200,000?\ast Percentage=10\ast Value=$200,000 x 0.10 = $20,000

2. Calculating a Percentage Change:
   * Percentage Change = ((New Value – Old Value) / Old Value) x 100
   * Example: A property sold for $250,000lastyearand$275,000 this year. What is the percentage increase in value?
   * Percentage Change = (($275,000-$250,000) / $250,000) x 100 = 10%

K. Direct Capitalization

Direct capitalization is a method used in the income approach to value. It estimates value by dividing a property’s net operating income (NOI) by a capitalization rate (cap rate):

• Value = NOI / Cap Rate

Example: A property generates an NOI of $50,000 per year, and the appropriate cap rate is 8%❓. The estimated value of the property is $625,000($50,000 / 0.08 = $625,000). Understanding cap rates is critical; they reflect the relationship between income and value in a specific market.

L. Interest

Interest is the cost of borrowing money or the return on an investment. Simple interest is calculated on the principal amount only. Compound interest is calculated on the principal amount plus accumulated interest. Interest calculations are important for understanding mortgage payments, investment returns, and discounted cash flow❓❓ analysis.

VI. FINANCIAL CALCULATIONS

Financial calculations are essential for more advanced appraisal techniques, particularly in income property valuation.

A. Present and Future Value
Present Value (PV) is the current worth of a future sum of money or stream of cash flows given a specified rate of return. Future Value (FV) is the value of an asset at a specific date in the future, based on an assumed rate of growth.

• Future Value Formula: FV = PV (1 + i)^n

  • Where:
    • FV = Future Value
    • PV = Present Value
    • i = Interest rate per period
    • n = Number of periods

• Present Value Formula: PV = FV / (1 + i)^n

  • Where:
    • PV = Present Value
    • FV = Future Value
    • i = Discount rate per period
    • n = Number of periods

B. Interest Compounding

Interest compounding refers to the frequency with which interest is added to the principal. The more frequently interest is compounded, the higher the effective interest rate.

• Formula for Compound Interest: 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

C. “Hoskold” or Sinking Fund Method
This method is primarily used to calculate the present value of a wasting asset (an asset that depletes over time, like mineral rights). It assumes that a portion of the income generated by the asset is set aside in a sinking fund to recover the initial investment. The sinking fund earns interest, contributing to the recovery of capital. The Hoskold formula allows appraisers to determine the present worth of these income streams, recognizing both the return on and of capital. It’s less common now but important to understand for historical context.

D. “Inwood” Method
The Inwood method (or present value of an annuity method) is a widely used discounted cash flow technique. It involves discounting a stream of future income to its present value using an appropriate discount rate. It is used to value properties that generate income over a defined period, such as leasehold interests or development projects. It is more aligned with discounted cash flow analysis practices.

VII. MEASURES OF CENTRAL TENDENCY

Understanding statistical measures is important for analyzing comparable data, especially in the sales comparison approach.

1. Mean: The average of a set of numbers. Calculated by summing all the numbers and dividing by the total number of numbers. Sensitive to outliers.
2. Median: The middle number in a set of numbers that are arranged in order. Not sensitive to outliers.
3. Mode: The number that appears most often in a set of numbers.

Choosing the appropriate measure of central tendency depends on the specific data and the presence of outliers. The median is often preferred when outliers are present, as it provides a more stable representation of the “typical” value.

VIII. CHAPTER SUMMARY

This chapter covered the crucial topics of property description and appraisal math. Mastery of these principles is fundamental for accurate and reliable real estate appraisal. An appraiser must be capable of interpreting legal descriptions, performing accurate calculations, and applying these skills to the valuation process. Proficiency in these areas is essential for ethical and competent appraisal practice.

IX. CHAPTER QUIZ

(Chapter quiz content would be added here, consisting of multiple-choice and problem-solving questions related to the material covered in the chapter)