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Measurement Principles and Calculations in Property Valuation
Units of Measurement
- Length: Inch, foot, yard, mile, meter, kilometer.
- Area: Square foot, square yard, acre, square mile, square meter, hectare.
- Volume: Cubic foot, cubic yard, cubic meter.
Conversions:
- 1 foot = 12 inches
- 1 yard = 3 feet
- 1 acre = 43,560 square feet
Area Calculation
- Square and Rectangle: Area = Length x Width
- Triangle: Area = 0.5 x Base x Height
- Circle: Area = πr², where π ≈ 3.14159
- Irregular Shape: Divide into simple geometric shapes, calculate each area separately, then sum.
Example: A rectangular plot of land with a length of 100 ft and a width of 50 ft has an area of 5000 sq ft.
Volume Calculation
- Cube and Rectangular Prism: Volume = Length x Width x Height
- Cylinder: Volume = πr²h
Example: A rectangular room with a length of 20 ft, width of 15 ft, and height of 10 ft has a volume of 3000 cubic feet.
Reciprocal
The reciprocal of a number is 1 divided by that number. If the interest rate is (i), then its reciprocal is 1/i.
Example: The reciprocal of 5 is 1/5 = 0.2
Basic Formulas in Real Estate Appraisal
Percentage
Part = Percentage x Whole
Example: If a property price of $200,000 increases by 5%, the increase is $10,000.
Capitalization
Income = Rate x Value
Value = Income / Rate
Example: If a property’s net operating income is $20,000 and the capitalization rate is 10%, the property value is $200,000.
simple interest❓
Interest = Principal x Rate x Time
Example: A loan of $10,000 at a simple interest rate of 5% per year❓ for 3 years yields a total interest of $1,500.
Compound Interest
Financial calculations involving compound interest are complex and often require financial calculators or tables.
Basic Variables:
- Present Value (PV): The value of an amount today.
- Future Value (FV): The value of an amount at a future date.
- Interest Rate (i): The interest rate per compounding period.
- Number of Periods (n): The total number of compounding periods.
- Periodic Payment (PMT): The regular payment amount (if any).
Measures of Central Tendency, Range, and Standard Deviation
Measures of Central Tendency
- Mean: Sum of values❓ divided by the number of values.
- Median: The middle value in a sorted dataset.
- Mode: The most frequent value in a dataset.
Range
The difference between the highest and lowest values in a dataset.
Standard Deviation
Measures how far values deviate from the mean.
Example: Sale prices of 5 similar properties: $190,000, $200,000, $210,000, $220,000, $230,000.
- Mean: $210,000
- Median: $210,000
- Range: $40,000
Chapter Summary
- Volume Calculation: The volume of a rectangular room is calculated by multiplying the floor area❓ (length × width) by the height. Consistent units of measurement must❓ be used.
- Reciprocal: The reciprocal of a number is 1 divided by that number. Reciprocals come in pairs.
- Mathematical Formulas: The formula A = B x C can be rearranged to find B or C using division: B = A ÷ C or C = A ÷ B.
- Percentage: Part = Percentage × Whole. (Percentage means “divided by 100”).
- Capitalization: Income = Rate × Value.
- Simple Interest: Interest = Principal × Rate × Time. (Rate and time units must be compatible).
- Compound Interest: Compound interest problems are complex and are typically solved using computers, calculators, or financial factor tables. Financial calculations involve present value, future value, interest rate per compounding period, total number of compounding periods, and payment amount. Knowing four of these variables allows calculation of the fifth. Factors from financial tables can be used to solve financial calculations.
- Measures of Central Tendency: Mean, median, and mode are measures of central tendency used to describe the center of a data set. The range is the difference between the lowest and highest value in the sample. Standard deviation measures the dispersion of prices from the mean.
- Accuracy in Measurements: Accuracy in area and volume calculation is critical for accurate value estimation, especially in construction cost or land value estimation.
- Understanding Ratios and Rates: Understanding how to calculate percentages and rates (e.g., capitalization rate or interest rate) is necessary for evaluating future cash flows and determining the present value of property.
- Importance of Financial Tools: Using financial tools (calculators, tables, software) facilitates solving complex compound interest problems, contributing to more accurate property valuation.
- Statistical Analysis: Understanding how to use measures of central tendency to characterize market data.
