Percentages, Markups, and Area Calculation

Percentages

Percentages are a mathematical tool used in real estate appraisal in market analysis, sales comparison, return calculation, and determining value changes.

A percentage expresses a number as a fraction of 100. The “%” symbol means “divided by 100”. For example, 10% means 10 divided by 100, or 0.1.

• Converting Percentages to Decimals: Divide the percentage by 100 or move the decimal point two places to the left. Example: 8.5% = 0.085

• Converting Decimals to Percentages: Multiply the decimal by 100 or move the decimal point two places to the right and add the “%” sign. Example: 0.095 = 9.5%

• Basic Percentage Equation: Part = Percentage x Whole. Example: $10.00 = 10% x $100.00

Percentage applications in real estate:
* Occupancy Rate: Used to calculate the percentage of occupied units in a building or project.
* Value Ratio: Used to determine the ratio of land value to the total property value.
* Profit Margin: Used to calculate the percentage of profit earned from selling a property.
* Sales Comparison Analysis: Used to adjust comparable sales prices based on differences in features and characteristics.

Solving for Part: Part = Percentage x Whole
Solving for Percentage: Percentage = Part ÷ Whole
Solving for Whole: Whole = Part ÷ Percentage
Example: A 1500 sq. ft. house is on a 7500 sq. ft. lot. Percentage = 1500 sq. ft. ÷ 7500 sq. ft = 0.2. The house covers 20% of the lot area.

Direct Capitalization

Direct capitalization is a method to estimate property value based on its expected net income❓ and an appropriate capitalization rate.

Direct capitalization relies on the relationship between income and value, assuming a direct and constant relationship between a property’s income and its value.

• Basic Equations: I = R x V, R = I ÷ V, V = I ÷ R (I = Income (Net Operating Income), R = Capitalization Rate, V = Value)
• Capitalization Rate: The ratio between a property’s net operating income and its value, reflecting the required return on investment and factors like risk and expected growth.

• Income Multiplier: The inverse of the capitalization rate, used to estimate value by multiplying income by the appropriate multiplier.

• Relationship between Capitalization Rate and Income Multiplier: They are reciprocal❓ values. Income Multiplier = 1 ÷ Capitalization Rate. Capitalization Rate = 1 ÷ Income Multiplier
  Example: Using a 25% capitalization rate, a property with a $40,000 annual income would be valued at $160,000. Value = $40,000 ÷ 25% (0.25) = $160,000. The corresponding income multiplier is 4, which is the reciprocal of 0.25 (1 ÷ 0.25 = 4).

Direct Capitalization applications in real estate appraisal:
* Commercial Property Valuation: Used to value offices, retail stores, and industrial buildings.
* Investment Analysis: Helps investors determine the expected return on investment in real estate.
* Purchase and Sale Decisions: Provides information for informed decisions about buying or selling properties.

Area Calculation

Accurate area calculation is necessary in real estate appraisal, including land area, building area, and leasable areas.

• Basic Areas: Square: Area = Length x Width; Rectangle: Area = Length x Width; Triangle: Area = (Base x Height) / 2

• Calculating Irregular Shapes: Divide irregular shapes into regular shapes (squares, rectangles, and triangles), calculate the area of each shape individually, and then sum the areas to get the total area.

• Units of Measurement: Ensure appropriate and consistent units of measurement are used (e.g., square feet or square meters).

• Volume Calculation: Volume = Length x Width x Height. Example: A room with dimensions 15 ft x 10 ft x 10 ft. Volume = 15 ft x 10 ft x 10 ft = 1500 cubic feet.

• Practical Examples:

  • Calculating the area of an irregular plot of land: (as explained in the book)
    • Divide the plot of land into a square, rectangle and triangle.
    • Calculate the area of each shape individually:
      • Square (S) Area = 40 ft x 40 ft = 1600 sq ft.
      • Rectangle (R) Area = 30 ft x 25 ft = 750 sq ft.
      • Triangle (T) Area = (30 ft x 30 ft) ÷ 2 = 450 sq ft.
    • Sum the areas: Total area = 1600 + 750 + 450 = 2800 sq ft.