Percentage Ratios and Direct Proportion

Percentages: Basics and Applications

• A percentage is a ratio expressed as a fraction of 100, denoted by the symbol “%”.
• To convert a number to a percentage, multiply❓ by 100.
• To convert a percentage to a decimal, divide❓ by 100 (e.g., 25% = 0.25).
• To convert a decimal to a percentage, multiply by 100 (e.g., 0.75 = 75%).
• The fundamental percentage formula is: <a data-bs-toggle="modal" data-bs-target="#questionModal-115797" role="button" aria-label="Open Question" class="keyword-wrapper question-trigger"><span class="keyword-container"><a data-bs-toggle="modal" data-bs-target="#questionModal-399999" role="button" aria-label="Open Question" class="keyword-wrapper question-trigger"><span class="keyword-container">part</span><span class="flag-trigger">❓</span></a></span><span class="flag-trigger">❓</span></a> = Percentage * Whole.
• Percentage can be calculated as: Percentage = Part / Whole.
• Whole can be calculated as: Whole = Part / Percentage.
• Example: Building area percentage of land area: If the building area is 1500 sq ft and the land area is 7500 sq ft, then Percentage = 1500 / 7500 = 20%.
• Example: Percentage change in property value: If a property increases in value from $200,000 to $250,000, then Increase = $50,000 and Percentage Change = ($50,000 / $200,000) * 100 = 25%.
• Example: Occupancy rate: If 80❓ units are occupied out of 100, then Occupancy Rate = (80 / 100) * 100 = <a data-bs-toggle="modal" data-bs-target="#questionModal-115803" role="button" aria-label="Open Question" class="keyword-wrapper question-trigger"><span class="keyword-container">80%</span><span class="flag-trigger">❓</span></a>.

direct❓ Capitalization: Estimating Value Based on Income

• Direct capitalization is a real estate valuation method that converts expected property income into an estimate of its current value.
• Net Operating Income❓❓ (NOI) is the income generated after deducting operating expenses, but before debt service and taxes.
• Capitalization Rate (Cap Rate) is the ratio between NOI and property value, reflecting the required return on investment considering risk.
• Value is the estimated property value based on expected income and the appropriate cap rate.
• The basic formula is: Income = Rate * Value or I = R * V.
• Rate can be calculated as: Rate = Income / Value or R = I / V.
• Value can be calculated as: Value = Income / Rate or V = I / R.
• Cap rate depends on risks, interest rates, market conditions, and property characteristics.
• Cap rates can be derived from comparable property sales.
• Example: Estimating property value: If NOI is $40,000 and the cap rate is 10% (0.10), then Value = $40,000 / 0.10 = $400,000.
• Example: Calculating cap rate: If a property sells for $500,000 with an NOI of $50,000, then Rate = $50,000 / $500,000 = 10%.

Relationship Between Capitalization Rate and Gross Income Multiplier (GIM)

• Gross Income Multiplier (GIM) is the ratio between the property’s sale price and its annual gross income.
• Cap rate and GIM are inversely related; they are reciprocals❓ of each other.
• GIM = 1 / Cap Rate.
• Cap Rate = 1 / GIM.
• Example: If the cap rate is 25% (0.25), then GIM = 1 / 0.25 = 4.