A property generates a net operating income of $75,000 and has a value of $1,000,000. What is the capitalization rate?
Correct Answer
B) 7.5%
Capitalization rate = NOI ÷ Value. $75,000 ÷ $1,000,000 = 0.075 or 7.5%.
Why This Is the Correct Answer
Option B is correct because the capitalization rate formula is NOI ÷ Value = Cap Rate. Substituting the given values: $75,000 ÷ $1,000,000 = 0.075. To convert this decimal to a percentage, we multiply by 100, which gives us 7.5%. This calculation follows the standard mathematical procedure for determining cap rates in real estate valuation.
Why the Other Options Are Wrong
Option A: 13.33%
Option A (13.33%) results from incorrectly dividing the property value by the NOI ($1,000,000 ÷ $75,000), which reverses the proper cap rate formula and would actually give you a gross income multiplier-type calculation rather than a capitalization rate.
Option C: 0.75%
Option C (0.75%) represents the decimal form of the correct calculation (0.075) but fails to convert it to percentage form by multiplying by 100, resulting in an answer that is off by a factor of 10.
Option D: 133.3%
Option D (133.3%) appears to be the result of multiple calculation errors, possibly involving incorrect formula application and decimal placement, resulting in an unrealistically high cap rate that would never be seen in real estate markets.
NOI Over Value (NOV)
Remember 'NOV' - NOI Over Value = Cap Rate. Think of November (NOV) as the month when you 'cap off' the year by calculating returns. Also remember: 'Nice Over Valuable' - put the Nice income Over the Valuable property price.
How to use: When you see a cap rate question, immediately think 'NOV' and set up the fraction with NOI on top and Value on the bottom, then convert the decimal result to a percentage by moving the decimal point two places to the right.
Exam Tip
Always double-check that your cap rate answer falls within a reasonable range (typically 3-15%) and remember to convert your decimal answer to a percentage - this is where many test-takers make careless errors.
Common Mistakes to Avoid
- -Reversing the formula by dividing value by NOI instead of NOI by value
- -Forgetting to convert the decimal result to a percentage
- -Using gross income instead of net operating income in the calculation
Concept Deep Dive
Analysis
The capitalization rate (cap rate) is a fundamental concept in real estate valuation that measures the relationship between a property's net operating income and its market value. It represents the rate of return an investor can expect from a property based on the income it generates, expressed as a percentage. The cap rate is calculated by dividing the annual net operating income (NOI) by the property's current market value or purchase price. This metric is essential for comparing investment properties and determining whether a property is appropriately priced relative to its income-generating potential.
Background Knowledge
Net Operating Income (NOI) represents the annual income generated by a property after deducting operating expenses but before debt service and taxes. Capitalization rates typically range from 3% to 12% in most real estate markets, with higher cap rates indicating higher risk or lower-quality properties, and lower cap rates suggesting premium properties or markets.
Real-World Application
Appraisers use cap rates to value income-producing properties through the income approach, compare similar investment properties, and help investors determine if a property's asking price aligns with market expectations based on its income potential.
More Math & Stats Questions
What is the area of a triangular lot with a base of 120 feet and a height of 80 feet?
An irregular lot has the following measurements: Side A = 100', Side B = 150', Side C = 120', Side D = 180'. If the lot can be divided into two rectangles (100' × 150' and 120' × 30'), what is the total area?
A property has a potential gross income of $180,000, vacancy and collection loss of 7%, and operating expenses of $65,000. What is the NOI?
A property generates $120,000 in net operating income and is valued at $1,500,000. What is the capitalization rate?
A building has potential gross income of $180,000, vacancy and collection loss of 8%, and operating expenses of $54,000. What is the net operating income?
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