A property generates annual NOI of $75,000. If the capitalization rate is 7.5%, what is the indicated value?
Correct Answer
B) $1,000,000
Value = NOI ÷ Cap Rate: $75,000 ÷ 0.075 = $1,000,000.
Why This Is the Correct Answer
Option B is correct because it properly applies the income capitalization formula: Value = NOI ÷ Capitalization Rate. Substituting the given values: $75,000 ÷ 0.075 = $1,000,000. The calculation requires converting the percentage cap rate (7.5%) to its decimal equivalent (0.075) before performing the division. This straightforward application of the formula yields the indicated market value of the income-producing property.
Why the Other Options Are Wrong
Option A: $900,000
This answer of $900,000 suggests an error in the cap rate conversion or calculation, possibly using an incorrect divisor of approximately 0.083 instead of 0.075.
Option C: $562,500
This answer of $562,500 indicates the student multiplied NOI by the cap rate ($75,000 × 0.075) instead of dividing, which is the opposite operation and a fundamental conceptual error.
Option D: $800,000
This answer of $800,000 suggests an error in decimal conversion or arithmetic, possibly using 0.09375 as the divisor instead of the correct 0.075.
NOI Divided by Cap = Value Pride
Remember 'NOI over Cap gives you the MAP' - NOI over (divided by) Cap rate gives you the Market value And Price. Visualize NOI sitting on top of Cap rate in a fraction, with the result being the property's value.
How to use: When you see NOI and cap rate given, immediately set up the fraction NOI/Cap Rate. Always convert percentage cap rates to decimals (move decimal point two places left). The result will always be larger than the NOI since you're dividing by a number less than 1.
Exam Tip
Always double-check that you're dividing NOI by cap rate, not multiplying - the value should be significantly larger than the annual NOI for typical cap rates between 4-12%.
Common Mistakes to Avoid
- -Multiplying NOI by cap rate instead of dividing
- -Forgetting to convert percentage cap rate to decimal form
- -Using gross income instead of net operating income
Concept Deep Dive
Analysis
This question tests the fundamental income capitalization approach formula, which is one of the three primary valuation methods in real estate appraisal. The capitalization rate method converts a single year's net operating income into an estimate of market value by applying a market-derived capitalization rate. This approach assumes that the NOI represents a stabilized, typical year of income and that the cap rate accurately reflects market expectations for similar properties. The formula Value = NOI ÷ Cap Rate is the cornerstone of income property valuation and must be memorized and applied correctly.
Background Knowledge
The income capitalization approach is based on the principle that value equals the present worth of future income benefits. The capitalization rate represents the relationship between net operating income and market value, derived from comparable sales of similar income properties. Net Operating Income is calculated as gross income minus vacancy and operating expenses, but excludes debt service and depreciation.
Real-World Application
Appraisers use this method daily when valuing apartment buildings, office buildings, retail centers, and other income properties. They gather market cap rates from recent sales of comparable properties and apply them to the subject property's stabilized NOI to estimate market value.
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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