A comparable sold at a cash-equivalent price of $1,000,000 and has stabilized annual NOI of $75,000. What overall capitalization rate does this comparable indicate?
Correct Answer
C) 7.5%
75000÷1000000×100 = 7.5. Common errors: inverting the ratio (price ÷ NOI) gives 13.3%; dividing by price plus NOI gives 7.0%; misplacing the decimal (×10 instead of ×100) gives 0.8%.
Why This Is the Correct Answer
Option C is correct because $75,000 ÷ $1,000,000 = 0.075, which is 7.5%. A market-derived overall rate is net income divided by the cash-equivalent sale price.
Why the Other Options Are Wrong
Option A: 0.8%
Option A, 0.8%, comes from misplacing the decimal: $75,000 ÷ $1,000,000 × 10 = 0.75, rounded to 0.8. Converting the ratio 0.075 to a percentage requires multiplying by 100, giving 7.5%.
Option B: 7.0%
Option B, 7.0%, results from dividing NOI by the price plus NOI: $75,000 ÷ $1,075,000 ≈ 7.0%. The price alone is the denominator, so the rate is $75,000 ÷ $1,000,000 = 7.5%.
Option D: 13.3%
Option D, 13.3%, comes from inverting the ratio: $1,000,000 ÷ $75,000 ≈ 13.33, which is a price-to-income multiplier, not a rate. The overall rate is NOI ÷ price = 7.5%.
Rate is income over price
In I = R × V, rearranging gives R = I ÷ V, so the small number (income) goes on top.
How to use: Use R = I ÷ V whenever you extract a cap rate from a sale.
Exam Tip
Always set up the cap rate as NOI over price. A size check alone is not enough: the inverted ratio here, 13.33, looks like a believable percentage, so confirm which number is on top before choosing.
Common Mistakes to Avoid
- -Dividing price by NOI and calling it a rate
- -Adding NOI to the price in the denominator
- -Mis-converting a decimal to a percentage
Concept Deep Dive
Analysis
This question tests extraction of an overall capitalization rate from a comparable sale. The rate is NOI divided by the cash-equivalent sale price, expressed as a percentage.
Background Knowledge
An overall capitalization rate expresses the relationship between one year's NOI and value. Rates extracted from comparable sales are preferred when the sales are similar and their income and prices are measured on a consistent, cash-equivalent basis.
Real-World Application
An appraiser verifies the NOI of a recently sold industrial building with the buyer, confirms the price was cash equivalent, and divides the NOI by the price to extract an overall rate for use in valuing a similar subject.
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