Market data show a sale at a cash-equivalent price of $2,625,000, with stabilized annual NOI of $210,000. What overall rate does the sale indicate?
Correct Answer
B) 8.00%
210000÷2625000×100 = 8. Common errors: reporting the price ÷ NOI multiplier as if it were the rate gives 12.50%; misplacing the decimal (×1,000 instead of ×100) gives 80.00%; misplacing the decimal (×10 instead of ×100) gives 0.80%.
Why This Is the Correct Answer
Option B is correct because the overall rate equals NOI ÷ price: $210,000 ÷ $2,625,000 = 0.08, which is 8.00%. Net income divided by the cash-equivalent sale price produces a market-derived overall rate. Converting the decimal 0.08 to a percentage means multiplying by 100.
Why the Other Options Are Wrong
Option A: 0.80%
Option A, 0.80%, results from multiplying by 10 instead of 100: $210,000 ÷ $2,625,000 × 10 = 0.80. The correct conversion is 0.08 × 100 = 8.00%.
Option C: 12.50%
Option C, 12.50%, reports the price-to-NOI multiplier as if it were a rate: $2,625,000 ÷ $210,000 = 12.5. That figure is a net income multiplier, not a capitalization rate; the rate is $210,000 ÷ $2,625,000 = 8.00%.
Option D: 80.00%
Option D, 80.00%, results from multiplying by 1,000 instead of 100: $210,000 ÷ $2,625,000 × 1,000 = 80. The correct rate is 0.08 × 100 = 8.00%.
IRV: income, rate, value
Income equals rate times value, so rate equals income divided by value and value equals income divided by rate.
How to use: Use IRV to rearrange any direct capitalization problem for the unknown.
Exam Tip
A capitalization rate is income over price; if your answer is greater than 1 before converting, you likely divided the wrong way.
Common Mistakes to Avoid
- -Dividing price by NOI and calling the result a rate
- -Shifting the decimal when converting to a percentage
- -Using a non-cash-equivalent price
Concept Deep Dive
Analysis
This question tests extracting an overall capitalization rate from a comparable sale. The overall rate is net operating income divided by cash-equivalent price. Here $210,000 ÷ $2,625,000 = 0.08, or 8.00%.
Background Knowledge
The overall capitalization rate expresses the relationship between one year's net operating income and value. Comparable sales are a preferred source of capitalization rates when they are adjusted to cash-equivalent terms and the income is measured consistently. The rate and the net income multiplier are reciprocals of each other.
Real-World Application
An appraiser verifies the sale of a neighborhood retail center, confirms the price was cash equivalent, and stabilizes the buyer's first-year NOI. Dividing that NOI by the price gives an overall rate she lists with other sales. She then reconciles a rate for capitalizing the subject's NOI.
More Income Approach Questions
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While verifying a fourplex sale, an appraiser learns that the buyer paid $900,000 cash equivalent. Potential gross income over the prior year was $100,000, but an above-market lease on one unit was ending, and the buyer projected potential gross income of $90,000 less a 5% vacancy allowance. The subject fourplex has market potential gross income of $110,000. What value does a potential gross income multiplier from this sale indicate?
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