A property with NOI of $96,000 sold for $1,280,000. The overall capitalization rate extracted is:
Correct Answer
D) 7.5%
Why this is correct: The overall capitalization rate (R) is extracted from a comparable sale by dividing its Net Operating Income (NOI) by its sale price (V). Calculation: R = NOI / V = $96,000 / $1,280,000 = 0.075 or 7.5%. Why the other choices are wrong: '8.2%, adjusted for typical financing' incorrectly adjusts the extracted rate. '13.3%, inverting the relationship' results from dividing price by NOI (V/NOI). '6.0%, after a management allowance' incorrectly deducts an extra expense from NOI. Exam tip: To extract a cap rate from a sale: R = NOI / Sale Price. Ensure the NOI is computed on a consistent, stabilized basis.
Why This Is the Correct Answer
Option D is correct because $96,000 divided by $1,280,000 is exactly 0.075, and it is the only choice presenting the number without an unsupported modification. Its bare presentation is itself a signal, since a correctly extracted rate requires no explanatory clause. Cross-checking confirms it: 7.5 percent of $1,280,000 is $96,000, closing the loop. Any further adjustment would substitute the appraiser's speculation for observed market behavior.
Why the Other Options Are Wrong
Option A: 8.2%, adjusted for typical financing
Adjusting an extracted overall rate for typical financing has no place in this calculation, because an overall rate relates net operating income before debt service to the whole property price. Financing enters rate development only through explicit mortgage-equity techniques such as band of investment, which build a rate rather than adjust an extracted one. The phrase 'adjusted for typical financing' is included to sound rigorous while describing an operation nobody performs here.
Option B: 13.3%, inverting the relationship
Roughly 13.3 results from dividing the price by the income, producing a net income multiplier and then mislabeling it as a percentage. The reciprocal relationship means the two always travel together, and 1 divided by 0.075 is about 13.3, so recognizing that pairing is a quick way to catch the flip. A capitalization rate above ten percent is possible, but one above thirteen on ordinary income property should prompt a second look at the setup.
Option C: 6.0%, after a management allowance
Deducting a further management allowance from an NOI the stem has already given restates the property's income without any basis for doing so. If the appraiser had evidence that the reported NOI omitted management, the correct response would be to reconstruct the NOI transparently and show the restated figure, not to quietly lower the rate. As presented, this choice changes the data to fit a preferred answer.
Bare Number Wins
In extraction questions the bare number wins. The right answer says seven and a half percent and stops. The wrong answers come dressed in explanations, because the explanation is doing the work the arithmetic could not. Do the division first, then read the clauses.
How to use: Compute the quotient before looking at any justification text, then find the choice matching your figure. If your number appears with a clause attached and also appears bare, take the bare one. Verify by multiplying the rate back against the price to see whether it reproduces the stated income.
Exam Tip
Cover the explanatory clauses in the answer choices with your finger and solve the arithmetic on its own; the clauses exist to make wrong numbers sound deliberate.
Common Mistakes to Avoid
- -Modifying an extracted rate for financing terms that overall rates do not reflect
- -Confusing the overall rate with its reciprocal, the net income multiplier
- -Silently restating a comparable's NOI instead of disclosing the reconstruction and its effect
Concept Deep Dive
Analysis
This question is a second exercise in rate extraction, and the discipline it rewards is refusing to alter a directly observed figure. Dividing the sale's net operating income of $96,000 by its price of $1,280,000 gives 0.075, or 7.5 percent, and that number is a fact about the transaction rather than a conclusion requiring judgment. What makes the item harder than plain arithmetic is that three of the four choices attach a justification to their number, and a plausible-sounding rationale can make a wrong figure feel considered. The appraiser's protection is to compute first and read the rationales second, because an extracted rate needs no rationale. Judgment does enter afterward, when the appraiser decides how much weight this sale deserves and whether its NOI was built on the same basis as the subject's, but that judgment affects reconciliation of several rates, not the arithmetic of any one extraction.
Background Knowledge
You need the IRV relationship and the reciprocal link between an overall rate and a net income multiplier. You should also know what belongs in a properly reconstructed operating statement, including vacancy and collection loss, management, and reserves for replacement, and that comparability of rates depends on the NOI behind each one being derived on the same basis as the subject's.
Real-World Application
Extracting rates for a small retail subject, an appraiser computes 7.5 percent on one sale, then discovers through verification that the buyer's NOI excluded a $9,600 management fee. Restating the income lowers the extracted rate to about 6.8 percent, and the report shows both figures with the reason for the restatement.
More Income Approach Questions
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