A property sold for $2,400,000 with NOI of $168,000. Its overall rate is:
Correct Answer
C) 7.0%
Why this is correct: The overall capitalization rate (R) is calculated as Net Operating Income (NOI) divided by Sale Price (Value). The formula is R = NOI / Sale Price. Here, R = 168,000 / 2,400,000 = 0.07, which is 7.0%. Why the other choices are wrong: "0.7%, misplacing the decimal" results from dividing 168,000 by 2,400,000 and incorrectly moving the decimal. "14.3%, inverting the ratio" results from dividing the sale price by the NOI (2,400,000 / 168,000). "8.4%, adjusting for financing" introduces a financing adjustment not supported by the basic cap rate extraction formula. Exam tip: The cap rate formula is fundamental: R = NOI / Value. Always set up the division as NOI divided by Price.
Why This Is the Correct Answer
Option C is correct because $168,000 divided by $2,400,000 equals 0.07, or 7.0 percent, with no adjustment of any kind required. The extraction is a direct observation of what one buyer paid per dollar of net income, and it stands on its own as market evidence. Reasonableness confirms it, since a 7 percent overall rate is an ordinary figure for income property while the alternatives offered are either implausible or arithmetically impossible. Nothing in the stem introduces financing terms or expense issues that would justify altering the extracted number.
Why the Other Options Are Wrong
Option A: 0.7%, misplacing the decimal
Seven-tenths of one percent is the correct quotient with the decimal shifted one place, and it should fail an immediate plausibility check: at that rate the property would take well over a century of net income to return the purchase price. Catching this requires only a rough estimate before computing, since $168,000 is clearly in the neighborhood of seven percent of $2.4 million. Decimal errors are the most preventable mistakes in rate work.
Option B: 14.3%, inverting the ratio
Dividing price by income rather than income by price yields roughly 14.3, which is a net income multiplier, not a rate expressed in percent. The two are reciprocals and both are legitimate measures, but they answer different questions and are never interchangeable. Attaching a percent sign to a multiplier is the specific error this distractor rewards.
Option D: 8.4%, adjusting for financing
Extraction of an overall rate uses the actual price and the property's net operating income before debt service, so no financing adjustment enters the calculation. A rate that accounts for a specific loan structure is an equity or mortgage-equity concept, developed through techniques such as band of investment, not something layered onto a directly extracted rate. Inventing an adjustment the stem does not support introduces bias.
Rate Is a Small Number
A capitalization rate is a small number, usually between four and twelve percent, because income is a small slice of price. If your answer comes out above twenty or below one, you either flipped the division or lost the decimal. Small income over big price gives a small rate; that shape check catches almost every error.
How to use: Before dividing, estimate: ten percent of $2.4 million is $240,000, and $168,000 is clearly less, so the rate must be under ten percent. That single estimate eliminates the inverted and misplaced-decimal choices at once. Then compute, and refuse any adjustment the stem does not give you facts to support.
Exam Tip
Anchor on ten percent of the sale price as a mental benchmark; comparing NOI to that figure tells you instantly whether the rate is above or below ten percent.
Common Mistakes to Avoid
- -Inverting the division and reporting a net income multiplier as a percentage
- -Extracting a rate from a broker's pro forma NOI without verifying expenses and reserves
- -Using a rate derived from a stabilized property to capitalize a subject that is not stabilized
Concept Deep Dive
Analysis
This question tests extraction of an overall capitalization rate from a comparable sale. The IRV relationship ties three quantities together: income equals rate times value, so the rate equals income divided by value and value equals income divided by rate. Extracting a rate from a sale means dividing that sale's net operating income by its price, which here is $168,000 divided by $2,400,000, or 0.07. The result is a decimal that becomes 7.0 percent when expressed as a percentage. The arithmetic is trivial, so what the item is really testing is whether the candidate sets up the division in the correct direction and keeps the decimal in place. Beyond the mechanics, a rate is only usable if the NOI behind it was computed the way the appraiser computes the subject's NOI, meaning the same treatment of vacancy and collection loss, management, reserves for replacement, and any expenses the buyer's pro forma may have understated.
Background Knowledge
You need the IRV relationship and fluency moving among its three forms, plus the understanding that an overall rate is extracted before debt service and before income taxes. You should also know that a rate is comparable only when the NOI supporting it was derived consistently, including consistent treatment of reserves for replacement, management fees, and vacancy and collection loss.
Real-World Application
Building rate support for a small office building, an appraiser extracts overall rates from four sales, recomputing each NOI to include a three percent management fee and reserves the buyers' brokers had omitted. Two of the four rates move by more than fifty basis points once restated, and the report shows both the reported and the restated figures.
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