A property's NOI is $88,000 and comparable sales indicate rates of 6.5%, 6.8% and 7.1%. Using 6.8%, the indicated value is:
Correct Answer
B) $1,294,118
This question tests the direct capitalization method, where Value = Net Operating Income (NOI) ÷ Capitalization Rate. The correct calculation uses the 6.8% rate specified in the question. Why this is correct: The indicated value is calculated by dividing the NOI of $88,000 by the capitalization rate of 6.8% (expressed as a decimal: 0.068). $88,000 ÷ 0.068 = $1,294,118. Why the other choices are wrong: "$598,400, multiplying instead of dividing" results from incorrectly multiplying NOI by the rate. "$12,941,176, misplacing the decimal" is off by a factor of 10, likely from a decimal error in the rate. "$1,353,846, using the 6.5 percent rate" is the result of using the 6.5% rate from the comparables instead of the 6.8% rate specified for the calculation. Exam tip: In direct cap, always divide NOI by the rate. Double-check that you've converted the percentage rate to its decimal form (e.g., 6.8% = 0.068) before calculating.
Why This Is the Correct Answer
Option B is correct because $88,000 divided by 0.068 equals $1,294,118 when rounded to the nearest dollar. The rate must be converted from 6.8 percent to the decimal 0.068 before dividing, and the division is income over rate, never the reverse. Multiplying the answer back by 0.068 returns approximately $88,000, which confirms the work. A value near $1.29 million for $88,000 of net income is also intuitively reasonable, since a rate slightly under 7 percent implies a multiple of roughly fifteen times income.
Why the Other Options Are Wrong
Option A: $598,400, multiplying instead of dividing
$598,400 is $88,000 multiplied by 6.8 rather than divided by 0.068, so the operation is inverted. Multiplication by a rate answers a different question, namely how much income a given value would produce. A quick reasonableness check exposes it, because a value below $600,000 would imply an overall rate near 15 percent, far outside the range the comparables indicate.
Option C: $12,941,176, misplacing the decimal
$12,941,176 is the correct division with the decimal shifted one place, the result of dividing by 0.0068 instead of 0.068. That implies a rate of two thirds of one percent, which no income property market supports. Writing the rate as a decimal carefully, and sanity-checking the magnitude against the comparables, prevents this error.
Option D: $1,353,846, using the 6.5 percent rate
$1,353,846 is a correct calculation performed with the wrong input, dividing $88,000 by 0.065 rather than the specified 0.068. The lowest rate in a range always produces the highest value, which is why the figure looks plausible. The stem explicitly directs the use of 6.8 percent, so selecting a rate is not part of this task.
Small rate, big value
Value and rate move in opposite directions. Before computing, predict the direction: a lower rate must give a bigger number. Then check that your answer obeys the prediction.
How to use: Convert the percentage to a decimal, divide income by it, and multiply back to verify. Any answer choice annotated with its own error, such as inverting or misplacing the decimal, is telling you which mistake it represents.
Exam Tip
Estimate the magnitude before dividing. A 6.8 percent rate is roughly one fifteenth, so the value should land near fifteen times the income, which instantly eliminates the far-off choices.
Common Mistakes to Avoid
- -Multiplying net operating income by the rate instead of dividing
- -Dividing by the percentage rather than its decimal equivalent
- -Substituting a different rate than the one the question specifies
- -Capitalizing effective gross income or pre-expense income instead of net operating income
Concept Deep Dive
Analysis
This tests direct capitalization plus the judgment of using the rate the question specifies. Direct capitalization converts a single year's stabilized net operating income into a value indication by dividing it by an overall rate, so value equals income divided by rate. The comparable sales here bracket the subject with rates of 6.5, 6.8, and 7.1 percent, which is exactly how appraisers develop a rate: extract from several transactions, then select within the range based on which comparables most resemble the subject in risk, location, tenancy, and condition. The stem removes that judgment by directing you to 6.8 percent, the middle indication, so the task is purely computational. Dividing $88,000 by 0.068 gives $1,294,118, and the answer choices are constructed from the standard mishandlings: inverting the operation, misplacing the decimal, and using the wrong rate from the range.
Background Knowledge
You need the direct capitalization formula and the IRV relationships among income, rate, and value. You should also know how overall rates are extracted from comparable sales by dividing each sale's net operating income by its price, and that rate selection within an extracted range is a judgment based on comparability of risk and property characteristics.
Real-World Application
Valuing a small apartment building, you extract overall rates from three recent sales, find they run from 6.5 to 7.1 percent, and select 6.8 percent because the middle sale matches the subject in age and unit mix. You document each extraction so a reviewer can see the rate came from the market rather than from a survey.
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