An appraiser values a property by direct capitalization at a 6% overall rate. If annual NOI decreases by $12,000 and the rate does not change, by how much does the indicated value decrease?
Correct Answer
D) $200,000
12000÷0.06 = 200000. Common errors: multiplying the change by the rate instead of dividing gives $720; reporting the NOI change as the value change gives $12,000; misplacing the decimal in the 6% rate gives $20,000.
Why This Is the Correct Answer
Option D is correct because the value change equals the NOI change divided by the unchanged rate: $12,000 ÷ 0.06 = $200,000. Since V = NOI ÷ rate is linear in NOI, the decrease in value is simply the capitalized decrease in income.
Why the Other Options Are Wrong
Option A: $720
Option A, $720, comes from multiplying the change by the rate instead of dividing: $12,000 × 0.06 = $720. The correct calculation is $12,000 ÷ 0.06 = $200,000.
Option B: $12,000
Option B, $12,000, reports the NOI change as if it were the value change. The income change must be capitalized: $12,000 ÷ 0.06 = $200,000.
Option C: $20,000
Option C, $20,000, comes from misplacing the decimal in the 6% rate: $12,000 ÷ 0.60 = $20,000. Using 0.06 gives $12,000 ÷ 0.06 = $200,000.
Capitalize the change too
A change in income is income like any other, so divide it by the rate. At 6%, one dollar of NOI is worth about 16.67 dollars of value.
How to use: Use this to find the value effect of an expense increase or rent loss without recomputing the whole value.
Exam Tip
Check the size of your answer: dividing by a rate below 100% makes the value change larger than the income change, not smaller.
Common Mistakes to Avoid
- -Multiplying the income change by the rate instead of dividing
- -Treating the income change as equal to the value change
- -Entering 6% as 0.6 instead of 0.06
Concept Deep Dive
Analysis
This question tests how sensitive value is to a change in NOI under direct capitalization. Because value equals NOI divided by the rate, a change in NOI changes value by that change divided by the same rate. At a 6% rate, each dollar of NOI is worth about 16.67 dollars of value.
Background Knowledge
Direct capitalization converts a single year's NOI into value with the formula V = I ÷ R. With the rate held constant, any change in income produces a proportional change in value equal to the income change divided by the rate. Low capitalization rates magnify the effect of income changes on value.
Real-World Application
An appraiser learns that a property's insurance cost has risen by $12,000 a year with no offsetting rent increase. Using the market-supported 6% overall rate, the appraiser recognizes the NOI loss reduces indicated value by about $200,000. This helps the client understand why the value changed from a prior report.
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Which model describes yield capitalization of property benefits?
Next Question
The subject property has annual potential base rental income of $122,000. Vacancy and collection loss is 5% of base rent. Other real property operating income, already net of its own collection loss, is $7,200. Annual property operating expenses are $21,600, including property taxes and any replacement reserve but excluding debt service. The overall capitalization rate is 10%. What is the indicated value, to the nearest dollar?