The subject property has stabilized annual NOI of $180,000. Comparable sales, with income measured on the same basis, indicate an overall capitalization rate of 8.5%. What value is indicated by direct capitalization, rounded to the nearest dollar?
Correct Answer
C) $2,117,647
180000÷0.085 = 2117647.06. Common errors: multiplying NOI by the rate instead of dividing gives $15,300; misplacing the decimal in the rate gives $211,765; shifting the rate’s decimal the other way (0.85% for 8.5%) gives $21,176,471.
Why This Is the Correct Answer
Option C is correct because $180,000 / 0.085 = $2,117,647.06, which rounds to $2,117,647. Direct capitalization divides NOI by the overall rate expressed as a decimal. The NOI and rate are on the same income basis, so no further adjustment is needed.
Why the Other Options Are Wrong
Option A: $15,300
Option A, $15,300, comes from multiplying NOI by the rate instead of dividing: $180,000 x 0.085 = $15,300. The correct calculation is $180,000 / 0.085 = $2,117,647.
Option B: $211,765
Option B, $211,765, comes from misplacing the decimal in the rate, using 0.85 instead of 0.085: $180,000 / 0.85 = about $211,765. The correct value is $180,000 / 0.085 = $2,117,647.
Option D: $21,176,471
Option D, $21,176,471, comes from shifting the rate's decimal the other way, using 0.85% (0.0085) for 8.5%: $180,000 / 0.0085 = about $21,176,471. Using 0.085 gives $2,117,647.
IRV: income, rate, value
Income equals rate times value, so value equals income divided by rate. Convert the percent to a decimal first.
How to use: Use this to set up any one-step capitalization problem.
Exam Tip
Estimate the answer first: $180,000 divided by roughly 0.085 should be about $2 million, which quickly rules out decimal-shift options.
Common Mistakes to Avoid
- -Multiplying NOI by the cap rate
- -Entering 8.5% as 0.85
- -Entering 8.5% as 0.0085
Concept Deep Dive
Analysis
This question tests basic direct capitalization with V = I / R. The rate must be converted from 8.5% to the decimal 0.085 before dividing. The distractors come from multiplying instead of dividing or shifting the decimal in the rate.
Background Knowledge
Direct capitalization estimates value by dividing a single year's NOI by an appropriate overall capitalization rate. Overall rates are commonly derived from comparable sales by dividing NOI by sale price.
Real-World Application
An appraiser has stabilized NOI of $180,000 for a neighborhood shopping strip and market support for an 8.5% overall rate. Dividing gives an indicated value of about $2,117,647, which is then rounded for the report.
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