An external influence has reduced the annual net income of the subject property by $21,600. Market data indicate an 8% capitalization rate for this income loss, and all other economic factors are unchanged. What is the capitalized loss to the whole property, before allocation between site and improvements?
Correct Answer
D) $270,000
21600÷0.08 = 270000. Common errors: multiplying the loss by the rate instead of dividing gives $1,728; treating the annual income loss as the value loss gives $21,600; misplacing the decimal in the 8% rate gives $27,000.
Why This Is the Correct Answer
Option D is correct because the capitalized loss equals the annual net income loss divided by the rate: $21,600 / 0.08 = $270,000. This is the whole-property loss before any allocation between site and improvements. The technique may be used to measure loss of value from any cause, including an external influence.
Why the Other Options Are Wrong
Option A: $1,728
Option A, $1,728, comes from $21,600 x 0.08 = $1,728, which multiplies the loss by the rate instead of dividing. Capitalizing requires $21,600 / 0.08 = $270,000.
Option B: $21,600
Option B, $21,600, treats the annual income loss itself as the value loss. A one-year income figure must be capitalized into value: $21,600 / 0.08 = $270,000.
Option C: $27,000
Option C, $27,000, comes from $21,600 / 0.8 = $27,000, which misplaces the decimal in the 8% rate. Eight percent is 0.08, so the result is $21,600 / 0.08 = $270,000.
Income over rate equals value
Use I / R = V: divide the annual loss by the capitalization rate to get the value loss. Dividing by a rate below 1 makes the number larger, not smaller.
How to use: Use this as a quick check that a capitalized loss is larger than the annual loss when the rate is below 100%.
Exam Tip
If your answer is smaller than the annual income loss, you probably multiplied instead of divided. Convert the percentage to a decimal carefully before dividing.
Common Mistakes to Avoid
- -Multiplying the income loss by the rate
- -Reporting the annual loss as the value loss
- -Writing 8% as 0.8 instead of 0.08
Concept Deep Dive
Analysis
This question applies the capitalization of rental (income) loss technique to measure an external loss. An annual net income loss is converted into a lump-sum value loss by dividing it by a compatible capitalization rate. The distractors come from multiplying instead of dividing, failing to capitalize, or misplacing the rate's decimal.
Background Knowledge
Capitalization of income loss converts a supported annual loss in net income into an estimate of value loss using the formula value = income / rate. The rate must be compatible with the income being capitalized. When the influence is external, the resulting whole-property loss may then need to be allocated between site and improvements before use in the cost approach.
Real-World Application
A new truck route next to a small apartment building causes supported rent concessions that reduce net income by a measurable amount each year. The appraiser capitalizes that annual loss at a market-supported rate to estimate the value loss from this external obsolescence. In the cost approach, the appraiser then allocates the loss between land and improvements as appropriate.
More Cost Approach Questions
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