A functional deficiency causes an annual net income loss of $18,000 that is expected to persist. The capitalization rate for the loss, on the same income basis, is 7.5%. What is the indicated loss in value?
Correct Answer
D) $240,000
18000÷0.075 = 240000. Common errors: multiplying the loss by the rate instead of dividing gives $1,350; treating the annual income loss as the value loss gives $18,000; misplacing the decimal in the 7.5% rate gives $24,000.
Why This Is the Correct Answer
Option D is correct because $18,000 / 0.075 = $240,000. Dividing a persistent annual net income loss by a compatible rate converts it into a present value loss. This is the capitalization of rental (income) loss technique.
Why the Other Options Are Wrong
Option A: $1,350
Option A is wrong because $1,350 comes from multiplying the loss by the rate, $18,000 x 0.075 = $1,350, instead of dividing. The value loss is $18,000 / 0.075 = $240,000.
Option B: $18,000
Option B is wrong because $18,000 is the annual income loss, not the value loss. An ongoing income loss must be capitalized: $18,000 / 0.075 = $240,000.
Option C: $24,000
Option C is wrong because $24,000 results from misplacing the decimal in the 7.5% rate: $18,000 / 0.75 = $24,000. The rate is 0.075, so $18,000 / 0.075 = $240,000.
Income over rate equals value
IRV: Value = Income / Rate. A lost income stream becomes a lost value by dividing by the rate.
How to use: Use this whenever an annual income loss must be converted to a value loss.
Exam Tip
Whenever the rate is below 100%, the capitalized value loss exceeds the annual income loss, and at typical rates it is many times larger. If your answer is smaller than the annual loss, you probably multiplied instead of dividing.
Common Mistakes to Avoid
- -Multiplying the income loss by the rate
- -Reporting the annual income loss as the value loss
- -Converting 7.5% to 0.75 instead of 0.075
Concept Deep Dive
Analysis
This question tests capitalizing an income loss into a value loss. When an annual net income loss is expected to persist, value loss equals the annual loss divided by a compatible capitalization rate. Here $18,000 / 0.075 = $240,000.
Background Knowledge
The capitalization of rental loss technique can measure loss in value from any cause, including functional and external obsolescence. The income loss and the rate must be on a compatible basis, such as net income with a net-based rate.
Real-World Application
A small office building's outdated layout forces lower rent, cutting net income by $18,000 a year. Using a market-supported 7.5% rate, the appraiser estimates about $240,000 of functional obsolescence.
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