An external influence causes an annual net income loss of $9,600. The capitalization rate for the loss is 8%, and no other economic factors change. What is the indicated loss in value of the whole property, before allocation between site and improvements?
Correct Answer
D) $120,000
9600÷0.08 = 120000. Common errors: multiplying the loss by the rate instead of dividing gives $768; treating the annual income loss as the value loss gives $9,600; misplacing the decimal in the 8% rate gives $12,000.
Why This Is the Correct Answer
Option D is correct because capitalizing the annual net income loss gives $9,600 / 0.08 = $120,000. Dividing an annual income stream by a capitalization rate converts it to a value, so the loss in value is $120,000 before allocation.
Why the Other Options Are Wrong
Option A: $768
Option A, $768, comes from multiplying the loss by the rate instead of dividing: $9,600 x 0.08 = $768. Capitalization divides income by the rate, giving $9,600 / 0.08 = $120,000.
Option B: $9,600
Option B, $9,600, treats one year's income loss as the loss in value. The annual loss must be capitalized: $9,600 / 0.08 = $120,000.
Option C: $12,000
Option C, $12,000, misplaces the decimal in the 8% rate: $9,600 / 0.8 = $12,000. Eight percent is 0.08, so the correct result is $9,600 / 0.08 = $120,000.
IRV: Income over Rate
In IRV, Value = Income / Rate. Put the annual loss in the Income spot and divide by the rate to get the value loss.
How to use: Use IRV whenever an annual income or rent loss must be turned into a value loss.
Exam Tip
Sanity-check the size of the answer: a value loss from capitalization at a single-digit rate should be many times the annual loss, not smaller than it.
Common Mistakes to Avoid
- -Multiplying the income loss by the rate instead of dividing
- -Writing 8% as 0.8 instead of 0.08
- -Treating a one-year income loss as the full value loss
Concept Deep Dive
Analysis
This question tests capitalizing an annual net income loss into a loss in value. Value equals income divided by rate, so an annual loss is divided by the capitalization rate. The result is a whole-property loss before any allocation between site and improvements.
Background Knowledge
The capitalization of rental (income) loss technique converts a measurable annual income loss into a loss in value using an appropriate capitalization rate. It can be used to measure loss in value from any cause, including external obsolescence, and the total loss may then be allocated between land and improvements.
Real-World Application
A new highway interchange creates noise that reduces achievable net rent at a small office property by a supported amount each year. The appraiser capitalizes that annual loss at a market-derived rate to estimate external obsolescence before allocating part of it to the land.
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Previous Question
The historical cost of a structure was $380,000, and a suitable index multiplier for the same construction scope is 1.40. Total depreciation of the improvements is $95,000, and site value is $175,000. What is the indicated value?
Next Question
An appraiser is developing the cost approach for a dwelling using replacement cost. A highly comparable dwelling recently sold for $390,000. At the sale date, its site was worth $110,000 and its improvement cost new was $350,000 on a replacement basis and $410,000 on a reproduction basis. What overall depreciation rate does this sale indicate for the subject?