The current cost new of the improvements is $680,000. Straight-line physical depreciation is 14/56 of cost new. In addition, an annual net income loss of $12,000 is attributable only to the improvements and is not included in physical depreciation; the appropriate capitalization rate for this loss is 8%. There are no other losses, and land is excluded. What amount remains for the improvements after both deductions?
Correct Answer
A) $360,000
680000−680000×14÷56−12000÷0.08 = 360000. Common errors: leaving out the capitalized income loss gives $510,000; deducting the annual income loss instead of its capitalized value gives $498,000; leaving out the physical depreciation gives $530,000.
Why This Is the Correct Answer
Option A is correct because physical depreciation is $680,000 x 14 / 56 = $170,000, and the capitalized income loss is $12,000 / 0.08 = $150,000. Deducting both from cost new gives $680,000 - $170,000 - $150,000 = $360,000.
Why the Other Options Are Wrong
Option B: $498,000
Option B, $498,000, deducts the annual income loss rather than its capitalized value: $680,000 - $170,000 - $12,000 = $498,000. An annual loss must be capitalized, $12,000 / 0.08 = $150,000, giving $360,000.
Option C: $510,000
Option C, $510,000, leaves out the capitalized income loss: $680,000 - $680,000 x 14 / 56 = $510,000. Deducting the $150,000 capitalized loss gives $360,000.
Option D: $530,000
Option D, $530,000, leaves out the physical depreciation: $680,000 - $12,000 / 0.08 = $530,000. Deducting the $170,000 physical depreciation as well gives $360,000.
Income loss divided by rate
An annual income loss becomes a value loss when you divide it by the cap rate: income over rate equals value.
How to use: Use income over rate to convert any annual loss into a lump-sum depreciation figure.
Exam Tip
Do not subtract an annual dollar loss directly from a value figure; convert it with the capitalization rate first. Then check that each loss is deducted once.
Common Mistakes to Avoid
- -Deducting the annual loss without capitalizing it
- -Multiplying the income loss by the rate instead of dividing
- -Leaving out physical depreciation
Concept Deep Dive
Analysis
This question tests combining linear physical depreciation with a capitalized income loss. Physical depreciation is a fraction of cost new, while the income loss must be converted to a value loss by dividing the annual net income loss by the capitalization rate. Both are then deducted from cost new.
Background Knowledge
The capitalization of rental or income loss technique converts an annual loss into a value loss by dividing it by an appropriate capitalization rate. It can measure loss from any cause when the loss is supported and allocated correctly. Physical depreciation measured separately with the age-life method is then added to reach total depreciation.
Real-World Application
A small office building loses rent because of a nearby nuisance that affects the building's income. The appraiser capitalizes the annual net income loss at a market-supported rate, deducts that amount along with physical depreciation, and arrives at a depreciated improvement value.
More Cost Approach Questions
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