Improvements with a current cost new of $520,000 have an effective age of 22 years and a total economic life of 55 years. Using the straight-line age-life method, with no salvage value or other deductions, what is the depreciated cost of the improvements?
Correct Answer
C) $312,000
Age-life depreciation=520000×22÷55=208000; remainder=520000−208000−0+0=312000. Common errors: reporting the depreciation instead of the depreciated amount gives $208,000; stopping at cost new, before depreciation gives $520,000; dividing by the 33-year remaining life instead of the 55-year total life gives $173,333.
Why This Is the Correct Answer
Option C is correct because age-life depreciation is $520,000 x 22 / 55 = $208,000. Subtracting it from cost new gives $520,000 - $208,000 = $312,000, the depreciated improvement amount.
Why the Other Options Are Wrong
Option A: $173,333
Option A, $173,333, uses the 33-year remaining life instead of the 55-year total life: $520,000 x (1 - 22/33) = $173,333. The age-life ratio uses total life, so the remainder is $520,000 x (1 - 22/55) = $312,000.
Option B: $208,000
Option B, $208,000, is the depreciation, not the depreciated amount: $520,000 x 22 / 55 = $208,000. Subtracting it from cost new gives $312,000.
Option D: $520,000
Option D, $520,000, is cost new with no depreciation taken. Deducting $208,000 of age-life depreciation gives $312,000.
Age over life comes off
Effective age over total life is the share that comes off cost new. What is left is the depreciated value.
How to use: Use age over life comes off to separate depreciation from the value remaining.
Exam Tip
Expect options for both depreciation and the depreciated amount. Re-read the question's final words to see which it wants.
Common Mistakes to Avoid
- -Reporting depreciation when the depreciated value is asked
- -Using remaining life as the denominator
- -Leaving cost new undepreciated
Concept Deep Dive
Analysis
This question tests straight-line age-life depreciation and the resulting depreciated improvement value. Compute depreciation as cost new times effective age over total life, then subtract it from cost new. The question asks for the depreciated amount, not depreciation itself.
Background Knowledge
Straight-line age-life depreciation divides effective age by total economic life to get a depreciation percentage. That percentage times cost new is the depreciation, and cost new minus depreciation is the depreciated improvement value. Remaining life over total life gives the same depreciated value directly.
Real-World Application
An appraiser estimates that a 22-year effective-age building has a 55-year total economic life. She depreciates cost new by 40% and carries the remaining 60% forward as the depreciated improvement value in her cost approach.
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Previous Question
A review appraiser is checking a depreciation extraction from a $625,000 improved sale with improvement cost new of $520,000. The appraisal used a site value of $175,000, but better land sales show that the site was worth $150,000 at the sale date. What effect did the site value error have on the extracted depreciation?
Next Question
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?