The current cost new of the improvements is $640,000, with an effective age of 18 years and a total economic life of 60 years. A separately measured depreciation amount of $28,000 applies to the improvements in addition to straight-line age-life depreciation and is not reflected in it. There are no other deductions and no salvage value. What is the depreciated cost of the improvements?
Correct Answer
B) $420,000
Age-life depreciation=640000×18÷60=192000; remainder=640000−192000−28000+0=420000. Common errors: leaving out the separate $28,000 depreciation gives $448,000; leaving out the age-life depreciation gives $612,000; reporting total depreciation instead of the depreciated amount gives $220,000.
Why This Is the Correct Answer
Option B is correct because age-life depreciation is $640,000 x 18 / 60 = $192,000. Subtracting that and the separate $28,000 from cost new gives $640,000 - $192,000 - $28,000 = $420,000. Both losses are deducted once because they do not overlap.
Why the Other Options Are Wrong
Option A: $220,000
Option A, $220,000, is total depreciation rather than the depreciated amount: $640,000 x 18 / 60 + $28,000 = $220,000. Subtracting that from $640,000 gives the requested $420,000.
Option C: $448,000
Option C, $448,000, leaves out the separate $28,000 depreciation: $640,000 - $192,000 = $448,000. That loss is additional, so the result is $420,000.
Option D: $612,000
Option D, $612,000, leaves out the age-life depreciation: $640,000 - $28,000 = $612,000. The $192,000 age-life amount must also be deducted, giving $420,000.
Add the losses, then subtract
Add all the nonoverlapping losses into one total, then subtract that total from cost new.
How to use: Use add then subtract when a problem gives more than one depreciation item.
Exam Tip
Check whether a separate depreciation item is stated as additional or already included. If it is additional and nonoverlapping, deduct it along with the age-life amount.
Common Mistakes to Avoid
- -Reporting total depreciation instead of the depreciated value
- -Dropping the separately measured depreciation item
- -Double-counting a loss already in the age-life estimate
Concept Deep Dive
Analysis
This question tests combining age-life depreciation with a separate, nonoverlapping depreciation item. Compute age-life depreciation from effective age over total life, add the separate $28,000 loss, and subtract both from cost new. The question asks for the depreciated amount, not total depreciation.
Background Knowledge
Total depreciation can be built by adding separate estimates for different causes, as in the breakdown method. When an item is measured separately and not already captured in the age-life estimate, it is added to the total. Care is needed to avoid counting the same loss twice.
Real-World Application
An appraiser applies age-life depreciation to a building and separately measures a loss from an outdated floor plan that the age-life estimate does not capture. She deducts both from cost new to find the depreciated improvement value.
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