An appraiser uses the straight-line age-life method for improvements with a current cost new of $710,000, an effective age of 21 years and a total economic life of 70 years. An additional, separately measured depreciation amount of $35,000 is not reflected in the age-life estimate. There are no other deductions and no salvage value. What is the depreciated cost of the improvements?
Correct Answer
B) $462,000
Age-life depreciation=710000×21÷70=213000; remainder=710000−213000−35000+0=462000. Common errors: leaving out the separate $35,000 depreciation gives $497,000; leaving out the age-life depreciation gives $675,000; reporting total depreciation instead of the depreciated amount gives $248,000.
Why This Is the Correct Answer
Option B is correct because age-life depreciation is $710,000 × 21 ÷ 70 = $213,000. Subtracting that and the separate $35,000 item from cost new gives $710,000 − $213,000 − $35,000 = $462,000. The $35,000 is stated to be additional and not already reflected in age-life, so both deductions apply.
Why the Other Options Are Wrong
Option A: $248,000
Option A, $248,000, is total depreciation rather than the depreciated amount: $213,000 + $35,000 = $248,000. The question asks what remains after deductions, which is $710,000 − $248,000 = $462,000.
Option C: $497,000
Option C, $497,000, leaves out the separate $35,000 depreciation: $710,000 − $213,000 = $497,000. Because that item is additional and nonoverlapping, it must also be deducted, giving $462,000.
Option D: $675,000
Option D, $675,000, leaves out the age-life depreciation: $710,000 − $35,000 = $675,000. The $213,000 age-life amount ($710,000 × 21 ÷ 70) must also be deducted, giving $462,000.
Ratio, add, subtract
Find the age-life ratio, add each nonoverlapping depreciation item, then subtract the total from cost new. Stop at the remainder when the question asks for the depreciated amount.
How to use: Use this sequence on cost approach problems that mix age-life depreciation with separately measured items.
Exam Tip
Check whether the question asks for depreciation or for the depreciated amount, since the wrong choices often include both.
Common Mistakes to Avoid
- -Reporting total depreciation instead of the depreciated amount
- -Forgetting a separately measured nonoverlapping depreciation item
- -Double counting an item already captured in the age-life estimate
Concept Deep Dive
Analysis
This question tests straight-line age-life depreciation combined with a separate, nonoverlapping depreciation item. First compute age-life depreciation as cost new times effective age divided by total economic life, then subtract both depreciation amounts from cost new. The answer asked for is the depreciated improvement amount, not total depreciation.
Background Knowledge
In the straight-line age-life method, depreciation equals effective age divided by total economic life, applied to cost new. When another depreciation item is measured separately and does not overlap the age-life estimate, total depreciation is the sum of the individual estimates. Cost new minus total depreciation gives the depreciated improvement amount.
Real-World Application
An appraiser estimates replacement cost new for a house, applies age-life depreciation based on a supported effective age, and separately measures a functional loss from an outdated floor plan that the age-life ratio does not capture. Both deductions are taken from cost new to reach the depreciated improvement contribution.
More Cost Approach Questions
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