Total improvement cost new is $420,000, including separately treated short-lived cost $58,000 with supported loss $24,000. Apply an 18% physical-loss ratio only to the remaining long-lived cost. No other loss applies. What TOTAL physical depreciation results?
Correct Answer
C) $89,160
(420000−58000)×0.18+24000 = 89160. Common errors: applying the 18% to total cost instead of only the long-lived cost gives $99,600; leaving out the short-lived component loss gives $65,160; applying 18% to total cost and ignoring the short-lived loss gives $75,600.
Why This Is the Correct Answer
Option C is correct because the long-lived cost is $420,000 - $58,000 = $362,000, and 18% of that is $65,160. Adding the separately supported short-lived loss of $24,000 gives total physical depreciation of $89,160.
Why the Other Options Are Wrong
Option A: $65,160
Option A, $65,160, is wrong because it is only the long-lived loss ($362,000 x 0.18) and leaves out the $24,000 short-lived loss. The total is $89,160.
Option B: $75,600
Option B, $75,600, is wrong because it applies 18% to the whole $420,000 cost ($420,000 x 0.18) and ignores the separate $24,000 short-lived loss. The ratio belongs only on the $362,000 long-lived cost, giving $89,160 after adding $24,000.
Option D: $99,600
Option D, $99,600, is wrong because it applies 18% to the full $420,000 ($75,600) and then adds $24,000, so the short-lived cost is depreciated twice. Using the $362,000 long-lived base gives $89,160.
Pull short-lived out first
Remove short-lived cost from the base, apply the long-lived rate to what is left, then add back the short-lived loss.
How to use: Use this whenever a question separates short-lived and long-lived components.
Exam Tip
When a rate is said to apply only to the remaining long-lived cost, subtract the short-lived cost before multiplying. Then remember to add the short-lived loss.
Common Mistakes to Avoid
- -Applying the long-lived rate to total cost including short-lived items
- -Forgetting to add the short-lived component loss
- -Depreciating short-lived items twice through both the rate and their own loss
Concept Deep Dive
Analysis
This question tests separating short-lived and long-lived components when measuring physical depreciation. The short-lived items ($58,000) carry their own supported loss of $24,000, and the 18% ratio applies only to the remaining long-lived cost, $420,000 - $58,000 = $362,000. Total physical depreciation is $362,000 x 0.18 + $24,000 = $89,160.
Background Knowledge
In the breakdown method, short-lived components such as roofs and finishes are often depreciated separately from long-lived structural components. To avoid double counting, the long-lived depreciation rate is applied only to the cost that remains after short-lived items are removed, and the separate estimates are then summed.
Real-World Application
An appraiser depreciates a worn roof and old carpet separately based on their observed condition, then applies an age-based percentage to the rest of the structure. Adding the two results gives total physical deterioration without counting the roof and carpet twice.
More Cost Approach Questions
Why can equivalent-utility replacement cost be useful for an obsolete improvement?
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What best supports a claimed loss from a bathroom-layout deficiency?
Improvement cost new is $1,850,000. Separately supported improvement depreciation deductions of $310,000, $620,000 are expressly nonoverlapping and not already excluded from cost new. No site is included. What depreciated improvement amount results?
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A cost total $650,000 explicitly includes $40,000 of non-realty FF&E outside the appraised real-property interest. Exclude it. Supported realty-only total depreciation is $55,000. Add site $200,000, with no overlap. What real-property cost indication results?
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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?
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