After curable and short-lived components are excluded, the remaining long-lived cost new is $240,000. The long-lived components have an effective age of 12 years and a total life of 60 years, with straight-line depreciation. What is the long-lived physical depreciation?
Correct Answer
B) $48,000
240000×12÷60=48000. Common errors: reporting the remaining (undepreciated) amount instead of depreciation gives $192,000; taking only one year of depreciation (240,000 ÷ 60) gives $4,000; dividing by the 48-year remaining life instead of the 60-year total life gives $60,000.
Why This Is the Correct Answer
Option B is correct because $240,000 x 12/60 = $48,000. The ratio is applied only to the long-lived base, so short-lived and curable items are not depreciated twice. The question asks for the depreciation, not the remaining value.
Why the Other Options Are Wrong
Option A: $4,000
Option A is wrong because $4,000 is only one year of depreciation: $240,000 / 60 = $4,000. With an effective age of 12 years, depreciation is $4,000 x 12 = $48,000.
Option C: $60,000
Option C is wrong because $60,000 comes from dividing by the 48-year remaining life instead of the 60-year total life: $240,000 x 12 / 48 = $60,000. The correct figure is $240,000 x 12 / 60 = $48,000.
Option D: $192,000
Option D is wrong because $192,000 is the remaining, undepreciated amount: $240,000 x (1 - 12/60) = $192,000. The question asks for the depreciation, which is $48,000.
Right base, right ratio
Apply the age-life ratio only to the long-lived base that remains after short-lived and curable items are taken out.
How to use: Use this when a breakdown question asks for long-lived physical depreciation.
Exam Tip
Check that you apply the ratio to the stated base and that you report depreciation rather than the remaining value.
Common Mistakes to Avoid
- -Applying the ratio to full cost new instead of the long-lived base
- -Reporting the remaining value instead of the depreciation
- -Using remaining life in the denominator
Concept Deep Dive
Analysis
This question tests applying age-life depreciation only to the long-lived component base after curable and short-lived items are removed. The ratio is 12/60 = 20%, applied to the $240,000 long-lived base. The result is $48,000 of long-lived physical depreciation.
Background Knowledge
In the breakdown method, physical deterioration is calculated separately for short-lived and long-lived components to avoid depreciating short-lived items twice. The long-lived base is what remains of cost new after curable and short-lived items are removed.
Real-World Application
After separately handling the roof, carpet and water heater, an appraiser has $240,000 of long-lived building cost left. Using a 12-year effective age and 60-year life, the appraiser estimates $48,000 of long-lived physical deterioration.
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