For an arithmetic schedule only, allocate historical cost $2,500,000 over 40 years with zero residual. After 8 years, what unindexed scheduled amount remains? This is not an estimate of current market value.
Correct Answer
C) $2,000,000
2500000×(1−8÷40) = 2000000. Common errors: reporting the accumulated depreciation instead of the remaining amount gives $500,000; not depreciating the historical cost gives $2,500,000; dividing by the 32-year remaining life instead of the 40-year schedule gives $1,875,000.
Why This Is the Correct Answer
Option C is correct because $2,500,000 x (1 - 8/40) = $2,500,000 x 0.80 = $2,000,000 remains on the schedule after 8 years. The annual charge is $62,500, and 8 years of it total $500,000, leaving $2,000,000.
Why the Other Options Are Wrong
Option A: $500,000
Option A, $500,000, is $2,500,000 x 8/40, the accumulated amount allocated so far, not the remaining amount. The remainder is $2,500,000 - $500,000 = $2,000,000.
Option B: $1,875,000
Option B, $1,875,000, comes from $2,500,000 x (1 - 8/32), which wrongly divides by the 32-year remaining life instead of the 40-year schedule. The schedule uses 40 years, giving $2,000,000.
Option D: $2,500,000
Option D, $2,500,000, is the full historical cost with no allocation applied. After 8 of 40 years, $500,000 has been allocated, leaving $2,000,000.
Used fraction out, rest remains
Years used over total years is the share gone; one minus that share is what remains on the schedule.
How to use: Use this when a question asks for the remaining amount on a straight-line schedule.
Exam Tip
Check whether the question asks for the amount allocated or the amount remaining, since both figures usually appear as options.
Common Mistakes to Avoid
- -Reporting accumulated depreciation instead of the remaining amount
- -Dividing by remaining life instead of total scheduled life
- -Treating a book value as an estimate of market value
Concept Deep Dive
Analysis
This is an arithmetic schedule question, not a market-value question. A straight-line schedule over 40 years allocates the same amount each year, so after 8 years, 8/40 of the cost has been allocated and 32/40 remains. The question asks for the remaining scheduled amount.
Background Knowledge
Accounting depreciation sets a rate when an asset is new based on a preselected life and allocates historical cost over that life. Appraisal depreciation instead measures loss in value from cost new as of the effective date, so a book schedule is not a market value estimate.
Real-World Application
An owner shows an appraiser a book value from an accounting depreciation schedule. The appraiser notes that the schedule figure reflects historical cost allocation and does not by itself indicate the building's market-supported depreciation or value.
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The subject is a 10-year-old dwelling with improvement cost new of $640,000. A highly comparable 7-year-old dwelling recently sold for $580,000; at the sale date its site was worth $150,000 and its improvement cost new was $500,000. Market evidence shows depreciation accruing evenly with actual age. What is the depreciated value of the subject improvements?
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