For an arithmetic illustration, allocate historical construction cost $2,400,000 over 40 years on a zero-salvage equal annual schedule. After 8 years, what scheduled unindexed amount remains? This is not a current market-value conclusion.
Correct Answer
C) $1,920,000
2400000×(1−8÷40) = 1920000. Common errors: reporting the accumulated depreciation instead of the remaining amount gives $480,000; not depreciating the historical cost gives $2,400,000; dividing by the 32-year remaining life instead of the 40-year schedule gives $1,800,000.
Why This Is the Correct Answer
Option C is correct because an equal annual zero-salvage schedule allocates 8/40, or 20%, of the cost after 8 years, leaving 80%. $2,400,000 × (1 − 8 ÷ 40) = $1,920,000. The figure is a scheduled book amount and is not a current market-value conclusion.
Why the Other Options Are Wrong
Option A: $480,000
Option A, $480,000, is the accumulated allocation, not the remaining amount: $2,400,000 × 8 ÷ 40 = $480,000. The remaining scheduled amount is $2,400,000 − $480,000 = $1,920,000.
Option B: $1,800,000
Option B, $1,800,000, results from using 8/32 (elapsed years over the 32-year remaining period) as the allocated fraction: $2,400,000 × (1 − 8/32) = $1,800,000. The schedule runs over 40 years, so the remainder is $2,400,000 × (1 − 8/40) = $1,920,000.
Option D: $2,400,000
Option D, $2,400,000, is the original historical cost with nothing allocated. After 8 years of a 40-year schedule, $480,000 has been charged, leaving $1,920,000.
Book Schedule Is Not Market
Book remainder = Historical cost × (1 − Years elapsed ÷ Scheduled life). It is a bookkeeping figure, not a value opinion.
How to use: Use this to separate accounting schedules from appraisal depreciation on the exam.
Exam Tip
When a question labels a figure as an accounting or scheduled amount, compute it as asked but do not treat it as market value.
Common Mistakes to Avoid
- -Reporting accumulated depreciation instead of the remaining amount
- -Treating book value as market value
- -Dividing by the remaining years instead of the full schedule
Concept Deep Dive
Analysis
This question uses an accounting-style equal annual schedule, not a market-value measure of depreciation. After 8 of 40 years, 8/40 of the historical cost has been allocated, and the question asks what unindexed amount remains on the schedule.
Background Knowledge
For accounting purposes, depreciation is set when the asset is new, based on a preselected life that determines the periodic charge. This book depreciation differs from appraisal depreciation, which measures loss in value from all causes as of the effective date. A book remainder does not by itself indicate market value.
Real-World Application
A client shows an appraiser a depreciation schedule for a building that cost $2,400,000 eight years ago. The appraiser notes the $1,920,000 book remainder but estimates market value from current cost, market-derived depreciation and other evidence.
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