For an arithmetic illustration only, depreciate a historical $2,000,000 construction cost on a zero-salvage straight-line 40-year schedule for 10 years. What unindexed scheduled amount remains? This is not a conclusion of current market value or current replacement cost.
Correct Answer
C) $1,500,000
2000000×(1−10÷40) = 1500000. Common errors: reporting the accumulated depreciation instead of the remaining amount gives $500,000; not depreciating the historical cost gives $2,000,000; dividing by the 30-year remaining life instead of the 40-year schedule gives $1,333,333.
Why This Is the Correct Answer
Option C is correct because 10 of 40 years have passed, so 10/40 = 25% of the cost is written off and 75% remains. $2,000,000 x (1 - 10/40) = $2,000,000 x 0.75 = $1,500,000. This is the unindexed scheduled amount remaining.
Why the Other Options Are Wrong
Option A: $500,000
Option A, $500,000, is the accumulated depreciation, not the amount remaining: $2,000,000 x 10/40 = $500,000. The remaining amount is $2,000,000 - $500,000 = $1,500,000.
Option B: $1,333,333
Option B, $1,333,333, divides by the 30-year remaining life instead of the 40-year schedule: $2,000,000 x (1 - 10/30) = $1,333,333. The schedule is 40 years, so the remainder is $2,000,000 x (1 - 10/40) = $1,500,000.
Option D: $2,000,000
Option D, $2,000,000, is the original historical cost with no depreciation taken. Ten years on a 40-year schedule reduce it by $500,000, leaving $1,500,000.
Book life is not market
A book schedule tells you how much cost has been written off, not what a buyer would pay. Keep the two ideas separate.
How to use: Use this reminder when a question mixes historical cost schedules with appraisal concepts.
Exam Tip
Check whether the question wants the amount written off or the amount remaining. A disclaimer that the result is not market value signals a straight arithmetic exercise.
Common Mistakes to Avoid
- -Reporting accumulated depreciation as the remaining amount
- -Using remaining life as the schedule denominator
- -Treating a book value as a market value
Concept Deep Dive
Analysis
This question tests a purely arithmetic straight-line schedule applied to a historical cost. You compute the share of the 40-year schedule that has elapsed and subtract it from the original cost. The stem stresses that the result is a book-style remainder, not a market value or current replacement cost.
Background Knowledge
Accounting depreciation uses a preselected life set when the asset is new to spread its cost over time. Appraisal depreciation, by contrast, measures the loss in value from current cost new based on market evidence. A scheduled book remainder is not by itself an estimate of market value.
Real-World Application
A client hands an appraiser a depreciation schedule from the company's tax records showing a building's remaining book value. The appraiser explains that this figure reflects an accounting write-off and that her cost approach starts instead from current cost new with market-supported depreciation.
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