An improved property sold for $480,000. Current replacement cost new of its improvements is $360,000, with accrued depreciation of 25% of cost new. Using extraction and no other adjustments, what land value is indicated?
Correct Answer
B) $210,000
Depreciated improvement cost is $360,000 × (1 − 0.25) = $270,000. Subtract it from the sale price: $480,000 − $270,000 = $210,000. Subtracting depreciation alone or the full undepreciated cost would use the wrong component.
Why This Is the Correct Answer
Option B is correct because the depreciated improvement cost is $360,000 × (1 − 0.25) = $270,000, and $480,000 − $270,000 = $210,000. Extraction subtracts the value contribution of the improvements from total property value. Using the depreciated figure, not cost new or depreciation alone, gives the correct land indication.
Why the Other Options Are Wrong
Option A: $120,000
Option A, $120,000, subtracts the full undepreciated cost: $480,000 − $360,000 = $120,000. The improvements contribute only their depreciated cost of $270,000, so land is $480,000 − $270,000 = $210,000.
Option C: $270,000
Option C, $270,000, is the depreciated improvement cost ($360,000 × 0.75), not the land. Land is what remains after subtracting it from the sale price: $480,000 − $270,000 = $210,000.
Option D: $390,000
Option D, $390,000, subtracts only the depreciation amount: $360,000 × 0.25 = $90,000, and $480,000 − $90,000 = $390,000. The deduction should be the depreciated improvement cost of $270,000, giving $210,000.
Depreciate first, then subtract
Turn cost new into depreciated cost before subtracting it from the sale price; what remains is land.
How to use: Use this sequence when an extraction problem gives cost new and a depreciation percentage.
Exam Tip
Label each figure as cost new, depreciation or depreciated cost before you subtract, so you deduct the right component.
Common Mistakes to Avoid
- -Subtracting cost new instead of depreciated cost
- -Subtracting only the depreciation amount
Concept Deep Dive
Analysis
This question tests extraction when the improvement contribution must first be computed from cost new and a depreciation percentage. Depreciated cost equals cost new times one minus the depreciation rate. That depreciated cost is then subtracted from the sale price to find land value.
Background Knowledge
In the cost approach, depreciated improvement cost equals cost new minus accrued depreciation. Extraction uses that depreciated contribution to separate land value from an improved sale. Errors usually come from subtracting the wrong component.
Real-World Application
An older home sold for $480,000. The appraiser estimates replacement cost new of the house at $360,000 with 25% accrued depreciation, giving a $270,000 contribution and an extracted land value of $210,000.
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