An improved property sold for $525,000. Current replacement cost new of its improvements is $390,000, with accrued depreciation of 30% of cost new. Using extraction and no other adjustments, what land value is indicated?
Correct Answer
A) $252,000
Depreciated improvement cost is $390,000 × (1 − 0.3) = $273,000. Subtract it from the sale price: $525,000 − $273,000 = $252,000. Subtracting depreciation alone or the full undepreciated cost would use the wrong component.
Why This Is the Correct Answer
Option A is correct because depreciated improvement cost is $390,000 × (1 − 0.30) = $273,000. Subtracting that from the sale price gives $525,000 − $273,000 = $252,000 as the extracted land value.
Why the Other Options Are Wrong
Option B: $135,000
Option B, $135,000, subtracts the full undepreciated cost: $525,000 − $390,000 = $135,000. The improvements contribute only their depreciated cost of $273,000, so land is $252,000.
Option C: $273,000
Option C, $273,000, is the depreciated improvement value, $390,000 × 0.70, not the land value. Land is the remainder: $525,000 − $273,000 = $252,000.
Option D: $408,000
Option D, $408,000, subtracts only the depreciation: $525,000 − ($390,000 × 0.30) = $525,000 − $117,000 = $408,000. The full depreciated improvement contribution of $273,000 must be subtracted, giving $252,000.
Price minus depreciated building
Land equals what the buyer paid minus what the building is worth today, which is cost new less depreciation.
How to use: Use this to set up an extraction problem and avoid subtracting the wrong cost figure.
Exam Tip
Compute depreciated cost first, then subtract it from the price; distractors often subtract cost new or depreciation alone.
Common Mistakes to Avoid
- -Subtracting replacement cost new instead of depreciated cost
- -Subtracting only the depreciation amount
- -Reporting the depreciated improvement value as land value
Concept Deep Dive
Analysis
This question tests the extraction method of land valuation. You compute the depreciated contribution of the improvements and subtract it from the sale price. The key is to subtract depreciated cost, not cost new and not depreciation alone.
Background Knowledge
Extraction estimates site value by subtracting the contribution of the improvements from the total price of an improved sale. It works best when improvements contribute little to value or their depreciated cost can be estimated reliably.
Real-World Application
In a rural area with few vacant land sales, an appraiser finds a sale of an older home on acreage. Estimating replacement cost and depreciation for the house, the appraiser subtracts its depreciated value from the price to extract a land value indication.
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