An improved property sold for $675,000. Replacement cost new of the improvements is $510,000 and total accrued depreciation is estimated at $140,000. Using the extraction method, what is the indicated site value?
Correct Answer
D) $305,000
Depreciated improvement contribution is $510,000 − $140,000 = $370,000. Subtract it from $675,000 to obtain $305,000 for land. The sale and improvement estimate must refer to matching property rights and condition; that compatibility is assumed in this calculation.
Why This Is the Correct Answer
Option D is correct because extraction subtracts the value contribution of the improvements from total property value. The depreciated improvement contribution is $510,000 − $140,000 = $370,000, and $675,000 − $370,000 = $305,000 for the site.
Why the Other Options Are Wrong
Option A: $165,000
Option A, $165,000, subtracts the full replacement cost new without deducting depreciation: $675,000 − $510,000 = $165,000. The improvements contribute only their depreciated value of $370,000, so the site is $305,000.
Option B: $370,000
Option B, $370,000, is the depreciated improvement contribution ($510,000 − $140,000), not the site value. The site is the remainder: $675,000 − $370,000 = $305,000.
Option C: $535,000
Option C, $535,000, subtracts only the depreciation from the sale price: $675,000 − $140,000 = $535,000. The correct step subtracts the depreciated improvement value: $675,000 − ($510,000 − $140,000) = $305,000.
Price minus depreciated building
Extraction: site = sale price − (cost new − depreciation). Depreciate the building first, then subtract.
How to use: Use this order of operations on each extraction calculation.
Exam Tip
When a question gives both cost new and depreciation, compute depreciated cost before subtracting from the sale price.
Common Mistakes to Avoid
- -Subtracting replacement cost new instead of depreciated cost
- -Reporting the improvement contribution as site value
- -Subtracting only the depreciation from the sale price
Concept Deep Dive
Analysis
This question tests the extraction method. First compute the depreciated value contribution of the improvements, then subtract it from the sale price. The remainder indicates site value.
Background Knowledge
Extraction is often used for properties where improvements contribute little to total value or where depreciation can be estimated reliably, such as in rural areas. The sale price and the improvement estimate must refer to the same property rights and condition.
Real-World Application
An appraiser in a rural county with few vacant land sales analyzes a recent sale of an older farmhouse on acreage. She estimates the house's replacement cost and accrued depreciation and subtracts the depreciated contribution from the sale price to extract a land indication.
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