A property sold for $315,000. The improvements had a replacement cost new of $240,000 and accrued depreciation of $90,000. What land value does extraction indicate?
Correct Answer
C) $165,000
Why this is correct: The extraction method calculates land value as Sale Price - Depreciated Improvement Cost. Here, depreciated improvement cost is $240,000 - $90,000 = $150,000. Land value is $315,000 - $150,000 = $165,000. Why the other choices are wrong: "$75,000" is wrong; it results from subtracting replacement cost new ($240,000) from sale price. "$150,000" is wrong; it is the depreciated improvement cost, not the land value. "$225,000" is wrong; it results from adding depreciation to the sale price. Exam tip: In extraction, land value = sale price - (cost new - total accrued depreciation).
Why This Is the Correct Answer
Depreciated improvement value is $240,000 less $90,000 of accrued depreciation, or $150,000, and $315,000 − $150,000 leaves $165,000 as the indicated land value.
Why the Other Options Are Wrong
Option A: $75,000
$75,000 subtracts the full replacement cost new of $240,000 from the sale price, ignoring accrued depreciation.
Option B: $150,000
$150,000 is the depreciated value of the improvements, not the land residual.
Option D: $225,000
$225,000 subtracts only the $90,000 of depreciation from the sale price, omitting the improvements' remaining value.
Price Minus Depreciated Improvements
Price Minus Depreciated Improvements. Cost new less depreciation first, then subtract from the price.
How to use: Do the depreciation subtraction before touching the sale price. Every wrong answer skips or reverses that step.
Exam Tip
Any depreciation error passes straight into the land figure, so extraction is least reliable where improvements dominate the value.
Common Mistakes to Avoid
- -Subtracting cost new rather than depreciated cost
- -Subtracting only the accrued depreciation
- -Using extraction where improvements dominate the property's value
Concept Deep Dive
Analysis
Extraction values land by subtraction: take the total sale price and remove the depreciated value of the improvements, leaving the land as the residual. Here the improvements' contribution is replacement cost new of $240,000 less accrued depreciation of $90,000, or $150,000, and $315,000 − $150,000 = $165,000 for the land. The method is most useful where land sales are scarce but improved sales are available, and it works best where improvements are a small proportion of total value — because any error in estimating depreciation transfers dollar for dollar into the land figure. That sensitivity is its principal weakness: on a property where improvements represent most of the value, a modest depreciation misestimate can swamp the land conclusion entirely. The distractors correspond to the three arithmetic slips available: subtracting cost new instead of depreciated cost, subtracting only the depreciation, and subtracting only the depreciation from cost new without reference to the sale price.
Background Knowledge
Extraction estimates land value by deducting the depreciated value of improvements from a property's sale price. It is used where land sales are scarce and is most reliable where improvements represent a small share of total value.
Real-World Application
An appraiser lacking vacant land sales extracts land value from three improved sales, deducting depreciated improvement costs and reconciling the residuals.
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In a land residual analysis for a proposed office development, the appraiser estimates total annual net operating income (NOI) will be $1,250,000. The improvement value, derived via the cost approach, is $15,000,000. Market evidence indicates a 7.0% overall capitalization rate is appropriate for similar improved properties. What is the indicated land value?