An improved property sold for $480,000. The improvements have a replacement cost new of $360,000 and have suffered 25 percent accrued depreciation. Using extraction, what is the indicated land value?
Correct Answer
B) $210,000
Why this is correct: Depreciated improvement value = $360,000 × (1 - 0.25) = $270,000. Land value = Sale price - depreciated improvement value = $480,000 - $270,000 = $210,000. Why the other choices are wrong: '$120,000' subtracts full cost new without depreciation. '$270,000' is the improvement value, not land. '$330,000' incorrectly adds depreciation. Exam tip: In extraction, land value = sale price - depreciated improvement value.
Why This Is the Correct Answer
The two-step arithmetic gives $210,000. Depreciated improvement value equals $360,000 times one minus 0.25, which is $360,000 times 0.75, or $270,000. Land value equals the sale price of $480,000 less that $270,000, which is $210,000. The order matters: depreciation is applied to the improvements before the subtraction, never to the sale price, because the sale price already reflects the market's view of the depreciated whole.
Why the Other Options Are Wrong
Option A: $120,000
$120,000 is what you get by subtracting the full replacement cost new of $360,000 from the $480,000 sale price without deducting the 25 percent depreciation first. That treats the buyer as having paid for a brand-new building, which overstates the improvement contribution by $90,000 and understates land by the same amount. It is the single most common extraction error and it always pushes land value too low.
Option C: $270,000
$270,000 is the depreciated value of the improvements, not the land. It is the intermediate figure produced by the first step, offered as though it were the answer to skim past the subtraction. Anyone who computes $360,000 times 0.75 and stops has done half the technique.
Option D: $330,000
$330,000 comes from adding the $90,000 of depreciation to the $240,000 that a different wrong path produces, or equivalently from crediting the depreciation to land instead of removing it from the improvements. Depreciation is a loss in improvement value and never becomes an addition anywhere in the calculation. The figure has no defensible derivation from the given data.
Age The Building, Then Subtract
Two moves in a fixed order. First age the building by multiplying cost new by what is left after depreciation, so 25 percent gone means 0.75 remains. Then subtract that aged number from the sale price. The leftover is the dirt.
How to use: Whenever a stem gives a sale price, a cost new, and a depreciation percentage, write the multiplier before touching the sale price. If your answer matches sale price minus cost new exactly, you skipped the aging step and picked the trap.
Exam Tip
Extraction problems seed the answer set with the intermediate figures, so before selecting, confirm that your number is a land value and not the depreciated improvement value you calculated on the way there.
Common Mistakes to Avoid
- -Subtracting replacement cost new instead of the depreciated improvement value
- -Applying the depreciation percentage to the sale price rather than to the improvements
- -Reporting the depreciated improvement value as the land value indication
Concept Deep Dive
Analysis
Extraction is a site valuation technique used when vacant land sales are scarce, and it works by backing the improvements out of an improved sale price. The logic runs in one direction only: take a sale of an improved property, estimate the depreciated contributory value of the improvements, and treat the remainder as the indicated land value. The critical step, and the one this item is built around, is that the improvements must be carried at their depreciated value rather than at replacement cost new, because a buyer of a used building does not pay for the depreciation already suffered. Here the improvements cost $360,000 new and have lost 25 percent, so their depreciated value is $360,000 multiplied by 0.75, which is $270,000. Subtracting that from the $480,000 sale price leaves $210,000 as the indicated land value. Extraction is generally regarded as less reliable than direct comparison of vacant land sales, since every error in the depreciation estimate lands entirely on the land figure.
Background Knowledge
You need the extraction formula, which is sale price less depreciated improvement contribution equals indicated land value, and the fact that depreciated value equals cost new times one minus the accrued depreciation rate. You should know that extraction is used where vacant land sales are unavailable, that it is most reliable when improvements are a small share of total value, and that it is distinct from allocation, which applies a typical land-to-value ratio. You also need comfort converting a percentage of depreciation into a remaining-value multiplier.
Real-World Application
Appraising a rural site in a market with no vacant land sales in two years, the appraiser extracts land value from three improved sales by estimating each building's cost new from a cost service and its accrued depreciation from effective age and total economic life. The three extracted indications are reconciled to a per-acre figure, and the report notes the reduced reliability caused by the depreciation estimates.
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