A property sold for $525,000. Improvements had a replacement cost new of $390,000 with 30 percent accrued depreciation. What land value does extraction indicate?
Correct Answer
A) $252,000
Why this is correct: Land value by extraction = Sale Price - Depreciated Value of Improvements. Depreciated improvement value = Replacement Cost New × (1 - Depreciation Rate) = $390,000 × 0.70 = $273,000. Land value = $525,000 - $273,000 = $252,000. Why the other choices are wrong: $135,000 is the accrued depreciation amount ($390,000 × 0.30). $273,000 is the depreciated improvement value, not the land value. $117,000 is an incorrect subtraction ($390,000 - $273,000). Exam tip: In extraction, subtract the improvement's depreciated value from the total price to isolate land value.
Why This Is the Correct Answer
Option A is correct at $252,000, following the two-step sequence exactly. Applying the 70 percent remaining factor to cost new gives $273,000 of depreciated improvement contribution, and deducting that from the $525,000 price isolates the land. Each step uses the figures as given, with no additional adjustment introduced. A reasonableness check supports it as well, since $252,000 is roughly 48 percent of the total, a plausible land-to-value ratio in many markets.
Why the Other Options Are Wrong
Option B: $135,000
The $135,000 figure is the accrued depreciation itself, $390,000 times 0.30, which is an intermediate quantity rather than a value of anything. Depreciation is what you remove from cost new, not what you attribute to the land. Stopping at this number means the candidate computed the deduction and then subtracted from the wrong base, or simply reported the wrong intermediate.
Option C: $273,000
The $273,000 figure is the depreciated contribution of the improvements, which is the number you deduct from the sale price rather than the answer. It is the correct output of step one and the correct input to step two, which makes it the most attractive wrong choice in the set. Anyone who computes carefully but stops one step early lands exactly here.
Option D: $117,000
The $117,000 figure comes from subtracting the depreciated improvement value from cost new, $390,000 less $273,000, which mixes two quantities that were never meant to be differenced and in fact just recomputes the depreciation with rounding. The sale price never enters that calculation, so the land value cannot possibly emerge from it. Whenever a candidate answer ignores the sale price entirely, it cannot be an extraction result.
Peel the Building Off the Price
Extraction peels the building off the price. First figure out what the building is worth today, cost new less depreciation, then peel that off the sale price and whatever is left underneath is the dirt. Two steps, and the price must appear in the second one.
How to use: Write the two lines before computing: depreciated improvements equals cost new times one minus the depreciation rate, then land equals sale price minus that result. Then check whether the answer you chose used the sale price at all, because every wrong choice in these items is an intermediate that skipped it.
Exam Tip
In multi-step math items, identify which intermediate values the distractors represent; if your answer matches an intermediate, you stopped one step early.
Common Mistakes to Avoid
- -Reporting the depreciated improvement value as the land value
- -Applying the depreciation rate to the sale price rather than to cost new
- -Relying on extraction where improvements are new and dominate value, magnifying depreciation error
Concept Deep Dive
Analysis
This question tests the extraction method of site valuation, sometimes called abstraction, which derives land value by removing the depreciated contribution of the improvements from an improved sale price. The sequence is fixed: estimate the improvements' cost new, subtract all accrued depreciation to get their present contribution, then subtract that contribution from the sale price, and what remains is the indicated land value. Here cost new is $390,000 and depreciation is 30 percent, so the improvements contribute $390,000 times 0.70, or $273,000, and $525,000 minus $273,000 leaves $252,000 for the land. Extraction is most reliable where improvements are a small share of total value and depreciation is modest, such as rural or older properties, because any error in the depreciation estimate transfers dollar for dollar into the land conclusion. It is a secondary technique used when vacant land sales are scarce, and its result should be tested against whatever direct land evidence exists.
Background Knowledge
You need to know the recognized site valuation techniques, including sales comparison, extraction, allocation, subdivision development, land residual, and ground rent capitalization, and when each is appropriate. You should also know that accrued depreciation comprises physical deterioration, functional obsolescence, and external obsolescence, and that extraction is most dependable where improvements are relatively minor or the depreciation estimate is well supported.
Real-World Application
In a rural county with almost no vacant land sales, an appraiser extracts site value from five improved sales, estimating cost new from a national cost service with a local multiplier and supporting depreciation from effective age and remaining economic life. The five indications cluster between $46,000 and $53,000 per acre, and the report notes extraction's sensitivity to the depreciation estimate.
More Land/Site Questions
Under which condition is the land residual technique most applicable?
Why can the same physical parcel carry different values in two assignments?
In a built-up area where no vacant land has sold for years, which approach to site value is the usual fallback?
How is entrepreneurial profit treated in the subdivision development method?
A land comparable sold 18 months ago in a market rising about 4 percent a year. What adjustment direction applies?
Why does a developer's required profit rise for a longer subdivision project?
How does holding cost enter the valuation of land bought for future development?
Excess land is best described as land that has which characteristic?
Plottage value arises in which of the following situations?
Which of the following is an off-site improvement rather than a site improvement?
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