A comparable sold for $390,000; its site is worth $110,000 and its improvements would cost $350,000 new. Total depreciation by market extraction is:
Correct Answer
B) $70,000, or 20% of cost new
Why this is correct: The governing concept is the market extraction method for total depreciation. Step 1: Extract the market value of improvements from the sale: Sale Price ($390,000) - Land Value ($110,000) = $280,000. Step 2: Calculate total depreciation: Cost New ($350,000) - Extracted Improvement Value ($280,000) = $70,000. Step 3: Calculate the depreciation percentage: ($70,000 / $350,000) * 100 = 20%. Why the other choices are wrong: "$40,000, about 11% of cost" is wrong; this incorrectly subtracts cost new from sale price ($390,000 - $350,000). "$280,000, the improvement residual" is wrong; this is the extracted improvement value, not the depreciation. "$110,000, matching the land value" is wrong; this is the land value, not depreciation. Exam tip: Market extraction formula: Total Depreciation = Cost New - (Sale Price - Land Value).
Why This Is the Correct Answer
The two-step computation gives $390,000 minus $110,000 equals $280,000 of improvement value, then $350,000 minus $280,000 equals $70,000 of total depreciation, which is 20 percent of the $350,000 cost new. Both the dollar amount and the percentage in the answer are consistent with that arithmetic. The percentage matters more than the dollar figure in practice, because it is the transportable unit the appraiser carries over to the subject. Note that the extracted figure is lump-sum total depreciation and does not separate physical, functional, and external components.
Why the Other Options Are Wrong
Option A: $40,000, about 11% of cost
$40,000 comes from subtracting cost new from the sale price, $390,000 minus $350,000, which compares a whole-property price to an improvements-only cost and leaves site value dangling. The result is not depreciation at all; it is a meaningless mixture of two different scopes. The step that must never be skipped is removing site value from the sale price before touching cost.
Option C: $280,000, the improvement residual
$280,000 is the extracted contribution of the improvements, which is the intermediate result of step one rather than the answer. Selecting it means stopping one operation short, a mistake made easy by the fact that the number appears cleanly in the calculation. Depreciation is the gap between cost new and this residual, not the residual itself.
Option D: $110,000, matching the land value
$110,000 is the site value, restated. Land does not depreciate in the appraisal sense, since depreciation is a loss in improvement value from any cause, so a figure that equals land value cannot be the depreciation figure. The option is included to catch candidates who grab a familiar number under time pressure.
Sale Minus Land, Cost Minus That
Two subtractions, always in the same order. First, sale price minus land gives what the market paid for the building. Second, cost new minus that gives what the market took away. Then divide by cost new for the percentage.
How to use: Write the two subtractions as separate lines before checking the options, and label the intermediate result improvement value so you do not mistake it for the answer. If a question asks for a rate, divide the second line by cost new.
Exam Tip
The extraction method needs a reliable, independently supported site value. If a question tells you site value came from vacant land sales, that is confirmation the method is being applied properly, not scenery.
Common Mistakes to Avoid
- -Stopping at the improvement residual and reporting it as depreciation
- -Failing to deduct site value from the sale price before comparing to cost
- -Applying an extracted percentage from a comparable with a very different effective age without converting to an annual rate
Concept Deep Dive
Analysis
Market extraction, sometimes called the extraction or abstraction method, derives total accrued depreciation from the market rather than estimating each category separately. The logic runs backward through the cost approach. Start with a comparable sale of an improved property, subtract a supportable site value to leave the amount the market paid for the improvements, then compare that residual to what those improvements would cost new. The shortfall is what the market has taken away for age, wear, design, and external influences combined. Here the sale is $390,000, site value is $110,000, so the improvements drew $280,000; against a $350,000 cost new, the market has extracted $70,000, or 20 percent of cost new. That percentage can then be applied to the subject's cost new, ideally after converting it to an annual rate by dividing by the comparable's effective age.
Background Knowledge
You need the cost approach identity of site value plus depreciated improvement cost, the definition of accrued depreciation as a loss in improvement value from any cause, and the extraction method's steps. You should also know the age-life method as the alternative, where depreciation equals effective age divided by total economic life times cost new.
Real-World Application
An appraiser needs depreciation for a 30-year-old ranch and finds three improved sales in the same tract with vacant lot sales nearby. She extracts total depreciation from each, converts to a percentage of cost new, notes the range clusters near 20 percent, and applies that market-derived rate to the subject's cost new rather than relying on a textbook economic life table.
More Cost Approach Questions
In a cost approach for a proposed building, the appropriate cost basis is generally:
A warehouse cost $210,000 to build when the cost index stood at 105. The index is now 210. Its indicated current cost is:
The age-life method expresses depreciation as:
Market extraction of depreciation is limited by the fact that it:
Functional obsolescence caused by a deficiency is measured as curable when:
Curable physical deterioration is measured at cost to cure because:
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Direct costs in a construction budget include:
An appraiser writes that a 40-year-old house has an effective age of 10 but describes original wiring, original kitchen and a 25-year-old roof. The report's problem is:
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