An appraiser is testing the depreciation estimate for a house that recently sold for $640,000 in a cash transaction. Recent vacant lot sales in the subdivision indicate a site value of $190,000, and the current replacement cost new of the house is $800,000. What total accrued depreciation does the sale indicate?
Correct Answer
D) $350,000
The sale less the land leaves the improvement contribution: $640,000 − $190,000 = $450,000. Cost new less that contribution is the implied depreciation: $800,000 − $450,000 = $350,000. Comparing cost new with the sale price and ignoring the land gives $160,000, and reporting the land figure gives $190,000. Subtracting the land twice leaves $260,000, which is not a depreciation measure at all.
Why This Is the Correct Answer
Option D is correct because the sale price less the supported land value leaves the improvement contribution: $640,000 − $190,000 = $450,000. Replacement cost new less that contribution is the depreciation the market recognized: $800,000 − $450,000 = $350,000.
Why the Other Options Are Wrong
Option A: $160,000
Option A, $160,000, comes from $800,000 − $640,000, which compares cost new with a price that includes the land. The correct route removes the land first: $800,000 − ($640,000 − $190,000) = $350,000.
Option B: $190,000
Option B, $190,000, is the supported lot value, not a measure of depreciation. It is only an input; the implied depreciation is $800,000 − $450,000 = $350,000.
Option C: $260,000
Option C, $260,000, results from subtracting the land twice: $640,000 − $190,000 − $190,000. The land is removed once to give a $450,000 contribution, and $800,000 − $450,000 = $350,000.
Price, Land, Contribution, Cost
Walk down the chain: price minus land gives contribution, then cost new minus contribution gives depreciation. Each step uses the answer from the step before.
How to use: Use this chain whenever a sale, a land value and a cost new appear together and the unknown is depreciation.
Exam Tip
Before calculating, identify which component is missing. When the land value is given, land is not the unknown.
Common Mistakes to Avoid
- -Comparing cost new directly with a sale price that still includes land
- -Stopping at the $450,000 contribution and treating it as depreciation
- -Reporting the land value out of habit when the unknown is depreciation
Concept Deep Dive
Analysis
The extraction relationship can be solved for any one unknown. Price equals land plus the improvement contribution, and the contribution equals cost new less depreciation. With land known from vacant sales, the contribution comes out first and depreciation follows from it.
Background Knowledge
Extraction treats a property's total value as land plus the contribution of the improvements. That contribution is typically estimated as replacement cost new less depreciation. The same relationship can be rearranged to solve for whichever one component is unknown.
Real-World Application
An appraiser in a built-up subdivision has good vacant lot sales and several house sales. By removing the supported lot value from each house sale and comparing the remainder with current cost new, the appraiser tests the depreciation estimate used in the cost approach.
More Land/Site Questions
How should an appraiser account for a site's access to public sewer compared with competing sites that require septic systems?
Which fact, if supported by competitive-market evidence, most directly supports a unit-price premium for an otherwise comparable site?
A rectangular site's frontage is doubled while its depth is halved, keeping area constant. What is the likely value effect in a retail district?
A downtown site's zoning height limit is reduced from six stories to three. Buyers in this market had been paying for six-story development potential. What effect on land value is most supportable?
A zoning change increases permitted density from four to eight units per acre. What is the likely effect on site value?
Using the allocation method, market evidence supports a typical land-to-total-property-value ratio of 28% for similar improved properties in the subject’s location. An improved comparable sold for $825,000. What land (site) contribution is indicated by applying that ratio?
An appraiser is valuing a vacant site near a landfill. A similar vacant site that is not affected by the landfill sold for $480,000. Paired land sales indicate that proximity to the landfill lowers site prices by $70,000. No other adjustments apply. What is the indicated value of the subject site?
An appraiser is extracting site value from a $600,000 cash sale. The seller's records show an original construction cost of $250,000 and a depreciated book value of $110,000. The appraiser estimates current replacement cost new at $400,000 and accrued depreciation from all causes at $100,000. What is the indicated site value?
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