An appraiser is extracting site value from the $600,000 cash sale of a house with an over-built addition. Replacement cost new less physical deterioration totals $500,000. Paired sales indicate that the over-improvement causes a further $120,000 loss in the value of the improvements. What is the indicated site value?
Correct Answer
D) $220,000
Extraction subtracts the value contribution of the improvements, and cost less physical wear leaves out the over-improvement. The contribution is $500,000 − $120,000 = $380,000, so site value is $600,000 − $380,000 = $220,000. Subtracting the $500,000 alone gives $100,000, which charges the land with the over-improvement. Reporting the $120,000 loss as the answer, or averaging the $500,000 and $380,000 to reach $160,000, does not follow the method.
Why This Is the Correct Answer
Option D is correct because cost less physical wear omits the over-improvement loss, so the improvements contribute $500,000 − $120,000 = $380,000. Extraction subtracts that contribution from the price: $600,000 − $380,000 = $220,000.
Why the Other Options Are Wrong
Option A: $100,000
Option A, $100,000, comes from $600,000 − $500,000. It treats cost less physical wear as the contribution, which pushes the over-improvement loss onto the land; the contribution is $380,000, which gives $600,000 − $380,000 = $220,000.
Option B: $120,000
Option B, $120,000, is the over-improvement loss itself. That loss is a form of depreciation, not land value; land is $600,000 − ($500,000 − $120,000) = $220,000.
Option C: $160,000
Option C, $160,000, averages the $500,000 and the $380,000 contribution to $440,000 and subtracts from $600,000. Averaging a contribution with a figure that omits a known loss has no basis; land is $600,000 − $380,000 = $220,000.
Contribution Beats Cost
Ask what the improvements add to the price, not what they would cost. Cost is a tool for estimating contribution, and the market's figure wins when supported.
How to use: Use this reminder when both a depreciated cost and a market-derived contribution are available.
Exam Tip
Watch for wording such as 'physical deterioration' alone. It signals that a cost figure may not reflect all depreciation.
Common Mistakes to Avoid
- -Treating cost less physical wear as if it captured all depreciation
- -Reducing land value for an over-improvement loss that belongs to the improvements
- -Averaging two improvement figures rather than deciding which is supported
Concept Deep Dive
Analysis
The candidate must see that the cost figure is not yet the contribution. Cost less only physical wear does not account for the over-improvement, so the loss comes off first, and the resulting contribution is what is subtracted from the price.
Background Knowledge
Depreciation in appraisal covers all sources of loss in value, not physical wear alone. An over-improvement can make an improvement contribute less than its cost. Depreciated cost is a typical way to estimate contribution, and it serves that purpose only when it captures those losses.
Real-World Application
A homeowner in a modest neighborhood built an oversized wing that buyers do not pay for in full. Paired sales show the improvements add less than cost less wear, so the appraiser subtracts the lower market-supported figure when extracting land.
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Market data show that vacant sites near a wastewater treatment plant sell for $77,000 less than similar sites elsewhere, based on paired land sales. The subject vacant site is near such a plant. A comparable vacant site that is not near one sold for $512,000. No other adjustments apply. What is the indicated land value of the subject?
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Frontage is the primary unit of comparison for the subject site, which has 75 front feet. Market data indicate a unit price of $2,800 per front foot. What is the indicated land value?