An appraiser extracted site value from the $500,000 cash sale of a heavily improved house. A review finds that the improvements contribute $420,000 and that the appraiser's estimate of that contribution was 5% too high. By what percentage of the correct site value was the site understated?
Correct Answer
D) 26.25%
Correct land is $500,000 − $420,000 = $80,000. A 5% overstatement adds $21,000 to the contribution ($420,000 × 0.05), and that whole error falls on the land, so $21,000 ÷ $80,000 = 26.25%. Measuring the error against the sale price gives 4.20%, and assuming the land carries the same percentage error gives 5.00%. The 16.00% figure is the land's share of the price, not the error. This is why extraction is most reliable for properties with limited improvements.
Why This Is the Correct Answer
Option D is correct because the 5% overstatement equals $420,000 × 0.05 = $21,000, and all of it reduces the land remainder. Against the correct land value of $500,000 − $420,000 = $80,000, the understatement is $21,000 ÷ $80,000 = 26.25%.
Why the Other Options Are Wrong
Option A: 4.20%
Option A, 4.20%, divides the $21,000 error by the $500,000 sale price. The error is measured here as a share of correct site value, so the base is $80,000 and the result is 26.25%.
Option B: 5.00%
Option B, 5.00%, assumes the percentage error carries over unchanged. The 5% applies to the $420,000 contribution; the same $21,000 is 26.25% of the $80,000 land value.
Option C: 16.00%
Option C, 16.00%, is $80,000 ÷ $500,000, the land's share of the price. That ratio describes the property and does not measure the error, which is $21,000 ÷ $80,000 = 26.25%.
Same Dollars, Smaller Base
The dollar error stays the same when it moves from improvements to land, but the base shrinks. A smaller base means a bigger percentage.
How to use: Use this idea to judge how an improvement estimate error affects an extracted land value.
Exam Tip
For a percentage error, find the base first. Here the base is the correct site value, not the price or the contribution.
Common Mistakes to Avoid
- -Assuming a 5% improvement error produces a 5% land error
- -Measuring the land error against the whole sale price
- -Confusing the land-to-total ratio with the size of the error
Concept Deep Dive
Analysis
Sensitivity can be measured directly. Land is what remains after the improvements are removed, so a dollar error in the improvements becomes the same dollar error in the land. When the land is a small part of the price, that dollar error is a large percentage of the land.
Background Knowledge
Extraction estimates land by subtracting the value contribution of the improvements from total property value. Because land is the remainder, any error in the improvement estimate lands on it in full. The method is therefore most reliable where improvements are limited and the remainder is relatively large.
Real-World Application
An appraiser extracts land from the sale of a nearly new, heavily improved property and gets a small remainder. Knowing that a modest cost error could swing that remainder widely, the appraiser gives the indication less weight than one from a sale with limited improvements.
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?
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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?
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Comparable sales indicate that land accounts for 28% of total property value. An improved property is valued at $1,650,000. What land value does allocation indicate?
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