The subject property is an 8,000-sf vacant lot. No vacant lots have sold recently in the subdivision, but a house on a similar 10,000-sf lot sold for $420,000 cash. The improvements on that property contribute $270,000, and lots in the subdivision trade on a price-per-square-foot basis. What is the indicated value of the subject lot?
Correct Answer
A) $120,000
Extraction gives land of $420,000 − $270,000 = $150,000, or $150,000 ÷ 10,000 = $15 per square foot. Applied to the subject, $15 × 8,000 = $120,000. Stopping at $150,000 skips the size difference, and scaling by 10,000 ÷ 8,000 gives $187,500, which inverts the ratio. Using the improvement contribution per square foot gives $27 × 8,000 = $216,000.
Why This Is the Correct Answer
Option A is correct because the sale's land remainder is $420,000 − $270,000 = $150,000, which equals $15 per square foot on 10,000 square feet. Lots in this subdivision trade by the square foot, so $15 × 8,000 = $120,000.
Why the Other Options Are Wrong
Option B: $150,000
Option B, $150,000, is the land value of the comparable's 10,000-square-foot lot ($420,000 − $270,000). The subject is smaller, and the $15 rate gives $15 × 8,000 = $120,000.
Option C: $187,500
Option C, $187,500, equals $150,000 × 10,000 ÷ 8,000, which inverts the size ratio and makes the smaller lot worth more. The correct scaling is $15 × 8,000 = $120,000.
Option D: $216,000
Option D, $216,000, equals $27 × 8,000, where $27 is $270,000 ÷ 10,000. That unitizes the improvement contribution rather than the land; the land rate is $15, which gives $120,000.
Extract, Unitize, Then Apply
Three moves in order: subtract improvements, divide by the comparable's size, multiply by the subject's size.
How to use: Use this sequence when an improved sale must support the value of a lot of a different size.
Exam Tip
Check which property each figure belongs to. A smaller subject at the same supported unit rate should show a smaller land value than the comparable.
Common Mistakes to Avoid
- -Using the comparable's extracted land value without adjusting for size
- -Dividing the improvement contribution or total price by lot area instead of the land value
- -Inverting the size ratio when scaling between lots
Concept Deep Dive
Analysis
Two skills are linked: extracting land from an improved sale, then converting that land value into a unit of comparison. The extracted figure belongs to the comparable's lot, not the subject's. It has to be expressed per square foot before it can be applied to a different size.
Background Knowledge
Sale prices are often converted into units of comparison so that properties of different sizes can be compared. Extraction can supply a land figure when vacant sales are limited. Once extracted, that figure can be unitized in the same way as a vacant land sale when the market supports it.
Real-World Application
In an infill neighborhood, an appraiser finds no recent vacant lot sales but several small-house sales. The appraiser extracts a land value from each, converts it to a price per square foot and applies the resulting rate to the vacant lot being appraised.
More Land/Site Questions
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Which fact, if supported by competitive-market evidence, most directly supports a unit-price premium for an otherwise comparable site?
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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?
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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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An improved property sold for $1,760,000 on a cash-equivalent basis. For similar properties in the market area, land represents 25% of total value. What land value does the allocation method indicate?
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