Sale price per acre is a vacant-land unit of comparison. A comparable vacant tract of 15.0 acres sold for a cash-equivalent $1,800,000 and is otherwise similar to the subject in HBU and market conditions. What indicated site value does that unadjusted per-acre rate support for a subject tract of 11.0 acres?
Correct Answer
B) $1,320,000
Rate = $1,800,000/15 = $120,000/acre; subject = 11 × $120,000 = $1,320,000. The indicated result is $1,320,000. Common errors: using the comparable price without adjusting for acreage gives $1,800,000; inverting the acreage ratio gives $2,454,545; valuing only the acreage difference gives $480,000.
Why This Is the Correct Answer
Option B is correct because the comparable's unit rate is $1,800,000 / 15 acres = $120,000 per acre, and the subject indication is 11 x $120,000 = $1,320,000. The comparable is otherwise similar in highest and best use and market conditions. Price per acre is a recognized unit of comparison for vacant land.
Why the Other Options Are Wrong
Option A: $480,000
Option A, $480,000, values only the acreage difference: (15 - 11) x $120,000 = $480,000. The subject has 11 acres, so 11 x $120,000 = $1,320,000.
Option C: $1,800,000
Option C, $1,800,000, uses the comparable's total price without adjusting for the difference in acreage. The subject is smaller: 11 x ($1,800,000 / 15) = $1,320,000.
Option D: $2,454,545
Option D, $2,454,545, inverts the acreage ratio: $1,800,000 / 11 x 15 = $2,454,545. The correct calculation is $1,800,000 / 15 x 11 = $1,320,000.
Divide the comp, multiply the subject
Divide the comparable's price by its acres, then multiply by the subject's acres.
How to use: Use this order to set up any price-per-unit extraction problem.
Exam Tip
A smaller subject should indicate less total value than the larger comparable at the same unit rate; use that to eliminate inverted answers.
Common Mistakes to Avoid
- -Inverting the acreage ratio
- -Using the comparable's total price as the subject's value
- -Ignoring possible size effects on unit price when market evidence shows them
Concept Deep Dive
Analysis
This question tests extracting a price per acre from a comparable and applying it to the subject. The comparable's price is divided by its acreage to get a unit rate, which is then multiplied by the subject's acreage. Keeping the ratio direction right avoids inverted results.
Background Knowledge
Units of comparison such as price per acre let appraisers compare parcels of different sizes. The unit rate is extracted by dividing price by size and is applied to the subject's size. Size differences may also affect unit price, which the appraiser considers when market evidence shows it.
Real-World Application
An appraiser values an 11-acre tract of agricultural land. A nearby 15-acre tract with similar soils and access recently sold, so the appraiser extracts its price per acre and applies it to the subject.
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