Three recent vacant-land sales of similar highest-and-best-use acreage closed at: Comp A $1,050,000 for 12.0 acres; Comp B $960,000 for 10.0 acres; Comp C $1,250,000 for 12.5 acres. The subject is 8.0 acres and is otherwise comparable after unit-price reconciliation. Per standard appraisal guidance sales-comparison land valuation using $/acre, what indicated land value results after taking the arithmetic mean of the three $/acre unit prices and applying it to the subject?
Correct Answer
B) $756,000
Rates = $1,050,000/12 = $87,500; $960,000/10 = $96,000; $1,250,000/12.5 = $100,000; mean = $94,500/acre; 8 × $94,500 = $756,000. The indicated value is $756,000. This is the result under the stated inputs, not a universal market ratio or an approval of a proposed development. Common errors: dividing the sum of the unit rates by 2 instead of 3 gives $1,134,000; using the lowest unit rate gives $700,000; using the highest unit rate gives $800,000.
Why This Is the Correct Answer
Option B is correct because the rates are $1,050,000 / 12 = $87,500, $960,000 / 10 = $96,000 and $1,250,000 / 12.5 = $100,000. Their mean is $283,500 / 3 = $94,500 per acre, and 8 × $94,500 = $756,000. This follows the stated method exactly.
Why the Other Options Are Wrong
Option A: $700,000
Option A, $700,000, uses the lowest unit rate: 8 × $87,500 = $700,000. The mean rate of $94,500 gives 8 × $94,500 = $756,000.
Option C: $800,000
Option C, $800,000, uses the highest unit rate: 8 × $100,000 = $800,000. The mean rate of $94,500 gives $756,000.
Option D: $1,134,000
Option D, $1,134,000, divides the sum of the unit rates by 2 instead of 3: $283,500 / 2 = $141,750, and 8 × $141,750 = $1,134,000. Dividing by 3 gives $94,500 and $756,000.
Unitize, average, apply
Turn each sale into a price per acre, average those rates, then apply the average to the subject's acres.
How to use: Use this three-step routine on any multi-comparable acreage problem.
Exam Tip
Compute each comparable's unit rate separately; averaging total prices or total acres can give a different and incorrect result for this method.
Common Mistakes to Avoid
- -Dividing the sum of rates by the wrong count
- -Using the lowest or highest rate instead of the mean
- -Averaging total prices before converting to unit rates
Concept Deep Dive
Analysis
This question tests computing unit prices per acre, averaging them, and applying the mean to the subject. Each comparable's price must be divided by its own acreage before averaging. The mean rate is then multiplied by the subject's 8.0 acres.
Background Knowledge
Price per acre is a common unit of comparison for larger vacant tracts. Converting each sale to a unit price allows sales of different sizes to be compared. The arithmetic mean is one way to summarize the unit prices, though appraisers also weigh the comparability of each sale.
Real-World Application
An appraiser valuing an 8-acre rural tract finds three recent sales of similar acreage with the same highest and best use. After converting each to a price per acre and confirming they bracket the subject, the appraiser applies the mean rate.
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