Three recent vacant-land sales of similar highest-and-best-use acreage closed at: Comp A $1,320,000 for 15.0 acres; Comp B $990,000 for 11.0 acres; Comp C $1,140,000 for 12.0 acres. The subject is 9.5 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) $864,500
Rates = $1,320,000/15 = $88,000; $990,000/11 = $90,000; $1,140,000/12 = $95,000; mean = $91,000/acre; 9.5 × $91,000 = $864,500. The indicated result is $864,500. Common errors: dividing the sum of the unit rates by 2 instead of 3 gives $1,296,750; using the lowest unit rate gives $836,000; using the highest unit rate gives $902,500.
Why This Is the Correct Answer
Option B is correct because the unit rates are $1,320,000 ÷ 15 = $88,000, $990,000 ÷ 11 = $90,000 and $1,140,000 ÷ 12 = $95,000. Their mean is $273,000 ÷ 3 = $91,000 per acre, and 9.5 × $91,000 = $864,500.
Why the Other Options Are Wrong
Option A: $836,000
Option A, $836,000, applies only the lowest unit rate: 9.5 × $88,000 = $836,000. The question asks for the mean rate, so 9.5 × $91,000 = $864,500.
Option C: $902,500
Option C, $902,500, applies only the highest unit rate: 9.5 × $95,000 = $902,500. The mean rate of $91,000 gives 9.5 × $91,000 = $864,500.
Option D: $1,296,750
Option D, $1,296,750, divides the sum of the rates by 2 instead of 3: $273,000 ÷ 2 = $136,500, and 9.5 × $136,500 = $1,296,750. The correct mean is $273,000 ÷ 3 = $91,000, giving $864,500.
Divide, average, multiply
Divide each price by its size, average the unit rates, then multiply by the subject's size.
How to use: Use this three-step sequence for any mean unit price land problem.
Exam Tip
Count the comparables and divide by that number when averaging rates.
Common Mistakes to Avoid
- -Dividing the sum of rates by the wrong count
- -Using only the lowest or highest comparable rate
- -Averaging total prices instead of unit prices
Concept Deep Dive
Analysis
This question tests deriving a mean unit price per acre and applying it to the subject. Each comparable's price is divided by its acreage, the three rates are averaged, and the mean is multiplied by the subject's 9.5 acres.
Background Knowledge
Price per acre is one of the standard units of comparison for vacant land. Appraisers convert each sale to a unit price so differently sized parcels can be compared, then reconcile the unit prices into a rate for the subject. An arithmetic mean is one way to summarize the rates when the comparables are equally reliable.
Real-World Application
An appraiser values a 9.5-acre tract using three recent acreage sales of similar highest and best use. After converting each to price per acre and finding no remaining differences, she averages the rates and applies the result to the subject's acreage.
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A comparable commercial site with 65 front feet sold for a cash-equivalent price of $585,000. Per standard appraisal guidance, sale price per front foot is a vacant-land unit of comparison when frontage is a primary value determinant. The subject site has 72 front feet and is otherwise similar. What indicated land value does the front-foot unit support before other adjustments?