The subject is a vacant site of 19,500 square feet. Three recent sales of vacant parcels with a similar highest and best use are: Comp A, $900,000 for 18,000 square feet; Comp B, $1,040,000 for 20,000 square feet; Comp C, $1,188,000 for 22,000 square feet. No other adjustments are needed. Based on the mean of the three sales' prices per square foot, what is the indicated land value?
Correct Answer
B) $1,014,000
Rates = $900,000/18,000 = $50; $1,040,000/20,000 = $52; $1,188,000/22,000 = $54; mean = $52/SF; 19,500 SF × $52/SF = $1,014,000. The indicated result is $1,014,000. Common errors: pooling total prices and areas instead of averaging the unit rates gives $1,016,600; using the lowest unit rate gives $975,000; applying the mean rate to the comparables' average size of 20,000 SF instead of the subject's 19,500 SF gives $1,040,000.
Why This Is the Correct Answer
Option B is correct because the rates are $900,000 ÷ 18,000 = $50, $1,040,000 ÷ 20,000 = $52 and $1,188,000 ÷ 22,000 = $54 per square foot. Their mean is $52, and 19,500 × $52 = $1,014,000.
Why the Other Options Are Wrong
Option A: $975,000
Option A, $975,000, applies only the lowest rate: 19,500 × $50 = $975,000. The mean rate of $52 gives 19,500 × $52 = $1,014,000.
Option C: $1,016,600
Option C, $1,016,600, pools totals instead of averaging rates: $3,128,000 ÷ 60,000 = about $52.13, and × 19,500 = $1,016,600. The question asks for the mean of the unit rates, $52, giving $1,014,000.
Option D: $1,040,000
Option D, $1,040,000, applies the $52 mean rate to the comparables' average size, (18,000 + 20,000 + 22,000) ÷ 3 = 20,000 square feet, instead of the subject's area: 20,000 × $52 = $1,040,000. The subject's 19,500 square feet gives 19,500 × $52 = $1,014,000.
Average the rates, not totals
A mean unit price averages each comparable's rate; pooling total prices over total area is a different, size-weighted figure.
How to use: Use this when a question specifies the mean of unit prices.
Exam Tip
Follow the exact averaging method the question names, since a pooled rate and a mean of rates can give different answers.
Common Mistakes to Avoid
- -Pooling total prices and areas when the mean of rates is required
- -Using only the lowest rate
- -Applying the mean rate to the comparables' average size instead of the subject's area
Concept Deep Dive
Analysis
This question tests deriving a mean price per square foot from several comparables and applying it to the subject. Each sale is converted to a unit rate, the rates are averaged, and the mean is multiplied by the subject's 19,500 square feet.
Background Knowledge
Price per square foot is a standard unit of comparison for vacant land. Converting each sale to a unit price allows comparison of parcels of different sizes. A simple mean of unit rates differs slightly from a pooled rate, which weights larger sales more heavily.
Real-World Application
An appraiser values a 19,500-square-foot infill lot using three similar vacant sales. She converts each to price per square foot, averages the rates because the sales are equally comparable, and applies the result to the subject's area.
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