Vacant land may be valued by a multi-comparable mean unit price ($/acre) applied to the subject’s acreage. Three similar vacant sales: Comp A $840,000 for 8.0 acres; Comp B $1,080,000 for 10.0 acres; Comp C $714,000 for 7.0 acres. Subject is 6.4 acres (no other adjustments). What indicated land value by mean $/acre results?
Correct Answer
B) $672,000
Unit prices = $840,000/8 = $105,000; $1,080,000/10 = $108,000; $714,000/7 = $102,000; mean = $105,000/acre; 6.4 × $105,000 = $672,000. The indicated value is $672,000. This is the result under the stated inputs, not a universal market ratio or an approval of a proposed development. Common errors: averaging the total sale prices instead of unit prices, with no size adjustment, gives $2,634,000 ÷ 3 = $878,000; using the lowest unit rate gives $652,800; dividing total price by total acreage (a size-weighted $105,360 per acre) gives $674,304.
Why This Is the Correct Answer
Option B is correct because the unit prices are $840,000 ÷ 8 = $105,000, $1,080,000 ÷ 10 = $108,000 and $714,000 ÷ 7 = $102,000, with a mean of $315,000 ÷ 3 = $105,000 per acre. Applying it gives 6.4 × $105,000 = $672,000.
Why the Other Options Are Wrong
Option A: $652,800
Option A, $652,800, uses the lowest unit rate: 6.4 × $102,000 = $652,800. The mean rate is $105,000, giving 6.4 × $105,000 = $672,000.
Option C: $674,304
Option C, $674,304, divides total price by total acreage, $2,634,000 ÷ 25 = $105,360, a size-weighted rate, and applies it: 6.4 × $105,360 = $674,304. The question calls for the mean of the three unit prices, $105,000, giving $672,000.
Option D: $878,000
Option D, $878,000, averages the total sale prices, $2,634,000 ÷ 3 = $878,000, and ignores that the comparables are larger than the 6.4-acre subject. Converting to price per acre first gives a $105,000 mean and 6.4 × $105,000 = $672,000.
Convert, average, apply
First turn each sale into a per-acre price, then average them, then multiply by the subject's acres.
How to use: Use this order when a question gives sale prices and sizes rather than unit rates.
Exam Tip
Average unit prices, not whole sale prices, and check that the mean falls between the lowest and highest unit rates.
Common Mistakes to Avoid
- -Averaging total sale prices instead of unit prices
- -Pooling total price over total acreage instead of averaging unit prices
- -Using a single extreme sale's unit rate
Concept Deep Dive
Analysis
This question tests deriving a mean unit price from several sales. Convert each sale to price per acre, average the three unit prices, then apply the mean to the subject's acreage. Averaging whole sale prices skips the unit conversion and ignores the size differences.
Background Knowledge
Converting each sale to a common unit such as price per acre allows sales of different sizes to be compared. The arithmetic mean sums the values and divides by the number of observations.
Real-World Application
An appraiser values a 6.4-acre parcel using three nearby acreage sales of different sizes. She converts each to price per acre, compares the mean with her adjusted analysis, and considers whether size differences call for further adjustment.
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