Three recent vacant-land sales of similar highest-and-best-use acreage closed at: Comp A $960,000 for 8.0 acres; Comp B $1,100,000 for 10.0 acres; Comp C $1,040,000 for 8.0 acres. The subject is 7.5 acres in the same competitive market (no other adjustments). Per standard appraisal guidance sales comparison for land, what indicated land value by mean $/acre × subject acres results?
Correct Answer
B) $900,000
Rates = $960,000/8 = $120,000; $1,100,000/10 = $110,000; $1,040,000/8 = $130,000; mean = $120,000/acre; subject = 7.5 × $120,000 = $900,000. The indicated result is $900,000. Common errors: dividing the sum of the unit rates by 2 instead of 3 gives $1,350,000; pooling total prices and acreage ($3,100,000 ÷ 26 acres × 7.5) gives about $894,231; using the highest unit rate gives $975,000.
Why This Is the Correct Answer
Option B is correct because the rates are $960,000 / 8 = $120,000, $1,100,000 / 10 = $110,000 and $1,040,000 / 8 = $130,000. Their mean is $360,000 / 3 = $120,000 per acre, and 7.5 × $120,000 = $900,000. This follows the stated mean-rate method.
Why the Other Options Are Wrong
Option A: $894,231
Option A, $894,231, pools total prices and acreage instead of averaging the unit rates: $3,100,000 ÷ 26 acres = about $119,230.77 per acre, and 7.5 × $119,230.77 = about $894,231. The mean of the three unit rates is $120,000, giving 7.5 × $120,000 = $900,000.
Option C: $975,000
Option C, $975,000, uses the highest unit rate: 7.5 × $130,000 = $975,000. The mean rate of $120,000 gives $900,000.
Option D: $1,350,000
Option D, $1,350,000, divides the sum of the unit rates by 2 instead of 3: $360,000 / 2 = $180,000, and 7.5 × $180,000 = $1,350,000. Dividing by 3 gives $120,000 and $900,000.
Per-acre first, then the mean
Convert every sale to dollars per acre before averaging, then apply the average to the subject's acres.
How to use: Use this sequence for any mean dollars-per-acre land question.
Exam Tip
After computing the mean, check that it falls between the lowest and highest unit rates; a mean outside that range signals a divisor error.
Common Mistakes to Avoid
- -Dividing the sum of rates by the wrong number
- -Using a single extreme rate instead of the mean
- -Pooling total prices and acreage instead of averaging the unit rates
- -Applying the mean to the comparable acreage instead of the subject's
Concept Deep Dive
Analysis
This question tests converting acreage sales to unit rates, averaging them and applying the mean to the subject. Divide each comparable's price by its own acreage, average the three rates, then multiply by 7.5 acres. Distractors use the wrong divisor, a single extreme rate or a pooled rate.
Background Knowledge
Price per acre lets sales of different sizes be compared on a common basis. The arithmetic mean of the unit prices is one summary measure, applied here because the stem specifies it and no other adjustments are needed. In practice, appraisers also consider each sale's comparability when reconciling.
Real-World Application
An appraiser valuing a 7.5-acre parcel in a competitive market finds three similar acreage sales with no other adjustments needed. The appraiser converts each sale to a price per acre, averages the rates and applies the mean to the subject.
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