An appraiser is valuing a 4.0-acre vacant parcel. Three cash-equivalent sales of similar vacant parcels indicate $82,000, $88,000, and $85,000 per acre. Based on the mean price per acre, what is the indicated land value?
Correct Answer
B) $340,000
Mean = ($82,000 + $88,000 + $85,000)/3 = $85,000/acre; value = 4 × $85,000 = $340,000. The indicated result is $340,000. Common errors: stopping at the mean rate without multiplying by the acreage gives $85,000; using the highest unit rate instead of the mean gives $352,000; dividing the sum of the rates by 2 instead of 3 gives $510,000.
Why This Is the Correct Answer
Option B is correct because the mean is ($82,000 + $88,000 + $85,000) ÷ 3 = $85,000 per acre. Multiplying by 4.0 acres gives 4 × $85,000 = $340,000.
Why the Other Options Are Wrong
Option A: $85,000
Option A, $85,000, is the mean rate per acre, ($82,000 + $88,000 + $85,000) ÷ 3 = $85,000, with no multiplication by the subject's acreage. Applying that rate to the 4.0 acres gives 4 × $85,000 = $340,000.
Option C: $352,000
Option C, $352,000, uses the highest unit rate instead of the mean: 4 × $88,000 = $352,000. The mean rate gives 4 × $85,000 = $340,000.
Option D: $510,000
Option D, $510,000, divides the sum of the three rates by 2 instead of 3: $255,000 ÷ 2 = $127,500, and 4 × $127,500 = $510,000. Dividing by 3 gives $85,000, and 4 × $85,000 = $340,000.
Add, divide by count
The mean is the total of the values divided by how many values there are.
How to use: Use this when a question asks for the mean or average unit price.
Exam Tip
Count the comparables before dividing; dividing by the wrong number is a common distractor.
Common Mistakes to Avoid
- -Dividing the total by the wrong number of sales
- -Using the highest rate instead of the mean
- -Forgetting to multiply the unit rate by the subject's acreage
Concept Deep Dive
Analysis
This question tests finding the mean of several unit prices and applying it to the subject's size. Add the three per-acre prices, divide by three, and multiply by the subject's 4.0 acres. The mean is $85,000 per acre.
Background Knowledge
Price per acre is a common unit of comparison for vacant land. The mean is the sum of the values divided by their count. Applying a unit rate is reliable only when the comparables are similar to the subject in the characteristics that drive value.
Real-World Application
An appraiser valuing a 4-acre parcel finds three comparable vacant sales at $82,000, $88,000 and $85,000 per acre. Because the comparables are closely matched to the subject, she uses the mean of $85,000 per acre to indicate $340,000.
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Comparable vacant sites support a market unit rate of $87,500 per acre for similar utility land. The subject site contains 9.6 acres and is otherwise comparable (no other adjustments). Applying that unit rate in a land sales comparison, what indicated land value results?