Three cash-equivalent sales of similar vacant lots indicate $1,200, $1,280, and $1,270 per front foot. The subject lot has 160 front feet. Based on the mean price per front foot, what is the indicated land value?
Correct Answer
B) $200,000
Mean = ($1,200 + $1,280 + $1,270)/3 = $1,250/front foot; subject = 160 × $1,250 = $200,000. The indicated value is $200,000. This is the result under the stated inputs, not a universal market ratio or an approval of a proposed development. Common errors: using the lowest unit rate instead of the mean gives $192,000; using the highest unit rate instead of the mean gives $204,800; dividing the sum of the rates by 2 instead of 3 gives $300,000.
Why This Is the Correct Answer
Option B is correct because the mean is ($1,200 + $1,280 + $1,270) / 3 = $1,250 per front foot. Multiplying by the subject's frontage gives 160 × $1,250 = $200,000. Price per front foot is a recognized unit of comparison for vacant land.
Why the Other Options Are Wrong
Option A: $192,000
Option A, $192,000, uses the lowest rate instead of the mean: $1,200 × 160. The mean rate is $1,250, giving 160 × $1,250 = $200,000.
Option C: $204,800
Option C, $204,800, uses the highest rate instead of the mean: $1,280 × 160. The mean of the three rates is $1,250, giving $200,000.
Option D: $300,000
Option D, $300,000, divides the sum of the rates by 2 instead of 3: ($3,750 / 2) × 160 = $1,875 × 160. With three sales the mean is $3,750 / 3 = $1,250, giving $200,000.
Frontage times rate
Find the average dollars per front foot, then multiply by how many feet the subject has on the street.
How to use: Use this whenever a land question gives front-foot rates and subject frontage.
Exam Tip
Divide by the number of sales when averaging, and confirm the mean lies between the lowest and highest rates.
Common Mistakes to Avoid
- -Dividing the sum by the wrong count
- -Using the high or low rate when the mean is asked
- -Applying front-foot pricing without considering depth differences
Concept Deep Dive
Analysis
This question tests using a mean price per front foot. Add the three front-foot rates and divide by three to get the mean, then multiply by the subject's 160 front feet.
Background Knowledge
Front-foot pricing measures land by its frontage along a street or waterfront and is common where frontage drives value, such as commercial strips or lakefront lots. Lots of typical depth are compared by price per front foot, and differences in depth may need further analysis.
Real-World Application
An appraiser values a lakefront lot where buyers price property mainly by shoreline footage. Three recent similar lake lot sales give front-foot rates that the appraiser averages and applies to the subject's frontage.
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A cash-equivalent vacant-site sale of $810,000 contains 22,500 square feet. Market analysis supports applying its price per square foot to an otherwise matched 18,750-square-foot subject. What value does the unit rate indicate?
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