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?
Correct Answer
A) $675,000
Unit rate = $810,000/22,500 SF = $36/SF; subject = 18,750 SF × $36/SF = $675,000. The indicated value is $675,000. This is the result under the stated inputs, not a universal market ratio or an approval of a proposed development. Common errors: using the comparable price without adjusting for size gives $810,000; adding the value of the 3,750 SF size difference instead of subtracting it gives $810,000 + 3,750 × $36 = $945,000; inverting the size ratio gives $972,000.
Why This Is the Correct Answer
Option A is correct because the unit rate is $810,000 / 22,500 SF = $36 per SF. Applying it to the subject gives 18,750 × $36 = $675,000. The stem states market analysis supports applying the comparable's price per square foot to the subject.
Why the Other Options Are Wrong
Option B: $810,000
Option B, $810,000, is the comparable's price with no adjustment for size. The subject is 3,750 SF smaller, so its value is 18,750 × $36 = $675,000.
Option C: $945,000
Option C, $945,000, adds the value of the size difference instead of subtracting it: $810,000 + 3,750 × $36 = $945,000. The subject is smaller, so the adjustment is downward, $810,000 − $135,000 = $675,000.
Option D: $972,000
Option D, $972,000, inverts the size ratio: $810,000 / 18,750 × 22,500. The rate must come from the comparable's own area ($810,000 / 22,500 = $36), giving $675,000 for the subject.
Divide the comp, multiply the subject
Comparable price over comparable area gives the rate; rate times subject area gives the value.
How to use: Use this for any single-comparable unit price problem.
Exam Tip
Sanity-check direction: a smaller subject at the same unit rate should be worth less than the comparable.
Common Mistakes to Avoid
- -Dividing the comparable price by the subject's area
- -Adjusting for size in the wrong direction
- -Ignoring size differences between sites
Concept Deep Dive
Analysis
This question tests extracting a price per square foot from one sale and applying it to a smaller subject. Divide the comparable's price by its area to find the unit rate, then multiply by the subject's area. Since the subject is smaller and otherwise matched, its indicated value should be lower than the comparable's price.
Background Knowledge
Price per square foot is a common unit of comparison for vacant land. The unit price is derived from comparable sales and applied to the subject's size when the market supports that unit. Appraisers also consider whether larger or smaller sites sell at different unit prices.
Real-World Application
An appraiser values a commercial pad site using a recent cash sale of a larger, similar pad nearby. After confirming the market prices such sites per square foot without a strong size discount, the appraiser applies the extracted rate to the subject's area.
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