Competitive vacant industrial sites support an applicable market rate of $45 per square foot for the subject, after all relevant comparisons. The subject contains 19,000 square feet. What land value does that supported rate indicate?
Correct Answer
C) $855,000
Land indication = 19,000 SF × $45/SF = $855,000. The indicated value is $855,000. This is the result under the stated inputs, not a universal market ratio or an approval of a proposed development. Common errors: converting to square yards before applying the per-square-foot rate gives $95,000; misplacing the decimal in the area gives $85,500; misplacing the decimal in the rate gives $8,550,000.
Why This Is the Correct Answer
Option C is correct because 19,000 square feet × $45 per square foot = $855,000. The rate is already expressed per square foot, which matches the way the subject's area is measured, so no conversion is needed. The result is the land value indicated by the supported market rate.
Why the Other Options Are Wrong
Option A: $85,500
Option A, $85,500, comes from misplacing the decimal in the area: 19,000 × $45 ÷ 10 = $85,500. The correct calculation is 19,000 × $45 = $855,000.
Option B: $95,000
Option B, $95,000, comes from converting the area to square yards before applying a per-square-foot rate: 19,000 × $45 ÷ 9 = $95,000. The rate is per square foot, so the correct calculation is 19,000 × $45 = $855,000.
Option D: $8,550,000
Option D, $8,550,000, comes from misplacing the decimal in the rate: 19,000 × $45 × 10 = $8,550,000. The correct calculation is 19,000 × $45 = $855,000.
Match the units, then multiply
A rate per square foot multiplies square feet; a rate per square yard multiplies square yards. Keep the two units separate in one step.
How to use: Use this check whenever a land problem gives a unit rate and a site size.
Exam Tip
Estimate the answer roughly first (about 20,000 × $45 is about $900,000) so you can quickly reject choices that are off by a factor of ten.
Common Mistakes to Avoid
- -Dividing by 9 as if converting to square yards when the rate is already per square foot
- -Dropping or adding a zero when multiplying large numbers
Concept Deep Dive
Analysis
This question tests applying a supported price per square foot to the subject's land area. Because the rate and the area are both stated in square feet, the land indication is simply area times rate. The main risk is a unit or decimal error, so check that the units match before multiplying.
Background Knowledge
Vacant land is commonly compared using units such as price per front foot, per square foot, per acre, per building site or per buildable unit. Analysis of sales should use a market-derived unit of comparison. Once a unit rate is supported, it is applied to the subject's quantity of that same unit.
Real-World Application
An appraiser valuing a 19,000-square-foot industrial lot finds that competing vacant industrial sites support about $45 per square foot after adjustments. Applying that rate to the subject's area gives a land indication of $855,000 for the cost approach.
More Land/Site Questions
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Which fact, if supported by competitive-market evidence, most directly supports a unit-price premium for an otherwise comparable site?
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Using the allocation method, market evidence supports a typical land-to-total-property-value ratio of 28% for similar improved properties in the subject’s location. An improved comparable sold for $825,000. What land (site) contribution is indicated by applying that ratio?
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