An appraiser is using sales comparison to value a vacant site of 5,200 square feet. Market data show comparable vacant land selling at $55 per square foot. What is the indicated land value?
Correct Answer
C) $286,000
Value = 5200 square feet × $55/square feet = $286,000. The indicated result is $286,000. Common errors: converting to square yards before applying the per-square-foot rate gives $31,778; misplacing the decimal in the area gives $28,600; misplacing the decimal in the rate gives $2,860,000.
Why This Is the Correct Answer
Option C is correct because 5,200 square feet × $55 per square foot = $286,000. The rate and the area are both stated in square feet, so the multiplication directly gives the indicated land value.
Why the Other Options Are Wrong
Option A: $28,600
Option A, $28,600, results from misplacing the decimal in the area, effectively using 520 square feet (5,200 × $55 ÷ 10). The correct value is 5,200 × $55 = $286,000.
Option B: $31,778
Option B, $31,778, results from converting the area to square yards (5,200 ÷ 9 = about 577.8) before applying the per-square-foot rate. The rate is per square foot, so 5,200 × $55 = $286,000.
Option D: $2,860,000
Option D, $2,860,000, results from misplacing the decimal in the rate, effectively using $550 per square foot (5,200 × $55 × 10). The correct value is $286,000.
Match the units
A per-square-foot rate multiplies square feet, and a per-acre rate multiplies acres. If the units match, the multiplication is all you need.
How to use: Use this check before multiplying any unit rate by a subject quantity.
Exam Tip
Round the inputs, for example 5,000 × $55 = $275,000, to spot choices that are off by a factor of 10 or 9.
Common Mistakes to Avoid
- -Converting to square yards when the rate is per square foot
- -Misplacing a decimal in the area or rate
- -Reporting the unit rate instead of the total value
Concept Deep Dive
Analysis
This question tests applying a supported price per square foot to the subject site area. Multiply the area in square feet by the rate per square foot. The wrong choices reflect a square-yard conversion and decimal errors.
Background Knowledge
Vacant land is commonly compared using units such as price per square foot, per front foot, per acre, or per site. Once the market supports a unit rate for competitive parcels, the appraiser applies it to the subject's quantity of the same unit.
Real-World Application
An appraiser values a small infill residential lot in an urban neighborhood where lot sales are analyzed on a per-square-foot basis. After reviewing competitive sales, the appraiser applies the supported rate to the subject's 5,200 square feet.
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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