The subject is a vacant site of 17,500 square feet. Sales of comparable vacant land indicate a price of $48 per square foot. What is the indicated land value?
Correct Answer
C) $840,000
Value = 17500 square feet × $48/square feet = $840,000. The indicated result is $840,000. Common errors: converting to square yards before applying the per-square-foot rate gives $93,333; misplacing the decimal in the area gives $84,000; misplacing the decimal in the rate gives $8,400,000.
Why This Is the Correct Answer
Option C is correct because 17,500 sf × $48 per sf = $840,000. The rate and the area are both in square feet, so no conversion is needed.
Why the Other Options Are Wrong
Option A: $84,000
Option A ($84,000) results from misplacing the decimal in the area, effectively using 1,750 sf: 17,500 × $48 ÷ 10. The correct value is 17,500 × $48 = $840,000.
Option B: $93,333
Option B ($93,333) comes from converting to square yards: 17,500 × $48 ÷ 9. The rate is per square foot, so it is applied directly to square feet: 17,500 × $48 = $840,000.
Option D: $8,400,000
Option D ($8,400,000) results from misplacing the decimal in the rate, effectively $480 per sf: 17,500 × $48 × 10. The correct value is 17,500 × $48 = $840,000.
Same units, straight multiply
If the rate is per square foot and the area is in square feet, just multiply.
How to use: Use this to check that no unit conversion is needed before multiplying.
Exam Tip
Do a quick magnitude check: about 17,500 times about $50 is roughly $875,000, which points straight to $840,000.
Common Mistakes to Avoid
- -Converting to square yards when the rate is already per square foot
- -Misplacing a decimal in the area or rate
- -Using a unit of comparison the market does not use
Concept Deep Dive
Analysis
This question tests applying a per-square-foot unit price to the subject's area. Multiply the subject area by the market-supported unit price, keeping units consistent.
Background Knowledge
Common units of comparison for vacant land include price per front foot, per square foot, per acre, per building site and per buildable unit. The unit chosen should reflect how buyers in the market actually price land. The unit price must be applied to the subject in the same unit it was extracted in.
Real-World Application
An appraiser valuing an urban infill lot finds that comparable vacant sales cluster around $48 per square foot. Applying that rate to the subject's 17,500 sf gives the land indication.
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