A rectangular lot measures 100 feet by 150 feet. If similar lots in the area sell for $8.50 per square foot, what is the indicated land value?
Correct Answer
D) $127,500
Why this is correct: First, calculate the lot area: 100 ft × 150 ft = 15,000 sq ft. Then multiply by the price per square foot: 15,000 × $8.50 = $127,500. Why the other choices are wrong: "$125,000" might use $8.33/sq ft or miscalculate area. "$115,000" could result from using perimeter or incorrect dimensions. "$132,000" might use $8.80/sq ft or add extra footage. Exam tip: For rectangular lots, area = length × width. Always include units and double-check multiplication.
Why This Is the Correct Answer
Option A is correct because it follows the proper mathematical sequence for land valuation. First, calculate the total area: 100 feet × 150 feet = 15,000 square feet. Then multiply by the market rate: 15,000 square feet × $8.50 per square foot = $127,500. This demonstrates the sales comparison approach to land valuation, where comparable sales data provides a per-unit price that can be applied to the subject property. The calculation is straightforward multiplication with no complex adjustments needed.
Why the Other Options Are Wrong
Option A: $125,000
Option A ($125,000) indicates a calculation error, likely from using a per-square-foot rate of approximately $8.33 instead of the correct $8.50, possibly from rounding errors or misreading the given rate.
Option B: $115,000
Option B ($115,000) appears to result from a calculation error, possibly using an incorrect per-square-foot rate of approximately $7.67 instead of the given $8.50, or from miscalculating the lot area.
Option C: $132,000
Option C ($132,000) suggests a calculation error, possibly from using an inflated per-square-foot rate of approximately $8.80 instead of $8.50, or from adding an unnecessary adjustment factor.
Area × Rate = Value (ARV Method)
Remember ARV: Area × Rate = Value. For rectangular lots, use L×W×R=V (Length × Width × Rate = Value). Think 'Always Remember Valuation' to recall the sequence.
How to use: When you see a land valuation problem, immediately identify: 1) What shape is the lot? 2) What are the dimensions? 3) What is the per-unit rate? Then apply ARV: calculate area first, then multiply by rate.
Exam Tip
Always double-check your area calculation before applying the rate - most errors occur in the basic math step, not in understanding the valuation concept.
Common Mistakes to Avoid
- -Forgetting to calculate total area first before applying the rate
- -Mixing up length and width measurements
- -Using the wrong per-unit rate or misreading decimal places
Concept Deep Dive
Analysis
This question tests fundamental site valuation using the sales comparison approach, which is one of the three primary approaches to real estate valuation. The problem requires calculating the total area of a rectangular lot and then applying a per-square-foot market rate to determine land value. This type of calculation is essential in appraisal practice as land valuation forms the foundation for many property assessments, particularly in the cost approach where land value must be separated from improvement value. Understanding area calculations and unit pricing is crucial for appraisers who regularly need to value vacant land or allocate total property value between land and improvements.
Background Knowledge
Land valuation using the sales comparison approach requires understanding of area calculations and the application of market-derived unit prices. Appraisers must be proficient in basic geometry to calculate lot areas and understand how comparable sales data translates into per-unit pricing for different property types.
Real-World Application
Appraisers regularly use this method when valuing vacant land for development, determining land value for cost approach calculations, or when analyzing highest and best use scenarios where land value must be isolated from total property value.
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