Sales of comparable vacant sites indicate a consistent price of $35 per square foot. The subject vacant site contains 12,000 square feet. What is the indicated land value?
Correct Answer
D) $420,000
Multiply subject area by the market-supported unit price: 12,000 square feet × $35 per square foot = $420,000. The area units cancel. A rate taken from unlike sites would require further analysis; here its applicability is expressly given.
Why This Is the Correct Answer
Option D is correct because land value equals area times unit price: 12,000 square feet × $35 per square foot = $420,000. The rate is stated to be market supported for the subject.
Why the Other Options Are Wrong
Option A: $42,000
Option A, $42,000, misplaces the decimal in the rate, as if it were $3.50 per square foot: 12,000 × $3.50 = $42,000. At $35 per square foot, 12,000 × $35 = $420,000.
Option B: $3,780,000
Option B, $3,780,000, converts the $35 rate to a square-yard rate ($35 x 9 = $315) and then applies it to the area in square feet: 12,000 x $315 = $3,780,000. The area and the rate are both in square feet, so 12,000 x $35 = $420,000.
Option C: $46,667
Option C, $46,667, converts the area to square yards (12,000 / 9 = 1,333.33) and then applies the per-square-foot rate: 1,333.33 x $35 = $46,667. The rate is per square foot, so it applies to the 12,000 square feet: 12,000 x $35 = $420,000.
Rate times size
Value equals the unit rate times the number of units. Square feet times dollars per square foot leaves dollars.
How to use: Use unit cancellation to confirm you multiplied rather than divided.
Exam Tip
Do a quick estimate: 12,000 × 35 is a bit over 400,000. That rules out answers far from it.
Common Mistakes to Avoid
- -Mixing square feet and square yards between the area and the rate
- -Misplacing the decimal in the unit rate
- -Applying a rate from dissimilar sites without analysis
Concept Deep Dive
Analysis
This question tests applying a market-supported unit price to the subject's size. Multiply the subject's square footage by the supported price per square foot; the square-foot units cancel, leaving a dollar value. The distractors come from misplacing the decimal in the rate and from mixing square feet with square yards.
Background Knowledge
Vacant land is often compared using units such as price per square foot, per front foot, per acre, per site, or per buildable unit. The unit chosen should reflect how the market prices that type of land. The supported rate is applied to the subject's quantity of that unit.
Real-World Application
An appraiser finds that commercial pad sites in an area consistently sell around a certain price per square foot. She applies that rate to the subject's site area to indicate land value.
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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Sale price per acre is one of the vacant-land units of comparison. A comparable vacant tract of 8.0 acres sold for a cash-equivalent price of $960,000 and is otherwise similar to the subject in HBU and market conditions. What indicated unit price per acre should be applied before any remaining elements-of-comparison adjustments?