A property sold for $360,000. Market evidence indicates a site value of $90,000, the dwelling contains 2,000 square feet, and there are no other components. What is the indicated value of the improvements per square foot?
Correct Answer
B) $135.00 per sqft
(360000 − 90000) / 2000 = 135 dollars per sqft. This component decomposition does not supply an automatic marginal adjustment for a size difference.
Why This Is the Correct Answer
Option B is correct because the improvement residual is $360,000 − $90,000 = $270,000, and $270,000 ÷ 2,000 sqft = $135.00 per sqft. With no other components, the entire residual is attributed to the dwelling. This unit figure describes this decomposition and does not by itself supply a marginal adjustment rate for size differences.
Why the Other Options Are Wrong
Option A: $180.00 per sqft
Option A, $180.00 per sqft, is wrong because it divides the full sale price by the area: $360,000 ÷ 2,000 = $180. That figure includes the $90,000 site contribution; removing it first gives ($360,000 − $90,000) ÷ 2,000 = $135.
Option C: $45.00 per sqft
Option C, $45.00 per sqft, is wrong because it divides the site contribution by the dwelling area: $90,000 ÷ 2,000 = $45. The question asks for the improvement residual, which is ($360,000 − $90,000) ÷ 2,000 = $135.
Option D: $225.00 per sqft
Option D, $225.00 per sqft, is wrong because it adds the site contribution instead of subtracting it: ($360,000 + $90,000) ÷ 2,000 = $225. The correct residual is ($360,000 − $90,000) ÷ 2,000 = $135.
Subtract the site, then divide
Price minus site equals improvements; improvements divided by area equals the per-square-foot residual. Doing the division before removing the site leaves land value in the answer.
How to use: Use this whenever a question asks for an improvement value per square foot from a total sale price.
Exam Tip
Check that the figure you divide by area is the improvement residual, not the total price or the site value.
Common Mistakes to Avoid
- -Dividing the total sale price by area without removing the site contribution
- -Treating the residual price per square foot as the marginal size adjustment rate
- -Adding the site contribution instead of subtracting it
Concept Deep Dive
Analysis
This question tests extracting a residual improvement value per square foot from a sale. The site contribution is subtracted from the total price to isolate the improvement contribution, which is then divided by the dwelling area. The key is to subtract first and divide second.
Background Knowledge
In extraction, a sale price is broken into site and improvement components, and one is found by subtracting the other from the total. Stating the result per square foot creates a unit of comparison, but an average improvement price per square foot is not the same as the market's marginal reaction to a size difference.
Real-World Application
An appraiser studying building values in a tract subtracts a supported site value from each sale and divides the remainder by living area. She uses these residual figures as a check on her cost analysis, not as her size adjustment rate.
More Sales Comparison Questions
Which stated cause of supported value loss is external?
Improvement cost new is $450,000. Separately supported improvement depreciation deductions of $45,000, $25,000, $15,000 are expressly nonoverlapping and not already excluded from cost new. Add supported site value of $125,000, already reflecting any site losses. What total indicated value results?
Which two depreciation categories may each be classified as curable or incurable by comparing the cost to remedy a deficiency with the value gained?
Improvement cost new is $800,000. Separately supported improvement depreciation deductions of $120,000, $80,000, $40,000 are expressly nonoverlapping and not already excluded from cost new. No site is included. What depreciated improvement amount results?
The principle of anticipation in real estate valuation states that:
Which highest-and-best-use criterion addresses whether a proposed use is allowed by zoning and applicable legal restrictions?
Three comparables produce adjusted indications of $312,000, $309,000 and $315,000, requiring gross adjustments of 9%, 14% and 22% respectively. Verification also establishes that the first sale is the closest competitive substitute and its adjustments are better supported than the other two. Which indication deserves the most weight on those facts?
When reconciling value indications from the three approaches to value, an appraiser should:
A property sold at a cash-equivalent price of $1,062,500. Its stabilized annual NOI is $85,000. What is the indicated overall rate?
In reconciliation, an appraiser should:
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