A 2,500-sf house has a current cost new of $180 per square foot. Total depreciation of the improvements is estimated at 22% of cost new, and the site is valued at $170,000. What value does the cost approach indicate?
Correct Answer
C) $521,000
2500×180×0.78+170000=521000. Common errors: leaving out the site value gives $351,000; not deducting the 22% depreciation gives $620,000; applying the 22% depreciation as the remaining share gives $269,000.
Why This Is the Correct Answer
Option C is correct because cost new is 2,500 sf × $180 = $450,000. Deducting 22% leaves $450,000 × 0.78 = $351,000, and adding the $170,000 site gives $521,000. Each step uses the stated cost buildup and depreciation base.
Why the Other Options Are Wrong
Option A: $269,000
Option A, $269,000, applies the 22% depreciation as the remaining share: $450,000 × 0.22 + $170,000 = $269,000. The remaining share after a 22% deduction is 78%, giving $450,000 × 0.78 + $170,000 = $521,000.
Option B: $351,000
Option B, $351,000, leaves out the site value: $450,000 × 0.78 = $351,000. Adding the $170,000 site gives $521,000.
Option D: $620,000
Option D, $620,000, does not deduct the 22% depreciation: $450,000 + $170,000 = $620,000. After the deduction the total is $351,000 + $170,000 = $521,000.
Keep what remains
A 22% loss means 78% remains. Multiply by what remains, then add the land.
How to use: Use this to avoid multiplying by the depreciation percentage when you need the depreciated amount.
Exam Tip
Convert the depreciation percentage to its remaining share before multiplying, and confirm the site is added last.
Common Mistakes to Avoid
- -Multiplying by the depreciation percentage instead of the remaining share
- -Forgetting to add site value
- -Skipping the depreciation deduction
Concept Deep Dive
Analysis
This question tests a cost approach calculation with a percentage depreciation. Compute full cost new from area times unit cost, deduct 22% by multiplying by the 78% remaining share, then add site value. The wrong answers skip a step or apply the depreciation percentage as if it were the remaining share.
Background Knowledge
The square foot method applies a price per square foot to the subject's area to estimate cost new. A depreciation percentage is applied to cost new, and the depreciated improvement amount equals cost new times one minus that percentage. Site value is then added for the cost approach indication.
Real-World Application
An appraiser estimates a 2,500 sf house at $180 per square foot from cost service data and applies a market-supported 22% total depreciation. Adding land value from recent lot sales gives the cost approach indication reported in the appraisal.
More Cost Approach Questions
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