An improved property sold for $480,000, cash equivalent. The site value, estimated independently, is $120,000, and the cost new of the improvements is $400,000. The sale price includes no other assets. What is the total depreciation of the improvements extracted from this sale, as a percentage of cost new?
Correct Answer
B) 10%
(400000−(480000−120000))÷400000×100 = 10. Common errors: dividing by the sale price instead of cost new gives 8%; comparing sale price with cost new, ignoring the site value gives 20%; reporting the percent good (contribution ÷ cost new) instead of depreciation gives 90%.
Why This Is the Correct Answer
Option B is correct because the improvement contribution is $480,000 - $120,000 = $360,000, and $400,000 - $360,000 = $40,000 of depreciation. $40,000 / $400,000 = 10%. Market extraction expresses depreciation as a share of cost new.
Why the Other Options Are Wrong
Option A: 8%
Option A is wrong because 8% comes from dividing by the sale price instead of cost new: $40,000 / $480,000 = 8%. Depreciation is measured against cost new: $40,000 / $400,000 = 10%.
Option C: 20%
Option C is wrong because 20% compares the sale price with cost new and ignores the site value: ($480,000 - $400,000) / $400,000 = 20%. The site must be removed first, giving 10%.
Option D: 90%
Option D is wrong because 90% is the percent good, $360,000 / $400,000 = 90%, not the depreciation. Depreciation is the complement, 100% - 90% = 10%.
Sale minus site, then compare
Sale minus site gives the building's contribution. Cost new minus that contribution gives depreciation, divided by cost new for the percentage.
How to use: Use this whenever a question asks you to extract depreciation from a comparable sale.
Exam Tip
Remove the site value before comparing with cost new, and divide by cost new, not the sale price.
Common Mistakes to Avoid
- -Forgetting to subtract site value from the sale price
- -Dividing by the sale price instead of cost new
- -Reporting percent good as depreciation
Concept Deep Dive
Analysis
This question tests market extraction of depreciation. Subtract site value from the sale price to find the improvements' contribution ($480,000 - $120,000 = $360,000), then compare it to cost new ($400,000). Depreciation is $40,000, which is 10% of cost new.
Background Knowledge
In the market extraction (sales comparison) method of estimating depreciation, site value is subtracted from a sale price to isolate the building's contribution. That contribution is compared with current cost new, and the difference is total depreciation.
Real-World Application
An appraiser studies a recent sale of a similar home for $480,000 on a lot worth $120,000, with a cost new of $400,000. The extracted 10% depreciation helps support the depreciation applied to the subject.
More Cost Approach Questions
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Previous Question
An appraiser applying the cost approach estimates an improvement cost new of $620,000 and $80,000 of depreciation from other causes. An external factor also reduces annual net income by $4,000. That loss is allocated only to the improvements, has not been counted elsewhere, and is capitalized at 8%. The site is valued at $170,000, which already reflects site influences. What is the indicated value?
Next Question
After curable and short-lived components are excluded, the remaining long-lived cost new is $240,000. The long-lived components have an effective age of 12 years and a total life of 60 years, with straight-line depreciation. What is the long-lived physical depreciation?