An appraiser estimates depreciation at 35% of the $500,000 current cost new of the improvements. Excluding land, what is the depreciated cost of the improvements?
Correct Answer
B) $325,000
500000×(1−0.35) = 325000. Common errors: reporting the depreciation instead of the depreciated amount gives $175,000; not deducting the 35% depreciation gives $500,000; dividing by 1.35 instead of multiplying by 0.65 gives $370,370.
Why This Is the Correct Answer
Option B is correct because $500,000 x (1 - 0.35) = $500,000 x 0.65 = $325,000. Subtracting 35% depreciation leaves 65% of cost new. No land is included, so this is the depreciated improvement amount.
Why the Other Options Are Wrong
Option A: $175,000
Option A is wrong because $175,000 is the depreciation, $500,000 x 0.35 = $175,000, not the depreciated amount. Subtracting it from cost new gives $500,000 - $175,000 = $325,000.
Option C: $370,370
Option C is wrong because $370,370 comes from dividing by 1.35 instead of multiplying by 0.65: $500,000 / 1.35 = $370,370. Deducting 35% means $500,000 x 0.65 = $325,000.
Option D: $500,000
Option D is wrong because $500,000 is cost new with no depreciation deducted. Deducting the estimated 35% gives $325,000.
One minus depreciation
Depreciated value = cost new x (1 - depreciation rate). Thirty-five percent off leaves sixty-five percent good.
How to use: Use this whenever a question gives a depreciation percentage and asks for the depreciated amount.
Exam Tip
Multiply by percent good rather than dividing by one plus the rate. Dividing does not remove the stated percentage.
Common Mistakes to Avoid
- -Reporting the depreciation amount instead of the depreciated value
- -Dividing by 1.35 instead of multiplying by 0.65
- -Forgetting to deduct depreciation from cost new
Concept Deep Dive
Analysis
This question tests applying a depreciation percentage to cost new. With 35% depreciation, the percent good is 65%. The depreciated amount is $500,000 x 0.65 = $325,000.
Background Knowledge
Percent good is the complement of depreciation measured as a percentage. Multiplying cost new by percent good gives the depreciated value of the improvements.
Real-World Application
An appraiser estimates an older home's improvements at $500,000 cost new and supports 35% total depreciation from market extraction. The depreciated improvement value of $325,000 is then added to site value.
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