The current cost new of the improvements is $420,000, and depreciation is estimated at 30% of that cost. Excluding land, what is the depreciated cost of the improvements?
Correct Answer
B) $294,000
420000×(1−0.3) = 294000. Common errors: reporting the depreciation instead of the depreciated amount gives $126,000; not deducting the 30% depreciation gives $420,000; dividing by 1.30 instead of multiplying by 0.70 gives $323,077.
Why This Is the Correct Answer
Option B is correct because 30% depreciation leaves 70% percent good: $420,000 × 0.70 = $294,000.
Why the Other Options Are Wrong
Option A: $126,000
Option A, $126,000, is the depreciation amount ($420,000 × 0.30), not what remains. The depreciated improvement amount is $420,000 × 0.70 = $294,000.
Option C: $323,077
Option C, $323,077, divides cost new by 1.30 ($420,000 ÷ 1.30) instead of multiplying by 0.70. Deducting 30% means $420,000 × 0.70 = $294,000.
Option D: $420,000
Option D, $420,000, is cost new with no depreciation deducted. Removing the 30% ($126,000) gives $294,000.
Take off means times the rest
To take 30% off, multiply by 70%. Dividing by 1.30 is not the same thing.
How to use: Use this when converting a stated percentage deduction into a multiplier.
Exam Tip
Decide whether the question wants the depreciation or what remains. Avoid dividing by 1 plus the rate when the task is a simple deduction.
Common Mistakes to Avoid
- -Reporting the depreciation instead of the depreciated value
- -Dividing by 1.30 instead of multiplying by 0.70
- -Forgetting to deduct depreciation at all
Concept Deep Dive
Analysis
This question tests percentage depreciation and percent good. Deducting 30% leaves 70% of cost new. No land is involved, so the answer is the depreciated improvement amount alone.
Background Knowledge
Percent good is the complement of depreciation expressed as a percentage. Multiplying cost new by percent good gives the depreciated cost. Dividing by one plus a rate is a different operation and does not deduct a percentage of cost.
Real-World Application
An appraiser estimates that a home's improvements are 30% depreciated. Multiplying cost new by 70% gives the depreciated improvement value before site value is considered separately.
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An affected-site estimate already reflects part of a whole-property external loss. Why analyze the allocation before deducting improvement depreciation?
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Dwelling cost new is $296,000. A separate 528 sf garage costs $52/sf; additional site improvements cost $14,500. No components overlap and land is excluded. What total improvement cost new results?