Improvements have a current cost new of $600,000, an effective age of 20 years and a total economic life of 50 years. There are no other deductions and no salvage value. By the straight-line age-life method, what is the depreciated cost of the improvements?
Correct Answer
C) $360,000
Age-life depreciation=600000×20÷50=240000; remainder=600000−240000−0+0=360000. Common errors: reporting the depreciation instead of the depreciated amount gives $240,000; stopping at cost new, before depreciation gives $600,000; dividing by the 30-year remaining life instead of the 50-year total life gives $200,000.
Why This Is the Correct Answer
Option C is correct because depreciation is $600,000 × 20 ÷ 50 = $240,000. The depreciated improvement amount is $600,000 − $240,000 = $360,000. No other deductions or salvage value apply.
Why the Other Options Are Wrong
Option A: $200,000
Option A, $200,000, comes from dividing by the 30-year remaining life instead of the 50-year total life: depreciation of $600,000 × 20 ÷ 30 = $400,000 leaves $200,000. The age-life ratio uses total economic life, giving $600,000 − $240,000 = $360,000.
Option B: $240,000
Option B, $240,000, is the depreciation itself: $600,000 × 20 ÷ 50 = $240,000. The question asks for the depreciated amount, which is $600,000 − $240,000 = $360,000.
Option D: $600,000
Option D, $600,000, stops at cost new before any depreciation. Deducting $600,000 × 20 ÷ 50 = $240,000 gives $360,000.
Effective over total
The age-life ratio is effective age over total economic life. Remaining life belongs in the identity, not the denominator.
How to use: Use this to set up the age-life fraction correctly before multiplying by cost new.
Exam Tip
Check whether the question wants the depreciation or the depreciated amount; both figures usually appear among the choices.
Common Mistakes to Avoid
- -Dividing effective age by remaining life instead of total life
- -Reporting depreciation instead of the depreciated amount
- -Using actual age in place of effective age
Concept Deep Dive
Analysis
This question tests the straight-line age-life method. Depreciation is cost new times effective age divided by total economic life, and the depreciated amount is cost new minus that depreciation. The key is to divide by total economic life, not remaining life, and to report the remainder.
Background Knowledge
In the age-life method, depreciation is estimated by dividing effective age by total economic life. Total economic life equals effective age plus remaining economic life. Applying the ratio to cost new gives depreciation, and subtracting it gives the depreciated improvement amount.
Real-World Application
An appraiser estimates replacement cost new of a house at $600,000 and concludes an effective age of 20 years and a 50-year economic life from market data. The age-life ratio of 40% produces $240,000 of depreciation and a $360,000 depreciated improvement contribution.
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Previous Question
Improvement cost new is $595,000. Separately supported improvement depreciation deductions of $48,000, $27,000 are expressly nonoverlapping and not already excluded from cost new. Add supported site value of $155,000, already reflecting any site losses. What total indicated value results?
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