The cost new of the improvements is $310,000. The dwelling has an actual age of 15 years, an estimated effective age of 12 years and a total economic life of 60 years. What is the depreciation by the straight-line age-life method?
Correct Answer
B) $62,000
310000×12÷60=62000. Common errors: using the 15-year actual age instead of the 12-year effective age gives $77,500; reporting the depreciated amount instead of depreciation gives $248,000; taking only one year of depreciation (310,000 ÷ 60) gives $5,167.
Why This Is the Correct Answer
Option B is correct because $310,000 x 12/60 = $310,000 x 0.20 = $62,000. The age-life ratio uses the 12-year effective age, not the 15-year actual age, over the 60-year total life.
Why the Other Options Are Wrong
Option A: $5,167
Option A, $5,167, is $310,000 / 60, which is only one year of depreciation. Twelve years of effective age give $310,000 x 12/60 = $62,000.
Option C: $77,500
Option C, $77,500, is $310,000 x 15/60, which uses the 15-year actual age instead of the 12-year effective age. The supported effective age gives $62,000.
Option D: $248,000
Option D, $248,000, is $310,000 x (1 - 12/60), the depreciated amount rather than the depreciation. The question asks for depreciation, which is $62,000.
Effective age, not birthday age
The age-life ratio uses how old the building acts, its effective age, not how old it actually is.
How to use: Use this whenever a stem gives both actual and effective age.
Exam Tip
When both ages are given, use effective age in the age-life ratio and confirm whether depreciation or remaining value is asked.
Common Mistakes to Avoid
- -Using actual age instead of effective age
- -Reporting the depreciated amount when depreciation is asked
- -Computing only one year of depreciation
Concept Deep Dive
Analysis
This question tests the difference between actual and effective age in the age-life method. The method uses effective age, so depreciation is cost new times 12/60. The question asks for depreciation, not the depreciated amount.
Background Knowledge
Effective age reflects a building's condition and utility compared with new and can differ from its actual age because of maintenance or renovation. The age-life method divides effective age by economic life.
Real-World Application
A 15-year-old house has been well maintained, so the appraiser supports an effective age of 12 years. Depreciation is based on 12 of 60 years.
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A 30-year-old dwelling has a current cost new of $480,000, an effective age of 12 years and a total economic life of 60 years. There is no salvage value and no other depreciation. By the straight-line age-life method, what is the depreciated cost of the improvements, excluding the site?