The current cost new of the improvements is $2,400,000, with an effective age of 18 years and a total economic life of 40 years. There are no other deductions and no salvage value. What is the depreciation indicated by the straight-line age-life method alone?
Correct Answer
B) $1,080,000
Age-life depreciation=2400000×18÷40=1080000. Common errors: reporting the depreciated amount instead of depreciation gives $1,320,000; dividing by the 22-year remaining life instead of the 40-year total life gives $1,963,636; taking only one year of depreciation (2,400,000 ÷ 40) gives $60,000.
Why This Is the Correct Answer
Option B is correct because the age-life ratio is 18 / 40 = 0.45, and $2,400,000 x 0.45 = $1,080,000. That figure is the depreciation itself. Only depreciation is asked for, so no subtraction from cost new is needed.
Why the Other Options Are Wrong
Option A: $60,000
Option A, $60,000, is only one year of depreciation: $2,400,000 / 40 = $60,000. The building has an effective age of 18 years, so depreciation is $60,000 x 18 = $1,080,000.
Option C: $1,320,000
Option C, $1,320,000, is the depreciated improvement amount rather than the depreciation: $2,400,000 x (1 - 18/40) = $1,320,000. The question asks for depreciation, which is $2,400,000 x 18/40 = $1,080,000.
Option D: $1,963,636
Option D, $1,963,636, divides by the 22-year remaining life instead of the 40-year total life: $2,400,000 x 18 / 22 = $1,963,636. The age-life ratio uses total economic life as the denominator, giving $1,080,000.
Age over life
Depreciation percentage is effective age over total life. Put the age on top and the whole life on the bottom.
How to use: Use age over life to set up the fraction before multiplying by cost new.
Exam Tip
Read whether the question asks for depreciation or for the depreciated value; the test often offers both. The denominator in the age-life ratio is total economic life, not remaining life.
Common Mistakes to Avoid
- -Reporting the depreciated value when depreciation is requested
- -Dividing effective age by remaining life instead of total life
- -Using only one year of depreciation
Concept Deep Dive
Analysis
This question tests the straight-line age-life method for estimating depreciation. Depreciation equals cost new multiplied by the ratio of effective age to total economic life. The question asks for the depreciation amount, not the value remaining after depreciation.
Background Knowledge
The age-life method estimates accrued depreciation by dividing effective age by total economic life and applying that percentage to cost new. Effective age reflects condition and utility rather than chronological age. The method is a simplified model and assumes depreciation accrues evenly over the economic life.
Real-World Application
An appraiser estimates that a large custom house with a $2.4 million cost new has an effective age of 18 years and a total economic life of 40 years. She computes depreciation of 45% of cost new and reports that amount on the depreciation line before deducting it from cost new.
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Previous Question
The subject improvements have a current replacement cost new of $360,000. Accrued depreciation from all causes is $72,000, and land value is $90,000. These figures include all necessary cost components and depreciation. What is the indicated property value?
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