The current cost new of the improvements is $2,500,000. They have an actual age of 5 years, an effective age of 8 years and a total economic life of 50 years. What is the depreciation by the straight-line age-life method?
Correct Answer
B) $400,000
2500000×8÷50=400000. Common errors: using the 5-year actual age instead of the 8-year effective age gives $250,000; reporting the depreciated amount instead of depreciation gives $2,100,000; dividing by the 42-year remaining life instead of the 50-year total life gives $476,190.
Why This Is the Correct Answer
Option B is correct because age-life depreciation is effective age divided by total economic life, applied to cost new. Here 8 / 50 = 16%, and 16% of $2,500,000 is $400,000.
Why the Other Options Are Wrong
Option A: $250,000
Option A, $250,000, is wrong because it uses the 5-year actual age instead of the 8-year effective age ($2,500,000 x 5 / 50). The age-life method uses effective age, giving $400,000.
Option C: $476,190
Option C, $476,190, is wrong because it divides by the 42-year remaining life ($2,500,000 x 8 / 42) instead of the 50-year total life. The correct calculation is $2,500,000 x 8 / 50 = $400,000.
Option D: $2,100,000
Option D, $2,100,000, is wrong because it is the depreciated cost remaining ($2,500,000 x (1 - 8/50)), not the depreciation. Depreciation is $2,500,000 - $2,100,000 = $400,000.
Effective over total, times cost
Depreciation equals cost new times effective age divided by total economic life.
How to use: Use this formula for any age-life depreciation question.
Exam Tip
Divide by total economic life, not remaining life, and use effective age when it is given. Check whether the question wants depreciation or the depreciated cost.
Common Mistakes to Avoid
- -Using actual age instead of effective age
- -Dividing by remaining life instead of total life
- -Reporting depreciated cost instead of depreciation
Concept Deep Dive
Analysis
This question tests the age-life method using effective age rather than actual age. Depreciation equals cost new times effective age divided by total economic life. With $2,500,000 cost, an 8-year effective age and a 50-year life, depreciation is $2,500,000 x 8 / 50 = $400,000.
Background Knowledge
The age-life method estimates depreciation by dividing effective age by total economic life and applying that ratio to cost new. Effective age, not chronological age, is used because it reflects the improvement's actual condition and utility.
Real-World Application
An appraiser values a 5-year-old house that shows more wear than typical, supporting an effective age of 8 years. Using a 50-year economic life, the appraiser estimates depreciation as 16% of current cost new.
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