An appraiser is applying the straight-line age-life method to improvements with a current cost new of $360,000, an effective age of 15 years and a total economic life of 50 years. There are no other deductions and no salvage value. What is the age-life depreciation?
Correct Answer
B) $108,000
Age-life depreciation=360000×15÷50=108000. Common errors: reporting the depreciated amount instead of depreciation gives $252,000; dividing by the 35-year remaining life instead of the 50-year total life gives $154,286; taking only one year of depreciation (360,000 ÷ 50) gives $7,200.
Why This Is the Correct Answer
Option B is correct because age-life depreciation equals cost new times effective age divided by total economic life. Here $360,000 × 15 ÷ 50 = $108,000. That figure is the amount of accrued depreciation, which is exactly what the question asks for.
Why the Other Options Are Wrong
Option A: $7,200
Option A, $7,200, is only one year of depreciation: $360,000 ÷ 50 = $7,200. The improvement has an effective age of 15 years, so the correct depreciation is $360,000 × 15 ÷ 50 = $108,000.
Option C: $154,286
Option C, $154,286, comes from dividing by the 35-year remaining life instead of the 50-year total life: $360,000 × 15 ÷ 35 = $154,286. The age-life fraction uses total economic life, so the answer is $360,000 × 15 ÷ 50 = $108,000.
Option D: $252,000
Option D, $252,000, is the depreciated amount, not the depreciation: $360,000 × (1 − 15/50) = $252,000. The question asks for depreciation alone, which is $360,000 × 15 ÷ 50 = $108,000.
Age over Life, times Cost
Depreciation = Cost new × (Effective age ÷ Total life). Age goes on top, the full life goes on the bottom.
How to use: Use this whenever an age-life question asks for depreciation rather than the remaining value.
Exam Tip
Read whether the question asks for depreciation or depreciated value; both figures usually appear among the options.
Common Mistakes to Avoid
- -Reporting the depreciated value instead of the depreciation
- -Dividing effective age by remaining life instead of total life
- -Calculating only one year of depreciation
Concept Deep Dive
Analysis
This question tests the basic straight-line age-life method for measuring accrued depreciation. The depreciation fraction is effective age divided by total economic life, and that fraction is applied to current cost new. The question asks for the depreciation itself, not the depreciated value that remains.
Background Knowledge
In the age-life method, depreciation is estimated by dividing the effective age of the improvement by its total economic life. The resulting percentage is applied to current cost new to give accrued depreciation. Subtracting that depreciation from cost new gives the depreciated cost of the improvement.
Real-World Application
An appraiser estimates a 15-year effective age for a house with a 50-year economic life and current cost new of $360,000. Using the age-life method, she reports $108,000 of accrued depreciation in the cost approach before adding site value.
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Previous Question
An appraiser is estimating depreciation by the economic age-life method. The improvement has a physical life of 90 years and a total economic life of 55 years. Which figure is the denominator of the age-life ratio?
Next Question
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