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?
Correct Answer
D) $384,000
480000×(1−12÷60)=384000. Common errors: using the 30-year actual age instead of the 12-year effective age gives $240,000; reporting the depreciation instead of the depreciated amount gives $96,000; dividing by the 48-year remaining life instead of the 60-year total life gives $360,000.
Why This Is the Correct Answer
Option D is correct because $480,000 x (1 - 12/60) = $480,000 x 0.80 = $384,000. The age-life method uses the 12-year effective age and the 60-year total life.
Why the Other Options Are Wrong
Option A: $96,000
Option A, $96,000, is $480,000 x 12/60, the depreciation rather than the depreciated amount. Subtracting it from cost new gives $384,000.
Option B: $240,000
Option B, $240,000, is $480,000 x (1 - 30/60), which uses the 30-year actual age instead of the 12-year effective age. The effective age gives $384,000.
Option C: $360,000
Option C, $360,000, comes from $480,000 x (1 - 12/48), dividing by the 48-year remaining life instead of the 60-year total life. The correct ratio is 12/60, giving $384,000.
Effective over total, keep remainder
Depreciation share is effective age over total life; the depreciated amount is cost new times one minus that share.
How to use: Use this to compute depreciated cost in age-life questions.
Exam Tip
Expect distractors built from actual age and from remaining life; check both the numerator and the denominator.
Common Mistakes to Avoid
- -Using actual age in the age-life ratio
- -Dividing by remaining life
- -Reporting depreciation instead of depreciated cost
Concept Deep Dive
Analysis
This question tests age-life remaining value with an actual-age distractor. The supported 12-year effective age over 60-year total life gives 20% depreciation, so 80% of cost new remains.
Background Knowledge
Effective age, not chronological age, drives the age-life ratio. Remaining economic life equals total life minus effective age, but the ratio itself divides effective age by total life.
Real-World Application
A 30-year-old building was extensively renovated, and the appraiser supports a 12-year effective age. The depreciated cost reflects 80% of cost new rather than half.
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Previous Question
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?
Next Question
Building cost new $540,000 has total building depreciation $72,000. Separate site improvements cost new $35,000 have their own total loss $5,000. Add supported land $190,000 excluding sitework, and do not double count any component. What total results?