The roof of a dwelling has a current cost new of $18,000, an effective age of 10 years and a component economic life of 25 years. Assuming straight-line depreciation with no salvage value, what is the depreciation of the roof?
Correct Answer
B) $7,200
18000×10÷25=7200. Common errors: reporting the remaining (undepreciated) amount instead of depreciation gives $10,800; dividing by the 15-year remaining life instead of the 25-year total life gives $12,000; taking only one year of depreciation (18,000 ÷ 25) gives $720.
Why This Is the Correct Answer
Option B is correct because the age-life ratio is 10 ÷ 25 = 0.40. Applying it to the roof's cost new gives $18,000 × 0.40 = $7,200. This uses the component's own 25-year economic life as directed.
Why the Other Options Are Wrong
Option A: $720
Option A, $720, is only one year of depreciation ($18,000 ÷ 25). The roof has an effective age of 10 years, so depreciation is $18,000 × 10 ÷ 25 = $7,200.
Option C: $10,800
Option C, $10,800, is the remaining undepreciated amount, $18,000 × (1 − 10/25). Depreciation is $18,000 × 10 ÷ 25 = $7,200.
Option D: $12,000
Option D, $12,000, divides by the 15-year remaining life instead of the 25-year total life: $18,000 × 10 ÷ 15. The age-life method uses total economic life, giving $7,200.
Age over life, times cost
Depreciation equals effective age divided by total economic life, multiplied by cost new.
How to use: Use this formula for any straight-line age-life depreciation question, whole building or component.
Exam Tip
The denominator is total economic life, not remaining life. Check that you are reporting the depreciation, not what is left.
Common Mistakes to Avoid
- -Dividing by remaining life instead of total economic life
- -Reporting the undepreciated balance as depreciation
- -Using the dwelling's economic life for a short-lived component
Concept Deep Dive
Analysis
This question tests age-life depreciation applied to a short-lived component. The roof's own effective age and component economic life are used, not the dwelling's life. Depreciation equals cost new times effective age divided by total economic life.
Background Knowledge
The age-life method estimates depreciation by dividing effective age by total economic life and applying that ratio to cost new. Short-lived components such as roofs have economic lives shorter than the main structure, so they are often depreciated separately using their own lives.
Real-World Application
An appraiser using the breakdown method separates the roof covering from the long-lived structure. Based on the roof's condition and a typical component life, the appraiser applies a separate age-life ratio to the roof's current cost.
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Previous Question
An appraiser reviews three items of physical deterioration at a dwelling: roofing, with a cost to cure of $9,200 and a benefit of $18,000; foundation, with a cost to cure of $45,000 and a benefit of $12,000; and paint, with a cost to cure of $3,800 and a benefit of $5,500. An item is economically curable only if its benefit exceeds its cost to cure, and there are no other costs or benefits. What is the total cost to cure of the curable items?
Next Question
Short-lived components already have separately measured depreciation. Why exclude their cost from this model’s long-lived ratio base?