An improvement with an effective age of 20 years has 20% total depreciation, all on a straight-line basis. What average annual percentage of original cost does that represent?
Correct Answer
A) 1.0%
20 percent÷20 years = 1 percent per year. Common errors: reporting the total depreciation percentage instead of the annual rate gives 20.0%; dividing 100% by 20 years, ignoring that only 20% is depreciated gives 5.0%; reporting the percent good instead of the annual rate gives 80.0%.
Why This Is the Correct Answer
Option A is correct because a straight-line model spreads total depreciation evenly across the effective years. Dividing 20% by 20 years gives 1.0% of original cost per year.
Why the Other Options Are Wrong
Option B: 5.0%
Option B, 5.0%, is wrong because it divides 100% by 20 years, as if the whole cost were used up in 20 years. Only 20% has been depreciated, so the rate is 20% / 20 = 1.0%.
Option C: 20.0%
Option C, 20.0%, is wrong because it is the total depreciation over all 20 years, not the annual rate. Spreading 20% over 20 years gives 1.0% per year.
Option D: 80.0%
Option D, 80.0%, is wrong because it is the percent good (100% - 20%), the share of cost remaining. It is not an annual depreciation rate, which is 1.0%.
Total loss over years
Annual rate equals total percent lost divided by effective years; percent good is what is left, not a yearly rate.
How to use: Use this whenever a question gives total depreciation and years and asks for an annual percentage.
Exam Tip
Check whether the question wants a total, an annual rate or a remaining percentage. Each is a likely distractor for the others.
Common Mistakes to Avoid
- -Reporting the total depreciation percentage as the annual rate
- -Dividing 100% by the years instead of the actual depreciation percentage
- -Confusing percent good with a depreciation rate
Concept Deep Dive
Analysis
This question tests converting a total depreciation percentage into an average annual rate under a straight-line model. If 20% of original cost is lost over 20 effective years, the average loss is 20% / 20 = 1% per year. The rate rests on effective age, not chronological age.
Background Knowledge
Under the age-life (straight-line) approach, depreciation accrues evenly over time. The depreciation percentage equals effective age divided by total economic life, and the average annual rate is the total percentage divided by the years over which it accrued.
Real-World Application
An appraiser's analysis attributes a 20% loss to a building with a 20-year effective age. To compare with other buildings, the appraiser expresses this as an average of about 1% of cost per effective year under a linear model.
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Previous Question
Direct improvement costs $402,000, additional indirect costs $63,000 and separate supported entrepreneurial incentive $85,000 are expressly nonoverlapping. Land is excluded. What full improvement cost new results?
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Three independently supported, nonoverlapping improvement loss allowances are physical $54,000, functional $21,000 and external $33,000. What total accrued improvement depreciation results? Cost new and land are not requested.