Using straight-line depreciation, what is the annual depreciation rate for a building with a 50-year economic life?
Correct Answer
B) 2.0%
Why this is correct: Straight-line depreciation assumes an equal loss in value each year over the economic life. The annual rate is 100% divided by the total life in years: 100% ÷ 50 years = 2% per year. Why the other choices are wrong: 2.5% corresponds to a 40-year life. 5.0% corresponds to a 20-year life. 1.5% corresponds to a 66.7-year life. Exam tip: For straight-line, the formula is simple: Annual Depreciation Rate = 100% / Economic Life (in years).
Why This Is the Correct Answer
Option B (2.0%) is correct because it properly applies the straight-line depreciation formula: 100% ÷ 50 years = 2.0% per year. This means the building depreciates 2% of its original value each year over its 50-year economic life. The calculation is straightforward division that results in an equal annual depreciation rate. After 50 years, the building will have depreciated 100% of its depreciable value (50 years × 2% = 100%).
Why the Other Options Are Wrong
Option A: 2.5%
Option A (2.5%) results from incorrectly dividing 100% by 40 years instead of 50 years, suggesting confusion about the economic life period given in the problem.
Option C: 5.0%
Option C (5.0%) would result from dividing 100% by 20 years, indicating a significant error in identifying the correct economic life from the problem statement.
Option D: 1.5%
Option D (1.5%) would be the result if the economic life were approximately 67 years (100% ÷ 67 ≈ 1.5%), showing misreading of the given economic life.
The 100-Divide Rule
Remember '100 ÷ Life = Rate' - Always divide 100% by the economic life in years to get the annual straight-line depreciation rate.
How to use: When you see a straight-line depreciation question, immediately identify the economic life and divide 100 by that number. Write '100 ÷ [economic life] = [answer]%' to avoid calculation errors.
Exam Tip
Double-check your division by multiplying your answer by the economic life - it should equal 100%. For example: 2.0% × 50 years = 100%.
Common Mistakes to Avoid
- -Confusing economic life with physical life or tax depreciation periods
- -Dividing the economic life by 100 instead of dividing 100 by the economic life
- -Forgetting to convert the decimal result to a percentage
Concept Deep Dive
Analysis
This question tests understanding of straight-line depreciation calculation, a fundamental concept in real estate appraisal for determining annual depreciation rates. Straight-line depreciation assumes equal depreciation amounts each year over the economic life of a building. The formula divides 100% (total depreciation over the building's life) by the number of years in the economic life to determine the annual percentage rate. This method is widely used in appraisal practice because of its simplicity and acceptance in various valuation approaches.
Background Knowledge
Straight-line depreciation is one of three main depreciation methods used in real estate appraisal, alongside declining balance and sum-of-years digits methods. Economic life represents the period over which a building is expected to contribute to property value, which may differ from physical life or tax depreciation periods.
Real-World Application
Appraisers use straight-line depreciation when applying the cost approach to value older buildings, helping determine the depreciated replacement cost by calculating how much value the building has lost due to age and obsolescence over its economic life.
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