A building has an effective age of 15 years and a total economic life of 50 years. Using the age-life method, what is the percentage of accrued depreciation?
Correct Answer
A) 30%
Accrued depreciation = Effective age ÷ Total economic life = 15 ÷ 50 = 0.30 or 30%.
Why This Is the Correct Answer
Option A (30%) is correct because the age-life method uses a simple division formula: effective age divided by total economic life. In this case, 15 years ÷ 50 years = 0.30 or 30%. This represents the percentage of the building's total economic life that has already been consumed. The calculation is straightforward and linear, assuming depreciation occurs at a constant rate throughout the building's economic life.
Why the Other Options Are Wrong
Option B: 35%
Option B (35%) is incorrect because it results from an improper calculation or misunderstanding of the formula. This percentage would require an effective age of 17.5 years (35% × 50 years), which doesn't match the given effective age of 15 years.
Option C: 25%
Option C (25%) is incorrect as it would represent an effective age of 12.5 years (25% × 50 years), not the actual effective age of 15 years given in the problem. This error might occur from misreading the effective age or making a calculation mistake.
Option D: 70%
Option D (70%) is completely incorrect and represents a fundamental misunderstanding of the concept. This percentage would indicate that 70% of the building's life has been consumed, requiring an effective age of 35 years, which is more than double the actual effective age of 15 years.
EAT Formula
Remember 'EAT' - Effective Age over Total economic life. Just like eating consumes food over time, effective age consumes the building's economic life over its total lifespan.
How to use: When you see an age-life depreciation question, immediately think 'EAT' and set up the fraction: Effective Age (top) ÷ Total economic life (bottom). Convert the decimal result to a percentage.
Exam Tip
Always double-check your division by multiplying your percentage answer by the total economic life - it should equal the effective age. For example: 30% × 50 years = 15 years ✓
Common Mistakes to Avoid
- -Dividing total economic life by effective age (inverting the formula)
- -Forgetting to convert the decimal result to a percentage
- -Confusing effective age with actual chronological age
Concept Deep Dive
Analysis
The age-life method is a fundamental depreciation calculation technique used in the cost approach to real estate appraisal. This method assumes that depreciation occurs at a steady, linear rate over the building's total economic life. The effective age represents the apparent age of the building based on its condition and utility, which may differ from its actual chronological age due to maintenance, renovations, or deferred maintenance. The total economic life is the period over which the building is expected to contribute value to the property, after which it would typically be demolished or require major renovation.
Background Knowledge
The age-life method is one of three primary methods for calculating accrued depreciation in the cost approach, alongside the breakdown method and the market extraction method. This method assumes straight-line depreciation and is most appropriate when the building is experiencing typical wear and tear without significant functional or external obsolescence.
Real-World Application
An appraiser evaluating a 15-year-old office building would use the age-life method when the building shows normal wear consistent with its age, has been properly maintained, and doesn't suffer from significant functional obsolescence or adverse external factors that would warrant more complex depreciation methods.
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