A building cost $800,000 to construct 15 years ago and has an estimated total economic life of 60 years. Using the age-life method, what is the accrued depreciation?
Correct Answer
A) $200,000
Age-life method: Depreciation = (Effective Age ÷ Total Economic Life) × Reproduction/Replacement Cost. (15 ÷ 60) × $800,000 = 0.25 × $800,000 = $200,000.
Why This Is the Correct Answer
Option A ($200,000) is correct because it properly applies the age-life formula: (Effective Age ÷ Total Economic Life) × Cost. The calculation is (15 years ÷ 60 years) × $800,000 = 0.25 × $800,000 = $200,000. This represents 25% of the original construction cost, which logically reflects that the building has consumed 25% of its total economic life. The result indicates that one-quarter of the building's value has been lost to depreciation over the 15-year period.
Why the Other Options Are Wrong
Option B: $600,000
$600,000 represents 75% of the original cost, which would be the remaining value after depreciation, not the accrued depreciation itself. This appears to be the result of calculating (45 ÷ 60) × $800,000, using the remaining life instead of the effective age.
Option C: $53,333
$53,333 appears to result from an incorrect calculation, possibly dividing the cost by the economic life ($800,000 ÷ 15) or some other mathematical error. This amount doesn't correspond to any logical application of the age-life method.
Option D: $25,000
$25,000 represents only about 3% of the original cost, which would be far too low for a building that has consumed 25% of its economic life. This might result from incorrectly using annual depreciation rather than total accrued depreciation.
ALE Formula
Remember 'ALE' - Age over Life times Expense: (A)ge ÷ (L)ife × (E)xpense = Accrued Depreciation
How to use: When you see an age-life depreciation question, immediately think 'ALE' and set up the fraction: effective age on top, total economic life on bottom, multiply by the original cost
Exam Tip
Always double-check that you're calculating accrued depreciation (what's lost) rather than remaining value (what's left) - they should add up to the original cost
Common Mistakes to Avoid
- -Calculating remaining value instead of accrued depreciation
- -Using remaining life instead of effective age in the numerator
- -Forgetting to multiply the percentage by the original cost
Concept Deep Dive
Analysis
The age-life method is a fundamental depreciation calculation technique used in real estate appraisal to estimate accrued depreciation based on the relationship between a property's effective age and its total economic life. This method assumes that depreciation occurs at a straight-line rate over the property's useful life, making it a simple but effective tool for appraisers. The calculation involves determining what percentage of the property's economic life has been consumed and applying that percentage to the reproduction or replacement cost. This method is particularly useful when market data is limited and provides a systematic approach to quantifying physical deterioration and functional obsolescence.
Background Knowledge
The age-life method assumes straight-line depreciation over a property's economic life and requires knowledge of the property's effective age (actual age unless renovated) and total economic life (period over which improvements contribute to property value). Appraisers must distinguish between accrued depreciation (amount lost) and remaining value (amount retained).
Real-World Application
Appraisers use the age-life method when appraising older properties where comparable sales are limited, such as unique commercial buildings or properties in rural areas where market data is scarce but construction costs and typical economic lives are known
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