Using the age-life method, what is the accrued depreciation for a 15-year-old building with a total economic life of 60 years and a reproduction cost of $400,000?
Correct Answer
A) $100,000
Why this is correct: The accrued depreciation is $100,000. Using the straight-line age-life method: Depreciation = (Effective Age / Total Economic Life) x Reproduction Cost New. Here, (15 years / 60 years) = 0.25 or 25%. 25% of $400,000 = $100,000. Why the other choices are wrong: $150,000 would be (15/40) x $400,000, using an incorrect economic life. $300,000 would be (45/60) x $400,000, using an incorrect age. $200,000 would be (15/30) x $400,000, again using an incorrect economic life. Exam tip: In age-life problems, always set up the fraction as (Age / Total Life) first. Double-check that you are using the correct 'age' (usually effective age) and the correct 'life' (total economic life).
Why This Is the Correct Answer
Option B ($100,000) correctly applies the age-life formula: (Effective Age ÷ Economic Life) × Reproduction Cost. The calculation is (15 ÷ 60) × $400,000 = 0.25 × $400,000 = $100,000. This represents 25% depreciation over 25% of the building's economic life (15 years out of 60 years). The straight-line depreciation assumption means the building loses value uniformly over its economic life.
Why the Other Options Are Wrong
ALE Formula Memory
Remember 'ALE' - Age over Life times Expense. Age (effective age) divided by Life (economic life) multiplied by Expense (reproduction cost) equals 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, economic life on bottom, multiply by the cost figure given.
Exam Tip
Always double-check that you're calculating depreciation (the amount lost) rather than remaining value - these are commonly confused on exams.
Common Mistakes to Avoid
- -Calculating remaining value instead of accrued depreciation
- -Using chronological age instead of effective age when they differ
- -Forgetting to convert the decimal result to a dollar amount by multiplying by reproduction cost
Concept Deep Dive
Analysis
The age-life method is a fundamental depreciation calculation technique used in the cost approach to real estate valuation. This method assumes that depreciation occurs at a uniform rate over the economic life of a building, creating a straight-line depreciation pattern. The formula calculates what percentage of the building's useful life has been consumed and applies that same percentage to the reproduction cost to determine total accrued depreciation. This method is most reliable when the building has been well-maintained and the effective age closely matches the actual age.
Background Knowledge
The age-life method assumes depreciation occurs uniformly over time and requires knowing the effective age (actual wear and tear equivalent) and total economic life (total useful lifespan). Economic life represents the period during which improvements contribute to property value, while effective age may differ from chronological age based on maintenance and condition.
Real-World Application
Appraisers use this method when valuing older commercial buildings or residential properties where detailed condition analysis isn't feasible, providing a quick estimate of physical deterioration for cost approach calculations.
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