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
B) $100,000
Accrued depreciation = (Effective Age ÷ Economic Life) × Reproduction Cost = (15 ÷ 60) × $400,000 = 0.25 × $400,000 = $100,000.
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
Option A: $300,000
This represents 75% of the reproduction cost ($300,000), which would be the remaining value after depreciation, not the accrued depreciation itself. This confuses depreciation with the depreciated value.
Option C: $200,000
This represents 50% of the reproduction cost, which would only be correct if the building were 30 years old (half of its 60-year economic life), not 15 years old.
Option D: $150,000
This represents 37.5% of the reproduction cost, which doesn't correspond to any logical calculation using the given variables in the age-life method.
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.
More Math & Stats Questions
What is the area of a triangular lot with a base of 120 feet and a height of 80 feet?
An irregular lot has the following measurements: Side A = 100', Side B = 150', Side C = 120', Side D = 180'. If the lot can be divided into two rectangles (100' × 150' and 120' × 30'), what is the total area?
A property has a potential gross income of $180,000, vacancy and collection loss of 7%, and operating expenses of $65,000. What is the NOI?
A property generates $120,000 in net operating income and is valued at $1,500,000. What is the capitalization rate?
A building has potential gross income of $180,000, vacancy and collection loss of 8%, and operating expenses of $54,000. What is the net operating income?
People Also Study
Valuation Principles & Procedures
25% of exam
Property Description & Analysis
20% of exam
Market Analysis & Highest/Best Use
15% of exam
USPAP (Ethics & Standards)
15% of exam
Report Writing & Compliance
10% of exam