A 20-year-old building has an economic life of 50 years and cost $1,000,000 to build. Using the age-life method, what is the accrued depreciation?
Correct Answer
B) $400,000
Age-life method: (Effective Age ÷ Economic Life) × Reproduction Cost. (20 ÷ 50) × $1,000,000 = 0.40 × $1,000,000 = $400,000.
Why This Is the Correct Answer
Option B ($400,000) correctly applies the age-life formula: (Effective Age ÷ Economic Life) × Reproduction Cost. The calculation is (20 years ÷ 50 years) × $1,000,000 = 0.40 × $1,000,000 = $400,000. This represents 40% of the building's economic life having been consumed, resulting in $400,000 of accrued depreciation. The remaining value would be $600,000 ($1,000,000 - $400,000).
Why the Other Options Are Wrong
Option A: $600,000
$600,000 represents the remaining value after depreciation, not the accrued depreciation amount itself
Option C: $200,000
$200,000 would result from incorrectly calculating 20% depreciation instead of the correct 40%
Option D: $800,000
$800,000 would represent 80% depreciation, which would occur if the building were 40 years old, not 20 years old
ALE Formula
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 original cost
Exam Tip
Always double-check that you're calculating depreciation (what's lost) versus remaining value (what's left) - the question will specifically ask for one or the other
Common Mistakes to Avoid
- -Confusing accrued depreciation with remaining value
- -Using actual age instead of effective age when they differ
- -Forgetting to convert the decimal result to dollars 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 constant 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 percentage to the original construction cost. This approach is most reliable when the building has been reasonably 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 (how old the building appears to be) and economic life (total useful life expectancy). Economic life is the period over which improvements contribute to property value, typically determined by market analysis and building type standards.
Real-World Application
Appraisers use this method when valuing older commercial buildings or residential properties where comparable sales are limited, helping determine how much value has been lost due to age and wear
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
Related Tools
Previous Question
An irregular lot has the following dimensions: Side A = 100 ft, Side B = 150 ft, Side C = 120 ft, Side D = 180 ft. Using the coordinate method, if the area calculates to 17,400 sq ft, how many acres is this?
Next Question
Given the following sale prices: $285,000, $295,000, $310,000, $290,000, and $320,000, what is the median sale price?