A building cost $450,000 to construct and has an effective age of 8 years with a total economic life of 50 years. Using the age-life method, the depreciation amount is:
Correct Answer
A) $72,000
Why this is correct: Using the age-life method, depreciation = (Effective Age / Total Economic Life) x Cost New. Here, (8 / 50) x $450,000 = 0.16 x $450,000 = $72,000. Why the other choices are wrong: "$90,000" might result from using actual age if different, or a miscalculation. "$56,250" appears to be a misapplication of a percentage. "$378,000" is the depreciated value (cost new minus depreciation), not the depreciation amount. Exam tip: Depreciation amount = (Effective Age / Total Economic Life) x Cost. The result is the dollar loss in value, not the remaining value.
Why This Is the Correct Answer
Option A ($72,000) correctly applies the age-life formula: (Effective Age ÷ Total Economic Life) × Cost. The calculation is (8 years ÷ 50 years) × $450,000 = 0.16 × $450,000 = $72,000. This represents 16% of the building's total cost, which corresponds to the 16% of its economic life that has already passed. The result shows the accumulated depreciation that has occurred over the 8-year effective age period.
Why the Other Options Are Wrong
Option B: $90,000
Option B ($90,000) suggests using an incorrect effective age or economic life figure, possibly calculating (10 ÷ 50) × $450,000 instead of the given 8-year effective age.
Option C: $56,250
Option C ($56,250) appears to use an incorrect percentage calculation, possibly confusing the depreciation rate or making an arithmetic error in the formula application.
Option D: $378,000
Option D ($378,000) represents the remaining value after depreciation (cost minus depreciation), not the depreciation amount itself. This is a common error where candidates calculate the wrong component of the equation.
DEAL Formula
DEAL = Depreciation = Effective Age ÷ Life × Cost. Remember: 'Make a DEAL to find depreciation - Divide Effective Age by Life, then multiply by Cost.'
How to use: When you see an age-life depreciation problem, immediately write 'DEAL' and set up the formula: D = (EA ÷ L) × C, then plug in the given numbers.
Exam Tip
Always double-check that you're calculating depreciation (the amount lost) rather than remaining value, as both are commonly asked and easily confused.
Common Mistakes to Avoid
- -Calculating remaining value instead of depreciation amount
- -Confusing effective age with chronological age
- -Using incorrect economic life estimates for the property type
Concept Deep Dive
Analysis
The age-life method is a fundamental depreciation calculation technique used in the cost approach to real estate valuation. It assumes that depreciation occurs at a constant rate over the economic life of a building, making it a straight-line depreciation method. The method calculates accumulated depreciation by determining what percentage of the building's total economic life has already passed (effective age), then applying that percentage to the original construction cost. This approach is most reliable when the effective age accurately reflects the building's condition and remaining utility, and when the total economic life estimate is realistic for the property type and market conditions.
Background Knowledge
The age-life method assumes straight-line depreciation where a building loses value uniformly over its economic life. Effective age represents the apparent age based on condition and utility, while total economic life is the period over which the building contributes value to the property.
Real-World Application
Appraisers use the age-life method when estimating depreciation for insurance claims, tax assessments, and cost approach valuations, particularly for newer buildings where physical deterioration follows predictable patterns.
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