A building cost $2,500,000 to construct five years ago. It has an effective age of 8 years and a total economic life of 50 years. Using the age-life method, what is the amount of accrued depreciation?
Correct Answer
B) $400,000
Accrued depreciation = (Effective Age ÷ Total Economic Life) × Current Cost = (8 ÷ 50) × $2,500,000 = 0.16 × $2,500,000 = $400,000.
Why This Is the Correct Answer
Option B ($400,000) correctly applies the age-life method formula: Accrued Depreciation = (Effective Age ÷ Total Economic Life) × Current Cost. Using the given values: (8 years ÷ 50 years) × $2,500,000 = 0.16 × $2,500,000 = $400,000. The calculation properly uses the effective age of 8 years (not the chronological age of 5 years) and applies it against the current replacement cost. This represents 16% total depreciation over the building's economic life.
Why the Other Options Are Wrong
Option A: $250,000
Option A ($250,000) appears to incorrectly use the chronological age of 5 years instead of the effective age of 8 years, resulting in (5 ÷ 50) × $2,500,000 = $250,000, which ignores the building's actual condition.
Option C: $200,000
Option C ($200,000) represents only 8% depreciation, which doesn't correspond to any logical application of the given data and appears to be an arbitrary calculation error.
Option D: $500,000
Option D ($500,000) represents 20% depreciation, which would require either a 10-year effective age or a 40-year total economic life, neither of which matches the given information.
EARL Formula
EARL: Effective Age Ratio × Life cost. Remember 'Earl ages effectively' - always use Effective age, not chronological age, in the Ratio calculation against total economic Life, then multiply by current cost.
How to use: When you see an age-life depreciation problem, immediately identify the EARL components: find the Effective Age (not chronological), create the Ratio with total economic life, then multiply by current cost (Life cost).
Exam Tip
Always double-check that you're using effective age, not chronological age, and verify your percentage calculation makes sense (8÷50 = 16% = 0.16).
Common Mistakes to Avoid
- -Using chronological age instead of effective age
- -Forgetting to convert the ratio to a decimal before multiplying
- -Using original cost instead of current replacement cost
Concept Deep Dive
Analysis
The age-life method is a fundamental depreciation calculation technique used in the cost approach to valuation. It assumes that depreciation occurs at a steady, linear rate over the economic life of a building. The method uses effective age (which reflects the actual condition and utility of the building) rather than chronological age, as buildings can age differently based on maintenance, use, and market conditions. This question tests the appraiser's ability to apply the basic age-life formula and understand that the current replacement cost, not the original construction cost, should be used in the calculation.
Background Knowledge
The age-life method assumes depreciation occurs linearly over time and uses effective age (condition-based age) rather than chronological age. Effective age can be greater or less than chronological age depending on maintenance, use, and obsolescence factors.
Real-World Application
An appraiser evaluating a 5-year-old office building that appears to be in 8-year-old condition due to deferred maintenance would use the effective age of 8 years to calculate depreciation, reflecting the building's actual market appeal and functionality.
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