A component with a 20-year life is 5 years old and costs $12,000 new. Its accrued depreciation is:
Correct Answer
B) $3,000
Why this is correct: Accrued depreciation = (Effective Age ÷ Total Economic Life) × Cost New. Here, (5 years ÷ 20 years) × $12,000 = 0.25 × $12,000 = $3,000. Why the other choices are wrong: "$9,000, the remaining life portion" is wrong; that would be remaining value, not depreciation. "$2,400, at one-fifth per year" is wrong; that uses 1/5 of cost ($2,400) but not based on age-life ratio. "$12,000, its full replacement cost" is wrong; that is the cost new, not depreciation. Exam tip: For age-life depreciation, use: (Effective Age / Total Life) × Cost.
Why This Is the Correct Answer
Five divided by twenty is 0.25, and 0.25 times $12,000 equals $3,000. That figure is the depreciation, the amount already used up, not the amount left. The complement, $9,000, is what the component still contributes and would be carried into the depreciated cost of the improvements. Checking that depreciation plus remaining value equals cost new confirms the arithmetic in one step.
Why the Other Options Are Wrong
Option A: $9,000, the remaining life portion
$9,000 is the remaining value after depreciation, the three quarters of life still ahead, not the depreciation itself. Selecting it means computing correctly and then reporting the wrong side of the calculation. The stem asks specifically for accrued depreciation, which is always the consumed portion.
Option C: $2,400, at one-fifth per year
$2,400 divides the $12,000 cost by five rather than applying the five-over-twenty ratio, which treats the component as having a five-year life instead of a five-year age. It confuses the age with the life, using the wrong number as the denominator's basis. A quick check helps: one-fifth of cost after only a quarter of the life has passed does not reconcile.
Option D: $12,000, its full replacement cost
$12,000 is the full cost new, which would be the depreciation only if the component were entirely worn out and contributing nothing. A five-year-old component with fifteen years of life ahead of it plainly retains value. Selecting the cost new means reading the question as asking for the cost rather than the loss.
Age Over Life, Times Cost
Three words in fixed order: age over life, times cost. The fraction is always used up over total, never used up over remaining. Write the fraction first and confirm it is less than one before multiplying.
How to use: After computing, name what you produced out loud: this is the used-up portion. If the question wants remaining value instead, subtract from cost new rather than recalculating.
Exam Tip
Effective age, not chronological age, belongs in the numerator. A stem that mentions renovation, unusual maintenance, or modernization is signaling that effective age differs from the calendar figure.
Common Mistakes to Avoid
- -Reporting remaining value when the question asks for depreciation
- -Using chronological age when effective age differs
- -Dividing cost by the age rather than applying the age-over-life ratio
Concept Deep Dive
Analysis
The straight-line age-life method spreads a component's cost evenly across its total economic life and treats the portion already consumed as accrued depreciation. The formula is effective age divided by total economic life, multiplied by cost new. Effective age is the age the component appears to be based on its condition and utility, which may be more or less than chronological age depending on maintenance, and total economic life is the period over which the component is expected to contribute to value. Here the component is five years into a twenty-year life, so one quarter of its life is consumed and one quarter of its cost has depreciated. Applying the ratio to $12,000 of cost new gives $3,000 of accrued depreciation and leaves $9,000 of remaining contributory value.
Background Knowledge
You need the straight-line age-life formula, the distinction between effective age and chronological age, and the difference between total economic life and remaining economic life. You should also know that the age-life method produces total depreciation as a lump sum without separating physical, functional, and external causes.
Real-World Application
An appraiser estimating depreciation on a five-year-old HVAC system with a twenty-year expected life applies the age-life ratio to its installed cost, carries $9,000 of remaining contribution into the cost approach, and revisits the effective age when a service record shows the unit was neglected and is performing like a ten-year-old system.
More Cost Approach Questions
In a cost approach for a proposed building, the appropriate cost basis is generally:
A warehouse cost $210,000 to build when the cost index stood at 105. The index is now 210. Its indicated current cost is:
The age-life method expresses depreciation as:
Market extraction of depreciation is limited by the fact that it:
Functional obsolescence caused by a deficiency is measured as curable when:
Curable physical deterioration is measured at cost to cure because:
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A house has three bedrooms sharing one bathroom, and adding a second bath is economically justified. This is:
Direct costs in a construction budget include:
An appraiser writes that a 40-year-old house has an effective age of 10 but describes original wiring, original kitchen and a 25-year-old roof. The report's problem is:
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Physical deterioration that is curable is measured by cost to cure, while incurable deterioration is measured by:
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