An appraiser is estimating depreciation for a retail strip center using the age-life method. She determines the building’s total economic life is 40 years and its effective age is 18 years. The reproduction cost new (RCN) is $2,400,000. What is the amount of accrued depreciation?
Correct Answer
B) $1,080,000
Accrued depreciation = (Effective Age ÷ Total Economic Life) × RCN = (18 ÷ 40) × $2,400,000 = 0.45 × $2,400,000 = $1,080,000. This is the standard age-life (straight-line) depreciation calculation required under the cost approach per The Appraisal of Real Estate (15th ed.) Ch. 13 and USPAP Standards Rule 1-4. Option A results from misapplying 18% instead of 45%; C incorrectly uses (40−18)/40; D reverses the ratio.
Why This Is the Correct Answer
Option B is right because eighteen divided by forty is forty-five percent, and forty-five percent of two million four hundred thousand dollars is one million eighty thousand dollars. The formula is effective age divided by total economic life, multiplied by cost new. That figure is subtracted from reproduction cost new, leaving a depreciated improvement value of one million three hundred twenty thousand dollars, to which site value is then added. USPAP Standards Rule 1-4(b) requires that where a cost approach is necessary for credible assignment results the appraiser analyze such comparable data as are available to estimate the difference between cost new and the present worth of the improvements.
Why the Other Options Are Wrong
Option A: $432,000
Four hundred thirty-two thousand is eighteen percent of the cost new, which comes from treating the effective age of eighteen years as a percentage rather than as the numerator of a ratio. The forty-year economic life never enters the calculation, which is the tell. Always form the ratio first and confirm it is a decimal between zero and one before multiplying.
Option C: $1,320,000
One million three hundred twenty thousand is fifty-five percent of cost new, or twenty-two over forty, which is the remaining economic life rather than the consumed portion. That figure is in fact the depreciated value of the improvements, not the depreciation, so the candidate has computed the right number and answered the wrong question. Read the stem for whether it asks for accrued depreciation or for depreciated cost.
Option D: $1,968,000
One million nine hundred sixty-eight thousand is eighty-two percent of cost new, obtained by inverting the ratio to forty over forty-nine or by some similar transposition, and it would leave a building worth only four hundred thirty-two thousand after eighteen of forty years. A quick reasonableness check catches it: a building not quite halfway through its economic life should not have lost four-fifths of its value. Sanity-check every depreciation figure against the fraction of life consumed.
Life used over life total
Depreciation is the fraction of life used up. Effective age is life used; total economic life is life total. Put used over total, multiply by cost new, and you have depreciation. Flip the fraction and you have what is left, not what is lost.
How to use: Write the fraction before touching the calculator and read it aloud - eighteen of forty years used, so forty-five percent gone. Then check whether the question wants the amount lost or the amount remaining, because both numbers will be in the answer choices.
Exam Tip
Effective age is not chronological age; a stem that gives you both is testing whether you use the one that reflects condition and market acceptance.
Common Mistakes to Avoid
- -Using chronological age when effective age is given
- -Inverting the ratio and computing remaining value instead of depreciation
- -Applying the percentage to total property value rather than to cost new of the improvements
- -Expecting the age-life method to isolate physical, functional, and external causes
Concept Deep Dive
Analysis
This question tests the economic age-life method, the simplest of the depreciation techniques and the one most often computed on the exam. The method treats total accrued depreciation as a straight-line function of how much of a building's economic life has been consumed: the ratio of effective age to total economic life, applied to the cost new of the improvements. Effective age is a judgment about condition, utility, and market acceptance rather than a count of years since construction, so a well-maintained building can carry an effective age below its chronological age and a neglected one above it. Total economic life is the period over which the improvements are expected to contribute to property value. Because the method lumps physical deterioration, functional obsolescence, and external obsolescence into a single percentage, it cannot isolate causes, which is why the breakdown method exists for assignments where the components matter.
Background Knowledge
You need the age-life formula and the definitions behind it - effective age as a judgment reflecting condition and utility, total economic life as the period the improvements contribute to value, and remaining economic life as the difference. You should also know the cost approach sequence of site value plus depreciated cost of improvements, the distinction between reproduction cost and replacement cost, and that the breakdown method separates physical, functional, and external causes where the age-life method cannot.
Real-World Application
A strip center built twenty-six years ago but renovated throughout may carry an effective age of eighteen years, which is what the appraiser applies against a forty-year economic life. The renovation shows up not as a separate credit but as a reduction in effective age, which is how the method absorbs capital improvements.
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:
A 2,050 sq ft dwelling is priced at $178 per square foot with a $34,000 detached garage and $21,500 of site improvements. Cost new is:
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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