A building has an effective age of 15 years and a total economic life of 60 years. Its cost new is $380,000. What is the age-life depreciation?
Correct Answer
C) $95,000, using the 15/60 ratio
Why this is correct: Age-life depreciation uses the ratio of effective age to total economic life. The ratio is 15 years / 60 years = 0.25 or 25%. Depreciation amount is this ratio multiplied by the cost new: 0.25 * 380,000 = 95,000. Why the other choices are wrong: "$76,000, at one-fifth of cost" uses 1/5 (20%) incorrectly. "$57,000, at fifteen sixtieths" incorrectly calculates 15/60 of 380,000 as 57,000 (a math error; 15/60 of 380,000 is 95,000). "$63,300, on remaining life" incorrectly uses remaining life (45 years) in the calculation. Exam tip: Depreciation = (Effective Age / Total Economic Life) * Cost New. Double-check your arithmetic.
Why This Is the Correct Answer
Fifteen years of effective age against a sixty-year total economic life is a ratio of 15 over 60, which reduces to one quarter or 25 percent. Applying that to the $380,000 cost new yields $95,000 of accrued depreciation. The remaining forty-five years of economic life are consistent with the 75 percent of value still intact, which is a useful check on the arithmetic.
Why the Other Options Are Wrong
Option A: $76,000, at one-fifth of cost
$76,000 is 20 percent of cost new, obtained by treating the ratio as one fifth rather than one quarter. Fifteen sixtieths is 0.25, not 0.20; the slip usually comes from a hurried mental division. The dollar difference here is $19,000, enough to matter in any conclusion.
Option B: $57,000, at fifteen sixtieths
$57,000 is 15 percent of $380,000, which comes from reading the effective age of fifteen as a percentage instead of dividing it by the sixty-year life. The option's label even claims to be fifteen sixtieths, but the arithmetic behind the number is not. Always convert the fraction to a decimal before multiplying.
Option D: $63,300, on remaining life
$63,300 is built off the forty-five-year remaining life rather than the effective age and matches no valid form of the age-life formula. Remaining economic life tells you the share of value still present, not the share consumed. Depreciation always uses the age at the top of the fraction.
Age Over Life, Times Cost
Three words in order: age, life, cost. Age goes on top, life goes on the bottom, and the resulting decimal multiplies cost new. Say it before every age-life problem and you will never invert the fraction.
How to use: Write the fraction as digits on scratch paper, reduce it, then convert it to a decimal before touching cost new. Reducing 15 over 60 to one quarter takes a second and eliminates the 20 percent and 15 percent distractors immediately.
Exam Tip
Sanity-check with the complement: if depreciation is 25 percent, the remaining 75 percent should square with the remaining economic life the numbers imply.
Common Mistakes to Avoid
- -Reading effective age as a percentage instead of dividing it by total economic life
- -Inverting the ratio and putting economic life on top
- -Building the calculation on remaining economic life when depreciation is asked for
Concept Deep Dive
Analysis
The straight-line age-life method converts age into a percentage of value already consumed. The ratio is effective age over total economic life, and that percentage is applied to cost new to produce total accrued depreciation from all causes. Because the method is a single ratio, the only two inputs that matter are the numerator, effective age, and the denominator, total economic life; remaining economic life is the complement, not a separate input. Candidates lose points here in two ways: by converting the fraction to the wrong percentage, and by reaching for remaining life when the question asks for depreciation. Total economic life is the full expected span, so effective age plus remaining economic life must equal it.
Background Knowledge
You need the age-life formula: depreciation equals effective age divided by total economic life, multiplied by cost new. You also need to know that total economic life is the sum of effective age and remaining economic life, which lets you verify a ratio quickly.
Real-World Application
In a summary appraisal report on a suburban office building, the appraiser states cost new, an effective age drawn from inspection, and a total economic life drawn from a cost service, then shows the resulting straight-line depreciation as a single line item on the cost approach grid.
More Cost Approach Questions
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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:
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A house has three bedrooms sharing one bathroom, and adding a second bath is economically justified. This is:
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Previous Question
A 45-year-old office building has undergone extensive system upgrades (HVAC, electrical, fire suppression) and interior modernization, resulting in strong tenant demand and rental rates exceeding those of newer buildings in the area. The appraiser estimates its total economic life at 65 years. Which statement best reflects the likely relationship among its chronological age, effective age, and remaining economic life?
Next Question
A 12,000-square-foot retail strip center was constructed in 2005 with four identical 3,000-sf tenant spaces, each featuring a dedicated 200-sf enclosed storage room. Market analysis reveals that today’s comparable centers allocate only 75 sf of storage per unit, and tenants consistently lease adjacent spaces or use off-site storage due to the excess on-site capacity. The appraiser estimates the incremental construction cost of the excess 125 sf per unit (500 sf total) was $8,500 at time of construction. Physical depreciation has reduced the building’s reproduction cost new by 22%. What is the most supportable measure of functional obsolescence caused by this superadequacy?