A roof with a 25-year life is 10 years old and would cost $18,000 to replace new. What is its depreciation as a short-lived item?
Correct Answer
C) $7,200, the portion of its life used up
Why this is correct: For a short-lived item, depreciation is based on its effective age relative to its total economic life. The formula is: (Effective Age / Total Economic Life) * Cost New. Here: (10 years / 25 years) * $18,000 = 0.4 * $18,000 = $7,200. Why the other choices are wrong: $18,000 is the full replacement cost, not the depreciation. $10,800 represents the remaining value (60% of $18,000), not the depreciation. 'Nothing, since the roof does not leak yet' confuses physical failure with accrued depreciation; value is lost as the item ages, not just when it breaks. Exam tip: For age-life depreciation: Depreciation = (Effective Age / Total Economic Life) * Cost New. The result is the dollar amount of value already consumed.
Why This Is the Correct Answer
Option C is correct because ten years of a twenty-five-year life is 40 percent consumed, and 40 percent of the $18,000 cost new equals $7,200. The question asks for depreciation, meaning value already lost, which is exactly what that fraction measures. Checking the complement confirms it, since $7,200 plus the $10,800 remaining equals the full $18,000. This figure would enter the breakdown analysis as the short-lived component's depreciation line.
Why the Other Options Are Wrong
Option A: $18,000, the full replacement figure
The full $18,000 is cost new, the starting point of the calculation rather than its result, and deducting all of it would treat a roof with fifteen years of service left as worthless. Full depreciation of a component is appropriate only when it is at or past the end of its life and contributes nothing. Confusing the base with the deduction discards value the property clearly still has.
Option B: $10,800, the life remaining in the roof
The $10,800 figure is the remaining value, the 60 percent of the roof's life still ahead of it, which is the mirror image of what the question asked. It is the most attractive distractor because the arithmetic behind it is correct; only the direction is wrong. Reading the question word for word, depreciation versus remaining value, is what separates these two.
Option D: Nothing, since the roof does not leak yet
Waiting for physical failure confuses functionality with value, since a buyer paying for a house with a fifteen-year-old roof knows a replacement is approaching and prices accordingly. Depreciation accrues throughout a component's life as its remaining service shrinks, not in a single step when it fails. This reasoning would also make deferred maintenance the only recognized form of physical deterioration.
Used Up Versus Left Over
Every age-life problem has two answers hiding in it: used up and left over. Ten of twenty-five years used means 40 percent used up and 60 percent left over. Depreciation is always the used-up half. Compute both, then read the question again to see which one it wants.
How to use: Write the fraction of life consumed first, apply it to cost new, then note the complement so you can see both candidate answers. Match the one the stem requested. If two choices sum to cost new, you have found the used-up and left-over pair and the question is testing direction, not arithmetic.
Exam Tip
Underline the words depreciation, remaining value, or contributory value in the stem before computing; these items almost always place both the correct figure and its complement among the choices.
Common Mistakes to Avoid
- -Reporting remaining value when the question asked for depreciation
- -Using chronological age when observed condition indicates a different effective age
- -Leaving separately depreciated component costs in the long-lived base and double counting
Concept Deep Dive
Analysis
This question tests the age-life computation for a single short-lived component. Depreciation for such an item equals its effective age divided by its total economic life, multiplied by its cost new, which measures the share of the component's useful life already consumed. Here the roof has used ten of its twenty-five years, so 40 percent of its life is gone, and 40 percent of $18,000 is $7,200. The complementary figure, $10,800, is what remains, and the two always sum to cost new, which gives you a fast internal check. The distinction that trips candidates is between depreciation, the amount already lost, and remaining value, the amount still there, since the question can ask for either and both appear among the choices. Note also that effective age is not automatically chronological age: a roof poorly maintained in a harsh climate may have an effective age above ten, while one under a shaded, well-drained slope may perform better than its years suggest. The appraiser observes condition and judges effective age rather than reading it off the installation date.
Background Knowledge
You need the age-life formula, effective age divided by total economic life times cost new, and the understanding that the complement of depreciation is remaining value. You should also know that effective age is a judgment based on observed condition rather than a calendar count, and that in a full breakdown analysis the cost of items depreciated separately is removed from the long-lived component base to avoid double counting.
Real-World Application
Valuing a house with a ten-year-old architectural shingle roof in good condition, an appraiser judges the effective age at ten against a twenty-five-year life, deducts $7,200 as short-lived depreciation, removes the $18,000 roof cost from the long-lived base, and applies the building's effective age to what remains.
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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