A 15-year-old house has cost new of $420,000 with short-lived items totaling $58,000 in cost and $24,000 of depreciation charged against them. If the long-lived ratio is 18%, total physical depreciation is:
Correct Answer
A) $89,160
Why this is correct: $89,160. The governing concept is the breakdown method for depreciation. Step 1: Subtract short-lived cost from total cost: $420,000 - $58,000 = $362,000 (long-lived cost). Step 2: Apply the long-lived depreciation ratio: $362,000 * 18% = $65,160 depreciation on long-lived items. Step 3: Add the already charged short-lived depreciation: $65,160 + $24,000 = $89,160 total physical depreciation. Why the other choices are wrong: $99,600 applying the ratio to the full cost new is wrong because it double-counts depreciation on short-lived items (applying 18% to their cost and adding their $24k depreciation). $75,600 counting only the long-lived portion is wrong because it omits the $24k short-lived depreciation. $24,000, the short-lived charge alone is wrong because it ignores depreciation on the long-lived structure. Exam tip: In the breakdown method, apply the long-lived depreciation ratio only to the long-lived cost base to avoid double-counting.
Why This Is the Correct Answer
Separate the bases first: $420,000 cost new minus $58,000 of short-lived cost leaves a $362,000 long-lived base. Applying the 18 percent long-lived ratio gives $362,000 x 0.18 = $65,160. Adding the $24,000 already charged against the short-lived items yields $89,160 of total physical depreciation. The two components are computed on non-overlapping cost bases and then summed.
Why the Other Options Are Wrong
Option B: $99,600 applying the ratio to the full cost new
$99,600 comes from applying 18 percent to the entire $420,000 cost new, producing $75,600, and then adding the $24,000 short-lived charge on top. That charges the short-lived items twice, once at the long-lived rate and once at their own measured depreciation. The whole point of the breakdown method is to keep those bases separate.
Option C: $75,600 counting only the long-lived portion
$75,600 is 18 percent of the full cost new and stops there. It both uses the wrong base, since the short-lived cost should have been removed, and omits the $24,000 of short-lived depreciation entirely. Two errors happen to partially offset, which is what makes the figure look plausible.
Option D: $24,000, the short-lived charge alone
$24,000 counts only the short-lived charge and ignores the structural shell completely. A fifteen-year-old house has measurable depreciation in its framing, foundation, wiring and envelope, which is precisely what the 18 percent long-lived ratio quantifies. Reporting only short-lived depreciation would grossly understate accrued depreciation.
Strip, Then Age
Peel the short-lived items off the top of cost new like removing the toppings before weighing the pizza base. Age only what is left at the long-lived rate, then set the short-lived depreciation back on top as a separate dollar figure. Nothing gets weighed twice.
How to use: Any time a stem gives you cost new, a short-lived cost, a short-lived depreciation dollar amount and a long-lived percentage, do the subtraction before the multiplication. The distractor built from the unsubtracted base will always be sitting in the option list.
Exam Tip
Circle the short-lived cost figure as soon as you see it; its only job in the problem is to be removed from the base.
Common Mistakes to Avoid
- -Applying the long-lived percentage to full cost new instead of the reduced base
- -Forgetting to add the separately measured short-lived depreciation
- -Treating the long-lived ratio as if it covered the entire structure including replaceable components
Concept Deep Dive
Analysis
This is the breakdown method of estimating accrued depreciation, specifically the physical component. The breakdown method splits the improvements into short-lived items, those that will be replaced at least once during the building's economic life such as roof cover, carpet, paint, water heater and HVAC, and long-lived items, the structural shell that lasts as long as the building. Each group is depreciated on its own schedule, so the depreciation charged to short-lived items must be excluded from the base to which the long-lived percentage is applied. Failing to remove the short-lived cost before applying the long-lived ratio is the classic double count that this question is built to catch.
Background Knowledge
You need to know the breakdown method's split between short-lived and long-lived items and that each is depreciated against its own cost base. You also need the ordering rule: strip short-lived cost out of cost new before applying any long-lived depreciation percentage.
Real-World Application
In a cost approach on an older single-family home, the appraiser prices the roof, HVAC and finishes as short-lived items with their own effective ages, then applies an age-life ratio to the remaining structural cost so that the roof is not depreciated both as a component and as part of the shell.
More Cost Approach Questions
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