Cost new is $500,000, short-lived items cost $70,000 with $30,000 of depreciation, and the long-lived ratio is 22%. Total physical depreciation is:
Correct Answer
C) $124,600
Why this is correct: First, subtract the cost of short-lived items ($70,000) from cost new ($500,000), leaving $430,000 for long-lived items. Apply the 22% depreciation ratio to the long-lived cost: $430,000 × 0.22 = $94,600. Then add the given short-lived depreciation ($30,000): $94,600 + $30,000 = $124,600. Why the other choices are wrong: $110,000 counting only the long-lived portion is wrong; it omits the short-lived depreciation. $140,000 applying the ratio to full cost is wrong; it incorrectly applies the ratio to the short-lived cost, double-counting. $30,000, the short-lived charge alone is wrong; it omits depreciation on the long-lived portion. Exam tip: Avoid double depreciation: remove short-lived cost before applying the overall ratio.
Why This Is the Correct Answer
Removing the $70,000 of short-lived cost leaves $430,000, and 22 percent of that is $94,600, which added to the $30,000 of short-lived depreciation gives $124,600.
Why the Other Options Are Wrong
Option A: $110,000 counting only the long-lived portion
$110,000 counts only a long-lived figure and omits the short-lived depreciation already measured.
Option B: $140,000 applying the ratio to full cost
$140,000 applies the 22 percent ratio to the full cost new, double-counting the short-lived items.
Option D: $30,000, the short-lived charge alone
$30,000 is the short-lived charge alone, stopping before the long-lived component is computed.
Remove, Then Apply
Remove, Then Apply. Take the short-lived cost out first or you charge for it twice.
How to use: Write the basis reduction explicitly: cost new less short-lived cost. Every wrong answer skips that line.
Exam Tip
The same removal principle applies to curable items in the wider depreciation breakdown — anything measured separately comes out of the basis.
Common Mistakes to Avoid
- -Applying the ratio to full cost new
- -Omitting one of the two components
- -Removing short-lived depreciation rather than short-lived cost from the basis
Concept Deep Dive
Analysis
Breakdown analysis separates physical deterioration into short-lived and long-lived components so that neither is counted twice. Short-lived items — roofing, mechanical equipment, floor coverings and the like — are depreciated individually against their own effective ages and lives, giving $30,000 here. The long-lived ratio is then applied only to what remains after those items are removed from the cost basis: $500,000 less $70,000 of short-lived cost leaves $430,000, and 22 percent of that is $94,600. The two components sum to $124,600. The distractors each capture a specific misstep: applying the ratio to the full $500,000 double-counts the short-lived items, taking only the long-lived portion omits the short-lived depreciation already measured, and reporting $30,000 alone stops after the first component. The removal step is the whole point of the method, and it is where the arithmetic usually goes wrong.
Background Knowledge
Breakdown analysis measures short-lived item depreciation individually, removes their cost from the basis, and applies an age-life ratio to the remaining long-lived cost, summing the two to give total physical deterioration.
Real-World Application
An appraiser measures $30,000 of short-lived depreciation, applies 22 percent to the remaining $430,000, and reports $124,600 of total physical deterioration.
More Cost Approach Questions
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