An appraiser estimates the current cost new of the improvements at $2,500,000. Depreciation is measured as a 15% deduction from cost new, followed by a further deduction of 8% of the remaining amount. No other loss applies, and land is not included. What is the depreciated cost of the improvements?
Correct Answer
C) $1,955,000
2500000×0.85×0.92 = 1955000. Common errors: applying the 8% to the original cost instead of the remaining amount gives $1,925,000; leaving out the second (8%) deduction gives $2,125,000; reporting the combined deduction (15% + 8% of cost) instead of the remaining amount gives $575,000.
Why This Is the Correct Answer
Option C is correct because a 15% deduction leaves $2,500,000 x 0.85 = $2,125,000, and an 8% deduction from that remaining amount leaves $2,125,000 x 0.92 = $1,955,000. The second percentage applies to the reduced base, as the stem instructs.
Why the Other Options Are Wrong
Option A: $575,000
Option A, $575,000, is the combined deduction of 15% plus 8% of the original cost: $2,500,000 x (0.15 + 0.08) = $575,000. The question asks for the remaining amount, and the actual sequential deduction is $545,000, leaving $1,955,000.
Option B: $1,925,000
Option B, $1,925,000, applies the 8% to the original cost instead of the remaining amount: $2,500,000 x (1 - 0.15 - 0.08) = $1,925,000. The stem says to take 8% of the remaining $2,125,000, which gives $1,955,000.
Option D: $2,125,000
Option D, $2,125,000, takes only the first deduction: $2,500,000 x 0.85 = $2,125,000. The 8% second deduction must also be applied, giving $1,955,000.
Multiply the complements
For deductions in sequence, multiply the complements: 0.85 times 0.92. Do not add the percentages together.
How to use: Use multiply the complements whenever the second percentage applies to what is left.
Exam Tip
Read whether each percentage applies to the original cost or to the remaining amount. The words remaining amount mean you multiply in sequence.
Common Mistakes to Avoid
- -Adding the two percentages and applying them to the original cost
- -Stopping after the first deduction
- -Reporting the deduction instead of the remaining amount
Concept Deep Dive
Analysis
This question tests applying two percentage deductions in sequence. The second deduction is taken from the amount remaining after the first, not from the original cost. Multiply cost new by the two complements in turn.
Background Knowledge
When depreciation items are stated as percentages of different bases, the base for each one matters. Applying a percentage to a remaining amount produces a smaller deduction than applying it to the original cost. Appraisers need to state clearly which base each deduction uses to avoid overstating or understating total depreciation.
Real-World Application
An appraiser's model first deducts 15% of cost new for physical wear and then takes a further 8% from the remaining amount for a separately measured issue. She computes each step on its stated base so the total deduction is not overstated.
More Cost Approach Questions
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