An improvement had a historical cost of $210,000. A suitable cost index for the same construction scope was 105 at that time and is 210 today. What is the trended current cost?
Correct Answer
C) $420,000
210000×210÷105 = 420000. Common errors: inverting the index ratio (105 ÷ 210) gives $105,000; not trending the historical cost gives $210,000; treating the current index of 210 as a percentage of 100 gives $441,000.
Why This Is the Correct Answer
Option C is correct because trending multiplies historical cost by current index over historical index: $210,000 × 210 ÷ 105 = $420,000. The index doubled, so the cost doubles for the same construction scope.
Why the Other Options Are Wrong
Option A: $105,000
Option A, $105,000, inverts the index ratio: $210,000 × 105 ÷ 210 = $105,000. Trending forward uses current over historical, giving $210,000 × 210 ÷ 105 = $420,000.
Option B: $210,000
Option B, $210,000, does not trend the historical cost at all. Applying the index ratio gives $210,000 × 210 ÷ 105 = $420,000.
Option D: $441,000
Option D, $441,000, treats the current index of 210 as a percentage of 100: $210,000 × 210 ÷ 100 = $441,000. The historical index is 105, not 100, so the correct ratio is 210 ÷ 105, giving $420,000.
Now Over Then
Trended cost = Historical cost × (Current index ÷ Historical index). Now on top, then on the bottom.
How to use: Use this whenever a question gives two index numbers and a past cost.
Exam Tip
Divide by the historical index given in the problem, not by 100, unless the historical index is 100.
Common Mistakes to Avoid
- -Inverting the index ratio
- -Dividing by 100 instead of the historical index
- -Treating trended cost as modern replacement cost
Concept Deep Dive
Analysis
This question tests the trended historical cost method. Historical cost is multiplied by the ratio of the current index to the historical index. The result estimates current reproduction cost for the same scope, not a modern replacement.
Background Knowledge
The trended historical cost method adjusts an original cost to the current date using a cost index ratio. Price indices only approximately measure cost changes over time, so results are best used as a check. Trending reflects the original construction scope and does not by itself show the cost of a modern equivalent-utility replacement.
Real-World Application
An appraiser has the original $210,000 construction cost for a house and a cost index that rose from 105 to 210. She trends the cost to $420,000 as a check on her cost-service estimate.
More Cost Approach Questions
Why can equivalent-utility replacement cost be useful for an obsolete improvement?
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