The historical cost of an improvement was $350,000, and an appropriate index multiplier for the same scope of work is 1.20. Total depreciation is 20% of the trended cost, and site value is $175,000. What is the total indicated value?
Correct Answer
C) $511,000
350000×1.20×0.80+175000 = 511000. Common errors: leaving out the site value gives $336,000; not trending the historical cost gives $455,000; not deducting the 20% depreciation gives $595,000.
Why This Is the Correct Answer
Option C is correct because $350,000 x 1.20 = $420,000 trended cost, $420,000 x 0.80 = $336,000 after 20% depreciation, and adding the $175,000 site gives $511,000.
Why the Other Options Are Wrong
Option A: $336,000
Option A, $336,000, leaves out the site value: $350,000 x 1.20 x 0.80 = $336,000. Adding the $175,000 site gives $511,000.
Option B: $455,000
Option B, $455,000, does not trend the historical cost: $350,000 x 0.80 + $175,000 = $455,000. Applying the 1.20 multiplier first gives $420,000 x 0.80 + $175,000 = $511,000.
Option D: $595,000
Option D, $595,000, does not deduct the 20% depreciation: $420,000 + $175,000 = $595,000. Applying 80% percent good gives $336,000 + $175,000 = $511,000.
Trend, percent good, add land
Multiply by the index, multiply by percent good, then add the land.
How to use: Use this chain for trended-cost questions with a percentage depreciation.
Exam Tip
Apply the depreciation percentage to the trended cost, not the original historical cost.
Common Mistakes to Avoid
- -Depreciating the historical cost before trending it
- -Forgetting to add site value
- -Skipping the depreciation deduction
Concept Deep Dive
Analysis
This question tests trending a historical cost with an index multiplier, applying a percentage depreciation to the trended cost, and adding site value. Depreciation of 20% means multiplying by 80% percent good. Trend first, then depreciate, then add the site.
Background Knowledge
Trending adjusts initial costs up or down with an index to estimate current cost. Because price indices only approximately measure cost changes, the trended figure is an estimate, and depreciation and site value are still needed to reach a cost approach indication.
Real-World Application
An appraiser has original building cost from construction records and applies a cost index multiplier to reach current cost. The appraiser then applies supported depreciation and adds land value supported by vacant land sales.
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