The subject improvements have a cost new of $490,000, a remaining economic life of 33 years and a total economic life of 55 years. The site is valued at $171,000. Using straight-line age-life depreciation with no salvage value and no additional loss, what value does the cost approach indicate?
Correct Answer
C) $465,000
490000×33÷55+171000 = 465000. Common errors: leaving out the site value gives $294,000; applying the depreciation share instead of the remaining-life share gives $367,000; not depreciating the improvements gives $661,000.
Why This Is the Correct Answer
Option C is correct because the remaining share is 33 / 55 = 0.60, so the depreciated improvement value is $490,000 x 0.60 = $294,000. Adding the $171,000 site gives $294,000 + $171,000 = $465,000.
Why the Other Options Are Wrong
Option A: $294,000
Option A, $294,000, leaves out the site value: $490,000 x 33 / 55 = $294,000. Adding the $171,000 site gives $465,000.
Option B: $367,000
Option B, $367,000, applies the depreciation share instead of the remaining-life share: $490,000 x (1 - 33/55) = $196,000, plus $171,000 = $367,000. The value remaining uses 33/55, which gives $294,000 plus site, or $465,000.
Option D: $661,000
Option D, $661,000, does not depreciate the improvements: $490,000 + $171,000 = $661,000. With 22 of 55 years used, only 60% of cost new remains, giving $465,000.
Remaining over total stays
Remaining life over total life is the share of cost that stays. Effective age over total life is the share that goes.
How to use: Use stays versus goes to pick the right fraction for the figure you need.
Exam Tip
If the question gives remaining life and total life, you can multiply cost new by remaining over total to reach the depreciated value in one step.
Common Mistakes to Avoid
- -Using the depreciation fraction when the remaining fraction is needed
- -Leaving out the site value
- -Skipping depreciation altogether
Concept Deep Dive
Analysis
This question tests using the remaining-life ratio to find the depreciated improvement value directly, then adding the site. Under a linear age-life model, the share of cost new that remains equals remaining life divided by total life. Multiply cost new by that share and add the site value.
Background Knowledge
In a straight-line age-life model, depreciation equals effective age divided by total economic life, and the remaining value share equals remaining life divided by total life. The two shares add to 100%. Land is valued separately and added after the improvements are depreciated.
Real-World Application
An appraiser estimates that a house has 33 of its 55 years of economic life left. She applies 60% to cost new to find the depreciated improvement contribution and adds the site value from local land sales.
More Cost Approach Questions
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Previous Question
A suitable cost index is used to trend a historical construction cost of $300,000, for the same scope of work, from index 180 to index 270. Total depreciation of the improvements is $85,000, and the site value is $120,000. What value does the cost approach indicate?
Next Question
An appraiser reviewing a trainee's cost approach for a dwelling finds that an 18% depreciation rate, developed for the improvements, was applied to the combined total of $1,170,000 improvement cost new and $365,000 land. By how much does this mistake understate the indicated value?