Improvements with a cost new of $580,000 have a remaining economic life of 40 years out of a total economic life of 50 years, and the site is worth $90,000. Assuming straight-line depreciation with no salvage value and no additional losses, what is the cost approach indication?
Correct Answer
C) $554,000
580000×40÷50+90000 = 554000. Common errors: leaving out the site value gives $464,000; not depreciating the improvements gives $670,000; applying the depreciation share (10/50) instead of the remaining-life share gives $206,000.
Why This Is the Correct Answer
Option C is correct because the remaining-life share 40/50 = 80% is the percent good, so the depreciated improvement is $580,000 × 40 ÷ 50 = $464,000. Adding the $90,000 site gives $554,000.
Why the Other Options Are Wrong
Option A: $206,000
Option A, $206,000, applies the depreciation share (10/50) instead of the remaining-life share: $580,000 × 10/50 + $90,000 = $116,000 + $90,000 = $206,000. The correct figure is $580,000 × 40/50 + $90,000 = $554,000.
Option B: $464,000
Option B, $464,000, leaves out the site value: $580,000 × 40 ÷ 50 = $464,000. Adding the $90,000 site gives $554,000.
Option D: $670,000
Option D, $670,000, does not depreciate the improvements: $580,000 + $90,000 = $670,000. Straight-line depreciation means multiplying cost new by 40/50 first, giving $464,000 + $90,000 = $554,000.
Remaining Life Means Percent Good
Remaining life ÷ Total life = percent good, the share of cost that survives. Effective age ÷ Total life = the share lost.
How to use: Use this to check whether a fraction measures value lost or value remaining.
Exam Tip
Check which life figure is in the numerator; remaining life gives the value left, effective age gives the depreciation.
Common Mistakes to Avoid
- -Applying the depreciation share where the remaining share is needed
- -Omitting site value from the total
- -Skipping depreciation entirely
Concept Deep Dive
Analysis
This question expresses the age-life model through the remaining-life share: remaining economic life divided by total life gives the percent good. Multiplying cost new by that share gives the depreciated improvement, and site value is then added.
Background Knowledge
Under a straight-line age-life model, the depreciation fraction is effective age over total life, and its complement is the remaining-life fraction, or percent good. Multiplying cost new by percent good gives depreciated cost directly. Site value is added separately in the cost approach.
Real-World Application
An appraiser estimates that a building with a 50-year total life has 40 years of remaining economic life. She multiplies the $580,000 cost new by 80% percent good and adds the $90,000 site value for a $554,000 cost approach indication.
More Cost Approach Questions
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Previous Question
The subject improvements contain 2,150 sf, and current cost new is $240 per square foot. Total depreciation of the improvements is $66,000, and site value is $100,000. No other costs or losses apply. What value does the cost approach indicate?
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