A building has two wings that do not overlap. The unrebuilt wing has a cost new of $480,000, an effective age of 25 years and a total life of 50 years, and is depreciated by the age-life method. The rebuilt wing has a cost new of $320,000 and no depreciation. The site is valued at $175,000. No other physical, functional, external or completion effects apply. What value does the cost approach indicate?
Correct Answer
C) $735,000
480000×(1−25÷50)+320000+175000 = 735000. Common errors: leaving out the rebuilt wing gives $415,000; depreciating the rebuilt wing as well gives $575,000; not depreciating the unrebuilt wing gives $975,000.
Why This Is the Correct Answer
Option C is correct because the unrebuilt wing's age-life ratio is 25 / 50 = 50%, so it contributes $480,000 x 0.50 = $240,000. Adding the rebuilt wing at $320,000 and the $175,000 site gives $240,000 + $320,000 + $175,000 = $735,000.
Why the Other Options Are Wrong
Option A: $415,000
Option A, $415,000, leaves out the rebuilt wing: $240,000 + $175,000 = $415,000. The rebuilt wing's $320,000 must be added, giving $735,000.
Option B: $575,000
Option B, $575,000, depreciates the rebuilt wing as well: ($480,000 + $320,000) x 0.50 + $175,000 = $575,000. The rebuilt wing has zero supported loss, so only the unrebuilt wing is depreciated, giving $735,000.
Option D: $975,000
Option D, $975,000, does not depreciate the unrebuilt wing: $480,000 + $320,000 + $175,000 = $975,000. Applying the 50% age-life loss to that wing gives $735,000.
Each wing, its own age
Give each building section its own age-life ratio, depreciate them separately, then add them with the land.
How to use: Use this when a property has sections of different ages or rebuild status.
Exam Tip
Apply a depreciation ratio only to the cost it describes; do not spread one section's loss over the whole building.
Common Mistakes to Avoid
- -Applying one wing's depreciation to the whole building
- -Omitting a building section from the summation
- -Forgetting to depreciate the older section
Concept Deep Dive
Analysis
This question tests valuing two separate building sections with different depreciation. The unrebuilt wing is depreciated by its age-life ratio, the rebuilt wing has no supported loss, and site value is added. Each wing's cost and depreciation must be kept separate.
Background Knowledge
The age-life method estimates depreciation by dividing effective age by total economic life. When parts of a building differ in age or condition, they can be analyzed separately so each part's depreciation reflects its own effective age.
Real-World Application
After a fire, one wing of a house is fully rebuilt while the other wing remains original. The appraiser depreciates the original wing by its age-life ratio, treats the rebuilt wing as having no supported loss, and adds land value.
More Cost Approach Questions
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