A 2,200-sf dwelling costs $200 per square foot, and a separate 400-sf garage costs $75 per square foot. These costs are complete and do not overlap. Both have an effective age of 15 years and a total life of 50 years, with straight-line depreciation and no salvage value. No site value or other loss is involved. What is the combined depreciated cost of the dwelling and garage?
Correct Answer
C) $329,000
(2200×200+400×75)×(1−15÷50)=329000. Common errors: leaving out the garage cost gives $308,000; reporting the depreciation instead of the depreciated amount gives $141,000; stopping at cost new, before depreciation gives $470,000.
Why This Is the Correct Answer
Option C is correct because the cost new is 2,200 x $200 + 400 x $75 = $440,000 + $30,000 = $470,000, and $470,000 x (1 - 15/50) = $470,000 x 0.70 = $329,000. Both components use the same model, so the factor applies to the combined total.
Why the Other Options Are Wrong
Option A: $141,000
Option A, $141,000, is $470,000 x 15/50, the depreciation itself rather than the depreciated amount. Subtracting it from cost new gives $470,000 - $141,000 = $329,000.
Option B: $308,000
Option B, $308,000, is $440,000 x 0.70, which leaves out the $30,000 garage cost. Including it gives $470,000 x 0.70 = $329,000.
Option D: $470,000
Option D, $470,000, is the combined cost new before any depreciation. Applying the 0.70 remaining factor gives $329,000.
Add the parts, then depreciate
Build the full cost first, then multiply by one minus effective age over life.
How to use: Use this order for any multi-component age-life question with a shared age and life.
Exam Tip
Decide whether the question wants depreciation or the depreciated amount before choosing; both are usually offered.
Common Mistakes to Avoid
- -Omitting a separately costed component
- -Reporting depreciation when the depreciated value is asked
- -Stopping at cost new without applying depreciation
Concept Deep Dive
Analysis
This question combines component costing with age-life depreciation. You first total the dwelling and garage costs, then apply the remaining-value factor 1 - 15/50 = 0.70 because both components share the same age and life.
Background Knowledge
The age-life method estimates depreciation by dividing effective age by economic life and applying that ratio to cost new. When components have different costs but the same age and life, they can be totaled before applying the ratio.
Real-World Application
An appraiser costs a home and its detached garage at different unit rates. Since both were built together and have the same effective age, one age-life ratio is applied to the combined cost.
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