An appraiser separates the improvements into two component groups that do not overlap. The long-lived group has a cost new of $500,000, an effective age of 10 years and a total life of 50 years. The short-lived group has a cost new of $80,000, an effective age of 4 years and a total life of 16 years. Using straight-line age-life depreciation with no salvage value, and with no site value or other losses, what is the combined depreciated cost?
Correct Answer
B) $460,000
500000×(1−10÷50)+80000×(1−4÷16) = 460000. Common errors: leaving out the short-lived group gives $400,000; applying the long-lived 10/50 ratio to both groups gives $464,000; not depreciating either group gives $580,000.
Why This Is the Correct Answer
Option B is correct because each group is depreciated on its own ratio. Long-lived: $500,000 × (1 − 10/50) = $400,000; short-lived: $80,000 × (1 − 4/16) = $60,000. The combined depreciated amount is $460,000.
Why the Other Options Are Wrong
Option A: $400,000
Option A, $400,000, leaves out the short-lived group: $500,000 × (1 − 10/50) = $400,000. Adding the short-lived group's $60,000 gives $460,000.
Option C: $464,000
Option C, $464,000, applies the long-lived 10/50 ratio to both groups: $580,000 × 0.8 = $464,000. The short-lived group has its own 4/16 ratio, so the total is $400,000 + $60,000 = $460,000.
Option D: $580,000
Option D, $580,000, does not depreciate either group: $500,000 + $80,000 = $580,000. Applying each group's ratio gives $460,000.
Each Group, Own Clock
Short-lived and long-lived items run on different clocks; depreciate each with its own age and life, then add.
How to use: Use this when a question splits costs into component groups.
Exam Tip
Compute each group separately before adding; a single blended ratio usually leads to a distractor.
Common Mistakes to Avoid
- -Applying one ratio to all components
- -Leaving out a component group
- -Forgetting to depreciate at all
Concept Deep Dive
Analysis
This question tests depreciating long-lived and short-lived component groups separately and then combining them. Each group uses its own age-life ratio, and the depreciated amounts are added because the groups do not overlap.
Background Knowledge
In the breakdown method, short-lived and long-lived components are depreciated separately because they wear out at different rates. Each group's age-life ratio is applied to its own cost new. Total depreciation, or total depreciated cost, is the sum of the separate, nonoverlapping results.
Real-World Application
An appraiser separates a building's $80,000 of roof, HVAC and finishes from its $500,000 structure. She depreciates each group on its own effective age and life and totals $460,000 of depreciated cost.
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Annual effective gross income at an income property is $18.50 per square foot without an influence and $14.20 per square foot with it, on 25,000 square feet. Market data indicate an EGI multiplier of 7.5 for this income loss. Independent evidence assigns 70% of the resulting loss to the improvements. What is the loss attributable to the improvements?