An improvement cost $500,000 to construct new. It is 8 years old with a total economic life of 40 years. Using straight-line depreciation, what is the current depreciated value?
Correct Answer
A) $400,000
Annual depreciation = $500,000 ÷ 40 years = $12,500. Total depreciation = $12,500 × 8 years = $100,000. Depreciated value = $500,000 - $100,000 = $400,000.
Why This Is the Correct Answer
Option A ($400,000) correctly applies the straight-line depreciation formula. The annual depreciation is calculated as $500,000 ÷ 40 years = $12,500 per year. After 8 years, the total accumulated depreciation is $12,500 × 8 = $100,000. The current depreciated value is therefore $500,000 - $100,000 = $400,000. This represents the remaining value of the improvement after accounting for 8 years of wear and obsolescence.
Why the Other Options Are Wrong
Option B: $100,000
Option B ($100,000) represents the total accumulated depreciation amount, not the remaining depreciated value of the improvement. This is a common error where test-takers calculate the depreciation correctly but forget to subtract it from the original cost to find the current value.
Option C: $500,000
Option C ($500,000) is the original construction cost without any depreciation applied. This would only be correct if the improvement were brand new (0 years old) or if no depreciation was being considered, which contradicts the question's requirement to calculate depreciated value.
Option D: $320,000
Option D ($320,000) appears to result from an incorrect calculation, possibly using the wrong economic life or age in the depreciation formula. This could occur from mathematical errors or misreading the given information in the problem.
The ROAD Formula
ROAD: Replacement cost ÷ Overall life = Annual depreciation; then subtract (Annual × Age) from Replacement cost. Think of a road wearing down evenly over time - each year takes the same toll.
How to use: When you see a straight-line depreciation problem, immediately think ROAD and set up: (1) Divide cost by total life for annual depreciation, (2) Multiply annual by actual age for total depreciation, (3) Subtract total depreciation from original cost.
Exam Tip
Always double-check that you're calculating the remaining value, not just the depreciation amount - the question usually asks for current depreciated value, not the depreciation itself.
Common Mistakes to Avoid
- -Providing the depreciation amount instead of the depreciated value
- -Using the wrong time period (confusing actual age with remaining life)
- -Forgetting to subtract the calculated depreciation from the original cost
Concept Deep Dive
Analysis
This question tests the fundamental concept of straight-line depreciation in real estate appraisal, which is used in the cost approach to determine the current value of improvements. Straight-line depreciation assumes that an asset loses value at a constant rate over its economic life, making it the simplest and most commonly used depreciation method in appraisal. The calculation involves determining the annual depreciation amount by dividing the original cost by the total economic life, then multiplying by the actual age to find total accumulated depreciation. The depreciated value is then calculated by subtracting the total depreciation from the original construction cost.
Background Knowledge
Straight-line depreciation is the most basic depreciation method used in real estate appraisal, assuming equal annual loss of value over an asset's economic life. Economic life represents the period during which an improvement contributes to property value, which may differ from physical life or accounting life.
Real-World Application
Appraisers use straight-line depreciation when applying the cost approach to value older improvements like houses, where they need to account for physical deterioration, functional obsolescence, and economic obsolescence that accumulates over time.
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