A building cost $750,000 new and is 8 years old with a 60-year economic life. Using straight-line depreciation, what is the current depreciated value?
Correct Answer
D) $650,000
Why this is correct: Straight-line depreciation divides cost by economic life to get annual depreciation: $750,000 ÷ 60 years = $12,500/year. For 8 years: $12,500 × 8 = $100,000 depreciation. Current value = cost - depreciation = $750,000 - $100,000 = $650,000. Why the other choices are wrong: '$750,000' ignores all depreciation. '$100,000' is the total depreciation, not the current value. '$550,000' results from miscalculation. Exam tip: For straight-line, use: (Cost ÷ Total Life) × Age = Depreciation; Cost - Depreciation = Current Value.
Why This Is the Correct Answer
Option A ($650,000) correctly applies the straight-line depreciation formula. First, the annual depreciation is calculated: $750,000 ÷ 60 years = $12,500 per year. Then, the total depreciation over 8 years is: $12,500 × 8 = $100,000. Finally, the current depreciated value is: $750,000 - $100,000 = $650,000. This systematic approach properly accounts for the building's age-related loss in value while maintaining its remaining economic utility.
Why the Other Options Are Wrong
Option A: $750,000
Option A ($750,000) represents the original cost with no depreciation applied, which ignores the 8 years of age and economic obsolescence. This would only be correct if the building were brand new or if no depreciation method were being applied.
Option B: $100,000
Option B ($100,000) represents only the total accumulated depreciation amount, not the current depreciated value of the building. This is a common error where test-takers stop at calculating the depreciation amount rather than completing the final step of subtracting it from the original cost.
Option C: $550,000
Option C ($550,000) appears to result from an incorrect calculation, possibly using the wrong economic life or applying an incorrect depreciation rate. This amount would suggest total depreciation of $200,000, which doesn't align with the given parameters.
The CAD Formula
CAD = Cost ÷ Age ÷ Depreciation. Remember: Cost divided by economic life gives annual depreciation, multiply by actual age for total depreciation, then subtract from original cost for Current value After Depreciation.
How to use: When you see a straight-line depreciation problem, immediately write 'CAD' and set up three steps: 1) Cost ÷ economic life = annual depreciation, 2) Annual depreciation × actual age = total depreciation, 3) Original cost - total depreciation = current value.
Exam Tip
Always double-check that your final answer represents the current depreciated value, not just the depreciation amount - many wrong answers on the exam are actually correct calculations of depreciation rather than the remaining value.
Common Mistakes to Avoid
- -Providing the depreciation amount instead of the depreciated value
- -Using the wrong economic life or confusing it with actual age
- -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 a key component of the cost approach to valuation. Straight-line depreciation assumes that a building loses value at a constant rate over its economic life, creating equal annual depreciation amounts. The calculation involves determining the annual depreciation rate by dividing the original cost by the total economic life, then multiplying by the actual age to find total accumulated depreciation. The current depreciated value is then calculated by subtracting the total accumulated depreciation from the original cost.
Background Knowledge
Straight-line depreciation is the most basic depreciation method used in real estate appraisal, assuming equal annual loss of value over the economic life of an improvement. Economic life represents the period during which a building contributes to property value, which may differ from its physical or functional life.
Real-World Application
Appraisers use straight-line depreciation when applying the cost approach to value older buildings, particularly for insurance appraisals, tax assessments, and situations where comparable sales are limited. This method helps establish the contributory value of improvements separate from land value.
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