A building cost $2,000,000 to construct 10 years ago. Using straight-line depreciation over a 40-year life, what is the current depreciated value?
Correct Answer
C) $1,500,000
Why this is correct: Straight-line depreciation spreads cost evenly over the useful life. Annual depreciation = $2,000,000 / 40 years = $50,000. For 10 years: $50,000 * 10 = $500,000 total depreciation. Current depreciated value = $2,000,000 - $500,000 = $1,500,000. Why the other choices are wrong: $1,750,000 would result from incorrect math. $200,000 is not supported by the calculation. $500,000 is the total depreciation, not the current value. Exam tip: Straight-line formula: (Cost / Total Life) * Years = Depreciation. Then subtract from cost.
Why This Is the Correct Answer
Option A ($1,500,000) correctly applies the straight-line depreciation formula by first calculating the annual depreciation rate ($2,000,000 ÷ 40 years = $50,000 per year), then multiplying by the elapsed time (10 years × $50,000 = $500,000 total depreciation). The current depreciated value is determined by subtracting the accumulated depreciation from the original cost ($2,000,000 - $500,000 = $1,500,000). This systematic approach ensures that the building's value reflects the proportional loss over the 10-year period within its 40-year useful life.
Why the Other Options Are Wrong
Option A: $1,750,000
Option A ($1,750,000) represents only $250,000 in total depreciation over 10 years, which would incorrectly suggest an annual depreciation of only $25,000 per year instead of the correct $50,000 per year calculated from the 40-year useful life.
Option B: $200,000
Option B ($200,000) is far too low and doesn't follow any logical depreciation calculation based on the given parameters, suggesting either a calculation error or misunderstanding of the depreciation concept.
Option D: $500,000
Option D ($500,000) represents only the amount of accumulated depreciation over 10 years, not the remaining depreciated value of the building, showing a fundamental misunderstanding of what the question is asking for.
The COST-LIFE-TIME Formula
Remember 'CLT': Cost ÷ Life = annual depreciation, then multiply by Time elapsed. Think of it as 'Can't Lose Track' of these three essential components.
How to use: When you see a straight-line depreciation question, immediately identify the three CLT components: original Cost, useful Life, and Time elapsed. Write down the formula: (Cost ÷ Life) × Time = total depreciation, then subtract from original cost.
Exam Tip
Always double-check that you're calculating the remaining value, not just the depreciation amount - many test questions will include the depreciation amount as a distractor answer choice.
Common Mistakes to Avoid
- -Confusing the depreciation amount with the remaining value
- -Using the wrong time period in calculations
- -Forgetting to subtract accumulated 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 useful life, making it one of the simplest and most commonly used depreciation methods in appraisal practice. The calculation requires understanding three key variables: the original cost, the total useful life of the building, and the number of years that have elapsed since construction. This method is particularly important in the cost approach because it helps appraisers estimate the current value of improvements by accounting for physical deterioration, functional obsolescence, and economic obsolescence over time.
Background Knowledge
Straight-line depreciation is based on the assumption that a building depreciates at a uniform rate throughout its economic life, with the annual depreciation calculated by dividing the total cost by the useful life in years. This method is widely used in real estate appraisal because it's simple to calculate and provides a reasonable estimate of value loss for most commercial and residential properties.
Real-World Application
Appraisers use straight-line depreciation when applying the cost approach to value older buildings, particularly when comparable sales are limited or when valuing special-purpose properties like schools or churches where the cost approach may be the most reliable valuation method.
More Cost Approach Questions
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