A building cost $2,400,000 to construct new. After 8 years with straight-line depreciation over 40 years, what is the depreciated value?
Correct Answer
C) $1,920,000
Why this is correct: Straight-line depreciation allocates cost evenly over the useful life. Annual depreciation = Cost / Life = 2400000 / 40 = 60000. Total depreciation for 8 years = 60000 * 8 = 480000. Depreciated value = Cost - Total Depreciation = 2400000 - 480000 = 1920000. Why the other choices are wrong: 2080000 is an incorrect calculation. 480000 is the total depreciation, not the depreciated value. 2400000 is the original cost. Exam tip: Straight-line formula: Annual Depreciation = Cost / Useful Life. Depreciated Value = Cost - (Annual Depreciation * Age).
Why This Is the Correct Answer
Option A ($1,920,000) correctly applies the straight-line depreciation formula by first calculating the annual depreciation rate ($2,400,000 ÷ 40 years = $60,000 per year). After 8 years, the total accumulated depreciation equals $480,000 ($60,000 × 8 years). The depreciated value is then calculated by subtracting the total depreciation from the original cost: $2,400,000 - $480,000 = $1,920,000. This represents the remaining value of the building after accounting for 8 years of wear and obsolescence.
Why the Other Options Are Wrong
Option A: $2,080,000
Option A ($2,080,000) appears to result from an incorrect calculation, possibly using the wrong depreciation period or making an arithmetic error in the depreciation calculation process.
Option B: $480,000
Option B ($480,000) represents only the total accumulated depreciation amount rather than the remaining depreciated value of the building, confusing the depreciation expense with the actual remaining worth.
Option D: $2,400,000
Option D ($2,400,000) represents the original construction cost without any depreciation applied, which ignores the 8 years of aging and wear that would naturally reduce the building's value over time.
The DART Method
DART: Divide (cost by life), Annual (depreciation amount), Remaining (years × annual), Total (original cost minus accumulated depreciation). Think of throwing a DART straight at the target - straight-line depreciation goes straight down at a constant rate.
How to use: When you see a straight-line depreciation problem, immediately think DART: Divide the original cost by total life to get annual depreciation, multiply by years elapsed for total depreciation, then subtract from original cost for remaining value.
Exam Tip
Always double-check your arithmetic by working backwards - the depreciated value plus the accumulated depreciation should equal the original cost ($1,920,000 + $480,000 = $2,400,000).
Common Mistakes to Avoid
- -Confusing accumulated depreciation with remaining value
- -Using the wrong time period in calculations
- -Forgetting to subtract depreciation from original cost to get current value
Concept Deep Dive
Analysis
This question tests the fundamental concept of straight-line depreciation in real estate appraisal, specifically within the cost approach to valuation. Straight-line depreciation assumes that a building loses value at a constant rate over its useful life, creating equal annual depreciation amounts. The concept is critical for appraisers when estimating the current value of improvements by accounting for physical deterioration, functional obsolescence, and economic obsolescence over time. Understanding this calculation is essential for the cost approach, where the appraiser estimates what it would cost to replace the building today, then subtracts accumulated depreciation to arrive at the depreciated cost of the improvements.
Background Knowledge
Straight-line depreciation is one of the primary methods used in real estate appraisal to estimate the loss in value of improvements over time. The method assumes equal annual depreciation amounts over the building's economic life, calculated by dividing the original cost by the total useful life in years.
Real-World Application
Appraisers use straight-line depreciation when applying the cost approach to value older commercial buildings, helping determine how much value has been lost due to physical wear, outdated systems, or changing market preferences since construction.
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