Math Problem Statement

A new piece of equipment costs $18,000 with a residual value of $600 and estimated useful life of 5 years. Assuming twice the straight line rate, the book value at the end of year 2 using the declining balance method would be?

Solution

To find the book value of the equipment at the end of year 2 using the double-declining balance method (DDB), we follow these steps:

  1. Identify key values:

    • Initial cost: $18,000
    • Residual value: $600
    • Useful life: 5 years
  2. Calculate the straight-line depreciation rate: The straight-line rate is calculated as: Straight-line rate=1Useful life=15=0.20 or 20%\text{Straight-line rate} = \frac{1}{\text{Useful life}} = \frac{1}{5} = 0.20 \text{ or } 20\%

  3. Double the straight-line rate: Under the double-declining balance method, the rate is doubled: Double-declining rate=2×0.20=0.40 or 40%\text{Double-declining rate} = 2 \times 0.20 = 0.40 \text{ or } 40\%

  4. Apply depreciation for each year until the end of year 2:

    • Year 1: Depreciation expense=40%×18,000=7,200\text{Depreciation expense} = 40\% \times 18,000 = 7,200 Book value at the end of Year 1=18,0007,200=10,800\text{Book value at the end of Year 1} = 18,000 - 7,200 = 10,800

    • Year 2: Depreciation expense=40%×10,800=4,320\text{Depreciation expense} = 40\% \times 10,800 = 4,320 Book value at the end of Year 2=10,8004,320=6,480\text{Book value at the end of Year 2} = 10,800 - 4,320 = 6,480

Therefore, the book value of the equipment at the end of year 2 is $6,480.

Would you like a further breakdown of these steps, or do you have any questions?


  1. How does the double-declining balance method differ from straight-line depreciation?
  2. Why does the declining balance method ignore the residual value in annual calculations?
  3. How would the depreciation schedule look for the remaining years in this problem?
  4. What would be the effect of a higher initial cost on book value under this method?
  5. How is the declining balance method useful in financial decision-making?

Tip: In the double-declining balance method, you stop depreciating once the book value reaches the residual value.

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Math Problem Analysis

Mathematical Concepts

Depreciation
Double-Declining Balance Method
Book Value Calculation

Formulas

Straight-line rate = 1 / Useful life
Double-declining rate = 2 * Straight-line rate
Depreciation expense (Year N) = Double-declining rate * Book value at start of Year N
Book value (Year N) = Book value at start of Year N - Depreciation expense (Year N)

Theorems

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Suitable Grade Level

Grades 10-12