Math Problem Statement

Apex Fitness Club uses straight-line depreciation for a machine costing $19,200, with an estimated four-year life and a $1,950 salvage value. At the beginning of the third year, Apex determines that the machine has three more years of remaining useful life, after which it will have an estimated $1,500 salvage value. Compute the machine’s book value at the end of its second year. Compute the amount of depreciation for each of the final three years given the revised estimates.

Solution

To solve this problem, let's go through each step carefully.

Given Information

  1. Initial Cost of Machine: $19,200
  2. Estimated Life: 4 years
  3. Initial Salvage Value: $1,950
  4. Straight-Line Depreciation

After two years:

  • Revised Salvage Value: $1,500
  • Remaining Useful Life: 3 years

Required 1: Compute Book Value at the End of Year 2

For straight-line depreciation, the formula is:

Annual Depreciation=CostSalvage ValueUseful Life\text{Annual Depreciation} = \frac{\text{Cost} - \text{Salvage Value}}{\text{Useful Life}}

Step 1: Calculate initial annual depreciation: Annual Depreciation=19,2001,9504=17,2504=4,312.5\text{Annual Depreciation} = \frac{19,200 - 1,950}{4} = \frac{17,250}{4} = 4,312.5

Step 2: Compute depreciation over the first two years: Depreciation for 2 years=4,312.5×2=8,625\text{Depreciation for 2 years} = 4,312.5 \times 2 = 8,625

Step 3: Calculate Book Value at the end of Year 2: Book Value at end of Year 2=Initial CostDepreciation for 2 years\text{Book Value at end of Year 2} = \text{Initial Cost} - \text{Depreciation for 2 years} =19,2008,625=10,575= 19,200 - 8,625 = 10,575

So, the book value at the end of the second year is $10,575.

Required 2: Revised Depreciation for Years 3–5

Now that the machine has a revised salvage value and remaining useful life, let's compute the new depreciation.

  1. Book Value at Point of Revision (start of Year 3): $10,575
  2. Revised Salvage Value: $1,500
  3. Remaining Useful Life: 3 years

Step 1: Calculate Remaining Depreciable Cost

Remaining Depreciable Cost=Book Value at Point of RevisionRevised Salvage Value\text{Remaining Depreciable Cost} = \text{Book Value at Point of Revision} - \text{Revised Salvage Value} =10,5751,500=9,075= 10,575 - 1,500 = 9,075

Step 2: Calculate Revised Annual Depreciation (for Years 3–5)

Revised Annual Depreciation=Remaining Depreciable CostRemaining Useful Life\text{Revised Annual Depreciation} = \frac{\text{Remaining Depreciable Cost}}{\text{Remaining Useful Life}} =9,0753=3,025= \frac{9,075}{3} = 3,025

Therefore, the revised annual depreciation for each of the final three years is $3,025.

Summary of Answers

  • Book Value at End of Year 2: $10,575
  • Revised Annual Depreciation (Years 3–5): $3,025

Would you like more details on any of these calculations or have questions?


Here are 5 related questions to expand on this topic:

  1. How would the depreciation change if the salvage value was increased instead of decreased?
  2. What would the book value be at the end of Year 4 using the revised depreciation?
  3. How would double-declining balance depreciation compare with straight-line in this scenario?
  4. If the useful life was extended to 5 years, how would the depreciation calculation change?
  5. How would you calculate accumulated depreciation at the end of Year 5?

Tip: When using straight-line depreciation, always review the salvage value and useful life regularly, as changes will impact annual depreciation.

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Math Problem Analysis

Mathematical Concepts

Depreciation
Straight-Line Depreciation
Book Value Calculation

Formulas

Annual Depreciation = (Cost - Salvage Value) / Useful Life
Remaining Depreciable Cost = Book Value at Point of Revision - Revised Salvage Value
Revised Annual Depreciation = Remaining Depreciable Cost / Remaining Useful Life

Theorems

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Suitable Grade Level

College Level