Math Problem Statement

Solve

Determine the machine's second-year depreciation and year-end book value under the straight-line method.

Solution

Let's solve the problem step by step based on the straight-line depreciation method described.


Straight-Line Depreciation Formula:

Annual Depreciation Expense=Cost of the AssetSalvage ValueUseful Life (in years)\text{Annual Depreciation Expense} = \frac{\text{Cost of the Asset} - \text{Salvage Value}}{\text{Useful Life (in years)}}

Data Provided:

  • Cost of the machine = $86,200
  • Salvage value = $7,000
  • Useful life = 10 years

Step 1: Compute the Annual Depreciation Expense

Annual Depreciation Expense=86,2007,00010=79,20010=7,920\text{Annual Depreciation Expense} = \frac{86,200 - 7,000}{10} = \frac{79,200}{10} = 7,920

Thus, the annual depreciation expense is $7,920.


Step 2: Determine Year 2 Depreciation

Under the straight-line method, depreciation is the same each year. Hence, Year 2 Depreciation = $7,920.


Step 3: Compute Year-End Book Value for Year 2

The book value at the end of Year 2 is calculated as: Year-End Book Value=Cost of the Machine(Depreciation Expense×Years of Depreciation)\text{Year-End Book Value} = \text{Cost of the Machine} - (\text{Depreciation Expense} \times \text{Years of Depreciation})

Year-End Book Value=86,200(7,920×2)\text{Year-End Book Value} = 86,200 - (7,920 \times 2)

Year-End Book Value=86,20015,840=70,360\text{Year-End Book Value} = 86,200 - 15,840 = 70,360


Summary of Results:

  • Year 2 Depreciation = $7,920
  • Year-End Book Value (Year 2) = $70,360

Would you like a detailed breakdown of this computation or have further questions?


Relative Questions:

  1. What happens if the salvage value changes over the machine's lifetime?
  2. How does the straight-line depreciation differ from units-of-production depreciation?
  3. Can salvage value ever be zero, and what would that imply for depreciation calculations?
  4. Why do we assume equal depreciation every year in the straight-line method?
  5. How would the calculation change if the machine had a different useful life?

Tip:

When using straight-line depreciation, always verify that the total accumulated depreciation equals the original cost minus salvage value over the asset's lifetime.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Straight-Line Depreciation
Depreciation Calculation
Book Value Computation

Formulas

Annual Depreciation Expense = (Cost of Asset - Salvage Value) / Useful Life
Year-End Book Value = Cost of Machine - (Depreciation Expense × Years of Depreciation)

Theorems

-

Suitable Grade Level

College or advanced high school accounting courses