Questions: Ramirez Company installs a computerized manufacturing machine in its factory at the beginning of the year at a cost of 43,500. The machine's useful life is estimated at 10 years, or 385,000 units of product, with a 5,000 salvage value. During its second year, the machine produces 32,500 units of product. Determine the machine's second-year depreciation and year end book value under the straight-line method.

Solution Steps

To determine the machine's second-year depreciation and year-end book value under the straight-line method, follow these steps:

1. Calculate the annual depreciation expense using the formula: \[ \text{Annual Depreciation Expense} = \frac{\text{Cost} - \text{Salvage Value}}{\text{Useful Life (years)}} \]
2. Multiply the annual depreciation expense by the number of years to get the total depreciation for the second year.
3. Subtract the total depreciation from the initial cost to get the year-end book value.

To determine the annual depreciation expense under the straight-line method, use the formula: \[ \text{Annual Depreciation Expense} = \frac{\text{Cost} - \text{Salvage Value}}{\text{Useful Life (years)}} \] Given: \[ \text{Cost} = \$43,500, \quad \text{Salvage Value} = \$5,000, \quad \text{Useful Life} = 10 \text{ years} \] Substitute the values: \[ \text{Annual Depreciation Expense} = \frac{43500 - 5000}{10} = \frac{38500}{10} = 3850.0 \]

To find the total depreciation for the second year, multiply the annual depreciation expense by the number of years: \[ \text{Total Depreciation Year 2} = \text{Annual Depreciation Expense} \times 2 \] Substitute the value: \[ \text{Total Depreciation Year 2} = 3850.0 \times 2 = 7700.0 \]

To find the year-end book value for the second year, subtract the total depreciation from the initial cost: \[ \text{Year-End Book Value Year 2} = \text{Cost} - \text{Total Depreciation Year 2} \] Substitute the values: \[ \text{Year-End Book Value Year 2} = 43500 - 7700.0 = 35800.0 \]

Final Answer