Final answer:
The depreciation expense in Year 4 for the equipment using the Double-Declining-Balance Method is $875. The double-declining rate is applied each year, and by Year 4 the depreciation expense ensures that the equipment's book value equals the residual value.
Step-by-step explanation:
The cost of equipment is given as $15,000 with a residual value of $1,000 and a useful life of four years. To find the depreciation expense for Year 4 using the Double-Declining-Balance Method, we first need to calculate the straight-line depreciation rate which would be 1/4 or 25% since the useful life is four years. Since it's a double-declining method, we would double this rate to 50%.
To calculate the depreciation expense for each year, you subtract the accumulated depreciation from the previous years from the book value of the asset (cost minus accumulated depreciation), and then apply the double-declining rate.
For Year 4, however, there is a catch. Because the Double-Declining-Balance Method tends to front-load the depreciation expense, towards the end of an asset's useful life, you might find that depreciating the asset using the double-declining rate would reduce its book value to less than its residual value. In this case, the depreciation expense would be calculated to ensure that the asset's book value equals the residual value at the end of its useful life.
Let's calculate:
- Year 1 Depreciation = ($15,000 - $0) * 50% = $7,500
- Year 2 Depreciation = ($15,000 - $7,500) * 50% = $3,750
- Year 3 Depreciation = ($15,000 - $11,250) * 50% = $1,875 (Since the residual value is not reached, full depreciation applies)
- Year 4 Depreciation = $15,000 - $1,000 (residual value) - $13,125 (accumulated depreciation from Years 1-3) = $875
For Year 4, the depreciation expense would be $875, making the correct answer (a) $875.