Final answer:
To calculate equipment depreciation using double declining balance with a switch to straight line depreciation and half year convention, the initial depreciation is 20% of the cost, prorated for the first and last years, and then applied to the book value annually until straight line provides a higher annual depreciation, ensuring full depreciation over 10 years with a salvage value of zero.
Step-by-step explanation:
To calculate the depreciation for a piece of equipment worth $82,000 over 10 years using the double declining balance method with a switch to straight line depreciation when it becomes more efficient, we apply the half year convention. First, we determine the double declining balance rate. For a 10-year life, the straight-line rate is 1/10, or 10%. Under double declining, this rate is doubled to 20%. Because we're using the half year convention, we'll prorate the depreciation for the first and last years by 50%. For the first year, the depreciation expense is $82,000 × 20% × 0.5 = $8,200. For subsequent years, we apply the 20% rate to the book value at the beginning of each year until the annual straight line depreciation exceeds the double declining balance amount, at which point we switch to straight line depreciation.
We need to keep in mind that with a zero salvage value, the equipment should be fully depreciated by the end of the 10th year. The book value is calculated by subtracting the accumulated depreciation from the original cost of the equipment each year. Continue calculating annual depreciation and book value until the equipment is fully depreciated after 10 years.