Final answer:
The depreciation for the first year can be calculated using the double-declining-balance method. The depreciation for the first year is $125,758.68.
Step-by-step explanation:
The depreciation for the first year can be calculated using the double-declining-balance method. To calculate the depreciation, you need to determine the depreciation rate, which is 1 divided by the estimated useful life of the equipment multiplied by 2. In this case, the depreciation rate is 1/9 * 2 = 2/9. Now, you can calculate the depreciation for the first year by multiplying the depreciation rate by the beginning value of the equipment (cost minus residual value). So, the depreciation for the first year is (2/9) * ($637,500 - $43,195) = $125,758.68.