1. **Problem Statement:** A firm buys equipment for $120000$ with a useful life of $8$ years and a salvage value of $8000$. We need to create a depreciation schedule using the double-declining balance (DDB) method. 2. **Formula and Rules:** The DDB depreciation rate is twice the straight-line rate: $$\text{DDB rate} = 2 \times \frac{1}{\text{useful life}} = 2 \times \frac{1}{8} = 0.25 = 25\%$$ Depreciation expense each year is: $$\text{Depreciation expense} = \text{Book value at start of year} \times \text{DDB rate}$$ The book value cannot go below the salvage value $8000$. 3. **Calculations:** | Year | Beginning Book Value | Depreciation Expense | Accumulated Depreciation | Ending Book Value | |-------|---------------------|----------------------|--------------------------|-------------------| | 1 | 120000 | $120000 \times 0.25 = 30000$ | 30000 | $120000 - 30000 = 90000$ | | 2 | 90000 | $90000 \times 0.25 = 22500$ | $30000 + 22500 = 52500$ | $90000 - 22500 = 67500$ | | 3 | 67500 | $67500 \times 0.25 = 16875$ | $52500 + 16875 = 69375$ | $67500 - 16875 = 50625$ | | 4 | 50625 | $50625 \times 0.25 = 12656.25$ | $69375 + 12656.25 = 82031.25$ | $50625 - 12656.25 = 37968.75$ | | 5 | 37968.75 | $37968.75 \times 0.25 = 9492.19$ | $82031.25 + 9492.19 = 91523.44$ | $37968.75 - 9492.19 = 28476.56$ | | 6 | 28476.56 | $28476.56 \times 0.25 = 7119.14$ | $91523.44 + 7119.14 = 98642.58$ | $28476.56 - 7119.14 = 21357.42$ | | 7 | 21357.42 | $21357.42 \times 0.25 = 5339.36$ | $98642.58 + 5339.36 = 103981.94$ | $21357.42 - 5339.36 = 16018.06$ | | 8 | 16018.06 | Depreciate only to salvage value: $16018.06 - 8000 = 8018.06$ | $103981.94 + 8018.06 = 112000$ | $8000$ | 4. **Explanation:** - Each year, multiply the beginning book value by 25% to get depreciation expense. - Accumulate depreciation by adding each year's expense. - Subtract depreciation expense from beginning book value to get ending book value. - In the last year, adjust depreciation so book value equals salvage value. **Final depreciation schedule:** | Year | Depreciation Expense | Accumulated Depreciation | Book Value End | |-------|----------------------|--------------------------|----------------| | 1 | 30000 | 30000 | 90000 | | 2 | 22500 | 52500 | 67500 | | 3 | 16875 | 69375 | 50625 | | 4 | 12656.25 | 82031.25 | 37968.75 | | 5 | 9492.19 | 91523.44 | 28476.56 | | 6 | 7119.14 | 98642.58 | 21357.42 | | 7 | 5339.36 | 103981.94 | 16018.06 | | 8 | 8018.06 | 112000 | 8000 |