Advanced Depreciation Methods: Double Declining Balance and Units of Activity

Double Declining Balance Method Calculation Details

• Initial Asset Valuation (Year One)   - At the start of year one, the asset has not yet undergone depreciation; therefore, the Accumulated Depreciation is zero.   - The Book Value is defined as the cost of the asset minus the accumulated depreciation.   - Calculation for Year 1 Book Value:     - $\text{Book Value} = \text{Cost} - \text{Accumulated Depreciation}$     - $\text{Book Value} = 150,000 - 0 = 150,000$   - The cost of the asset in this specific example is $150,000$.

• Depreciation Rate and Expense for Year One   - The depreciation rate used in this method is 40%, which is described as "double the slope on the rate."   - To calculate the depreciation expense for the first year, multiply the book value at the beginning of the year by the rate:     - $\text{Depreciation Expense} = 150,000 \times 40\% = 60,000$   - The resulting Accumulated Depreciation at the end of Year One is $60,000$.

• Partial Depreciation Policy   - The instructor notes that they will ignore partial-year depreciation calculations in these examples to avoid unnecessary complication. These will not be included on exams.

• Depreciation Calculation for Year Two   - To find the depreciation for the following year, a new Book Value must be established by subtracting the previous year's accumulated depreciation from the original cost.   - Calculation for Year 2 Book Value:     - $\text{Book Value} = 150,000 - 60,000 = 90,000$   - The depreciation expense for Year Two is calculated by applying the constant 40% rate to the new book value:     - $\text{Depreciation Expense} = 90,000 \times 40\% = 36,000$   - The total Accumulated Depreciation at the end of Year Two is updated as follows:     - $\text{Accumulated Depreciation} = 60,000 + 36,000 = 96,000$

• Salvage Value Limitations   - The depreciation process continues annually based on the declining book value.   - However, in the final year of the asset's useful life, the full calculated depreciation is not taken if it would reduce the book value below the Salvage Value.   - In this problem set, the Salvage Value is established at $12,000$.

Units of Activity Method

• Step-by-Step Procedure   - Step One: Determine Depreciation per Unit     - In this stage, you figure out the depreciation cost for every single unit of activity (e.g., one hour of machine operation).     - For the current problem, the calculated rate is approximately $13.80$ per hour (referenced in the exchange as both eighteen-eighty and thirteen-eighty, with the final calculation relying on $13.80$).   - Step Two: Calculate Annual Depreciation Expense     - To find the expense for the entire year, multiply the rate per unit determined in Step One by the actual number of units used during that period.     - In the specific example provided, the machine ran for $1,700$ hours.     - $\text{Depreciation Expense} = 1,700 \times 13.80$   - Future Projections     - If the usage increases in subsequent years (e.g., adding $20,000$ hours), the depreciation would be calculated by multiplying that new total of hours by the same rate per unit.

Questions & Discussion

• Topic: Clarification on Units of Activity (Step Two)   - Question: A student asked for clarification on Step Two of the units of activity method, specifically regarding the source of the $1,700$ hour figure.   - Response: The instructor clarified that Step One involves finding the depreciation per unit (determined to be $13.80$). Since the machine was run for $1,700$ hours during the year mentioned in the problem, that figure must be multiplied by the rate ($1,700 \times 13.80$). The instructor confirmed that the usage hours (like the $1,700$ hours) must be provided in the problem text for the student to complete the calculation. If usage was $20,000$ hours in a different year, that number would be used instead.