Problem 10 - Accounting

Question

A diesel-powered tractor with a cost of \(145,000 and estimated residual value of \)7,000 is expected to have a useful operating life of 75,000 hours. During July, the generator was operated 150 hours. Determine the depreciation for the month.

Step-by-Step Solution

Answer

The depreciation for the month of July is $276.

Step 1: Identify the Variables

First, let's identify the variables we have. The cost of the tractor is $145,000, and the estimated residual value is $7,000. The useful operating life is expected to be 75,000 hours. In July, the tractor was used for 150 hours.

Step 2: Calculate the Depreciable Cost

To find the depreciable cost, subtract the residual value from the initial cost of the tractor. This is calculated as follows:\[\text{Depreciable Cost} = 145,000 - 7,000 = 138,000\]

Step 3: Calculate the Depreciation Rate per Hour

The depreciation rate per hour is found by dividing the depreciable cost by the total estimated useful hours. So,\[\text{Depreciation per Hour} = \frac{138,000}{75,000} = 1.84\]

Step 4: Calculate the Monthly Depreciation

Finally, calculate the depreciation for the month of July by multiplying the depreciation rate per hour by the number of hours used in July. Thus,\[\text{Monthly Depreciation} = 1.84 \times 150 = 276\]

Step 5: Conclusion: Monthly Depreciation for July

Therefore, the depreciation of the tractor for the month of July is $276.

Key Concepts

Useful Life of Asset

When it comes to accounting for the cost of assets over time, one essential concept is the "useful life of an asset." The useful life of an asset refers to the estimated time span an asset is expected to be used before it becomes unproductive or obsolete. For instance, in this exercise, the useful life of a diesel-powered tractor is expected to be 75,000 hours. This means that over these hours, the tractor will be contributing effectively to operations.

• Aids in estimating how long an asset will be productive.
• Facilitates budgeting for replacement or disposal.

The concept is crucial because it helps determine how the cost of an asset will be distributed over its productive life. Understanding this concept ensures businesses don't dilute their financial results with erratic expenses, but instead gradually recognize the asset’s value reduction.

Residual Value

Residual value is another key term utilized in depreciation calculations. This represents the expected monetary value of an asset at the end of its useful life. Simply put, it's how much you think you'll be able to sell the asset for (or trade it in) once you're done using it. In the case of the diesel-powered tractor, the estimated residual value is $7,000. Thus, when the tractor has reached its 75,000 hours of usage, it's anticipated to have retained this amount of value.

• Considers future asset disposal or sale.
• Crucial for accurate depreciation calculation.

The residual value reduces the amount you depreciate. Businesses subtract it from the initial cost to find the amount that needs to be spread over the useful life. This ensures that they're only depreciating the value that diminishes over time.

Depreciable Cost

Depreciable cost is probably the most vital component in straightforward depreciation accounting. It indicates the total cost that will be allocated over the useful life of the asset. To calculate this, one simply subtracts the residual value from the asset's initial purchase cost. In our scenario, the tractor's depreciable cost is calculated like so: \[\text{Depreciable Cost} = 145,000 - 7,000 = 138,000\]

• This cost is spread over the asset’s useful life.
• Ensures accurate reflection of the asset’s depreciation over time.

Calculating this cost is essential because it identifies the real amount of value loss expected from the asset. This figure guides how much of the asset's cost will appear as an expense each accounting period, ensuring there are no drastic fluctuations in expenses due to asset purchasing.

Depreciation Rate

The concept of a depreciation rate is about understanding how quickly an asset loses its value over its useful life. It’s expressed as a ratio or rate, often calculated on a per usage basis for assets like machinery/vehicles, as this provides a more clear picture of the asset's expense.For the tractor example, the depreciation rate per hour is calculated by dividing the depreciable cost by the total estimated useful hours: \[\text{Depreciation per Hour} = \frac{138,000}{75,000} = 1.84\]

• Depicts the expense cost attributed to each unit of usage (e.g., hour of operation).
• Helps in forecasting expenses over the asset’s life span.

This helps businesses in not just regular accounting but also budgeting and forecasting operations. Such insight means they can better plan for maintenance and eventual replacement, ultimately leading to more efficient operations and financial management.