Problem 10 - Accounting

Question

A diesel-powered tractor with a cost of \( 215,000\) and estimated residual value of \( 27,000\) is expected to have a useful operating life of 80,000 hours. During October, the generator was operated 380 hours. Determine the depreciation for the month.

Step-by-Step Solution

Answer

The depreciation for October is \( 893 \).

Step 1: Determine the Depreciable Cost

The depreciable cost of an asset is calculated by subtracting the estimated residual value from the initial cost of the asset. Here, the initial cost is \( 215,000 \) and the residual value is \( 27,000 \).\[ \text{Depreciable Cost} = 215,000 - 27,000 = 188,000 \]

Step 2: Calculate the Depreciation Rate per Hour

To find the depreciation rate per hour, divide the depreciable cost by the total expected operating hours. Here, the operating life is 80,000 hours.\[ \text{Depreciation Rate per Hour} = \frac{188,000}{80,000} = 2.35 \text{ per hour} \]

Step 3: Calculate the Monthly Depreciation

Now, calculate the depreciation for October by multiplying the hourly depreciation rate by the number of hours the generator operated.\[ \text{Monthly Depreciation} = 2.35 \times 380 = 893 \]

Key Concepts

Depreciable Cost

When you're determining how much value an asset will lose over time, the first step is figuring out its **depreciable cost**. This is the amount by which the asset’s value is expected to decrease during its useful life.
Depreciable cost is calculated by subtracting the asset's **residual value** from its initial purchase cost.

• **Initial Cost**: The price paid to acquire the asset.
• **Residual Value**: The estimated value of the asset at the end of its useful life.

For instance, if you purchase a truck for \(215,000\) with an estimated residual value of \(27,000\), your depreciable cost would be \(215,000 - 27,000 = 188,000\). This means over its operating life, the truck is expected to lose \(188,000\) in value.
Calculating the depreciable cost is crucial as it sets the foundation for further calculations, like figuring out the depreciation rate.

Depreciation Rate

Once you have the depreciable cost, the next step is to determine the **depreciation rate**. This measures how quickly an asset loses its value, typically expressed as a rate per hour or year.

• Divide the **depreciable cost** by the **total expected operating hours** to find the hourly rate.

For example, using the truck's depreciable cost of \(188,000\) and an operating life of 80,000 hours, the hourly depreciation rate is \(\frac{188,000}{80,000} = 2.35\) per hour.
Knowing the depreciation rate helps you understand how much the asset is being "used up" every hour it operates. This rate is crucial for businesses to track asset value depletion accurately and to manage finances effectively.

Residual Value

The **residual value** represents the scrap or salvage value that an asset is expected to have at the end of its useful life. It's an important factor because it indicates the estimated recovery amount after the usage phase.
This estimation is often based on:

• Market conditions
• Usage patterns
• Technological advancements

In our example, the tractor's residual value is set at \(27,000\). If you initially purchased the tractor for \(215,000\), then after it has completed its operational life of 80,000 hours, you might expect to sell or scrap it for \(27,000\).
Understanding residual value is vital in depreciation calculations as it directly affects the depreciable cost and, consequently, the calculated depreciation expense.

Operating Life

An asset's **operating life** refers to the total period during which the asset is expected to be usable for its intended function, measured in terms of hours, months, or years. In depreciation calculations, this is often expressed in hours when dealing with machinery or vehicles.
In this case, the tractor's operating life is specified as 80,000 hours. By understanding the operating life, one can efficiently allocate depreciation expenses over the asset's useful span.
For example, any maintenance, repairs, or operational activities directly impact how long an asset can be expected to function effectively. Knowing the asset's operating life guide owners in planning capital expenditures and maintenance schedules. It is pivotal for financial planning and ensuring optimal utilization of the asset during its lifespan.