Question

Straight-Line Depreciation: A certain milling machine has an initial value of \(\$ 150,000\) and a scrap value of \(\$ 10,000\) twenty years later. Assuming that the machine depreciates the same amount each year, find its value after 8 years. To find the amount of depreciation for each year, divide the total depreciation (initial value - scrap value) by the number of years of depreciation.

Short answer

The value of the milling machine after 8 years is $82,000.

Step-by-step solution

Calculate Total Depreciation

Find the difference between the initial value and the scrap value to determine the total amount of depreciation over the twenty-year period. This can be calculated using the formula: Total Depreciation = Initial Value - Scrap Value.

Annual Depreciation

Divide the total depreciation by the number of years the machine depreciates to find the annual depreciation amount. Use the formula: Annual Depreciation = Total Depreciation / Number of Years.

Determine Value after 8 Years

Multiply the annual depreciation by 8 to find the total depreciation after 8 years. Then subtract this value from the initial value to get the machine's value after 8 years. Use the formula: Value after 8 Years = Initial Value - (Annual Depreciation * 8).

Key concepts

Depreciation Calculations

Depreciation is an accounting method of allocating the cost of a tangible asset over its useful life. It reflects how much of an asset's value has been used up. In the case of straight-line depreciation, the process is straightforward: the cost of the asset is evenly spread over its estimated life span.

For example, if a milling machine has an initial purchase price and diminishes in value at a constant rate until it reaches its estimated end of useful life or scrap value, the annual depreciation is calculated by subtracting the scrap value from the initial value, dividing by the number of years of useful life. Using this method ensures that the same amount is depreciated each year, simplifying the calculation and providing a clear view of the asset's expense for each period.

Initial Value and Scrap Value

When discussing depreciation, two crucial values must be considered: the initial value and the scrap value. The initial value refers to the purchase price or the cost of acquiring the asset. On the other hand, the scrap value, also known as salvage value, is the expected value of the asset at the end of its useful life.

In our example, the milling machine's initial value is given as \(\$150,000\), and the scrap value is expected to be \(\$10,000\) after twenty years. These two figures are essential in calculating depreciation, as they mark the upper and lower bounds of the asset's valuation over time. Knowing both values is key to understanding the full financial impact of asset utilization.

Annual Depreciation Rate

The annual depreciation rate represents the fixed percentage of an asset's value that will be depreciated each year. In straight-line depreciation, this rate is consistent throughout the asset's usable life. To calculate the annual depreciation rate, you divide the total depreciation by the number of years the asset will be in use.

For our milling machine with a cost of \(\$150,000\) and scrap value of \(\$10,000\), over a useful life of 20 years, the annual depreciation rate is calculated as follows: \((\$150,000 - \$10,000) / 20\) years, resulting in an annual depreciation rate of \(\$7,000\) per year. This rate is the amount that will be recorded each year as an expense for the use of the machine.

Asset Valuation Over Time

Understanding how an asset's value changes over time is important for financial reporting and decision making. With the straight-line method, the asset's book value decreases by a fixed amount each year, which is the annual depreciation expense. As such, the book value of the asset at any point in time can be easily calculated by subtracting the accumulated depreciation up to that point from the initial value.

In the context of the milling machine example, after 8 years, the accumulated depreciation would be \(8 \times \$7,000\), resulting in a decrease in value of \(\$56,000\). The value of the machine after 8 years can be calculated by subtracting this accumulated depreciation from the initial value of \(\$150,000\), giving a remaining value of \(\$94,000\). This process shows the diminution of the asset's value over time and is essential for businesses to track their assets' worth and plan for future investments.