Problem 13 - Accounting

Question

A storage tank acquired at the beginning of the fiscal year at a cost of \( 86,000\) has an estimated residual value of \( 10,000\) and an estimated useful life of eight years. Determine the following: (a) the amount of annual depreciation by the straight-line method and (b) the amount of depreciation for the first and second year computed by the double-decliningbalance method.

Step-by-Step Solution

Answer

(a) The annual depreciation is $9,500. (b) The first year depreciation is $21,500, and the second year is $16,125, using the double-declining balance method.

Step 1: Calculate Depreciable Amount

The depreciable amount is the difference between the cost of the asset and its residual value. For the storage tank, the depreciable amount is calculated as follows:\[\text{Depreciable Amount} = \text{Cost} - \text{Residual Value} = 86,000 - 10,000 = 76,000.\]

Step 2: Compute Annual Depreciation - Straight-Line Method

The straight-line method calculates annual depreciation by dividing the depreciable amount by the useful life of the asset. The formula is:\[\text{Annual Depreciation} = \frac{\text{Depreciable Amount}}{\text{Useful Life}} = \frac{76,000}{8} = 9,500.\]

Step 3: Determine Initial Double-Declining Balance Rate

The double-declining balance method involves an initial rate calculated as twice the rate of the straight-line method. The straight-line rate is \(\frac{1}{8} = 0.125\) or 12.5%. Thus, the double rate is:\[\text{Double-Declining Rate} = 2 \times 0.125 = 0.25 \text{ or } 25%.\]

Step 4: Calculate First Year Depreciation - Double-Declining Balance

First year depreciation is calculated by applying the double-declining rate to the asset's initial cost:\[\text{First Year Depreciation} = \text{Cost} \times \text{Double-Declining Rate} = 86,000 \times 0.25 = 21,500.\]

Step 5: Calculate Second Year Depreciation - Double-Declining Balance

For the second year, apply the double-declining rate to the reduced book value after the first year. Reduce the cost by the first year's depreciation to find the new book value:\[\text{Book Value at Beginning of Second Year} = 86,000 - 21,500 = 64,500.\]Then calculate the second year depreciation:\[\text{Second Year Depreciation} = 64,500 \times 0.25 = 16,125.\]

Key Concepts

Straight-Line Method

The Straight-Line Method is a simple and commonly used way to calculate depreciation. Under this method, you spread the asset's cost equally over its useful life. In other words, you take the total amount that you expect the asset to lose in value over time (also known as the depreciable amount) and divide it by the number of years the asset is expected to be used. This results in the same depreciation expense every year, making it predictable and easy to apply.

To use the Straight-Line Method, start by determining the depreciable amount, which is the cost of the asset minus its estimated residual value. Then, take this amount and divide by the asset's useful life in years.

For example, if an asset costs $86,000, with a residual value of $10,000 and helps your operations for eight years, the depreciable amount is $76,000 ($86,000 - $10,000). You then divide the $76,000 by 8 to find an annual depreciation of $9,500. This is how much of the asset's cost you'd allocate every year as an expense until the asset is "used up" at the end of its life.

Double-Declining Balance Method

The Double-Declining Balance Method is an accelerated depreciation method. This means it reduces the book value of an asset faster than the Straight-Line Method, especially in the first few years of the asset's life. This approach can be advantageous for assets that quickly become obsolete or lose value rapidly.

The Double-Declining Balance Method involves using a constant rate of depreciation, which is twice the rate used in the Straight-Line Method. Here's how it works:

• First, calculate the straight-line depreciation rate as a percentage by dividing 1 by the number of useful years. For example, with an asset useful for 8 years, the rate is 12.5%.
• Double this straight-line rate to find the Double-Declining rate: 2 times 12.5% equals 25%.
• In the first year, apply this 25% rate to the asset's initial cost. For instance, with an initial cost of $86,000, the first-year depreciation is $21,500 ($86,000 times 25%).
• For the subsequent years, apply the same rate of 25% to the asset's book value at the beginning of that year, after subtracting any accumulated depreciation from previous years.

It's crucial to understand that the depreciation expense will decrease each year since it's based on the reduced book value of the asset that continues to decline as depreciation accumulates over time.

Depreciable Amount

The Depreciable Amount is key when calculating depreciation since it represents the total value that will be spread out over the asset's useful life. Calculating it is straightforward: simply subtract the asset's residual value from its purchase price.

Think of the depreciable amount as the portion of the asset's cost that you expect to "use up" over time. In the storage tank example, the initial cost is $86,000, and the residual value is estimated at $10,000. Hence, the depreciable amount is $76,000 ($86,000 minus $10,000).

This figure is important because it's the basis for all calculations of depreciation, regardless of the method you choose. The method you pick (Straight-Line or Double-Declining) will dictate how you spread this amount across the asset's life, impacting financial statements and, potentially, tax computations. Understanding and accurately pinpointing the depreciable amount helps ensure proper accounting and a clear view of an asset’s value diminution over time.