Problem 13 - Accounting

Question

A storage tank acquired at the beginning of the fiscal year at a cost of \(172,000 has an estimated residual value of \)20,000 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 years computed by the double-declining-balance method.

Step-by-Step Solution

Answer

(a) Annual straight-line depreciation is $19,000. (b) First-year double-declining depreciation is $43,000; second-year is $32,250.

Step 1: Determine Annual Depreciation Using Straight-Line Method

To find the annual depreciation using the straight-line method, subtract the estimated residual value from the original cost, and divide the result by the estimated useful life of the asset. This gives the formula: \( \frac{\text{Cost} - \text{Residual Value}}{\text{Useful Life}} \). Here, it is \( \frac{172,000 - 20,000}{8} = 19,000 \). Thus, the annual depreciation is \( 19,000 \).

Step 2: Find Double-Declining Balance Rate

The double-declining balance rate is twice the straight-line depreciation rate. First, find the straight-line rate: \( \frac{1}{\text{Useful Life}} = \frac{1}{8} = 12.5\% \). Then, double this rate for the double-declining balance method: \( 12.5\% \times 2 = 25\% \).

Step 3: Calculate First-Year Depreciation Using Double-Declining Method

Apply the 25% rate to the cost of the asset to determine the first-year depreciation: \( 172,000 \times 0.25 = 43,000 \). This means the depreciation expense for the first year is \( 43,000 \).

Step 4: Calculate Second-Year Depreciation Using Double-Declining Method

Subtract the first year's depreciation from the original cost to find the book value at the beginning of the second year: \( 172,000 - 43,000 = 129,000 \). Apply the 25% rate to this new book value: \( 129,000 \times 0.25 = 32,250 \). This gives a second-year depreciation of \( 32,250 \).

Key Concepts

Straight-line Depreciation

When we talk about straight-line depreciation, we're discussing one of the simplest methods to calculate depreciation. Basically, it spreads the cost of an asset evenly over its useful life. Imagine you buy an item for a certain amount, and you want to know how much it "loses" in value each year. This method is great because:

• It's easy to calculate.
• It offers a steady, predictable expense each year.
• It's widely used and accepted for accounting purposes.

To find the annual depreciation expense using this method, you use the formula:\[\text{Annual Depreciation} = \frac{\text{Cost} - \text{Residual Value}}{\text{Useful Life}}\]In our example, we had a storage tank purchased for \(172,000, expected to be worth \)20,000 at the end of 8 years. The calculation would be:\[\frac{172,000 - 20,000}{8} = 19,000\]This means each year, we depreciate $19,000. Simple and straightforward!

Double-declining Balance Method

Now let's dive into the double-declining balance method, which is a bit more aggressive. It's considered an accelerated depreciation method. Unlike the straight-line approach, this method assumes that the asset will lose more value in the earlier years.Here's how it typically works:

• You start with the same calculation as with straight-line depreciation, but then double the rate.
• This leads to higher depreciation expenses earlier in the asset's life.
• It's beneficial for items that rapidly lose value, like high-tech equipment.

To calculate it, first, we find the straight-line rate:\[\text{Straight-line Rate} = \frac{1}{\text{Useful Life}} = \frac{1}{8} = 12.5\%\]Then, double it to get 25%. For our storage tank, the first-year depreciation would be:\[172,000 \times 0.25 = 43,000\]And for the second year, we'd calculate using the new book value:\[129,000 \times 0.25 = 32,250\]This method highlights how costs can vary significantly from year to year.

Useful Life of Asset

Understanding the concept of an asset's useful life is crucial for accurate depreciation calculations. The useful life is basically the period during which an asset is expected to be functional and productive. Several key points can influence this estimate:

• Physical wear and tear.
• Technological obsolescence.
• Company policies regarding asset replacement.

Essentially, if you have an asset like our storage tank with a useful life set at 8 years, that's the framework for your depreciation calculations. Knowing this helps predict future expenses and assists in planning for asset replacement. It may not always be a fixed duration. Changes in usage or technology might affect it, but it's the best estimate based on current knowledge at the purchase time. Overall, having a clear understanding of the useful life helps businesses spread out costs and make informed financial decisions.