Problem 12 - Accounting

Question

A Kubota tractor acquired on January 9 at a cost of $75,000 has an estimated useful life of 20 years. Assuming that it will have no residual value, determine the depreciation for each of the first two years (a) by the straight-line method and (b) by the doubledeclining-balance method.

Step-by-Step Solution

Answer

Straight-line: $3,750 each year; Double-declining: Year 1 - $7,500, Year 2 - $6,750.

Step 1: Understand the Straight-Line Depreciation Formula

The straight-line method calculates depreciation by evenly spreading the cost of an asset over its useful life. The formula is: \[ \text{Depreciation Expense} = \frac{\text{Cost} - \text{Residual Value}}{\text{Useful Life}}. \] Here, Cost = \(75,000 and Residual Value = \)0 over a Useful Life = 20 years.

Step 2: Calculate Straight-Line Depreciation for One Year

Applying the formula: \[ \text{Depreciation Expense} = \frac{75000 - 0}{20} = 3750. \] This means the depreciation expense for each year is $3,750.

Step 3: Find Yearly Depreciation for First Two Years (Straight-Line)

Both the first and second year depreciation expenses remain consistent at $3,750 using the straight-line method.

Step 4: Understand the Double-Declining-Balance Depreciation Formula

This method involves applying double the straight-line rate to the asset's remaining book value. The straight-line rate is \(\frac{1}{20} = 0.05\), so the double-declining rate is \(2 \times 0.05 = 0.1\).

Step 5: Calculate Depreciation for Year 1 (Double-Declining)

The first year's depreciation is \(0.1 \times 75000 = 7500\). Thus, for Year 1, the depreciation expense is $7,500.

Step 6: Calculate Depreciation for Year 2 (Double-Declining)

After Year 1, the book value becomes \(75000 - 7500 = 67500\). Year 2 depreciation is \(0.1 \times 67500 = 6750\). Thus, for Year 2, the depreciation expense becomes $6,750.

Key Concepts

Straight-Line Depreciation

Straight-line depreciation is a method where you allocate the same amount of depreciation expense for an asset each year over its useful life. It is straightforward and widely used because of its simplicity.
To calculate straight-line depreciation, you need to know:

• The initial cost of the asset.
• The asset's useful life.
• The residual value, which is the value you expect to get from the asset at the end of its useful life (often zero, if the asset is fully used up).

The formula is: \[ \text{Depreciation Expense} = \frac{\text{Cost} - \text{Residual Value}}{\text{Useful Life}}. \] In the given exercise, the tractor has a cost of \(75,000 and no residual value with a useful life of 20 years. By plugging these figures into the formula, the yearly depreciation expense is \( \frac{75000 - 0}{20} = 3750 \).
This means each year, \)3,750 is considered as depreciation expense for the tractor, reflecting a consistent reduction in its value over time.

Double-Declining-Balance Depreciation

The double-declining-balance method is a type of accelerated depreciation. It allows for more depreciation expense during the early years of an asset's life compared to later years. This is useful for assets that lose value faster in their initial years or become obsolete quickly.
The process involves two main steps:

• Determine the straight-line depreciation rate. It's the reciprocal of the asset's useful life, so for a 20-year life, it is \( \frac{1}{20} = 0.05 \).
• Double this rate to get the double-declining rate, which is \( 0.1 \) or 10%.

For the first year, apply this rate to the original cost: \[ 0.1 \times 75000 = 7500. \] After the first year, subtract the depreciation from the initial cost to get the book value for the new year. Then, apply the double-declining rate again: For Year 2, depreciate \( 0.1 \times 67500 = 6750 \).
Notice how the depreciation value decreases every year. This reflects a higher initial depreciation that lowers over time as the asset ages.

Asset Useful Life

The asset useful life is the period over which an asset is expected to be usable for the purpose it was acquired. During this time, it contributes to the production of revenue. The concept of useful life is fundamental in depreciation calculations, as it determines how quickly an asset will depreciate. There are several factors that can influence the estimation of an asset's useful life:

• Usage rate: More intensive use can shorten useful life.
• Technological advances: New technologies can make an asset obsolete faster.
• Legal restrictions or regulations: Certain assets might be limited to a specific operational timeframe.

In many cases, the useful life is estimated based on industry standards or historical data from similar assets. In the exercise's context, the tractor's useful life is set at 20 years, which suggests it will reliably serve its intended function within this period.
Keep in mind that while useful life is a guiding parameter, it might need reassessment if circumstances change.