Problem 14 - Accounting

Question

Sandblasting equipment acquired at a cost of \(85,000 has an estimated residual value of \)5,000 and an estimated useful life of 10 years. It was placed in service on October 1 of the current fiscal year, which ends on December 31. Determine the depreciation for the current fiscal year and for the following fiscal year by (a) the straight- line method and (b) the double-declining-balance method.

Step-by-Step Solution

Answer

Straight-line: $2,000 for current year, $8,000 for next year. Double-declining: $4,250 for current year, $16,150 for next year.

Step 1: Calculate Straight-Line Depreciation Rate

The straight-line depreciation method evenly splits the cost of an asset over its useful life. First, calculate the annual depreciation using the formula: \( \text{Annual Depreciation} = \frac{\text{Cost} - \text{Residual Value}}{\text{Useful Life}} \). Here: \( \text{Annual Depreciation} = \frac{85,000 - 5,000}{10} = 8,000 \).

Step 2: Calculate Straight-Line Depreciation for Current Year

Since the equipment was placed into service on October 1 and the fiscal year ends on December 31, it was used for 3 months in the first fiscal year. Calculate the depreciation for this period: \( \text{Depreciation for Current Year} = \frac{8,000}{12} \times 3 = 2,000 \).

Step 3: Calculate Straight-Line Depreciation for Next Year

In the following fiscal year, the equipment will be used for the entire year. Thus, the depreciation would be the full annual amount: \( 8,000 \).

Step 4: Calculate Double-Declining Rate

The double-declining-balance method applies a higher rate at the beginning of the asset's life. Calculate the rate first: \( \text{Double-Declining Rate} = \frac{2}{\text{Useful Life}} = \frac{2}{10} = 20\% \).

Step 5: Calculate Double-Declining Depreciation for Current Year

For the current year, apply the rate to the cost, then adjust for the partial year. First calculate the full year depreciation: \( 85,000 \times 20\% = 17,000 \). Then, adjust for the 3 months in use: \( \text{Depreciation for Current Year} = \frac{17,000}{12} \times 3 = 4,250 \).

Step 6: Calculate Double-Declining Depreciation for Next Year

For the next fiscal year, apply the rate to the remaining value. First, compute the depreciable base: \( 85,000 - 4,250 = 80,750 \). Then, calculate the depreciation: \( 80,750 \times 20\% = 16,150 \).

Key Concepts

Straight-Line Depreciation

Straight-line depreciation is one of the simplest and most commonly used methods for allocating the cost of an asset over its useful life. The idea is to spread the cost evenly across each period of the asset's life. To calculate straight-line depreciation, you use the formula:\[\text{Annual Depreciation} = \frac{\text{Cost} - \text{Residual Value}}{\text{Useful Life}}\]This method assumes that the asset will lose the same amount of value each year, leading to a straight-line effect on the financial statements. This approach is straightforward, making it easy to implement and understand.A few key points about straight-line depreciation:

• The total depreciation expense over the useful life of the asset is equal to the initial cost minus the residual value.
• Useful in organizations where the asset's utility is uniform over its life.
• Tends to smooth out expenses over time.

So, if you had equipment costing \(85,000, with a residual value of \)5,000, and a useful life of 10 years, you'd record $8,000 in depreciation every year.

Double-Declining-Balance Method

The double-declining-balance (DDB) method is an accelerated depreciation method that writes off the asset's cost more quickly in its earlier years. This is especially useful for assets that lose value faster early on, like computers or vehicles.Here's the formula to compute the double-declining rate:\[\text{Double-Declining Rate} = \frac{2}{\text{Useful Life}}\]For a 10-year useful life, this results in a 20% depreciation rate each year. You apply this rate to the asset's book value at the start of the year (cost minus accumulated depreciation), and not just the original cost. Key aspects of the DDB method include:

• Higher depreciation expenses in the early years.
• The method reflects the rapid consumption of asset value more accurately during initial years.
• Expenses decrease over time as the asset's book value declines.

For example, if your equipment was acquired for \(85,000, in the first partial year, depreciation would be calculated using the \)85,000 cost, leading to larger depreciation amounts beginning upfront.

Residual Value

Residual value, also known as salvage value, is the estimated amount that an asset will be worth at the end of its useful life. This figure is crucial because it represents the expected recoverable amount from selling or scrapping the asset once its productive life has ended. Understanding the significance of residual value:

• It influences the total depreciable amount of the asset. Depreciation is calculated on the cost minus this value, representing the anticipated potential sales price or remaining usability.
• Accurate estimation is vital for realistic financial forecasting and matching costs with generated revenues.
• Residual value forces businesses to consider the future utility and market conditions of their assets at purchase.

In exercise terms, an $85,000 piece of equipment with a $5,000 residual value suggests that depreciation will be charged on $80,000 over its life, acknowledging the expected future cash inflow upon disposal.

Useful Life Calculation

The concept of useful life refers to the period over which an asset is expected to be in use before it needs replacement or disposal. Determining the useful life of an asset is critical since it dictates how quickly the asset's cost will be expensed through depreciation. Useful life is determined by:

• The expected timeframe over which the asset will be in service and providing economic benefit.
• Industry-specific norms and company experiences that guide the estimation of an average lifespan.
• Expected physical wear and technological obsolescence which might lead to early replacements.

For the equipment in question, this was set to 10 years, representing the time the company expects to derive economic benefit from it. This assumption helps in planning, capital investments, and financial statements conformity.