Problem 14 - Accounting

Question

Sandblasting equipment acquired at a cost of \( 68,000\) has an estimated residual value of \( 18,000\) 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

Current fiscal year: $1,250 (straight-line), $3,400 (DDB); following year: $5,000 (straight-line), $12,920 (DDB).

Step 1: Understanding Equipment Cost and Residual Value

First, identify the initial cost of the sandblasting equipment and its residual value. The equipment was purchased for \( 68,000\) and has a residual value of \( 18,000\). This means it is expected to lose \( 68,000 - 18,000 = 50,000\) in value over its useful life.

Step 2: Straight-Line Depreciation Calculation

For the straight-line method, the annual depreciation expense is calculated by subtracting the residual value from the cost and dividing by the useful life. The formula is: \( \frac{68,000 - 18,000}{10} = 5,000\). Thus, the annual depreciation is \( 5,000 \).

Step 3: Calculating Depreciation for Current Fiscal Year (Straight-Line)

The equipment was placed in service on October 1, which is 3 months before the fiscal year ends. To find the depreciation for the current fiscal year under the straight-line method, calculate \( \frac{5,000}{12} \times 3 = 1,250\).

Step 4: Calculating Depreciation for Following Fiscal Year (Straight-Line)

Depreciation for the entire following fiscal year using the straight-line method is \( 5,000\), as the equipment will be in service for the whole year.

Step 5: Understanding Double-Declining-Balance Method

The double-declining-balance (DDB) method calculates depreciation based on a percentage that is double the straight-line rate. First, determine the straight-line rate: \( \frac{1}{10} = 0.10\), so the double rate is \( 0.20\) or 20%.

Step 6: Initial Depreciation Calculation (DDB)

Apply the 20% rate to the full cost of the equipment for the portion of the current fiscal year it was in use. The depreciation for three months is \( \frac{0.20 \times 68,000}{12} \times 3 = 3,400\).

Step 7: Calculating Depreciation for Following Fiscal Year (DDB)

Subtract the accumulated depreciation from the cost to find the new book value before the next fiscal year: \( 68,000 - 3,400 = 64,600\). Apply the 20% rate to this new book value: \( 0.20 \times 64,600 = 12,920\).

Key Concepts

Straight-line depreciation

Straight-line depreciation is one of the simplest methods to calculate depreciation of an asset. This method evenly spreads the cost over its useful life. Essentially, it assumes that the asset will enjoy equal usage in each period. For instance, if you bought equipment for \(68,000 with a residual value of \)18,000 and it has a useful life of 10 years, you'd spread the decline in value over ten years.
To find the annual depreciation, you subtract the residual value from the purchase cost:

• Cost: \(68,000
• Residual Value: \)18,000
• Useful Life: 10 years

Using the formula, \[\text{Annual Depreciation} = \frac{\text{Cost} - \text{Residual Value}}{\text{Useful Life}}\]Annual depreciation would be: \[\frac{68,000 - 18,000}{10} = 5,000\]Thus, each year's expense is $5,000, reflecting how much the asset devalues annually. This method benefits businesses with assets that wear out evenly over time.

Double-declining-balance method

The double-declining-balance (DDB) method is an accelerated depreciation technique. It allows for larger depreciation expenses in the early years of an asset's life. This method can be quite useful for assets that quickly lose their value after purchase. Here's how it works:
First, calculate the straight-line depreciation rate as a percentage. If the useful life is 10 years, the rate is \[\frac{1}{10} = 10\%.\]Double that rate to get 20%. This rate will be applied to the book value of the asset, not the original cost.
In our case, starting with the equipment cost of $68,000, for the first 3 months:

• Calculate the depreciation by: \[0.20 \times 68,000 = 13,600 \]
• Since it was only in use for 3 months:\[\frac{13,600}{12} \times 3 = 3,400\]

For the following fiscal year, the book value becomes \[68,000 - 3,400 = 64,600\] and you'll apply the same rate again. Thus, \[0.20 \times 64,600 = 12,920\]. This method acknowledges quicker wear and tear early on, which can be more aligned with some assets' real-world devaluation.

Residual value

Residual value represents the estimated amount an asset is worth at the end of its useful life. It's sometimes called salvage value. When you depreciate an asset like equipment, you don't depreciate it all the way to zero unless you plan for it to have zero value at the end.
For instance, if you purchase equipment for $68,000 and anticipate it will be worth $18,000 after 10 years, then $18,000 is your residual value. It's essentially the book value you aim not to depreciate. Subtract this value from the asset's cost to determine the total amount to depreciate over its life.
The concept ensures that depreciation calculations don't overlook the potential worth of an asset when it's no longer in primary use, capturing its expected future market or trade-in value.

Useful life in accounting

Useful life in accounting refers to the period during which an asset is expected to add value and contribute to revenue generation. It isn't a fixed number and differs based on asset types and industry standards.
For our sandblasting equipment, the useful life was considered to be 10 years. This means over a decade, this equipment is expected to serve in capacities that warrant its initial purchase cost.
Determining useful life influences how companies calculate depreciation. It affects financial statements as it spreads the asset's cost across these years. Understanding this concept helps businesses budget, predict future expenses, and make informed financial decisions.