Problem 17 - Accounting

Question

Equipment acquired on January 3,2005 , at a cost of \( 360,000\), has an estimated useful life of 12 years, has an estimated residual value of \( 30,000\), and is depreciated by the straightline method. a. What was the book value of the equipment at December 31,2008 , the end of the year? b. Assuming that the equipment was sold on April 1, 2009, for \( 220,000\), journalize the entries to record (1) depreciation for the three months until the sale date, and (2) the sale of the equipment.

Step-by-Step Solution

Answer

The book value at December 31, 2008, was \( 250,000 \). Post-sale journal entries include a \( 6,875 \) depreciation expense and a \( 3,125 \) loss on sale.

Step 1: Calculate Annual Depreciation Expense

The formula for annual depreciation using the straight-line method is:\[\text{Annual Depreciation} = \frac{\text{Cost} - \text{Residual Value}}{\text{Useful Life}}\]Substituting the given values:\[\text{Annual Depreciation} = \frac{360,000 - 30,000}{12} = 27,500\]So, the annual depreciation expense is \( 27,500 \).

Step 2: Calculate Accumulated Depreciation by December 31, 2008

The equipment was in use from January 3, 2005, to December 31, 2008, which is 4 complete years. The accumulated depreciation is the annual depreciation multiplied by the number of years.\[\text{Accumulated Depreciation} = 27,500 \times 4 = 110,000\]

Step 3: Determine Book Value as of December 31, 2008

The book value is calculated by subtracting accumulated depreciation from the cost of the equipment. \[\text{Book Value} = 360,000 - 110,000 = 250,000\]Thus, the book value of the equipment as of December 31, 2008, is \( 250,000 \).

Step 4: Calculate Depreciation for January 1 to April 1, 2009

The quarterly depreciation for the first three months of 2009 is a fraction of the annual depreciation. Since there are 3 months (or 1/4 of a year), calculate:\[\text{Depreciation for 3 months} = 27,500 \times \frac{3}{12} = 6,875\]

Step 5: Record Journal Entry for Depreciation Ending April 1, 2009

On March 31, to record the depreciation expense for the first quarter of 2009:- Debit: Depreciation Expense \( 6,875 \)- Credit: Accumulated Depreciation \( 6,875 \)

Step 6: Calculate Book Value at the Date of Sale

Add the additional depreciation to the previous accumulated depreciation and subtract from the initial cost to find the book value on April 1, 2009:\[\text{Total Accumulated Depreciation} = 110,000 + 6,875 = 116,875\]\[\text{Book Value on April 1, 2009} = 360,000 - 116,875 = 243,125\]

Step 7: Record the Sale of the Equipment

On April 1, when the equipment is sold for \( 220,000 \):- Debit: Cash \( 220,000 \)- Debit: Accumulated Depreciation \( 116,875 \)- Credit: Equipment \( 360,000 \)- Debit: Loss on Sale of Equipment \( 3,125 \) (since Book Value \( 243,125 \) > Sale Proceeds \( 220,000 \))

Key Concepts

Book Value Calculation

When talking about the book value of an asset, we mean its recorded value in the company's financial books. This doesn't necessarily match its market value, as book value starts with the cost of an asset and is adjusted for depreciation.
To calculate book value, the formula is:\[\text{Book Value} = \text{Initial Cost} - \text{Accumulated Depreciation}\]In our example, we initially purchased the equipment for \(360,000. By December 31, 2008, the accumulated depreciation was \)110,000. Thus, the book value at that point was:\[360,000 - 110,000 = 250,000\]This figure represents how the value of the asset appears in the accounting records by the end of 2008 after accounting for loss in value from use over the first four years.

Journal Entry for Asset Sale

When a company sells an asset, it needs to record this transaction in its financial records. This is done through a journal entry, which ensures all accounts reflect this sale accurately.
For the sale of an asset, key elements to include in your journal entry are:

• Cash Received: The actual amount received from the sale.
• Accumulated Depreciation: The total depreciation recorded up to the point of sale. It must be removed from the books.
• Loss or Gain on Sale: If the cash received differs from the book value, a gain or loss is recorded.

In our scenario, let's cover the steps done on April 1, 2009:

• We received cash of \(220,000.
• We needed to reverse the accumulated depreciation, which by then totaled \)116,875.
• The equipment's cost was $360,000, which we also needed to remove from the books.
• Since the cash received was less than the book value (\(243,125\), we recorded a loss of \(3,125\).

Accumulated Depreciation

Accumulated depreciation is a critical accounting concept representing the total amount of depreciation that has been recorded against an asset since its acquisition.
This measure helps stakeholders understand how much of an asset's value has been "used up" over time.

• Each year, the asset depreciates, reducing its book value.
• The straight-line depreciation method implies constant annual deprecated amounts to distribute over the useful life of the asset.
• Accumulated depreciation increases cumulatively with each passing year.

In our scenario, at the end of four years (2005 to 2008), the accumulated depreciation was calculated as:\[27,500 \times 4 = 110,000\]By April 2009, an additional three months of depreciation (\(6,875\)) was added, bringing the total to:\[116,875\]This comprehensive figure accounts for depreciation over the length of ownership and reduces the book value of the asset accordingly.