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Chapter 5: Problem 41

Restaurant equipment purchased at a cost of \(\$ 150,000\) is to be depreciated by the double declining-balance method over \(10 \mathrm{yr}\). What is the book value of the equipment at the end of 6 yr? By what amount has the equipment been depreciated at the end of the sixth year?

Short Answer

Expert verified
The book value of the restaurant equipment at the end of 6 years is \(\$39,321.60\), and the total depreciation amount after 6 years is \(\$110,678.40\).

Step by step solution

01

1. Find the Annual Depreciation Rate

Let's first determine the annual depreciation rate. The double declining-balance method calculates depreciation by taking double the straight-line depreciation rate. The straight-line depreciation rate can be found by dividing \(100 \%\) by the number of years in the equipment's useful life. Annual straight-line depreciation rate = \( \frac{100 \%}{10 \mathrm{yr}} \) = \( 10 \% \) Now, let's find the double declining-balance depreciation rate: Double declining-balance depreciation rate = 2 脳 (annual straight-line depreciation rate) = 2 脳 (10%) = 20%
02

2. Calculate the Depreciation Amount for Each Year

We will now find the depreciation amounts for each year. To calculate the depreciation amount for a specific year, multiply the book value at the beginning of the year by the double declining-balance depreciation rate. Year 1: Initial book value: \(\$150,000\) Depreciation amount: (20%)(\$150,000) = \(\$30,000\) Year 2: Initial book value: (\$150,000 - \$30,000) = \(\$120,000\) Depreciation amount: (20%)(\$120,000) = \(\$24,000\) Year 3: Initial book value: (\$120,000 - \$24,000) = \(\$96,000\) Depreciation amount: (20%)(\$96,000) = \(\$19,200\) Year 4: Initial book value: (\$96,000 - \$19,200) = \(\$76,800\) Depreciation amount: (20%)(\$76,800) = \(\$15,360\) Year 5: Initial book value: (\$76,800 - \$15,360) = \(\$61,440\) Depreciation amount: (20%)(\$61,440) = \(\$12,288\) Year 6: Initial book value: (\$61,440 - \$12,288) = \(\$49,152\) Depreciation amount: (20%)(\$49,152) = \(\$9,830.40\)
03

3. Calculate the Book Value at the End of 6 Years

To find the book value of the equipment at the end of 6 years, subtract the depreciation amount in the 6th year from the initial book value at the beginning of the 6th year. Book value at the end of 6 years = \$49,152 - \$9,830.40 = \(\$39,321.60\)
04

4. Calculate the Total Depreciation Amount at the End of the Sixth Year

Add the depreciation amounts for each year to find the total depreciation amount at the end of the sixth year. Total depreciation amount = \$30,000 + \$24,000 + \$19,200 + \$15,360 + \$12,288 + \$9,830.40 = \(\$110,678.40\) The book value of the equipment at the end of 6 years is \(\$39,321.60\). The equipment has been depreciated by \(\$110,678.40\) at the end of the sixth year.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Straight-Line Depreciation Rate
When we talk about depreciation, the straight-line method is by far the most straightforward. It assumes an asset will lose an equal amount of value each year over its useful life. To calculate the straight-line depreciation rate, simply divide 100% by the number of years the asset is expected to be useful. For instance, if a piece of restaurant equipment is estimated to last 10 years, the straight-line depreciation rate would be \( 100\% \div 10 \mathrm{yr} = 10\% \). That means, each year, the equipment's book value will decrease by this fixed percentage, providing a consistent annual depreciation expense. This contrasts with accelerated methods like the double declining-balance that front-load the depreciation expenses.
Book Value Calculation
The book value of an asset represents its carrying value on the balance sheet. It's calculated by subtracting the accumulated depreciation from the asset's original cost. To keep track of the decreasing book value when using the double declining-balance method of depreciation, you multiply the book value at the beginning of the year by twice the straight-line depreciation rate.

This method demonstrates a higher depreciation expense early on and gradually diminishes as the asset ages. By the end of the sixth year in our example, the book value calculation would involve subtracting the accumulated depreciation over those six years from the initial purchase price. This results in a remaining book value that reflects the declining worth of the restaurant equipment year by year.
Depreciation Methods
There are several depreciation methods available to account for the expense of an asset over time. Each serves different accounting strategies and financial objectives. Aside from the straight-line method we've discussed, the double declining-balance method is a form of accelerated depreciation. It's often used to match the higher costs associated with new assets such as repair and maintenance and then reduce the expense as the asset gets older.

Other methods include the units-of-production, which bases depreciation on an asset's usage, and the sum-of-the-years'-digits method, another type of accelerated depreciation. The choice of method can affect a company's financial statements and tax liabilities, thus it's not just about the calculation鈥攊t also encompasses financial strategy and planning.

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