7.f Accumulated Value¶

Introduction¶

Depreciation refers to the gradual decrease in the value of an asset over time due to factors such as wear and tear, usage, aging, or obsolescence. It is commonly applied to tangible assets like machinery, vehicles, and equipment. Understanding depreciation is crucial for businesses as it affects asset valuation, tax calculations, and financial reporting.

The two main methods of calculating depreciation are: 1. Straight-Line Depreciation: The asset loses the same amount of value each year. 2. Declining Balance Depreciation: The asset loses value by a fixed percentage each year.

1. Straight-Line Depreciation¶

The formula for straight-line depreciation is:

\[ \text{Annual Depreciation} = \frac{\text{Initial Cost} - \text{Salvage Value}}{\text{Useful Life}} \]

Where: - Initial Cost = Original purchase price of the asset - Salvage Value = Estimated value of the asset at the end of its useful life - Useful Life = Number of years the asset is expected to be in use

2. Declining Balance Depreciation¶

The formula for declining balance depreciation is:

\[ \text{Depreciation for the Year} = \text{Book Value} \times \text{Depreciation Rate} \]

Where: - Book Value = Value of the asset at the beginning of the year - Depreciation Rate = Fixed percentage rate at which the asset depreciates

Example 1: Calculating Straight-Line Depreciation¶

Problem¶

A company purchases a machine for $10,000. The machine is expected to have a useful life of 5 years, with a salvage value of $2,000. Calculate the annual depreciation using the straight-line method.

Solution¶

Given: - Initial Cost = $10,000 - Salvage Value = $2,000 - Useful Life = 5 years

Using the straight-line depreciation formula:

\[ \text{Annual Depreciation} = \frac{10000 - 2000}{5} \]

\[ \text{Annual Depreciation} = \frac{8000}{5} = 1600 \]

Explanation¶

The annual depreciation for the machine is $1,600. This means the machine will lose $1,600 in value each year over its 5-year useful life. After 5 years, the machine's book value will be reduced to its salvage value of $2,000.

Example 2: Calculating Declining Balance Depreciation¶

Problem¶

A company buys a vehicle for $15,000, and it is estimated to depreciate at a rate of 20% per year using the declining balance method. Calculate the depreciation for the first two years.

Solution¶

Given: - Initial Cost (Year 0 Book Value) = $15,000 - Depreciation Rate = 20%

Year 1¶

\[ \text{Depreciation for Year 1} = 15000 \times 0.20 = 3000 \]

The book value at the end of Year 1:

\[ \text{Book Value} = 15000 - 3000 = 12000 \]

Year 2¶

\[ \text{Depreciation for Year 2} = 12000 \times 0.20 = 2400 \]

The book value at the end of Year 2:

\[ \text{Book Value} = 12000 - 2400 = 9600 \]

Explanation¶

In this example, the vehicle depreciates by 20% of its book value each year. In Year 1, the depreciation amount was $3,000, leaving a book value of $12,000. In Year 2, the depreciation was $2,400, further reducing the book value to $9,600. The declining balance method results in higher depreciation in the earlier years.

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