Understanding Machine Depreciation and Scrap Value

Depreciation is the decrease in the value of an asset over time due to wear and tear, obsolescence, or usage. Scrap value, also known as salvage value or residual value, is the estimated value of an asset at the end of its useful life.

There are different methods to calculate depreciation, such as the Straight-Line Method and the Reducing Balance Method. The question specifies depreciation at a percentage of the written down value each year, indicating the use of the Reducing Balance Method.

Reducing Balance Method Explained

The Reducing Balance Method (also known as the Diminishing Balance Method or Written Down Value Method) calculates depreciation on the book value (or written down value) of the asset each year, rather than on its original cost. This results in higher depreciation charges in the initial years and lower charges in later years.

Calculating Scrap Value using Reducing Balance Method

The formula to calculate the value of an asset (scrap value) after 'n' years using the Reducing Balance Method is:

\( V_n = P(1 - r)^n \)

Where:

• \( V_n \) = Value of the asset after 'n' years (Scrap Value)
• \( P \) = Original Cost of the asset
• \( r \) = Annual rate of depreciation (as a decimal)
• \( n \) = Useful life of the asset in years

Step-by-Step Calculation

Let's apply the formula using the given information:

• Original Cost (\( P \)) = Rs. 20,000
• Annual Depreciation Rate (\( r \)) = 10% = \( \frac{10}{100} \) = 0.10
• Useful Life (\( n \)) = 10 years

We need to calculate the Scrap Value (\( V_{10} \)) after 10 years.

Using the formula:

\( V_{10} = 20000 \times (1 - 0.10)^{10} \)

\( V_{10} = 20000 \times (0.9)^{10} \)

The question provides the value of \( (0.9)^{10} \) as 0.35.

\( V_{10} = 20000 \times 0.35 \)

Now, we perform the multiplication:

\( V_{10} = 7000 \)

So, the scrap value of the machine after 10 years, depreciating at 10% per annum using the reducing balance method, is Rs. 7000.

Summary of Calculation

The calculated scrap value matches option 2.

Revision Table: Key Depreciation Concepts

Additional Information: Depreciation Methods

Apart from the Reducing Balance Method, another common method is the Straight-Line Method.

Straight-Line Method

In the Straight-Line Method, the depreciation expense is the same amount each year. The formula is:

\( \text{Annual Depreciation} = \frac{\text{Original Cost} - \text{Scrap Value}}{\text{Useful Life}} \)

This method is simpler but doesn't reflect the potentially higher usage or efficiency of an asset in its early years compared to later years, which the Reducing Balance Method attempts to do.

The choice of depreciation method can impact the reported profit of a company each year because the depreciation expense is deducted from revenue.