Understanding Asset Depreciation Calculation

When an asset is purchased, its value decreases over time due to wear and tear, obsolescence, or usage. This decrease in value is called depreciation. There are different methods to calculate depreciation, and the question specifies the Written Down Value (WDV) method.

What is the Written Down Value Method?

The Written Down Value method, also known as the Reducing Balance Method, calculates depreciation on the book value (or written down value) of the asset at the beginning of the year, rather than on the original cost. This means the depreciation amount is higher in the initial years and decreases over time. The asset value reduces year after year.

Calculating Asset Depreciation Year by Year

Let's calculate the asset value at the end of the third year step-by-step using the 20% depreciation rate on the written down value.

Initial Cost of Asset: Rs. 12,500

Depreciation Rate: 20% per annum

End of Year 1:

• Depreciation for Year 1 = 20% of Initial Cost
• Depreciation for Year 1 = $\text{Rs. } 12,500 \times \frac{20}{100} = \text{Rs. } 2,500$
• Value of asset at the end of Year 1 = Initial Cost - Depreciation for Year 1
• Value of asset at the end of Year 1 = $\text{Rs. } 12,500 - \text{Rs. } 2,500 = \text{Rs. } 10,000$

End of Year 2:

For the WDV method, depreciation is calculated on the value at the beginning of the year (which is the value at the end of the previous year).

• Value at the beginning of Year 2 = Rs. 10,000
• Depreciation for Year 2 = 20% of Value at the beginning of Year 2
• Depreciation for Year 2 = $\text{Rs. } 10,000 \times \frac{20}{100} = \text{Rs. } 2,000$
• Value of asset at the end of Year 2 = Value at the beginning of Year 2 - Depreciation for Year 2
• Value of asset at the end of Year 2 = $\text{Rs. } 10,000 - \text{Rs. } 2,000 = \text{Rs. } 8,000$

End of Year 3:

Again, we calculate depreciation on the written down value at the start of the year.

• Value at the beginning of Year 3 = Rs. 8,000
• Depreciation for Year 3 = 20% of Value at the beginning of Year 3
• Depreciation for Year 3 = $\text{Rs. } 8,000 \times \frac{20}{100} = \text{Rs. } 1,600$
• Value of asset at the end of Year 3 = Value at the beginning of Year 3 - Depreciation for Year 3
• Value of asset at the end of Year 3 = $\text{Rs. } 8,000 - \text{Rs. } 1,600 = \text{Rs. } 6,400$

So, the value of the asset at the end of the third year is Rs. 6,400.

Summarizing the Asset Depreciation Calculation (WDV)

Alternatively, you can use the formula for calculating the asset value under the Written Down Value method:

$$ \text{Value at end of n years} = \text{Original Cost} \times \left(1 - \text{Depreciation Rate}\right)^{\text{n}} $$

Here, Original Cost = Rs. 12,500, Depreciation Rate = 20% or 0.20, and n = 3 years.

$$ \text{Value at end of 3 years} = 12500 \times (1 - 0.20)^3 $$

$$ \text{Value at end of 3 years} = 12500 \times (0.80)^3 $$

$$ \text{Value at end of 3 years} = 12500 \times 0.512 $$

$$ \text{Value at end of 3 years} = 6400 $$

Both methods confirm that the asset value at the end of the third year is Rs. 6,400. This asset depreciation calculation is a key concept in accounting.