The cost of a machinery is ₹8,00,000. Its scrap value will be one-tenth of its original cost in 15 years. Using the linear method of depreciation, the book value of the machine at the end of the 10th year will be:
- ₹4,80,000
- ₹3,20,000
- ₹3,68,000
- ₹4,32,000
The Correct Option is B
Approach Solution - 1
The linear method of depreciation, also known as straight-line depreciation, involves reducing the value of an asset uniformly over its useful life. To determine the book value of the machinery after 10 years, follow these steps:
Determine the initial cost of the machinery: ₹8,00,000.
Calculate the scrap value (residual value), which is one-tenth of the original cost:
Scrap Value = \( \frac{8,00,000}{10} = 80,000 \).
Find the total depreciable amount, which is equal to the original cost minus the scrap value:
Depreciable Amount = ₹8,00,000 - ₹80,000 = ₹7,20,000.
Calculate the annual depreciation using the formula:
Annual Depreciation = \( \frac{\text{Depreciable Amount}}{\text{Useful Life}} \)
Annual Depreciation = \( \frac{7,20,000}{15} = 48,000 \).
Determine the total depreciation over 10 years:
Total Depreciation (10 years) = 48,000 × 10 = ₹4,80,000.
Calculate the book value at the end of the 10th year:
Book Value = Original Cost - Total Depreciation.
Book Value = ₹8,00,000 - ₹4,80,000 = ₹3,20,000.
Therefore, the book value of the machinery at the end of the 10th year is ₹3,20,000.
Approach Solution -2
Using the linear method of depreciation, the annual depreciation is calculated as:
\[ \text{Annual Depreciation} = \frac{\text{Cost of Machinery} - \text{Scrap Value}}{\text{Useful Life}}. \]
Here:
Cost of Machinery = 8,00,000, Scrap Value = \(\frac{8,00,000}{10} = 80,000\), Useful Life = 15 years.
\[ \text{Annual Depreciation} = \frac{8,00,000 - 80,000}{15} = \frac{7,20,000}{15} = 48,000 \text{ per year}. \]
The depreciation over 10 years is:
\[ \text{Depreciation for 10 years} = 48,000 \times 10 = 4,80,000. \]
The book value at the end of the 10th year is:
\[ \text{Book Value} = \text{Cost of Machinery} - \text{Depreciation for 10 years} = 8,00,000 - 4,80,000 = 3,20,000. \]
Thus, the book value at the end of the 10th year is Rs. 3,20,000.
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