Question

An equipment has been purchased at an initial cost of ₹160000 and has an estimated salvage value of ₹10000. The equipment has an estimated life of 5 years. The difference between the book values (in ₹, in integer) obtained at the end of the 4\(^\text{th}\) year using straight line method and sum of years digit method of depreciation is \(\underline{\hspace{1cm}}\).

Hint:

The sum of years digit method accelerates depreciation in earlier years compared to the straight-line method, resulting in a different book value at the end of the same period.

Answer 1

Correct Answer: 20000

The straight-line method of depreciation is given by: \[ \text{Depreciation per year} = \frac{\text{Cost} - \text{Salvage Value}}{\text{Life}} = \frac{160000 - 10000}{5} = 30000 \, \text{₹}. \] Thus, the book value at the end of the 4\(^\text{th}\) year using the straight-line method is: \[ \text{Book Value} = 160000 - 4 \times 30000 = 160000 - 120000 = 40000 \, \text{₹}. \] For the sum of years digit method, the sum of the years is: \[ S = 1 + 2 + 3 + 4 + 5 = 15. \] The depreciation fraction for the 4\(^\text{th}\) year is: \[ \frac{4}{15}. \] Thus, the depreciation in the 4\(^\text{th}\) year is: \[ \text{Depreciation} = \frac{4}{15} \times (160000 - 10000) = \frac{4}{15} \times 150000 = 40000 \, \text{₹}. \] The book value at the end of the 4\(^\text{th}\) year using the sum of years method is: \[ \text{Book Value} = 160000 - 4 \times 40000 = 160000 - 160000 = 0 \, \text{₹}. \] The difference between the book values is: \[ 40000 - 0 = 20000 \, \text{₹}. \] Thus, the difference in book values is \( \boxed{20000} \, \text{₹} \).