Question

The capital cost of a distillation column is Rs. 90 lakhs. The cost is to be fully depreciated (salvage value is zero) using the double-declining balance method over 10 years. At the end of two years of continuous operation, the book value of the column, in lakhs of rupees, rounded off to 1 decimal place, is:

Hint:

In the double-declining balance method, the depreciation is calculated on the reducing book value. Use \( \text{Depreciation Rate} = \frac{2}{\text{Useful Life}} \) for each year.

Answer 1

Step 1: Understand the double-declining balance (DDB) method. The DDB depreciation rate is calculated as: \[ \text{Depreciation Rate} = \frac{2}{\text{Useful Life (years)}} = \frac{2}{10} = 0.2 \, \text{(20\% per year)}. \] Step 2: Calculate the book value after 2 years. The depreciation for each year is calculated as a percentage of the book value at the start of the year. 1. Year 1 depreciation: \[ \text{Depreciation} = 0.2 \times 90 = 18 \, \text{lakhs}. \] \[ \text{Book Value after Year 1} = 90 - 18 = 72 \, \text{lakhs}. \] 2. Year 2 depreciation: \[ \text{Depreciation} = 0.2 \times 72 = 14.4 \, \text{lakhs}. \] \[ \text{Book Value after Year 2} = 72 - 14.4 = 57.6 \, \text{lakhs}. \] Step 3: Conclusion. The book value of the column after 2 years is \( 57.6 \, \text{lakhs} \).