A concrete batching plant was purchased 6 years ago for Rs. 50 lakhs. The company uses the straight-line depreciation method with an assumed useful life of 10 years and a scrap value of Rs. 5 lakhs. The current market value of the plant is Rs. 18 lakhs. Which of the following statements is correct?
- AThe book value is Rs. 18 lakhs and the market value is also Rs. 18 lakhs, so no gain or loss will occur if sold today.
- BThe book value is Rs. 23 lakhs and the market value is Rs. 18 lakhs, resulting in a book loss of Rs. 5 lakhs if sold today.Correct
- CThe book value is Rs. 27 lakhs and the market value is Rs. 18 lakhs, resulting in a book loss of Rs. 9 lakhs if sold today.
- DThe book value is Rs. 18 lakhs, but the market value is Rs. 23 lakhs, resulting in a book gain of Rs. 5 lakhs if sold today.
Solution
Concept
Straight-line depreciation and book loss calculation
Formula
Annual D = (C - S)/n; Book Value = C - (D × t); Loss = Book Value - Market Value
Step-by-step solution
1. Original Cost C = 50 lakhs, Scrap Value S = 5 lakhs, Useful Life n = 10 years. 2. Annual Depreciation D = (50 - 5) / 10 = 45 / 10 = 4.5 lakhs per year. 3. Accumulated depreciation after 6 years = 6 × 4.5 = 27 lakhs. 4. Book Value after 6 years = 50 - 27 = 23 lakhs. 5. Market Value = 18 lakhs. Loss on sale = Book Value - Market Value = 23 - 18 = 5 lakhs. Answer: B
Explanation
Under straight-line depreciation, annual depreciation is D = (Purchase Cost - Scrap Value) / Life = (50 - 5) / 10 = 4.5 lakhs/year. After 6 years, accumulated depreciation is 6 × 4.5 = 27 lakhs, yielding a book value of 50 - 27 = 23 lakhs. Selling at a current market value of 18 lakhs results in a book loss of 23 - 18 = 5 lakhs.
Why the other options are wrong
A) Incorrect because the book value after 6 years is Rs. 23 lakhs, not Rs. 18 lakhs. C) Rs. 27 lakhs is the accumulated depreciation after 6 years, not the remaining book value. D) The market value is Rs. 18 lakhs (less than book value of Rs. 23 lakhs), representing a book loss of Rs. 5 lakhs, not a gain.
Shortcut
D = 45/10 = 4.5/yr; 6 yrs D = 27; Book Value = 23; Loss = 23 - 18 = 5 lakhs.
Common mistake
Forgetting to subtract scrap value when calculating annual depreciation, or confusing book loss with market loss.
Correct answer: B) The book value is Rs. 23 lakhs and the market value is Rs. 18 lakhs, resulting in a book loss of Rs. 5 lakhs if sold today.