A machine costing Rs. 50,000 has a useful life of 4 years. The estimated scrap value is Rs. 10,000. The rate of depreciation per annum is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 20%
Note: The given answer is as per the official NTA Answer Key. However, the rate can also be taken on the depreciable amount, and with that reading Option (3) could also be a possible answer, as explained below.
By the straight line method, the yearly depreciation is
\( \displaystyle D = \frac{\text{Cost} - \text{Scrap value}}{\text{Useful life}} = \frac{50000 - 10000}{4} = 10000 \)
\( \displaystyle \text{As a percentage of the cost: } \frac{10000}{50000} \times 100 = 20\% \)
\( \displaystyle \text{As a percentage of the depreciable amount: } \frac{10000}{40000} \times 100 = 25\% \)
Option (1) 20% — Correct. Each year the machine loses Rs. 10,000 of its value. Compared with its cost of Rs. 50,000, that is 10,000 out of 50,000, or 20% per year. This is the usual way the rate is stated.
Option (2) 30% — Incorrect. It matches neither reading.
Option (3) 25% — Should also be correct, though not the answer given by NTA. The machine will still be sold for Rs. 10,000 as scrap, so only Rs. 40,000 of its value is actually used up over the 4 years (the depreciable amount). Compared with this Rs. 40,000, the yearly loss of Rs. 10,000 is 25% per year.
Option (4) 15% — Incorrect. It matches neither reading.