An equipment costs Rs 25 lakhs with an estimated salvage value of Rs 5 lakhs after 5 years of useful life. What is the approximate equated annual cost for the use of the equipment?
- A4 lakhsCorrect
- B8 lakhs
- C12 lakhs
- D16 lakhs
Solution
Concept
The equated annual cost (depreciation) of an asset is the total loss in its value divided equally across its useful life.
Formula
Annual Cost = (Initial Cost - Salvage Value) / Useful Life
Step-by-step solution
1. Identify the given values: Initial cost of equipment (C) = Rs 25 lakhs Salvage value at the end of life (S) = Rs 5 lakhs Useful life (n) = 5 years 2. Find the total depreciable cost: Total cost = C - S = 25 - 5 = 20 lakhs 3. Calculate the equated annual cost: Annual Cost = 20 lakhs / 5 years = 4 lakhs per year Answer: (A) 4 lakhs
Explanation
The machine loses Rs 20 lakhs of value over a period of 5 years. Dividing this total value loss equally gives Rs 4 lakhs per year. Hence, the equated annual cost is 4 lakhs.
Why the other options are wrong
B: 8 lakhs is incorrect because it overestimates the annual loss. C: 12 lakhs is incorrect and much higher than the actual annual depreciation. D: 16 lakhs is incorrect because it is close to the total 5-year loss rather than the annual cost.
Shortcut
Subtract salvage value from initial cost and simply divide by the number of years: (25 - 5) / 5 = 4.
Common mistake
Students often forget to subtract the salvage value and divide 25 directly by 5 to get 5 lakhs.
Correct answer: A) 4 lakhs