Model Answer
0 min readIntroduction
Equipment replacement is a crucial decision for any firm, impacting operational efficiency and profitability. Determining the optimal time to replace an asset requires careful consideration of costs, including initial investment, maintenance, and the time value of money. The economic order of replacement model helps businesses make informed decisions by comparing the average annual cost of retaining the existing asset with the cost of replacing it. This analysis becomes more complex when considering the interest rate, as it affects the present value of future costs.
(i) Replacement Decision at 0% Interest Rate
At a 0% interest rate, the time value of money is not considered. We simply compare the cumulative costs of operating the existing equipment versus replacing it. We need to calculate the annual maintenance cost for each year and compare the cumulative maintenance cost with the cost of a new equipment (₹4,000).
| Year | Maintenance Cost (₹) | Cumulative Maintenance Cost (₹) |
|---|---|---|
| 1 | 0 | 0 |
| 2 | 1,000 | 1,000 |
| 3 | 1,300 | 2,300 |
| 4 | 1,600 | 3,900 |
| 5 | 1,900 | 5,800 |
From the table, we can see that the cumulative maintenance cost exceeds the cost of the new equipment (₹4,000) in the 4th year. Therefore, the equipment should be replaced at the end of the 3rd year.
(ii) Replacement Decision at 12% Interest Rate
At a 12% interest rate, we need to calculate the present value of the maintenance costs for each year and compare the present value of cumulative maintenance costs with the cost of the new equipment. The present value (PV) is calculated as: PV = Future Value / (1 + interest rate)^year.
| Year | Maintenance Cost (₹) | Present Value (₹) | Cumulative Present Value (₹) |
|---|---|---|---|
| 1 | 0 | 0 | 0 |
| 2 | 1,000 | 1,000 / (1+0.12)^2 = 797.19 | 797.19 |
| 3 | 1,300 | 1,300 / (1+0.12)^3 = 928.41 | 1,725.60 |
| 4 | 1,600 | 1,600 / (1+0.12)^4 = 1,067.64 | 2,793.24 |
| 5 | 1,900 | 1,900 / (1+0.12)^5 = 1,144.78 | 3,938.02 |
| 6 | 2,200 | 2,200 / (1+0.12)^6 = 1,186.41 | 5,124.43 |
The cumulative present value of maintenance costs exceeds the cost of the new equipment (₹4,000) at the end of the 5th year. Therefore, the equipment should be replaced at the end of the 4th year.
Conclusion
In conclusion, the optimal replacement time for the equipment differs based on the interest rate. At a 0% interest rate, the equipment should be replaced at the end of the 3rd year. However, when considering a 12% interest rate and the time value of money, the optimal replacement time shifts to the end of the 4th year. This highlights the importance of incorporating the cost of capital in capital budgeting decisions to ensure economic efficiency and maximize firm value.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.