Math Problem Statement
Solution
The image shows a decision-making problem for PQR Ltd. concerning two alternative machines using the Net Present Value (NPV) method. Here's a summary of the relevant details:
- Cost of each machine: Rs. 4,00,000
- Additional working capital at the end of year 1: Rs. 30,000
- Target return on capital: 10%
- Expected EAT (Earnings After Tax) for each machine over 5 years:
Year | Machine A (Rs.) | Machine B (Rs.) |
---|---|---|
1 | 40,000 | 120,000 |
2 | 120,000 | 160,000 |
3 | 160,000 | 200,000 |
4 | 240,000 | 120,000 |
5 | 160,000 | 80,000 |
Total | 720,000 | 680,000 |
To solve this, we need to calculate the NPV for both machines using a discount rate of 10%.
Steps:
-
Discount each year's cash flow using the formula: where and is the respective year.
-
Sum up the discounted cash flows for each machine.
-
Deduct the initial investment and working capital (Rs. 4,30,000) to calculate NPV.
I'll calculate this next.The Net Present Values (NPV) for the two machines are as follows:
- Machine A NPV: Rs. 89,018.20
- Machine B NPV: Rs. 93,220.59
Since Machine B has a higher NPV, it is the more profitable option based on the NPV method.
Would you like further details on any part of this calculation or another related topic?
Related Questions:
- How is the NPV method different from the IRR method?
- What would happen if the discount rate was higher or lower than 10%?
- How does working capital influence NPV decisions?
- What assumptions are made when using the NPV method?
- Can you explain the significance of discounting future cash flows?
Tip: A higher NPV indicates a better return on investment, but always consider other factors such as risk and liquidity when making decisions.
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Math Problem Analysis
Mathematical Concepts
Net Present Value (NPV)
Discounted Cash Flows
Finance
Formulas
Present Value = Cash Flow / (1 + r)^t
NPV = Σ (Present Value of Cash Flows) - Initial Investment
Theorems
NPV method
Suitable Grade Level
University Level / Financial Management
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