Math Problem Statement

PQR Ltd. is considering the purchase of a new machine. Two machines, A and B, are suggested, both costing Rs. 4,00,000 and requiring Rs. 30,000 as additional working capital. The earnings after tax (EAT) for each machine over 5 years are provided. The company has a target return on capital of 10%, and you're required to select the most profitable machine using the NPV method.

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:
YearMachine A (Rs.)Machine B (Rs.)
140,000120,000
2120,000160,000
3160,000200,000
4240,000120,000
5160,00080,000
Total720,000680,000

To solve this, we need to calculate the NPV for both machines using a discount rate of 10%.

Steps:

  1. Discount each year's cash flow using the formula: Present Value=Cash Flow(1+r)t\text{Present Value} = \frac{\text{Cash Flow}}{(1 + r)^t} where r=10%r = 10\% and tt is the respective year.

  2. Sum up the discounted cash flows for each machine.

  3. 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:

  1. How is the NPV method different from the IRR method?
  2. What would happen if the discount rate was higher or lower than 10%?
  3. How does working capital influence NPV decisions?
  4. What assumptions are made when using the NPV method?
  5. 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