To solve this problem using the Net Present Value (NPV) method, we need to discount the expected net cash inflows for both machines at the company's required rate of return (10%) and then compare the two NPVs. The machine with the higher NPV will be considered more profitable.

Steps to calculate NPV:

1. Determine the initial investment:

   • For both machines, the initial investment is Rs. 4,00,000.
   • Machine A requires Rs. 30,000 as additional working capital at the end of the 1st year.

2. Determine the annual cash inflows:

   • The EAT (Earnings After Tax) for each machine is given for 5 years.

3. Discount the cash inflows:

   • Using the discount rate of 10%, the formula to calculate the Present Value (PV) of each cash flow is: $PV = \frac{{\text{{Cash Flow}}}}{{(1 + r)^t}}$ where $r$ is the discount rate (10% or 0.10) and $t$ is the year.

4. Calculate the NPV: $NPV = \text{{Present Value of cash inflows}} - \text{{Initial Investment}}$

Now, let's calculate the NPV for both Machine A and Machine B using the provided data.

---

Discount Factors for 10% rate:

We will use the following discount factors for 10%:

• Year 1: 0.9091
• Year 2: 0.8264
• Year 3: 0.7513
• Year 4: 0.6830
• Year 5: 0.6209

NPV for Machine A:

1. Cash inflows:

   • Year 1: Rs. 40,000
   • Year 2: Rs. 1,20,000
   • Year 3: Rs. 1,60,000
   • Year 4: Rs. 2,40,000
   • Year 5: Rs. 1,60,000

2. Additional working capital in year 1: Rs. 30,000

3. Discounted cash inflows:

   • Year 1: $40,000 \times 0.9091 = 36,364$
   • Year 2: $1,20,000 \times 0.8264 = 99,168$
   • Year 3: $1,60,000 \times 0.7513 = 1,20,208$
   • Year 4: $2,40,000 \times 0.6830 = 1,63,920$
   • Year 5: $1,60,000 \times 0.6209 = 99,344$

   Total discounted cash inflows = $36,364 + 99,168 + 1,20,208 + 1,63,920 + 99,344 = 5,18,004$

4. Initial investment and working capital = Rs. 4,00,000 + Rs. 30,000 = Rs. 4,30,000

5. NPV for Machine A: $NPV = 5,18,004 - 4,30,000 = 88,004$

NPV for Machine B:

1. Cash inflows:

   • Year 1: Rs. 1,20,000
   • Year 2: Rs. 1,60,000
   • Year 3: Rs. 2,00,000
   • Year 4: Rs. 1,20,000
   • Year 5: Rs. 80,000

2. Discounted cash inflows:

   • Year 1: $1,20,000 \times 0.9091 = 1,09,092$
   • Year 2: $1,60,000 \times 0.8264 = 1,32,224$
   • Year 3: $2,00,000 \times 0.7513 = 1,50,260$
   • Year 4: $1,20,000 \times 0.6830 = 81,960$
   • Year 5: $80,000 \times 0.6209 = 49,672$

   Total discounted cash inflows = $1,09,092 + 1,32,224 + 1,50,260 + 81,960 + 49,672 = 5,23,208$

3. Initial investment = Rs. 4,00,000

4. NPV for Machine B: $NPV = 5,23,208 - 4,00,000 = 1,23,208$

---

Conclusion:

• NPV for Machine A = Rs. 88,004
• NPV for Machine B = Rs. 1,23,208

Since Machine B has a higher NPV, it is the more profitable investment.

---

Would you like more details on any part of this? Here are some related questions:

1. How does the working capital adjustment impact NPV calculations?
2. What happens if the discount rate is changed to something other than 10%?
3. Can you explain other methods like IRR or payback period for the same scenario?
4. What if the company wants to evaluate the risk of the cash flows?
5. How would depreciation affect this analysis?

Tip: When calculating NPV, remember that future cash flows are worth less than present cash flows, hence the need for discounting.