Q. PQR Ltd. is considering the purchase of new machine. Two alternative machines have
been suggested, cash costing 4,00,000 and requiring 30,000 as additional working capital
at the end of the 1st year. EAT are expected to be as follows:
Year Machine A ( Rs.) Machine B (Rs.)
1 40000 120000
2 120000 160000
3 160000 200000
4 240000 120000
5 160000 80000
Total 720000 680000

The company has a target return on capital of 10%, you are required to select the
most profitable machine on the N. P. V. method.

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.

PQR Ltd. is considering the purchase of a new machine. Two alternative machines have been suggested, costing Rs. 4,00,000 and requiring Rs. 30,000 as additional working capital at the end of the 1st year. EAT are expected to be as follows: Year 1: Machine A (Rs. 40,000), Machine B (Rs. 1,20,000), Year 2: Machine A (Rs. 1,20,000), Machine B (Rs. 1,60,000), Year 3: Machine A (Rs. 1,60,000), Machine B (Rs. 2,00,000), Year 4: Machine A (Rs. 2,40,000), Machine B (Rs. 1,20,000), Year 5: Machine A (Rs. 1,60,000), Machine B (Rs. 80,000). The company has a target return on capital of 10%. You are required to select the most profitable machine using the NPV method.

Learn how to evaluate two machine investment options using the Net Present Value (NPV) method. Machine A and Machine B have different cash inflows over 5 years, and the company requires a 10% return on capital. Detailed NPV calculations and a comparison are provided to help choose the more profitable machine.

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