To solve this problem, we need to calculate both the Net Present Value (NPV) and the Internal Rate of Return (IRR) for the given investment. Let’s break it down step by step.

Part (a): Calculate the Net Present Value (NPV)

Step 1: Calculate the nominal required rate of return (r_nominal)

The required profitability (real rate of return) in the absence of inflation is given as 8%, and inflation is 3% per year. To account for inflation, we use the Fisher equation:

$r_{\text{nominal}} = (1 + r_{\text{real}})(1 + \text{inflation rate}) - 1$

Where:

• $r_{\text{real}} = 8\% = 0.08$
• Inflation rate = $3\% = 0.03$

$r_{\text{nominal}} = (1 + 0.08)(1 + 0.03) - 1 = 0.1124 = 11.24\%$

So, the nominal rate of return is 11.24%.

Step 2: Calculate the NPV

The formula for NPV is:

$NPV = \sum \left( \frac{CF_t}{(1 + r_{\text{nominal}})^t} \right) - \text{Initial Investment}$

Where:

• $CF_t$ is the cash flow in year $t$
• $r_{\text{nominal}}$ is the nominal rate of return (11.24%)
• Initial Investment = €2,500,000
• Cash flows are:
  • Year 1: €1,500,000
  • Year 2: €3,700,000
  • Year 3: €4,100,000

We will now calculate each term of the NPV formula.

$NPV = \frac{1,500,000}{(1 + 0.1124)^1} + \frac{3,700,000}{(1 + 0.1124)^2} + \frac{4,100,000}{(1 + 0.1124)^3} - 2,500,000$

Let’s compute this.The Net Present Value (NPV) of the investment is approximately €4,817,018.

Part (b): Calculate the actual Internal Rate of Return (IRR)

The Internal Rate of Return (IRR) is the discount rate that makes the NPV equal to zero. It can be found by solving the following equation:

$0 = \sum \left( \frac{CF_t}{(1 + IRR)^t} \right) - \text{Initial Investment}$

We will solve this equation iteratively to find the IRR. Let me calculate it.The actual Internal Rate of Return (IRR) for this investment is approximately 86.50%.

Summary:

• Net Present Value (NPV): €4,817,018
• Internal Rate of Return (IRR): 86.50%

Would you like more details on any of these calculations?

Here are 5 related questions to consider:

1. How does inflation affect the calculation of NPV?
2. What are the differences between nominal and real rates of return?
3. How would a change in the initial investment impact the NPV?
4. What are the limitations of using IRR in decision-making?
5. Can you calculate NPV and IRR when cash flows vary irregularly over time?

Tip: When comparing investment options, always consider both the NPV and IRR to evaluate profitability and risk.