An investment requires an initial disbursement of € 2,500,000 and the duration of the project is 3 years, in the first of which it generates a cash flow of € 1,500,000, in the second € 3,700,000 and the third € 4,100,000. 
a)	Calculate the Net Present Value of the investment, knowing that inflation is 3% cumulative annually and that the required profitability in the absence of inflation is 8%.
b)	Calculate the actual internal rate of return of the previous investment.


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.

An investment requires an initial disbursement of € 2,500,000 and the duration of the project is 3 years, in the first of which it generates a cash flow of € 1,500,000, in the second € 3,700,000 and the third € 4,100,000.
a) Calculate the Net Present Value of the investment, knowing that inflation is 3% cumulative annually and that the required profitability in the absence of inflation is 8%.
b) Calculate the actual internal rate of return of the previous investment.

Learn how to calculate the Net Present Value (NPV) and Internal Rate of Return (IRR) for a €2,500,000 investment over three years with cash flows of €1,500,000, €3,700,000, and €4,100,000. This finance problem covers inflation adjustments using the Fisher equation and is ideal for college-level students studying finance or economics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation