The Hudson Corporation makes an investment of $57,640 that provides the following cash flow:

YearCash Flow1

$ 29,000

2

29,000

3

8,000

Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods.

What is the net present value at a discount rate of 3 percent?

**Note: Do not round intermediate calculations and round your answer to 2 decimal places.**


What is the internal rate of return?

**Note: Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.**


Would you make the same decision under both parts a and b?

multiple choice

Yes

No


To calculate the Net Present Value (NPV) and the Internal Rate of Return (IRR), we'll follow these steps:

### Part A: Net Present Value (NPV)
The formula for NPV is:

\[
NPV = \sum_{t=1}^{n} \frac{CF_t}{(1 + r)^t} - I_0
\]

Where:
- $CF_t$ is the cash flow in year $t$,
- $r$ is the discount rate (in this case, 3% or 0.03),
- $I_0$ is the initial investment, $57,640,
- $t$ is the year, and
- $n$ is the number of years (3 years in this case).

The cash flows provided are:
- Year 1: $29,000
- Year 2: $29,000
- Year 3: $8,000

Let's calculate the NPV:

\[
NPV = \frac{29,000}{(1 + 0.03)^1} + \frac{29,000}{(1 + 0.03)^2} + \frac{8,000}{(1 + 0.03)^3} - 57,640
\]

I'll now calculate this step by step.

### Part B: Internal Rate of Return (IRR)
The IRR is the discount rate that makes the NPV of an investment zero. The formula is:

\[
NPV = \sum_{t=1}^{n} \frac{CF_t}{(1 + IRR)^t} - I_0 = 0
\]

We will use a financial calculator or trial-and-error method to solve for IRR. Let's calculate it next.

I'll calculate both now.### Part A: Net Present Value (NPV)

The NPV at a discount rate of 3% is approximately **$5,171.75**.

### Part B: Internal Rate of Return (IRR)

The IRR for this investment is approximately **8.48%**.

### Decision:
Since the NPV is positive at a discount rate of 3%, the investment is considered profitable. Additionally, the IRR (8.48%) is greater than the discount rate (3%), confirming that this is a favorable investment. Therefore, based on both the NPV and IRR, the decision to invest is consistent.

**Answer to the multiple choice:** Yes, you would make the same decision under both parts a and b.

Do you need further details or have any questions?

Here are 5 related questions for practice:
1. How would the NPV change if the discount rate was increased to 5%?
2. What is the significance of a positive NPV in investment analysis?
3. How does IRR compare to NPV in terms of decision-making?
4. What happens to the NPV when cash flows are delayed in later years?
5. Can the IRR method lead to incorrect decisions in certain cases? Why?

**Tip:** When comparing two projects, the one with the higher NPV should generally be preferred, but always check the IRR to ensure it's above the desired rate of return.

The Hudson Corporation makes an investment of $57,640 that provides the following cash flow: Year 1: $29,000, Year 2: $29,000, Year 3: $8,000. What is the net present value at a discount rate of 3 percent? What is the internal rate of return? Would you make the same decision under both parts a and b?

This page provides a step-by-step solution for calculating the Net Present Value (NPV) and Internal Rate of Return (IRR) for a Hudson Corporation investment of $57,640 with cash flows of $29,000 in years 1 and 2, and $8,000 in year 3. The solution uses financial formulas and explains decision-making at a 3% discount rate.

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