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.