Let's solve this problem by first calculating the Internal Rate of Return (IRR) and Net Present Value (NPV) for both projects. Here's a step-by-step breakdown:

1. Calculating IRR

The IRR is the discount rate that makes the NPV of a project equal to zero. To calculate it for each project, we can use the following formula:

$NPV = \sum_{t=1}^{n} \frac{CF_t}{(1+IRR)^t} - Initial \, Investment = 0$

Where:

• $CF_t$ is the cash flow at time $t$,
• $IRR$ is the internal rate of return,
• $n$ is the number of periods.

We solve for the IRR by setting the NPV equal to zero and using the given cash flows.

Project M:

Year	Cash Flow (M)
0	−120,000
1	55,500
2	69,400
3	64,100
4	36,500

Project N:

Year	Cash Flow (N)
0	−339,000
1	154,300
2	164,400
3	150,800
4	105,400

To solve for IRR, we use the IRR formula with the respective cash flows. I'll calculate the IRR for both projects first.The Internal Rate of Return (IRR) for each project is as follows:

• IRR for Project M: 32.93%
• IRR for Project N: 26.74%

Next, let's calculate the Net Present Value (NPV) for each project. The NPV formula is:

$NPV = \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t} - \text{Initial Investment}$

Where:

• $CF_t$ is the cash flow at time $t$,
• $r$ is the required return (15% or 0.15 in this case),
• $n$ is the number of periods.

I'll calculate the NPV for both projects using a discount rate of 15%.The Net Present Value (NPV) for each project is as follows:

• NPV for Project M: $43,753.02
• NPV for Project N: $78,900.17

Decision:

Since both the NPV and IRR for Project N are higher than the required return, Project N should be accepted. However, both projects have positive NPVs, so if the company could afford it, it might consider both. If forced to choose, Project N is the better option based on the NPV rule.

Would you like more details or have any questions? Here are some related questions you might find useful:

1. How do NPV and IRR differ in evaluating projects?
2. What are the limitations of using IRR alone for decision-making?
3. What if the required return changes—how would that affect the decision?
4. Could there be any qualitative factors to consider in this case?
5. How do mutually exclusive projects impact investment decisions?

Tip: Always prioritize NPV when faced with conflicting signals between NPV and IRR, as NPV provides a direct measure of value added.