To calculate the Internal Rate of Return (IRR) for both projects, we would typically use the following approach:

Formula for IRR Calculation

The IRR is the discount rate that makes the Net Present Value (NPV) of all cash flows (both inflows and outflows) equal to zero. Mathematically, the NPV formula is:

$NPV = \sum \frac{C_t}{(1 + r)^t} - I_0 = 0$

Where:

• $C_t$ is the cash inflow in year $t$,
• $I_0$ is the initial investment,
• $r$ is the IRR (which we need to calculate),
• $t$ is the year.

To find IRR, you can solve the equation by trial and error or use financial calculators or software like Excel, where the "IRR" function can calculate the rate for a series of cash flows.

Project Details:

• Project T-Shirt:

  • Initial Investment = $21,167
  • Cash Inflows = $6,500 per year for 7 years
  • IRR (given) = 23.83%

• Project Board Shorts:

  • Initial Investment = $39,167
  • Cash Inflows = $13,000 per year for 8 years
  • IRR (given) = 18.56%

Which Project to Recommend?

The IRR is a measure of the efficiency or profitability of an investment. Typically, the higher the IRR, the more desirable the project.

• Project T-Shirt has an IRR of 23.83%, which is higher than Project Board Shorts' IRR of 18.56%.
• Based solely on the IRR measure, Project T-Shirt would be recommended as the better option because it has a higher rate of return.

However, it's important to consider other factors like the project's risk profile, capital availability, and the company's required rate of return.

Would you like me to go into more details on how the IRR is calculated, or do you have any other questions?

Here are 5 related questions that could expand on this topic:

1. How is the IRR different from the Net Present Value (NPV)?
2. What are the limitations of using IRR as the only decision-making tool?
3. How can you calculate IRR using a financial calculator or Excel?
4. What factors could influence the selection of projects beyond just the IRR?
5. What is the significance of the "required rate of return" when evaluating projects?

Tip: When comparing projects with different durations, IRR alone might not be sufficient. You may also want to consider the Modified Internal Rate of Return (MIRR) or the Net Present Value (NPV) for a more comprehensive analysis.