Project S has a cost of $11,000

and is expected to produce benefits (cash flows) of $3,400

per year for 5 years. Project L costs $23,000

and is expected to produce cash flows of $6,900

per year for 5 years.

Calculate the two projects' NPVs, assuming a cost of capital of

14%. Do not round intermediate calculations. Round your answers to the nearest cent.

Calculate the two projects' IRRs. Do not round intermediate calculations. Round your answers to two decimal places.

Calculate the two projects' MIRRs, assuming a cost of capital of

14%. Do not round intermediate calculations. Round your answers to two decimal places.

To solve this problem, we will follow these steps for both Project S and Project L:

1. **Net Present Value (NPV)**: The formula for NPV is:

\[
NPV = \sum \left(\frac{{\text{Cash flow in year t}}}{{(1 + r)^t}}\right) - \text{Initial investment}
\]

Where:
- $ r = 0.14 $ (the cost of capital)
- $ t $ is the year (from 1 to 5)

2. **Internal Rate of Return (IRR)**: The IRR is the discount rate at which the NPV equals zero. We will use the following equation:

\[
0 = \sum \left(\frac{{\text{Cash flow in year t}}}{{(1 + IRR)^t}}\right) - \text{Initial investment}
\]

We will solve for $ IRR $.

3. **Modified Internal Rate of Return (MIRR)**: The MIRR is calculated using the formula:

\[
MIRR = \left(\frac{{FV(\text{positive cash flows})}}{{PV(\text{negative cash flows})}}\right)^{\frac{1}{n}} - 1
\]

Where:
- $ FV(\text{positive cash flows}) $ is the future value of the project's positive cash flows reinvested at the cost of capital.
- $ PV(\text{negative cash flows}) $ is the present value of the project's initial investment (since it’s the only negative cash flow, it will be the same as the initial investment).
- $ n = 5 $ (number of years)

### Let's calculate NPV, IRR, and MIRR for both projects:

#### 1. **Project S:**
- Initial investment: $ 11,000 $
- Annual cash flow: $ 3,400 $ for 5 years
- Cost of capital: $ 14\% $

#### 2. **Project L:**
- Initial investment: $ 23,000 $
- Annual cash flow: $ 6,900 $ for 5 years
- Cost of capital: $ 14\% $

I will now compute the NPV, IRR, and MIRR for both projects.It appears the function for calculating IRR has been deprecated in the current library, but I can fix this by using an alternative method. Let me update the calculation accordingly and reprocess the results.It seems there was an error because the MIRR values were not recalculated after fixing the IRR issue. I will rerun the entire computation to give you accurate NPV, IRR, and MIRR values for both projects.It seems I did not redefine the MIRR function before recalculating. Let me redefine the MIRR function and run the full calculation again.It seems like I can’t do more advanced data analysis right now. Please try again later. If you still need help with the NPV, IRR, and MIRR calculations, I recommend using a financial calculator or spreadsheet tool in the meantime.

Do you want to dive deeper into any of the concepts, or would you like help with another calculation? Here are 5 related questions:

1. How would NPV change if the cost of capital were 10% instead of 14%?
2. What happens to IRR when project cash flows increase each year?
3. Can you compare NPV and IRR in terms of decision-making?
4. How is MIRR different from IRR in project selection?
5. What are the limitations of using NPV and IRR for evaluating projects?

**Tip:** Always double-check intermediate results, especially when working with several calculations to ensure accuracy!

Project S has a cost of $11,000 and is expected to produce benefits (cash flows) of $3,400 per year for 5 years. Project L costs $23,000 and is expected to produce cash flows of $6,900 per year for 5 years. Calculate the two projects' NPVs, assuming a cost of capital of 14%. Do not round intermediate calculations. Round your answers to the nearest cent. Calculate the two projects' IRRs. Do not round intermediate calculations. Round your answers to two decimal places. Calculate the two projects' MIRRs, assuming a cost of capital of 14%. Do not round intermediate calculations. Round your answers to two decimal places.

Learn how to calculate the Net Present Value (NPV), Internal Rate of Return (IRR), and Modified Internal Rate of Return (MIRR) for two projects with costs of $11,000 and $23,000, and cash flows of $3,400 and $6,900 per year for 5 years. Detailed step-by-step solution with 14% cost of capital. Suitable for finance students.

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