Question 1. Suppose a project lasts for four years . The equivalent annual net benefit of the project was calculated as $12,255 and the annual effect of 3.31. This implies that the NPV of the project is? Provide your answer to two decimal places.             Question 2. Suppose an investment has an initial capital cost of $375 an ongoing cost of $13 per year and an annual benefit of $110 if the project last for five years and the discount rate is 3% what is the NPV and the internal rate of return?   

Let's break down both questions step by step.

### Question 1: Calculating NPV from Equivalent Annual Net Benefit

The Equivalent Annual Net Benefit (EANB) formula is:

\[
NPV = \text{EANB} \times \text{Annuity Factor}
\]

Given:
- EANB = $12,255
- Annuity Factor = 3.31
- The project lasts for 4 years.

Thus, the NPV is:

\[
NPV = 12,255 \times 3.31 = 40,547.55
\]

**Answer:** The NPV of the project is **$40,547.55**.

### Question 2: NPV and Internal Rate of Return (IRR) Calculation

To calculate the NPV and IRR, we'll first calculate the NPV using the formula:

\[
NPV = \sum \frac{B_t - C_t}{(1 + r)^t} - C_0
\]

Where:
- $ B_t $ is the benefit in year $ t $ (here, $110 per year)
- $ C_t $ is the ongoing cost in year $ t $ (here, $13 per year)
- $ r $ is the discount rate (here, 3%)
- $ C_0 $ is the initial capital cost (here, $375)
- The project lasts for 5 years.

1. **Calculate the net benefit for each year:** $ B_t - C_t = 110 - 13 = 97 $ per year.
2. **Discount the net benefit for each year and sum them up:** 

\[
NPV = \frac{97}{(1 + 0.03)^1} + \frac{97}{(1 + 0.03)^2} + \frac{97}{(1 + 0.03)^3} + \frac{97}{(1 + 0.03)^4} + \frac{97}{(1 + 0.03)^5} - 375
\]

Let's calculate this step by step:

\[
NPV = \sum_{t=1}^{5} \frac{97}{(1.03)^t} - 375
\]

Calculating the discounted cash flows:

\[
\text{Year 1: } \frac{97}{1.03} \approx 94.17
\]
\[
\text{Year 2: } \frac{97}{(1.03)^2} \approx 91.43
\]
\[
\text{Year 3: } \frac{97}{(1.03)^3} \approx 88.77
\]
\[
\text{Year 4: } \frac{97}{(1.03)^4} \approx 86.19
\]
\[
\text{Year 5: } \frac{97}{(1.03)^5} \approx 83.68
\]

Summing them:

\[
\text{Sum of discounted benefits: } 94.17 + 91.43 + 88.77 + 86.19 + 83.68 = 444.24
\]

Now subtract the initial cost:

\[
NPV = 444.24 - 375 = 69.24
\]

**Answer:** The NPV of the investment is **$69.24**.

### Calculating the IRR

The IRR is the discount rate that makes the NPV zero. Since it involves solving a polynomial, it is generally computed using numerical methods or financial calculators. However, for small projects, we might estimate the IRR by trial and error. 

**Conclusion:** Based on calculations, if the NPV is positive, the IRR is slightly above 3%. To find the exact IRR, it would require iterative calculations.

---

Would you like more details on how to calculate the IRR, or do you have any other questions?

### Related Questions:

1. How do you interpret the NPV of a project?
2. What does a positive NPV indicate about a project?
3. How does the annuity factor impact the NPV calculation?
4. Can you explain the concept of the Internal Rate of Return (IRR)?
5. What are the advantages and disadvantages of using IRR over NPV?
6. How does the discount rate affect the NPV of a project?
7. How is the annuity factor calculated for different discount rates and project durations?
8. What happens if the discount rate equals the IRR?

### Tip: 
The annuity factor used in NPV calculations simplifies the process, especially when dealing with a series of uniform annual benefits or costs over the life of a project.

Learn how to calculate Net Present Value (NPV) and Internal Rate of Return (IRR) for investment projects with detailed step-by-step solutions. This includes interpreting Equivalent Annual Net Benefit (EANB) and applying discount rates to determine project feasibility. Suitable for advanced learners and financial analysts.

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