What is the NPV of a(n) 6-year project with equal annual cash flows if the IRR is 17.9% and the initial cost is $333,000? Assume that the discount rate is 8.0%.
Question 10
Answer
a.
$130,674
b.
$229,161
c.
$88,340
d.
-$80,410
e.
$106,008


To find the NPV of a project with an initial cost of $333,000 and equal annual cash flows over six years, given an IRR of 17.9% and a discount rate of 8.0%, we can follow these steps:

1. **Calculate the annual cash flow (CF):**
   Since the IRR (17.9%) represents the rate at which the project’s NPV is zero, we can set up an equation with the initial investment and solve for the cash flow using the IRR as the discount rate.

   \[
   333,000 = CF \times \left(\frac{1 - (1 + 0.179)^{-6}}{0.179}\right)
   \]

2. **Calculate the present value of each cash flow:**
   With the annual cash flow calculated, we then discount each cash flow at the 8.0% discount rate over six years to get the NPV.

3. **Calculate the NPV:**
   The NPV formula is:
   
   \[
   \text{NPV} = -\text{Initial Investment} + \sum_{t=1}^{6} \frac{CF}{(1 + 0.08)^t}
   \]

Let me calculate this step-by-step.The annual cash flow (CF) that makes the NPV zero at an IRR of 17.9% is approximately $94,964. 

Using this cash flow and a discount rate of 8.0%, the NPV of the project is about **$106,008**, which corresponds to answer choice **(e)**.

Would you like further details or have any questions?

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Here are 5 related questions to further your understanding:

1. How does the IRR influence a project's viability when compared to the discount rate?
2. What is the relationship between NPV and cash flows in evaluating project profitability?
3. How would the NPV change if the discount rate increased?
4. How does the IRR reflect the project’s risk and return compared to the discount rate?
5. Why is it essential to consider both NPV and IRR when making investment decisions?

**Tip:** When the IRR is greater than the discount rate, it usually suggests that the project is financially viable.

What is the NPV of a(n) 6-year project with equal annual cash flows if the IRR is 17.9% and the initial cost is $333,000? Assume that the discount rate is 8.0%.

Understand how to calculate the NPV of a 6-year project with equal cash flows, given an IRR of 17.9% and an initial cost of $333,000. This finance problem involves using the discount rate and internal rate of return to assess project profitability.

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