If your firm's cost of capital is 10%, what is the NPV of a project that costs $10,000 and is expected to generate net cash flows of $3500 for the next 3 years?

To calculate the Net Present Value (NPV) of the project, we’ll discount each of the cash flows at the firm's cost of capital (10%) and subtract the initial investment.

### Given:
- Initial Investment $ I_0 = 10,000 $
- Cost of Capital $ r = 10\% $
- Cash Flows for Years 1, 2, and 3: $ CF_1 = CF_2 = CF_3 = 3,500 $

The formula for NPV is:
\[
NPV = \sum_{t=1}^{n} \frac{CF_t}{(1 + r)^t} - I_0
\]

### Step-by-Step Calculation

1. **Discount Year 1 Cash Flow**:
   \[
   \frac{3,500}{(1 + 0.10)^1} = \frac{3,500}{1.10} = 3,181.82
   \]

2. **Discount Year 2 Cash Flow**:
   \[
   \frac{3,500}{(1 + 0.10)^2} = \frac{3,500}{1.21} = 2,892.56
   \]

3. **Discount Year 3 Cash Flow**:
   \[
   \frac{3,500}{(1 + 0.10)^3} = \frac{3,500}{1.331} = 2,629.63
   \]

4. **Calculate NPV**:
   \[
   NPV = (3,181.82 + 2,892.56 + 2,629.63) - 10,000
   \]
   \[
   NPV = 8,703.01 - 10,000
   \]
   \[
   NPV = -1,296.99
   \]

### Conclusion
The NPV of the project is **-1,296.99**. Since the NPV is negative, it indicates that the project is expected to decrease the firm's value, and therefore, it may not be a financially viable project.

Would you like more details on the calculation steps or have any questions?

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Here are some related questions that you might find useful:
1. What does a negative NPV imply about a project’s financial viability?
2. How does the cost of capital impact the NPV of a project?
3. What if the project's cash flows were expected to grow annually; how would that affect the NPV calculation?
4. How would extending the project's duration to 5 years impact the NPV, assuming similar cash flows?
5. What are some alternative investment appraisal methods besides NPV?

**Tip:** Always compare the NPV against the firm's hurdle rate to determine if a project is worthwhile.

Learn how to calculate the Net Present Value (NPV) for a project that costs $10,000 and generates net cash flows of $3500 for 3 years, with a 10% cost of capital. This step-by-step guide will help you understand discounting cash flows and evaluating financial viability.

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