A project under consideration will have an upfront cost of $10,000 and a shutdown cost of $5,000 in 7 years. In years 1 through 6, the project will generate cash flows of $7,000 per year. At cost of capital of 10%, what is the net present value of this project?

To calculate the Net Present Value (NPV) of the project, we need to consider the following cash flows:

- Initial cost (Year 0): $-10,000$
- Annual cash flows from Year 1 to Year 6: $7,000$ per year
- Shutdown cost at Year 7: $-5,000$

We will use the formula for NPV, which is:

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

Where:
- $C_t$ is the cash flow at time $t$
- $r$ is the discount rate (10% or 0.10)
- $t$ is the time period

### Step-by-Step Calculation:

#### 1. Present Value of Cash Flows from Year 1 to Year 6:

For each year, the cash flow is $7,000$. We will discount these cash flows using the formula for each year:

\[
PV = \frac{C_t}{(1 + r)^t} = \frac{7,000}{(1 + 0.10)^t}
\]

We sum these present values for years 1 through 6.

#### 2. Present Value of Shutdown Cost in Year 7:

The shutdown cost is $-5,000$, and the present value will be:

\[
PV = \frac{-5,000}{(1 + 0.10)^7}
\]

#### 3. NPV Calculation:

Finally, subtract the initial cost and sum all present values together.

Let me compute this now.The Net Present Value (NPV) of the project is approximately **$17,921.03**.

This positive NPV suggests that the project is likely to be profitable, as it exceeds the cost of capital (10%).

Would you like more details or have any questions?

Here are 5 related questions you might find useful:
1. How would the NPV change if the cost of capital was 12% instead of 10%?
2. What would be the impact on NPV if the project generated $8,000 per year instead of $7,000?
3. How is the NPV impacted if the shutdown cost increases to $6,000?
4. How does NPV compare to other methods like Internal Rate of Return (IRR) for evaluating this project?
5. What would happen if the project lasted for 10 years instead of 7?

**Tip:** When comparing projects, a higher NPV means better potential returns. Always choose the project with the highest NPV, assuming no resource constraints.

Learn how to calculate the net present value (NPV) of a project with an upfront cost of $10,000, annual cash flows of $7,000 for 6 years, and a shutdown cost of $5,000 in year 7, using a 10% discount rate. This solution covers key financial concepts like the time value of money and cash flow discounting.

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