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 $6,000 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 this project, we need to determine the present value (PV) of all cash flows, both inflows and outflows, discounted at the cost of capital of 10%.

1. **Upfront Cost (Year 0)**: This is an immediate cost of $10,000, so the PV is simply $-10,000$.

2. **Annual Cash Flows (Years 1 through 6)**: Each year generates a cash flow of $6,000 for 6 years. We need to calculate the PV of these cash flows.

3. **Shutdown Cost (Year 7)**: There’s a shutdown cost of $5,000 at the end of Year 7, which we also need to discount to present value.

Let's calculate the NPV step-by-step.

### Step 1: PV of Annual Cash Flows from Year 1 to Year 6
The PV of an annuity (in this case, $6,000 per year for 6 years) can be calculated using the annuity formula:

\[
PV_{\text{annuity}} = C \times \frac{1 - (1 + r)^{-n}}{r}
\]

where:
- $ C = 6,000 $ (annual cash flow),
- $ r = 0.10 $ (discount rate),
- $ n = 6 $ (number of years).

Substituting these values:

\[
PV_{\text{annuity}} = 6,000 \times \frac{1 - (1 + 0.10)^{-6}}{0.10}
\]

Calculating this gives the PV of cash flows from Years 1 to 6.

### Step 2: PV of Shutdown Cost in Year 7
The shutdown cost occurs at the end of Year 7, so we need to discount it back to present value:

\[
PV_{\text{shutdown}} = 5,000 \times (1 + 0.10)^{-7}
\]

### Step 3: Calculate NPV
Finally, the NPV of the project is the sum of the PV of all cash flows:

\[
NPV = PV_{\text{annuity}} - 10,000 - PV_{\text{shutdown}}
\]

Let me calculate these values.The Net Present Value (NPV) of the project is approximately **$13,565.77**.

### Summary:
- **Initial Cost (Year 0)**: $-10,000$
- **PV of Cash Flows (Years 1–6)**: Calculated as part of an annuity formula, contributing significantly to the NPV.
- **PV of Shutdown Cost (Year 7)**: $-3,500.51$

Given the positive NPV, the project is financially viable, as it generates a positive return when discounted at a 10% cost of capital.

Do you have any questions, or would you like further details?

---

1. How would the NPV change if the discount rate increased?
2. What happens to the NPV if the cash flows are higher?
3. How is the PV of a single future payment (like shutdown cost) calculated?
4. What if the project had a recurring shutdown cost every few years?
5. How does the time value of money impact these calculations?

**Tip:** In NPV calculations, be sure to adjust each cash flow to its present value, especially for irregular expenses like shutdown costs.

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 $6,000 per year. At a cost of capital of 10%, what is the net present value of this project?

This guide walks through calculating the Net Present Value (NPV) of a project with an initial $10,000 cost, annual cash flows of $6,000 for six years, and a shutdown cost of $5,000 in year 7. Explore key finance concepts, including NPV, time value of money, and annuity formulas. Suitable for undergraduate finance students.

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