A project costing $102,000 initially should produce cash inflows of $54,000 per year for six years. At the end of the six years, the project will be shut down and will be sold for an estimated net cash amount of $48,000. What is the net present value of this project if the required rate of return is 11 percent?

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

- **Initial investment (outflow):** $102,000
- **Annual cash inflows:** $54,000 for 6 years
- **Salvage value at the end of 6 years:** $48,000
- **Required rate of return (discount rate):** 11% or 0.11

The formula for NPV is:

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

Where:
- $ C_t $ is the cash inflow at time $ t $,
- $ r $ is the discount rate (11% or 0.11),
- $ t $ is the time period (in years),
- $ C_0 $ is the initial investment.

We need to break this problem into two parts:
1. The present value of the cash inflows over 6 years.
2. The present value of the salvage value at the end of 6 years.

### 1. Present Value of Annual Cash Inflows
The present value of the cash inflows can be calculated using the formula for the present value of an annuity:

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

Where:
- $ C = 54,000 $ (annual cash inflows),
- $ r = 0.11 $ (discount rate),
- $ n = 6 $ (years).

### 2. Present Value of Salvage Value
The present value of the salvage value can be calculated by discounting it back to the present using the following formula:

\[
PV_{\text{salvage}} = \frac{F}{(1 + r)^n}
\]

Where:
- $ F = 48,000 $ (salvage value),
- $ r = 0.11 $,
- $ n = 6 $.

Finally, we will subtract the initial investment ($102,000) from the sum of the present values of the cash inflows and salvage value to get the NPV.

Let me compute this for you.The Net Present Value (NPV) of the project is approximately **$152,111.80**.

This positive NPV indicates that the project is expected to generate more value than the cost of the investment, making it a worthwhile endeavor at the 11% required rate of return.

Would you like further details or have any other questions?

Here are 5 related questions for deeper understanding:
1. How would the NPV change if the required rate of return was higher?
2. What is the impact of extending the project duration to more than 6 years?
3. How would a delayed cash inflow affect the NPV?
4. What is the significance of the NPV in capital budgeting decisions?
5. How would increasing the initial investment affect the NPV?

**Tip:** A positive NPV indicates a project is expected to add value and is generally considered a good investment. Always compare NPV to other project opportunities.

Calculate the NPV of a project with a $102,000 initial investment, producing $54,000 annual inflows for six years and a salvage value of $48,000. Learn how to apply the NPV formula and discount future cash flows using a required rate of return of 11%.

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