Some particulars for a project are as follows.

Initial Capital Cost in year 0 ($Mn)

1000

Follow-up ‘one-off’ cost in year 1 ($Mn)

300

Annual Operating Cost ($Mn/yr)

10% of capital cost

Annual Benefits ($Mn/yr)

400

Project Closure Cost, at end of project life ($Mn)

200

Useful Life (years)

20

Interest/Discount rate (percent)

7
 
What is the NPV of the project with year 15 as the base year? 

(your answer must be rounded off to the nearest dollars, i.e., no decimal places)

The Net Present Value (NPV) is calculated by summing the present values of all cash flows over the project's useful life. We will use the formula for NPV:

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

Where:
- $ C_t $ is the net cash flow in year $ t $
- $ r $ is the discount rate (in decimal form)
- $ t $ is the year number

We need to compute the NPV with year 15 as the base year, so all cash flows will be discounted to year 15.

### Cash Flows:
1. **Initial Capital Cost in year 0**: $ -1000 $ million
2. **Follow-up one-off cost in year 1**: $ -300 $ million
3. **Annual Operating Cost**: 10% of capital cost = $ 0.1 \times 1000 = 100 $ million per year
4. **Annual Benefits**: $ 400 $ million per year
5. **Project Closure Cost at year 20**: $ -200 $ million

The net annual cash flow from year 1 to year 20 is:
\[
\text{Net Cash Flow} = \text{Annual Benefits} - \text{Annual Operating Cost} = 400 - 100 = 300 \text{ million per year}
\]

### Discounting to Year 15:
We will calculate the present value (in year 15) of each cash flow using the discount rate of 7% (0.07). Let me calculate it step by step.The Net Present Value (NPV) of the project, with year 15 as the base year, is approximately **$5,094 million**.

Would you like further clarification or details on any of the steps? Here are 5 related questions for further exploration:

1. How does the discount rate affect the NPV of long-term projects?
2. What would be the NPV if the discount rate were 5% instead of 7%?
3. How would the NPV change if the useful life of the project were 25 years?
4. What are the main risks in relying on NPV for project decisions?
5. How is the NPV different from the Internal Rate of Return (IRR)?

**Tip:** A positive NPV indicates that the project is expected to generate more value than its costs, making it a potentially good investment.

What is the NPV of the project with year 15 as the base year? Initial Capital Cost in year 0 ($Mn): 1000, Follow-up 'one-off' cost in year 1 ($Mn): 300, Annual Operating Cost ($Mn/yr): 10% of capital cost, Annual Benefits ($Mn/yr): 400, Project Closure Cost, at end of project life ($Mn): 200, Useful Life (years): 20, Interest/Discount rate (percent): 7

This page explains how to calculate the Net Present Value (NPV) for a 20-year project, taking year 15 as the base year. The project involves an initial capital cost of $1000Mn, a one-off follow-up cost of $300Mn, annual benefits of $400Mn, and a 7% discount rate. Learn how to apply the NPV formula and discount cash flows to year 15 for accurate financial analysis.

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