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You are considering opening a new plant. The plant will cost $99.1 million upfront and will take one year to build. After that, it is expected to produce profits of $29.7 million at the end of every year of production. The cash flows are expected to last forever.

1. Calculate the NPV (Net Present Value) of this investment opportunity if your cost of capital is 6.8%.

2. Should you make the investment? Calculate the IRR (Internal Rate of Return). Does the IRR rule agree with the NPV rule?

**Cash Flow Timeline:**
- Year 0: -$99.1 million
- Year 2 and onwards: $29.7 million per year

Note: All cash flows are in millions of dollars. Calculate the NPV of this investment opportunity if your cost of capital is 6.8%.

Answer :

To calculate the Net Present Value (NPV) of the investment opportunity, we need to discount the cash flows to their present value using the cost of capital.

The cash flow timeline is as follows:

Year 0: -$99.1 million (initial investment)

Year 1: $0 million

Year 2 onwards: $29.7 million per year

The NPV formula is:

NPV = CF0 + CF1 / (1 + r) + CF2 / (1 + r)^2 + CF3 / (1 + r)^3 + ...

Where CF0 is the initial investment, CF1 is the cash flow in Year 1, CF2 is the cash flow in Year 2, and so on, and r is the discount rate (cost of capital).

Given that the initial investment is -$99.1 million and the cash flows start from Year 2, we can calculate the NPV.

NPV = -99.1 + (29.7 / (1 + 0.068)^2) + (29.7 / (1 + 0.068)^3) + ...

To calculate the infinite series, we can use the formula for the sum of an infinite geometric series:

Sum = a / (1 - r)

Where a is the first term and r is the common ratio.

In this case, a = 29.7 and r = (1 + 0.068)^-1.

Sum = 29.7 / (1 - (1 + 0.068)^-1)

Now we can calculate the NPV:

NPV = -99.1 + Sum

Please note that the calculation of the infinite series involves an infinite number of terms, but we can approximate it by summing a sufficient number of terms.

To determine whether to make the investment, we compare the NPV to zero. If NPV is positive, it indicates that the investment is expected to generate positive returns and would be considered a good investment. If NPV is negative, it suggests that the investment may not generate sufficient returns and should be avoided.

Regarding the Internal Rate of Return (IRR), we can solve the equation NPV = 0 to find the discount rate at which the NPV becomes zero. If the IRR is greater than the cost of capital, it implies that the investment is expected to generate returns higher than the required rate of return, making it an attractive opportunity.

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