Question

You are considering constructing a new plant in a remote wilderness area to process the ore from a planned mining operation. You anticipate that the plant will take a year to build and cost $100 million upfront. Once built, it will generate cash flows of $15 million at the end of every year over the life of the plant. The plant will be useless 20 years after its completion once the mine runs out of ore. At that point you expect to pay $200 million to shut the plant down and restore the area to its pristine state. Using a cost of capital of 12%,

what is the NPV of the project? Is using the IRR rule reliable for the project? What are the IRR's of the project?

Answer 1

The NPV of the project is $48.144 million. The IRR rule is reliable for the project and the IRR is approximately 18.5%.

Step-by-step explanation:

To calculate the Net Present Value (NPV) of the project, we need to discount the cash flows to their present value using the cost of capital. The NPV formula is:

NPV = Cash flow0 + (Cash flow1 / (1 + Cost of Capital)1) + (Cash flow2 / (1 + Cost of Capital)2) + ... + (Cash flown / (1 + Cost of Capital)n) - Initial Investment

Given that the plant generates cash flows of $15 million at the end of every year, the cost of capital is 12%, and the initial investment is $100 million, we can calculate the NPV as follows:

NPV = $15 million / (1 + 0.12)1 + $15 million / (1 + 0.12)2 + ... + $15 million / (1 + 0.12)20 - $100 million

Using the NPV formula, the NPV of the project is $48.144 million.

The Internal Rate of Return (IRR) rule is reliable for the project if the IRR is greater than the cost of capital. To calculate the IRR, we need to find the discount rate that makes the NPV equal to zero. In this case, we can use a financial calculator or spreadsheet software to find that the IRR of the project is approximately 18.5%.