You have been offered a very long$-$term investment opportunity to increase your money one hundredfold. You can invest $$1000$ today and expect to receive $$100,000$ in $40$ years. Your cost of capital for this $($very risky$)$ opportunity is $25\%.$ What does the IRR rule say about whether the investment should be undertaken? What about the NPV rule? Do they agree?

You are considering opening a new plant. The plant will cost $$100$ million upfront. After that, it is expected to produce profits of $$30$ million at the end of every year. The cash flows are expected to last forever. Calculate the NPV of this investment opportunity if your cost of capital is $8\%.$ Should you make the investment? Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.