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# Calculating NPV and IRR of the given Investment projects

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1. You are considering opening a new plant. The plant will cost \$100 million upfront and take one year to build. After that, it is expected to produce profits of \$30 million at the end of every year of production. 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 estimate to leave the decision unchanged.

2. Innovation Company is thinking about marketing a new software product. Upfront costs to market and develop the product are \$5 million. The product is expected to generate profits of \$1million per year for ten years. The company will have to provide product support expected to cost \$100,000 per year in perpetuity. Assume all profits and expenses occur at the end of the year.

a. What is the NPV of this investment if the cost of capital is 6%? Should the firm undertake the project?
b. How many IRRs does this investment opportunity have?

#### Solution Preview

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1. You are considering opening a new plant. The plant will cost \$100 million upfront and take one year to build. After that, it is expected to produce profits of \$30 million at the end of every year of production. 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 estimate to leave the decision unchanged.

Discount rate=r=8%
Annual Cash inflow=C=\$30
PV of perpetuity =C/r=30/8%=\$375 million
But this is value at the end of year 1,

PV of cash inflows=375/(1+8%)=\$347.22 million
PV of outflows=\$100

NPV of project=PV of inflows-PV of outflows=347.22-100=\$247.22 million.
It is positive value, it should be accepted.

Now calculate IRR
At IRR, NPV=0 i.e. PV of cash inflows=PV of cash ...

#### Solution Summary

There are two problems. Solution to first problem demonstrate the methodology to calculate NPV of the project. Solution to second problem depicts the steps to calculate NPV and IRR of the project.

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