Question

You are considering opening a new plant. The plant will cost $ 97.9 million up front and will take one year to build. After that it is expected to produce profits of $ 28.6 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 8.2 %. 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.

Answer 1

Initial investment =97.9 million
Cash flow in year 1 =0 (As it takes one year to build the plant)
Cash flow from year 2 =28.6
NPV =PV of Cash Flows -Initial Investment =28.6/(r*(1+r)-97.9 =28.6/(8.2%*(1+8.2%))-27.9 =294.45 million

For IRR we use following formula
Initial Cost =Profits/(IRR*(1+IRR))
97.9 =28.6/(IRR*(1+IRR))
IRR using hit and trial method

At IRR =10%; 28.6/(IRR*(1+IRR))=260
At IRR =20%; 28.6/(IRR*(1+IRR))=119.17
At IRR =24.63%; 28.6/(IRR*(1+IRR))=97.9

Hence IRR =24.63%
Standard Deviation =24.63%-8.2% =16.43% to leave the decision unchanged