High School

You are considering opening a new plant. The plant will cost $ 97.7 million up front and will take one year to build. After that it is expected to produce profits of $ 28.3 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 8.4 % .Should you make the?investment? Calculate the IRR.

Answer :

The value of the investment and the discount rate, indicates that the NPV, the business decision, and the the IRR are;

NPV ≈ $239.2 million

Yes, the business is profitable, therefore investment should made

IRR ≈ 28.966%

What is NPV?

NPV, which is an acronym for Net Present Value, is the measure of the value of an investment, which is calculated as the present value of the expected cash flow of the investment.

The initial cost of the investment = $97.7 million

The expected cash flow = $28.3 million per year, starting from now till forever

The expected cash flow is a perpetuity. The formula for a perpetuity indicates that we get;

PV = C/r

Where;

C = The cash flow per period = $28.3 million
r = The discount rate = 8.4%

Therefore; PV = $28.3 million/0.084 = $336,904,761.905

The NPV of the investment is therefore; NPV = PV - Initial Cost = 336,904,761.905 - 97,700,000 = 239,204,761.905

  • NPV ≈ $239.2 million

  • The NPV is positive, indicating that the business is profitable, and therefore, should be invested in or undertaken

The Internal Rate of Return, IRR, is the discount rate that makes the makes the NPV of an investment zero.

The IRR can be found from solving for r in the equation;

0 = PV - Initial Cost 0 = C/r - Initial Cost

Which indicates; 0 = 28.3/r - 97.7

r = 28.3/97.7 ≈ 0.28966 = 28.966%

The IRR of the investment is about 28.966%

Learn more on Net Present Value (NPV) here: https://brainly.com/question/34118869

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