Question

You are considering opening a new plant. The plant will cost $100.5 million up front and will take one year to build. After that it is expected to produce profits of $29.1 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 7.1%. 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

NPV of the investment is $ 309,359,154.93

We should make the investment.

IRR of the investment is 28.96 %

Maximum deviation allowable in cost of capital to leave the decision unchanged is 21.86 %

Explanation:

Present value of cash inflows can be computed using formula for PV of perpetuity as:

PV = C/r

PV = Present value of perpetuity

C = Periodic cash flow for ever = $ 29,100,000

r = Periodic rate = 0.071

PV = $ 29,100,000/0.071

     = $ 409,859,154.93

NPV = PV of perpetuity – Initial cost

          = $ 409,859,154.93 - $ 105,500,000

          = $ 309,359,154.93

AS NPV is positive, we can make the investment.

At discount rate of IRR, NPV of investment is 0.

$ 0 = C/IRR – Initial investment

$ 0 = $ 29,100,000/IRR – $ 105,500,000

$ 29,100,000/IRR = $ 105,500,000

IRR = $ 29,100,000/$ 105,500,000

     = 0.289552239 or 28.96 %

Maximum allowable deviation = IRR – discount rate

                                                = 28.96 % - 7.1 % = 21.86 %