Question

You are considering opening a new plant. The plant will cost $ 97.5 million up front and will take one year to build. After that it is expected to produce profits of $ 28.1 million at the end of every year of production​ (starting two years from​ now). The cash flows are expected to last forever. Calculate the NPV of this investment opportunity if your cost of capital is 7.9 %. 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

Year	Cash Flow	Cost of capital @ 7.9% prsent value
0	$-97.5	1
1	0	0.927
2 and till perpetuity	$ 28.1	0.859

Net present value = Present value of cash inflow - present value of cash outflow

Present value of cash inflow = Profits/cost of capital, since the profits are in perpetuity but in year 1 there will be 0 profits as per the information since the plant will take one year to build

28.1/7.9% - 28.1/(1+7.9%) = 355.70 - 26.04 = 329.66

Present value of cash outflow ( this expense happens in year 0) = 97.5

Net present value = 329.66-97.5 = 232.16

A positive NPV indicates that project can be taken up.

IRR is the rate at which NPV is zero, Using the above logic of formula and by hit & trial method, IRR = 23.35%.

Maximum deviation allowed in the cost of capital so that decision is not changed is = 23.35-7.9 = 15.45%