A company is using a silver nanoparticle catalyzed fixed bed technology for producing ethylene oxide. They make ethylene, with capacity to produce and sell $10$M tons$/$year of ethylene oxide. Their internal manufacturing cost of ethylene is $$800/$ton$.$ Beginning trials showed the catalyst to be robust with full conversion and a net usage $30-$kg catalyst$/$ton of ethylene oxide. Catalyst licensing cost is $$50$ per ton of ethylene oxide produced. Expected selling price is $$1300/$ton$,$ expected to increase at $3\%/$year$.$ The cost to build the plant is $$500$M and time to build and start production of EO is $2-$years. Operating costs are $$400/$ton$.$ The company expects to exceed a hurdle rate of $40\%$ per annum over a $6$ year period. How long before the investment is profitable? Is this a good investment? What if operating costs are $$500/$ton$?$

Hint: Use excel and the formula for compound interest to calculate the internal rate of return $($IRR$)$ and Net Present Value $($NPV$),$ which is sum of all present values or PV $=$ FV$/(1+$i$)$ n $,$ where PV$=$ Present Value and FV$=$ Future inflows, i $=$ interest rate per compounding period and n $=$ number of periods