Solution

flows = [Cashflow(-150,0,.1), Cashflow(50*.8,1,.1), Cashflow(50*.85,2,.1), Cashflow(50*.9,3,.1), Cashflow(50*.95,4,.1)]
print(NPV(flows))

Now the NPV is negative so we wouldn’t want to take the project! But who do we trust, the forward prices or our pricing prediction. It turns out there is something else we can do. If we think our prices are correct and the market is wrong then we can make more money by entering into a forward contract where we buy at that price and then sell for the prices we expect. The below code will show us the profit in each period if we buy for the forward price and are able to sell for the predicted price.

flows = [Cashflow(50*(1.05-.8),1,.1), Cashflow(50*(1.1-.85),2,.1), Cashflow(50*(1.15-.9),3,.1), Cashflow(50*(1.2-.95),4,.1)]
print(NPV(flows))

The NPV here is 39.62 and we don’t even need to put any money down. Of course the issue is that if we are wrong about the prices we might end up taking a loss, but if we are correct we get a higher NPV. We can also scale this to be more than 50 million gallons each year, it can be as much as we want if we are using contracts because we don’t put any money down (technically we would need to pay the money first before we sell it but we will pretend we could pay and then instantly sell it after.)

Source Code