Forward contracts are agreements to buy or sell an asset for a specified price. They can either be settled in cash (meaning no assets are actually traded, but instead there is a cash settlement based on the real price versus forward price) or with the actual asset. Companies use these to hedge their risks. If a company takes steel as an input, they might buy a forward contract to buy steel at a designated price to make sure that if there is a spike in steel prices their company is not hurt. Nothing is traded until the execution date, so when you enter into a forward contract you don’t pay anything until the execution date.

Now imagine a project that your company is considering. You would put 100 million down in year 0 to buy a drilling station and then get 50 million barrels of oil for the next 4 years. Valuing this project would be somewhat difficult, how much is that worth? You could use the current price of oil but with inflation it could grow, or it might be lower in the future if there was a huge surplus of oil. Let’s first get the NPV of the project if we were to assume the yearly prices were: $1.05, $1.10, $1.15 and $1.20.

class Cashflow:
    def __init__(self, val,t,r):
        self.val = val
        self.t = t
        self.r = r
        self.PV = self.valAt(0)
    def valAt(self,time):
        return self.val*(1+self.r)**(time-self.t)
def NPV(arr):
    return sum([x.PV for x in arr])
flows = [Cashflow(-150,0,.1), Cashflow(50*1.05,1,.1), Cashflow(50*1.1,2,.1), Cashflow(50*1.15,3,.1), Cashflow(50*1.2,4,.1)]
print(NPV(flows))

With an NPV of 27.36 we might be tempted to take the project! If the prices are accurate then it makes sense. But what if we aren’t sure totally about the prices? Let’s see how this would differ if we entered into forward contracts to sell. Let’s pretend the contracts were for prices .8, .85, .9, and .95.