You are considering buying a machine to produce widgets (again). It takes you one year to finetune the machine so that it produces exactly the kind of widgets you want. The machine costs $40,000 today and produces 100,000 widgets in year 2. (You cannot produce in year 1 because you have to fine-tune the machine first.) Expected revenues are $1 per widget. The cost of producing widgets depends on the type of gas the machine uses. The machine uses one unit of gas per widget produced. In its current version the machine runs on a gas called “Gas A”. The price of “Gas A” in year 2 is uncertain and will be known only at the beginning of year 2. This price will be either $0.75 or $0.25 per unit of gas with equal probability. All revenues and costs (except the cost of the machine) accrue at the end of year 2. The discount rate is 10%.
a) What is the NPV of the project?
b) The manufacturer of the machine offers you a device that can be attached to the machine. You will have to buy the device together with the machine, that is, today. The device allows the machine to run on either “Gas A” or “Gas B” (a different type of gas). If you buy the device you can choose between the two gases at the beginning of year 2 (after observing the prices). The prices of the two gases are: • With probability 0.5 the price of “Gas A” will be $0.75 per unit and the price of “Gas B” will be $0.80 per unit.
• With probability 0.5 the price of “Gas A” will be $0.25 per unit and the price of “Gas B” will be $0.20 per unit.
How much would you be willing to pay for the device?
c) Suppose now instead that the prices of the two types of gas are:
• With probability 0.5 the price of “Gas A” will be $0.75 per unit and the price of “Gas B” will be $0.20 per unit. • With probability 0.5 the price of “Gas A” will be $0.25 per unit and the price of “Gas B” will be $0.80 per unit.
How much would you be willing to pay for the device now?