Question 1:

a) You have a potential project for which you want to establish a value regardless of any possible real options. The project will have an initial cost of $75 million, which must be paid at the time of investment, and expected annual cash flows of $4.25 million per year starting in year one and continuing forever. The risk-free rate and appropriate discount rate for the project is 4%. What is the value of the project without any options? You realize that the expected cash flow actually comes from a 25% chance of earning $1.25 million per year starting in year 1, and a 75% chance of earning $5.25 million per year starting in year 1. These will depend on the economy. In one year, you will be able to expand the project if you would like to. The cost of this will be $10 million paid in year 1, and the cash flows will increase beginning in year two and remain at the new level through the end of the project, if you choose to expand. This change will have the largest impact in the good economy when demand is high (when you will earn $5.25 million per year): you will be able to increase your cash inflows (beginning with the year two cash flow) by 50%. If your economy is bad (and you will earn $1.25 million per year), you will be able to increase your cash flows by 30% of what they would have been. What is the value today of this option to expand in one year?

b) Use all of the information from part a, except you do not have the option to expand. Instead, you have the option to abandon the project after you know the first cash flow but before you receive the first cash flow. You can shut down the project and sell off the assets for $32.5 million investment at year 1. What is the value today of this option to abandon after you receive the first cash flow?