OpTION TO SWITCh INpUTSCrystal Ball exerCISe The Central and Southeast Power Company of Mobile, Alabama, is considering a new power plant that will allow it to switch between gas and oil. The company has a contract to provide it with gas for $8 that is sufficient to produce one unit of electric power. (The numbers are standardized to one unit for ease of computation.) However, the plant can also be run using fuel oil. The price of fuel oil is uncertain, and the firms analysts believe that the uncertain future price can be characterized as a triangular distribution with a minimum value of $2, a most likely value of $7, and a maximum value of $12. Next year, the plant is expected to produce one standard unit of electrical power that can be sold for $10.

a. What is the expected cash flow from the power plant for next year if the cost of fuel is set equal to the minimum of the expected costs of gas and oil? (Hint: There are no taxes, and the only expenses that the plant incurs are for fuel.)

For part a) think about a situation where you have to choose a fuel with no information about the costs of fuel other than their probability distributions. What is the expected value of fuel oil? Or gas? Given those costs what would fuel would you choose? What is the annual cash flow from operations? This is analogous to choosing what size truck to rent before you know what size the load actually is.

b. Construct a simple Crystal Ball simulation model for the plants cash flow using a triangular distribution for the cost of fuel oil and selecting the minimum-cost source of fuel to run the plant. What is the expected cash flow from the power plant based on your simulation?

Part b) Simulate the fuel oil price and pick the best option of either gas or oil. What is the annual cash flow from operations?

c. If the cost of capital for the plant is 10% and the cash flows for the plant are expected to be constant forever, what is the value of the plant?

Part c). Assuming that we don't know the fuel prices before choosing a fuel (use part a) cash flows). What is the value of a perpetuity based on the ability to choose the cheapest fuel (use part b) cash flows)? What is the most you would pay to have perfect information about the costs of each fuel option?