Questions 1. Draw a decision tree representing the decision problem facing the 2. Suppose that D 8. What is the optimal policy for the investors to follow? What is the expected net present value obtained by the investors in this case? Justify your answer. 3. What is the maximum price D that the investors should be willing to pay for the option to set up the project in period 1? Explain your answer 4. Suppose now that the investors have an additional choice in period 0. By paying the investment cost lo 140 and the additional price P in period 0, the investors can set up the project in period 0 with an option to abandon the project in period 1 after they find out whether the project's net present value in period 1 will be VH or Vi. By abandoning the project in period 1, the investors obtain a "scrap value" with a present value S in period 1 instead of VH or VL i. Explain why the option to abandon the project in period 1 resembles a put option for a share of stock. ii. Suppose that the option to defer setting up the project in period 1 is not available and that S 90. What is the maximum amount P that the investors should be willing to pay for the option to abandon the project in period 0? Justify your answer iii. Continue to assume that the option to defer setting up the project in period 1 is not available, so that the project must be set up in period 0 or not at all Write down a formula showing how the maximum amount P that the investors should be willing to pay for the option to abandon the project depends on the values of the parameters, Vo, VH. Vi, and S. Explain your reasoning. 5. Suppose that S 90. For what values of the option prices P and D would the investors prefer to wait by purchasing the call option to setup the project in period 1 rather than setting up the project in period 0 and purchasing the put option to abandon the project in period 1 or simply setting up the project in period 0 without the put option? Explain your answer Note: In answering questions 4 and 5, you are welcome to include one or two additional decision trees that include the option to abandon the project if you feel that doing so would help you to explain your answers. However, you are not required to do so Problem 1: Investing in a Carbon Capture Project A group of investors is considering whether or not to invest in a project to generate electricity using coal that includes capturing the carbon emissions from the coal and sequestering these emissions in unused oil wells. There are two periods, period 0 and period 1 If the investment is made in period 0, then the investors must pay an investment cost lo 140 in period 0 to set up the project. The investors also obtains a net profit in period 0 from the sale of electricity with a present value Vo 37. In addition, the investors receive the net present value of the profit produced by the project in period 1 From the perspective of period 0, the net present value in period 1 produced by the project is uncertain due to uncertainty in the future price of electricity With probability 0.5, the net present value produced by the project in period 1 takes the high value VH 220. With probabilty 0.5, the net present value from the project in period 1 takes the low value V-70 Note that the net present values, Vo, VL, and VH do not include the investment cost of setting up the project.) The investors have three choices in period 0. First, the investors can choose not to invest in the project. In this case, they pay nothing and receive nothing so the net present value associated with this choice is 0. Second, the investors can choose to invest and set up the carbon capture project in period 0 Finally, the investors can choose to defer the decision to invest in the project by paying a cost D in period 0 to keep open the option of setting up the project in period1 By waiting until period 1, the investors learn whether the net present value which they obtain from the project in period 1 will be VH or VL before having to decide whether to set up the project. Moreover, the investors save a bit on the cost of setting up the project. If the investors decide to set up the project in period 1, they must pay an investment cost with a present value 110 The present value is less than the present value lo in part because of discounting. Of course, the investors do not have to pay the investment cost l1 if they chooses not to set up the project in period 1. However, since the deferral cost D is paid in period 0, that cost must be paid even if the investors decide not to set up the project in period 1. By choosing to wait, the investors also lose the net present value of the project in period 0, Vo. Suppose that the investors are risk neutral and wish to maximize the expected net present value produced by the opportunity to invest in the carbon capture project. All the present values are specified in millions of pounds