Your company can undertake an investment project today, next year, or the second year. The cost of the investment is $102, and the cost will remain at $102 regardless of when the investment is made. The current gross value of the investment (i.e., the expected discounted value of all subsequent cash flows) is $100, and the value is expected to increase by 40% or decrease by 20% with equal likelihood each period. The cost of capital is 10% and the risk free rate is 2.5%. Answer the following:

1. a) Draw the binomial tree depicting the value of the project.
2. b) Compute the risk-neutral probability.
3. c) Compute the value of the option to defer investment, OD.
4. d) Suppose that at the end of year one management can choose to either maintain the base scale operation or expand by x=0.30 the scale of the project value by incurring the extra investment outlay IE =25. Ignoring the option to defer investment (i.e., assuming that the firm invests at t=0), compute the value of the option to expand, OE.
5. e) Now suppose that the firm has the option to defer investment (until either t=1 or t=2) and the option to expand the scale of operations at t=1 (note, you can not expand at t=2). Compute the joint value of the options to defer and utilize higher capacity, OD&E.
6. f) If you made it to this point, you are ready to observe an interesting real options interaction effect. Note that the sum of the values of the option to defer investment in part (c) and the option to expand in part (d) is larger than the value of the options computed jointly in part (e). What causes this negative real option interaction effect?