Consider a production facility, where the present value of expected future cash inflows from production, V = 80, may fluctuate in line with the random fluctuation in demand (u = 1.4, d = 0.71 per period and the risk-free rate, r = 5%). Suppose management has the option in two years, to contract to half the scale and half the value of the project (c = 50%), and recover $40m (Rc = $40m). Thus, in year 2 management has the flexibility either to maintain the same scale of operations (i.e., receive project value, V, at no extra cost) or contract the scale of operations and receive the recovery amount, whichever is highest. What are the pay-offs of this option at the end nodes (thus in the different states after 2 periods)?

The payoffs, F, of the option in the end note states are respectively: F = 0 , F = 0, F = 20

The payoffs, F, of the option in the end note states are respectively: F = 0 , F = 0, F = 14

The payoffs, F, of the option in the end note states are respectively: F = 196 , F = 100, F = 51

The payoffs, F, of the option in the end note states are respectively: F = 157 , F = 80, F = 41

The above question should be the one taken into consideration when solving the question below:

Consider again the production facility (from question above). Again, suppose that management has the option in two years, to halve the scale and the value of the project and recover some value. Thus, in year 2 management has the flexibility either to maintain the same scale of operations or contract the scale of operations, whichever is highest.

For this question, assume the end node pay-offs are 0, 20, 50. Calculate the option value by discounting with the risk neutral probability of 0.5 and a risk free rate of 5%. What is the option value?