Semico is considering whether to add capacity to their microchip fabrication plant. Adding capacity would cost $600M, to be paid in one year. The value of an added-capacity plant depends on the demand for Semico’s chips. If demand is “high” (25 percent chance), then the value of the added-capacity plant would be $1,600M (one year from now). If demand is “low” (75 percent chance), then the value of the added-capacity plant would be $400M. If Semico chooses to keep the current capacity, then there is no incremental cost. If demand is “high” (25 percent chance), then the value of the current-capacity plant would be $600M (one year from now). If demand is “low” (75 percent chance), then the value of the current-capacity plant would be $400M. We will use the CAPM to estimate expected returns in this problem, where the expected market premium is 7 percent, and the riskfree rate is 5 percent.

(a) Draw the decision tree for Semico’s problem, where its first decision (node 1) is whether to commit today to add capacity at a cost of $600M (to be paid in one year), or to wait one year until information about demand is revealed.

(b) Suppose that Semico chooses to commit at node 1. Solve for the NPV of the project as a function of its beta. Compute this value in the special cases of β 5 1 and β 5 0.

(c) Suppose that Semico chooses to wait at node 1. Use replication methods to solve for the NPV under the same cases as in part (b).

(d) What is the value of the real option to wait?

(e) Compute the risk-neutral probabilities of high demand and low demand under the same cases as in part (b). Use these risk-neutral probabilities to calculate the NPV of the project with flexibility. Verify that these NPVs are the same as found in part (c).