Suppose a large manufacturing firm decides to hedge against risk through the use of strategic options. Specifically, it has the option to choose between two strategies.
• Expanding its current manufacturing operations.
• Contracting its current manufacturing operations at any time within the next two years.
• Neither expanding not contracting.
Suppose that the firm has a current operating structure whose static valuation of future profitability based on a discounted cash-flow model is found to be $100 million. Suppose also that the firm estimates the implied volatility of the returns on the projected future cash flows to be 15%. The risk-free interest rate is 5%. Finally, suppose that the firm has the option to contract 10% of its current operations at any time over the next two years, creating an additional $25 million in savings after the contraction. The expansion option will increase the firm's operations by 30% with a $20 million implementation cost.11
(a) Show the binomial lattice of the underlying asset over two years.
(b) What is the value of retaining the option to choose between both alternatives (i.e., consider both the expanding option and the contracting option together)?