Youre planning to expand the operations of your manufacturing plant by 50% sometime in the next six months. Suppose the value of the plant today is 100m. The cost from expansion is 40m. Risk uncertainty in the operating environment is estimated by an annualized variance of 25% in cash flows. The risk-free rate of return is 3% per half annum. Use the binomial option pricing approach with a time step of three months to value the option to expand operations. Is there an optimal time for taking such an action? Explain.