After extensive forecasting and developing a production plan, a chocolate manufacturer knows it will need 10 tons of sugar 6 months from now. The purchasing manager has three options for acquiring the necessary sugar:

a. She could buy the sugar now at the current market price and inventory it until needed.

b. She could buy a futures contract now, in which she would pay a set price now for delivery in 6 months.

c. She could wait and buy the sugar in 6 months at the going market price at that time.

The current market price is $0.084 per pound. Due to lost interest and other factors, the inventory holding cost rate is 10% per year. For example, holding $100 of sugar for a year would cost $10. The price of sugar bought now, for delivery in 6 months (the futures contract), is

$0.0851 per pound. The transaction costs for 5- and 10-ton futures contracts are $65 and $110, respectively.

The forecasting group has estimated the possible sugar prices in 6 months (in $/pound) and their associated probabilities (Table 3.5):

For this exercise, assume that no sugar can be bought in the intervening 6 months and that sugar can only be bought in 5 ton increments.

a. Construct a decision tree to calculate the optimum decision.

b. Construct a simulation to calculate the probability distribution for each option and the optimum decision.

c. What information does the simulation provide that the decision tree does not—and vice versa?

Table 3.5 Estimated Probability Distribution of Price in 6 Months Price ($) 0.078 Probability 0.05 0.083 0.25 0.087 0.35 0.091 0.20 0.096 0.15