The Sweet Tooth Candy Company knows it will need 10 tons of sugar six months from now to implement its production plans. Jean Dobson, Sweet Tooth’s purchasing manager, has essentially two options for acquiring the needed sugar. She can either buy the sugar at the going market price when she needs it, six months from now, or she can buy a futures contract now. The contract guarantees delivery of the sugar in six months but the cost of purchasing it will be based on today’s market price. Assume that possible sugar futures contracts available for purchase are for five tons or ten tons only. No futures contracts can be purchased or sold in the intervening months. Thus, Sweet Tooth’s possible decisions are to
(1) Purchase a futures contract for ten tons of sugar now,
(2) Purchase a futures contract for five tons of sugar now and purchase five tons of sugar in six months, or
(3) Purchase all ten tons of needed sugar in six months.
The price of sugar bought now for delivery in six months is $0.0851 per pound. The transaction costs for five-ton and ten-ton futures contracts are $65 and $110, respectively. Finally, Ms. Dobson has assessed the probability distribution for the possible prices of sugar six months from now (in dollars per pound). The file P06_37.xlsx contains these possible prices and their corresponding probabilities.
a. Given that Sweet Tooth wants to acquire the needed sugar in the least costly way, create a cost table that specifies the cost (in dollars) associated with each possible decision and possible sugar price in the future.
b. Use Precision Tree to identify the decision that minimizes Sweet Tooth’s expected cost of meeting its sugar demand.
c. Perform a sensitivity analysis on the optimal decision, letting each of the three currency inputs vary one at a time plus or minus 25% from its base value, and summarize your findings. In response to which of these inputs is the expected cost value most sensitive?