Question

The SweetTooth Candy Company knows it will need 10 tons (20,000 lbs) of sugar six months from now to implement its production plans. Jean Dobson, SweetTooth's purchasing manager, has essentially two options for acquiring the needed sugar. One option is to by buy the sugar at the going market price when she needs it, six months from now. Ms. Dobson has assessed the probability distribution for the possible prices of sugar six months from now (in dollars per pound) as shown below:

Price in 6 month Probability
$0.078    0.05
   0.083    0.25
   0.087    0.35
   0.091    0.20
   0.096    0.15     

The second purchasing option is to 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'smarket 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, SweetTooth's possible decision alternative 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 later in six months, or (3) purchase all ten tons of needed sugar later in six months. The price of sugar now is $0.0851 per pound. The transaction costs for five-ton and ten-ton futures contracts are $65 and $110, respectively.

Q1) There are ___ decision alternatives for SweetTooth.

Q2)There are ___ states of nature.

Q3)They buy the futures contract for 10 tons now and the price per pound in six months turns out to be $0.087. The total cost is?

Q4)They buy the futures contract for 10 tons now and the price per pound in six months turns out to be $0.078. The total cost is ?

Q5)They do not buy the futures contract and the price per pound in six months turns out to be $0.083. The total cost is ?

Q6)They buy the futures contract for 5 tons now and the price per pound in six months turns out to be $0.096. The total cost is ?

Q7)They do not buy the futures contract and the price per pound in six months turns out to be $0.096. The total cost is ?

Q8)The best decision alternative by the Maxmin method is?

Q9)The best decision alternative by the Maxmax method is?

Q10)The expected cost of buying the futures contract for 10 tons is?

Q11)The expected cost of buying the futures contract for 5 tons now is?

Q12)The expected cost of not buying the futures contract is?

Q13)The best decision alternative by the expected value method is?

Answer 1

1. There are 3 decision alternatives namely - unhedged, partially hedged and fully hedged

2. 2 states - hedged and unhedged

3. Total Cost = Market Price * 20000 lbs - Profit on futures + transaction cost = (0.087 * 20000) - (0.087-0.0851)*20000 + 110 = 1812

4. Total Cost = Market Price * 20000 lbs + Loss on futures + transaction cost = (0.078 * 20000) + (0.0851-0.078)*20000 + 110 = 1812

5. Total Cost = 0.083 * 20000 = 1660

6. Cost of hedged 5 tons = Market Price * 10000 lbs - Profit on futures + transaction cost = (0.096*10000) - (0.096-0.0851)*10000 + 65 = 916

Cost of unhedged 5 tons = 0.096 * 10000 = 960

Total cost = 1876

7. Total cost = 20000 * 0.096 = 1920