Question

BUYU Manufacturing has been contracted to provide SAEL Electronics with printed circuit and motherboards (PC) boards under the following terms:

100,000 PC boards will be delivered to SAEL in one month.

In 3 months, SAEL has an option to take the delivery of an additional 100,000 boards by giving BUYU a 30-day notice.

SAEL will pay $5 for each board it takes.

BUYU manufactures the PC boards through a process called batching, and manufacturing costs are as follows:

The manufacturing batch run has a fixed setup cost of $250,000, regardless of the run size.

The marginal manufacturing cost is $2.00 per board, regardless of the size of the batch run.

BUYU must decide whether it should manufacture all 200,000 PC boards now, or if it should manufacture 100,000 now and the other 100,000 boards only if SAEL decides to buy them. If BUYU manufactures 200,000 now and SAEL does not exercise its option, then BUYU will lose the manufacturing cost of the extra 100,000 boards. BUYU believes that there is a 50% chance that SAEL will exercise its option to buy the additional 100,000 PC boards.

Discuss the potential profit of manufacturing all 200,000 boards now.

Draw a decision tree for the decision that BUYU faces.

If BUYU uses its expected profit as the basis for its decision, determine the preferred course of action.

Determine the range of values of the probability that SAEL will exercise its option, making the decision found in part c as optimal, and determine the expected value of perfect information about whether SAEL will exercise its option.

Assume now that BUYU is constantly risk averse with a risk tolerance of $100,000, and answer parts 3 and 4 again.

Answer 1

1. Potential profit from manufacturing all 200,000 boards now = $ 5 X 200000 - $ 250,000 - $ 2 X 200,000 = $ 350,000

2.

Immediate Cost Immediate Revenue Future Cost Revenue Net Quantity Quantity Manufactured Profit Required 100 $450 $500 $100 $450 $500 OXEV-$75 (0.5) GO Sti) EV=$100 $350 (0.5 EV=$100 (05) 0 $0 $0 豺) -$150

3. The preferred course of action is to manufacture all 200,000 boards now.

4. We derived the parts 2 & 3 assuming that the probability that SAEL will exercise its option to buy another set of 100,000 boards is 0.5. However, if this probability changes, the pay-off will change as well.

Let x be the probability that SAEL will exercise its option to buy again. So 1-x is the probability that it will decide against buying again.

The expected pay-off from the first path, of setting up twice, is 100x + 50(1-x) = 50x + 50

The expected pay-off from the second path, of manufacturing 200,000 boards now, is 350x - 150 (1-x)

= 350x-150+150x = 500x - 150

The pay-offs from both the paths are equal when 50x + 50 = 500x - 150

Solving, x = 200/450 = 0.444

so, for the range of values of probability for SAEL to exercise its option, 0.444 till 1.0, the second path is optimal.

Under perfect information, we know for sure whether SAEL will exercise its option or not, i.e., x = 0 or 1.

The minimum profit under perfect information = $ 50, when x = 0 and the first path is adopted.

So the expected value of perfect information = expected value under uncertainty - expected value using perfect information = $ 100 - $ 50= $ 50.