A manager is trying to decide whether to buy one machine or

A manager is trying to decide whether to buy one machine or two. If only one machine is purchased and demand proves to be excessive, the second machine can be purchased later. Some sales would be lost, however, because the lead time for delivery of this type of machine is six months. In addition, the cost per machine will be lower if both machines are purchased at the same time. The probability of low demand is estimated to be 0.30 and that of high demand to be 0.70. The after-tax NPV of the benefits from purchasing two machines together is $90,000 if demand is low and $180,000 if demand is high If one machine is purchased and demand is low, the NPV is $120,000. If demand is high, the manager has three options: (1) doing nothing, which has an NPV of $110,000; (2) subcontracting, with an NPV of $150,000; and (3) buying the second machine, with an NPV of $120,000 a. Choose the correct decision tree for this problem. Note that each payoff is given in thousands of dollars.

Solution

The case mentions that under both options i.e. buying of 1 machine or buying of 2 machines, probability of low demand is 0.3 and Probability of high demand is 0.70.

The Figure B does not highlight these probabilities and thus can be ruled out as possible option. Also to be noted that If one machine is purchased and demand is low , NPV is $120,000. Option B however wrongly depicts this as $90,000. Figure B is thus ruled out as possible option.

Figure C wrongly highlights probability of low demand as 0.7 ( I/O 0.3 ) and probability of high demand as 0.3 ( I/O 0.7)

Thus Figure B and Figure C are ruled out as possible options

We are thus left with 3 choices now: Figure A and Figure D

After tax NPV of the benefits from purchasing two machines together $90,000 if demand is low and $ 180,000 if demand is high. This is correctly represented only in Figure A ( and thus Figure D is ruled out)

The correct decision tree therefore is “ FIGURE A”

CORRECT DECISION TREE FOR THIS PROBLEM : FIGURE A

CORRECT DECISION TREE FOR THIS PROBLEM : FIGURE A