Question

A manager is trying to decide whether to buy one machine or two. If only one is purchased and demand proves to be excessive, the second machine can be purchased later. Some sales will be lost, however, because the lead time for producing this type of machine is a few months. In addition, the cost per machine will be lower if both are purchased at the same time. The probability of low demand is estimated to be 0.45. The after-tax net present value of the benefits from purchasing the 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 net present value is $120,000. If demand is high, the manager has three options. Doing nothing has a net present value of $120,000; subcontracting, $160,000; and buying the second machine, $140,000. Draw a decision tree for this problem and solve it; that is, specify the expected payoff of different alternatives and suggest the optimal number of machines that should be purchased initially. Please take a picture of your work and upload it in the provided space.

Answer 1

Answer and Explanation:

We will start from the point where the manager has three options over here we see that the payoffs for doing nothing is $110000, $160000 for subcontracting and $120000 for 2 machines bought, in this case subcontracting gives the best outcome of $160000.

Now if we move back on decision tree where two machines are bought and if demand is low then payoff is 0.2 * 80000 + 0.8 * 160000 for high demand = 16000 + 128000 = $144000.

Now if decide to buy only one machine then the payoff are 0.2 * 100000 + 0.8* 160000 (value for subcontracting)

= 20000 + 128000 = $148000

In case of event 1 we can see the benefits can be either $144000 or $148000 calculated above.

Se we see the best outcome is when the manager subcontracts and the benefit is $160000.

Best option is to buy no machines and the expected payoff is $160000.