Are you able to see the problem and its solution? As mentioned in the problem, t

Question

Are you able to see the problem and its solution?

As mentioned in the problem, the probability of low demand is estimated to be 0.2, but does it reflect the decision tree at all? I'm looking over the solution and nowhere do I see the low demand estimated anywhere. I'm wondering if it's a mistake in the solution shown.

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 six 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 0.20. 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. a. Draw a decision tree for this problem. b. Howr many machines should the company buy initially? What is the expected payoff for this alternative?

Explanation / Answer

Yes. I am able to see the problem and the given solution to it. The method of the solution is correct but it was a mistake to take 0.3 and 0.7 as probabilities and also instead of taking 120,000; 160,000 and 140,000, it was taken as 120,000; 140,000 and 130,000 for net present value of doing nothing, subcontract and buying 2nd machine respectively. This is also a mistake.

As the question clearly mentioned that the probability of low demand is 0.20, we need to consider 0.2 and 0.8 as the probabilities of low demand and high demand respectively and also correct the net present values of three options given when one machine is purchased.

So, it's mistake in the solution shown.

Take 0.2 and 0.8 as probabilities of low demand and high demand respectively and correct the net present values and calculate as below:

Pay off at node 4 = Max(120,000 160,000 140,000)

= 160,000 which is to subcontract.

Pay off at node 3 =0.2*90,000 + 0.8*170,000 =$154,000

Pay off at node 2=0.2*120,000 +0.8*160,000=$152,000

Pay off at node 1 = Max(152,000 154,000)= $154,000

Thus, the company should go for 2 machines.

b) Initially, the company should buy 2 machines and its expected value is $154,000

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