Question

Please provide correct answer for part B.

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 0.30. The​ after-tax net present value of the benefits from purchasing the two machines together is ​$ 70000 if demand is low and ​$ 170000 if demand is high.

If one machine is purchased and demand is​ low, the net present value is ​$120,000. If demand is​ high, the manager has three options. Doing nothing has a net present value of ​$ 100,000​; ​subcontracting, ​$150,000​; and buying the second​ machine, ​$130,000.

a. Choose the correct decision tree for this problem. Note that each payoff is given in thousands of dollars.
b. How many machines should the company buy​ initially? What is the expected payoff for this​ alternative?

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 0.30. The after-tax net present value of the benefits from purchasing the two machines together is $70,000 if demand is low and $170,000 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 $100,000; subcontracting, $150,000; and buying the second machine, $130,000. a. Choose the correct decision tree for this problem. Note that each payoff is given in thousands of dollars. OA. B. Low demand -70 Do nothing Buy 1 machine -100Q 100 Buy 1 machine High demand Subcontract Buy 2 Low demand -120 machines High demand 170 - 150 € 130 Low demand 120 Do nothing 0.30 High demand Subcontract 0.70 Buy 2 Low demand -70 machines 0.30 High demand 470 0.70 130 Buy 2 machines Buy 2 machines

Answer 1

1. From the Two machine given data, the decision tree becomes: - Low $20000 (0-3) achine ③ High $170000 (0.7) Do nothing $100000 / Subcontract $150000 High e machine d (0.7) 7 Buy 2nd $130000 Low k120000 o Ohe machine e - machine (0.3) $120000 - Correct decision tree is in figure B). Now, - Expected ralue at o = {(Probability xpayoff) Expected value at o= Max {Payoff, Payoff 2,...} b) E(4)= Max { 100, 150, 130} = 150k → €13) = 0.7(150K) + 0.31120%) = $141000 t → E (2) = 0.34701) + 0.71170K) = $140000 » Since E(3) > E(2), Best deision is to buy One machine & its expected pay off is $141.000 ma 111