A manager is trying to decide whether to buy one machine or two. If only one is

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 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

.20.

The after-tax net present value of the benefits from purchasing the two machines together is

$90,000

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

$100,000.

If demand is high, the manager has three options. Doing nothing has a net present value of

$100,000;

subcontracting,

$140,000;

and buying the second machine,

$120,000.

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?

Best decision is to buy ? machine(s) and its expected payoff is?

Explanation / Answer

Answer:

b.

EV(node 4) = Max{120,000, 140,000, 130,000} = $140,000 (subcontract)

EV(node 3) = 0.3´90,000+0.7´170,000 = $146,000

EV(node 2) = 0.3´120,000+0.7´140,000 = $134,000

EV(node 1) = Max{134,000, 146,000} = $146,000 (2 machines, node 3)

Hence, the best option is to buy 2 machines.

The expected payoff is $146,000.

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