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Part $1$

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$$ addition, the cost per machine will be lower if both machines are purchased at the same time. The probability of low demand is estimated to be $0\mathrm{.}300\mathrm{.}30$ and that of high demand to be $0\mathrm{.}700\mathrm{.}70.$ The$$ after$-$tax NPV of the benefits from purchasing two machines together is $$$$90$ comma $00090,000$ if demand is low and $$$$160$ comma $000160,000$ if demand is high.