A manager is trying to decide whether to buy one machine or two. If only one is purchased and demand proves to be high, the second machine can still be purchased later. In this case, however, some sales will be lost due to the long $(6-$months$)$ lead time for making this type of machine. However, if both are purchased at once, the cost per machine will be lower. The probability of 'low' demand is estimated to be $40$ percent $(0\mathrm{.}4).$ The after$-$tax net present value of the benefits $($i$.$e$.,$ payoff$)$ from purchasing the two machines together is $$60,000$ if demand is low and $$240,000$ if demand is high. If one machine is purchased and demand is low, the net present value $($payoff$)$ is $$120,000,$ while, if one machine is purchased and demand proves to be high, the manager actually has three options; $$Doing nothing$$ afterwards has net present value of $$100,000$; 'subcontracting' $$180,000$; and 'buying the second machine' $$140,000.$