A company plans to purchase a new machine to improve its productivity in the next 5 years. A standard machine can satisfy the current demand; it costs $100,000 and generates an annual profit $25,000. Meanwhile, the company foresees that with X% probability, after 2 years (i.e., starting from Year 3) the demand may be increased to a level beyond the capacity of the standard machine, and hence the company may lose the additional business opportunity valued at annual profit $11,000. There are two additional choices now. Choice 1 is to buy a premium machine that costs $120,000 and can satisfy all future demand. Choice 2 is to buy an optional upgrade package with the standard machine that allows for the company, if needed, to swap to the premium machine after 2 years by paying $20,000; the price of the upgrade package is Y.
(1) Between the standard (without upgrade package) and premium machines, do a breakeven analysis with respect to X. Let X0 be the break even probability.
(2) For the case ofX0. Then the premium machine is less profitable than the standard machine. So the company can only buy the standard one, with or without the upgrade package. What is the highest price of the upgrade package, as a function of X, so that the company is willing to buy the package?
(3) For the case of X>X0.Then the standard machine is less profitable than the premium machine. So the company needs to consider two options: to buy the standard machine with upgrade package, or to but the premium. What is the highest price of the upgrade package, as a function of X, so that the company is willing to buy the package?