Opti plc operates a single machine on a project to produce its output. The purchase price of the machine is 300. Technically, the machine lasts 3 years and would yield a cash inflow of 200 each year (e.g., from sales of its output). However, the cost of maintenance increases with the age of the machine. These costs are shown in the table below, along with the salvage values i.e., the resale value of the machine at the end of each year). In order to maximise the value of this project, the company needs to consider whether t ta Maintenance costs 35 65 125 Salvage value 240 165 114 to keep the machine or not at each point in time. You have been asked by the senior management of Opti plc to make optimal decisions on the following. Assume a constant discount rate of 10%. (a) If the project can only be conducted once, what's the optimal machine life, i.e., how long should the company plan to operate the machine? Show that you can solve this problem by using the NPV rule by treating the alternative machine lives as separate investment projects. (b) What's the optimal machine life (at each cycle) if the project can be repeated once through the replacement by an identical machine with same price, cash inflows, main- tenance costs and salvage values? What's the NPV of the overall investment? Provide an economie intuition for your result. Hint: Solve this problem backwards, i.e., by starting with the second cycle and then, given that result, deciding what's optimal in the first cycle